Subgroups — C₄₁×#61922 #23838123

Order 10496.

1640 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3402	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#3398	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#3395	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#3377	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3374	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3363	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3360	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3225	C₂	1	2	yes	maximal
16	C₄₁×#3223	C₂	1	2	yes	maximal, complemented
17	C₄₁×#3218	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄₁×#3209	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#3127	C₂	1	2	yes	maximal, complemented
20	C₄₁×#3121	C₂	1	2	yes	maximal, complemented
21	C₄₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄₁×#3102	C₂	1	1	yes	maximal, characteristic
23	C₄₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄₁×#563	—	2	2	no	—
25	Q₈²×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#557	C₂²	1	1	yes	characteristic
27	C₄₁×#557	C₂²	1	1	yes	characteristic
28	C₄₁×#557	C₂²	1	1	yes	characteristic
29	C₄₁×#557	C₂²	1	2	yes	—
30	C₄₁×#557	C₂²	1	2	yes	—
31	C₄₁×#556	—	2	1	no	—
32	C₄₁×#556	C₂²	1	1	yes	characteristic
33	C₄₁×#556	C₂²	1	2	yes	—
34	C₄₁×#556	C₂²	1	1	yes	characteristic
35	C₄₁×#556	C₂²	1	1	yes	characteristic
36	C₄₁×#556	C₂²	1	2	yes	—
37	C₄₁×#554	C₂²	1	1	yes	characteristic
38	C₄₁×#552	—	2	1	no	—
39	C₄₁×#552	—	2	1	no	—
40	C₄₁×#552	—	2	1	no	—
41	C₄₁×#552	—	2	2	no	—
42	C₄₁×#544	—	2	1	no	—
43	C₄₁×#542	C₂²	1	2	yes	—
44	C₄₁×#541	—	2	1	no	—
45	C₄₁×#541	—	2	2	no	—
46	C₄₁×#541	—	2	2	no	—
47	C₄₁×#541	C₂²	1	2	yes	—
48	C₄₁×#536	C₂²	1	2	yes	—
49	C₄₁×#533	—	2	1	no	—
50	C₄₁×#533	—	2	1	no	—
51	C₄₁×#533	C₂²	1	1	yes	characteristic
52	C₄₁×#533	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
54	C₄₁×#529	C₂²	1	1	yes	characteristic
55	C₄₁×#519	C₂²	1	2	yes	—
56	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
57	C₄₁×#497	C₂²	1	2	yes	—
58	C₄₁×#497	C₂²	1	2	yes	—
59	C₄₁×#497	C₂²	1	2	yes	—
60	C₄₁×#495	C₂²	1	2	yes	—
61	C₄₁×#494	C₂²	1	1	yes	characteristic
62	C₄₁×#494	C₂²	1	2	yes	—
63	C₄₁×#494	C₂²	1	1	yes	characteristic
64	C₄₁×#491	C₂²	1	2	yes	—
65	C₄₁×#491	C₂²	1	2	yes	—
66	C₄₁×#489	C₂²	1	2	yes	—
67	C₄₁×#488	C₂²	1	2	yes	—
68	C₄₁×#487	C₂²	1	1	yes	characteristic
69	C₄₁×#487	C₂²	1	2	yes	—
70	C₄₁×#487	C₂²	1	1	yes	characteristic
71	C₄₁×#485	C₂²	1	1	yes	characteristic
72	C₄₁×#485	C₂²	1	2	yes	—
73	C₄₁×#482	C₂²	1	1	yes	characteristic
74	C₄₁×#479	C₂²	1	1	yes	characteristic
75	C₄₁×#479	C₂²	1	2	yes	—
76	C₄₁×#479	C₂²	1	2	yes	—
77	C₄₁×#478	C₂²	1	1	yes	characteristic
78	C₄₁×#477	C₂²	1	1	yes	characteristic
79	C₄₁×#477	C₂²	1	2	yes	—
80	C₄₁×#476	C₂²	1	1	yes	characteristic
81	C₄₁×#475	C₂²	1	2	yes	—
82	C₄₁×#464	C₂²	1	1	yes	characteristic
83	C₄₁×#464	C₂²	1	2	yes	—
84	C₄₁×#464	C₂²	1	2	yes	—
85	C₄₁×#464	C₂²	1	2	yes	—
86	C₄₁×#464	C₂²	1	2	yes	—
87	C₄₁×#464	C₂²	1	2	yes	—
88	C₄₁×#463	C₂²	1	1	yes	characteristic
89	C₄₁×#463	C₂²	1	2	yes	—
90	C₄₁×#462	C₂²	1	1	yes	characteristic
91	C₄₁×#462	C₂²	1	2	yes	—
92	C₄₁×#462	C₂²	1	1	yes	characteristic
93	C₄₁×#462	C₂²	1	1	yes	characteristic
94	C₄₁×#462	C₂²	1	2	yes	—
95	C₄₁×#462	C₂²	1	2	yes	—
96	C₄₁×#462	C₂²	1	2	yes	—
97	C₄₁×#462	C₂²	1	2	yes	—
98	C₄₁×#462	C₂²	1	2	yes	—
99	C₄₁×#462	C₂²	1	2	yes	—
100	C₄₁×#461	C₂²	1	1	yes	characteristic
101	C₄₁×#461	C₂²	1	1	yes	characteristic
102	C₄₁×#461	C₂²	1	1	yes	characteristic
103	C₄₁×#461	C₂²	1	2	yes	—
104	C₄₁×#452	C₂²	1	1	yes	characteristic
105	C₄₁×#452	C₂²	1	2	yes	—
106	C₄₁×#451	C₂²	1	2	yes	—
107	C₄₁×#451	C₂²	1	2	yes	—
108	C₄₁×#451	C₂²	1	2	yes	—
109	C₄₁×#449	C₂²	1	1	yes	characteristic
110	C₄₁×#448	C₂²	1	2	yes	—
111	C₄₁×#446	C₂²	1	1	yes	characteristic
112	C₄₁×#446	C₂²	1	1	yes	characteristic
113	C₄₁×#446	C₂²	1	2	yes	—
114	C₄₁×#446	C₂²	1	2	yes	—
115	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
117	C₄₁×#441	C₂²	1	2	yes	—
118	C₄₁×#441	C₂²	1	2	yes	—
119	C₄₁×#441	C₂²	1	2	yes	—
120	C₄₁×#441	C₂²	1	2	yes	—
121	C₄₁×#440	C₂²	1	2	yes	—
122	C₄₁×#440	C₂²	1	2	yes	—
123	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
124	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	—
126	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
129	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
130	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
131	C₄₁×#433	C₂²	1	2	yes	—
132	C₄₁×#433	C₂²	1	2	yes	—
133	C₄₁×#432	C₂²	1	1	yes	characteristic
134	C₄₁×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
137	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
138	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
139	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
150	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈×C₄₁	—	2	2	no	—
152	C₄⋊Q₈×C₄₁	—	2	2	no	—
153	C₄⋊Q₈×C₄₁	—	2	1	no	—
154	C₄⋊Q₈×C₄₁	—	2	1	no	—
155	C₄⋊Q₈×C₄₁	—	2	1	no	—
156	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
157	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
158	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
164	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
167	#126×C₄₁	—	2	2	no	—
168	#126×C₄₁	—	2	2	no	—
169	#126×C₄₁	—	2	2	no	—
170	#126×C₄₁	—	2	2	no	—
171	#126×C₄₁	—	2	2	no	—
172	#126×C₄₁	—	2	2	no	—
173	#126×C₄₁	—	2	2	no	—
174	#126×C₄₁	—	2	2	no	—
175	#126×C₄₁	—	2	2	no	—
176	#126×C₄₁	—	2	2	no	—
177	#126×C₄₁	—	2	1	no	—
178	#125×C₄₁	—	2	1	no	—
179	#125×C₄₁	—	2	1	no	—
180	#125×C₄₁	—	2	2	no	—
181	#125×C₄₁	—	2	2	no	—
182	#125×C₄₁	—	2	2	no	—
183	#125×C₄₁	—	2	2	no	—
184	#125×C₄₁	—	2	2	no	—
185	#125×C₄₁	—	2	2	no	—
186	#125×C₄₁	—	2	2	no	—
187	#125×C₄₁	—	2	2	no	—
188	#125×C₄₁	—	2	2	no	—
189	#125×C₄₁	—	2	2	no	—
190	#125×C₄₁	—	2	1	no	—
191	#125×C₄₁	—	2	1	no	—
192	#125×C₄₁	D₄	1	2	yes	—
193	#125×C₄₁	C₂³	1	1	yes	characteristic
194	#125×C₄₁	C₂³	1	2	yes	—
195	#124×C₄₁	—	2	2	no	—
196	#124×C₄₁	C₂³	1	1	yes	characteristic
197	#124×C₄₁	C₂³	1	2	yes	—
198	#124×C₄₁	C₂³	1	2	yes	—
199	#124×C₄₁	C₂³	1	2	yes	—
200	#123×C₄₁	—	2	1	no	—
201	#123×C₄₁	—	2	2	no	—
202	#123×C₄₁	—	2	2	no	—
203	#123×C₄₁	—	2	2	no	—
204	C₂²⋊Q₈×C₄₁	—	2	1	no	—
205	C₂²⋊Q₈×C₄₁	—	2	1	no	—
206	C₂²⋊Q₈×C₄₁	—	2	2	no	—
207	C₂²⋊Q₈×C₄₁	—	2	1	no	—
208	C₂²⋊Q₈×C₄₁	—	2	1	no	—
209	C₂²⋊Q₈×C₄₁	—	2	2	no	—
210	C₂²⋊Q₈×C₄₁	—	2	1	no	—
211	C₂²⋊Q₈×C₄₁	—	2	2	no	—
212	C₂²⋊Q₈×C₄₁	—	2	2	no	—
213	C₂²⋊Q₈×C₄₁	—	2	2	no	—
214	C₂²⋊Q₈×C₄₁	—	2	2	no	—
215	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
216	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
217	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
218	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
219	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
220	#121×C₄₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₄₁	—	2	1	no	—
222	C₄×Q₈×C₄₁	—	2	1	no	—
223	C₄×Q₈×C₄₁	—	2	2	no	—
224	C₄×Q₈×C₄₁	—	2	1	no	—
225	C₄×Q₈×C₄₁	—	2	1	no	—
226	C₄×Q₈×C₄₁	—	2	2	no	—
227	C₄×Q₈×C₄₁	—	2	2	no	—
228	C₄×Q₈×C₄₁	—	2	2	no	—
229	C₄×Q₈×C₄₁	—	2	1	no	—
230	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
233	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
234	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
235	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
236	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
238	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
239	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
240	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
241	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
243	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₄₁	—	2	1	no	—
245	C₄×D₄×C₄₁	—	2	1	no	—
246	C₄×D₄×C₄₁	—	2	1	no	—
247	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₄₁	C₂³	1	2	yes	—
251	#117×C₄₁	—	2	1	no	—
252	#117×C₄₁	—	2	1	no	—
253	#117×C₄₁	—	2	1	no	—
254	#117×C₄₁	—	2	2	no	—
255	#117×C₄₁	—	2	2	no	—
256	#117×C₄₁	—	2	1	no	—
257	#117×C₄₁	—	2	2	no	—
258	#117×C₄₁	—	2	2	no	—
259	#117×C₄₁	—	2	1	no	—
260	#117×C₄₁	—	2	1	no	—
261	#117×C₄₁	C₂³	1	1	yes	characteristic
262	#117×C₄₁	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
264	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
265	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
266	C₂×C₄²×C₄₁	—	2	1	no	—
267	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
268	#107×C₄₁	C₂³	1	1	yes	characteristic
269	#107×C₄₁	C₂³	1	1	yes	characteristic
270	#107×C₄₁	C₂³	1	2	yes	—
271	#106×C₄₁	C₂³	1	1	yes	characteristic
272	#106×C₄₁	C₂³	1	2	yes	—
273	#106×C₄₁	C₂³	1	1	yes	characteristic
274	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
279	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
282	#103×C₄₁	C₂³	1	1	yes	characteristic
283	#103×C₄₁	C₂³	1	2	yes	—
284	#103×C₄₁	C₂³	1	1	yes	characteristic
285	#103×C₄₁	C₂³	1	1	yes	characteristic
286	#103×C₄₁	C₂³	1	2	yes	—
287	#103×C₄₁	C₂³	1	2	yes	—
288	#103×C₄₁	C₂³	1	2	yes	—
289	#103×C₄₁	C₂³	1	1	yes	characteristic
290	#103×C₄₁	C₂³	1	2	yes	—
291	#103×C₄₁	C₂³	1	2	yes	—
292	#103×C₄₁	C₂³	1	2	yes	—
293	#103×C₄₁	C₂³	1	2	yes	—
294	#103×C₄₁	C₂³	1	2	yes	—
295	#103×C₄₁	C₂³	1	2	yes	—
296	#103×C₄₁	C₂³	1	2	yes	—
297	#102×C₄₁	C₂³	1	1	yes	characteristic
298	#102×C₄₁	C₂³	1	1	yes	characteristic
299	#102×C₄₁	C₂³	1	1	yes	characteristic
300	#102×C₄₁	C₂³	1	1	yes	characteristic
301	#102×C₄₁	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
305	#97×C₄₁	C₂³	1	2	yes	—
306	#97×C₄₁	C₂³	1	2	yes	—
307	#97×C₄₁	C₂³	1	2	yes	—
308	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₄₁	C₂³	1	2	yes	—
311	C₄×C₈×C₄₁	C₂³	1	2	yes	—
312	#41×C₄₁	—	4	1	no	—
313	#41×C₄₁	—	4	1	no	—
314	C₂×Q₈×C₄₁	—	2	2	no	—
315	C₂×Q₈×C₄₁	—	2	1	no	—
316	C₂×Q₈×C₄₁	—	2	2	no	—
317	C₂×Q₈×C₄₁	—	4	2	no	—
318	C₂×Q₈×C₄₁	—	4	2	no	—
319	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
320	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
322	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
323	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
324	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
327	C₂×D₄×C₄₁	—	2	1	no	—
328	C₂×D₄×C₄₁	—	2	1	no	—
329	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₄₁	—	2	2	no	—
332	C₂²×C₄×C₄₁	—	2	1	no	—
333	C₂²×C₄×C₄₁	—	2	1	no	—
334	C₂²×C₄×C₄₁	—	2	1	no	—
335	C₂²×C₄×C₄₁	—	2	1	no	—
336	C₂²×C₄×C₄₁	—	2	2	no	—
337	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
338	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
340	Q₁₆×C₄₁	—	4	2	no	—
341	Q₁₆×C₄₁	—	4	2	no	—
342	Q₁₆×C₄₁	—	4	2	no	—
343	Q₁₆×C₄₁	—	4	2	no	—
344	Q₁₆×C₄₁	—	4	2	no	—
345	Q₁₆×C₄₁	—	4	2	no	—
346	Q₁₆×C₄₁	—	4	2	no	—
347	Q₁₆×C₄₁	—	4	1	no	—
348	SD₁₆×C₄₁	—	4	2	no	—
349	SD₁₆×C₄₁	—	4	2	no	—
350	SD₁₆×C₄₁	—	4	2	no	—
351	SD₁₆×C₄₁	—	4	1	no	—
352	SD₁₆×C₄₁	—	4	1	no	—
353	D₈×C₄₁	—	4	1	no	—
354	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
359	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₄₁	—	2	2	no	—
361	C₄⋊C₄×C₄₁	—	2	1	no	—
362	C₄⋊C₄×C₄₁	—	2	1	no	—
363	C₄⋊C₄×C₄₁	—	2	1	no	—
364	C₄⋊C₄×C₄₁	—	2	2	no	—
365	C₄⋊C₄×C₄₁	—	2	2	no	—
366	C₄⋊C₄×C₄₁	—	2	1	no	—
367	C₄⋊C₄×C₄₁	—	2	1	no	—
368	C₄⋊C₄×C₄₁	—	2	1	no	—
369	C₄⋊C₄×C₄₁	—	2	1	no	—
370	C₄⋊C₄×C₄₁	—	2	1	no	—
371	C₄⋊C₄×C₄₁	—	2	2	no	—
372	C₄⋊C₄×C₄₁	—	2	2	no	—
373	C₄⋊C₄×C₄₁	—	2	2	no	—
374	C₄⋊C₄×C₄₁	—	2	2	no	—
375	C₄⋊C₄×C₄₁	—	2	2	no	—
376	C₄⋊C₄×C₄₁	—	2	1	no	—
377	C₄⋊C₄×C₄₁	—	2	1	no	—
378	C₄⋊C₄×C₄₁	—	2	1	no	—
379	C₄⋊C₄×C₄₁	—	2	2	no	—
380	C₄⋊C₄×C₄₁	—	2	2	no	—
381	C₄⋊C₄×C₄₁	—	2	2	no	—
382	C₄⋊C₄×C₄₁	—	2	2	no	—
383	C₄⋊C₄×C₄₁	—	2	2	no	—
384	C₄⋊C₄×C₄₁	—	2	2	no	—
385	C₄⋊C₄×C₄₁	—	2	1	no	—
386	C₄⋊C₄×C₄₁	—	2	2	no	—
387	C₄⋊C₄×C₄₁	—	2	2	no	—
388	C₄⋊C₄×C₄₁	—	2	2	no	—
389	C₄⋊C₄×C₄₁	—	2	2	no	—
390	C₄⋊C₄×C₄₁	—	2	2	no	—
391	C₄⋊C₄×C₄₁	—	2	2	no	—
392	C₄⋊C₄×C₄₁	—	2	1	no	—
393	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
407	C₂²⋊C₄×C₄₁	—	2	1	no	—
408	C₂²⋊C₄×C₄₁	—	2	2	no	—
409	C₂²⋊C₄×C₄₁	—	2	1	no	—
410	C₂²⋊C₄×C₄₁	—	2	1	no	—
411	C₂²⋊C₄×C₄₁	—	2	1	no	—
412	C₂²⋊C₄×C₄₁	—	2	1	no	—
413	C₂²⋊C₄×C₄₁	—	2	1	no	—
414	C₂²⋊C₄×C₄₁	—	2	1	no	—
415	C₂²⋊C₄×C₄₁	—	2	2	no	—
416	C₂²⋊C₄×C₄₁	—	2	2	no	—
417	C₂²⋊C₄×C₄₁	—	2	2	no	—
418	C₂²⋊C₄×C₄₁	—	2	2	no	—
419	C₂²⋊C₄×C₄₁	—	2	2	no	—
420	C₂²⋊C₄×C₄₁	—	2	2	no	—
421	C₂²⋊C₄×C₄₁	—	2	1	no	—
422	C₂²⋊C₄×C₄₁	—	2	2	no	—
423	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
425	C₄²×C₄₁	—	2	1	no	—
426	C₄²×C₄₁	—	2	1	no	—
427	C₄²×C₄₁	—	2	1	no	—
428	C₄²×C₄₁	—	2	2	no	—
429	C₄²×C₄₁	—	2	2	no	—
430	C₄²×C₄₁	—	2	2	no	—
431	C₄²×C₄₁	—	2	2	no	—
432	C₄²×C₄₁	—	2	2	no	—
433	C₄²×C₄₁	—	2	1	no	—
434	C₄²×C₄₁	—	2	2	no	—
435	C₄²×C₄₁	—	2	2	no	—
436	C₄²×C₄₁	—	2	2	no	—
437	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
440	C₄²×C₄₁	C₂⁴	1	2	yes	—
441	C₄²×C₄₁	C₂⁴	1	2	yes	—
442	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
443	C₂³×C₄₁	—	2	1	no	—
444	C₂³×C₄₁	—	2	1	no	—
445	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
446	Q₈×C₄₁	—	2	2	no	—
447	Q₈×C₄₁	—	2	2	no	—
448	Q₈×C₄₁	—	2	1	no	—
449	Q₈×C₄₁	—	2	2	no	—
450	Q₈×C₄₁	—	2	2	no	—
451	Q₈×C₄₁	—	2	2	no	—
452	Q₈×C₄₁	—	2	1	no	—
453	Q₈×C₄₁	—	2	2	no	—
454	Q₈×C₄₁	—	2	1	no	—
455	Q₈×C₄₁	—	2	2	no	—
456	Q₈×C₄₁	—	2	2	no	—
457	Q₈×C₄₁	—	2	1	no	—
458	Q₈×C₄₁	—	4	2	no	—
459	Q₈×C₄₁	—	4	4	no	—
460	Q₈×C₄₁	—	8	1	no	—
461	Q₈×C₄₁	—	8	2	no	—
462	D₄×C₄₁	—	2	1	no	—
463	D₄×C₄₁	—	2	1	no	—
464	D₄×C₄₁	—	2	1	no	—
465	D₄×C₄₁	—	2	1	no	—
466	D₄×C₄₁	—	4	2	no	—
467	D₄×C₄₁	—	8	1	no	—
468	C₂×C₄×C₄₁	—	2	2	no	—
469	C₂×C₄×C₄₁	—	2	1	no	—
470	C₂×C₄×C₄₁	—	2	1	no	—
471	C₂×C₄×C₄₁	—	2	1	no	—
472	C₂×C₄×C₄₁	—	2	1	no	—
473	C₂×C₄×C₄₁	—	2	2	no	—
474	C₂×C₄×C₄₁	—	2	1	no	—
475	C₂×C₄×C₄₁	—	2	1	no	—
476	C₂×C₄×C₄₁	—	2	1	no	—
477	C₂×C₄×C₄₁	—	2	2	no	—
478	C₂×C₄×C₄₁	—	2	2	no	—
479	C₂×C₄×C₄₁	—	2	2	no	—
480	C₂×C₄×C₄₁	—	2	1	no	—
481	C₂×C₄×C₄₁	—	4	1	no	—
482	C₂×C₄×C₄₁	—	4	2	no	—
483	C₂×C₄×C₄₁	—	4	2	no	—
484	C₂×C₄×C₄₁	—	4	4	no	—
485	C₂×C₄×C₄₁	—	4	2	no	—
486	C₂×C₄×C₄₁	—	4	2	no	—
487	C₂×C₄×C₄₁	—	8	2	no	—
488	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
498	C₈×C₄₁	—	2	1	no	—
499	C₈×C₄₁	—	2	2	no	—
500	C₈×C₄₁	—	2	1	no	—
501	C₈×C₄₁	—	2	2	no	—
502	C₈×C₄₁	—	2	1	no	—
503	C₈×C₄₁	—	2	1	no	—
504	#61922	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
505	C₂²×C₄₁	—	2	1	no	—
506	C₂²×C₄₁	—	2	1	no	—
507	C₂²×C₄₁	—	2	1	no	—
508	C₂²×C₄₁	—	4	1	no	—
509	C₂²×C₄₁	—	4	1	no	—
510	C₂²×C₄₁	—	4	1	no	—
511	C₂²×C₄₁	—	4	1	no	—
512	C₂²×C₄₁	—	4	1	no	—
513	C₂²×C₄₁	—	4	1	no	—
514	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
515	C₄×C₄₁	—	2	1	no	—
516	C₄×C₄₁	—	2	1	no	—
517	C₄×C₄₁	—	2	2	no	—
518	C₄×C₄₁	—	2	2	no	—
519	C₄×C₄₁	—	2	1	no	—
520	C₄×C₄₁	—	2	1	no	—
521	C₄×C₄₁	—	2	2	no	—
522	C₄×C₄₁	—	2	2	no	—
523	C₄×C₄₁	—	4	1	no	—
524	C₄×C₄₁	—	4	2	no	—
525	C₄×C₄₁	—	4	1	no	—
526	C₄×C₄₁	—	4	1	no	—
527	C₄×C₄₁	—	4	2	no	—
528	C₄×C₄₁	—	4	2	no	—
529	C₄×C₄₁	—	4	2	no	—
530	C₄×C₄₁	—	4	1	no	—
531	C₄×C₄₁	—	4	1	no	—
532	C₄×C₄₁	—	4	1	no	—
533	C₄×C₄₁	#578	1	2	yes	—
534	C₄×C₄₁	#585	1	1	yes	characteristic
535	C₄×C₄₁	#585	1	1	yes	characteristic
536	#3555	C₂×C₄₁	1	1	yes	characteristic, complemented
537	#3509	C₂×C₄₁	1	1	yes	characteristic, complemented
538	#3402	C₂×C₄₁	1	2	yes	complemented
539	#3398	C₂×C₄₁	1	1	yes	characteristic, complemented
540	#3398	C₂×C₄₁	1	1	yes	characteristic, complemented
541	#3398	C₂×C₄₁	1	2	yes	complemented
542	#3395	C₂×C₄₁	1	1	yes	characteristic, complemented
543	#3393	C₂×C₄₁	1	1	yes	characteristic, complemented
544	#3377	C₂×C₄₁	1	2	yes	complemented
545	#3374	C₂×C₄₁	1	2	yes	complemented
546	#3372	C₂×C₄₁	1	1	yes	characteristic, complemented
547	#3369	C₂×C₄₁	1	1	yes	characteristic, complemented
548	#3363	C₂×C₄₁	1	1	yes	characteristic, complemented
549	#3360	C₂×C₄₁	1	1	yes	characteristic, complemented
550	#3225	C₂×C₄₁	1	2	yes	—
551	#3223	C₂×C₄₁	1	2	yes	complemented
552	#3218	C₂×C₄₁	1	1	yes	characteristic, complemented
553	#3209	C₂×C₄₁	1	1	yes	characteristic, complemented
554	#3127	C₂×C₄₁	1	2	yes	complemented
555	#3121	C₂×C₄₁	1	2	yes	complemented
556	#3116	C₂×C₄₁	1	1	yes	characteristic, complemented
557	#3102	C₂×C₄₁	1	1	yes	characteristic
558	#2985	C₂×C₄₁	1	1	yes	characteristic, complemented
559	C₂×C₄₁	—	4	1	no	—
560	C₂×C₄₁	—	8	1	no	—
561	C₂×C₄₁	—	8	1	no	—
562	C₂×C₄₁	#3487	1	1	yes	characteristic
563	C₂×C₄₁	C₂×#578	1	1	yes	characteristic
564	C₂×C₄₁	#3586	1	1	yes	characteristic
565	#563	—	2	2	no	—
566	Q₈²	C₂²×C₄₁	1	1	yes	characteristic
567	#557	C₂²×C₄₁	1	1	yes	characteristic
568	#557	C₂²×C₄₁	1	1	yes	characteristic
569	#557	C₂²×C₄₁	1	2	yes	—
570	#557	C₂²×C₄₁	1	1	yes	characteristic
571	#557	C₂²×C₄₁	1	2	yes	—
572	#556	—	2	1	no	—
573	#556	C₂²×C₄₁	1	1	yes	characteristic
574	#556	C₂²×C₄₁	1	1	yes	characteristic
575	#556	C₂²×C₄₁	1	2	yes	—
576	#556	C₂²×C₄₁	1	1	yes	characteristic
577	#556	C₂²×C₄₁	1	2	yes	—
578	#554	C₂²×C₄₁	1	1	yes	characteristic
579	#552	—	2	1	no	—
580	#552	—	2	1	no	—
581	#552	—	2	2	no	—
582	#552	—	2	1	no	—
583	#544	—	2	1	no	—
584	#542	C₂²×C₄₁	1	2	yes	—
585	#541	—	2	1	no	—
586	#541	—	2	2	no	—
587	#541	—	2	2	no	—
588	#541	C₂²×C₄₁	1	2	yes	—
589	#536	C₂²×C₄₁	1	2	yes	—
590	#533	—	2	1	no	—
591	#533	—	2	1	no	—
592	#533	C₂²×C₄₁	1	1	yes	characteristic
593	#533	C₂²×C₄₁	1	1	yes	characteristic
594	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
595	#529	C₂²×C₄₁	1	1	yes	characteristic
596	#519	C₂²×C₄₁	1	2	yes	—
597	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
598	#497	C₂²×C₄₁	1	2	yes	—
599	#497	C₂²×C₄₁	1	2	yes	—
600	#497	C₂²×C₄₁	1	2	yes	—
601	#495	C₂²×C₄₁	1	2	yes	—
602	#494	C₂²×C₄₁	1	1	yes	characteristic
603	#494	C₂²×C₄₁	1	2	yes	—
604	#494	C₂²×C₄₁	1	1	yes	characteristic
605	#491	C₂²×C₄₁	1	2	yes	—
606	#491	C₂²×C₄₁	1	2	yes	—
607	#489	C₂²×C₄₁	1	2	yes	—
608	#488	C₂²×C₄₁	1	2	yes	—
609	#487	C₂²×C₄₁	1	1	yes	characteristic
610	#487	C₂²×C₄₁	1	2	yes	—
611	#487	C₂²×C₄₁	1	1	yes	characteristic
612	#485	C₂²×C₄₁	1	1	yes	characteristic
613	#485	C₂²×C₄₁	1	2	yes	—
614	#482	C₂²×C₄₁	1	1	yes	characteristic
615	#479	C₂²×C₄₁	1	1	yes	characteristic
616	#479	C₂²×C₄₁	1	2	yes	—
617	#479	C₂²×C₄₁	1	2	yes	—
618	#478	C₂²×C₄₁	1	1	yes	characteristic
619	#477	C₂²×C₄₁	1	1	yes	characteristic
620	#477	C₂²×C₄₁	1	2	yes	—
621	#476	C₂²×C₄₁	1	1	yes	characteristic
622	#475	C₂²×C₄₁	1	2	yes	—
623	#464	C₂²×C₄₁	1	1	yes	characteristic
624	#464	C₂²×C₄₁	1	2	yes	—
625	#464	C₂²×C₄₁	1	2	yes	—
626	#464	C₂²×C₄₁	1	2	yes	—
627	#464	C₂²×C₄₁	1	2	yes	—
628	#464	C₂²×C₄₁	1	2	yes	—
629	#463	C₂²×C₄₁	1	1	yes	characteristic
630	#463	C₂²×C₄₁	1	2	yes	—
631	#462	C₂²×C₄₁	1	1	yes	characteristic
632	#462	C₂²×C₄₁	1	2	yes	—
633	#462	C₂²×C₄₁	1	1	yes	characteristic
634	#462	C₂²×C₄₁	1	1	yes	characteristic
635	#462	C₂²×C₄₁	1	2	yes	—
636	#462	C₂²×C₄₁	1	2	yes	—
637	#462	C₂²×C₄₁	1	2	yes	—
638	#462	C₂²×C₄₁	1	2	yes	—
639	#462	C₂²×C₄₁	1	2	yes	—
640	#462	C₂²×C₄₁	1	2	yes	—
641	#461	C₂²×C₄₁	1	1	yes	characteristic
642	#461	C₂²×C₄₁	1	1	yes	characteristic
643	#461	C₂²×C₄₁	1	1	yes	characteristic
644	#461	C₂²×C₄₁	1	2	yes	—
645	#452	C₂²×C₄₁	1	1	yes	characteristic
646	#452	C₂²×C₄₁	1	2	yes	—
647	#451	C₂²×C₄₁	1	2	yes	—
648	#451	C₂²×C₄₁	1	2	yes	—
649	#451	C₂²×C₄₁	1	2	yes	—
650	#449	C₂²×C₄₁	1	1	yes	characteristic
651	#448	C₂²×C₄₁	1	2	yes	—
652	#446	C₂²×C₄₁	1	1	yes	characteristic
653	#446	C₂²×C₄₁	1	1	yes	characteristic
654	#446	C₂²×C₄₁	1	2	yes	—
655	#446	C₂²×C₄₁	1	2	yes	—
656	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
657	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
658	#441	C₂²×C₄₁	1	2	yes	—
659	#441	C₂²×C₄₁	1	2	yes	—
660	#441	C₂²×C₄₁	1	2	yes	—
661	#441	C₂²×C₄₁	1	2	yes	—
662	#440	C₂²×C₄₁	1	2	yes	—
663	#440	C₂²×C₄₁	1	2	yes	—
664	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
665	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	—
666	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	—
667	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	—
668	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
669	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
670	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
671	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
672	#433	C₂²×C₄₁	1	2	yes	—
673	#433	C₂²×C₄₁	1	2	yes	—
674	#432	C₂²×C₄₁	1	1	yes	characteristic
675	#431	C₂²×C₄₁	1	1	yes	characteristic
676	C₄₁	#61922	1	1	yes	characteristic, direct product factor, Sylow
677	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
678	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
679	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
680	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
681	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
682	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
683	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
684	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
685	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
686	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
689	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
690	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
691	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
692	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
693	C₄⋊Q₈	—	2	2	no	—
694	C₄⋊Q₈	—	2	2	no	—
695	C₄⋊Q₈	—	2	1	no	—
696	C₄⋊Q₈	—	2	1	no	—
697	C₄⋊Q₈	—	2	1	no	—
698	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
699	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
701	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
702	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
703	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
705	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
706	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
707	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	1	no	—
720	#125	—	2	1	no	—
721	#125	—	2	1	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	2	no	—
727	#125	—	2	2	no	—
728	#125	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	—	2	2	no	—
731	#125	—	2	2	no	—
732	#125	—	2	1	no	—
733	#125	—	2	1	no	—
734	#125	D₄×C₄₁	1	2	yes	—
735	#125	C₂³×C₄₁	1	1	yes	characteristic
736	#125	C₂³×C₄₁	1	2	yes	—
737	#124	—	2	2	no	—
738	#124	C₂³×C₄₁	1	1	yes	characteristic
739	#124	C₂³×C₄₁	1	2	yes	—
740	#124	C₂³×C₄₁	1	2	yes	—
741	#124	C₂³×C₄₁	1	2	yes	—
742	#123	—	2	1	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
758	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
759	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
761	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
762	#121	C₂³×C₄₁	1	1	yes	characteristic
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	2	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	2	no	—
769	C₄×Q₈	—	2	2	no	—
770	C₄×Q₈	—	2	2	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
774	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
775	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
776	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
777	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
778	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
780	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
781	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
782	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
783	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
785	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
790	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
791	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
792	C₄×D₄	C₂³×C₄₁	1	2	yes	—
793	#117	—	2	1	no	—
794	#117	—	2	1	no	—
795	#117	—	2	1	no	—
796	#117	—	2	2	no	—
797	#117	—	2	2	no	—
798	#117	—	2	1	no	—
799	#117	—	2	2	no	—
800	#117	—	2	2	no	—
801	#117	—	2	1	no	—
802	#117	—	2	1	no	—
803	#117	C₂³×C₄₁	1	1	yes	characteristic
804	#117	C₂³×C₄₁	1	2	yes	—
805	C₂×C₄⋊C₄	—	2	1	no	—
806	C₂×C₄⋊C₄	—	2	1	no	—
807	C₂×C₄⋊C₄	—	2	1	no	—
808	C₂×C₄²	—	2	1	no	—
809	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
810	#107	C₂³×C₄₁	1	1	yes	characteristic
811	#107	C₂³×C₄₁	1	1	yes	characteristic
812	#107	C₂³×C₄₁	1	2	yes	—
813	#106	C₂³×C₄₁	1	1	yes	characteristic
814	#106	C₂³×C₄₁	1	2	yes	—
815	#106	C₂³×C₄₁	1	1	yes	characteristic
816	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
817	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
820	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
821	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
822	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
823	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
824	#103	C₂³×C₄₁	1	1	yes	characteristic
825	#103	C₂³×C₄₁	1	2	yes	—
826	#103	C₂³×C₄₁	1	1	yes	characteristic
827	#103	C₂³×C₄₁	1	1	yes	characteristic
828	#103	C₂³×C₄₁	1	2	yes	—
829	#103	C₂³×C₄₁	1	2	yes	—
830	#103	C₂³×C₄₁	1	2	yes	—
831	#103	C₂³×C₄₁	1	1	yes	characteristic
832	#103	C₂³×C₄₁	1	2	yes	—
833	#103	C₂³×C₄₁	1	2	yes	—
834	#103	C₂³×C₄₁	1	2	yes	—
835	#103	C₂³×C₄₁	1	2	yes	—
836	#103	C₂³×C₄₁	1	2	yes	—
837	#103	C₂³×C₄₁	1	2	yes	—
838	#103	C₂³×C₄₁	1	2	yes	—
839	#102	C₂³×C₄₁	1	1	yes	characteristic
840	#102	C₂³×C₄₁	1	1	yes	characteristic
841	#102	C₂³×C₄₁	1	1	yes	characteristic
842	#102	C₂³×C₄₁	1	1	yes	characteristic
843	#102	C₂³×C₄₁	1	2	yes	—
844	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
845	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
846	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
847	#97	C₂³×C₄₁	1	2	yes	—
848	#97	C₂³×C₄₁	1	2	yes	—
849	#97	C₂³×C₄₁	1	2	yes	—
850	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
851	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
852	C₄×C₈	C₂³×C₄₁	1	2	yes	—
853	C₄×C₈	C₂³×C₄₁	1	2	yes	—
854	#41	—	4	1	no	—
855	#41	—	4	1	no	—
856	C₂×Q₈	—	2	2	no	—
857	C₂×Q₈	—	2	1	no	—
858	C₂×Q₈	—	2	2	no	—
859	C₂×Q₈	—	4	2	no	—
860	C₂×Q₈	—	4	2	no	—
861	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
862	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
863	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
864	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
865	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
866	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
867	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
868	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
869	C₂×D₄	—	2	1	no	—
870	C₂×D₄	—	2	1	no	—
871	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
872	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
880	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
882	Q₁₆	—	4	2	no	—
883	Q₁₆	—	4	2	no	—
884	Q₁₆	—	4	2	no	—
885	Q₁₆	—	4	2	no	—
886	Q₁₆	—	4	2	no	—
887	Q₁₆	—	4	2	no	—
888	Q₁₆	—	4	2	no	—
889	Q₁₆	—	4	1	no	—
890	SD₁₆	—	4	2	no	—
891	SD₁₆	—	4	2	no	—
892	SD₁₆	—	4	2	no	—
893	SD₁₆	—	4	1	no	—
894	SD₁₆	—	4	1	no	—
895	D₈	—	4	1	no	—
896	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
897	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
898	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
899	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
900	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
901	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
936	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
937	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
938	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
939	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
940	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
941	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
942	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
943	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
944	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
945	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
946	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
947	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
966	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	2	no	—
971	C₄²	—	2	2	no	—
972	C₄²	—	2	2	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	2	no	—
979	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
980	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
981	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
982	C₄²	C₂⁴×C₄₁	1	2	yes	—
983	C₄²	C₂⁴×C₄₁	1	2	yes	—
984	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
985	C₂³	—	2	1	no	—
986	C₂³	—	2	1	no	—
987	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
988	Q₈	—	2	2	no	—
989	Q₈	—	2	2	no	—
990	Q₈	—	2	1	no	—
991	Q₈	—	2	2	no	—
992	Q₈	—	2	2	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	2	2	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	2	2	no	—
998	Q₈	—	2	2	no	—
999	Q₈	—	2	1	no	—
1000	Q₈	—	4	2	no	—
1001	Q₈	—	4	4	no	—
1002	Q₈	—	8	1	no	—
1003	Q₈	—	8	2	no	—
1004	D₄	—	2	1	no	—
1005	D₄	—	2	1	no	—
1006	D₄	—	2	1	no	—
1007	D₄	—	2	1	no	—
1008	D₄	—	4	2	no	—
1009	D₄	—	8	1	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	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	2	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	4	1	no	—
1024	C₂×C₄	—	4	2	no	—
1025	C₂×C₄	—	4	2	no	—
1026	C₂×C₄	—	4	4	no	—
1027	C₂×C₄	—	4	2	no	—
1028	C₂×C₄	—	4	2	no	—
1029	C₂×C₄	—	8	2	no	—
1030	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1031	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1032	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1033	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1034	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1035	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1036	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1037	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1038	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1039	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1040	C₈	—	2	1	no	—
1041	C₈	—	2	2	no	—
1042	C₈	—	2	1	no	—
1043	C₈	—	2	2	no	—
1044	C₈	—	2	1	no	—
1045	C₈	—	2	1	no	—
1046	C₂²	—	2	1	no	—
1047	C₂²	—	2	1	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	4	1	no	—
1050	C₂²	—	4	1	no	—
1051	C₂²	—	4	1	no	—
1052	C₂²	—	4	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1056	C₄	—	2	1	no	—
1057	C₄	—	2	2	no	—
1058	C₄	—	2	2	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	1	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	2	no	—
1072	C₄	—	4	2	no	—
1073	C₄	—	4	1	no	—
1074	C₄	C₄₁×#578	1	2	yes	—
1075	C₄	C₄₁×#585	1	1	yes	characteristic
1076	C₄	C₄₁×#585	1	1	yes	characteristic
1077	C₂	—	4	1	no	—
1078	C₂	—	8	1	no	—
1079	C₂	—	8	1	no	—
1080	C₂	C₄₁×#3487	1	1	yes	characteristic
1081	C₂	C₂×C₄₁×#578	1	1	yes	characteristic
1082	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×#449	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3555	C₂	semidirect
2. C₄₁×#3509	C₂	semidirect
3. C₄₁×#3402	C₂	semidirect
4. C₄₁×#3398	C₂	semidirect
5. C₄₁×#3398	C₂	semidirect
6. C₄₁×#3398	C₂	semidirect
7. C₄₁×#3395	C₂	semidirect
8. C₄₁×#3393	C₂	semidirect
9. C₄₁×#3377	C₂	semidirect
10. C₄₁×#3374	C₂	semidirect
11. C₄₁×#3372	C₂	semidirect
12. C₄₁×#3369	C₂	semidirect
13. C₄₁×#3363	C₂	semidirect
14. C₄₁×#3360	C₂	semidirect
16. C₄₁×#3223	C₂	semidirect
17. C₄₁×#3218	C₂	semidirect
18. C₄₁×#3209	C₂	semidirect
19. C₄₁×#3127	C₂	semidirect
20. C₄₁×#3121	C₂	semidirect
21. C₄₁×#3116	C₂	semidirect
23. C₄₁×#2985	C₂	semidirect
504. #61922	C₄₁	direct (N × H)
536. #3555	C₂×C₄₁	semidirect
537. #3509	C₂×C₄₁	semidirect
538. #3402	C₂×C₄₁	semidirect
539. #3398	C₂×C₄₁	semidirect
540. #3398	C₂×C₄₁	semidirect
541. #3398	C₂×C₄₁	semidirect
542. #3395	C₂×C₄₁	semidirect
543. #3393	C₂×C₄₁	semidirect
544. #3377	C₂×C₄₁	semidirect
545. #3374	C₂×C₄₁	semidirect
546. #3372	C₂×C₄₁	semidirect
547. #3369	C₂×C₄₁	semidirect
548. #3363	C₂×C₄₁	semidirect
549. #3360	C₂×C₄₁	semidirect
551. #3223	C₂×C₄₁	semidirect
552. #3218	C₂×C₄₁	semidirect
553. #3209	C₂×C₄₁	semidirect
554. #3127	C₂×C₄₁	semidirect
555. #3121	C₂×C₄₁	semidirect
556. #3116	C₂×C₄₁	semidirect
558. #2985	C₂×C₄₁	semidirect
676. C₄₁	#61922	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×#3555	2
C₄₁×#3509	2
C₄₁×#3402	2
C₄₁×#3398	2
C₄₁×#3395	2
C₄₁×#3393	2
C₄₁×#3377	2
C₄₁×#3374	2
C₄₁×#3372	2
C₄₁×#3369	2
C₄₁×#3363	2
C₄₁×#3360	2
C₄₁×#3225	2
C₄₁×#3223	2
C₄₁×#3218	2
C₄₁×#3209	2
C₄₁×#3127	2
C₄₁×#3121	2
C₄₁×#3116	2
C₄₁×#3102	2
C₄₁×#2985	2
#61922	41

Subgroups — C41×#61922 #23838123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61922 #23838123