Subgroups — C₄₁×#34476 #23810677

Order 10496.

2736 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#546	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2377	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2376	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2358	C₂	1	2	yes	maximal, complemented
8	C₄₁×#2354	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#2342	C₂	1	2	yes	maximal, complemented
11	C₄₁×#2341	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#2335	C₂	1	2	yes	maximal, complemented
14	C₄₁×#2326	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#2324	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#2324	C₂	1	2	yes	maximal, complemented
17	C₄₁×#2321	C₂	1	2	yes	maximal, complemented
18	C₄₁×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#2315	C₂	1	2	yes	maximal, complemented
20	C₄₁×#2311	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄₁×#390	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#546	C₄	1	16	yes	complemented
27	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#123×C₄₁	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#121×C₄₁	C₂²	1	2	yes	—
32	C₂×#120×C₄₁	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
41	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic, complemented
42	C₂×#117×C₄₁	C₂²	1	2	yes	complemented
43	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
46	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
47	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
48	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
49	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
50	C₄₁×#391	C₂²	1	1	yes	characteristic, complemented
51	C₄₁×#391	C₂²	1	1	yes	characteristic, complemented
52	C₄₁×#390	C₂²	1	1	yes	characteristic
53	C₄₁×#390	C₂²	1	1	yes	characteristic
54	C₄₁×#390	C₂²	1	2	yes	—
55	C₄₁×#390	C₂²	1	1	yes	characteristic
56	C₄₁×#390	C₂²	1	1	yes	characteristic
57	C₄₁×#390	C₂²	1	2	yes	—
58	C₄₁×#390	C₂²	1	1	yes	characteristic
59	C₄₁×#390	C₂²	1	1	yes	characteristic
60	C₄₁×#390	C₂²	1	2	yes	complemented
61	C₄₁×#390	C₂²	1	2	yes	complemented
62	C₄₁×#390	C₂²	1	2	yes	complemented
63	C₄₁×#389	C₂²	1	1	yes	characteristic, complemented
64	C₄₁×#389	C₂²	1	1	yes	characteristic, complemented
65	C₄₁×#389	C₂²	1	2	yes	complemented
66	C₄₁×#389	C₂²	1	2	yes	complemented
67	C₄₁×#388	C₂²	1	1	yes	characteristic, complemented
68	C₄₁×#388	C₂²	1	1	yes	characteristic, complemented
69	C₄₁×#388	C₂²	1	2	yes	complemented
70	C₄₁×#388	C₂²	1	2	yes	complemented
71	C₄₁×#388	C₂²	1	2	yes	complemented
72	C₄₁×#388	C₂²	1	2	yes	complemented
73	C₄₁×#388	C₂²	1	2	yes	complemented
74	C₄₁×#388	C₂²	1	2	yes	complemented
75	C₄₁×#388	C₂²	1	2	yes	complemented
76	C₄₁×#388	C₂²	1	2	yes	complemented
77	C₄₁×#388	C₂²	1	2	yes	complemented
78	C₄₁×#388	C₂²	1	2	yes	complemented
79	C₄₁×#387	C₂²	1	1	yes	characteristic, complemented
80	C₄₁×#387	C₂²	1	1	yes	characteristic, complemented
81	C₄₁×#387	C₂²	1	2	yes	complemented
82	C₄₁×#387	C₂²	1	2	yes	complemented
83	C₄₁×#386	C₂²	1	1	yes	characteristic
84	C₄₁×#386	C₂²	1	1	yes	characteristic
85	C₄₁×#386	C₂²	1	2	yes	—
86	C₄₁×#386	C₂²	1	2	yes	—
87	C₄₁×#386	C₂²	1	2	yes	complemented
88	C₄₁×#386	C₂²	1	2	yes	complemented
89	C₄₁×#386	C₂²	1	2	yes	complemented
90	C₄₁×#386	C₂²	1	2	yes	complemented
91	C₄₁×#385	C₂²	1	1	yes	characteristic
92	C₄₁×#385	C₂²	1	1	yes	characteristic
93	C₄₁×#385	C₂²	1	2	yes	—
94	C₄₁×#385	C₂²	1	2	yes	—
95	C₄₁×#385	C₂²	1	2	yes	—
96	C₄₁×#385	C₂²	1	2	yes	complemented
97	C₄₁×#385	C₂²	1	2	yes	complemented
98	C₄₁×#385	C₂²	1	2	yes	complemented
99	C₄₁×#385	C₂²	1	2	yes	complemented
100	C₄₁×#385	C₂²	1	2	yes	complemented
101	C₄₁×#385	C₂²	1	2	yes	complemented
102	C₄₁×#384	C₂²	1	1	yes	characteristic, complemented
103	C₄₁×#381	C₂²	1	2	yes	complemented
104	C₄₁×#380	C₂²	1	1	yes	characteristic
105	C₄₁×#380	C₂²	1	2	yes	complemented
106	C₄₁×#380	C₂²	1	2	yes	complemented
107	C₄₁×#380	C₂²	1	2	yes	complemented
108	C₄₁×#380	C₂²	1	2	yes	complemented
109	C₄₁×#380	C₂²	1	2	yes	complemented
110	C₄₁×#380	C₂²	1	1	yes	characteristic, complemented
111	C₄₁×#379	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	complemented
114	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
122	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
123	C₄₁×#376	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₄₁	C₂³	1	2	yes	—
125	C₂×#41×C₄₁	—	4	2	no	—
126	C₂×#41×C₄₁	—	4	2	no	—
127	C₂×#41×C₄₁	C₂×C₄	1	8	yes	complemented
128	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₄₁	—	4	2	no	—
130	C₂²×D₄×C₄₁	—	4	2	no	—
131	C₂²×D₄×C₄₁	C₂×C₄	1	8	yes	complemented
132	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
136	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
137	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
138	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
143	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
144	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
145	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
146	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
147	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
148	#124×C₄₁	C₂×C₄	1	8	yes	complemented
149	#123×C₄₁	C₂×C₄	1	16	yes	complemented
150	C₂²⋊Q₈×C₄₁	C₂×C₄	1	8	yes	complemented
151	#121×C₄₁	C₂×C₄	1	8	yes	complemented
152	#121×C₄₁	C₂×C₄	1	16	yes	complemented
153	#120×C₄₁	C₂×C₄	1	16	yes	complemented
154	C₄×Q₈×C₄₁	—	4	2	no	—
155	C₄×Q₈×C₄₁	—	4	2	no	—
156	C₄×D₄×C₄₁	—	4	4	no	—
157	C₄×D₄×C₄₁	—	4	2	no	—
158	C₄×D₄×C₄₁	—	4	2	no	—
159	C₄×D₄×C₄₁	—	4	4	no	—
160	C₄×D₄×C₄₁	C₂×C₄	1	8	yes	complemented
161	C₄×D₄×C₄₁	C₂×C₄	1	8	yes	complemented
162	#117×C₄₁	—	4	2	no	—
163	#117×C₄₁	—	4	4	no	—
164	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
165	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
166	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
186	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
187	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
188	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	16	yes	complemented
189	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	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	2	yes	—
210	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
218	C₂×C₄²×C₄₁	—	4	2	no	—
219	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
223	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
227	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
228	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
229	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
230	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
231	#95×C₄₁	C₂³	1	1	yes	characteristic
232	#95×C₄₁	C₂³	1	1	yes	characteristic
233	#95×C₄₁	C₂³	1	1	yes	characteristic
234	#95×C₄₁	C₂³	1	1	yes	characteristic
235	#95×C₄₁	C₂³	1	2	yes	—
236	#95×C₄₁	C₂³	1	2	yes	—
237	#95×C₄₁	C₂³	1	2	yes	—
238	#95×C₄₁	C₂³	1	2	yes	—
239	#95×C₄₁	C₂³	1	1	yes	characteristic
240	#95×C₄₁	C₂³	1	1	yes	characteristic
241	#95×C₄₁	C₂³	1	1	yes	characteristic
242	#95×C₄₁	C₂³	1	1	yes	characteristic
243	#95×C₄₁	C₂³	1	1	yes	characteristic
244	#95×C₄₁	C₂³	1	2	yes	—
245	#95×C₄₁	C₂³	1	2	yes	—
246	#95×C₄₁	C₂³	1	2	yes	—
247	#95×C₄₁	C₂³	1	2	yes	—
248	#95×C₄₁	C₂³	1	2	yes	—
249	#95×C₄₁	C₂³	1	2	yes	—
250	#95×C₄₁	C₂³	1	2	yes	—
251	#95×C₄₁	C₂³	1	1	yes	characteristic
252	C₂⁴×C₄₁	—	2	4	no	—
253	C₂⁴×C₄₁	—	2	4	no	—
254	C₂⁴×C₄₁	—	4	2	no	—
255	C₂⁴×C₄₁	—	4	2	no	—
256	C₂⁴×C₄₁	—	4	2	no	—
257	C₂⁴×C₄₁	—	4	2	no	—
258	C₂⁴×C₄₁	C₂²×C₄	1	8	yes	—
259	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
260	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
261	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
262	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
263	#41×C₄₁	—	4	16	no	—
264	C₂×Q₈×C₄₁	—	2	2	no	—
265	C₂×Q₈×C₄₁	—	2	2	no	—
266	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
267	C₂×D₄×C₄₁	—	2	2	no	—
268	C₂×D₄×C₄₁	—	2	2	no	—
269	C₂×D₄×C₄₁	—	2	2	no	—
270	C₂×D₄×C₄₁	—	2	2	no	—
271	C₂×D₄×C₄₁	—	2	2	no	—
272	C₂×D₄×C₄₁	—	2	2	no	—
273	C₂×D₄×C₄₁	—	4	16	no	—
274	C₂×D₄×C₄₁	—	4	2	no	—
275	C₂×D₄×C₄₁	—	4	2	no	—
276	C₂×D₄×C₄₁	—	4	2	no	—
277	C₂×D₄×C₄₁	—	4	2	no	—
278	C₂×D₄×C₄₁	—	4	2	no	—
279	C₂×D₄×C₄₁	—	4	2	no	—
280	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
281	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
282	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
283	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
284	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
285	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
286	C₂²×C₄×C₄₁	—	2	2	no	—
287	C₂²×C₄×C₄₁	—	2	2	no	—
288	C₂²×C₄×C₄₁	—	2	2	no	—
289	C₂²×C₄×C₄₁	—	2	2	no	—
290	C₂²×C₄×C₄₁	—	2	2	no	—
291	C₂²×C₄×C₄₁	—	2	2	no	—
292	C₂²×C₄×C₄₁	—	2	4	no	—
293	C₂²×C₄×C₄₁	—	2	2	no	—
294	C₂²×C₄×C₄₁	—	4	1	no	—
295	C₂²×C₄×C₄₁	—	4	1	no	—
296	C₂²×C₄×C₄₁	—	4	2	no	—
297	C₂²×C₄×C₄₁	—	4	2	no	—
298	C₂²×C₄×C₄₁	—	4	1	no	—
299	C₂²×C₄×C₄₁	—	4	2	no	—
300	C₂²×C₄×C₄₁	—	4	2	no	—
301	C₂²×C₄×C₄₁	—	4	2	no	—
302	C₂²×C₄×C₄₁	—	4	2	no	—
303	C₂²×C₄×C₄₁	—	4	2	no	—
304	C₂²×C₄×C₄₁	—	4	2	no	—
305	C₂²×C₄×C₄₁	—	4	2	no	—
306	C₂²×C₄×C₄₁	—	4	2	no	—
307	C₂²×C₄×C₄₁	—	4	2	no	—
308	C₂²×C₄×C₄₁	—	4	2	no	—
309	C₂²×C₄×C₄₁	—	4	2	no	—
310	C₂²×C₄×C₄₁	—	4	2	no	—
311	C₂²×C₄×C₄₁	—	4	2	no	—
312	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
313	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
314	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
315	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
316	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
335	C₄⋊C₄×C₄₁	—	2	2	no	—
336	C₄⋊C₄×C₄₁	—	2	2	no	—
337	C₄⋊C₄×C₄₁	—	2	2	no	—
338	C₄⋊C₄×C₄₁	—	2	2	no	—
339	C₄⋊C₄×C₄₁	—	2	2	no	—
340	C₄⋊C₄×C₄₁	—	4	2	no	—
341	C₄⋊C₄×C₄₁	—	4	2	no	—
342	C₄⋊C₄×C₄₁	—	4	1	no	—
343	C₄⋊C₄×C₄₁	—	4	2	no	—
344	C₄⋊C₄×C₄₁	—	4	2	no	—
345	C₄⋊C₄×C₄₁	—	4	1	no	—
346	C₄⋊C₄×C₄₁	—	4	1	no	—
347	C₄⋊C₄×C₄₁	—	4	2	no	—
348	C₄⋊C₄×C₄₁	—	4	2	no	—
349	C₄⋊C₄×C₄₁	—	4	2	no	—
350	C₄⋊C₄×C₄₁	—	4	2	no	—
351	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
352	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
353	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
354	C₂²⋊C₄×C₄₁	—	2	2	no	—
355	C₂²⋊C₄×C₄₁	—	2	4	no	—
356	C₂²⋊C₄×C₄₁	—	2	2	no	—
357	C₂²⋊C₄×C₄₁	—	2	4	no	—
358	C₂²⋊C₄×C₄₁	—	2	4	no	—
359	C₂²⋊C₄×C₄₁	—	2	2	no	—
360	C₂²⋊C₄×C₄₁	—	4	2	no	—
361	C₂²⋊C₄×C₄₁	—	4	2	no	—
362	C₂²⋊C₄×C₄₁	—	4	2	no	—
363	C₂²⋊C₄×C₄₁	—	4	2	no	—
364	C₂²⋊C₄×C₄₁	—	4	2	no	—
365	C₂²⋊C₄×C₄₁	—	4	2	no	—
366	C₂²⋊C₄×C₄₁	—	4	2	no	—
367	C₂²⋊C₄×C₄₁	—	4	2	no	—
368	C₂²⋊C₄×C₄₁	—	4	2	no	—
369	C₂²⋊C₄×C₄₁	—	4	1	no	—
370	C₂²⋊C₄×C₄₁	—	4	1	no	—
371	C₂²⋊C₄×C₄₁	—	4	1	no	—
372	C₂²⋊C₄×C₄₁	—	4	2	no	—
373	C₂²⋊C₄×C₄₁	—	4	2	no	—
374	C₂²⋊C₄×C₄₁	—	4	2	no	—
375	C₂²⋊C₄×C₄₁	—	4	2	no	—
376	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
377	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
378	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
379	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
380	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
381	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
382	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
383	C₄²×C₄₁	—	2	2	no	—
384	C₄²×C₄₁	—	2	2	no	—
385	C₄²×C₄₁	—	2	4	no	—
386	C₄²×C₄₁	—	2	2	no	—
387	C₄²×C₄₁	—	2	2	no	—
388	C₄²×C₄₁	—	4	1	no	—
389	C₄²×C₄₁	—	4	1	no	—
390	C₄²×C₄₁	—	4	2	no	—
391	C₄²×C₄₁	—	4	2	no	—
392	C₄²×C₄₁	—	4	2	no	—
393	C₄²×C₄₁	—	4	2	no	—
394	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
395	C₂³×C₄₁	—	2	1	no	—
396	C₂³×C₄₁	—	2	1	no	—
397	C₂³×C₄₁	—	2	1	no	—
398	C₂³×C₄₁	—	2	1	no	—
399	C₂³×C₄₁	—	2	2	no	—
400	C₂³×C₄₁	—	2	2	no	—
401	C₂³×C₄₁	—	2	1	no	—
402	C₂³×C₄₁	—	2	2	no	—
403	C₂³×C₄₁	—	2	1	no	—
404	C₂³×C₄₁	—	2	1	no	—
405	C₂³×C₄₁	—	2	2	no	—
406	C₂³×C₄₁	—	2	2	no	—
407	C₂³×C₄₁	—	2	2	no	—
408	C₂³×C₄₁	—	2	1	no	—
409	C₂³×C₄₁	—	2	2	no	—
410	C₂³×C₄₁	—	2	2	no	—
411	C₂³×C₄₁	—	2	1	no	—
412	C₂³×C₄₁	—	2	2	no	—
413	C₂³×C₄₁	—	2	2	no	—
414	C₂³×C₄₁	—	2	2	no	—
415	C₂³×C₄₁	—	2	1	no	—
416	C₂³×C₄₁	—	2	2	no	—
417	C₂³×C₄₁	—	2	16	no	—
418	C₂³×C₄₁	—	4	8	no	—
419	C₂³×C₄₁	—	4	8	no	—
420	C₂³×C₄₁	—	8	4	no	—
421	C₂³×C₄₁	—	8	4	no	—
422	C₂³×C₄₁	—	8	4	no	—
423	C₂³×C₄₁	—	8	4	no	—
424	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
425	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
426	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
427	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
428	C₂³×C₄₁	H(5,𝔽₂)	1	2	yes	—
429	C₂³×C₄₁	2₋¹⁺⁴	1	2	yes	—
430	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
431	Q₈×C₄₁	—	2	8	no	—
432	D₄×C₄₁	—	2	8	no	—
433	D₄×C₄₁	—	2	8	no	—
434	D₄×C₄₁	—	2	8	no	—
435	D₄×C₄₁	—	4	8	no	—
436	D₄×C₄₁	—	4	8	no	—
437	D₄×C₄₁	—	4	8	no	—
438	C₂×C₄×C₄₁	—	2	1	no	—
439	C₂×C₄×C₄₁	—	2	2	no	—
440	C₂×C₄×C₄₁	—	2	1	no	—
441	C₂×C₄×C₄₁	—	2	1	no	—
442	C₂×C₄×C₄₁	—	2	2	no	—
443	C₂×C₄×C₄₁	—	2	2	no	—
444	C₂×C₄×C₄₁	—	2	1	no	—
445	C₂×C₄×C₄₁	—	2	1	no	—
446	C₂×C₄×C₄₁	—	2	1	no	—
447	C₂×C₄×C₄₁	—	2	1	no	—
448	C₂×C₄×C₄₁	—	2	1	no	—
449	C₂×C₄×C₄₁	—	2	1	no	—
450	C₂×C₄×C₄₁	—	2	1	no	—
451	C₂×C₄×C₄₁	—	2	2	no	—
452	C₂×C₄×C₄₁	—	2	8	no	—
453	C₂×C₄×C₄₁	—	2	8	no	—
454	C₂×C₄×C₄₁	—	2	1	no	—
455	C₂×C₄×C₄₁	—	2	1	no	—
456	C₂×C₄×C₄₁	—	2	1	no	—
457	C₂×C₄×C₄₁	—	2	1	no	—
458	C₂×C₄×C₄₁	—	2	1	no	—
459	C₂×C₄×C₄₁	—	2	1	no	—
460	C₂×C₄×C₄₁	—	2	2	no	—
461	C₂×C₄×C₄₁	—	2	1	no	—
462	C₂×C₄×C₄₁	—	2	1	no	—
463	C₂×C₄×C₄₁	—	2	2	no	—
464	C₂×C₄×C₄₁	—	2	2	no	—
465	C₂×C₄×C₄₁	—	2	2	no	—
466	C₂×C₄×C₄₁	—	2	2	no	—
467	C₂×C₄×C₄₁	—	2	2	no	—
468	C₂×C₄×C₄₁	—	2	1	no	—
469	C₂×C₄×C₄₁	—	2	1	no	—
470	C₂×C₄×C₄₁	—	2	2	no	—
471	C₂×C₄×C₄₁	—	2	2	no	—
472	C₂×C₄×C₄₁	—	2	1	no	—
473	C₂×C₄×C₄₁	—	2	1	no	—
474	C₂×C₄×C₄₁	—	2	1	no	—
475	C₂×C₄×C₄₁	—	2	1	no	—
476	C₂×C₄×C₄₁	—	2	2	no	—
477	C₂×C₄×C₄₁	—	2	2	no	—
478	C₂×C₄×C₄₁	—	2	2	no	—
479	C₂×C₄×C₄₁	—	2	1	no	—
480	C₂×C₄×C₄₁	—	2	1	no	—
481	C₂×C₄×C₄₁	—	2	1	no	—
482	C₂×C₄×C₄₁	—	2	1	no	—
483	C₂×C₄×C₄₁	—	2	1	no	—
484	C₂×C₄×C₄₁	—	2	2	no	—
485	C₂×C₄×C₄₁	—	2	1	no	—
486	C₂×C₄×C₄₁	—	2	1	no	—
487	C₂×C₄×C₄₁	—	4	8	no	—
488	C₂×C₄×C₄₁	—	4	8	no	—
489	C₂×C₄×C₄₁	—	4	4	no	—
490	C₂×C₄×C₄₁	—	4	4	no	—
491	C₂×C₄×C₄₁	—	8	4	no	—
492	C₂×C₄×C₄₁	—	8	4	no	—
493	C₂×C₄×C₄₁	—	8	4	no	—
494	C₂×C₄×C₄₁	—	8	4	no	—
495	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
496	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
497	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
498	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
499	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
500	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
501	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
502	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
503	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
504	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
505	#34476	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
506	C₂²×C₄₁	—	2	2	no	—
507	C₂²×C₄₁	—	2	2	no	—
508	C₂²×C₄₁	—	2	2	no	—
509	C₂²×C₄₁	—	2	2	no	—
510	C₂²×C₄₁	—	2	2	no	—
511	C₂²×C₄₁	—	2	2	no	—
512	C₂²×C₄₁	—	2	2	no	—
513	C₂²×C₄₁	—	2	4	no	—
514	C₂²×C₄₁	—	2	4	no	—
515	C₂²×C₄₁	—	2	2	no	—
516	C₂²×C₄₁	—	2	4	no	—
517	C₂²×C₄₁	—	2	4	no	—
518	C₂²×C₄₁	—	2	4	no	—
519	C₂²×C₄₁	—	2	2	no	—
520	C₂²×C₄₁	—	2	4	no	—
521	C₂²×C₄₁	—	4	1	no	—
522	C₂²×C₄₁	—	4	2	no	—
523	C₂²×C₄₁	—	4	2	no	—
524	C₂²×C₄₁	—	4	2	no	—
525	C₂²×C₄₁	—	4	1	no	—
526	C₂²×C₄₁	—	4	2	no	—
527	C₂²×C₄₁	—	4	1	no	—
528	C₂²×C₄₁	—	4	2	no	—
529	C₂²×C₄₁	—	4	2	no	—
530	C₂²×C₄₁	—	4	1	no	—
531	C₂²×C₄₁	—	4	2	no	—
532	C₂²×C₄₁	—	4	2	no	—
533	C₂²×C₄₁	—	8	16	no	—
534	C₂²×C₄₁	#520	1	4	yes	—
535	C₂²×C₄₁	C₂⁴×C₄	1	1	yes	characteristic
536	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
537	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
538	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
539	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
540	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
541	C₂²×C₄₁	#585	1	1	yes	characteristic
542	C₄×C₄₁	—	2	2	no	—
543	C₄×C₄₁	—	2	2	no	—
544	C₄×C₄₁	—	2	4	no	—
545	C₄×C₄₁	—	2	2	no	—
546	C₄×C₄₁	—	2	2	no	—
547	C₄×C₄₁	—	2	4	no	—
548	C₄×C₄₁	—	2	2	no	—
549	C₄×C₄₁	—	4	1	no	—
550	C₄×C₄₁	—	4	1	no	—
551	C₄×C₄₁	—	4	1	no	—
552	C₄×C₄₁	—	4	1	no	—
553	C₄×C₄₁	—	4	2	no	—
554	C₄×C₄₁	—	4	1	no	—
555	C₄×C₄₁	—	4	2	no	—
556	C₄×C₄₁	—	4	2	no	—
557	C₄×C₄₁	—	4	1	no	—
558	C₄×C₄₁	—	4	2	no	—
559	C₄×C₄₁	—	4	1	no	—
560	C₄×C₄₁	#518	1	4	yes	—
561	C₂×#546	C₂×C₄₁	1	1	yes	characteristic
562	#2377	C₂×C₄₁	1	2	yes	complemented
563	#2376	C₂×C₄₁	1	2	yes	complemented
564	#2367	C₂×C₄₁	1	1	yes	characteristic, complemented
565	#2361	C₂×C₄₁	1	1	yes	characteristic, complemented
566	#2360	C₂×C₄₁	1	1	yes	characteristic, complemented
567	#2358	C₂×C₄₁	1	2	yes	complemented
568	#2354	C₂×C₄₁	1	1	yes	characteristic, complemented
569	D₄×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
570	#2342	C₂×C₄₁	1	2	yes	complemented
571	#2341	C₂×C₄₁	1	1	yes	characteristic, complemented
572	D₄×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
573	#2335	C₂×C₄₁	1	2	yes	complemented
574	#2326	C₂×C₄₁	1	1	yes	characteristic, complemented
575	#2324	C₂×C₄₁	1	1	yes	characteristic, complemented
576	#2324	C₂×C₄₁	1	2	yes	complemented
577	#2321	C₂×C₄₁	1	2	yes	complemented
578	#2319	C₂×C₄₁	1	1	yes	characteristic, complemented
579	#2315	C₂×C₄₁	1	2	yes	complemented
580	#2311	C₂×C₄₁	1	1	yes	characteristic, complemented
581	C₄×C₂²⋊Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
582	C₂×#390	C₂×C₄₁	1	1	yes	characteristic, complemented
583	#2290	C₂×C₄₁	1	1	yes	characteristic, complemented
584	C₂×C₄₁	—	2	4	no	—
585	C₂×C₄₁	—	4	2	no	—
586	C₂×C₄₁	—	4	4	no	—
587	C₂×C₄₁	—	4	4	no	—
588	C₂×C₄₁	C₂×#518	1	1	yes	characteristic
589	C₂×C₄₁	C₂×#520	1	1	yes	characteristic
590	C₂×C₄₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
591	C₂×C₄₁	#3536	1	1	yes	characteristic
592	C₂×C₄₁	#3542	1	1	yes	characteristic
593	C₂×C₄₁	#3543	1	1	yes	characteristic
594	C₂×C₄₁	#3561	1	1	yes	characteristic
595	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
596	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
597	#546	C₄×C₄₁	1	16	yes	complemented
598	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
599	C₂×#123	C₂²×C₄₁	1	2	yes	—
600	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
601	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
602	C₂×#121	C₂²×C₄₁	1	2	yes	—
603	C₂×#120	C₂²×C₄₁	1	2	yes	—
604	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
605	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
606	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
607	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
608	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
609	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
610	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
611	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
612	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic, complemented
613	C₂×#117	C₂²×C₄₁	1	2	yes	complemented
614	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
615	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
616	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
617	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
618	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
619	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
620	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
621	#391	C₂²×C₄₁	1	1	yes	characteristic, complemented
622	#391	C₂²×C₄₁	1	1	yes	characteristic, complemented
623	#390	C₂²×C₄₁	1	1	yes	characteristic
624	#390	C₂²×C₄₁	1	1	yes	characteristic
625	#390	C₂²×C₄₁	1	1	yes	characteristic
626	#390	C₂²×C₄₁	1	1	yes	characteristic
627	#390	C₂²×C₄₁	1	2	yes	—
628	#390	C₂²×C₄₁	1	1	yes	characteristic
629	#390	C₂²×C₄₁	1	1	yes	characteristic
630	#390	C₂²×C₄₁	1	2	yes	—
631	#390	C₂²×C₄₁	1	2	yes	complemented
632	#390	C₂²×C₄₁	1	2	yes	complemented
633	#390	C₂²×C₄₁	1	2	yes	complemented
634	#389	C₂²×C₄₁	1	1	yes	characteristic, complemented
635	#389	C₂²×C₄₁	1	1	yes	characteristic, complemented
636	#389	C₂²×C₄₁	1	2	yes	complemented
637	#389	C₂²×C₄₁	1	2	yes	complemented
638	#388	C₂²×C₄₁	1	2	yes	complemented
639	#388	C₂²×C₄₁	1	2	yes	complemented
640	#388	C₂²×C₄₁	1	2	yes	complemented
641	#388	C₂²×C₄₁	1	2	yes	complemented
642	#388	C₂²×C₄₁	1	2	yes	complemented
643	#388	C₂²×C₄₁	1	1	yes	characteristic, complemented
644	#388	C₂²×C₄₁	1	2	yes	complemented
645	#388	C₂²×C₄₁	1	2	yes	complemented
646	#388	C₂²×C₄₁	1	2	yes	complemented
647	#388	C₂²×C₄₁	1	2	yes	complemented
648	#388	C₂²×C₄₁	1	2	yes	complemented
649	#388	C₂²×C₄₁	1	1	yes	characteristic, complemented
650	#387	C₂²×C₄₁	1	1	yes	characteristic, complemented
651	#387	C₂²×C₄₁	1	2	yes	complemented
652	#387	C₂²×C₄₁	1	1	yes	characteristic, complemented
653	#387	C₂²×C₄₁	1	2	yes	complemented
654	#386	C₂²×C₄₁	1	1	yes	characteristic
655	#386	C₂²×C₄₁	1	2	yes	—
656	#386	C₂²×C₄₁	1	2	yes	—
657	#386	C₂²×C₄₁	1	1	yes	characteristic
658	#386	C₂²×C₄₁	1	2	yes	complemented
659	#386	C₂²×C₄₁	1	2	yes	complemented
660	#386	C₂²×C₄₁	1	2	yes	complemented
661	#386	C₂²×C₄₁	1	2	yes	complemented
662	#385	C₂²×C₄₁	1	1	yes	characteristic
663	#385	C₂²×C₄₁	1	2	yes	—
664	#385	C₂²×C₄₁	1	2	yes	—
665	#385	C₂²×C₄₁	1	2	yes	—
666	#385	C₂²×C₄₁	1	1	yes	characteristic
667	#385	C₂²×C₄₁	1	2	yes	complemented
668	#385	C₂²×C₄₁	1	2	yes	complemented
669	#385	C₂²×C₄₁	1	2	yes	complemented
670	#385	C₂²×C₄₁	1	2	yes	complemented
671	#385	C₂²×C₄₁	1	2	yes	complemented
672	#385	C₂²×C₄₁	1	2	yes	complemented
673	#384	C₂²×C₄₁	1	1	yes	characteristic, complemented
674	#381	C₂²×C₄₁	1	2	yes	complemented
675	#380	C₂²×C₄₁	1	1	yes	characteristic
676	#380	C₂²×C₄₁	1	2	yes	complemented
677	#380	C₂²×C₄₁	1	2	yes	complemented
678	#380	C₂²×C₄₁	1	2	yes	complemented
679	#380	C₂²×C₄₁	1	2	yes	complemented
680	#380	C₂²×C₄₁	1	2	yes	complemented
681	#380	C₂²×C₄₁	1	1	yes	characteristic, complemented
682	#379	C₂²×C₄₁	1	2	yes	—
683	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
684	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	complemented
685	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
686	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
687	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
688	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
689	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
690	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
691	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
692	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
693	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
694	#376	C₂²×C₄₁	1	1	yes	characteristic, complemented
695	C₄₁	#34476	1	1	yes	characteristic, direct product factor, Sylow
696	C₂⁵	C₂³×C₄₁	1	2	yes	—
697	C₂×#41	—	4	2	no	—
698	C₂×#41	—	4	2	no	—
699	C₂×#41	C₂×C₄×C₄₁	1	8	yes	complemented
700	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
701	C₂²×D₄	—	4	2	no	—
702	C₂²×D₄	—	4	2	no	—
703	C₂²×D₄	C₂×C₄×C₄₁	1	8	yes	complemented
704	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
705	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
706	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
707	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
708	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
709	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
710	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
711	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
712	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
713	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
714	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
715	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
716	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
717	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
718	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
719	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
720	#124	C₂×C₄×C₄₁	1	8	yes	complemented
721	#123	C₂×C₄×C₄₁	1	16	yes	complemented
722	C₂²⋊Q₈	C₂×C₄×C₄₁	1	8	yes	complemented
723	#121	C₂×C₄×C₄₁	1	8	yes	complemented
724	#121	C₂×C₄×C₄₁	1	16	yes	complemented
725	#120	C₂×C₄×C₄₁	1	16	yes	complemented
726	C₄×Q₈	—	4	2	no	—
727	C₄×Q₈	—	4	2	no	—
728	C₄×D₄	—	4	4	no	—
729	C₄×D₄	—	4	2	no	—
730	C₄×D₄	—	4	2	no	—
731	C₄×D₄	—	4	4	no	—
732	C₄×D₄	C₂×C₄×C₄₁	1	8	yes	complemented
733	C₄×D₄	C₂×C₄×C₄₁	1	8	yes	complemented
734	#117	—	4	2	no	—
735	#117	—	4	4	no	—
736	C₂×C₄⋊C₄	—	4	2	no	—
737	C₂×C₄⋊C₄	—	4	2	no	—
738	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
742	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
743	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
744	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
745	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
747	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
748	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
751	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
752	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
753	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
754	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
755	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
756	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
757	C₂×C₂²⋊C₄	—	4	4	no	—
758	C₂×C₂²⋊C₄	—	4	4	no	—
759	C₂×C₂²⋊C₄	—	4	4	no	—
760	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	16	yes	complemented
761	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
766	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
777	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
778	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
783	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
784	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
785	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
789	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
790	C₂×C₄²	—	4	2	no	—
791	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
792	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
793	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
794	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
795	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
796	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
797	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
798	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
799	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
800	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
801	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
802	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
803	#95	C₂³×C₄₁	1	1	yes	characteristic
804	#95	C₂³×C₄₁	1	1	yes	characteristic
805	#95	C₂³×C₄₁	1	1	yes	characteristic
806	#95	C₂³×C₄₁	1	1	yes	characteristic
807	#95	C₂³×C₄₁	1	2	yes	—
808	#95	C₂³×C₄₁	1	2	yes	—
809	#95	C₂³×C₄₁	1	2	yes	—
810	#95	C₂³×C₄₁	1	2	yes	—
811	#95	C₂³×C₄₁	1	1	yes	characteristic
812	#95	C₂³×C₄₁	1	1	yes	characteristic
813	#95	C₂³×C₄₁	1	1	yes	characteristic
814	#95	C₂³×C₄₁	1	1	yes	characteristic
815	#95	C₂³×C₄₁	1	1	yes	characteristic
816	#95	C₂³×C₄₁	1	2	yes	—
817	#95	C₂³×C₄₁	1	2	yes	—
818	#95	C₂³×C₄₁	1	2	yes	—
819	#95	C₂³×C₄₁	1	2	yes	—
820	#95	C₂³×C₄₁	1	2	yes	—
821	#95	C₂³×C₄₁	1	2	yes	—
822	#95	C₂³×C₄₁	1	2	yes	—
823	#95	C₂³×C₄₁	1	1	yes	characteristic
824	C₂⁴	—	2	4	no	—
825	C₂⁴	—	2	4	no	—
826	C₂⁴	—	4	2	no	—
827	C₂⁴	—	4	2	no	—
828	C₂⁴	—	4	2	no	—
829	C₂⁴	—	4	2	no	—
830	C₂⁴	C₂²×C₄×C₄₁	1	8	yes	—
831	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
832	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
833	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
834	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
835	#41	—	4	16	no	—
836	C₂×Q₈	—	2	2	no	—
837	C₂×Q₈	—	2	2	no	—
838	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	2	2	no	—
841	C₂×D₄	—	2	2	no	—
842	C₂×D₄	—	2	2	no	—
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	—	2	2	no	—
845	C₂×D₄	—	4	16	no	—
846	C₂×D₄	—	4	2	no	—
847	C₂×D₄	—	4	2	no	—
848	C₂×D₄	—	4	2	no	—
849	C₂×D₄	—	4	2	no	—
850	C₂×D₄	—	4	2	no	—
851	C₂×D₄	—	4	2	no	—
852	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
853	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
854	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
855	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
856	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
857	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	2	4	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	4	1	no	—
867	C₂²×C₄	—	4	1	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	—	4	1	no	—
873	C₂²×C₄	—	4	2	no	—
874	C₂²×C₄	—	4	2	no	—
875	C₂²×C₄	—	4	2	no	—
876	C₂²×C₄	—	4	2	no	—
877	C₂²×C₄	—	4	2	no	—
878	C₂²×C₄	—	4	2	no	—
879	C₂²×C₄	—	4	2	no	—
880	C₂²×C₄	—	4	2	no	—
881	C₂²×C₄	—	4	2	no	—
882	C₂²×C₄	—	4	2	no	—
883	C₂²×C₄	—	4	2	no	—
884	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
885	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
886	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
887	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
888	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
889	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
894	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
895	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
896	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
898	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
899	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
901	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
902	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
904	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
905	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
906	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	4	2	no	—
913	C₄⋊C₄	—	4	2	no	—
914	C₄⋊C₄	—	4	2	no	—
915	C₄⋊C₄	—	4	1	no	—
916	C₄⋊C₄	—	4	1	no	—
917	C₄⋊C₄	—	4	2	no	—
918	C₄⋊C₄	—	4	2	no	—
919	C₄⋊C₄	—	4	2	no	—
920	C₄⋊C₄	—	4	2	no	—
921	C₄⋊C₄	—	4	1	no	—
922	C₄⋊C₄	—	4	2	no	—
923	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
924	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
925	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	4	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	4	no	—
930	C₂²⋊C₄	—	2	4	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	4	2	no	—
933	C₂²⋊C₄	—	4	2	no	—
934	C₂²⋊C₄	—	4	2	no	—
935	C₂²⋊C₄	—	4	2	no	—
936	C₂²⋊C₄	—	4	2	no	—
937	C₂²⋊C₄	—	4	2	no	—
938	C₂²⋊C₄	—	4	2	no	—
939	C₂²⋊C₄	—	4	2	no	—
940	C₂²⋊C₄	—	4	1	no	—
941	C₂²⋊C₄	—	4	1	no	—
942	C₂²⋊C₄	—	4	2	no	—
943	C₂²⋊C₄	—	4	2	no	—
944	C₂²⋊C₄	—	4	2	no	—
945	C₂²⋊C₄	—	4	2	no	—
946	C₂²⋊C₄	—	4	2	no	—
947	C₂²⋊C₄	—	4	1	no	—
948	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
949	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
950	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
951	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
952	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
953	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
954	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	4	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	4	1	no	—
961	C₄²	—	4	1	no	—
962	C₄²	—	4	2	no	—
963	C₄²	—	4	2	no	—
964	C₄²	—	4	2	no	—
965	C₄²	—	4	2	no	—
966	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	1	no	—
969	C₂³	—	2	1	no	—
970	C₂³	—	2	1	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	2	no	—
973	C₂³	—	2	1	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	1	no	—
976	C₂³	—	2	1	no	—
977	C₂³	—	2	2	no	—
978	C₂³	—	2	2	no	—
979	C₂³	—	2	2	no	—
980	C₂³	—	2	1	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	2	2	no	—
983	C₂³	—	2	1	no	—
984	C₂³	—	2	2	no	—
985	C₂³	—	2	2	no	—
986	C₂³	—	2	2	no	—
987	C₂³	—	2	1	no	—
988	C₂³	—	2	2	no	—
989	C₂³	—	2	16	no	—
990	C₂³	—	4	8	no	—
991	C₂³	—	4	8	no	—
992	C₂³	—	8	4	no	—
993	C₂³	—	8	4	no	—
994	C₂³	—	8	4	no	—
995	C₂³	—	8	4	no	—
996	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
997	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
998	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
999	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
1000	C₂³	H(5,𝔽₂)×C₄₁	1	2	yes	—
1001	C₂³	2₋¹⁺⁴×C₄₁	1	2	yes	—
1002	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
1003	Q₈	—	2	8	no	—
1004	D₄	—	2	8	no	—
1005	D₄	—	2	8	no	—
1006	D₄	—	2	8	no	—
1007	D₄	—	4	8	no	—
1008	D₄	—	4	8	no	—
1009	D₄	—	4	8	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	8	no	—
1025	C₂×C₄	—	2	8	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	4	8	no	—
1060	C₂×C₄	—	4	8	no	—
1061	C₂×C₄	—	4	4	no	—
1062	C₂×C₄	—	4	4	no	—
1063	C₂×C₄	—	8	4	no	—
1064	C₂×C₄	—	8	4	no	—
1065	C₂×C₄	—	8	4	no	—
1066	C₂×C₄	—	8	4	no	—
1067	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
1068	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
1069	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
1070	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
1071	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
1072	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
1073	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
1074	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1075	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1076	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1077	C₂²	—	2	2	no	—
1078	C₂²	—	2	2	no	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	4	no	—
1085	C₂²	—	2	4	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	4	no	—
1088	C₂²	—	2	4	no	—
1089	C₂²	—	2	4	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	4	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	2	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	2	no	—
1104	C₂²	—	8	16	no	—
1105	C₂²	C₄₁×#520	1	4	yes	—
1106	C₂²	C₂⁴×C₄×C₄₁	1	1	yes	characteristic
1107	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1108	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1109	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1110	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1111	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
1112	C₂²	C₄₁×#585	1	1	yes	characteristic
1113	C₄	—	2	2	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	4	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	4	no	—
1119	C₄	—	2	2	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	1	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	2	no	—
1131	C₄	C₄₁×#518	1	4	yes	—
1132	C₂	—	2	4	no	—
1133	C₂	—	4	4	no	—
1134	C₂	—	4	4	no	—
1135	C₂	—	4	2	no	—
1136	C₂	C₂×C₄₁×#518	1	1	yes	characteristic
1137	C₂	C₂×C₄₁×#520	1	1	yes	characteristic
1138	C₂	C₄×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1139	C₂	C₄₁×#3536	1	1	yes	characteristic
1140	C₂	C₄₁×#3542	1	1	yes	characteristic
1141	C₂	C₄₁×#3543	1	1	yes	characteristic
1142	C₂	C₄₁×#3561	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₄₁
Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂×C₄₁×#546	C₂
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
2. C₄₁×#2377	C₂	semidirect
3. C₄₁×#2376	C₂	semidirect
4. C₄₁×#2367	C₂	semidirect
5. C₄₁×#2361	C₂	semidirect
6. C₄₁×#2360	C₂	semidirect
7. C₄₁×#2358	C₂	semidirect
8. C₄₁×#2354	C₂	semidirect
9. D₄×C₄⋊C₄×C₄₁	C₂	semidirect
10. C₄₁×#2342	C₂	semidirect
11. C₄₁×#2341	C₂	semidirect
12. D₄×C₂²⋊C₄×C₄₁	C₂	semidirect
13. C₄₁×#2335	C₂	semidirect
14. C₄₁×#2326	C₂	semidirect
15. C₄₁×#2324	C₂	semidirect
16. C₄₁×#2324	C₂	semidirect
17. C₄₁×#2321	C₂	semidirect
18. C₄₁×#2319	C₂	semidirect
19. C₄₁×#2315	C₂	semidirect
20. C₄₁×#2311	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₄₁	C₂	semidirect
22. C₂×C₄₁×#390	C₂	semidirect
23. C₄₁×#2290	C₂	semidirect
26. C₄₁×#546	C₄	semidirect
33. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
34. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
40. C₂×C₄×D₄×C₄₁	C₂²	semidirect
41. C₂×#117×C₄₁	C₂²	semidirect
42. C₂×#117×C₄₁	C₂²	semidirect
44. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
50. C₄₁×#391	C₂²	semidirect
51. C₄₁×#391	C₂²	semidirect
60. C₄₁×#390	C₂²	semidirect
61. C₄₁×#390	C₂²	semidirect
62. C₄₁×#390	C₂²	semidirect
63. C₄₁×#389	C₂²	semidirect
64. C₄₁×#389	C₂²	semidirect
65. C₄₁×#389	C₂²	semidirect
66. C₄₁×#389	C₂²	semidirect
67. C₄₁×#388	C₂²	semidirect
68. C₄₁×#388	C₂²	semidirect
69. C₄₁×#388	C₂²	semidirect
70. C₄₁×#388	C₂²	semidirect
71. C₄₁×#388	C₂²	semidirect
72. C₄₁×#388	C₂²	semidirect
73. C₄₁×#388	C₂²	semidirect
74. C₄₁×#388	C₂²	semidirect
75. C₄₁×#388	C₂²	semidirect
76. C₄₁×#388	C₂²	semidirect
77. C₄₁×#388	C₂²	semidirect
78. C₄₁×#388	C₂²	semidirect
79. C₄₁×#387	C₂²	semidirect
80. C₄₁×#387	C₂²	semidirect
81. C₄₁×#387	C₂²	semidirect
82. C₄₁×#387	C₂²	semidirect
87. C₄₁×#386	C₂²	semidirect
88. C₄₁×#386	C₂²	semidirect
89. C₄₁×#386	C₂²	semidirect
90. C₄₁×#386	C₂²	semidirect
96. C₄₁×#385	C₂²	semidirect
97. C₄₁×#385	C₂²	semidirect
98. C₄₁×#385	C₂²	semidirect
99. C₄₁×#385	C₂²	semidirect
100. C₄₁×#385	C₂²	semidirect
101. C₄₁×#385	C₂²	semidirect
102. C₄₁×#384	C₂²	semidirect
103. C₄₁×#381	C₂²	semidirect
105. C₄₁×#380	C₂²	semidirect
106. C₄₁×#380	C₂²	semidirect
107. C₄₁×#380	C₂²	semidirect
108. C₄₁×#380	C₂²	semidirect
109. C₄₁×#380	C₂²	semidirect
110. C₄₁×#380	C₂²	semidirect
112. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
113. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
114. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
115. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
116. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
123. C₄₁×#376	C₂²	semidirect
127. C₂×#41×C₄₁	C₂×C₄	semidirect
131. C₂²×D₄×C₄₁	C₂×C₄	semidirect
148. #124×C₄₁	C₂×C₄	semidirect
149. #123×C₄₁	C₂×C₄	semidirect
150. C₂²⋊Q₈×C₄₁	C₂×C₄	semidirect
151. #121×C₄₁	C₂×C₄	semidirect
152. #121×C₄₁	C₂×C₄	semidirect
153. #120×C₄₁	C₂×C₄	semidirect
160. C₄×D₄×C₄₁	C₂×C₄	semidirect
161. C₄×D₄×C₄₁	C₂×C₄	semidirect
188. C₂×C₂²⋊C₄×C₄₁	C₂×C₄	semidirect
505. #34476	C₄₁	direct (N × H)
562. #2377	C₂×C₄₁	semidirect
563. #2376	C₂×C₄₁	semidirect
564. #2367	C₂×C₄₁	semidirect
565. #2361	C₂×C₄₁	semidirect
566. #2360	C₂×C₄₁	semidirect
567. #2358	C₂×C₄₁	semidirect
568. #2354	C₂×C₄₁	semidirect
569. D₄×C₄⋊C₄	C₂×C₄₁	semidirect
570. #2342	C₂×C₄₁	semidirect
571. #2341	C₂×C₄₁	semidirect
572. D₄×C₂²⋊C₄	C₂×C₄₁	semidirect
573. #2335	C₂×C₄₁	semidirect
574. #2326	C₂×C₄₁	semidirect
575. #2324	C₂×C₄₁	semidirect
576. #2324	C₂×C₄₁	semidirect
577. #2321	C₂×C₄₁	semidirect
578. #2319	C₂×C₄₁	semidirect
579. #2315	C₂×C₄₁	semidirect
580. #2311	C₂×C₄₁	semidirect
581. C₄×C₂²⋊Q₈	C₂×C₄₁	semidirect
582. C₂×#390	C₂×C₄₁	semidirect
583. #2290	C₂×C₄₁	semidirect
597. #546	C₄×C₄₁	semidirect
604. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
605. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
611. C₂×C₄×D₄	C₂²×C₄₁	semidirect
612. C₂×#117	C₂²×C₄₁	semidirect
613. C₂×#117	C₂²×C₄₁	semidirect
615. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
621. #391	C₂²×C₄₁	semidirect
622. #391	C₂²×C₄₁	semidirect
631. #390	C₂²×C₄₁	semidirect
632. #390	C₂²×C₄₁	semidirect
633. #390	C₂²×C₄₁	semidirect
634. #389	C₂²×C₄₁	semidirect
635. #389	C₂²×C₄₁	semidirect
636. #389	C₂²×C₄₁	semidirect
637. #389	C₂²×C₄₁	semidirect
638. #388	C₂²×C₄₁	semidirect
639. #388	C₂²×C₄₁	semidirect
640. #388	C₂²×C₄₁	semidirect
641. #388	C₂²×C₄₁	semidirect
642. #388	C₂²×C₄₁	semidirect
643. #388	C₂²×C₄₁	semidirect
644. #388	C₂²×C₄₁	semidirect
645. #388	C₂²×C₄₁	semidirect
646. #388	C₂²×C₄₁	semidirect
647. #388	C₂²×C₄₁	semidirect
648. #388	C₂²×C₄₁	semidirect
649. #388	C₂²×C₄₁	semidirect
650. #387	C₂²×C₄₁	semidirect
651. #387	C₂²×C₄₁	semidirect
652. #387	C₂²×C₄₁	semidirect
653. #387	C₂²×C₄₁	semidirect
658. #386	C₂²×C₄₁	semidirect
659. #386	C₂²×C₄₁	semidirect
660. #386	C₂²×C₄₁	semidirect
661. #386	C₂²×C₄₁	semidirect
667. #385	C₂²×C₄₁	semidirect
668. #385	C₂²×C₄₁	semidirect
669. #385	C₂²×C₄₁	semidirect
670. #385	C₂²×C₄₁	semidirect
671. #385	C₂²×C₄₁	semidirect
672. #385	C₂²×C₄₁	semidirect
673. #384	C₂²×C₄₁	semidirect
674. #381	C₂²×C₄₁	semidirect
676. #380	C₂²×C₄₁	semidirect
677. #380	C₂²×C₄₁	semidirect
678. #380	C₂²×C₄₁	semidirect
679. #380	C₂²×C₄₁	semidirect
680. #380	C₂²×C₄₁	semidirect
681. #380	C₂²×C₄₁	semidirect
683. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
684. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
685. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
686. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
687. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
691. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
692. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
693. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
694. #376	C₂²×C₄₁	semidirect
695. C₄₁	#34476	direct (N × H)
699. C₂×#41	C₂×C₄×C₄₁	semidirect
703. C₂²×D₄	C₂×C₄×C₄₁	semidirect
720. #124	C₂×C₄×C₄₁	semidirect
721. #123	C₂×C₄×C₄₁	semidirect
722. C₂²⋊Q₈	C₂×C₄×C₄₁	semidirect
723. #121	C₂×C₄×C₄₁	semidirect
724. #121	C₂×C₄×C₄₁	semidirect
725. #120	C₂×C₄×C₄₁	semidirect
732. C₄×D₄	C₂×C₄×C₄₁	semidirect
733. C₄×D₄	C₂×C₄×C₄₁	semidirect
760. C₂×C₂²⋊C₄	C₂×C₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#546	2
C₄₁×#2377	2
C₄₁×#2376	2
C₄₁×#2367	2
C₄₁×#2361	2
C₄₁×#2360	2
C₄₁×#2358	2
C₄₁×#2354	2
D₄×C₄⋊C₄×C₄₁	2
C₄₁×#2342	2
C₄₁×#2341	2
D₄×C₂²⋊C₄×C₄₁	2
C₄₁×#2335	2
C₄₁×#2326	2
C₄₁×#2324	2
C₄₁×#2321	2
C₄₁×#2319	2
C₄₁×#2315	2
C₄₁×#2311	2
C₄×C₂²⋊Q₈×C₄₁	2
C₂×C₄₁×#390	2
C₄₁×#2290	2
#34476	41

Subgroups — C41×#34476 #23810677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#34476 #23810677