Subgroups — C₄₁×#61929 #23838130

Order 10496.

1654 conjugacy classes of subgroups.

The subgroup lattice has 1090 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×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3402	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#3395	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#3393	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3377	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3375	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3364	C₂	1	2	yes	maximal, complemented
13	C₄₁×#3363	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3225	C₂	1	2	yes	maximal, complemented
16	C₄₁×#3223	C₂	1	2	yes	maximal, complemented
17	C₄₁×#3212	C₂	1	1	yes	maximal, characteristic
18	C₄₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#3124	C₂	1	2	yes	maximal, complemented
20	C₄₁×#3120	C₂	1	2	yes	maximal, complemented
21	C₄₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄₁×#563	—	2	2	no	—
25	C₄₁×#559	C₂²	1	1	yes	characteristic
26	C₄₁×#559	C₂²	1	1	yes	characteristic
27	Q₈²×C₄₁	C₂²	1	1	yes	characteristic
28	C₄₁×#557	C₂²	1	1	yes	characteristic
29	C₄₁×#557	C₂²	1	1	yes	characteristic
30	C₄₁×#557	C₂²	1	1	yes	characteristic
31	C₄₁×#557	C₂²	1	2	yes	—
32	C₄₁×#556	—	2	1	no	—
33	C₄₁×#556	—	2	1	no	—
34	C₄₁×#556	C₂²	1	2	yes	—
35	C₄₁×#556	C₂²	1	1	yes	characteristic
36	C₄₁×#556	C₂²	1	2	yes	—
37	C₄₁×#556	C₂²	1	2	yes	—
38	C₄₁×#554	—	2	1	no	—
39	C₄₁×#554	C₂²	1	1	yes	characteristic
40	C₄₁×#552	—	2	2	no	—
41	C₄₁×#552	—	2	1	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	C₂²	1	2	yes	—
47	C₄₁×#539	—	2	2	no	—
48	C₄₁×#536	C₂²	1	2	yes	—
49	C₄₁×#533	C₂²	1	1	yes	characteristic
50	C₄₁×#533	C₂²	1	1	yes	characteristic
51	C₄₁×#532	C₂²	1	1	yes	characteristic
52	C₄₁×#529	—	2	1	no	—
53	C₄₁×#529	—	2	1	no	—
54	C₄₁×#529	C₂²	1	1	yes	characteristic
55	C₄₁×#520	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
57	C₄₁×#497	C₂²	1	2	yes	—
58	C₄₁×#497	C₂²	1	2	yes	—
59	C₄₁×#495	C₂²	1	2	yes	—
60	C₄₁×#495	C₂²	1	2	yes	—
61	C₄₁×#494	C₂²	1	2	yes	—
62	C₄₁×#494	C₂²	1	1	yes	characteristic
63	C₄₁×#492	C₂²	1	1	yes	characteristic
64	C₄₁×#491	C₂²	1	2	yes	—
65	C₄₁×#489	C₂²	1	2	yes	—
66	C₄₁×#488	C₂²	1	2	yes	—
67	C₄₁×#488	C₂²	1	2	yes	—
68	C₄₁×#487	C₂²	1	2	yes	—
69	C₄₁×#487	C₂²	1	1	yes	characteristic
70	C₄₁×#486	C₂²	1	1	yes	characteristic
71	C₄₁×#484	C₂²	1	2	yes	—
72	C₄₁×#483	C₂²	1	1	yes	characteristic
73	C₄₁×#480	C₂²	1	1	yes	characteristic
74	C₄₁×#479	C₂²	1	1	yes	characteristic
75	C₄₁×#479	C₂²	1	1	yes	characteristic
76	C₄₁×#479	C₂²	1	2	yes	—
77	C₄₁×#478	C₂²	1	2	yes	—
78	C₄₁×#477	C₂²	1	1	yes	characteristic
79	C₄₁×#477	C₂²	1	1	yes	characteristic
80	C₄₁×#477	C₂²	1	2	yes	—
81	C₄₁×#474	C₂²	1	2	yes	—
82	C₄₁×#464	C₂²	1	1	yes	characteristic
83	C₄₁×#464	C₂²	1	1	yes	characteristic
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×#464	C₂²	1	2	yes	—
89	C₄₁×#464	C₂²	1	2	yes	—
90	C₄₁×#463	C₂²	1	2	yes	—
91	C₄₁×#463	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	1	yes	characteristic
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×#461	C₂²	1	2	yes	—
100	C₄₁×#461	C₂²	1	1	yes	characteristic
101	C₄₁×#461	C₂²	1	2	yes	—
102	C₄₁×#460	C₂²	1	1	yes	characteristic
103	C₄₁×#459	C₂²	1	1	yes	characteristic
104	C₄₁×#452	C₂²	1	2	yes	—
105	C₄₁×#452	C₂²	1	2	yes	—
106	C₄₁×#452	C₂²	1	2	yes	—
107	C₄₁×#451	C₂²	1	2	yes	—
108	C₄₁×#451	C₂²	1	1	yes	characteristic
109	C₄₁×#449	C₂²	1	2	yes	—
110	C₄₁×#448	C₂²	1	1	yes	characteristic
111	C₄₁×#446	C₂²	1	1	yes	characteristic
112	C₄₁×#446	C₂²	1	1	yes	characteristic
113	C₄₁×#446	C₂²	1	2	yes	—
114	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
115	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₄₁	C₂²	1	2	yes	—
117	C₄₁×#441	C₂²	1	2	yes	—
118	C₄₁×#440	C₂²	1	2	yes	—
119	C₄₁×#440	C₂²	1	2	yes	—
120	C₄₁×#440	C₂²	1	2	yes	—
121	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	—
122	C₄×Q₁₆×C₄₁	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	1	yes	characteristic
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	2	yes	—
131	C₄₁×#433	C₂²	1	2	yes	—
132	C₄₁×#433	C₂²	1	2	yes	—
133	C₄₁×#431	C₂²	1	1	yes	characteristic
134	C₄₁×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₄₁	C₂³	1	2	yes	—
136	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
137	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
138	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
139	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
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×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
150	C₂×D₈×C₄₁	C₂³	1	2	yes	—
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	D₄	1	1	yes	characteristic
155	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
156	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
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	#127×C₄₁	C₂³	1	1	yes	characteristic
164	#126×C₄₁	—	2	2	no	—
165	#126×C₄₁	—	2	2	no	—
166	#126×C₄₁	—	2	2	no	—
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	1	no	—
175	#125×C₄₁	—	2	1	no	—
176	#125×C₄₁	—	2	1	no	—
177	#125×C₄₁	—	2	2	no	—
178	#125×C₄₁	—	2	2	no	—
179	#125×C₄₁	—	2	2	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	1	no	—
185	#125×C₄₁	—	2	1	no	—
186	#125×C₄₁	D₄	1	2	yes	—
187	#125×C₄₁	C₂³	1	1	yes	characteristic
188	#125×C₄₁	C₂³	1	2	yes	—
189	#124×C₄₁	—	2	1	no	—
190	#124×C₄₁	—	2	1	no	—
191	#124×C₄₁	—	2	2	no	—
192	#124×C₄₁	C₂³	1	1	yes	characteristic
193	#124×C₄₁	C₂³	1	2	yes	—
194	#124×C₄₁	C₂³	1	2	yes	—
195	#124×C₄₁	C₂³	1	2	yes	—
196	#124×C₄₁	C₂³	1	2	yes	—
197	#123×C₄₁	—	2	1	no	—
198	#123×C₄₁	—	2	2	no	—
199	#123×C₄₁	—	2	2	no	—
200	#123×C₄₁	—	2	2	no	—
201	#123×C₄₁	—	2	2	no	—
202	#123×C₄₁	—	2	2	no	—
203	C₂²⋊Q₈×C₄₁	—	2	2	no	—
204	C₂²⋊Q₈×C₄₁	—	2	2	no	—
205	C₂²⋊Q₈×C₄₁	—	2	1	no	—
206	C₂²⋊Q₈×C₄₁	—	2	1	no	—
207	C₂²⋊Q₈×C₄₁	—	2	2	no	—
208	C₂²⋊Q₈×C₄₁	—	2	1	no	—
209	C₂²⋊Q₈×C₄₁	—	2	2	no	—
210	C₂²⋊Q₈×C₄₁	—	2	2	no	—
211	C₂²⋊Q₈×C₄₁	—	2	2	no	—
212	C₂²⋊Q₈×C₄₁	—	2	2	no	—
213	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
214	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
215	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
216	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
217	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
218	#121×C₄₁	—	2	1	no	—
219	#121×C₄₁	—	2	1	no	—
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	1	no	—
224	C₄×Q₈×C₄₁	—	2	1	no	—
225	C₄×Q₈×C₄₁	—	2	2	no	—
226	C₄×Q₈×C₄₁	—	2	1	no	—
227	C₄×Q₈×C₄₁	—	2	1	no	—
228	C₄×Q₈×C₄₁	—	2	1	no	—
229	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
234	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
235	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
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	1	yes	characteristic
241	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
242	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₄₁	—	2	1	no	—
244	C₄×D₄×C₄₁	—	2	1	no	—
245	C₄×D₄×C₄₁	—	2	1	no	—
246	C₄×D₄×C₄₁	—	2	2	no	—
247	C₄×D₄×C₄₁	—	2	2	no	—
248	C₄×D₄×C₄₁	—	2	1	no	—
249	C₄×D₄×C₄₁	—	2	1	no	—
250	C₄×D₄×C₄₁	C₂³	1	2	yes	—
251	C₄×D₄×C₄₁	C₂³	1	2	yes	—
252	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₄₁	C₂³	1	2	yes	—
254	#117×C₄₁	—	2	1	no	—
255	#117×C₄₁	—	2	2	no	—
256	#117×C₄₁	—	2	2	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	2	yes	—
262	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
263	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
264	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
265	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
266	C₂×C₄²×C₄₁	—	2	1	no	—
267	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
268	#107×C₄₁	C₂³	1	2	yes	—
269	#107×C₄₁	C₂³	1	1	yes	characteristic
270	#107×C₄₁	C₂³	1	2	yes	—
271	#107×C₄₁	C₂³	1	1	yes	characteristic
272	#106×C₄₁	C₂³	1	1	yes	characteristic
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	2	yes	—
283	#103×C₄₁	C₂³	1	1	yes	characteristic
284	#103×C₄₁	C₂³	1	1	yes	characteristic
285	#103×C₄₁	C₂³	1	1	yes	characteristic
286	#103×C₄₁	C₂³	1	1	yes	characteristic
287	#103×C₄₁	C₂³	1	2	yes	—
288	#103×C₄₁	C₂³	1	1	yes	characteristic
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	#102×C₄₁	C₂³	1	1	yes	characteristic
297	#102×C₄₁	C₂³	1	2	yes	—
298	#102×C₄₁	C₂³	1	1	yes	characteristic
299	#102×C₄₁	C₂³	1	2	yes	—
300	#102×C₄₁	C₂³	1	2	yes	—
301	#102×C₄₁	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
305	#97×C₄₁	C₂³	1	2	yes	—
306	#97×C₄₁	C₂³	1	2	yes	—
307	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₄₁	C₂³	1	2	yes	—
310	C₄×C₈×C₄₁	C₂³	1	2	yes	—
311	C₄×C₈×C₄₁	C₂³	1	2	yes	—
312	#41×C₄₁	—	4	2	no	—
313	#41×C₄₁	—	4	2	no	—
314	C₂×Q₈×C₄₁	—	2	1	no	—
315	C₂×Q₈×C₄₁	—	2	1	no	—
316	C₂×Q₈×C₄₁	—	2	2	no	—
317	C₂×Q₈×C₄₁	—	4	1	no	—
318	C₂×Q₈×C₄₁	—	4	1	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	1	yes	characteristic
323	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
327	C₂×D₄×C₄₁	—	2	2	no	—
328	C₂×D₄×C₄₁	—	2	1	no	—
329	C₂×D₄×C₄₁	—	2	1	no	—
330	C₂×D₄×C₄₁	—	2	1	no	—
331	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
332	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
338	C₂²×C₄×C₄₁	—	2	2	no	—
339	C₂²×C₄×C₄₁	—	2	2	no	—
340	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
343	Q₁₆×C₄₁	—	4	2	no	—
344	Q₁₆×C₄₁	—	4	2	no	—
345	Q₁₆×C₄₁	—	4	2	no	—
346	Q₁₆×C₄₁	—	4	1	no	—
347	Q₁₆×C₄₁	—	4	2	no	—
348	Q₁₆×C₄₁	—	4	1	no	—
349	Q₁₆×C₄₁	—	4	2	no	—
350	SD₁₆×C₄₁	—	4	1	no	—
351	SD₁₆×C₄₁	—	4	2	no	—
352	SD₁₆×C₄₁	—	4	2	no	—
353	SD₁₆×C₄₁	—	4	2	no	—
354	SD₁₆×C₄₁	—	4	2	no	—
355	SD₁₆×C₄₁	—	4	1	no	—
356	D₈×C₄₁	—	4	2	no	—
357	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
359	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₄₁	—	2	1	no	—
364	C₄⋊C₄×C₄₁	—	2	1	no	—
365	C₄⋊C₄×C₄₁	—	2	2	no	—
366	C₄⋊C₄×C₄₁	—	2	2	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	1	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	1	no	—
380	C₄⋊C₄×C₄₁	—	2	1	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	2	yes	—
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	1	yes	characteristic
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	2	no	—
408	C₂²⋊C₄×C₄₁	—	2	1	no	—
409	C₂²⋊C₄×C₄₁	—	2	2	no	—
410	C₂²⋊C₄×C₄₁	—	2	1	no	—
411	C₂²⋊C₄×C₄₁	—	2	2	no	—
412	C₂²⋊C₄×C₄₁	—	2	2	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	2	no	—
422	C₂²⋊C₄×C₄₁	—	2	1	no	—
423	C₂²⋊C₄×C₄₁	—	2	2	no	—
424	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
426	C₄²×C₄₁	—	2	1	no	—
427	C₄²×C₄₁	—	2	1	no	—
428	C₄²×C₄₁	—	2	1	no	—
429	C₄²×C₄₁	—	2	1	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	1	yes	characteristic
441	C₄²×C₄₁	C₂⁴	1	2	yes	—
442	C₄²×C₄₁	C₂⁴	1	2	yes	—
443	C₂³×C₄₁	—	2	1	no	—
444	C₂³×C₄₁	—	2	2	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	1	no	—
452	Q₈×C₄₁	—	2	1	no	—
453	Q₈×C₄₁	—	2	2	no	—
454	Q₈×C₄₁	—	2	1	no	—
455	Q₈×C₄₁	—	2	1	no	—
456	Q₈×C₄₁	—	2	1	no	—
457	Q₈×C₄₁	—	2	2	no	—
458	Q₈×C₄₁	—	4	2	no	—
459	Q₈×C₄₁	—	4	2	no	—
460	Q₈×C₄₁	—	8	1	no	—
461	Q₈×C₄₁	—	8	2	no	—
462	D₄×C₄₁	—	2	1	no	—
463	D₄×C₄₁	—	2	2	no	—
464	D₄×C₄₁	—	2	1	no	—
465	D₄×C₄₁	—	2	2	no	—
466	D₄×C₄₁	—	4	4	no	—
467	D₄×C₄₁	—	4	2	no	—
468	D₄×C₄₁	—	8	1	no	—
469	D₄×C₄₁	—	8	1	no	—
470	C₂×C₄×C₄₁	—	2	2	no	—
471	C₂×C₄×C₄₁	—	2	1	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	2	no	—
476	C₂×C₄×C₄₁	—	2	1	no	—
477	C₂×C₄×C₄₁	—	2	1	no	—
478	C₂×C₄×C₄₁	—	2	1	no	—
479	C₂×C₄×C₄₁	—	2	1	no	—
480	C₂×C₄×C₄₁	—	2	1	no	—
481	C₂×C₄×C₄₁	—	2	2	no	—
482	C₂×C₄×C₄₁	—	2	2	no	—
483	C₂×C₄×C₄₁	—	4	1	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	—	8	2	no	—
489	C₂×C₄×C₄₁	—	8	2	no	—
490	C₂×C₄×C₄₁	—	8	1	no	—
491	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
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	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
501	C₈×C₄₁	—	2	2	no	—
502	C₈×C₄₁	—	2	1	no	—
503	C₈×C₄₁	—	2	1	no	—
504	C₈×C₄₁	—	2	2	no	—
505	C₈×C₄₁	—	2	1	no	—
506	C₈×C₄₁	—	2	1	no	—
507	#61929	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
508	C₂²×C₄₁	—	2	1	no	—
509	C₂²×C₄₁	—	2	1	no	—
510	C₂²×C₄₁	—	2	1	no	—
511	C₂²×C₄₁	—	4	2	no	—
512	C₂²×C₄₁	—	4	1	no	—
513	C₂²×C₄₁	—	4	2	no	—
514	C₂²×C₄₁	—	4	1	no	—
515	C₂²×C₄₁	—	4	1	no	—
516	C₂²×C₄₁	—	4	2	no	—
517	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
518	C₄×C₄₁	—	2	1	no	—
519	C₄×C₄₁	—	2	1	no	—
520	C₄×C₄₁	—	2	2	no	—
521	C₄×C₄₁	—	2	2	no	—
522	C₄×C₄₁	—	2	1	no	—
523	C₄×C₄₁	—	2	1	no	—
524	C₄×C₄₁	—	2	2	no	—
525	C₄×C₄₁	—	2	2	no	—
526	C₄×C₄₁	—	4	1	no	—
527	C₄×C₄₁	—	4	1	no	—
528	C₄×C₄₁	—	4	2	no	—
529	C₄×C₄₁	—	4	1	no	—
530	C₄×C₄₁	—	4	2	no	—
531	C₄×C₄₁	—	4	1	no	—
532	C₄×C₄₁	—	4	1	no	—
533	C₄×C₄₁	—	4	1	no	—
534	C₄×C₄₁	—	4	2	no	—
535	C₄×C₄₁	—	4	1	no	—
536	C₄×C₄₁	#578	1	2	yes	—
537	C₄×C₄₁	#585	1	1	yes	characteristic
538	C₄×C₄₁	#585	1	1	yes	characteristic
539	#3555	C₂×C₄₁	1	1	yes	characteristic, complemented
540	#3507	C₂×C₄₁	1	1	yes	characteristic, complemented
541	#3402	C₂×C₄₁	1	2	yes	complemented
542	#3400	C₂×C₄₁	1	1	yes	characteristic, complemented
543	#3398	C₂×C₄₁	1	1	yes	characteristic, complemented
544	#3395	C₂×C₄₁	1	1	yes	characteristic, complemented
545	#3394	C₂×C₄₁	1	1	yes	characteristic, complemented
546	#3393	C₂×C₄₁	1	2	yes	complemented
547	#3377	C₂×C₄₁	1	2	yes	complemented
548	#3375	C₂×C₄₁	1	1	yes	characteristic, complemented
549	#3372	C₂×C₄₁	1	1	yes	characteristic, complemented
550	#3364	C₂×C₄₁	1	2	yes	complemented
551	#3363	C₂×C₄₁	1	1	yes	characteristic, complemented
552	#3361	C₂×C₄₁	1	1	yes	characteristic, complemented
553	#3225	C₂×C₄₁	1	2	yes	complemented
554	#3223	C₂×C₄₁	1	2	yes	complemented
555	#3212	C₂×C₄₁	1	1	yes	characteristic
556	#3210	C₂×C₄₁	1	1	yes	characteristic, complemented
557	#3124	C₂×C₄₁	1	2	yes	complemented
558	#3120	C₂×C₄₁	1	2	yes	complemented
559	#3108	C₂×C₄₁	1	1	yes	characteristic, complemented
560	#3104	C₂×C₄₁	1	1	yes	characteristic, complemented
561	#2986	C₂×C₄₁	1	1	yes	characteristic, complemented
562	C₂×C₄₁	—	4	1	no	—
563	C₂×C₄₁	—	8	2	no	—
564	C₂×C₄₁	—	8	1	no	—
565	C₂×C₄₁	#3487	1	1	yes	characteristic
566	C₂×C₄₁	C₂×#578	1	1	yes	characteristic
567	C₂×C₄₁	#3584	1	1	yes	characteristic
568	#563	—	2	2	no	—
569	#559	C₂²×C₄₁	1	1	yes	characteristic
570	#559	C₂²×C₄₁	1	1	yes	characteristic
571	Q₈²	C₂²×C₄₁	1	1	yes	characteristic
572	#557	C₂²×C₄₁	1	1	yes	characteristic
573	#557	C₂²×C₄₁	1	1	yes	characteristic
574	#557	C₂²×C₄₁	1	1	yes	characteristic
575	#557	C₂²×C₄₁	1	2	yes	—
576	#556	—	2	1	no	—
577	#556	—	2	1	no	—
578	#556	C₂²×C₄₁	1	2	yes	—
579	#556	C₂²×C₄₁	1	2	yes	—
580	#556	C₂²×C₄₁	1	2	yes	—
581	#556	C₂²×C₄₁	1	1	yes	characteristic
582	#554	—	2	1	no	—
583	#554	C₂²×C₄₁	1	1	yes	characteristic
584	#552	—	2	2	no	—
585	#552	—	2	1	no	—
586	#544	—	2	1	no	—
587	#542	C₂²×C₄₁	1	2	yes	—
588	#541	—	2	1	no	—
589	#541	—	2	2	no	—
590	#541	C₂²×C₄₁	1	2	yes	—
591	#539	—	2	2	no	—
592	#536	C₂²×C₄₁	1	2	yes	—
593	#533	C₂²×C₄₁	1	1	yes	characteristic
594	#533	C₂²×C₄₁	1	1	yes	characteristic
595	#532	C₂²×C₄₁	1	1	yes	characteristic
596	#529	—	2	1	no	—
597	#529	—	2	1	no	—
598	#529	C₂²×C₄₁	1	1	yes	characteristic
599	#520	C₂²×C₄₁	1	2	yes	—
600	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
601	#497	C₂²×C₄₁	1	2	yes	—
602	#497	C₂²×C₄₁	1	2	yes	—
603	#495	C₂²×C₄₁	1	2	yes	—
604	#495	C₂²×C₄₁	1	2	yes	—
605	#494	C₂²×C₄₁	1	2	yes	—
606	#494	C₂²×C₄₁	1	1	yes	characteristic
607	#492	C₂²×C₄₁	1	1	yes	characteristic
608	#491	C₂²×C₄₁	1	2	yes	—
609	#489	C₂²×C₄₁	1	2	yes	—
610	#488	C₂²×C₄₁	1	2	yes	—
611	#488	C₂²×C₄₁	1	2	yes	—
612	#487	C₂²×C₄₁	1	2	yes	—
613	#487	C₂²×C₄₁	1	1	yes	characteristic
614	#486	C₂²×C₄₁	1	1	yes	characteristic
615	#484	C₂²×C₄₁	1	2	yes	—
616	#483	C₂²×C₄₁	1	1	yes	characteristic
617	#480	C₂²×C₄₁	1	1	yes	characteristic
618	#479	C₂²×C₄₁	1	1	yes	characteristic
619	#479	C₂²×C₄₁	1	1	yes	characteristic
620	#479	C₂²×C₄₁	1	2	yes	—
621	#478	C₂²×C₄₁	1	2	yes	—
622	#477	C₂²×C₄₁	1	1	yes	characteristic
623	#477	C₂²×C₄₁	1	1	yes	characteristic
624	#477	C₂²×C₄₁	1	2	yes	—
625	#474	C₂²×C₄₁	1	2	yes	—
626	#464	C₂²×C₄₁	1	1	yes	characteristic
627	#464	C₂²×C₄₁	1	1	yes	characteristic
628	#464	C₂²×C₄₁	1	2	yes	—
629	#464	C₂²×C₄₁	1	2	yes	—
630	#464	C₂²×C₄₁	1	2	yes	—
631	#464	C₂²×C₄₁	1	2	yes	—
632	#464	C₂²×C₄₁	1	2	yes	—
633	#464	C₂²×C₄₁	1	2	yes	—
634	#463	C₂²×C₄₁	1	2	yes	—
635	#463	C₂²×C₄₁	1	2	yes	—
636	#462	C₂²×C₄₁	1	1	yes	characteristic
637	#462	C₂²×C₄₁	1	1	yes	characteristic
638	#462	C₂²×C₄₁	1	1	yes	characteristic
639	#462	C₂²×C₄₁	1	2	yes	—
640	#462	C₂²×C₄₁	1	2	yes	—
641	#462	C₂²×C₄₁	1	2	yes	—
642	#462	C₂²×C₄₁	1	2	yes	—
643	#461	C₂²×C₄₁	1	2	yes	—
644	#461	C₂²×C₄₁	1	1	yes	characteristic
645	#461	C₂²×C₄₁	1	2	yes	—
646	#460	C₂²×C₄₁	1	1	yes	characteristic
647	#459	C₂²×C₄₁	1	1	yes	characteristic
648	#452	C₂²×C₄₁	1	2	yes	—
649	#452	C₂²×C₄₁	1	2	yes	—
650	#452	C₂²×C₄₁	1	2	yes	—
651	#451	C₂²×C₄₁	1	2	yes	—
652	#451	C₂²×C₄₁	1	1	yes	characteristic
653	#449	C₂²×C₄₁	1	2	yes	—
654	#448	C₂²×C₄₁	1	1	yes	characteristic
655	#446	C₂²×C₄₁	1	1	yes	characteristic
656	#446	C₂²×C₄₁	1	1	yes	characteristic
657	#446	C₂²×C₄₁	1	2	yes	—
658	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
659	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
660	C₈×Q₈	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	#440	C₂²×C₄₁	1	2	yes	—
665	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	—
666	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	—
667	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
668	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	—
669	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
670	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	—
671	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
672	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
673	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
674	C₄×D₈	C₂²×C₄₁	1	2	yes	—
675	#433	C₂²×C₄₁	1	2	yes	—
676	#433	C₂²×C₄₁	1	2	yes	—
677	#431	C₂²×C₄₁	1	1	yes	characteristic
678	#431	C₂²×C₄₁	1	1	yes	characteristic
679	C₄₁	#61929	1	1	yes	characteristic, direct product factor, Sylow
680	C₂×#41	C₂³×C₄₁	1	2	yes	—
681	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
682	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
683	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
684	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
685	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
686	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
687	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
688	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
689	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
690	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
691	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
692	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
693	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
694	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
695	C₂×D₈	C₂³×C₄₁	1	2	yes	—
696	C₄⋊Q₈	—	2	2	no	—
697	C₄⋊Q₈	—	2	2	no	—
698	C₄⋊Q₈	—	2	1	no	—
699	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
700	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
701	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
702	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
703	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
704	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
705	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
706	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
708	#127	C₂³×C₄₁	1	1	yes	characteristic
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	1	no	—
730	#125	—	2	1	no	—
731	#125	D₄×C₄₁	1	2	yes	—
732	#125	C₂³×C₄₁	1	1	yes	characteristic
733	#125	C₂³×C₄₁	1	2	yes	—
734	#124	—	2	1	no	—
735	#124	—	2	1	no	—
736	#124	—	2	2	no	—
737	#124	C₂³×C₄₁	1	1	yes	characteristic
738	#124	C₂³×C₄₁	1	2	yes	—
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	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
759	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
760	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
762	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
763	#121	—	2	1	no	—
764	#121	—	2	1	no	—
765	#121	C₂³×C₄₁	1	1	yes	characteristic
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	1	no	—
770	C₄×Q₈	—	2	2	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
775	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
778	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
779	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
780	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
782	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
783	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
784	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
785	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
787	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	C₂³×C₄₁	1	2	yes	—
796	C₄×D₄	C₂³×C₄₁	1	2	yes	—
797	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₄₁	1	2	yes	—
799	#117	—	2	1	no	—
800	#117	—	2	2	no	—
801	#117	—	2	2	no	—
802	#117	—	2	2	no	—
803	#117	—	2	2	no	—
804	#117	—	2	1	no	—
805	#117	—	2	1	no	—
806	#117	C₂³×C₄₁	1	2	yes	—
807	C₂×C₄⋊C₄	—	2	1	no	—
808	C₂×C₄⋊C₄	—	2	2	no	—
809	C₂×C₄⋊C₄	—	2	1	no	—
810	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
811	C₂×C₄²	—	2	1	no	—
812	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
813	#107	C₂³×C₄₁	1	2	yes	—
814	#107	C₂³×C₄₁	1	1	yes	characteristic
815	#107	C₂³×C₄₁	1	2	yes	—
816	#107	C₂³×C₄₁	1	1	yes	characteristic
817	#106	C₂³×C₄₁	1	1	yes	characteristic
818	#106	C₂³×C₄₁	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
820	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
821	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
822	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
823	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
824	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
825	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
826	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
827	#103	C₂³×C₄₁	1	2	yes	—
828	#103	C₂³×C₄₁	1	1	yes	characteristic
829	#103	C₂³×C₄₁	1	1	yes	characteristic
830	#103	C₂³×C₄₁	1	1	yes	characteristic
831	#103	C₂³×C₄₁	1	1	yes	characteristic
832	#103	C₂³×C₄₁	1	2	yes	—
833	#103	C₂³×C₄₁	1	1	yes	characteristic
834	#103	C₂³×C₄₁	1	1	yes	characteristic
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	#103	C₂³×C₄₁	1	2	yes	—
840	#103	C₂³×C₄₁	1	2	yes	—
841	#102	C₂³×C₄₁	1	1	yes	characteristic
842	#102	C₂³×C₄₁	1	2	yes	—
843	#102	C₂³×C₄₁	1	1	yes	characteristic
844	#102	C₂³×C₄₁	1	2	yes	—
845	#102	C₂³×C₄₁	1	2	yes	—
846	#102	C₂³×C₄₁	1	2	yes	—
847	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
848	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
849	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
850	#97	C₂³×C₄₁	1	2	yes	—
851	#97	C₂³×C₄₁	1	2	yes	—
852	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
853	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
854	C₄×C₈	C₂³×C₄₁	1	2	yes	—
855	C₄×C₈	C₂³×C₄₁	1	2	yes	—
856	C₄×C₈	C₂³×C₄₁	1	2	yes	—
857	#41	—	4	2	no	—
858	#41	—	4	2	no	—
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	4	1	no	—
863	C₂×Q₈	—	4	1	no	—
864	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
865	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
866	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
867	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
868	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
869	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
870	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
871	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	1	no	—
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	—	2	1	no	—
876	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
877	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
886	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
888	Q₁₆	—	4	2	no	—
889	Q₁₆	—	4	2	no	—
890	Q₁₆	—	4	2	no	—
891	Q₁₆	—	4	1	no	—
892	Q₁₆	—	4	2	no	—
893	Q₁₆	—	4	1	no	—
894	Q₁₆	—	4	2	no	—
895	SD₁₆	—	4	1	no	—
896	SD₁₆	—	4	2	no	—
897	SD₁₆	—	4	2	no	—
898	SD₁₆	—	4	2	no	—
899	SD₁₆	—	4	2	no	—
900	SD₁₆	—	4	1	no	—
901	D₈	—	4	2	no	—
902	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
904	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
905	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
906	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
907	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
939	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
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	1	yes	characteristic
943	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
951	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
970	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	1	no	—
973	C₄²	—	2	1	no	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
983	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
984	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
985	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
986	C₄²	C₂⁴×C₄₁	1	2	yes	—
987	C₄²	C₂⁴×C₄₁	1	2	yes	—
988	C₂³	—	2	1	no	—
989	C₂³	—	2	2	no	—
990	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
991	Q₈	—	2	2	no	—
992	Q₈	—	2	2	no	—
993	Q₈	—	2	1	no	—
994	Q₈	—	2	2	no	—
995	Q₈	—	2	2	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	2	1	no	—
998	Q₈	—	2	2	no	—
999	Q₈	—	2	1	no	—
1000	Q₈	—	2	1	no	—
1001	Q₈	—	2	1	no	—
1002	Q₈	—	2	2	no	—
1003	Q₈	—	4	2	no	—
1004	Q₈	—	4	2	no	—
1005	Q₈	—	8	1	no	—
1006	Q₈	—	8	2	no	—
1007	D₄	—	2	1	no	—
1008	D₄	—	2	2	no	—
1009	D₄	—	2	1	no	—
1010	D₄	—	2	2	no	—
1011	D₄	—	4	4	no	—
1012	D₄	—	4	2	no	—
1013	D₄	—	8	1	no	—
1014	D₄	—	8	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	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	4	1	no	—
1029	C₂×C₄	—	4	4	no	—
1030	C₂×C₄	—	4	2	no	—
1031	C₂×C₄	—	4	2	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	—	8	2	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	—	8	1	no	—
1036	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1037	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1038	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1039	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1040	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1041	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1042	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1043	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1044	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1045	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1046	C₈	—	2	2	no	—
1047	C₈	—	2	1	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	2	2	no	—
1050	C₈	—	2	1	no	—
1051	C₈	—	2	1	no	—
1052	C₂²	—	2	1	no	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	2	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	1	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	1	no	—
1061	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1062	C₄	—	2	1	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	2	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	2	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	2	no	—
1080	C₄	C₄₁×#578	1	2	yes	—
1081	C₄	C₄₁×#585	1	1	yes	characteristic
1082	C₄	C₄₁×#585	1	1	yes	characteristic
1083	C₂	—	4	1	no	—
1084	C₂	—	8	1	no	—
1085	C₂	—	8	2	no	—
1086	C₂	C₄₁×#3487	1	1	yes	characteristic
1087	C₂	C₂×C₄₁×#578	1	1	yes	characteristic
1088	C₂	C₄₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₄₁×#3212	C₂
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×#3507	C₂	semidirect
3. C₄₁×#3402	C₂	semidirect
4. C₄₁×#3400	C₂	semidirect
5. C₄₁×#3398	C₂	semidirect
6. C₄₁×#3395	C₂	semidirect
7. C₄₁×#3394	C₂	semidirect
8. C₄₁×#3393	C₂	semidirect
9. C₄₁×#3377	C₂	semidirect
10. C₄₁×#3375	C₂	semidirect
11. C₄₁×#3372	C₂	semidirect
12. C₄₁×#3364	C₂	semidirect
13. C₄₁×#3363	C₂	semidirect
14. C₄₁×#3361	C₂	semidirect
15. C₄₁×#3225	C₂	semidirect
16. C₄₁×#3223	C₂	semidirect
18. C₄₁×#3210	C₂	semidirect
19. C₄₁×#3124	C₂	semidirect
20. C₄₁×#3120	C₂	semidirect
21. C₄₁×#3108	C₂	semidirect
22. C₄₁×#3104	C₂	semidirect
23. C₄₁×#2986	C₂	semidirect
507. #61929	C₄₁	direct (N × H)
539. #3555	C₂×C₄₁	semidirect
540. #3507	C₂×C₄₁	semidirect
541. #3402	C₂×C₄₁	semidirect
542. #3400	C₂×C₄₁	semidirect
543. #3398	C₂×C₄₁	semidirect
544. #3395	C₂×C₄₁	semidirect
545. #3394	C₂×C₄₁	semidirect
546. #3393	C₂×C₄₁	semidirect
547. #3377	C₂×C₄₁	semidirect
548. #3375	C₂×C₄₁	semidirect
549. #3372	C₂×C₄₁	semidirect
550. #3364	C₂×C₄₁	semidirect
551. #3363	C₂×C₄₁	semidirect
552. #3361	C₂×C₄₁	semidirect
553. #3225	C₂×C₄₁	semidirect
554. #3223	C₂×C₄₁	semidirect
556. #3210	C₂×C₄₁	semidirect
557. #3124	C₂×C₄₁	semidirect
558. #3120	C₂×C₄₁	semidirect
559. #3108	C₂×C₄₁	semidirect
560. #3104	C₂×C₄₁	semidirect
561. #2986	C₂×C₄₁	semidirect
679. C₄₁	#61929	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×#3507	2
C₄₁×#3402	2
C₄₁×#3400	2
C₄₁×#3398	2
C₄₁×#3395	2
C₄₁×#3394	2
C₄₁×#3393	2
C₄₁×#3377	2
C₄₁×#3375	2
C₄₁×#3372	2
C₄₁×#3364	2
C₄₁×#3363	2
C₄₁×#3361	2
C₄₁×#3225	2
C₄₁×#3223	2
C₄₁×#3212	2
C₄₁×#3210	2
C₄₁×#3124	2
C₄₁×#3120	2
C₄₁×#3108	2
C₄₁×#3104	2
C₄₁×#2986	2
#61929	41

Subgroups — C41×#61929 #23838130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61929 #23838130