Subgroups — C₄₁×#61258 #23837459

Order 10496.

1866 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3492	C₂	1	2	yes	maximal, complemented
2	C₄₁×#3346	C₂	1	4	yes	maximal, complemented
3	C₄₁×#3343	C₂	1	4	yes	maximal, complemented
4	C₄₁×#3339	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3338	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3336	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3334	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#3098	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3092	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3083	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3061	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3050	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#2951	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#2929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#2913	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#107×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#554	—	2	2	no	—
22	C₄₁×#554	C₂²	1	4	yes	—
23	C₄₁×#553	—	2	2	no	—
24	C₄₁×#553	C₂²	1	4	yes	—
25	C₄₁×#552	—	2	2	no	—
26	C₄₁×#552	C₂²	1	4	yes	—
27	C₄₁×#547	—	2	2	no	—
28	C₄₁×#547	C₂²	1	4	yes	—
29	C₄₁×#544	C₂²	1	2	yes	—
30	C₄₁×#539	—	2	4	no	—
31	C₄₁×#537	C₂²	1	2	yes	—
32	C₄₁×#525	—	2	4	no	—
33	C₄₁×#525	C₂²	1	2	yes	—
34	C₄₁×#525	C₂²	1	1	yes	characteristic
35	C₄₁×#520	C₂²	1	2	yes	—
36	C₄₁×#520	C₂²	1	2	yes	—
37	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
38	C₄₁×#501	C₂²	1	4	yes	complemented
39	C₄₁×#500	C₂²	1	2	yes	complemented
40	C₄₁×#499	C₂²	1	2	yes	complemented
41	C₄₁×#485	C₂²	1	4	yes	complemented
42	C₄₁×#484	C₂²	1	4	yes	—
43	C₄₁×#484	C₂²	1	4	yes	complemented
44	C₄₁×#483	C₂²	1	4	yes	—
45	C₄₁×#482	C₂²	1	4	yes	complemented
46	C₄₁×#481	C₂²	1	4	yes	—
47	C₄₁×#480	C₂²	1	4	yes	—
48	C₄₁×#480	C₂²	1	4	yes	complemented
49	C₄₁×#479	C₂²	1	4	yes	complemented
50	C₄₁×#478	C₂²	1	4	yes	complemented
51	C₄₁×#477	C₂²	1	4	yes	complemented
52	C₄₁×#474	C₂²	1	4	yes	complemented
53	C₄₁×#468	C₂²	1	4	yes	complemented
54	C₄₁×#467	C₂²	1	1	yes	characteristic
55	C₄₁×#467	C₂²	1	1	yes	characteristic
56	C₄₁×#467	C₂²	1	2	yes	complemented
57	C₄₁×#466	C₂²	1	1	yes	characteristic
58	C₄₁×#466	C₂²	1	1	yes	characteristic
59	C₄₁×#466	C₂²	1	2	yes	complemented
60	C₄₁×#465	C₂²	1	2	yes	—
61	C₄₁×#465	C₂²	1	2	yes	—
62	C₄₁×#440	C₂²	1	4	yes	complemented
63	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
64	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
65	C₄₁×#435	C₂²	1	2	yes	—
66	C₄₁×#435	C₂²	1	2	yes	—
67	C₈×D₄×C₄₁	C₂²	1	2	yes	—
68	C₈×D₄×C₄₁	C₂²	1	2	yes	—
69	C₄₁×#428	C₂²	1	2	yes	—
70	C₄₁×#428	C₂²	1	2	yes	—
71	C₄₁×#428	C₂²	1	4	yes	complemented
72	C₄₁×#427	C₂²	1	1	yes	characteristic
73	C₄₁×#427	C₂²	1	2	yes	complemented
74	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
75	C₂×#107×C₄₁	C₂²	1	2	yes	—
76	C₂×#107×C₄₁	C₂²	1	2	yes	—
77	C₂×#107×C₄₁	C₂²	1	2	yes	—
78	C₂×#107×C₄₁	C₂²	1	2	yes	—
79	C₂×#107×C₄₁	C₂²	1	2	yes	—
80	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
81	C₂×#107×C₄₁	C₂²	1	2	yes	complemented
82	C₄₁×#424	C₂²	1	1	yes	characteristic
83	C₄₁×#417	C₂²	1	2	yes	—
84	C₄₁×#417	C₂²	1	2	yes	—
85	C₄₁×#416	C₂²	1	2	yes	—
86	C₄₁×#408	C₂²	1	1	yes	characteristic
87	C₄₁×#407	C₂²	1	1	yes	characteristic
88	C₄₁×#405	C₂²	1	1	yes	characteristic
89	C₂×#41×C₄₁	—	2	4	no	—
90	C₂×#41×C₄₁	C₂³	1	2	yes	—
91	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₄₁	—	2	2	no	—
93	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
94	#135×C₄₁	—	2	4	no	—
95	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
96	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
97	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
98	#131×C₄₁	—	2	4	no	—
99	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
101	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₁	—	2	4	no	—
103	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
109	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₄₁	—	2	2	no	—
111	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
112	#126×C₄₁	—	2	4	no	—
113	#126×C₄₁	—	2	4	no	—
114	#125×C₄₁	—	2	4	no	—
115	#125×C₄₁	—	2	4	no	—
116	#125×C₄₁	—	2	2	no	—
117	#125×C₄₁	C₂³	1	4	yes	—
118	#123×C₄₁	—	2	4	no	—
119	#123×C₄₁	—	2	2	no	—
120	#123×C₄₁	—	2	4	no	—
121	#123×C₄₁	—	2	4	no	—
122	#123×C₄₁	—	2	4	no	—
123	#123×C₄₁	D₄	1	2	yes	—
124	C₂²⋊Q₈×C₄₁	—	2	2	no	—
125	C₂²⋊Q₈×C₄₁	—	2	4	no	—
126	C₂²⋊Q₈×C₄₁	—	2	4	no	—
127	C₂²⋊Q₈×C₄₁	—	2	4	no	—
128	C₂²⋊Q₈×C₄₁	—	2	4	no	—
129	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
130	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
131	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
132	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
133	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
134	#121×C₄₁	—	2	4	no	—
135	#121×C₄₁	—	2	4	no	—
136	#121×C₄₁	—	2	2	no	—
137	#121×C₄₁	D₄	1	1	yes	characteristic
138	#121×C₄₁	D₄	1	1	yes	characteristic
139	#121×C₄₁	C₂³	1	2	yes	—
140	#121×C₄₁	C₂³	1	2	yes	—
141	#121×C₄₁	C₂³	1	4	yes	—
142	#120×C₄₁	—	2	2	no	—
143	#120×C₄₁	D₄	1	2	yes	—
144	C₄×Q₈×C₄₁	—	2	2	no	—
145	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
146	C₄×D₄×C₄₁	—	2	4	no	—
147	C₄×D₄×C₄₁	—	2	2	no	—
148	C₄×D₄×C₄₁	—	2	4	no	—
149	C₄×D₄×C₄₁	—	2	2	no	—
150	C₄×D₄×C₄₁	—	2	2	no	—
151	C₄×D₄×C₄₁	—	2	4	no	—
152	C₄×D₄×C₄₁	—	2	4	no	—
153	C₄×D₄×C₄₁	C₂³	1	4	yes	—
154	C₄×D₄×C₄₁	C₂³	1	2	yes	—
155	C₄×D₄×C₄₁	C₂³	1	2	yes	—
156	#117×C₄₁	—	2	2	no	—
157	#117×C₄₁	—	2	4	no	—
158	#117×C₄₁	C₂³	1	2	yes	—
159	#117×C₄₁	C₂³	1	4	yes	—
160	#117×C₄₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
162	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
163	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
164	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
165	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
168	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
169	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
170	#107×C₄₁	C₂³	1	1	yes	characteristic
171	#107×C₄₁	C₂³	1	4	yes	—
172	#107×C₄₁	C₂³	1	2	yes	—
173	#107×C₄₁	C₂³	1	2	yes	—
174	#107×C₄₁	C₂³	1	2	yes	—
175	#107×C₄₁	C₂³	1	2	yes	—
176	#107×C₄₁	C₂³	1	4	yes	—
177	#107×C₄₁	C₂³	1	4	yes	—
178	#107×C₄₁	C₂³	1	4	yes	—
179	#107×C₄₁	C₂³	1	1	yes	characteristic
180	#106×C₄₁	C₂³	1	2	yes	—
181	#106×C₄₁	C₂³	1	4	yes	—
182	#106×C₄₁	C₂³	1	4	yes	—
183	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
184	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
185	#103×C₄₁	C₂³	1	2	yes	—
186	#103×C₄₁	C₂³	1	2	yes	—
187	#103×C₄₁	C₂³	1	4	yes	—
188	#103×C₄₁	C₂³	1	4	yes	—
189	#102×C₄₁	C₂³	1	2	yes	—
190	#102×C₄₁	C₂³	1	2	yes	—
191	#102×C₄₁	C₂³	1	4	yes	—
192	#102×C₄₁	C₂³	1	4	yes	—
193	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
194	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
195	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
196	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
197	#97×C₄₁	C₂³	1	2	yes	—
198	C₄×C₈×C₄₁	C₂³	1	2	yes	—
199	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
200	#41×C₄₁	—	2	2	no	—
201	#41×C₄₁	—	2	2	no	—
202	#41×C₄₁	—	2	4	no	—
203	#41×C₄₁	—	2	4	no	—
204	#41×C₄₁	—	8	8	no	—
205	C₂×Q₈×C₄₁	—	2	4	no	—
206	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
207	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
208	C₂×D₄×C₄₁	—	2	2	no	—
209	C₂×D₄×C₄₁	—	2	2	no	—
210	C₂×D₄×C₄₁	—	2	2	no	—
211	C₂×D₄×C₄₁	—	2	4	no	—
212	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
213	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
214	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
215	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
216	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₄₁	—	2	2	no	—
218	C₂²×C₄×C₄₁	—	2	2	no	—
219	C₂²×C₄×C₄₁	—	2	4	no	—
220	C₂²×C₄×C₄₁	—	2	2	no	—
221	C₂²×C₄×C₄₁	—	2	4	no	—
222	C₂²×C₄×C₄₁	—	2	2	no	—
223	C₂²×C₄×C₄₁	—	2	4	no	—
224	C₂²×C₄×C₄₁	—	2	2	no	—
225	C₂²×C₄×C₄₁	—	2	4	no	—
226	C₂²×C₄×C₄₁	—	8	4	no	—
227	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
234	Q₁₆×C₄₁	—	2	2	no	—
235	SD₁₆×C₄₁	—	2	4	no	—
236	D₈×C₄₁	—	2	2	no	—
237	M₁₆×C₄₁	—	2	2	no	—
238	M₁₆×C₄₁	—	2	2	no	—
239	M₁₆×C₄₁	—	2	4	no	—
240	C₂×C₈×C₄₁	—	2	2	no	—
241	C₂×C₈×C₄₁	—	2	2	no	—
242	C₂×C₈×C₄₁	—	2	2	no	—
243	C₂×C₈×C₄₁	—	2	2	no	—
244	C₂×C₈×C₄₁	—	2	2	no	—
245	C₂×C₈×C₄₁	—	2	4	no	—
246	C₂×C₈×C₄₁	#41	1	4	yes	complemented
247	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
248	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
249	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
252	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
253	C₄⋊C₄×C₄₁	—	2	2	no	—
254	C₄⋊C₄×C₄₁	—	2	2	no	—
255	C₄⋊C₄×C₄₁	—	2	4	no	—
256	C₄⋊C₄×C₄₁	—	2	4	no	—
257	C₄⋊C₄×C₄₁	—	2	4	no	—
258	C₄⋊C₄×C₄₁	—	2	4	no	—
259	C₄⋊C₄×C₄₁	—	2	4	no	—
260	C₄⋊C₄×C₄₁	—	2	4	no	—
261	C₄⋊C₄×C₄₁	—	2	2	no	—
262	C₄⋊C₄×C₄₁	—	2	4	no	—
263	C₄⋊C₄×C₄₁	—	2	4	no	—
264	C₄⋊C₄×C₄₁	—	2	2	no	—
265	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
266	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
267	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
268	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
269	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
270	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
271	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
272	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
273	C₂²⋊C₄×C₄₁	—	2	2	no	—
274	C₂²⋊C₄×C₄₁	—	2	2	no	—
275	C₂²⋊C₄×C₄₁	—	2	4	no	—
276	C₂²⋊C₄×C₄₁	—	2	2	no	—
277	C₂²⋊C₄×C₄₁	—	2	4	no	—
278	C₂²⋊C₄×C₄₁	—	2	4	no	—
279	C₂²⋊C₄×C₄₁	—	2	4	no	—
280	C₂²⋊C₄×C₄₁	—	2	2	no	—
281	C₂²⋊C₄×C₄₁	—	2	2	no	—
282	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
283	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
284	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
285	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
286	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
287	C₄²×C₄₁	—	2	4	no	—
288	C₄²×C₄₁	—	2	4	no	—
289	C₄²×C₄₁	—	2	2	no	—
290	C₄²×C₄₁	C₂⁴	1	2	yes	—
291	C₂³×C₄₁	—	2	2	no	—
292	C₂³×C₄₁	—	2	2	no	—
293	C₂³×C₄₁	—	2	2	no	—
294	C₂³×C₄₁	—	2	2	no	—
295	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
296	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
297	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
298	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
299	Q₈×C₄₁	—	2	2	no	—
300	Q₈×C₄₁	—	2	2	no	—
301	Q₈×C₄₁	—	2	2	no	—
302	Q₈×C₄₁	—	8	4	no	—
303	D₄×C₄₁	—	2	4	no	—
304	D₄×C₄₁	—	2	4	no	—
305	D₄×C₄₁	—	2	4	no	—
306	D₄×C₄₁	—	2	2	no	—
307	D₄×C₄₁	—	2	2	no	—
308	D₄×C₄₁	—	2	2	no	—
309	D₄×C₄₁	—	4	4	no	—
310	D₄×C₄₁	—	4	4	no	—
311	D₄×C₄₁	—	4	4	no	—
312	D₄×C₄₁	—	8	4	no	—
313	C₂×C₄×C₄₁	—	2	2	no	—
314	C₂×C₄×C₄₁	—	2	2	no	—
315	C₂×C₄×C₄₁	—	2	2	no	—
316	C₂×C₄×C₄₁	—	2	1	no	—
317	C₂×C₄×C₄₁	—	2	1	no	—
318	C₂×C₄×C₄₁	—	2	2	no	—
319	C₂×C₄×C₄₁	—	2	1	no	—
320	C₂×C₄×C₄₁	—	2	1	no	—
321	C₂×C₄×C₄₁	—	2	2	no	—
322	C₂×C₄×C₄₁	—	2	2	no	—
323	C₂×C₄×C₄₁	—	2	2	no	—
324	C₂×C₄×C₄₁	—	2	4	no	—
325	C₂×C₄×C₄₁	—	2	2	no	—
326	C₂×C₄×C₄₁	—	2	4	no	—
327	C₂×C₄×C₄₁	—	4	8	no	—
328	C₂×C₄×C₄₁	—	4	4	no	—
329	C₂×C₄×C₄₁	—	8	4	no	—
330	C₂×C₄×C₄₁	—	8	2	no	—
331	C₂×C₄×C₄₁	—	8	4	no	—
332	C₂×C₄×C₄₁	—	8	2	no	—
333	C₂×C₄×C₄₁	—	8	4	no	—
334	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
341	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
342	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
343	C₈×C₄₁	—	2	1	no	—
344	C₈×C₄₁	—	2	1	no	—
345	C₈×C₄₁	—	2	2	no	—
346	C₈×C₄₁	—	2	2	no	—
347	C₈×C₄₁	C₂×#41	1	2	yes	—
348	C₈×C₄₁	C₂×#41	1	2	yes	—
349	#61258	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
350	C₂²×C₄₁	—	2	8	no	—
351	C₂²×C₄₁	—	2	1	no	—
352	C₂²×C₄₁	—	2	1	no	—
353	C₂²×C₄₁	—	2	1	no	—
354	C₂²×C₄₁	—	2	1	no	—
355	C₂²×C₄₁	—	2	1	no	—
356	C₂²×C₄₁	—	2	1	no	—
357	C₂²×C₄₁	—	2	2	no	—
358	C₂²×C₄₁	—	2	2	no	—
359	C₂²×C₄₁	—	2	2	no	—
360	C₂²×C₄₁	—	4	2	no	—
361	C₂²×C₄₁	—	4	2	no	—
362	C₂²×C₄₁	—	4	2	no	—
363	C₂²×C₄₁	#547	1	2	yes	—
364	C₂²×C₄₁	#576	1	2	yes	—
365	C₂²×C₄₁	#578	1	2	yes	—
366	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
367	C₄×C₄₁	—	2	1	no	—
368	C₄×C₄₁	—	2	1	no	—
369	C₄×C₄₁	—	2	2	no	—
370	C₄×C₄₁	—	2	2	no	—
371	C₄×C₄₁	—	2	2	no	—
372	C₄×C₄₁	—	4	2	no	—
373	C₄×C₄₁	—	4	4	no	—
374	C₄×C₄₁	—	4	4	no	—
375	C₄×C₄₁	—	4	2	no	—
376	C₄×C₄₁	—	4	2	no	—
377	C₄×C₄₁	#547	1	2	yes	—
378	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
379	C₄×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
380	#3492	C₂×C₄₁	1	2	yes	complemented
381	#3346	C₂×C₄₁	1	4	yes	complemented
382	#3343	C₂×C₄₁	1	4	yes	complemented
383	#3339	C₂×C₄₁	1	2	yes	complemented
384	#3338	C₂×C₄₁	1	2	yes	complemented
385	#3336	C₂×C₄₁	1	2	yes	complemented
386	#3334	C₂×C₄₁	1	2	yes	complemented
387	#3164	C₂×C₄₁	1	1	yes	characteristic, complemented
388	#3098	C₂×C₄₁	1	2	yes	complemented
389	#3092	C₂×C₄₁	1	2	yes	complemented
390	#3083	C₂×C₄₁	1	2	yes	complemented
391	#3061	C₂×C₄₁	1	1	yes	characteristic, complemented
392	#3050	C₂×C₄₁	1	1	yes	characteristic, complemented
393	#2951	C₂×C₄₁	1	1	yes	characteristic, complemented
394	#2929	C₂×C₄₁	1	1	yes	characteristic, complemented
395	#2913	C₂×C₄₁	1	1	yes	characteristic, complemented
396	C₂²×#107	C₂×C₄₁	1	1	yes	characteristic, complemented
397	C₂×C₄₁	—	2	2	no	—
398	C₂×C₄₁	—	2	2	no	—
399	C₂×C₄₁	—	2	2	no	—
400	C₂×C₄₁	—	4	2	no	—
401	C₂×C₄₁	—	8	2	no	—
402	C₂×C₄₁	C₂×#547	1	1	yes	characteristic
403	C₂×C₄₁	C₂×#576	1	1	yes	characteristic
404	C₂×C₄₁	C₂×#578	1	1	yes	characteristic
405	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
406	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic
407	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
408	#554	—	2	2	no	—
409	#554	C₂²×C₄₁	1	4	yes	—
410	#553	—	2	2	no	—
411	#553	C₂²×C₄₁	1	4	yes	—
412	#552	—	2	2	no	—
413	#552	C₂²×C₄₁	1	4	yes	—
414	#547	—	2	2	no	—
415	#547	C₂²×C₄₁	1	4	yes	—
416	#544	C₂²×C₄₁	1	2	yes	—
417	#539	—	2	4	no	—
418	#537	C₂²×C₄₁	1	2	yes	—
419	#525	—	2	4	no	—
420	#525	C₂²×C₄₁	1	2	yes	—
421	#525	C₂²×C₄₁	1	1	yes	characteristic
422	#520	C₂²×C₄₁	1	2	yes	—
423	#520	C₂²×C₄₁	1	2	yes	—
424	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
425	#501	C₂²×C₄₁	1	4	yes	complemented
426	#500	C₂²×C₄₁	1	2	yes	complemented
427	#499	C₂²×C₄₁	1	2	yes	complemented
428	#485	C₂²×C₄₁	1	4	yes	complemented
429	#484	C₂²×C₄₁	1	4	yes	—
430	#484	C₂²×C₄₁	1	4	yes	complemented
431	#483	C₂²×C₄₁	1	4	yes	—
432	#482	C₂²×C₄₁	1	4	yes	complemented
433	#481	C₂²×C₄₁	1	4	yes	—
434	#480	C₂²×C₄₁	1	4	yes	—
435	#480	C₂²×C₄₁	1	4	yes	complemented
436	#479	C₂²×C₄₁	1	4	yes	complemented
437	#478	C₂²×C₄₁	1	4	yes	complemented
438	#477	C₂²×C₄₁	1	4	yes	complemented
439	#474	C₂²×C₄₁	1	4	yes	complemented
440	#468	C₂²×C₄₁	1	4	yes	complemented
441	#467	C₂²×C₄₁	1	1	yes	characteristic
442	#467	C₂²×C₄₁	1	1	yes	characteristic
443	#467	C₂²×C₄₁	1	2	yes	complemented
444	#466	C₂²×C₄₁	1	1	yes	characteristic
445	#466	C₂²×C₄₁	1	1	yes	characteristic
446	#466	C₂²×C₄₁	1	2	yes	complemented
447	#465	C₂²×C₄₁	1	2	yes	—
448	#465	C₂²×C₄₁	1	2	yes	—
449	#440	C₂²×C₄₁	1	4	yes	complemented
450	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
451	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
452	#435	C₂²×C₄₁	1	2	yes	—
453	#435	C₂²×C₄₁	1	2	yes	—
454	C₈×D₄	C₂²×C₄₁	1	2	yes	—
455	C₈×D₄	C₂²×C₄₁	1	2	yes	—
456	#428	C₂²×C₄₁	1	2	yes	—
457	#428	C₂²×C₄₁	1	2	yes	—
458	#428	C₂²×C₄₁	1	4	yes	complemented
459	#427	C₂²×C₄₁	1	1	yes	characteristic
460	#427	C₂²×C₄₁	1	2	yes	complemented
461	C₂×#107	C₂²×C₄₁	1	2	yes	—
462	C₂×#107	C₂²×C₄₁	1	2	yes	—
463	C₂×#107	C₂²×C₄₁	1	2	yes	—
464	C₂×#107	C₂²×C₄₁	1	2	yes	—
465	C₂×#107	C₂²×C₄₁	1	2	yes	—
466	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
467	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
468	C₂×#107	C₂²×C₄₁	1	2	yes	complemented
469	#424	C₂²×C₄₁	1	1	yes	characteristic
470	#417	C₂²×C₄₁	1	2	yes	—
471	#417	C₂²×C₄₁	1	2	yes	—
472	#416	C₂²×C₄₁	1	2	yes	—
473	#408	C₂²×C₄₁	1	1	yes	characteristic
474	#407	C₂²×C₄₁	1	1	yes	characteristic
475	#405	C₂²×C₄₁	1	1	yes	characteristic
476	C₄₁	#61258	1	1	yes	characteristic, direct product factor, Sylow
477	C₂×#41	—	2	4	no	—
478	C₂×#41	C₂³×C₄₁	1	2	yes	—
479	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
480	C₂³×C₄	—	2	2	no	—
481	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
482	#135	—	2	4	no	—
483	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
484	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
485	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
486	#131	—	2	4	no	—
487	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
488	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
489	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
490	C₂²×C₈	—	2	4	no	—
491	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
496	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
497	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
498	C₄⋊Q₈	—	2	2	no	—
499	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
500	#126	—	2	4	no	—
501	#126	—	2	4	no	—
502	#125	—	2	4	no	—
503	#125	—	2	4	no	—
504	#125	—	2	2	no	—
505	#125	C₂³×C₄₁	1	4	yes	—
506	#123	—	2	4	no	—
507	#123	—	2	2	no	—
508	#123	—	2	4	no	—
509	#123	—	2	4	no	—
510	#123	—	2	4	no	—
511	#123	D₄×C₄₁	1	2	yes	—
512	C₂²⋊Q₈	—	2	2	no	—
513	C₂²⋊Q₈	—	2	4	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	—	2	4	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
518	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
519	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
520	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
521	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
522	#121	—	2	4	no	—
523	#121	—	2	4	no	—
524	#121	—	2	2	no	—
525	#121	D₄×C₄₁	1	1	yes	characteristic
526	#121	D₄×C₄₁	1	1	yes	characteristic
527	#121	C₂³×C₄₁	1	2	yes	—
528	#121	C₂³×C₄₁	1	2	yes	—
529	#121	C₂³×C₄₁	1	4	yes	—
530	#120	—	2	2	no	—
531	#120	D₄×C₄₁	1	2	yes	—
532	C₄×Q₈	—	2	2	no	—
533	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
534	C₄×D₄	—	2	4	no	—
535	C₄×D₄	—	2	2	no	—
536	C₄×D₄	—	2	4	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	4	no	—
540	C₄×D₄	—	2	4	no	—
541	C₄×D₄	C₂³×C₄₁	1	4	yes	—
542	C₄×D₄	C₂³×C₄₁	1	2	yes	—
543	C₄×D₄	C₂³×C₄₁	1	2	yes	—
544	#117	—	2	2	no	—
545	#117	—	2	4	no	—
546	#117	C₂³×C₄₁	1	2	yes	—
547	#117	C₂³×C₄₁	1	4	yes	—
548	#117	C₂³×C₄₁	1	1	yes	characteristic
549	C₂×C₄⋊C₄	—	2	2	no	—
550	C₂×C₄⋊C₄	—	2	2	no	—
551	C₂×C₄⋊C₄	—	2	2	no	—
552	C₂×C₄⋊C₄	—	2	2	no	—
553	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
556	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
557	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
558	#107	C₂³×C₄₁	1	2	yes	—
559	#107	C₂³×C₄₁	1	2	yes	—
560	#107	C₂³×C₄₁	1	2	yes	—
561	#107	C₂³×C₄₁	1	2	yes	—
562	#107	C₂³×C₄₁	1	4	yes	—
563	#107	C₂³×C₄₁	1	4	yes	—
564	#107	C₂³×C₄₁	1	1	yes	characteristic
565	#107	C₂³×C₄₁	1	4	yes	—
566	#107	C₂³×C₄₁	1	1	yes	characteristic
567	#107	C₂³×C₄₁	1	4	yes	—
568	#106	C₂³×C₄₁	1	2	yes	—
569	#106	C₂³×C₄₁	1	4	yes	—
570	#106	C₂³×C₄₁	1	4	yes	—
571	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
572	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
573	#103	C₂³×C₄₁	1	2	yes	—
574	#103	C₂³×C₄₁	1	2	yes	—
575	#103	C₂³×C₄₁	1	4	yes	—
576	#103	C₂³×C₄₁	1	4	yes	—
577	#102	C₂³×C₄₁	1	2	yes	—
578	#102	C₂³×C₄₁	1	2	yes	—
579	#102	C₂³×C₄₁	1	4	yes	—
580	#102	C₂³×C₄₁	1	4	yes	—
581	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
582	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
583	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
584	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
585	#97	C₂³×C₄₁	1	2	yes	—
586	C₄×C₈	C₂³×C₄₁	1	2	yes	—
587	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
588	#41	—	2	2	no	—
589	#41	—	2	2	no	—
590	#41	—	2	4	no	—
591	#41	—	2	4	no	—
592	#41	—	8	8	no	—
593	C₂×Q₈	—	2	4	no	—
594	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
595	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
601	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
602	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
603	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
604	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	8	4	no	—
615	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
622	Q₁₆	—	2	2	no	—
623	SD₁₆	—	2	4	no	—
624	D₈	—	2	2	no	—
625	M₁₆	—	2	2	no	—
626	M₁₆	—	2	2	no	—
627	M₁₆	—	2	4	no	—
628	C₂×C₈	—	2	2	no	—
629	C₂×C₈	—	2	2	no	—
630	C₂×C₈	—	2	2	no	—
631	C₂×C₈	—	2	2	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	—	2	4	no	—
634	C₂×C₈	#41×C₄₁	1	4	yes	complemented
635	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
636	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
637	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
638	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
639	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
640	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
654	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
655	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
656	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
657	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
658	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
659	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
660	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
671	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
672	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
673	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
674	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
675	C₄²	—	2	4	no	—
676	C₄²	—	2	4	no	—
677	C₄²	—	2	2	no	—
678	C₄²	C₂⁴×C₄₁	1	2	yes	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
684	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
685	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
686	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
687	Q₈	—	2	2	no	—
688	Q₈	—	2	2	no	—
689	Q₈	—	2	2	no	—
690	Q₈	—	8	4	no	—
691	D₄	—	2	4	no	—
692	D₄	—	2	4	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	2	no	—
697	D₄	—	4	4	no	—
698	D₄	—	4	4	no	—
699	D₄	—	4	4	no	—
700	D₄	—	8	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	4	8	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	8	4	no	—
718	C₂×C₄	—	8	2	no	—
719	C₂×C₄	—	8	4	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
723	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
724	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
726	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
727	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
728	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
729	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
730	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
731	C₈	—	2	1	no	—
732	C₈	—	2	1	no	—
733	C₈	—	2	2	no	—
734	C₈	—	2	2	no	—
735	C₈	C₂×#41×C₄₁	1	2	yes	—
736	C₈	C₂×#41×C₄₁	1	2	yes	—
737	C₂²	—	2	8	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	C₄₁×#547	1	2	yes	—
751	C₂²	C₄₁×#576	1	2	yes	—
752	C₂²	C₄₁×#578	1	2	yes	—
753	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	4	4	no	—
760	C₄	—	4	4	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	C₄₁×#547	1	2	yes	—
765	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
766	C₄	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
767	C₂	—	2	2	no	—
768	C₂	—	2	2	no	—
769	C₂	—	2	2	no	—
770	C₂	—	4	2	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂×C₄₁×#547	1	1	yes	characteristic
773	C₂	C₂×C₄₁×#576	1	1	yes	characteristic
774	C₂	C₂×C₄₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3492	C₂	semidirect
2. C₄₁×#3346	C₂	semidirect
3. C₄₁×#3343	C₂	semidirect
4. C₄₁×#3339	C₂	semidirect
5. C₄₁×#3338	C₂	semidirect
6. C₄₁×#3336	C₂	semidirect
7. C₄₁×#3334	C₂	semidirect
8. C₄₁×#3164	C₂	semidirect
9. C₄₁×#3098	C₂	semidirect
10. C₄₁×#3092	C₂	semidirect
11. C₄₁×#3083	C₂	semidirect
12. C₄₁×#3061	C₂	semidirect
13. C₄₁×#3050	C₂	semidirect
14. C₄₁×#2951	C₂	semidirect
15. C₄₁×#2929	C₂	semidirect
16. C₄₁×#2913	C₂	semidirect
17. C₂²×#107×C₄₁	C₂	semidirect
38. C₄₁×#501	C₂²	semidirect
39. C₄₁×#500	C₂²	semidirect
40. C₄₁×#499	C₂²	semidirect
41. C₄₁×#485	C₂²	semidirect
43. C₄₁×#484	C₂²	semidirect
45. C₄₁×#482	C₂²	semidirect
48. C₄₁×#480	C₂²	semidirect
49. C₄₁×#479	C₂²	semidirect
50. C₄₁×#478	C₂²	semidirect
51. C₄₁×#477	C₂²	semidirect
52. C₄₁×#474	C₂²	semidirect
53. C₄₁×#468	C₂²	semidirect
56. C₄₁×#467	C₂²	semidirect
59. C₄₁×#466	C₂²	semidirect
62. C₄₁×#440	C₂²	semidirect
63. C₄×Q₁₆×C₄₁	C₂²	semidirect
64. C₄×D₈×C₄₁	C₂²	semidirect
71. C₄₁×#428	C₂²	semidirect
73. C₄₁×#427	C₂²	semidirect
81. C₂×#107×C₄₁	C₂²	semidirect
246. C₂×C₈×C₄₁	#41	semidirect
349. #61258	C₄₁	direct (N × H)
380. #3492	C₂×C₄₁	semidirect
381. #3346	C₂×C₄₁	semidirect
382. #3343	C₂×C₄₁	semidirect
383. #3339	C₂×C₄₁	semidirect
384. #3338	C₂×C₄₁	semidirect
385. #3336	C₂×C₄₁	semidirect
386. #3334	C₂×C₄₁	semidirect
387. #3164	C₂×C₄₁	semidirect
388. #3098	C₂×C₄₁	semidirect
389. #3092	C₂×C₄₁	semidirect
390. #3083	C₂×C₄₁	semidirect
391. #3061	C₂×C₄₁	semidirect
392. #3050	C₂×C₄₁	semidirect
393. #2951	C₂×C₄₁	semidirect
394. #2929	C₂×C₄₁	semidirect
395. #2913	C₂×C₄₁	semidirect
396. C₂²×#107	C₂×C₄₁	semidirect
425. #501	C₂²×C₄₁	semidirect
426. #500	C₂²×C₄₁	semidirect
427. #499	C₂²×C₄₁	semidirect
428. #485	C₂²×C₄₁	semidirect
430. #484	C₂²×C₄₁	semidirect
432. #482	C₂²×C₄₁	semidirect
435. #480	C₂²×C₄₁	semidirect
436. #479	C₂²×C₄₁	semidirect
437. #478	C₂²×C₄₁	semidirect
438. #477	C₂²×C₄₁	semidirect
439. #474	C₂²×C₄₁	semidirect
440. #468	C₂²×C₄₁	semidirect
443. #467	C₂²×C₄₁	semidirect
446. #466	C₂²×C₄₁	semidirect
449. #440	C₂²×C₄₁	semidirect
450. C₄×Q₁₆	C₂²×C₄₁	semidirect
451. C₄×D₈	C₂²×C₄₁	semidirect
458. #428	C₂²×C₄₁	semidirect
460. #427	C₂²×C₄₁	semidirect
468. C₂×#107	C₂²×C₄₁	semidirect
476. C₄₁	#61258	direct (N × H)
634. C₂×C₈	#41×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3492	2
C₄₁×#3346	2
C₄₁×#3343	2
C₄₁×#3339	2
C₄₁×#3338	2
C₄₁×#3336	2
C₄₁×#3334	2
C₄₁×#3164	2
C₄₁×#3098	2
C₄₁×#3092	2
C₄₁×#3083	2
C₄₁×#3061	2
C₄₁×#3050	2
C₄₁×#2951	2
C₄₁×#2929	2
C₄₁×#2913	2
C₂²×#107×C₄₁	2
#61258	41

Subgroups — C41×#61258 #23837459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61258 #23837459