Subgroups — C₂×C₄₁×#3536 #23838924

Order 10496.

7962 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3536	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₄₁×#562	C₂	1	4	yes	maximal, complemented
3	C₂×C₄₁×#554	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₁×#548	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₁×#547	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₁×#546	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₁×#546	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₁×#543	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₁×#542	C₂	1	2	yes	maximal, complemented
10	C₂×C₄₁×#539	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₁×#538	C₂	1	2	yes	maximal, complemented
12	C₂×C₄₁×#537	C₂	1	2	yes	maximal, complemented
13	C₂×C₄₁×#537	C₂	1	2	yes	maximal, complemented
14	C₂×C₄₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₂²⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#121×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic, complemented
18	C₂²×#41×C₄₁	C₂²	1	4	yes	complemented
19	C₂²×#41×C₄₁	C₂²	1	2	yes	complemented
20	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
22	C₂³×D₄×C₄₁	C₂²	1	2	yes	—
23	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
24	C₄₁×#562	C₂²	1	64	yes	complemented
25	C₄₁×#554	C₂²	1	32	yes	complemented
26	C₄₁×#548	C₂²	1	32	yes	complemented
27	C₄₁×#547	C₂²	1	32	yes	complemented
28	C₄₁×#546	C₂²	1	64	yes	complemented
29	C₄₁×#546	C₂²	1	32	yes	complemented
30	C₄₁×#543	C₂²	1	32	yes	complemented
31	C₄₁×#542	C₂²	1	32	yes	complemented
32	C₄₁×#539	C₂²	1	32	yes	complemented
33	C₄₁×#538	C₂²	1	32	yes	complemented
34	C₄₁×#537	C₂²	1	32	yes	complemented
35	C₄₁×#537	C₂²	1	32	yes	complemented
36	C₂×C₄⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
37	C₂×#126×C₄₁	C₂²	1	4	yes	complemented
38	C₂×#125×C₄₁	C₂²	1	4	yes	complemented
39	C₂×#124×C₄₁	C₂²	1	4	yes	complemented
40	C₂×#124×C₄₁	C₂²	1	2	yes	complemented
41	C₂×#124×C₄₁	C₂²	1	4	yes	complemented
42	C₄₁×#525	C₂²	1	16	yes	complemented
43	C₂×#123×C₄₁	C₂²	1	2	yes	complemented
44	C₂×#123×C₄₁	C₂²	1	4	yes	complemented
45	C₂×#123×C₄₁	C₂²	1	4	yes	complemented
46	C₂×#123×C₄₁	C₂²	1	4	yes	complemented
47	C₂×#123×C₄₁	C₂²	1	4	yes	complemented
48	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
49	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
50	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	4	yes	—
52	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
53	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
54	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	4	yes	complemented
56	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	4	yes	complemented
57	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
58	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	4	yes	complemented
59	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	4	yes	complemented
60	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	4	yes	complemented
61	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	16	yes	complemented
62	C₂×#121×C₄₁	C₂²	1	2	yes	—
63	C₂×#121×C₄₁	C₂²	1	2	yes	—
64	C₂×#121×C₄₁	C₂²	1	2	yes	—
65	C₂×#121×C₄₁	C₂²	1	2	yes	—
66	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
67	C₂×#121×C₄₁	C₂²	1	16	yes	complemented
68	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic, complemented
69	C₂×#121×C₄₁	C₂²	1	4	yes	complemented
70	C₂×#121×C₄₁	C₂²	1	2	yes	complemented
71	C₂×#121×C₄₁	C₂²	1	4	yes	complemented
72	C₂×#121×C₄₁	C₂²	1	4	yes	complemented
73	C₂×#121×C₄₁	C₂²	1	4	yes	complemented
74	C₂×#121×C₄₁	C₂²	1	4	yes	complemented
75	C₂×#120×C₄₁	C₂²	1	2	yes	—
76	C₂×#120×C₄₁	C₂²	1	4	yes	—
77	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	complemented
78	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
79	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
80	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
81	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	complemented
82	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
83	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic, complemented
84	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
85	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	complemented
86	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
87	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	complemented
88	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
89	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
90	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
91	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
92	C₂⁵×C₄₁	C₂³	1	2	yes	—
93	C₂×#41×C₄₁	—	4	4	no	—
94	C₂×#41×C₄₁	—	4	16	no	—
95	C₂×#41×C₄₁	—	4	8	no	—
96	C₂×#41×C₄₁	C₂³	1	8	yes	complemented
97	C₂×#41×C₄₁	C₂³	1	32	yes	complemented
98	C₂×#41×C₄₁	C₂³	1	16	yes	complemented
99	C₂²×Q₈×C₄₁	—	4	4	no	—
100	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
101	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
103	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
104	C₂²×Q₈×C₄₁	C₂³	1	8	yes	complemented
105	C₂²×D₄×C₄₁	—	4	4	no	—
106	C₂²×D₄×C₄₁	—	4	8	no	—
107	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
108	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
109	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
110	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
111	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
112	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
113	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
114	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
115	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
116	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
118	C₂²×D₄×C₄₁	C₂³	1	16	yes	—
119	C₂³×C₄×C₄₁	—	4	4	no	—
120	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
121	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
123	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
127	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
128	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
129	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
130	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
132	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₄₁	C₂³	1	8	yes	—
134	C₄⋊Q₈×C₄₁	C₂³	1	16	yes	complemented
135	#126×C₄₁	C₂³	1	32	yes	complemented
136	#125×C₄₁	C₂³	1	32	yes	complemented
137	#124×C₄₁	C₂³	1	32	yes	complemented
138	#124×C₄₁	C₂³	1	16	yes	complemented
139	#124×C₄₁	C₂³	1	32	yes	complemented
140	#123×C₄₁	C₂³	1	16	yes	complemented
141	#123×C₄₁	C₂³	1	32	yes	complemented
142	#123×C₄₁	C₂³	1	32	yes	complemented
143	#123×C₄₁	C₂³	1	32	yes	complemented
144	#123×C₄₁	C₂³	1	32	yes	complemented
145	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	—
146	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	—
147	C₂²⋊Q₈×C₄₁	C₂³	1	8	yes	—
148	C₂²⋊Q₈×C₄₁	C₂³	1	32	yes	—
149	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	complemented
150	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	complemented
151	C₂²⋊Q₈×C₄₁	C₂³	1	8	yes	complemented
152	C₂²⋊Q₈×C₄₁	C₂³	1	32	yes	complemented
153	C₂²⋊Q₈×C₄₁	C₂³	1	32	yes	complemented
154	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	complemented
155	C₂²⋊Q₈×C₄₁	C₂³	1	32	yes	complemented
156	C₂²⋊Q₈×C₄₁	C₂³	1	32	yes	complemented
157	C₂²⋊Q₈×C₄₁	C₂³	1	32	yes	complemented
158	#121×C₄₁	C₂³	1	16	yes	—
159	#121×C₄₁	C₂³	1	16	yes	—
160	#121×C₄₁	C₂³	1	16	yes	—
161	#121×C₄₁	C₂³	1	16	yes	—
162	#121×C₄₁	C₂³	1	8	yes	—
163	#121×C₄₁	C₂³	1	8	yes	complemented
164	#121×C₄₁	C₂³	1	32	yes	complemented
165	#121×C₄₁	C₂³	1	16	yes	complemented
166	#121×C₄₁	C₂³	1	32	yes	complemented
167	#121×C₄₁	C₂³	1	32	yes	complemented
168	#121×C₄₁	C₂³	1	32	yes	complemented
169	#121×C₄₁	C₂³	1	32	yes	complemented
170	#120×C₄₁	C₂³	1	16	yes	—
171	#120×C₄₁	C₂³	1	32	yes	—
172	C₄×Q₈×C₄₁	C₂³	1	16	yes	complemented
173	C₄×D₄×C₄₁	C₂³	1	16	yes	—
174	C₄×D₄×C₄₁	C₂³	1	32	yes	—
175	C₄×D₄×C₄₁	C₂³	1	16	yes	complemented
176	C₄×D₄×C₄₁	C₂³	1	32	yes	complemented
177	C₄×D₄×C₄₁	C₂³	1	16	yes	complemented
178	#117×C₄₁	C₂³	1	8	yes	complemented
179	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
182	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
184	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
185	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
186	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
191	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
192	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
194	C₂×C₄⋊C₄×C₄₁	C₂³	1	16	yes	complemented
195	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	complemented
196	C₂×C₄⋊C₄×C₄₁	C₂³	1	16	yes	complemented
197	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
198	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
200	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
201	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
202	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
203	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
204	C₂×C₂²⋊C₄×C₄₁	C₂³	1	16	yes	—
205	C₂×C₂²⋊C₄×C₄₁	C₂³	1	16	yes	—
206	C₂×C₂²⋊C₄×C₄₁	C₂³	1	32	yes	—
207	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
210	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
212	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
213	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
214	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
215	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
216	C₂⁴×C₄₁	—	2	4	no	—
217	C₂⁴×C₄₁	—	2	4	no	—
218	C₂⁴×C₄₁	—	2	8	no	—
219	C₂⁴×C₄₁	—	4	2	no	—
220	C₂⁴×C₄₁	—	4	4	no	—
221	C₂⁴×C₄₁	—	4	4	no	—
222	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
223	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
224	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
225	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
226	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
227	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
228	C₂⁴×C₄₁	C₂⁴	1	8	yes	—
229	#41×C₄₁	—	4	16	no	—
230	#41×C₄₁	—	4	64	no	—
231	#41×C₄₁	—	4	32	no	—
232	C₂×Q₈×C₄₁	—	2	8	no	—
233	C₂×Q₈×C₄₁	—	4	4	no	—
234	C₂×Q₈×C₄₁	—	4	2	no	—
235	C₂×Q₈×C₄₁	—	4	8	no	—
236	C₂×Q₈×C₄₁	—	4	16	no	—
237	C₂×Q₈×C₄₁	C₂⁴	1	8	yes	—
238	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
239	C₂×Q₈×C₄₁	C₂⁴	1	8	yes	—
240	C₂×Q₈×C₄₁	C₂⁴	1	16	yes	—
241	C₂×D₄×C₄₁	—	2	16	no	—
242	C₂×D₄×C₄₁	—	2	8	no	—
243	C₂×D₄×C₄₁	—	2	8	no	—
244	C₂×D₄×C₄₁	—	2	8	no	—
245	C₂×D₄×C₄₁	—	4	16	no	—
246	C₂×D₄×C₄₁	—	4	4	no	—
247	C₂×D₄×C₄₁	—	4	8	no	—
248	C₂×D₄×C₄₁	—	4	4	no	—
249	C₂×D₄×C₄₁	—	4	2	no	—
250	C₂×D₄×C₄₁	—	4	8	no	—
251	C₂×D₄×C₄₁	—	4	8	no	—
252	C₂×D₄×C₄₁	—	4	32	no	—
253	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
254	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
255	C₂×D₄×C₄₁	C₂⁴	1	16	yes	—
256	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
257	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
258	C₂×D₄×C₄₁	C₂⁴	1	16	yes	—
259	C₂×D₄×C₄₁	C₂⁴	1	16	yes	—
260	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
261	C₂×D₄×C₄₁	C₂⁴	1	16	yes	—
262	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₄₁	—	2	8	no	—
264	C₂²×C₄×C₄₁	—	2	4	no	—
265	C₂²×C₄×C₄₁	—	2	4	no	—
266	C₂²×C₄×C₄₁	—	2	4	no	—
267	C₂²×C₄×C₄₁	—	2	8	no	—
268	C₂²×C₄×C₄₁	—	4	16	no	—
269	C₂²×C₄×C₄₁	—	4	2	no	—
270	C₂²×C₄×C₄₁	—	4	2	no	—
271	C₂²×C₄×C₄₁	—	4	2	no	—
272	C₂²×C₄×C₄₁	—	4	4	no	—
273	C₂²×C₄×C₄₁	—	4	4	no	—
274	C₂²×C₄×C₄₁	—	4	8	no	—
275	C₂²×C₄×C₄₁	—	4	8	no	—
276	C₂²×C₄×C₄₁	—	4	8	no	—
277	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
278	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
279	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
280	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
281	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
282	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
285	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
286	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
292	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
293	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
294	C₂²×C₄×C₄₁	C₂⁴	1	16	yes	—
295	C₂²×C₄×C₄₁	C₂⁴	1	16	yes	—
296	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
297	C₂²×C₄×C₄₁	C₂⁴	1	16	yes	—
298	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
299	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
300	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
301	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
302	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
303	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
304	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
305	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
306	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
307	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
308	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
309	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
310	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
311	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
312	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
313	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
314	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
315	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
316	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
317	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
318	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
319	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
320	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
321	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
322	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
323	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
324	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
325	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
326	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
327	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
328	C₄²×C₄₁	C₂⁴	1	8	yes	—
329	C₄²×C₄₁	C₂⁴	1	16	yes	—
330	C₂³×C₄₁	—	2	2	no	—
331	C₂³×C₄₁	—	2	2	no	—
332	C₂³×C₄₁	—	2	2	no	—
333	C₂³×C₄₁	—	2	2	no	—
334	C₂³×C₄₁	—	2	2	no	—
335	C₂³×C₄₁	—	2	4	no	—
336	C₂³×C₄₁	—	2	4	no	—
337	C₂³×C₄₁	—	2	8	no	—
338	C₂³×C₄₁	—	2	8	no	—
339	C₂³×C₄₁	—	2	8	no	—
340	C₂³×C₄₁	—	2	2	no	—
341	C₂³×C₄₁	—	2	4	no	—
342	C₂³×C₄₁	—	2	8	no	—
343	C₂³×C₄₁	—	2	2	no	—
344	C₂³×C₄₁	—	2	8	no	—
345	C₂³×C₄₁	—	2	16	no	—
346	C₂³×C₄₁	—	4	4	no	—
347	C₂³×C₄₁	—	4	8	no	—
348	C₂³×C₄₁	—	4	8	no	—
349	C₂³×C₄₁	—	4	16	no	—
350	C₂³×C₄₁	—	8	16	no	—
351	C₂³×C₄₁	H(5,𝔽₂)	1	4	yes	—
352	C₂³×C₄₁	2₋¹⁺⁴	1	4	yes	—
353	C₂³×C₄₁	C₂⁵	1	2	yes	—
354	C₂³×C₄₁	C₂⁵	1	8	yes	—
355	C₂³×C₄₁	C₂⁵	1	4	yes	—
356	C₂³×C₄₁	C₂⁵	1	2	yes	—
357	C₂³×C₄₁	C₂⁵	1	2	yes	—
358	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
359	Q₈×C₄₁	—	2	16	no	—
360	Q₈×C₄₁	—	4	8	no	—
361	Q₈×C₄₁	—	4	4	no	—
362	Q₈×C₄₁	—	4	16	no	—
363	D₄×C₄₁	—	2	32	no	—
364	D₄×C₄₁	—	2	16	no	—
365	D₄×C₄₁	—	2	16	no	—
366	D₄×C₄₁	—	2	16	no	—
367	D₄×C₄₁	—	4	8	no	—
368	D₄×C₄₁	—	4	16	no	—
369	D₄×C₄₁	—	4	8	no	—
370	D₄×C₄₁	—	4	4	no	—
371	D₄×C₄₁	—	4	16	no	—
372	D₄×C₄₁	—	4	16	no	—
373	C₂×C₄×C₄₁	—	2	2	no	—
374	C₂×C₄×C₄₁	—	2	8	no	—
375	C₂×C₄×C₄₁	—	2	2	no	—
376	C₂×C₄×C₄₁	—	2	4	no	—
377	C₂×C₄×C₄₁	—	2	2	no	—
378	C₂×C₄×C₄₁	—	2	16	no	—
379	C₂×C₄×C₄₁	—	2	8	no	—
380	C₂×C₄×C₄₁	—	2	4	no	—
381	C₂×C₄×C₄₁	—	2	8	no	—
382	C₂×C₄×C₄₁	—	2	4	no	—
383	C₂×C₄×C₄₁	—	2	8	no	—
384	C₂×C₄×C₄₁	—	2	8	no	—
385	C₂×C₄×C₄₁	—	2	8	no	—
386	C₂×C₄×C₄₁	—	2	16	no	—
387	C₂×C₄×C₄₁	—	4	4	no	—
388	C₂×C₄×C₄₁	—	4	4	no	—
389	C₂×C₄×C₄₁	—	4	4	no	—
390	C₂×C₄×C₄₁	—	4	8	no	—
391	C₂×C₄×C₄₁	—	4	8	no	—
392	C₂×C₄×C₄₁	—	4	16	no	—
393	C₂×C₄×C₄₁	—	4	16	no	—
394	C₂×C₄×C₄₁	—	4	16	no	—
395	C₂×C₄×C₄₁	H(5,𝔽₂)	1	4	yes	—
396	C₂×C₄×C₄₁	C₂⁵	1	4	yes	—
397	C₂×C₄×C₄₁	C₂⁵	1	4	yes	—
398	C₂×C₄×C₄₁	C₂⁵	1	8	yes	—
399	C₂×C₄×C₄₁	C₂⁵	1	8	yes	—
400	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
401	C₂×C₄×C₄₁	C₂⁵	1	4	yes	—
402	C₂×C₄×C₄₁	C₂⁵	1	8	yes	—
403	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
404	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
405	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
406	C₂×#3536	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
407	C₂²×C₄₁	—	2	2	no	—
408	C₂²×C₄₁	—	2	2	no	—
409	C₂²×C₄₁	—	2	2	no	—
410	C₂²×C₄₁	—	2	2	no	—
411	C₂²×C₄₁	—	2	8	no	—
412	C₂²×C₄₁	—	2	8	no	—
413	C₂²×C₄₁	—	2	2	no	—
414	C₂²×C₄₁	—	2	4	no	—
415	C₂²×C₄₁	—	2	4	no	—
416	C₂²×C₄₁	—	2	8	no	—
417	C₂²×C₄₁	—	2	8	no	—
418	C₂²×C₄₁	—	2	2	no	—
419	C₂²×C₄₁	—	2	4	no	—
420	C₂²×C₄₁	—	2	2	no	—
421	C₂²×C₄₁	—	2	8	no	—
422	C₂²×C₄₁	—	4	16	no	—
423	C₂²×C₄₁	—	4	8	no	—
424	C₂²×C₄₁	—	4	4	no	—
425	C₂²×C₄₁	—	4	16	no	—
426	C₂²×C₄₁	—	8	16	no	—
427	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	4	yes	—
428	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
429	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
430	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	4	yes	—
431	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	2	yes	—
432	C₂²×C₄₁	C₂⁶	1	1	yes	characteristic
433	C₄×C₄₁	—	2	2	no	—
434	C₄×C₄₁	—	2	8	no	—
435	C₄×C₄₁	—	2	2	no	—
436	C₄×C₄₁	—	2	4	no	—
437	C₄×C₄₁	—	2	2	no	—
438	C₄×C₄₁	—	2	8	no	—
439	C₄×C₄₁	—	2	4	no	—
440	C₄×C₄₁	—	2	8	no	—
441	C₄×C₄₁	—	2	4	no	—
442	C₄×C₄₁	C₂×H(5,𝔽₂)	1	4	yes	—
443	#3536	C₂×C₄₁	1	32	yes	direct product factor
444	C₂×#562	C₂×C₄₁	1	4	yes	complemented
445	C₂×#554	C₂×C₄₁	1	2	yes	complemented
446	C₂×#548	C₂×C₄₁	1	2	yes	complemented
447	C₂×#547	C₂×C₄₁	1	2	yes	complemented
448	C₂×#546	C₂×C₄₁	1	4	yes	complemented
449	C₂×#546	C₂×C₄₁	1	2	yes	complemented
450	C₂×#543	C₂×C₄₁	1	2	yes	complemented
451	C₂×#542	C₂×C₄₁	1	2	yes	complemented
452	C₂×#539	C₂×C₄₁	1	2	yes	complemented
453	C₂×#538	C₂×C₄₁	1	2	yes	complemented
454	C₂×#537	C₂×C₄₁	1	2	yes	complemented
455	C₂×#537	C₂×C₄₁	1	2	yes	complemented
456	C₂×#525	C₂×C₄₁	1	1	yes	characteristic, complemented
457	C₂²×C₂²⋊Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
458	C₂²×#121	C₂×C₄₁	1	1	yes	characteristic, complemented
459	C₂×C₄₁	—	2	4	no	—
460	C₂×C₄₁	—	2	4	no	—
461	C₂×C₄₁	—	4	4	no	—
462	C₂×C₄₁	—	4	2	no	—
463	C₂×C₄₁	—	4	8	no	—
464	C₂×C₄₁	#3536	1	4	yes	direct product factor
465	C₂×C₄₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
466	C₂×C₄₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂×C₄₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
468	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic, complemented
469	C₂²×#41	C₂²×C₄₁	1	4	yes	complemented
470	C₂²×#41	C₂²×C₄₁	1	2	yes	complemented
471	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
472	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
473	C₂³×D₄	C₂²×C₄₁	1	2	yes	—
474	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
475	#562	C₂²×C₄₁	1	64	yes	complemented
476	#554	C₂²×C₄₁	1	32	yes	complemented
477	#548	C₂²×C₄₁	1	32	yes	complemented
478	#547	C₂²×C₄₁	1	32	yes	complemented
479	#546	C₂²×C₄₁	1	64	yes	complemented
480	#546	C₂²×C₄₁	1	32	yes	complemented
481	#543	C₂²×C₄₁	1	32	yes	complemented
482	#542	C₂²×C₄₁	1	32	yes	complemented
483	#539	C₂²×C₄₁	1	32	yes	complemented
484	#538	C₂²×C₄₁	1	32	yes	complemented
485	#537	C₂²×C₄₁	1	32	yes	complemented
486	#537	C₂²×C₄₁	1	32	yes	complemented
487	C₂×C₄⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
488	C₂×#126	C₂²×C₄₁	1	4	yes	complemented
489	C₂×#125	C₂²×C₄₁	1	4	yes	complemented
490	C₂×#124	C₂²×C₄₁	1	4	yes	complemented
491	C₂×#124	C₂²×C₄₁	1	2	yes	complemented
492	C₂×#124	C₂²×C₄₁	1	4	yes	complemented
493	#525	C₂²×C₄₁	1	16	yes	complemented
494	C₂×#123	C₂²×C₄₁	1	2	yes	complemented
495	C₂×#123	C₂²×C₄₁	1	4	yes	complemented
496	C₂×#123	C₂²×C₄₁	1	4	yes	complemented
497	C₂×#123	C₂²×C₄₁	1	4	yes	complemented
498	C₂×#123	C₂²×C₄₁	1	4	yes	complemented
499	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
500	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
501	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
502	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	4	yes	—
503	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
504	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
505	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
506	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	4	yes	complemented
507	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	4	yes	complemented
508	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
509	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	4	yes	complemented
510	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	4	yes	complemented
511	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	4	yes	complemented
512	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	16	yes	complemented
513	C₂×#121	C₂²×C₄₁	1	2	yes	—
514	C₂×#121	C₂²×C₄₁	1	2	yes	—
515	C₂×#121	C₂²×C₄₁	1	2	yes	—
516	C₂×#121	C₂²×C₄₁	1	2	yes	—
517	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
518	C₂×#121	C₂²×C₄₁	1	16	yes	complemented
519	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic, complemented
520	C₂×#121	C₂²×C₄₁	1	4	yes	complemented
521	C₂×#121	C₂²×C₄₁	1	2	yes	complemented
522	C₂×#121	C₂²×C₄₁	1	4	yes	complemented
523	C₂×#121	C₂²×C₄₁	1	4	yes	complemented
524	C₂×#121	C₂²×C₄₁	1	4	yes	complemented
525	C₂×#121	C₂²×C₄₁	1	4	yes	complemented
526	C₂×#120	C₂²×C₄₁	1	2	yes	—
527	C₂×#120	C₂²×C₄₁	1	4	yes	—
528	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	complemented
529	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
530	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
531	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
532	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	complemented
533	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
534	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic, complemented
535	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
536	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	complemented
537	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
538	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	complemented
539	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
540	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
541	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
542	C₄₁	C₂×#3536	1	1	yes	characteristic, direct product factor, Sylow
543	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
544	C₂⁵	C₂³×C₄₁	1	2	yes	—
545	C₂×#41	—	4	4	no	—
546	C₂×#41	—	4	16	no	—
547	C₂×#41	—	4	8	no	—
548	C₂×#41	C₂³×C₄₁	1	8	yes	complemented
549	C₂×#41	C₂³×C₄₁	1	32	yes	complemented
550	C₂×#41	C₂³×C₄₁	1	16	yes	complemented
551	C₂²×Q₈	—	4	4	no	—
552	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
553	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
554	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
555	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
556	C₂²×Q₈	C₂³×C₄₁	1	8	yes	complemented
557	C₂²×D₄	—	4	4	no	—
558	C₂²×D₄	—	4	8	no	—
559	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
560	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
561	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
562	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
563	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
564	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
565	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
566	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
567	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
568	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
570	C₂²×D₄	C₂³×C₄₁	1	16	yes	—
571	C₂³×C₄	—	4	4	no	—
572	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
573	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
575	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
579	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
580	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
581	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
582	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
583	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
584	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
585	C₂³×C₄	C₂³×C₄₁	1	8	yes	—
586	C₄⋊Q₈	C₂³×C₄₁	1	16	yes	complemented
587	#126	C₂³×C₄₁	1	32	yes	complemented
588	#125	C₂³×C₄₁	1	32	yes	complemented
589	#124	C₂³×C₄₁	1	32	yes	complemented
590	#124	C₂³×C₄₁	1	16	yes	complemented
591	#124	C₂³×C₄₁	1	32	yes	complemented
592	#123	C₂³×C₄₁	1	16	yes	complemented
593	#123	C₂³×C₄₁	1	32	yes	complemented
594	#123	C₂³×C₄₁	1	32	yes	complemented
595	#123	C₂³×C₄₁	1	32	yes	complemented
596	#123	C₂³×C₄₁	1	32	yes	complemented
597	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	—
598	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	—
599	C₂²⋊Q₈	C₂³×C₄₁	1	8	yes	—
600	C₂²⋊Q₈	C₂³×C₄₁	1	32	yes	—
601	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	complemented
602	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	complemented
603	C₂²⋊Q₈	C₂³×C₄₁	1	8	yes	complemented
604	C₂²⋊Q₈	C₂³×C₄₁	1	32	yes	complemented
605	C₂²⋊Q₈	C₂³×C₄₁	1	32	yes	complemented
606	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	complemented
607	C₂²⋊Q₈	C₂³×C₄₁	1	32	yes	complemented
608	C₂²⋊Q₈	C₂³×C₄₁	1	32	yes	complemented
609	C₂²⋊Q₈	C₂³×C₄₁	1	32	yes	complemented
610	#121	C₂³×C₄₁	1	16	yes	—
611	#121	C₂³×C₄₁	1	16	yes	—
612	#121	C₂³×C₄₁	1	16	yes	—
613	#121	C₂³×C₄₁	1	16	yes	—
614	#121	C₂³×C₄₁	1	8	yes	—
615	#121	C₂³×C₄₁	1	8	yes	complemented
616	#121	C₂³×C₄₁	1	32	yes	complemented
617	#121	C₂³×C₄₁	1	16	yes	complemented
618	#121	C₂³×C₄₁	1	32	yes	complemented
619	#121	C₂³×C₄₁	1	32	yes	complemented
620	#121	C₂³×C₄₁	1	32	yes	complemented
621	#121	C₂³×C₄₁	1	32	yes	complemented
622	#120	C₂³×C₄₁	1	16	yes	—
623	#120	C₂³×C₄₁	1	32	yes	—
624	C₄×Q₈	C₂³×C₄₁	1	16	yes	complemented
625	C₄×D₄	C₂³×C₄₁	1	16	yes	—
626	C₄×D₄	C₂³×C₄₁	1	32	yes	—
627	C₄×D₄	C₂³×C₄₁	1	16	yes	complemented
628	C₄×D₄	C₂³×C₄₁	1	32	yes	complemented
629	C₄×D₄	C₂³×C₄₁	1	16	yes	complemented
630	#117	C₂³×C₄₁	1	8	yes	complemented
631	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
634	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
636	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
637	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
638	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
643	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
644	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
646	C₂×C₄⋊C₄	C₂³×C₄₁	1	16	yes	complemented
647	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	complemented
648	C₂×C₄⋊C₄	C₂³×C₄₁	1	16	yes	complemented
649	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₄₁	1	16	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₄₁	1	16	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₄₁	1	32	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
666	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
667	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
668	C₂⁴	—	2	4	no	—
669	C₂⁴	—	2	4	no	—
670	C₂⁴	—	2	8	no	—
671	C₂⁴	—	4	2	no	—
672	C₂⁴	—	4	4	no	—
673	C₂⁴	—	4	4	no	—
674	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
675	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
676	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
677	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
678	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
679	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
680	C₂⁴	C₂⁴×C₄₁	1	8	yes	—
681	#41	—	4	16	no	—
682	#41	—	4	64	no	—
683	#41	—	4	32	no	—
684	C₂×Q₈	—	2	8	no	—
685	C₂×Q₈	—	4	4	no	—
686	C₂×Q₈	—	4	2	no	—
687	C₂×Q₈	—	4	8	no	—
688	C₂×Q₈	—	4	16	no	—
689	C₂×Q₈	C₂⁴×C₄₁	1	8	yes	—
690	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
691	C₂×Q₈	C₂⁴×C₄₁	1	8	yes	—
692	C₂×Q₈	C₂⁴×C₄₁	1	16	yes	—
693	C₂×D₄	—	2	16	no	—
694	C₂×D₄	—	2	8	no	—
695	C₂×D₄	—	2	8	no	—
696	C₂×D₄	—	2	8	no	—
697	C₂×D₄	—	4	16	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	—	4	8	no	—
700	C₂×D₄	—	4	4	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	8	no	—
703	C₂×D₄	—	4	8	no	—
704	C₂×D₄	—	4	32	no	—
705	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
706	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
707	C₂×D₄	C₂⁴×C₄₁	1	16	yes	—
708	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
709	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
710	C₂×D₄	C₂⁴×C₄₁	1	16	yes	—
711	C₂×D₄	C₂⁴×C₄₁	1	16	yes	—
712	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
713	C₂×D₄	C₂⁴×C₄₁	1	16	yes	—
714	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
715	C₂²×C₄	—	2	8	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	8	no	—
720	C₂²×C₄	—	4	16	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	4	no	—
725	C₂²×C₄	—	4	4	no	—
726	C₂²×C₄	—	4	8	no	—
727	C₂²×C₄	—	4	8	no	—
728	C₂²×C₄	—	4	8	no	—
729	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
732	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
733	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
736	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
739	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
740	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
741	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
742	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
743	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
744	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
745	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
746	C₂²×C₄	C₂⁴×C₄₁	1	16	yes	—
747	C₂²×C₄	C₂⁴×C₄₁	1	16	yes	—
748	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
749	C₂²×C₄	C₂⁴×C₄₁	1	16	yes	—
750	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
751	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
752	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
753	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
754	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
755	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
756	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
757	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
758	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
759	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
760	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
761	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
762	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
763	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
764	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
765	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
766	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
767	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
768	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
769	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
770	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
771	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
772	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
773	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
774	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
775	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
776	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
777	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
778	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
779	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
780	C₄²	C₂⁴×C₄₁	1	8	yes	—
781	C₄²	C₂⁴×C₄₁	1	16	yes	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	4	no	—
788	C₂³	—	2	4	no	—
789	C₂³	—	2	8	no	—
790	C₂³	—	2	8	no	—
791	C₂³	—	2	8	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	4	no	—
794	C₂³	—	2	8	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	8	no	—
797	C₂³	—	2	16	no	—
798	C₂³	—	4	4	no	—
799	C₂³	—	4	8	no	—
800	C₂³	—	4	8	no	—
801	C₂³	—	4	16	no	—
802	C₂³	—	8	16	no	—
803	C₂³	H(5,𝔽₂)×C₄₁	1	4	yes	—
804	C₂³	2₋¹⁺⁴×C₄₁	1	4	yes	—
805	C₂³	C₂⁵×C₄₁	1	2	yes	—
806	C₂³	C₂⁵×C₄₁	1	8	yes	—
807	C₂³	C₂⁵×C₄₁	1	4	yes	—
808	C₂³	C₂⁵×C₄₁	1	2	yes	—
809	C₂³	C₂⁵×C₄₁	1	2	yes	—
810	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
811	Q₈	—	2	16	no	—
812	Q₈	—	4	8	no	—
813	Q₈	—	4	4	no	—
814	Q₈	—	4	16	no	—
815	D₄	—	2	32	no	—
816	D₄	—	2	16	no	—
817	D₄	—	2	16	no	—
818	D₄	—	2	16	no	—
819	D₄	—	4	8	no	—
820	D₄	—	4	16	no	—
821	D₄	—	4	8	no	—
822	D₄	—	4	4	no	—
823	D₄	—	4	16	no	—
824	D₄	—	4	16	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	8	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	4	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	16	no	—
831	C₂×C₄	—	2	8	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	8	no	—
834	C₂×C₄	—	2	4	no	—
835	C₂×C₄	—	2	8	no	—
836	C₂×C₄	—	2	8	no	—
837	C₂×C₄	—	2	8	no	—
838	C₂×C₄	—	2	16	no	—
839	C₂×C₄	—	4	4	no	—
840	C₂×C₄	—	4	4	no	—
841	C₂×C₄	—	4	4	no	—
842	C₂×C₄	—	4	8	no	—
843	C₂×C₄	—	4	8	no	—
844	C₂×C₄	—	4	16	no	—
845	C₂×C₄	—	4	16	no	—
846	C₂×C₄	—	4	16	no	—
847	C₂×C₄	H(5,𝔽₂)×C₄₁	1	4	yes	—
848	C₂×C₄	C₂⁵×C₄₁	1	4	yes	—
849	C₂×C₄	C₂⁵×C₄₁	1	4	yes	—
850	C₂×C₄	C₂⁵×C₄₁	1	8	yes	—
851	C₂×C₄	C₂⁵×C₄₁	1	8	yes	—
852	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
853	C₂×C₄	C₂⁵×C₄₁	1	4	yes	—
854	C₂×C₄	C₂⁵×C₄₁	1	8	yes	—
855	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
856	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
857	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
858	C₂²	—	2	2	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	8	no	—
863	C₂²	—	2	8	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	4	no	—
866	C₂²	—	2	4	no	—
867	C₂²	—	2	8	no	—
868	C₂²	—	2	8	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	8	no	—
873	C₂²	—	4	16	no	—
874	C₂²	—	4	4	no	—
875	C₂²	—	4	16	no	—
876	C₂²	—	4	8	no	—
877	C₂²	—	8	16	no	—
878	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	4	yes	—
879	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
880	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
881	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	4	yes	—
882	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	2	yes	—
883	C₂²	C₂⁶×C₄₁	1	1	yes	characteristic
884	C₄	—	2	2	no	—
885	C₄	—	2	8	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	4	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	8	no	—
890	C₄	—	2	4	no	—
891	C₄	—	2	8	no	—
892	C₄	—	2	4	no	—
893	C₄	C₂×H(5,𝔽₂)×C₄₁	1	4	yes	—
894	C₂	—	2	4	no	—
895	C₂	—	2	4	no	—
896	C₂	—	4	2	no	—
897	C₂	—	4	8	no	—
898	C₂	—	4	4	no	—
899	C₂	C₄₁×#3536	1	4	yes	direct product factor
900	C₂	C₂²×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
901	C₂	C₂²×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
902	C₂	C₂²×2₋¹⁺⁴×C₄₁	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×#3536	C₂	direct (N × H)
2. C₂×C₄₁×#562	C₂	semidirect
3. C₂×C₄₁×#554	C₂	semidirect
4. C₂×C₄₁×#548	C₂	semidirect
5. C₂×C₄₁×#547	C₂	semidirect
6. C₂×C₄₁×#546	C₂	semidirect
7. C₂×C₄₁×#546	C₂	semidirect
8. C₂×C₄₁×#543	C₂	semidirect
9. C₂×C₄₁×#542	C₂	semidirect
10. C₂×C₄₁×#539	C₂	semidirect
11. C₂×C₄₁×#538	C₂	semidirect
12. C₂×C₄₁×#537	C₂	semidirect
13. C₂×C₄₁×#537	C₂	semidirect
14. C₂×C₄₁×#525	C₂	semidirect
15. C₂²×C₂²⋊Q₈×C₄₁	C₂	semidirect
16. C₂²×#121×C₄₁	C₂	semidirect
17. C₂²×#41×C₄₁	C₂²	semidirect
18. C₂²×#41×C₄₁	C₂²	semidirect
19. C₂²×#41×C₄₁	C₂²	semidirect
20. C₂³×Q₈×C₄₁	C₂²	semidirect
24. C₄₁×#562	C₂²	semidirect
25. C₄₁×#554	C₂²	semidirect
26. C₄₁×#548	C₂²	semidirect
27. C₄₁×#547	C₂²	semidirect
28. C₄₁×#546	C₂²	semidirect
29. C₄₁×#546	C₂²	semidirect
30. C₄₁×#543	C₂²	semidirect
31. C₄₁×#542	C₂²	semidirect
32. C₄₁×#539	C₂²	semidirect
33. C₄₁×#538	C₂²	semidirect
34. C₄₁×#537	C₂²	semidirect
35. C₄₁×#537	C₂²	semidirect
36. C₂×C₄⋊Q₈×C₄₁	C₂²	semidirect
37. C₂×#126×C₄₁	C₂²	semidirect
38. C₂×#125×C₄₁	C₂²	semidirect
39. C₂×#124×C₄₁	C₂²	semidirect
40. C₂×#124×C₄₁	C₂²	semidirect
41. C₂×#124×C₄₁	C₂²	semidirect
42. C₄₁×#525	C₂²	semidirect
43. C₂×#123×C₄₁	C₂²	semidirect
44. C₂×#123×C₄₁	C₂²	semidirect
45. C₂×#123×C₄₁	C₂²	semidirect
46. C₂×#123×C₄₁	C₂²	semidirect
47. C₂×#123×C₄₁	C₂²	semidirect
52. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
53. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
54. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
55. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
56. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
57. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
58. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
59. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
60. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
61. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
67. C₂×#121×C₄₁	C₂²	semidirect
68. C₂×#121×C₄₁	C₂²	semidirect
69. C₂×#121×C₄₁	C₂²	semidirect
70. C₂×#121×C₄₁	C₂²	semidirect
71. C₂×#121×C₄₁	C₂²	semidirect
72. C₂×#121×C₄₁	C₂²	semidirect
73. C₂×#121×C₄₁	C₂²	semidirect
74. C₂×#121×C₄₁	C₂²	semidirect
77. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
80. C₂×C₄×D₄×C₄₁	C₂²	semidirect
81. C₂×C₄×D₄×C₄₁	C₂²	semidirect
82. C₂×C₄×D₄×C₄₁	C₂²	semidirect
83. C₂×#117×C₄₁	C₂²	semidirect
85. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
86. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
87. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
96. C₂×#41×C₄₁	C₂³	semidirect
97. C₂×#41×C₄₁	C₂³	semidirect
98. C₂×#41×C₄₁	C₂³	semidirect
104. C₂²×Q₈×C₄₁	C₂³	semidirect
134. C₄⋊Q₈×C₄₁	C₂³	semidirect
135. #126×C₄₁	C₂³	semidirect
136. #125×C₄₁	C₂³	semidirect
137. #124×C₄₁	C₂³	semidirect
138. #124×C₄₁	C₂³	semidirect
139. #124×C₄₁	C₂³	semidirect
140. #123×C₄₁	C₂³	semidirect
141. #123×C₄₁	C₂³	semidirect
142. #123×C₄₁	C₂³	semidirect
143. #123×C₄₁	C₂³	semidirect
144. #123×C₄₁	C₂³	semidirect
149. C₂²⋊Q₈×C₄₁	C₂³	semidirect
150. C₂²⋊Q₈×C₄₁	C₂³	semidirect
151. C₂²⋊Q₈×C₄₁	C₂³	semidirect
152. C₂²⋊Q₈×C₄₁	C₂³	semidirect
153. C₂²⋊Q₈×C₄₁	C₂³	semidirect
154. C₂²⋊Q₈×C₄₁	C₂³	semidirect
155. C₂²⋊Q₈×C₄₁	C₂³	semidirect
156. C₂²⋊Q₈×C₄₁	C₂³	semidirect
157. C₂²⋊Q₈×C₄₁	C₂³	semidirect
163. #121×C₄₁	C₂³	semidirect
164. #121×C₄₁	C₂³	semidirect
165. #121×C₄₁	C₂³	semidirect
166. #121×C₄₁	C₂³	semidirect
167. #121×C₄₁	C₂³	semidirect
168. #121×C₄₁	C₂³	semidirect
169. #121×C₄₁	C₂³	semidirect
172. C₄×Q₈×C₄₁	C₂³	semidirect
175. C₄×D₄×C₄₁	C₂³	semidirect
176. C₄×D₄×C₄₁	C₂³	semidirect
177. C₄×D₄×C₄₁	C₂³	semidirect
178. #117×C₄₁	C₂³	semidirect
194. C₂×C₄⋊C₄×C₄₁	C₂³	semidirect
195. C₂×C₄⋊C₄×C₄₁	C₂³	semidirect
196. C₂×C₄⋊C₄×C₄₁	C₂³	semidirect
406. C₂×#3536	C₄₁	direct (N × H)
443. #3536	C₂×C₄₁	direct (N × H)
444. C₂×#562	C₂×C₄₁	semidirect
445. C₂×#554	C₂×C₄₁	semidirect
446. C₂×#548	C₂×C₄₁	semidirect
447. C₂×#547	C₂×C₄₁	semidirect
448. C₂×#546	C₂×C₄₁	semidirect
449. C₂×#546	C₂×C₄₁	semidirect
450. C₂×#543	C₂×C₄₁	semidirect
451. C₂×#542	C₂×C₄₁	semidirect
452. C₂×#539	C₂×C₄₁	semidirect
453. C₂×#538	C₂×C₄₁	semidirect
454. C₂×#537	C₂×C₄₁	semidirect
455. C₂×#537	C₂×C₄₁	semidirect
456. C₂×#525	C₂×C₄₁	semidirect
457. C₂²×C₂²⋊Q₈	C₂×C₄₁	semidirect
458. C₂²×#121	C₂×C₄₁	semidirect
464. C₂×C₄₁	#3536	direct (N × H)
468. C₂²×#41	C₂²×C₄₁	semidirect
469. C₂²×#41	C₂²×C₄₁	semidirect
470. C₂²×#41	C₂²×C₄₁	semidirect
471. C₂³×Q₈	C₂²×C₄₁	semidirect
475. #562	C₂²×C₄₁	semidirect
476. #554	C₂²×C₄₁	semidirect
477. #548	C₂²×C₄₁	semidirect
478. #547	C₂²×C₄₁	semidirect
479. #546	C₂²×C₄₁	semidirect
480. #546	C₂²×C₄₁	semidirect
481. #543	C₂²×C₄₁	semidirect
482. #542	C₂²×C₄₁	semidirect
483. #539	C₂²×C₄₁	semidirect
484. #538	C₂²×C₄₁	semidirect
485. #537	C₂²×C₄₁	semidirect
486. #537	C₂²×C₄₁	semidirect
487. C₂×C₄⋊Q₈	C₂²×C₄₁	semidirect
488. C₂×#126	C₂²×C₄₁	semidirect
489. C₂×#125	C₂²×C₄₁	semidirect
490. C₂×#124	C₂²×C₄₁	semidirect
491. C₂×#124	C₂²×C₄₁	semidirect
492. C₂×#124	C₂²×C₄₁	semidirect
493. #525	C₂²×C₄₁	semidirect
494. C₂×#123	C₂²×C₄₁	semidirect
495. C₂×#123	C₂²×C₄₁	semidirect
496. C₂×#123	C₂²×C₄₁	semidirect
497. C₂×#123	C₂²×C₄₁	semidirect
498. C₂×#123	C₂²×C₄₁	semidirect
503. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
504. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
505. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
506. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
507. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
508. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
509. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
510. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
511. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
512. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
518. C₂×#121	C₂²×C₄₁	semidirect
519. C₂×#121	C₂²×C₄₁	semidirect
520. C₂×#121	C₂²×C₄₁	semidirect
521. C₂×#121	C₂²×C₄₁	semidirect
522. C₂×#121	C₂²×C₄₁	semidirect
523. C₂×#121	C₂²×C₄₁	semidirect
524. C₂×#121	C₂²×C₄₁	semidirect
525. C₂×#121	C₂²×C₄₁	semidirect
528. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
531. C₂×C₄×D₄	C₂²×C₄₁	semidirect
532. C₂×C₄×D₄	C₂²×C₄₁	semidirect
533. C₂×C₄×D₄	C₂²×C₄₁	semidirect
534. C₂×#117	C₂²×C₄₁	semidirect
536. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
537. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
538. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
542. C₄₁	C₂×#3536	direct (N × H)
548. C₂×#41	C₂³×C₄₁	semidirect
549. C₂×#41	C₂³×C₄₁	semidirect
550. C₂×#41	C₂³×C₄₁	semidirect
556. C₂²×Q₈	C₂³×C₄₁	semidirect
586. C₄⋊Q₈	C₂³×C₄₁	semidirect
587. #126	C₂³×C₄₁	semidirect
588. #125	C₂³×C₄₁	semidirect
589. #124	C₂³×C₄₁	semidirect
590. #124	C₂³×C₄₁	semidirect
591. #124	C₂³×C₄₁	semidirect
592. #123	C₂³×C₄₁	semidirect
593. #123	C₂³×C₄₁	semidirect
594. #123	C₂³×C₄₁	semidirect
595. #123	C₂³×C₄₁	semidirect
596. #123	C₂³×C₄₁	semidirect
601. C₂²⋊Q₈	C₂³×C₄₁	semidirect
602. C₂²⋊Q₈	C₂³×C₄₁	semidirect
603. C₂²⋊Q₈	C₂³×C₄₁	semidirect
604. C₂²⋊Q₈	C₂³×C₄₁	semidirect
605. C₂²⋊Q₈	C₂³×C₄₁	semidirect
606. C₂²⋊Q₈	C₂³×C₄₁	semidirect
607. C₂²⋊Q₈	C₂³×C₄₁	semidirect
608. C₂²⋊Q₈	C₂³×C₄₁	semidirect
609. C₂²⋊Q₈	C₂³×C₄₁	semidirect
615. #121	C₂³×C₄₁	semidirect
616. #121	C₂³×C₄₁	semidirect
617. #121	C₂³×C₄₁	semidirect
618. #121	C₂³×C₄₁	semidirect
619. #121	C₂³×C₄₁	semidirect
620. #121	C₂³×C₄₁	semidirect
621. #121	C₂³×C₄₁	semidirect
624. C₄×Q₈	C₂³×C₄₁	semidirect
627. C₄×D₄	C₂³×C₄₁	semidirect
628. C₄×D₄	C₂³×C₄₁	semidirect
629. C₄×D₄	C₂³×C₄₁	semidirect
630. #117	C₂³×C₄₁	semidirect
646. C₂×C₄⋊C₄	C₂³×C₄₁	semidirect
647. C₂×C₄⋊C₄	C₂³×C₄₁	semidirect
648. C₂×C₄⋊C₄	C₂³×C₄₁	semidirect
899. C₂	C₄₁×#3536	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×#3536	2
C₂×C₄₁×#562	2
C₂×C₄₁×#554	2
C₂×C₄₁×#548	2
C₂×C₄₁×#547	2
C₂×C₄₁×#546	2
C₂×C₄₁×#543	2
C₂×C₄₁×#542	2
C₂×C₄₁×#539	2
C₂×C₄₁×#538	2
C₂×C₄₁×#537	2
C₂×C₄₁×#525	2
C₂²×C₂²⋊Q₈×C₄₁	2
C₂²×#121×C₄₁	2
C₂×#3536	41

Subgroups — C2×C41×#3536 #23838924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#3536 #23838924