Subgroups — C₂×C₄₁×#3562 #23838941

Order 10496.

7354 conjugacy classes of subgroups.

The subgroup lattice has 1348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3562	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₄₁×#562	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#560	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₁×#553	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₁×#551	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₁×#550	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₁×#548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₁×#548	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₁×#547	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄₁×#541	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₁×#540	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄₁×#540	C₂	1	2	yes	maximal, complemented
17	C₂×C₄₁×#539	C₂	1	2	yes	maximal, complemented
18	C₂×C₄₁×#538	C₂	1	2	yes	maximal, complemented
19	C₂×C₄₁×#538	C₂	1	2	yes	maximal, complemented
20	C₂×C₄₁×#536	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₄₁×#535	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
26	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
27	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
28	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic, complemented
29	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
30	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
31	C₄₁×#562	C₂²	1	32	yes	complemented
32	C₄₁×#560	C₂²	1	32	yes	complemented
33	C₄₁×#559	C₂²	1	16	yes	complemented
34	C₄₁×#556	C₂²	1	16	yes	complemented
35	C₄₁×#553	C₂²	1	32	yes	complemented
36	C₄₁×#551	C₂²	1	32	yes	complemented
37	C₄₁×#550	C₂²	1	16	yes	complemented
38	C₄₁×#548	C₂²	1	16	yes	complemented
39	C₄₁×#548	C₂²	1	16	yes	complemented
40	C₄₁×#547	C₂²	1	16	yes	complemented
41	C₄₁×#546	C₂²	1	16	yes	complemented
42	C₄₁×#546	C₂²	1	16	yes	complemented
43	C₄₁×#541	C₂²	1	16	yes	complemented
44	C₄₁×#540	C₂²	1	16	yes	complemented
45	C₄₁×#540	C₂²	1	32	yes	complemented
46	C₄₁×#539	C₂²	1	32	yes	complemented
47	C₄₁×#538	C₂²	1	32	yes	complemented
48	C₄₁×#538	C₂²	1	32	yes	complemented
49	C₄₁×#536	C₂²	1	16	yes	complemented
50	C₄₁×#535	C₂²	1	16	yes	complemented
51	C₄₁×#532	C₂²	1	16	yes	complemented
52	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
54	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
55	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
56	C₂×#127×C₄₁	C₂²	1	2	yes	complemented
57	C₄₁×#529	C₂²	1	16	yes	complemented
58	C₄₁×#529	C₂²	1	16	yes	complemented
59	C₂×#126×C₄₁	C₂²	1	1	yes	characteristic
60	C₂×#126×C₄₁	C₂²	1	2	yes	—
61	C₂×#126×C₄₁	C₂²	1	2	yes	—
62	C₂×#126×C₄₁	C₂²	1	2	yes	complemented
63	C₂×#126×C₄₁	C₂²	1	1	yes	characteristic, complemented
64	C₂×#126×C₄₁	C₂²	1	2	yes	complemented
65	C₂×#126×C₄₁	C₂²	1	2	yes	complemented
66	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic, complemented
67	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic, complemented
68	C₂×#125×C₄₁	C₂²	1	2	yes	complemented
69	C₂×#125×C₄₁	C₂²	1	2	yes	complemented
70	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
71	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
72	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
73	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
74	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
75	C₂×#124×C₄₁	C₂²	1	2	yes	—
76	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic, complemented
77	C₂×#124×C₄₁	C₂²	1	2	yes	complemented
78	C₂×#124×C₄₁	C₂²	1	2	yes	complemented
79	C₂×#123×C₄₁	C₂²	1	1	yes	characteristic
80	C₂×#123×C₄₁	C₂²	1	2	yes	—
81	C₂×#123×C₄₁	C₂²	1	2	yes	—
82	C₂×#123×C₄₁	C₂²	1	2	yes	—
83	C₂×#123×C₄₁	C₂²	1	1	yes	characteristic, complemented
84	C₂×#123×C₄₁	C₂²	1	2	yes	complemented
85	C₂×#123×C₄₁	C₂²	1	2	yes	complemented
86	C₂×#123×C₄₁	C₂²	1	2	yes	complemented
87	C₂×#123×C₄₁	C₂²	1	2	yes	complemented
88	C₂×#123×C₄₁	C₂²	1	2	yes	complemented
89	C₂×#123×C₄₁	C₂²	1	2	yes	complemented
90	C₂×#123×C₄₁	C₂²	1	2	yes	complemented
91	C₂×#123×C₄₁	C₂²	1	2	yes	complemented
92	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
93	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
94	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
95	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
96	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
97	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
98	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
99	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
100	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
101	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
102	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
103	C₂×#121×C₄₁	C₂²	1	2	yes	—
104	C₂×#121×C₄₁	C₂²	1	2	yes	—
105	C₂×#121×C₄₁	C₂²	1	2	yes	—
106	C₂×#121×C₄₁	C₂²	1	2	yes	—
107	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
108	C₂×#121×C₄₁	C₂²	1	2	yes	—
109	C₂×#121×C₄₁	C₂²	1	2	yes	—
110	C₂×#121×C₄₁	C₂²	1	2	yes	complemented
111	C₂×#121×C₄₁	C₂²	1	2	yes	complemented
112	C₂×#121×C₄₁	C₂²	1	2	yes	complemented
113	C₂×#121×C₄₁	C₂²	1	2	yes	complemented
114	C₂×#121×C₄₁	C₂²	1	2	yes	complemented
115	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic, complemented
116	C₂×#121×C₄₁	C₂²	1	2	yes	complemented
117	C₂×#121×C₄₁	C₂²	1	2	yes	complemented
118	C₂×#120×C₄₁	C₂²	1	2	yes	—
119	C₂×#120×C₄₁	C₂²	1	2	yes	—
120	C₂×#120×C₄₁	C₂²	1	2	yes	—
121	C₂×#120×C₄₁	C₂²	1	2	yes	—
122	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
123	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
127	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
128	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
129	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
130	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
131	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
133	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
134	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
135	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
136	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
137	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
138	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
139	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
140	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic, complemented
141	C₂×#117×C₄₁	C₂²	1	2	yes	complemented
142	C₂×#117×C₄₁	C₂²	1	2	yes	complemented
143	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	complemented
144	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
145	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
146	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic, complemented
147	C₂⁵×C₄₁	C₂³	1	2	yes	—
148	C₂×#41×C₄₁	—	4	4	no	—
149	C₂×#41×C₄₁	—	4	4	no	—
150	C₂×#41×C₄₁	—	4	4	no	—
151	C₂×#41×C₄₁	—	4	4	no	—
152	C₂×#41×C₄₁	C₂³	1	8	yes	—
153	C₂×#41×C₄₁	C₂³	1	8	yes	—
154	C₂×#41×C₄₁	C₂³	1	8	yes	—
155	C₂×#41×C₄₁	C₂³	1	8	yes	complemented
156	C₂²×Q₈×C₄₁	—	4	4	no	—
157	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
158	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
159	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
160	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
161	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
162	C₂²×Q₈×C₄₁	C₂³	1	8	yes	complemented
163	C₂²×D₄×C₄₁	—	4	4	no	—
164	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
165	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
166	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
167	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
168	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
169	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
170	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
171	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
172	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
173	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
174	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
175	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
176	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
177	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
178	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
179	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
180	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
181	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
182	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
183	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
184	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
185	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
186	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
187	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
188	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
189	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
190	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
191	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
192	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
193	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
194	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
195	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
196	C₄⋊Q₈×C₄₁	C₂³	1	8	yes	complemented
197	C₄⋊Q₈×C₄₁	C₂³	1	8	yes	complemented
198	#127×C₄₁	C₂³	1	8	yes	—
199	#127×C₄₁	C₂³	1	8	yes	—
200	#127×C₄₁	C₂³	1	16	yes	complemented
201	#126×C₄₁	C₂³	1	8	yes	—
202	#126×C₄₁	C₂³	1	16	yes	—
203	#126×C₄₁	C₂³	1	16	yes	—
204	#126×C₄₁	C₂³	1	16	yes	complemented
205	#126×C₄₁	C₂³	1	8	yes	complemented
206	#126×C₄₁	C₂³	1	16	yes	complemented
207	#126×C₄₁	C₂³	1	16	yes	complemented
208	#125×C₄₁	C₂³	1	8	yes	complemented
209	#125×C₄₁	C₂³	1	8	yes	complemented
210	#125×C₄₁	C₂³	1	16	yes	complemented
211	#125×C₄₁	C₂³	1	16	yes	complemented
212	#124×C₄₁	C₂³	1	8	yes	—
213	#124×C₄₁	C₂³	1	8	yes	—
214	#124×C₄₁	C₂³	1	8	yes	—
215	#124×C₄₁	C₂³	1	8	yes	—
216	#124×C₄₁	C₂³	1	8	yes	—
217	#124×C₄₁	C₂³	1	16	yes	—
218	#124×C₄₁	C₂³	1	8	yes	complemented
219	#124×C₄₁	C₂³	1	16	yes	complemented
220	#124×C₄₁	C₂³	1	16	yes	complemented
221	#123×C₄₁	C₂³	1	8	yes	—
222	#123×C₄₁	C₂³	1	16	yes	—
223	#123×C₄₁	C₂³	1	16	yes	—
224	#123×C₄₁	C₂³	1	16	yes	—
225	#123×C₄₁	C₂³	1	8	yes	complemented
226	#123×C₄₁	C₂³	1	16	yes	complemented
227	#123×C₄₁	C₂³	1	16	yes	complemented
228	#123×C₄₁	C₂³	1	16	yes	complemented
229	#123×C₄₁	C₂³	1	16	yes	complemented
230	#123×C₄₁	C₂³	1	16	yes	complemented
231	#123×C₄₁	C₂³	1	16	yes	complemented
232	#123×C₄₁	C₂³	1	16	yes	complemented
233	#123×C₄₁	C₂³	1	16	yes	complemented
234	C₂²⋊Q₈×C₄₁	C₂³	1	8	yes	—
235	C₂²⋊Q₈×C₄₁	C₂³	1	8	yes	—
236	C₂²⋊Q₈×C₄₁	C₂³	1	8	yes	complemented
237	C₂²⋊Q₈×C₄₁	C₂³	1	8	yes	complemented
238	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	complemented
239	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	complemented
240	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	complemented
241	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	complemented
242	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	complemented
243	#121×C₄₁	C₂³	1	8	yes	—
244	#121×C₄₁	C₂³	1	8	yes	—
245	#121×C₄₁	C₂³	1	16	yes	—
246	#121×C₄₁	C₂³	1	16	yes	—
247	#121×C₄₁	C₂³	1	16	yes	—
248	#121×C₄₁	C₂³	1	16	yes	—
249	#121×C₄₁	C₂³	1	8	yes	—
250	#121×C₄₁	C₂³	1	16	yes	—
251	#121×C₄₁	C₂³	1	16	yes	—
252	#121×C₄₁	C₂³	1	16	yes	complemented
253	#121×C₄₁	C₂³	1	16	yes	complemented
254	#121×C₄₁	C₂³	1	16	yes	complemented
255	#121×C₄₁	C₂³	1	16	yes	complemented
256	#121×C₄₁	C₂³	1	16	yes	complemented
257	#121×C₄₁	C₂³	1	8	yes	complemented
258	#121×C₄₁	C₂³	1	16	yes	complemented
259	#121×C₄₁	C₂³	1	16	yes	complemented
260	#120×C₄₁	C₂³	1	16	yes	—
261	#120×C₄₁	C₂³	1	16	yes	—
262	#120×C₄₁	C₂³	1	16	yes	—
263	#120×C₄₁	C₂³	1	16	yes	—
264	C₄×Q₈×C₄₁	C₂³	1	8	yes	complemented
265	C₄×Q₈×C₄₁	C₂³	1	8	yes	complemented
266	C₄×Q₈×C₄₁	C₂³	1	8	yes	complemented
267	C₄×Q₈×C₄₁	C₂³	1	8	yes	complemented
268	C₄×D₄×C₄₁	C₂³	1	8	yes	—
269	C₄×D₄×C₄₁	C₂³	1	8	yes	—
270	C₄×D₄×C₄₁	C₂³	1	8	yes	—
271	C₄×D₄×C₄₁	C₂³	1	8	yes	—
272	C₄×D₄×C₄₁	C₂³	1	16	yes	complemented
273	C₄×D₄×C₄₁	C₂³	1	8	yes	complemented
274	C₄×D₄×C₄₁	C₂³	1	16	yes	complemented
275	C₄×D₄×C₄₁	C₂³	1	16	yes	complemented
276	C₄×D₄×C₄₁	C₂³	1	16	yes	complemented
277	C₄×D₄×C₄₁	C₂³	1	16	yes	complemented
278	C₄×D₄×C₄₁	C₂³	1	16	yes	complemented
279	C₄×D₄×C₄₁	C₂³	1	8	yes	complemented
280	C₄×D₄×C₄₁	C₂³	1	16	yes	complemented
281	#117×C₄₁	C₂³	1	8	yes	—
282	#117×C₄₁	C₂³	1	8	yes	complemented
283	#117×C₄₁	C₂³	1	16	yes	complemented
284	#117×C₄₁	C₂³	1	16	yes	complemented
285	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
287	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
289	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
293	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
296	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
297	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
300	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
301	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
302	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
303	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
304	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
305	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
306	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
307	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
308	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
309	C₂×C₄⋊C₄×C₄₁	C₂³	1	16	yes	complemented
310	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
311	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
312	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
313	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
314	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
315	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
316	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
317	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
318	C₂×C₂²⋊C₄×C₄₁	C₂³	1	16	yes	—
319	C₂×C₂²⋊C₄×C₄₁	C₂³	1	16	yes	—
320	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
321	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
322	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
323	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
324	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
325	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
326	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
327	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
328	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
329	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
330	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
331	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
332	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
333	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
334	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
335	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
336	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
337	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
338	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
340	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
341	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
342	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
343	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
344	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
345	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
347	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
348	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
349	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
350	C₂×C₄²×C₄₁	C₂³	1	8	yes	complemented
351	C₂⁴×C₄₁	—	4	4	no	—
352	C₂⁴×C₄₁	—	4	4	no	—
353	C₂⁴×C₄₁	—	4	4	no	—
354	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
355	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
356	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
357	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
358	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
359	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
360	C₂⁴×C₄₁	C₂⁴	1	8	yes	—
361	#41×C₄₁	—	4	16	no	—
362	#41×C₄₁	—	4	16	no	—
363	#41×C₄₁	—	4	16	no	—
364	#41×C₄₁	—	4	16	no	—
365	C₂×Q₈×C₄₁	—	2	4	no	—
366	C₂×Q₈×C₄₁	—	2	4	no	—
367	C₂×Q₈×C₄₁	—	2	4	no	—
368	C₂×Q₈×C₄₁	—	4	4	no	—
369	C₂×Q₈×C₄₁	—	4	2	no	—
370	C₂×Q₈×C₄₁	—	4	16	no	—
371	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
372	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
373	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
374	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
375	C₂×Q₈×C₄₁	C₂⁴	1	8	yes	—
376	C₂×D₄×C₄₁	—	2	4	no	—
377	C₂×D₄×C₄₁	—	2	4	no	—
378	C₂×D₄×C₄₁	—	2	4	no	—
379	C₂×D₄×C₄₁	—	4	16	no	—
380	C₂×D₄×C₄₁	—	4	4	no	—
381	C₂×D₄×C₄₁	—	4	2	no	—
382	C₂×D₄×C₄₁	—	4	4	no	—
383	C₂×D₄×C₄₁	—	4	4	no	—
384	C₂×D₄×C₄₁	—	4	4	no	—
385	C₂×D₄×C₄₁	—	4	4	no	—
386	C₂×D₄×C₄₁	—	4	4	no	—
387	C₂×D₄×C₄₁	—	4	2	no	—
388	C₂×D₄×C₄₁	—	4	4	no	—
389	C₂×D₄×C₄₁	—	4	2	no	—
390	C₂×D₄×C₄₁	—	4	4	no	—
391	C₂×D₄×C₄₁	—	4	4	no	—
392	C₂×D₄×C₄₁	—	4	4	no	—
393	C₂×D₄×C₄₁	—	4	4	no	—
394	C₂×D₄×C₄₁	—	4	4	no	—
395	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
396	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
397	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
398	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
399	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
400	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
401	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
402	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
403	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
404	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
405	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
406	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
407	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
408	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
409	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
410	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
411	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
412	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
413	C₂²×C₄×C₄₁	—	2	4	no	—
414	C₂²×C₄×C₄₁	—	2	4	no	—
415	C₂²×C₄×C₄₁	—	2	4	no	—
416	C₂²×C₄×C₄₁	—	4	4	no	—
417	C₂²×C₄×C₄₁	—	4	2	no	—
418	C₂²×C₄×C₄₁	—	4	4	no	—
419	C₂²×C₄×C₄₁	—	4	4	no	—
420	C₂²×C₄×C₄₁	—	4	2	no	—
421	C₂²×C₄×C₄₁	—	4	4	no	—
422	C₂²×C₄×C₄₁	—	4	4	no	—
423	C₂²×C₄×C₄₁	—	4	4	no	—
424	C₂²×C₄×C₄₁	—	4	4	no	—
425	C₂²×C₄×C₄₁	—	4	4	no	—
426	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
427	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
428	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
429	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
432	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
433	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
434	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
436	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
437	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
438	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
439	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
440	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
441	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
442	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
443	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
444	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
445	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
446	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
447	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
448	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
449	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
450	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
451	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
452	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
453	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
454	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
455	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
456	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
457	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
458	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
459	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
460	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
461	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
462	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
463	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
464	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
465	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
466	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
467	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
468	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
469	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
470	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
471	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
472	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
473	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
474	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
475	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
476	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
477	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
478	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
479	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
480	C₂²⋊C₄×C₄₁	C₂⁴	1	4	yes	—
481	C₂²⋊C₄×C₄₁	C₂⁴	1	4	yes	—
482	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
483	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
484	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
485	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
486	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
487	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
488	C₂²⋊C₄×C₄₁	C₂⁴	1	4	yes	—
489	C₂²⋊C₄×C₄₁	C₂⁴	1	4	yes	—
490	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
491	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
492	C₂²⋊C₄×C₄₁	C₂⁴	1	4	yes	—
493	C₂²⋊C₄×C₄₁	C₂⁴	1	4	yes	—
494	C₂²⋊C₄×C₄₁	C₂⁴	1	4	yes	—
495	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
496	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
497	C₂²⋊C₄×C₄₁	C₂⁴	1	4	yes	—
498	C₂²⋊C₄×C₄₁	C₂⁴	1	4	yes	—
499	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
500	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
501	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
502	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
503	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
504	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
505	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
506	C₂²⋊C₄×C₄₁	C₂⁴	1	4	yes	—
507	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
508	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
509	C₄²×C₄₁	C₂⁴	1	4	yes	—
510	C₄²×C₄₁	C₂⁴	1	4	yes	—
511	C₄²×C₄₁	C₂⁴	1	4	yes	—
512	C₄²×C₄₁	C₂⁴	1	4	yes	—
513	C₄²×C₄₁	C₂⁴	1	4	yes	—
514	C₄²×C₄₁	C₂⁴	1	8	yes	—
515	C₄²×C₄₁	C₂⁴	1	4	yes	—
516	C₄²×C₄₁	C₂⁴	1	8	yes	—
517	C₄²×C₄₁	C₂⁴	1	8	yes	—
518	C₂³×C₄₁	—	2	2	no	—
519	C₂³×C₄₁	—	2	2	no	—
520	C₂³×C₄₁	—	2	2	no	—
521	C₂³×C₄₁	—	2	4	no	—
522	C₂³×C₄₁	—	2	4	no	—
523	C₂³×C₄₁	—	2	4	no	—
524	C₂³×C₄₁	—	2	2	no	—
525	C₂³×C₄₁	—	2	2	no	—
526	C₂³×C₄₁	—	2	4	no	—
527	C₂³×C₄₁	—	2	4	no	—
528	C₂³×C₄₁	—	2	4	no	—
529	C₂³×C₄₁	—	2	2	no	—
530	C₂³×C₄₁	—	2	2	no	—
531	C₂³×C₄₁	—	2	4	no	—
532	C₂³×C₄₁	—	2	4	no	—
533	C₂³×C₄₁	—	2	4	no	—
534	C₂³×C₄₁	—	2	2	no	—
535	C₂³×C₄₁	—	2	2	no	—
536	C₂³×C₄₁	—	4	8	no	—
537	C₂³×C₄₁	—	4	8	no	—
538	C₂³×C₄₁	—	4	8	no	—
539	C₂³×C₄₁	—	8	16	no	—
540	C₂³×C₄₁	C₂⁵	1	2	yes	—
541	C₂³×C₄₁	C₂⁵	1	4	yes	—
542	C₂³×C₄₁	C₂⁵	1	4	yes	—
543	C₂³×C₄₁	C₂⁵	1	2	yes	—
544	C₂³×C₄₁	C₂⁵	1	2	yes	—
545	C₂³×C₄₁	C₂⁵	1	4	yes	—
546	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
547	Q₈×C₄₁	—	2	8	no	—
548	Q₈×C₄₁	—	2	8	no	—
549	Q₈×C₄₁	—	2	8	no	—
550	Q₈×C₄₁	—	4	8	no	—
551	Q₈×C₄₁	—	4	4	no	—
552	D₄×C₄₁	—	2	8	no	—
553	D₄×C₄₁	—	2	8	no	—
554	D₄×C₄₁	—	2	8	no	—
555	D₄×C₄₁	—	4	8	no	—
556	D₄×C₄₁	—	4	4	no	—
557	D₄×C₄₁	—	4	8	no	—
558	D₄×C₄₁	—	4	8	no	—
559	D₄×C₄₁	—	4	8	no	—
560	D₄×C₄₁	—	4	8	no	—
561	D₄×C₄₁	—	4	8	no	—
562	D₄×C₄₁	—	4	4	no	—
563	D₄×C₄₁	—	4	8	no	—
564	D₄×C₄₁	—	4	4	no	—
565	D₄×C₄₁	—	4	8	no	—
566	D₄×C₄₁	—	4	8	no	—
567	D₄×C₄₁	—	4	8	no	—
568	D₄×C₄₁	—	4	8	no	—
569	D₄×C₄₁	—	4	8	no	—
570	C₂×C₄×C₄₁	—	2	2	no	—
571	C₂×C₄×C₄₁	—	2	2	no	—
572	C₂×C₄×C₄₁	—	2	2	no	—
573	C₂×C₄×C₄₁	—	2	4	no	—
574	C₂×C₄×C₄₁	—	2	4	no	—
575	C₂×C₄×C₄₁	—	2	4	no	—
576	C₂×C₄×C₄₁	—	2	2	no	—
577	C₂×C₄×C₄₁	—	2	4	no	—
578	C₂×C₄×C₄₁	—	2	2	no	—
579	C₂×C₄×C₄₁	—	2	2	no	—
580	C₂×C₄×C₄₁	—	2	2	no	—
581	C₂×C₄×C₄₁	—	2	4	no	—
582	C₂×C₄×C₄₁	—	2	2	no	—
583	C₂×C₄×C₄₁	—	2	2	no	—
584	C₂×C₄×C₄₁	—	2	2	no	—
585	C₂×C₄×C₄₁	—	2	2	no	—
586	C₂×C₄×C₄₁	—	2	8	no	—
587	C₂×C₄×C₄₁	—	2	8	no	—
588	C₂×C₄×C₄₁	—	2	8	no	—
589	C₂×C₄×C₄₁	—	4	8	no	—
590	C₂×C₄×C₄₁	—	4	4	no	—
591	C₂×C₄×C₄₁	—	4	8	no	—
592	C₂×C₄×C₄₁	—	4	8	no	—
593	C₂×C₄×C₄₁	—	4	4	no	—
594	C₂×C₄×C₄₁	—	4	8	no	—
595	C₂×C₄×C₄₁	—	4	8	no	—
596	C₂×C₄×C₄₁	—	4	8	no	—
597	C₂×C₄×C₄₁	—	4	8	no	—
598	C₂×C₄×C₄₁	—	4	8	no	—
599	C₂×C₄×C₄₁	H(5,𝔽₂)	1	4	yes	—
600	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
601	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
602	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
603	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
604	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
605	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
606	C₂×C₄×C₄₁	C₂⁵	1	4	yes	—
607	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
608	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
609	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
610	C₂×C₄×C₄₁	C₂⁵	1	4	yes	—
611	C₂×C₄×C₄₁	C₂⁵	1	4	yes	—
612	C₂×C₄×C₄₁	C₂⁵	1	4	yes	—
613	C₂×C₄×C₄₁	C₂⁵	1	4	yes	—
614	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
615	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
616	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
617	C₂×#3562	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
618	C₂²×C₄₁	—	2	2	no	—
619	C₂²×C₄₁	—	2	2	no	—
620	C₂²×C₄₁	—	2	2	no	—
621	C₂²×C₄₁	—	2	4	no	—
622	C₂²×C₄₁	—	2	4	no	—
623	C₂²×C₄₁	—	2	4	no	—
624	C₂²×C₄₁	—	2	2	no	—
625	C₂²×C₄₁	—	2	2	no	—
626	C₂²×C₄₁	—	2	4	no	—
627	C₂²×C₄₁	—	2	4	no	—
628	C₂²×C₄₁	—	2	4	no	—
629	C₂²×C₄₁	—	2	2	no	—
630	C₂²×C₄₁	—	2	2	no	—
631	C₂²×C₄₁	—	2	4	no	—
632	C₂²×C₄₁	—	2	4	no	—
633	C₂²×C₄₁	—	2	4	no	—
634	C₂²×C₄₁	—	2	2	no	—
635	C₂²×C₄₁	—	2	2	no	—
636	C₂²×C₄₁	—	4	4	no	—
637	C₂²×C₄₁	—	4	4	no	—
638	C₂²×C₄₁	—	4	8	no	—
639	C₂²×C₄₁	—	4	8	no	—
640	C₂²×C₄₁	—	4	8	no	—
641	C₂²×C₄₁	—	4	4	no	—
642	C₂²×C₄₁	—	8	16	no	—
643	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
644	C₂²×C₄₁	#585	1	2	yes	—
645	C₂²×C₄₁	#585	1	2	yes	—
646	C₂²×C₄₁	C₂⁶	1	1	yes	characteristic
647	C₄×C₄₁	—	2	2	no	—
648	C₄×C₄₁	—	2	2	no	—
649	C₄×C₄₁	—	2	2	no	—
650	C₄×C₄₁	—	2	4	no	—
651	C₄×C₄₁	—	2	4	no	—
652	C₄×C₄₁	—	2	4	no	—
653	C₄×C₄₁	—	2	2	no	—
654	C₄×C₄₁	—	2	4	no	—
655	C₄×C₄₁	—	2	2	no	—
656	C₄×C₄₁	—	2	2	no	—
657	C₄×C₄₁	—	2	2	no	—
658	C₄×C₄₁	—	2	4	no	—
659	C₄×C₄₁	—	2	2	no	—
660	C₄×C₄₁	—	2	2	no	—
661	C₄×C₄₁	—	2	2	no	—
662	C₄×C₄₁	—	2	2	no	—
663	C₄×C₄₁	C₂×H(5,𝔽₂)	1	4	yes	—
664	#3562	C₂×C₄₁	1	32	yes	direct product factor
665	C₂×#562	C₂×C₄₁	1	2	yes	complemented
666	C₂×#560	C₂×C₄₁	1	2	yes	complemented
667	C₂×#559	C₂×C₄₁	1	1	yes	characteristic, complemented
668	C₂×#556	C₂×C₄₁	1	1	yes	characteristic, complemented
669	C₂×#553	C₂×C₄₁	1	2	yes	complemented
670	C₂×#551	C₂×C₄₁	1	2	yes	complemented
671	C₂×#550	C₂×C₄₁	1	1	yes	characteristic, complemented
672	C₂×#548	C₂×C₄₁	1	1	yes	characteristic, complemented
673	C₂×#548	C₂×C₄₁	1	1	yes	characteristic, complemented
674	C₂×#547	C₂×C₄₁	1	1	yes	characteristic, complemented
675	C₂×#546	C₂×C₄₁	1	1	yes	characteristic, complemented
676	C₂×#546	C₂×C₄₁	1	1	yes	characteristic, complemented
677	C₂×#541	C₂×C₄₁	1	1	yes	characteristic, complemented
678	C₂×#540	C₂×C₄₁	1	1	yes	characteristic, complemented
679	C₂×#540	C₂×C₄₁	1	2	yes	complemented
680	C₂×#539	C₂×C₄₁	1	2	yes	complemented
681	C₂×#538	C₂×C₄₁	1	2	yes	complemented
682	C₂×#538	C₂×C₄₁	1	2	yes	complemented
683	C₂×#536	C₂×C₄₁	1	1	yes	characteristic, complemented
684	C₂×#535	C₂×C₄₁	1	1	yes	characteristic, complemented
685	C₂×#532	C₂×C₄₁	1	1	yes	characteristic, complemented
686	C₂×#529	C₂×C₄₁	1	1	yes	characteristic, complemented
687	C₂×#529	C₂×C₄₁	1	1	yes	characteristic, complemented
688	C₂×C₄₁	—	4	2	no	—
689	C₂×C₄₁	—	4	2	no	—
690	C₂×C₄₁	—	4	4	no	—
691	C₂×C₄₁	—	4	4	no	—
692	C₂×C₄₁	—	4	4	no	—
693	C₂×C₄₁	—	4	2	no	—
694	C₂×C₄₁	#3562	1	4	yes	direct product factor
695	C₂×C₄₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
696	C₂×C₄₁	C₂×#585	1	1	yes	characteristic
697	C₂×C₄₁	C₂×#585	1	1	yes	characteristic
698	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
699	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
700	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
701	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic, complemented
702	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
703	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
704	#562	C₂²×C₄₁	1	32	yes	complemented
705	#560	C₂²×C₄₁	1	32	yes	complemented
706	#559	C₂²×C₄₁	1	16	yes	complemented
707	#556	C₂²×C₄₁	1	16	yes	complemented
708	#553	C₂²×C₄₁	1	32	yes	complemented
709	#551	C₂²×C₄₁	1	32	yes	complemented
710	#550	C₂²×C₄₁	1	16	yes	complemented
711	#548	C₂²×C₄₁	1	16	yes	complemented
712	#548	C₂²×C₄₁	1	16	yes	complemented
713	#547	C₂²×C₄₁	1	16	yes	complemented
714	#546	C₂²×C₄₁	1	16	yes	complemented
715	#546	C₂²×C₄₁	1	16	yes	complemented
716	#541	C₂²×C₄₁	1	16	yes	complemented
717	#540	C₂²×C₄₁	1	16	yes	complemented
718	#540	C₂²×C₄₁	1	32	yes	complemented
719	#539	C₂²×C₄₁	1	32	yes	complemented
720	#538	C₂²×C₄₁	1	32	yes	complemented
721	#538	C₂²×C₄₁	1	32	yes	complemented
722	#536	C₂²×C₄₁	1	16	yes	complemented
723	#535	C₂²×C₄₁	1	16	yes	complemented
724	#532	C₂²×C₄₁	1	16	yes	complemented
725	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
726	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
727	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
728	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
729	C₂×#127	C₂²×C₄₁	1	2	yes	complemented
730	#529	C₂²×C₄₁	1	16	yes	complemented
731	#529	C₂²×C₄₁	1	16	yes	complemented
732	C₂×#126	C₂²×C₄₁	1	1	yes	characteristic
733	C₂×#126	C₂²×C₄₁	1	2	yes	—
734	C₂×#126	C₂²×C₄₁	1	2	yes	—
735	C₂×#126	C₂²×C₄₁	1	2	yes	complemented
736	C₂×#126	C₂²×C₄₁	1	1	yes	characteristic, complemented
737	C₂×#126	C₂²×C₄₁	1	2	yes	complemented
738	C₂×#126	C₂²×C₄₁	1	2	yes	complemented
739	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic, complemented
740	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic, complemented
741	C₂×#125	C₂²×C₄₁	1	2	yes	complemented
742	C₂×#125	C₂²×C₄₁	1	2	yes	complemented
743	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
744	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
745	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
746	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
747	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
748	C₂×#124	C₂²×C₄₁	1	2	yes	—
749	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic, complemented
750	C₂×#124	C₂²×C₄₁	1	2	yes	complemented
751	C₂×#124	C₂²×C₄₁	1	2	yes	complemented
752	C₂×#123	C₂²×C₄₁	1	1	yes	characteristic
753	C₂×#123	C₂²×C₄₁	1	2	yes	—
754	C₂×#123	C₂²×C₄₁	1	2	yes	—
755	C₂×#123	C₂²×C₄₁	1	2	yes	—
756	C₂×#123	C₂²×C₄₁	1	1	yes	characteristic, complemented
757	C₂×#123	C₂²×C₄₁	1	2	yes	complemented
758	C₂×#123	C₂²×C₄₁	1	2	yes	complemented
759	C₂×#123	C₂²×C₄₁	1	2	yes	complemented
760	C₂×#123	C₂²×C₄₁	1	2	yes	complemented
761	C₂×#123	C₂²×C₄₁	1	2	yes	complemented
762	C₂×#123	C₂²×C₄₁	1	2	yes	complemented
763	C₂×#123	C₂²×C₄₁	1	2	yes	complemented
764	C₂×#123	C₂²×C₄₁	1	2	yes	complemented
765	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
766	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
767	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
768	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
769	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
770	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
771	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
772	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
773	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
774	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
775	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
776	C₂×#121	C₂²×C₄₁	1	2	yes	—
777	C₂×#121	C₂²×C₄₁	1	2	yes	—
778	C₂×#121	C₂²×C₄₁	1	2	yes	—
779	C₂×#121	C₂²×C₄₁	1	2	yes	—
780	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
781	C₂×#121	C₂²×C₄₁	1	2	yes	—
782	C₂×#121	C₂²×C₄₁	1	2	yes	—
783	C₂×#121	C₂²×C₄₁	1	2	yes	complemented
784	C₂×#121	C₂²×C₄₁	1	2	yes	complemented
785	C₂×#121	C₂²×C₄₁	1	2	yes	complemented
786	C₂×#121	C₂²×C₄₁	1	2	yes	complemented
787	C₂×#121	C₂²×C₄₁	1	2	yes	complemented
788	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic, complemented
789	C₂×#121	C₂²×C₄₁	1	2	yes	complemented
790	C₂×#121	C₂²×C₄₁	1	2	yes	complemented
791	C₂×#120	C₂²×C₄₁	1	2	yes	—
792	C₂×#120	C₂²×C₄₁	1	2	yes	—
793	C₂×#120	C₂²×C₄₁	1	2	yes	—
794	C₂×#120	C₂²×C₄₁	1	2	yes	—
795	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
796	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
797	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
798	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
799	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
800	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
801	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
802	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
803	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
804	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
805	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
806	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
807	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
808	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
809	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
810	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
811	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
812	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
813	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic, complemented
814	C₂×#117	C₂²×C₄₁	1	2	yes	complemented
815	C₂×#117	C₂²×C₄₁	1	2	yes	complemented
816	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	complemented
817	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
818	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
819	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic, complemented
820	C₄₁	C₂×#3562	1	1	yes	characteristic, direct product factor, Sylow
821	C₂⁵	C₂³×C₄₁	1	2	yes	—
822	C₂×#41	—	4	4	no	—
823	C₂×#41	—	4	4	no	—
824	C₂×#41	—	4	4	no	—
825	C₂×#41	—	4	4	no	—
826	C₂×#41	C₂³×C₄₁	1	8	yes	—
827	C₂×#41	C₂³×C₄₁	1	8	yes	—
828	C₂×#41	C₂³×C₄₁	1	8	yes	—
829	C₂×#41	C₂³×C₄₁	1	8	yes	complemented
830	C₂²×Q₈	—	4	4	no	—
831	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
832	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
833	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
834	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
835	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
836	C₂²×Q₈	C₂³×C₄₁	1	8	yes	complemented
837	C₂²×D₄	—	4	4	no	—
838	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
839	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
840	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
841	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
842	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
843	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
844	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
845	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
846	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
847	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
848	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
849	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
850	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
851	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
852	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
853	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
854	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
855	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
856	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
857	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
858	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
859	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
860	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
861	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
862	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
863	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
864	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
865	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
866	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
867	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
868	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
869	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
870	C₄⋊Q₈	C₂³×C₄₁	1	8	yes	complemented
871	C₄⋊Q₈	C₂³×C₄₁	1	8	yes	complemented
872	#127	C₂³×C₄₁	1	8	yes	—
873	#127	C₂³×C₄₁	1	8	yes	—
874	#127	C₂³×C₄₁	1	16	yes	complemented
875	#126	C₂³×C₄₁	1	8	yes	—
876	#126	C₂³×C₄₁	1	16	yes	—
877	#126	C₂³×C₄₁	1	16	yes	—
878	#126	C₂³×C₄₁	1	16	yes	complemented
879	#126	C₂³×C₄₁	1	8	yes	complemented
880	#126	C₂³×C₄₁	1	16	yes	complemented
881	#126	C₂³×C₄₁	1	16	yes	complemented
882	#125	C₂³×C₄₁	1	8	yes	complemented
883	#125	C₂³×C₄₁	1	8	yes	complemented
884	#125	C₂³×C₄₁	1	16	yes	complemented
885	#125	C₂³×C₄₁	1	16	yes	complemented
886	#124	C₂³×C₄₁	1	8	yes	—
887	#124	C₂³×C₄₁	1	8	yes	—
888	#124	C₂³×C₄₁	1	8	yes	—
889	#124	C₂³×C₄₁	1	8	yes	—
890	#124	C₂³×C₄₁	1	8	yes	—
891	#124	C₂³×C₄₁	1	16	yes	—
892	#124	C₂³×C₄₁	1	8	yes	complemented
893	#124	C₂³×C₄₁	1	16	yes	complemented
894	#124	C₂³×C₄₁	1	16	yes	complemented
895	#123	C₂³×C₄₁	1	8	yes	—
896	#123	C₂³×C₄₁	1	16	yes	—
897	#123	C₂³×C₄₁	1	16	yes	—
898	#123	C₂³×C₄₁	1	16	yes	—
899	#123	C₂³×C₄₁	1	8	yes	complemented
900	#123	C₂³×C₄₁	1	16	yes	complemented
901	#123	C₂³×C₄₁	1	16	yes	complemented
902	#123	C₂³×C₄₁	1	16	yes	complemented
903	#123	C₂³×C₄₁	1	16	yes	complemented
904	#123	C₂³×C₄₁	1	16	yes	complemented
905	#123	C₂³×C₄₁	1	16	yes	complemented
906	#123	C₂³×C₄₁	1	16	yes	complemented
907	#123	C₂³×C₄₁	1	16	yes	complemented
908	C₂²⋊Q₈	C₂³×C₄₁	1	8	yes	—
909	C₂²⋊Q₈	C₂³×C₄₁	1	8	yes	—
910	C₂²⋊Q₈	C₂³×C₄₁	1	8	yes	complemented
911	C₂²⋊Q₈	C₂³×C₄₁	1	8	yes	complemented
912	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	complemented
913	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	complemented
914	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	complemented
915	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	complemented
916	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	complemented
917	#121	C₂³×C₄₁	1	8	yes	—
918	#121	C₂³×C₄₁	1	8	yes	—
919	#121	C₂³×C₄₁	1	16	yes	—
920	#121	C₂³×C₄₁	1	16	yes	—
921	#121	C₂³×C₄₁	1	16	yes	—
922	#121	C₂³×C₄₁	1	16	yes	—
923	#121	C₂³×C₄₁	1	8	yes	—
924	#121	C₂³×C₄₁	1	16	yes	—
925	#121	C₂³×C₄₁	1	16	yes	—
926	#121	C₂³×C₄₁	1	16	yes	complemented
927	#121	C₂³×C₄₁	1	16	yes	complemented
928	#121	C₂³×C₄₁	1	16	yes	complemented
929	#121	C₂³×C₄₁	1	16	yes	complemented
930	#121	C₂³×C₄₁	1	16	yes	complemented
931	#121	C₂³×C₄₁	1	8	yes	complemented
932	#121	C₂³×C₄₁	1	16	yes	complemented
933	#121	C₂³×C₄₁	1	16	yes	complemented
934	#120	C₂³×C₄₁	1	16	yes	—
935	#120	C₂³×C₄₁	1	16	yes	—
936	#120	C₂³×C₄₁	1	16	yes	—
937	#120	C₂³×C₄₁	1	16	yes	—
938	C₄×Q₈	C₂³×C₄₁	1	8	yes	complemented
939	C₄×Q₈	C₂³×C₄₁	1	8	yes	complemented
940	C₄×Q₈	C₂³×C₄₁	1	8	yes	complemented
941	C₄×Q₈	C₂³×C₄₁	1	8	yes	complemented
942	C₄×D₄	C₂³×C₄₁	1	8	yes	—
943	C₄×D₄	C₂³×C₄₁	1	8	yes	—
944	C₄×D₄	C₂³×C₄₁	1	8	yes	—
945	C₄×D₄	C₂³×C₄₁	1	8	yes	—
946	C₄×D₄	C₂³×C₄₁	1	16	yes	complemented
947	C₄×D₄	C₂³×C₄₁	1	8	yes	complemented
948	C₄×D₄	C₂³×C₄₁	1	16	yes	complemented
949	C₄×D₄	C₂³×C₄₁	1	16	yes	complemented
950	C₄×D₄	C₂³×C₄₁	1	16	yes	complemented
951	C₄×D₄	C₂³×C₄₁	1	16	yes	complemented
952	C₄×D₄	C₂³×C₄₁	1	16	yes	complemented
953	C₄×D₄	C₂³×C₄₁	1	8	yes	complemented
954	C₄×D₄	C₂³×C₄₁	1	16	yes	complemented
955	#117	C₂³×C₄₁	1	8	yes	—
956	#117	C₂³×C₄₁	1	8	yes	complemented
957	#117	C₂³×C₄₁	1	16	yes	complemented
958	#117	C₂³×C₄₁	1	16	yes	complemented
959	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
960	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
961	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
962	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
963	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
964	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
965	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
966	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
967	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
968	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
969	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
970	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
971	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
972	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
973	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
974	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
975	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
976	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
977	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
978	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
979	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
980	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
981	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
982	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
983	C₂×C₄⋊C₄	C₂³×C₄₁	1	16	yes	complemented
984	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
985	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
986	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
987	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
988	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
989	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
990	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
991	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
992	C₂×C₂²⋊C₄	C₂³×C₄₁	1	16	yes	—
993	C₂×C₂²⋊C₄	C₂³×C₄₁	1	16	yes	—
994	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
995	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
996	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
997	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
998	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
999	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
1000	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
1001	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
1002	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
1003	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
1004	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
1005	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
1006	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
1007	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
1008	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
1009	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
1010	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
1011	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
1012	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
1013	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
1014	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
1015	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
1016	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
1017	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
1018	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
1019	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
1020	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
1021	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
1022	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
1023	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
1024	C₂×C₄²	C₂³×C₄₁	1	8	yes	complemented
1025	C₂⁴	—	4	4	no	—
1026	C₂⁴	—	4	4	no	—
1027	C₂⁴	—	4	4	no	—
1028	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
1029	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
1030	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
1031	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
1032	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
1033	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
1034	C₂⁴	C₂⁴×C₄₁	1	8	yes	—
1035	#41	—	4	16	no	—
1036	#41	—	4	16	no	—
1037	#41	—	4	16	no	—
1038	#41	—	4	16	no	—
1039	C₂×Q₈	—	2	4	no	—
1040	C₂×Q₈	—	2	4	no	—
1041	C₂×Q₈	—	2	4	no	—
1042	C₂×Q₈	—	4	4	no	—
1043	C₂×Q₈	—	4	2	no	—
1044	C₂×Q₈	—	4	16	no	—
1045	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
1046	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
1047	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
1048	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
1049	C₂×Q₈	C₂⁴×C₄₁	1	8	yes	—
1050	C₂×D₄	—	2	4	no	—
1051	C₂×D₄	—	2	4	no	—
1052	C₂×D₄	—	2	4	no	—
1053	C₂×D₄	—	4	16	no	—
1054	C₂×D₄	—	4	4	no	—
1055	C₂×D₄	—	4	4	no	—
1056	C₂×D₄	—	4	4	no	—
1057	C₂×D₄	—	4	4	no	—
1058	C₂×D₄	—	4	4	no	—
1059	C₂×D₄	—	4	2	no	—
1060	C₂×D₄	—	4	4	no	—
1061	C₂×D₄	—	4	4	no	—
1062	C₂×D₄	—	4	4	no	—
1063	C₂×D₄	—	4	4	no	—
1064	C₂×D₄	—	4	4	no	—
1065	C₂×D₄	—	4	2	no	—
1066	C₂×D₄	—	4	4	no	—
1067	C₂×D₄	—	4	2	no	—
1068	C₂×D₄	—	4	4	no	—
1069	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
1070	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
1071	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
1072	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
1073	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
1074	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
1075	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
1076	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
1077	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
1078	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
1079	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
1080	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
1081	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
1082	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
1083	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
1084	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
1085	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
1086	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
1087	C₂²×C₄	—	2	4	no	—
1088	C₂²×C₄	—	2	4	no	—
1089	C₂²×C₄	—	2	4	no	—
1090	C₂²×C₄	—	4	4	no	—
1091	C₂²×C₄	—	4	4	no	—
1092	C₂²×C₄	—	4	4	no	—
1093	C₂²×C₄	—	4	4	no	—
1094	C₂²×C₄	—	4	4	no	—
1095	C₂²×C₄	—	4	4	no	—
1096	C₂²×C₄	—	4	2	no	—
1097	C₂²×C₄	—	4	4	no	—
1098	C₂²×C₄	—	4	4	no	—
1099	C₂²×C₄	—	4	2	no	—
1100	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1101	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1102	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1103	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1104	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1105	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1106	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
1107	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1108	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1109	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1110	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
1111	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
1112	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
1113	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
1114	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
1115	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1116	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1117	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
1118	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
1119	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
1120	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
1121	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
1122	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
1123	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
1124	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
1125	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
1126	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
1127	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
1128	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
1129	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1130	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1131	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1132	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1133	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1134	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1135	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1136	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1137	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1138	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1139	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1140	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1141	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1142	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1143	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1144	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1145	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1146	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1147	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1148	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1149	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1150	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1151	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1152	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1153	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1154	C₂²⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1155	C₂²⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1156	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1157	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1158	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1159	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1160	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1161	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1162	C₂²⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1163	C₂²⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1164	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1165	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1166	C₂²⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1167	C₂²⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1168	C₂²⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1169	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1170	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1171	C₂²⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1172	C₂²⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1173	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1174	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1175	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1176	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1177	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1178	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1179	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1180	C₂²⋊C₄	C₂⁴×C₄₁	1	4	yes	—
1181	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1182	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
1183	C₄²	C₂⁴×C₄₁	1	4	yes	—
1184	C₄²	C₂⁴×C₄₁	1	4	yes	—
1185	C₄²	C₂⁴×C₄₁	1	4	yes	—
1186	C₄²	C₂⁴×C₄₁	1	4	yes	—
1187	C₄²	C₂⁴×C₄₁	1	4	yes	—
1188	C₄²	C₂⁴×C₄₁	1	8	yes	—
1189	C₄²	C₂⁴×C₄₁	1	4	yes	—
1190	C₄²	C₂⁴×C₄₁	1	8	yes	—
1191	C₄²	C₂⁴×C₄₁	1	8	yes	—
1192	C₂³	—	2	2	no	—
1193	C₂³	—	2	2	no	—
1194	C₂³	—	2	2	no	—
1195	C₂³	—	2	4	no	—
1196	C₂³	—	2	4	no	—
1197	C₂³	—	2	4	no	—
1198	C₂³	—	2	2	no	—
1199	C₂³	—	2	2	no	—
1200	C₂³	—	2	4	no	—
1201	C₂³	—	2	4	no	—
1202	C₂³	—	2	4	no	—
1203	C₂³	—	2	2	no	—
1204	C₂³	—	2	2	no	—
1205	C₂³	—	2	4	no	—
1206	C₂³	—	2	4	no	—
1207	C₂³	—	2	4	no	—
1208	C₂³	—	2	2	no	—
1209	C₂³	—	2	2	no	—
1210	C₂³	—	4	8	no	—
1211	C₂³	—	4	8	no	—
1212	C₂³	—	4	8	no	—
1213	C₂³	—	8	16	no	—
1214	C₂³	C₂⁵×C₄₁	1	2	yes	—
1215	C₂³	C₂⁵×C₄₁	1	4	yes	—
1216	C₂³	C₂⁵×C₄₁	1	4	yes	—
1217	C₂³	C₂⁵×C₄₁	1	2	yes	—
1218	C₂³	C₂⁵×C₄₁	1	2	yes	—
1219	C₂³	C₂⁵×C₄₁	1	4	yes	—
1220	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
1221	Q₈	—	2	8	no	—
1222	Q₈	—	2	8	no	—
1223	Q₈	—	2	8	no	—
1224	Q₈	—	4	8	no	—
1225	Q₈	—	4	4	no	—
1226	D₄	—	2	8	no	—
1227	D₄	—	2	8	no	—
1228	D₄	—	2	8	no	—
1229	D₄	—	4	8	no	—
1230	D₄	—	4	8	no	—
1231	D₄	—	4	8	no	—
1232	D₄	—	4	8	no	—
1233	D₄	—	4	8	no	—
1234	D₄	—	4	4	no	—
1235	D₄	—	4	8	no	—
1236	D₄	—	4	8	no	—
1237	D₄	—	4	8	no	—
1238	D₄	—	4	8	no	—
1239	D₄	—	4	8	no	—
1240	D₄	—	4	4	no	—
1241	D₄	—	4	8	no	—
1242	D₄	—	4	4	no	—
1243	D₄	—	4	8	no	—
1244	C₂×C₄	—	2	2	no	—
1245	C₂×C₄	—	2	2	no	—
1246	C₂×C₄	—	2	2	no	—
1247	C₂×C₄	—	2	4	no	—
1248	C₂×C₄	—	2	4	no	—
1249	C₂×C₄	—	2	4	no	—
1250	C₂×C₄	—	2	2	no	—
1251	C₂×C₄	—	2	4	no	—
1252	C₂×C₄	—	2	2	no	—
1253	C₂×C₄	—	2	2	no	—
1254	C₂×C₄	—	2	2	no	—
1255	C₂×C₄	—	2	4	no	—
1256	C₂×C₄	—	2	2	no	—
1257	C₂×C₄	—	2	2	no	—
1258	C₂×C₄	—	2	2	no	—
1259	C₂×C₄	—	2	2	no	—
1260	C₂×C₄	—	2	8	no	—
1261	C₂×C₄	—	2	8	no	—
1262	C₂×C₄	—	2	8	no	—
1263	C₂×C₄	—	4	8	no	—
1264	C₂×C₄	—	4	8	no	—
1265	C₂×C₄	—	4	8	no	—
1266	C₂×C₄	—	4	8	no	—
1267	C₂×C₄	—	4	8	no	—
1268	C₂×C₄	—	4	8	no	—
1269	C₂×C₄	—	4	4	no	—
1270	C₂×C₄	—	4	8	no	—
1271	C₂×C₄	—	4	8	no	—
1272	C₂×C₄	—	4	4	no	—
1273	C₂×C₄	H(5,𝔽₂)×C₄₁	1	4	yes	—
1274	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
1275	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
1276	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
1277	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
1278	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
1279	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
1280	C₂×C₄	C₂⁵×C₄₁	1	4	yes	—
1281	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
1282	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
1283	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
1284	C₂×C₄	C₂⁵×C₄₁	1	4	yes	—
1285	C₂×C₄	C₂⁵×C₄₁	1	4	yes	—
1286	C₂×C₄	C₂⁵×C₄₁	1	4	yes	—
1287	C₂×C₄	C₂⁵×C₄₁	1	4	yes	—
1288	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
1289	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
1290	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
1291	C₂²	—	2	2	no	—
1292	C₂²	—	2	2	no	—
1293	C₂²	—	2	2	no	—
1294	C₂²	—	2	4	no	—
1295	C₂²	—	2	4	no	—
1296	C₂²	—	2	4	no	—
1297	C₂²	—	2	2	no	—
1298	C₂²	—	2	2	no	—
1299	C₂²	—	2	4	no	—
1300	C₂²	—	2	4	no	—
1301	C₂²	—	2	4	no	—
1302	C₂²	—	2	2	no	—
1303	C₂²	—	2	2	no	—
1304	C₂²	—	2	4	no	—
1305	C₂²	—	2	4	no	—
1306	C₂²	—	2	4	no	—
1307	C₂²	—	2	2	no	—
1308	C₂²	—	2	2	no	—
1309	C₂²	—	4	4	no	—
1310	C₂²	—	4	8	no	—
1311	C₂²	—	4	8	no	—
1312	C₂²	—	4	4	no	—
1313	C₂²	—	4	4	no	—
1314	C₂²	—	4	8	no	—
1315	C₂²	—	8	16	no	—
1316	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
1317	C₂²	C₄₁×#585	1	2	yes	—
1318	C₂²	C₄₁×#585	1	2	yes	—
1319	C₂²	C₂⁶×C₄₁	1	1	yes	characteristic
1320	C₄	—	2	2	no	—
1321	C₄	—	2	2	no	—
1322	C₄	—	2	2	no	—
1323	C₄	—	2	4	no	—
1324	C₄	—	2	4	no	—
1325	C₄	—	2	4	no	—
1326	C₄	—	2	2	no	—
1327	C₄	—	2	4	no	—
1328	C₄	—	2	2	no	—
1329	C₄	—	2	2	no	—
1330	C₄	—	2	2	no	—
1331	C₄	—	2	4	no	—
1332	C₄	—	2	2	no	—
1333	C₄	—	2	2	no	—
1334	C₄	—	2	2	no	—
1335	C₄	—	2	2	no	—
1336	C₄	C₂×H(5,𝔽₂)×C₄₁	1	4	yes	—
1337	C₂	—	4	2	no	—
1338	C₂	—	4	4	no	—
1339	C₂	—	4	4	no	—
1340	C₂	—	4	2	no	—
1341	C₂	—	4	2	no	—
1342	C₂	—	4	4	no	—
1343	C₂	C₄₁×#3562	1	4	yes	direct product factor
1344	C₂	C₂²×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1345	C₂	C₂×C₄₁×#585	1	1	yes	characteristic
1346	C₂	C₂×C₄₁×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₄₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₄₁×#3562	C₂	direct (N × H)
2. C₂×C₄₁×#562	C₂	semidirect
3. C₂×C₄₁×#560	C₂	semidirect
4. C₂×C₄₁×#559	C₂	semidirect
5. C₂×C₄₁×#556	C₂	semidirect
6. C₂×C₄₁×#553	C₂	semidirect
7. C₂×C₄₁×#551	C₂	semidirect
8. C₂×C₄₁×#550	C₂	semidirect
9. C₂×C₄₁×#548	C₂	semidirect
10. C₂×C₄₁×#548	C₂	semidirect
11. C₂×C₄₁×#547	C₂	semidirect
12. C₂×C₄₁×#546	C₂	semidirect
13. C₂×C₄₁×#546	C₂	semidirect
14. C₂×C₄₁×#541	C₂	semidirect
15. C₂×C₄₁×#540	C₂	semidirect
16. C₂×C₄₁×#540	C₂	semidirect
17. C₂×C₄₁×#539	C₂	semidirect
18. C₂×C₄₁×#538	C₂	semidirect
19. C₂×C₄₁×#538	C₂	semidirect
20. C₂×C₄₁×#536	C₂	semidirect
21. C₂×C₄₁×#535	C₂	semidirect
22. C₂×C₄₁×#532	C₂	semidirect
23. C₂×C₄₁×#529	C₂	semidirect
24. C₂×C₄₁×#529	C₂	semidirect
28. C₂²×#41×C₄₁	C₂²	semidirect
29. C₂³×Q₈×C₄₁	C₂²	semidirect
31. C₄₁×#562	C₂²	semidirect
32. C₄₁×#560	C₂²	semidirect
33. C₄₁×#559	C₂²	semidirect
34. C₄₁×#556	C₂²	semidirect
35. C₄₁×#553	C₂²	semidirect
36. C₄₁×#551	C₂²	semidirect
37. C₄₁×#550	C₂²	semidirect
38. C₄₁×#548	C₂²	semidirect
39. C₄₁×#548	C₂²	semidirect
40. C₄₁×#547	C₂²	semidirect
41. C₄₁×#546	C₂²	semidirect
42. C₄₁×#546	C₂²	semidirect
43. C₄₁×#541	C₂²	semidirect
44. C₄₁×#540	C₂²	semidirect
45. C₄₁×#540	C₂²	semidirect
46. C₄₁×#539	C₂²	semidirect
47. C₄₁×#538	C₂²	semidirect
48. C₄₁×#538	C₂²	semidirect
49. C₄₁×#536	C₂²	semidirect
50. C₄₁×#535	C₂²	semidirect
51. C₄₁×#532	C₂²	semidirect
52. C₂×C₄⋊Q₈×C₄₁	C₂²	semidirect
53. C₂×C₄⋊Q₈×C₄₁	C₂²	semidirect
56. C₂×#127×C₄₁	C₂²	semidirect
57. C₄₁×#529	C₂²	semidirect
58. C₄₁×#529	C₂²	semidirect
62. C₂×#126×C₄₁	C₂²	semidirect
63. C₂×#126×C₄₁	C₂²	semidirect
64. C₂×#126×C₄₁	C₂²	semidirect
65. C₂×#126×C₄₁	C₂²	semidirect
66. C₂×#125×C₄₁	C₂²	semidirect
67. C₂×#125×C₄₁	C₂²	semidirect
68. C₂×#125×C₄₁	C₂²	semidirect
69. C₂×#125×C₄₁	C₂²	semidirect
76. C₂×#124×C₄₁	C₂²	semidirect
77. C₂×#124×C₄₁	C₂²	semidirect
78. C₂×#124×C₄₁	C₂²	semidirect
83. C₂×#123×C₄₁	C₂²	semidirect
84. C₂×#123×C₄₁	C₂²	semidirect
85. C₂×#123×C₄₁	C₂²	semidirect
86. C₂×#123×C₄₁	C₂²	semidirect
87. C₂×#123×C₄₁	C₂²	semidirect
88. C₂×#123×C₄₁	C₂²	semidirect
89. C₂×#123×C₄₁	C₂²	semidirect
90. C₂×#123×C₄₁	C₂²	semidirect
91. C₂×#123×C₄₁	C₂²	semidirect
94. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
95. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
96. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
97. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
98. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
99. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
100. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
110. C₂×#121×C₄₁	C₂²	semidirect
111. C₂×#121×C₄₁	C₂²	semidirect
112. C₂×#121×C₄₁	C₂²	semidirect
113. C₂×#121×C₄₁	C₂²	semidirect
114. C₂×#121×C₄₁	C₂²	semidirect
115. C₂×#121×C₄₁	C₂²	semidirect
116. C₂×#121×C₄₁	C₂²	semidirect
117. C₂×#121×C₄₁	C₂²	semidirect
122. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
123. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
124. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
125. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
130. C₂×C₄×D₄×C₄₁	C₂²	semidirect
131. C₂×C₄×D₄×C₄₁	C₂²	semidirect
132. C₂×C₄×D₄×C₄₁	C₂²	semidirect
133. C₂×C₄×D₄×C₄₁	C₂²	semidirect
134. C₂×C₄×D₄×C₄₁	C₂²	semidirect
135. C₂×C₄×D₄×C₄₁	C₂²	semidirect
136. C₂×C₄×D₄×C₄₁	C₂²	semidirect
137. C₂×C₄×D₄×C₄₁	C₂²	semidirect
138. C₂×C₄×D₄×C₄₁	C₂²	semidirect
140. C₂×#117×C₄₁	C₂²	semidirect
141. C₂×#117×C₄₁	C₂²	semidirect
142. C₂×#117×C₄₁	C₂²	semidirect
143. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
146. C₂²×C₄²×C₄₁	C₂²	semidirect
155. C₂×#41×C₄₁	C₂³	semidirect
162. C₂²×Q₈×C₄₁	C₂³	semidirect
196. C₄⋊Q₈×C₄₁	C₂³	semidirect
197. C₄⋊Q₈×C₄₁	C₂³	semidirect
200. #127×C₄₁	C₂³	semidirect
204. #126×C₄₁	C₂³	semidirect
205. #126×C₄₁	C₂³	semidirect
206. #126×C₄₁	C₂³	semidirect
207. #126×C₄₁	C₂³	semidirect
208. #125×C₄₁	C₂³	semidirect
209. #125×C₄₁	C₂³	semidirect
210. #125×C₄₁	C₂³	semidirect
211. #125×C₄₁	C₂³	semidirect
218. #124×C₄₁	C₂³	semidirect
219. #124×C₄₁	C₂³	semidirect
220. #124×C₄₁	C₂³	semidirect
225. #123×C₄₁	C₂³	semidirect
226. #123×C₄₁	C₂³	semidirect
227. #123×C₄₁	C₂³	semidirect
228. #123×C₄₁	C₂³	semidirect
229. #123×C₄₁	C₂³	semidirect
230. #123×C₄₁	C₂³	semidirect
231. #123×C₄₁	C₂³	semidirect
232. #123×C₄₁	C₂³	semidirect
233. #123×C₄₁	C₂³	semidirect
236. C₂²⋊Q₈×C₄₁	C₂³	semidirect
237. C₂²⋊Q₈×C₄₁	C₂³	semidirect
238. C₂²⋊Q₈×C₄₁	C₂³	semidirect
239. C₂²⋊Q₈×C₄₁	C₂³	semidirect
240. C₂²⋊Q₈×C₄₁	C₂³	semidirect
241. C₂²⋊Q₈×C₄₁	C₂³	semidirect
242. C₂²⋊Q₈×C₄₁	C₂³	semidirect
252. #121×C₄₁	C₂³	semidirect
253. #121×C₄₁	C₂³	semidirect
254. #121×C₄₁	C₂³	semidirect
255. #121×C₄₁	C₂³	semidirect
256. #121×C₄₁	C₂³	semidirect
257. #121×C₄₁	C₂³	semidirect
258. #121×C₄₁	C₂³	semidirect
259. #121×C₄₁	C₂³	semidirect
264. C₄×Q₈×C₄₁	C₂³	semidirect
265. C₄×Q₈×C₄₁	C₂³	semidirect
266. C₄×Q₈×C₄₁	C₂³	semidirect
267. C₄×Q₈×C₄₁	C₂³	semidirect
272. C₄×D₄×C₄₁	C₂³	semidirect
273. C₄×D₄×C₄₁	C₂³	semidirect
274. C₄×D₄×C₄₁	C₂³	semidirect
275. C₄×D₄×C₄₁	C₂³	semidirect
276. C₄×D₄×C₄₁	C₂³	semidirect
277. C₄×D₄×C₄₁	C₂³	semidirect
278. C₄×D₄×C₄₁	C₂³	semidirect
279. C₄×D₄×C₄₁	C₂³	semidirect
280. C₄×D₄×C₄₁	C₂³	semidirect
282. #117×C₄₁	C₂³	semidirect
283. #117×C₄₁	C₂³	semidirect
284. #117×C₄₁	C₂³	semidirect
309. C₂×C₄⋊C₄×C₄₁	C₂³	semidirect
350. C₂×C₄²×C₄₁	C₂³	semidirect
617. C₂×#3562	C₄₁	direct (N × H)
664. #3562	C₂×C₄₁	direct (N × H)
665. C₂×#562	C₂×C₄₁	semidirect
666. C₂×#560	C₂×C₄₁	semidirect
667. C₂×#559	C₂×C₄₁	semidirect
668. C₂×#556	C₂×C₄₁	semidirect
669. C₂×#553	C₂×C₄₁	semidirect
670. C₂×#551	C₂×C₄₁	semidirect
671. C₂×#550	C₂×C₄₁	semidirect
672. C₂×#548	C₂×C₄₁	semidirect
673. C₂×#548	C₂×C₄₁	semidirect
674. C₂×#547	C₂×C₄₁	semidirect
675. C₂×#546	C₂×C₄₁	semidirect
676. C₂×#546	C₂×C₄₁	semidirect
677. C₂×#541	C₂×C₄₁	semidirect
678. C₂×#540	C₂×C₄₁	semidirect
679. C₂×#540	C₂×C₄₁	semidirect
680. C₂×#539	C₂×C₄₁	semidirect
681. C₂×#538	C₂×C₄₁	semidirect
682. C₂×#538	C₂×C₄₁	semidirect
683. C₂×#536	C₂×C₄₁	semidirect
684. C₂×#535	C₂×C₄₁	semidirect
685. C₂×#532	C₂×C₄₁	semidirect
686. C₂×#529	C₂×C₄₁	semidirect
687. C₂×#529	C₂×C₄₁	semidirect
694. C₂×C₄₁	#3562	direct (N × H)
701. C₂²×#41	C₂²×C₄₁	semidirect
702. C₂³×Q₈	C₂²×C₄₁	semidirect
704. #562	C₂²×C₄₁	semidirect
705. #560	C₂²×C₄₁	semidirect
706. #559	C₂²×C₄₁	semidirect
707. #556	C₂²×C₄₁	semidirect
708. #553	C₂²×C₄₁	semidirect
709. #551	C₂²×C₄₁	semidirect
710. #550	C₂²×C₄₁	semidirect
711. #548	C₂²×C₄₁	semidirect
712. #548	C₂²×C₄₁	semidirect
713. #547	C₂²×C₄₁	semidirect
714. #546	C₂²×C₄₁	semidirect
715. #546	C₂²×C₄₁	semidirect
716. #541	C₂²×C₄₁	semidirect
717. #540	C₂²×C₄₁	semidirect
718. #540	C₂²×C₄₁	semidirect
719. #539	C₂²×C₄₁	semidirect
720. #538	C₂²×C₄₁	semidirect
721. #538	C₂²×C₄₁	semidirect
722. #536	C₂²×C₄₁	semidirect
723. #535	C₂²×C₄₁	semidirect
724. #532	C₂²×C₄₁	semidirect
725. C₂×C₄⋊Q₈	C₂²×C₄₁	semidirect
726. C₂×C₄⋊Q₈	C₂²×C₄₁	semidirect
729. C₂×#127	C₂²×C₄₁	semidirect
730. #529	C₂²×C₄₁	semidirect
731. #529	C₂²×C₄₁	semidirect
735. C₂×#126	C₂²×C₄₁	semidirect
736. C₂×#126	C₂²×C₄₁	semidirect
737. C₂×#126	C₂²×C₄₁	semidirect
738. C₂×#126	C₂²×C₄₁	semidirect
739. C₂×#125	C₂²×C₄₁	semidirect
740. C₂×#125	C₂²×C₄₁	semidirect
741. C₂×#125	C₂²×C₄₁	semidirect
742. C₂×#125	C₂²×C₄₁	semidirect
749. C₂×#124	C₂²×C₄₁	semidirect
750. C₂×#124	C₂²×C₄₁	semidirect
751. C₂×#124	C₂²×C₄₁	semidirect
756. C₂×#123	C₂²×C₄₁	semidirect
757. C₂×#123	C₂²×C₄₁	semidirect
758. C₂×#123	C₂²×C₄₁	semidirect
759. C₂×#123	C₂²×C₄₁	semidirect
760. C₂×#123	C₂²×C₄₁	semidirect
761. C₂×#123	C₂²×C₄₁	semidirect
762. C₂×#123	C₂²×C₄₁	semidirect
763. C₂×#123	C₂²×C₄₁	semidirect
764. C₂×#123	C₂²×C₄₁	semidirect
767. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
768. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
769. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
770. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
771. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
772. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
773. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
783. C₂×#121	C₂²×C₄₁	semidirect
784. C₂×#121	C₂²×C₄₁	semidirect
785. C₂×#121	C₂²×C₄₁	semidirect
786. C₂×#121	C₂²×C₄₁	semidirect
787. C₂×#121	C₂²×C₄₁	semidirect
788. C₂×#121	C₂²×C₄₁	semidirect
789. C₂×#121	C₂²×C₄₁	semidirect
790. C₂×#121	C₂²×C₄₁	semidirect
795. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
796. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
797. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
798. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
803. C₂×C₄×D₄	C₂²×C₄₁	semidirect
804. C₂×C₄×D₄	C₂²×C₄₁	semidirect
805. C₂×C₄×D₄	C₂²×C₄₁	semidirect
806. C₂×C₄×D₄	C₂²×C₄₁	semidirect
807. C₂×C₄×D₄	C₂²×C₄₁	semidirect
808. C₂×C₄×D₄	C₂²×C₄₁	semidirect
809. C₂×C₄×D₄	C₂²×C₄₁	semidirect
810. C₂×C₄×D₄	C₂²×C₄₁	semidirect
811. C₂×C₄×D₄	C₂²×C₄₁	semidirect
813. C₂×#117	C₂²×C₄₁	semidirect
814. C₂×#117	C₂²×C₄₁	semidirect
815. C₂×#117	C₂²×C₄₁	semidirect
816. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
819. C₂²×C₄²	C₂²×C₄₁	semidirect
820. C₄₁	C₂×#3562	direct (N × H)
829. C₂×#41	C₂³×C₄₁	semidirect
836. C₂²×Q₈	C₂³×C₄₁	semidirect
870. C₄⋊Q₈	C₂³×C₄₁	semidirect
871. C₄⋊Q₈	C₂³×C₄₁	semidirect
874. #127	C₂³×C₄₁	semidirect
878. #126	C₂³×C₄₁	semidirect
879. #126	C₂³×C₄₁	semidirect
880. #126	C₂³×C₄₁	semidirect
881. #126	C₂³×C₄₁	semidirect
882. #125	C₂³×C₄₁	semidirect
883. #125	C₂³×C₄₁	semidirect
884. #125	C₂³×C₄₁	semidirect
885. #125	C₂³×C₄₁	semidirect
892. #124	C₂³×C₄₁	semidirect
893. #124	C₂³×C₄₁	semidirect
894. #124	C₂³×C₄₁	semidirect
899. #123	C₂³×C₄₁	semidirect
900. #123	C₂³×C₄₁	semidirect
901. #123	C₂³×C₄₁	semidirect
902. #123	C₂³×C₄₁	semidirect
903. #123	C₂³×C₄₁	semidirect
904. #123	C₂³×C₄₁	semidirect
905. #123	C₂³×C₄₁	semidirect
906. #123	C₂³×C₄₁	semidirect
907. #123	C₂³×C₄₁	semidirect
910. C₂²⋊Q₈	C₂³×C₄₁	semidirect
911. C₂²⋊Q₈	C₂³×C₄₁	semidirect
912. C₂²⋊Q₈	C₂³×C₄₁	semidirect
913. C₂²⋊Q₈	C₂³×C₄₁	semidirect
914. C₂²⋊Q₈	C₂³×C₄₁	semidirect
915. C₂²⋊Q₈	C₂³×C₄₁	semidirect
916. C₂²⋊Q₈	C₂³×C₄₁	semidirect
926. #121	C₂³×C₄₁	semidirect
927. #121	C₂³×C₄₁	semidirect
928. #121	C₂³×C₄₁	semidirect
929. #121	C₂³×C₄₁	semidirect
930. #121	C₂³×C₄₁	semidirect
931. #121	C₂³×C₄₁	semidirect
932. #121	C₂³×C₄₁	semidirect
933. #121	C₂³×C₄₁	semidirect
938. C₄×Q₈	C₂³×C₄₁	semidirect
939. C₄×Q₈	C₂³×C₄₁	semidirect
940. C₄×Q₈	C₂³×C₄₁	semidirect
941. C₄×Q₈	C₂³×C₄₁	semidirect
946. C₄×D₄	C₂³×C₄₁	semidirect
947. C₄×D₄	C₂³×C₄₁	semidirect
948. C₄×D₄	C₂³×C₄₁	semidirect
949. C₄×D₄	C₂³×C₄₁	semidirect
950. C₄×D₄	C₂³×C₄₁	semidirect
951. C₄×D₄	C₂³×C₄₁	semidirect
952. C₄×D₄	C₂³×C₄₁	semidirect
953. C₄×D₄	C₂³×C₄₁	semidirect
954. C₄×D₄	C₂³×C₄₁	semidirect
956. #117	C₂³×C₄₁	semidirect
957. #117	C₂³×C₄₁	semidirect
958. #117	C₂³×C₄₁	semidirect
983. C₂×C₄⋊C₄	C₂³×C₄₁	semidirect
1024. C₂×C₄²	C₂³×C₄₁	semidirect
1343. C₂	C₄₁×#3562	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄₁×#3562	2
C₂×C₄₁×#562	2
C₂×C₄₁×#560	2
C₂×C₄₁×#559	2
C₂×C₄₁×#556	2
C₂×C₄₁×#553	2
C₂×C₄₁×#551	2
C₂×C₄₁×#550	2
C₂×C₄₁×#548	2
C₂×C₄₁×#547	2
C₂×C₄₁×#546	2
C₂×C₄₁×#541	2
C₂×C₄₁×#540	2
C₂×C₄₁×#539	2
C₂×C₄₁×#538	2
C₂×C₄₁×#536	2
C₂×C₄₁×#535	2
C₂×C₄₁×#532	2
C₂×C₄₁×#529	2
C₂×#3562	41

Subgroups — C2×C41×#3562 #23838941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#3562 #23838941