Subgroups — C₄₁×#62167 #23838368

Order 10496.

1684 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3559	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3388	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3372	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3350	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3343	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3337	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3320	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3320	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3298	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3260	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3242	C₂	1	2	yes	maximal, complemented
14	C₄₁×#3236	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3126	C₂	1	2	yes	maximal, complemented
16	C₄₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#3082	C₂	1	2	yes	maximal, complemented
18	C₂×C₄₁×#479	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄₁×#563	—	2	1	no	—
21	C₄₁×#562	—	2	1	no	—
22	C₄₁×#557	—	2	1	no	—
23	C₄₁×#557	C₂²	1	1	yes	characteristic
24	C₄₁×#557	C₂²	1	1	yes	characteristic
25	C₄₁×#556	—	2	1	no	—
26	C₄₁×#556	C₂²	1	1	yes	characteristic
27	C₄₁×#554	C₂²	1	2	yes	—
28	C₄₁×#553	C₂²	1	2	yes	—
29	C₄₁×#553	C₂²	1	2	yes	—
30	C₄₁×#552	—	2	2	no	—
31	C₄₁×#552	C₂²	1	2	yes	—
32	D₄×Q₈×C₄₁	C₂²	1	2	yes	—
33	D₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
34	C₄₁×#547	—	2	2	no	—
35	C₄₁×#547	C₂²	1	2	yes	—
36	C₄₁×#544	C₂²	1	2	yes	—
37	C₄₁×#541	—	2	2	no	—
38	C₄₁×#541	C₂²	1	2	yes	—
39	C₄₁×#540	C₂²	1	2	yes	—
40	C₄₁×#539	—	2	2	no	—
41	C₄₁×#539	—	2	1	no	—
42	C₄₁×#537	—	2	1	no	—
43	C₄₁×#533	—	2	1	no	—
44	C₄₁×#533	C₂²	1	1	yes	characteristic
45	C₄₁×#532	C₂²	1	1	yes	characteristic
46	C₄₁×#529	—	2	1	no	—
47	C₄₁×#529	C₂²	1	1	yes	characteristic
48	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
49	C₄₁×#519	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
51	C₄₁×#501	C₂²	1	2	yes	—
52	C₄₁×#501	C₂²	1	2	yes	—
53	C₄₁×#499	C₂²	1	2	yes	—
54	C₄₁×#491	C₂²	1	2	yes	—
55	C₄₁×#491	C₂²	1	2	yes	—
56	C₄₁×#487	C₂²	1	2	yes	—
57	C₄₁×#485	C₂²	1	2	yes	—
58	C₄₁×#485	C₂²	1	2	yes	—
59	C₄₁×#484	C₂²	1	2	yes	—
60	C₄₁×#484	C₂²	1	2	yes	—
61	C₄₁×#483	C₂²	1	2	yes	—
62	C₄₁×#483	C₂²	1	2	yes	—
63	C₄₁×#482	C₂²	1	2	yes	—
64	C₄₁×#482	C₂²	1	2	yes	—
65	C₄₁×#480	C₂²	1	2	yes	—
66	C₄₁×#479	C₂²	1	2	yes	—
67	C₄₁×#479	C₂²	1	2	yes	—
68	C₄₁×#479	C₂²	1	2	yes	—
69	C₄₁×#479	C₂²	1	2	yes	—
70	C₄₁×#479	C₂²	1	2	yes	—
71	C₄₁×#479	C₂²	1	2	yes	—
72	C₄₁×#479	C₂²	1	2	yes	—
73	C₄₁×#479	C₂²	1	2	yes	—
74	C₄₁×#478	C₂²	1	2	yes	—
75	C₄₁×#478	C₂²	1	2	yes	—
76	C₄₁×#477	C₂²	1	1	yes	characteristic
77	C₄₁×#477	C₂²	1	2	yes	—
78	C₄₁×#477	C₂²	1	1	yes	characteristic
79	C₄₁×#476	C₂²	1	2	yes	—
80	C₄₁×#475	C₂²	1	2	yes	—
81	C₄₁×#475	C₂²	1	2	yes	—
82	C₄₁×#468	C₂²	1	2	yes	—
83	C₄₁×#468	C₂²	1	2	yes	—
84	C₄₁×#465	C₂²	1	2	yes	—
85	C₄₁×#465	C₂²	1	2	yes	—
86	C₄₁×#465	C₂²	1	2	yes	—
87	C₄₁×#465	C₂²	1	2	yes	—
88	C₄₁×#461	C₂²	1	2	yes	—
89	C₄₁×#461	C₂²	1	2	yes	—
90	C₄₁×#461	C₂²	1	2	yes	—
91	C₄₁×#460	C₂²	1	1	yes	characteristic
92	C₄₁×#460	C₂²	1	1	yes	characteristic
93	C₄₁×#460	C₂²	1	2	yes	—
94	C₄₁×#448	C₂²	1	2	yes	—
95	C₄₁×#448	C₂²	1	2	yes	—
96	C₄₁×#448	C₂²	1	2	yes	—
97	C₄₁×#446	C₂²	1	2	yes	—
98	C₄₁×#440	C₂²	1	2	yes	—
99	C₄₁×#440	C₂²	1	2	yes	—
100	C₄₁×#440	C₂²	1	2	yes	—
101	C₄₁×#440	C₂²	1	2	yes	—
102	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
103	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
104	C₄₁×#435	C₂²	1	2	yes	—
105	C₄₁×#435	C₂²	1	2	yes	—
106	C₈×D₄×C₄₁	C₂²	1	2	yes	—
107	C₄₁×#433	C₂²	1	2	yes	—
108	C₄₁×#432	C₂²	1	1	yes	characteristic
109	C₄₁×#428	C₂²	1	2	yes	—
110	C₄₁×#427	C₂²	1	2	yes	—
111	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
112	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
113	C₄₁×#424	C₂²	1	2	yes	—
114	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
115	C₄₁×#419	C₂²	1	2	yes	—
116	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
117	C₂×#103×C₄₁	C₂²	1	2	yes	—
118	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
119	C₂×#41×C₄₁	—	2	2	no	—
120	C₂×#41×C₄₁	—	2	1	no	—
121	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
127	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
128	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
131	C₄⋊Q₈×C₄₁	—	2	1	no	—
132	C₄⋊Q₈×C₄₁	—	2	1	no	—
133	C₄⋊Q₈×C₄₁	—	2	2	no	—
134	C₄⋊Q₈×C₄₁	—	2	2	no	—
135	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
139	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
140	#127×C₄₁	C₂³	1	1	yes	characteristic
141	#126×C₄₁	—	2	2	no	—
142	#126×C₄₁	—	2	2	no	—
143	#126×C₄₁	—	2	2	no	—
144	#126×C₄₁	—	2	2	no	—
145	#126×C₄₁	—	2	2	no	—
146	#126×C₄₁	—	2	2	no	—
147	#126×C₄₁	D₄	1	2	yes	—
148	#125×C₄₁	—	2	1	no	—
149	#125×C₄₁	—	2	2	no	—
150	#125×C₄₁	—	2	2	no	—
151	#125×C₄₁	—	2	2	no	—
152	#125×C₄₁	—	2	2	no	—
153	#125×C₄₁	—	2	2	no	—
154	#125×C₄₁	—	2	2	no	—
155	#125×C₄₁	—	2	1	no	—
156	#125×C₄₁	—	2	1	no	—
157	#125×C₄₁	—	2	1	no	—
158	#125×C₄₁	D₄	1	1	yes	characteristic
159	#125×C₄₁	C₂³	1	2	yes	—
160	#125×C₄₁	C₂³	1	2	yes	—
161	#125×C₄₁	C₂³	1	2	yes	—
162	#125×C₄₁	C₂³	1	2	yes	—
163	#124×C₄₁	—	2	1	no	—
164	#124×C₄₁	—	2	1	no	—
165	#124×C₄₁	D₄	1	1	yes	characteristic
166	#123×C₄₁	—	2	2	no	—
167	#123×C₄₁	—	2	2	no	—
168	#123×C₄₁	—	2	2	no	—
169	#123×C₄₁	—	2	2	no	—
170	#123×C₄₁	—	2	2	no	—
171	#123×C₄₁	—	2	2	no	—
172	#123×C₄₁	—	2	2	no	—
173	#123×C₄₁	D₄	1	2	yes	—
174	C₂²⋊Q₈×C₄₁	—	2	2	no	—
175	C₂²⋊Q₈×C₄₁	—	2	1	no	—
176	C₂²⋊Q₈×C₄₁	—	2	2	no	—
177	C₂²⋊Q₈×C₄₁	—	2	2	no	—
178	C₂²⋊Q₈×C₄₁	—	2	2	no	—
179	C₂²⋊Q₈×C₄₁	—	2	2	no	—
180	C₂²⋊Q₈×C₄₁	—	2	2	no	—
181	C₂²⋊Q₈×C₄₁	—	2	2	no	—
182	C₂²⋊Q₈×C₄₁	—	2	2	no	—
183	C₂²⋊Q₈×C₄₁	—	2	2	no	—
184	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
185	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
186	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
187	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
188	#121×C₄₁	—	2	2	no	—
189	#121×C₄₁	—	2	2	no	—
190	#121×C₄₁	—	2	1	no	—
191	#121×C₄₁	—	2	2	no	—
192	#121×C₄₁	—	2	2	no	—
193	#121×C₄₁	D₄	1	1	yes	characteristic
194	#121×C₄₁	C₂³	1	2	yes	—
195	#121×C₄₁	C₂³	1	2	yes	—
196	#121×C₄₁	C₂³	1	2	yes	—
197	C₄×Q₈×C₄₁	—	2	1	no	—
198	C₄×Q₈×C₄₁	—	2	2	no	—
199	C₄×Q₈×C₄₁	—	2	2	no	—
200	C₄×Q₈×C₄₁	—	2	1	no	—
201	C₄×Q₈×C₄₁	—	2	1	no	—
202	C₄×Q₈×C₄₁	—	2	1	no	—
203	C₄×Q₈×C₄₁	—	2	1	no	—
204	C₄×Q₈×C₄₁	—	2	1	no	—
205	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
207	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
208	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
209	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
210	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
211	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
212	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
213	C₄×D₄×C₄₁	—	2	2	no	—
214	C₄×D₄×C₄₁	—	2	1	no	—
215	C₄×D₄×C₄₁	—	2	2	no	—
216	C₄×D₄×C₄₁	—	2	2	no	—
217	C₄×D₄×C₄₁	—	2	1	no	—
218	C₄×D₄×C₄₁	C₂³	1	2	yes	—
219	C₄×D₄×C₄₁	C₂³	1	2	yes	—
220	C₄×D₄×C₄₁	C₂³	1	2	yes	—
221	C₄×D₄×C₄₁	C₂³	1	2	yes	—
222	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
223	#117×C₄₁	—	2	1	no	—
224	#117×C₄₁	—	2	2	no	—
225	#117×C₄₁	—	2	2	no	—
226	#117×C₄₁	—	2	2	no	—
227	#117×C₄₁	C₂³	1	2	yes	—
228	#117×C₄₁	C₂³	1	2	yes	—
229	#117×C₄₁	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
231	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
232	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
233	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
234	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
238	C₂×C₄²×C₄₁	—	2	1	no	—
239	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
240	#107×C₄₁	C₂³	1	2	yes	—
241	#107×C₄₁	C₂³	1	2	yes	—
242	#107×C₄₁	C₂³	1	2	yes	—
243	#107×C₄₁	C₂³	1	2	yes	—
244	#107×C₄₁	C₂³	1	2	yes	—
245	#107×C₄₁	C₂³	1	2	yes	—
246	#106×C₄₁	C₂³	1	2	yes	—
247	#106×C₄₁	C₂³	1	2	yes	—
248	#106×C₄₁	C₂³	1	2	yes	—
249	#106×C₄₁	C₂³	1	2	yes	—
250	#106×C₄₁	C₂³	1	2	yes	—
251	#106×C₄₁	C₂³	1	2	yes	—
252	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
253	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
254	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
255	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
256	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
257	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
258	#103×C₄₁	C₂³	1	2	yes	—
259	#103×C₄₁	C₂³	1	2	yes	—
260	#103×C₄₁	C₂³	1	2	yes	—
261	#103×C₄₁	C₂³	1	2	yes	—
262	#103×C₄₁	C₂³	1	2	yes	—
263	#103×C₄₁	C₂³	1	2	yes	—
264	#103×C₄₁	C₂³	1	2	yes	—
265	#103×C₄₁	C₂³	1	2	yes	—
266	#103×C₄₁	C₂³	1	2	yes	—
267	#103×C₄₁	C₂³	1	2	yes	—
268	#103×C₄₁	C₂³	1	2	yes	—
269	#103×C₄₁	C₂³	1	2	yes	—
270	#102×C₄₁	C₂³	1	2	yes	—
271	#102×C₄₁	C₂³	1	2	yes	—
272	#102×C₄₁	C₂³	1	2	yes	—
273	#102×C₄₁	C₂³	1	2	yes	—
274	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
277	#97×C₄₁	C₂³	1	2	yes	—
278	#97×C₄₁	C₂³	1	2	yes	—
279	C₄×C₈×C₄₁	C₂³	1	2	yes	—
280	#41×C₄₁	—	8	2	no	—
281	#41×C₄₁	—	8	4	no	—
282	C₂×Q₈×C₄₁	—	2	1	no	—
283	C₂×Q₈×C₄₁	—	2	2	no	—
284	C₂×Q₈×C₄₁	—	2	1	no	—
285	C₂×Q₈×C₄₁	—	2	2	no	—
286	C₂×Q₈×C₄₁	—	2	1	no	—
287	C₂×Q₈×C₄₁	—	2	2	no	—
288	C₂×Q₈×C₄₁	—	2	4	no	—
289	C₂×Q₈×C₄₁	—	4	1	no	—
290	C₂×Q₈×C₄₁	—	4	2	no	—
291	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
293	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
294	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
295	C₂×D₄×C₄₁	—	2	2	no	—
296	C₂×D₄×C₄₁	—	2	2	no	—
297	C₂×D₄×C₄₁	—	2	2	no	—
298	C₂×D₄×C₄₁	—	2	1	no	—
299	C₂×D₄×C₄₁	—	2	1	no	—
300	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
301	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
302	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₄₁	—	2	1	no	—
304	C₂²×C₄×C₄₁	—	2	1	no	—
305	C₂²×C₄×C₄₁	—	2	1	no	—
306	C₂²×C₄×C₄₁	—	2	2	no	—
307	C₂²×C₄×C₄₁	—	2	1	no	—
308	C₂²×C₄×C₄₁	—	2	2	no	—
309	C₂²×C₄×C₄₁	—	2	2	no	—
310	C₂²×C₄×C₄₁	—	2	2	no	—
311	C₂²×C₄×C₄₁	—	2	2	no	—
312	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
316	SD₁₆×C₄₁	—	2	4	no	—
317	SD₁₆×C₄₁	—	4	2	no	—
318	SD₁₆×C₄₁	—	4	2	no	—
319	SD₁₆×C₄₁	—	4	2	no	—
320	M₁₆×C₄₁	—	4	2	no	—
321	C₂×C₈×C₄₁	—	4	1	no	—
322	C₂×C₈×C₄₁	—	4	2	no	—
323	C₂×C₈×C₄₁	—	4	1	no	—
324	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
325	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
326	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
327	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
328	C₄⋊C₄×C₄₁	—	2	2	no	—
329	C₄⋊C₄×C₄₁	—	2	1	no	—
330	C₄⋊C₄×C₄₁	—	2	1	no	—
331	C₄⋊C₄×C₄₁	—	2	1	no	—
332	C₄⋊C₄×C₄₁	—	2	1	no	—
333	C₄⋊C₄×C₄₁	—	2	2	no	—
334	C₄⋊C₄×C₄₁	—	2	2	no	—
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	1	no	—
339	C₄⋊C₄×C₄₁	—	2	1	no	—
340	C₄⋊C₄×C₄₁	—	2	2	no	—
341	C₄⋊C₄×C₄₁	—	2	1	no	—
342	C₄⋊C₄×C₄₁	—	2	2	no	—
343	C₄⋊C₄×C₄₁	—	2	2	no	—
344	C₄⋊C₄×C₄₁	—	2	2	no	—
345	C₄⋊C₄×C₄₁	—	2	1	no	—
346	C₄⋊C₄×C₄₁	—	2	2	no	—
347	C₄⋊C₄×C₄₁	—	2	1	no	—
348	C₄⋊C₄×C₄₁	—	2	2	no	—
349	C₄⋊C₄×C₄₁	—	2	1	no	—
350	C₄⋊C₄×C₄₁	—	2	1	no	—
351	C₄⋊C₄×C₄₁	—	2	2	no	—
352	C₄⋊C₄×C₄₁	—	2	2	no	—
353	C₄⋊C₄×C₄₁	—	2	2	no	—
354	C₄⋊C₄×C₄₁	—	2	2	no	—
355	C₄⋊C₄×C₄₁	—	2	2	no	—
356	C₄⋊C₄×C₄₁	—	2	2	no	—
357	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
369	C₂²⋊C₄×C₄₁	—	2	2	no	—
370	C₂²⋊C₄×C₄₁	—	2	2	no	—
371	C₂²⋊C₄×C₄₁	—	2	2	no	—
372	C₂²⋊C₄×C₄₁	—	2	2	no	—
373	C₂²⋊C₄×C₄₁	—	2	2	no	—
374	C₂²⋊C₄×C₄₁	—	2	2	no	—
375	C₂²⋊C₄×C₄₁	—	2	2	no	—
376	C₂²⋊C₄×C₄₁	—	2	2	no	—
377	C₂²⋊C₄×C₄₁	—	2	2	no	—
378	C₂²⋊C₄×C₄₁	—	2	2	no	—
379	C₂²⋊C₄×C₄₁	—	2	2	no	—
380	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
381	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
382	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
383	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
384	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
385	C₄²×C₄₁	—	2	1	no	—
386	C₄²×C₄₁	—	2	1	no	—
387	C₄²×C₄₁	—	2	1	no	—
388	C₄²×C₄₁	—	2	1	no	—
389	C₄²×C₄₁	—	2	2	no	—
390	C₄²×C₄₁	—	2	2	no	—
391	C₄²×C₄₁	—	2	2	no	—
392	C₄²×C₄₁	—	2	2	no	—
393	C₄²×C₄₁	—	2	2	no	—
394	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
395	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₄₁	C₂⁴	1	2	yes	—
397	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
398	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
399	C₂³×C₄₁	—	2	2	no	—
400	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
401	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
402	Q₈×C₄₁	—	2	1	no	—
403	Q₈×C₄₁	—	2	1	no	—
404	Q₈×C₄₁	—	2	2	no	—
405	Q₈×C₄₁	—	2	2	no	—
406	Q₈×C₄₁	—	2	1	no	—
407	Q₈×C₄₁	—	4	1	no	—
408	Q₈×C₄₁	—	4	2	no	—
409	Q₈×C₄₁	—	4	4	no	—
410	Q₈×C₄₁	—	4	2	no	—
411	Q₈×C₄₁	—	8	1	no	—
412	Q₈×C₄₁	—	8	2	no	—
413	Q₈×C₄₁	2₋¹⁺⁴	1	2	yes	—
414	D₄×C₄₁	—	2	4	no	—
415	D₄×C₄₁	—	2	2	no	—
416	D₄×C₄₁	—	2	2	no	—
417	D₄×C₄₁	—	4	1	no	—
418	D₄×C₄₁	—	4	4	no	—
419	D₄×C₄₁	—	8	1	no	—
420	D₄×C₄₁	—	8	1	no	—
421	D₄×C₄₁	—	8	2	no	—
422	D₄×C₄₁	—	8	2	no	—
423	C₂×C₄×C₄₁	—	2	2	no	—
424	C₂×C₄×C₄₁	—	2	1	no	—
425	C₂×C₄×C₄₁	—	2	1	no	—
426	C₂×C₄×C₄₁	—	2	2	no	—
427	C₂×C₄×C₄₁	—	2	1	no	—
428	C₂×C₄×C₄₁	—	2	2	no	—
429	C₂×C₄×C₄₁	—	2	1	no	—
430	C₂×C₄×C₄₁	—	2	2	no	—
431	C₂×C₄×C₄₁	—	2	1	no	—
432	C₂×C₄×C₄₁	—	2	1	no	—
433	C₂×C₄×C₄₁	—	2	2	no	—
434	C₂×C₄×C₄₁	—	2	2	no	—
435	C₂×C₄×C₄₁	—	2	2	no	—
436	C₂×C₄×C₄₁	—	2	2	no	—
437	C₂×C₄×C₄₁	—	4	1	no	—
438	C₂×C₄×C₄₁	—	4	2	no	—
439	C₂×C₄×C₄₁	—	4	4	no	—
440	C₂×C₄×C₄₁	—	4	2	no	—
441	C₂×C₄×C₄₁	—	4	2	no	—
442	C₂×C₄×C₄₁	—	8	2	no	—
443	C₂×C₄×C₄₁	—	8	2	no	—
444	C₂×C₄×C₄₁	—	8	2	no	—
445	C₂×C₄×C₄₁	—	8	1	no	—
446	C₂×C₄×C₄₁	—	8	2	no	—
447	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
451	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
456	C₈×C₄₁	—	2	2	no	—
457	C₈×C₄₁	—	2	2	no	—
458	C₈×C₄₁	—	2	2	no	—
459	C₈×C₄₁	—	2	2	no	—
460	#62167	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₂²×C₄₁	—	2	1	no	—
462	C₂²×C₄₁	—	2	1	no	—
463	C₂²×C₄₁	—	2	2	no	—
464	C₂²×C₄₁	—	2	2	no	—
465	C₂²×C₄₁	—	2	2	no	—
466	C₂²×C₄₁	—	4	2	no	—
467	C₂²×C₄₁	—	4	2	no	—
468	C₂²×C₄₁	—	4	2	no	—
469	C₂²×C₄₁	#577	1	2	yes	—
470	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
471	C₄×C₄₁	—	2	1	no	—
472	C₄×C₄₁	—	2	1	no	—
473	C₄×C₄₁	—	2	2	no	—
474	C₄×C₄₁	—	2	1	no	—
475	C₄×C₄₁	—	2	2	no	—
476	C₄×C₄₁	—	2	2	no	—
477	C₄×C₄₁	—	2	1	no	—
478	C₄×C₄₁	—	2	1	no	—
479	C₄×C₄₁	—	2	2	no	—
480	C₄×C₄₁	—	4	2	no	—
481	C₄×C₄₁	—	4	2	no	—
482	C₄×C₄₁	—	4	1	no	—
483	C₄×C₄₁	—	4	2	no	—
484	C₄×C₄₁	—	4	1	no	—
485	C₄×C₄₁	—	4	1	no	—
486	C₄×C₄₁	—	4	2	no	—
487	C₄×C₄₁	—	4	2	no	—
488	C₄×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
489	C₄×C₄₁	#585	1	1	yes	characteristic
490	#3559	C₂×C₄₁	1	1	yes	characteristic
491	#3523	C₂×C₄₁	1	1	yes	characteristic, complemented
492	#3388	C₂×C₄₁	1	2	yes	complemented
493	#3372	C₂×C₄₁	1	2	yes	complemented
494	#3350	C₂×C₄₁	1	2	yes	complemented
495	#3343	C₂×C₄₁	1	2	yes	complemented
496	#3337	C₂×C₄₁	1	2	yes	complemented
497	#3320	C₂×C₄₁	1	2	yes	complemented
498	#3320	C₂×C₄₁	1	2	yes	complemented
499	#3298	C₂×C₄₁	1	2	yes	complemented
500	#3260	C₂×C₄₁	1	2	yes	complemented
501	#3246	C₂×C₄₁	1	1	yes	characteristic, complemented
502	#3242	C₂×C₄₁	1	2	yes	complemented
503	#3236	C₂×C₄₁	1	1	yes	characteristic, complemented
504	#3126	C₂×C₄₁	1	2	yes	complemented
505	#3112	C₂×C₄₁	1	1	yes	characteristic, complemented
506	#3082	C₂×C₄₁	1	2	yes	complemented
507	C₂×#479	C₂×C₄₁	1	1	yes	characteristic, complemented
508	#2992	C₂×C₄₁	1	1	yes	characteristic, complemented
509	C₂×C₄₁	—	2	2	no	—
510	C₂×C₄₁	—	4	2	no	—
511	C₂×C₄₁	—	8	2	no	—
512	C₂×C₄₁	#3489	1	1	yes	characteristic
513	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
514	C₂×C₄₁	#3586	1	1	yes	characteristic
515	#563	—	2	1	no	—
516	#562	—	2	1	no	—
517	#557	—	2	1	no	—
518	#557	C₂²×C₄₁	1	1	yes	characteristic
519	#557	C₂²×C₄₁	1	1	yes	characteristic
520	#556	—	2	1	no	—
521	#556	C₂²×C₄₁	1	1	yes	characteristic
522	#554	C₂²×C₄₁	1	2	yes	—
523	#553	C₂²×C₄₁	1	2	yes	—
524	#553	C₂²×C₄₁	1	2	yes	—
525	#552	—	2	2	no	—
526	#552	C₂²×C₄₁	1	2	yes	—
527	D₄×Q₈	C₂²×C₄₁	1	2	yes	—
528	D₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
529	#547	—	2	2	no	—
530	#547	C₂²×C₄₁	1	2	yes	—
531	#544	C₂²×C₄₁	1	2	yes	—
532	#541	—	2	2	no	—
533	#541	C₂²×C₄₁	1	2	yes	—
534	#540	C₂²×C₄₁	1	2	yes	—
535	#539	—	2	2	no	—
536	#539	—	2	1	no	—
537	#537	—	2	1	no	—
538	#533	—	2	1	no	—
539	#533	C₂²×C₄₁	1	1	yes	characteristic
540	#532	C₂²×C₄₁	1	1	yes	characteristic
541	#529	—	2	1	no	—
542	#529	C₂²×C₄₁	1	1	yes	characteristic
543	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
544	#519	C₂²×C₄₁	1	2	yes	—
545	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
546	#501	C₂²×C₄₁	1	2	yes	—
547	#501	C₂²×C₄₁	1	2	yes	—
548	#499	C₂²×C₄₁	1	2	yes	—
549	#491	C₂²×C₄₁	1	2	yes	—
550	#491	C₂²×C₄₁	1	2	yes	—
551	#487	C₂²×C₄₁	1	2	yes	—
552	#485	C₂²×C₄₁	1	2	yes	—
553	#485	C₂²×C₄₁	1	2	yes	—
554	#484	C₂²×C₄₁	1	2	yes	—
555	#484	C₂²×C₄₁	1	2	yes	—
556	#483	C₂²×C₄₁	1	2	yes	—
557	#483	C₂²×C₄₁	1	2	yes	—
558	#482	C₂²×C₄₁	1	2	yes	—
559	#482	C₂²×C₄₁	1	2	yes	—
560	#480	C₂²×C₄₁	1	2	yes	—
561	#479	C₂²×C₄₁	1	2	yes	—
562	#479	C₂²×C₄₁	1	2	yes	—
563	#479	C₂²×C₄₁	1	2	yes	—
564	#479	C₂²×C₄₁	1	2	yes	—
565	#479	C₂²×C₄₁	1	2	yes	—
566	#479	C₂²×C₄₁	1	2	yes	—
567	#479	C₂²×C₄₁	1	2	yes	—
568	#479	C₂²×C₄₁	1	2	yes	—
569	#478	C₂²×C₄₁	1	2	yes	—
570	#478	C₂²×C₄₁	1	2	yes	—
571	#477	C₂²×C₄₁	1	1	yes	characteristic
572	#477	C₂²×C₄₁	1	2	yes	—
573	#477	C₂²×C₄₁	1	1	yes	characteristic
574	#476	C₂²×C₄₁	1	2	yes	—
575	#475	C₂²×C₄₁	1	2	yes	—
576	#475	C₂²×C₄₁	1	2	yes	—
577	#468	C₂²×C₄₁	1	2	yes	—
578	#468	C₂²×C₄₁	1	2	yes	—
579	#465	C₂²×C₄₁	1	2	yes	—
580	#465	C₂²×C₄₁	1	2	yes	—
581	#465	C₂²×C₄₁	1	2	yes	—
582	#465	C₂²×C₄₁	1	2	yes	—
583	#461	C₂²×C₄₁	1	2	yes	—
584	#461	C₂²×C₄₁	1	2	yes	—
585	#461	C₂²×C₄₁	1	2	yes	—
586	#460	C₂²×C₄₁	1	1	yes	characteristic
587	#460	C₂²×C₄₁	1	1	yes	characteristic
588	#460	C₂²×C₄₁	1	2	yes	—
589	#448	C₂²×C₄₁	1	2	yes	—
590	#448	C₂²×C₄₁	1	2	yes	—
591	#448	C₂²×C₄₁	1	2	yes	—
592	#446	C₂²×C₄₁	1	2	yes	—
593	#440	C₂²×C₄₁	1	2	yes	—
594	#440	C₂²×C₄₁	1	2	yes	—
595	#440	C₂²×C₄₁	1	2	yes	—
596	#440	C₂²×C₄₁	1	2	yes	—
597	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
598	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
599	#435	C₂²×C₄₁	1	2	yes	—
600	#435	C₂²×C₄₁	1	2	yes	—
601	C₈×D₄	C₂²×C₄₁	1	2	yes	—
602	#433	C₂²×C₄₁	1	2	yes	—
603	#432	C₂²×C₄₁	1	1	yes	characteristic
604	#428	C₂²×C₄₁	1	2	yes	—
605	#427	C₂²×C₄₁	1	2	yes	—
606	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
607	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
608	#424	C₂²×C₄₁	1	2	yes	—
609	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
610	#419	C₂²×C₄₁	1	2	yes	—
611	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
612	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
613	C₂×#103	C₂²×C₄₁	1	2	yes	—
614	C₄₁	#62167	1	1	yes	characteristic, direct product factor, Sylow
615	C₂×#41	—	2	2	no	—
616	C₂×#41	—	2	1	no	—
617	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
618	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
619	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
620	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
621	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
622	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
623	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
624	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
625	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
626	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
627	C₄⋊Q₈	—	2	1	no	—
628	C₄⋊Q₈	—	2	1	no	—
629	C₄⋊Q₈	—	2	2	no	—
630	C₄⋊Q₈	—	2	2	no	—
631	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
632	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
633	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
634	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
635	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
636	#127	C₂³×C₄₁	1	1	yes	characteristic
637	#126	—	2	2	no	—
638	#126	—	2	2	no	—
639	#126	—	2	2	no	—
640	#126	—	2	2	no	—
641	#126	—	2	2	no	—
642	#126	—	2	2	no	—
643	#126	D₄×C₄₁	1	2	yes	—
644	#125	—	2	1	no	—
645	#125	—	2	2	no	—
646	#125	—	2	2	no	—
647	#125	—	2	2	no	—
648	#125	—	2	2	no	—
649	#125	—	2	2	no	—
650	#125	—	2	2	no	—
651	#125	—	2	1	no	—
652	#125	—	2	1	no	—
653	#125	—	2	1	no	—
654	#125	D₄×C₄₁	1	1	yes	characteristic
655	#125	C₂³×C₄₁	1	2	yes	—
656	#125	C₂³×C₄₁	1	2	yes	—
657	#125	C₂³×C₄₁	1	2	yes	—
658	#125	C₂³×C₄₁	1	2	yes	—
659	#124	—	2	1	no	—
660	#124	—	2	1	no	—
661	#124	D₄×C₄₁	1	1	yes	characteristic
662	#123	—	2	2	no	—
663	#123	—	2	2	no	—
664	#123	—	2	2	no	—
665	#123	—	2	2	no	—
666	#123	—	2	2	no	—
667	#123	—	2	2	no	—
668	#123	—	2	2	no	—
669	#123	D₄×C₄₁	1	2	yes	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	1	no	—
672	C₂²⋊Q₈	—	2	2	no	—
673	C₂²⋊Q₈	—	2	2	no	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
681	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
682	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
683	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
684	#121	—	2	2	no	—
685	#121	—	2	2	no	—
686	#121	—	2	1	no	—
687	#121	—	2	2	no	—
688	#121	—	2	2	no	—
689	#121	D₄×C₄₁	1	1	yes	characteristic
690	#121	C₂³×C₄₁	1	2	yes	—
691	#121	C₂³×C₄₁	1	2	yes	—
692	#121	C₂³×C₄₁	1	2	yes	—
693	C₄×Q₈	—	2	1	no	—
694	C₄×Q₈	—	2	2	no	—
695	C₄×Q₈	—	2	2	no	—
696	C₄×Q₈	—	2	1	no	—
697	C₄×Q₈	—	2	1	no	—
698	C₄×Q₈	—	2	1	no	—
699	C₄×Q₈	—	2	1	no	—
700	C₄×Q₈	—	2	1	no	—
701	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
702	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
703	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
704	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
705	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
706	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
707	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
708	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
709	C₄×D₄	—	2	2	no	—
710	C₄×D₄	—	2	1	no	—
711	C₄×D₄	—	2	2	no	—
712	C₄×D₄	—	2	2	no	—
713	C₄×D₄	—	2	1	no	—
714	C₄×D₄	C₂³×C₄₁	1	2	yes	—
715	C₄×D₄	C₂³×C₄₁	1	2	yes	—
716	C₄×D₄	C₂³×C₄₁	1	2	yes	—
717	C₄×D₄	C₂³×C₄₁	1	2	yes	—
718	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
719	#117	—	2	1	no	—
720	#117	—	2	2	no	—
721	#117	—	2	2	no	—
722	#117	—	2	2	no	—
723	#117	C₂³×C₄₁	1	2	yes	—
724	#117	C₂³×C₄₁	1	2	yes	—
725	#117	C₂³×C₄₁	1	2	yes	—
726	C₂×C₄⋊C₄	—	2	1	no	—
727	C₂×C₄⋊C₄	—	2	1	no	—
728	C₂×C₄⋊C₄	—	2	1	no	—
729	C₂×C₄⋊C₄	—	2	2	no	—
730	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
731	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
734	C₂×C₄²	—	2	1	no	—
735	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
736	#107	C₂³×C₄₁	1	2	yes	—
737	#107	C₂³×C₄₁	1	2	yes	—
738	#107	C₂³×C₄₁	1	2	yes	—
739	#107	C₂³×C₄₁	1	2	yes	—
740	#107	C₂³×C₄₁	1	2	yes	—
741	#107	C₂³×C₄₁	1	2	yes	—
742	#106	C₂³×C₄₁	1	2	yes	—
743	#106	C₂³×C₄₁	1	2	yes	—
744	#106	C₂³×C₄₁	1	2	yes	—
745	#106	C₂³×C₄₁	1	2	yes	—
746	#106	C₂³×C₄₁	1	2	yes	—
747	#106	C₂³×C₄₁	1	2	yes	—
748	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
749	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
750	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
751	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
752	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
753	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
754	#103	C₂³×C₄₁	1	2	yes	—
755	#103	C₂³×C₄₁	1	2	yes	—
756	#103	C₂³×C₄₁	1	2	yes	—
757	#103	C₂³×C₄₁	1	2	yes	—
758	#103	C₂³×C₄₁	1	2	yes	—
759	#103	C₂³×C₄₁	1	2	yes	—
760	#103	C₂³×C₄₁	1	2	yes	—
761	#103	C₂³×C₄₁	1	2	yes	—
762	#103	C₂³×C₄₁	1	2	yes	—
763	#103	C₂³×C₄₁	1	2	yes	—
764	#103	C₂³×C₄₁	1	2	yes	—
765	#103	C₂³×C₄₁	1	2	yes	—
766	#102	C₂³×C₄₁	1	2	yes	—
767	#102	C₂³×C₄₁	1	2	yes	—
768	#102	C₂³×C₄₁	1	2	yes	—
769	#102	C₂³×C₄₁	1	2	yes	—
770	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
771	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
772	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
773	#97	C₂³×C₄₁	1	2	yes	—
774	#97	C₂³×C₄₁	1	2	yes	—
775	C₄×C₈	C₂³×C₄₁	1	2	yes	—
776	#41	—	8	2	no	—
777	#41	—	8	4	no	—
778	C₂×Q₈	—	2	1	no	—
779	C₂×Q₈	—	2	2	no	—
780	C₂×Q₈	—	2	1	no	—
781	C₂×Q₈	—	2	2	no	—
782	C₂×Q₈	—	2	1	no	—
783	C₂×Q₈	—	2	2	no	—
784	C₂×Q₈	—	2	4	no	—
785	C₂×Q₈	—	4	1	no	—
786	C₂×Q₈	—	4	2	no	—
787	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
788	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
789	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
790	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
797	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
798	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
799	C₂²×C₄	—	2	1	no	—
800	C₂²×C₄	—	2	1	no	—
801	C₂²×C₄	—	2	1	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
809	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
812	SD₁₆	—	2	4	no	—
813	SD₁₆	—	4	2	no	—
814	SD₁₆	—	4	2	no	—
815	SD₁₆	—	4	2	no	—
816	M₁₆	—	4	2	no	—
817	C₂×C₈	—	4	1	no	—
818	C₂×C₈	—	4	2	no	—
819	C₂×C₈	—	4	1	no	—
820	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
821	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
822	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
823	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	1	no	—
828	C₄⋊C₄	—	2	1	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	1	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	1	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
854	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
855	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
856	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
857	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
858	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
859	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
860	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
861	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
862	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
863	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
864	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
877	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
878	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
879	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
880	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
881	C₄²	—	2	1	no	—
882	C₄²	—	2	1	no	—
883	C₄²	—	2	1	no	—
884	C₄²	—	2	1	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	2	no	—
887	C₄²	—	2	2	no	—
888	C₄²	—	2	2	no	—
889	C₄²	—	2	2	no	—
890	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
891	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
892	C₄²	C₂⁴×C₄₁	1	2	yes	—
893	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
894	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
895	C₂³	—	2	2	no	—
896	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
897	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
898	Q₈	—	2	1	no	—
899	Q₈	—	2	1	no	—
900	Q₈	—	2	2	no	—
901	Q₈	—	2	2	no	—
902	Q₈	—	2	1	no	—
903	Q₈	—	4	1	no	—
904	Q₈	—	4	2	no	—
905	Q₈	—	4	4	no	—
906	Q₈	—	4	2	no	—
907	Q₈	—	8	1	no	—
908	Q₈	—	8	2	no	—
909	Q₈	2₋¹⁺⁴×C₄₁	1	2	yes	—
910	D₄	—	2	4	no	—
911	D₄	—	2	2	no	—
912	D₄	—	2	2	no	—
913	D₄	—	4	1	no	—
914	D₄	—	4	4	no	—
915	D₄	—	8	1	no	—
916	D₄	—	8	1	no	—
917	D₄	—	8	2	no	—
918	D₄	—	8	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	4	2	no	—
935	C₂×C₄	—	4	4	no	—
936	C₂×C₄	—	4	2	no	—
937	C₂×C₄	—	4	2	no	—
938	C₂×C₄	—	8	2	no	—
939	C₂×C₄	—	8	2	no	—
940	C₂×C₄	—	8	2	no	—
941	C₂×C₄	—	8	2	no	—
942	C₂×C₄	—	8	1	no	—
943	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
944	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
945	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
946	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
947	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
948	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
949	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
950	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
951	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
952	C₈	—	2	2	no	—
953	C₈	—	2	2	no	—
954	C₈	—	2	2	no	—
955	C₈	—	2	2	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	C₄₁×#577	1	2	yes	—
965	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	1	no	—
970	C₄	—	2	1	no	—
971	C₄	—	2	2	no	—
972	C₄	—	2	1	no	—
973	C₄	—	2	2	no	—
974	C₄	—	2	2	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	1	no	—
977	C₄	—	4	1	no	—
978	C₄	—	4	2	no	—
979	C₄	—	4	2	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	1	no	—
982	C₄	—	4	2	no	—
983	C₄	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
984	C₄	C₄₁×#585	1	1	yes	characteristic
985	C₂	—	2	2	no	—
986	C₂	—	4	2	no	—
987	C₂	—	8	2	no	—
988	C₂	C₄₁×#3489	1	1	yes	characteristic
989	C₂	C₂×C₄₁×#577	1	1	yes	characteristic
990	C₂	C₄₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₄₁×#3559	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#3523	C₂	semidirect
3. C₄₁×#3388	C₂	semidirect
4. C₄₁×#3372	C₂	semidirect
5. C₄₁×#3350	C₂	semidirect
6. C₄₁×#3343	C₂	semidirect
7. C₄₁×#3337	C₂	semidirect
8. C₄₁×#3320	C₂	semidirect
9. C₄₁×#3320	C₂	semidirect
10. C₄₁×#3298	C₂	semidirect
11. C₄₁×#3260	C₂	semidirect
12. C₄₁×#3246	C₂	semidirect
13. C₄₁×#3242	C₂	semidirect
14. C₄₁×#3236	C₂	semidirect
15. C₄₁×#3126	C₂	semidirect
16. C₄₁×#3112	C₂	semidirect
17. C₄₁×#3082	C₂	semidirect
18. C₂×C₄₁×#479	C₂	semidirect
19. C₄₁×#2992	C₂	semidirect
460. #62167	C₄₁	direct (N × H)
491. #3523	C₂×C₄₁	semidirect
492. #3388	C₂×C₄₁	semidirect
493. #3372	C₂×C₄₁	semidirect
494. #3350	C₂×C₄₁	semidirect
495. #3343	C₂×C₄₁	semidirect
496. #3337	C₂×C₄₁	semidirect
497. #3320	C₂×C₄₁	semidirect
498. #3320	C₂×C₄₁	semidirect
499. #3298	C₂×C₄₁	semidirect
500. #3260	C₂×C₄₁	semidirect
501. #3246	C₂×C₄₁	semidirect
502. #3242	C₂×C₄₁	semidirect
503. #3236	C₂×C₄₁	semidirect
504. #3126	C₂×C₄₁	semidirect
505. #3112	C₂×C₄₁	semidirect
506. #3082	C₂×C₄₁	semidirect
507. C₂×#479	C₂×C₄₁	semidirect
508. #2992	C₂×C₄₁	semidirect
614. C₄₁	#62167	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×#3559	2
C₄₁×#3523	2
C₄₁×#3388	2
C₄₁×#3372	2
C₄₁×#3350	2
C₄₁×#3343	2
C₄₁×#3337	2
C₄₁×#3320	2
C₄₁×#3298	2
C₄₁×#3260	2
C₄₁×#3246	2
C₄₁×#3242	2
C₄₁×#3236	2
C₄₁×#3126	2
C₄₁×#3112	2
C₄₁×#3082	2
C₂×C₄₁×#479	2
C₄₁×#2992	2
#62167	41

Subgroups — C41×#62167 #23838368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#62167 #23838368