Subgroups — C₄₁×#61985 #23838186

Order 10496.

1842 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3398	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3367	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3313	C₂	1	4	yes	maximal, complemented
6	C₄₁×#3302	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3283	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3269	C₂	1	4	yes	maximal, complemented
9	C₄₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3249	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3216	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3116	C₂	1	2	yes	maximal, complemented
14	C₄₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#3035	C₂	1	2	yes	maximal, complemented
17	C₄₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₄₁	C₂²	1	2	yes	—
19	C₂×#135×C₄₁	C₂²	1	4	yes	—
20	C₄₁×#557	C₂²	1	1	yes	characteristic
21	C₄₁×#556	C₂²	1	2	yes	—
22	C₄₁×#556	C₂²	1	1	yes	characteristic
23	C₄₁×#556	C₂²	1	2	yes	—
24	C₄₁×#555	—	2	1	no	—
25	C₄₁×#554	—	2	1	no	—
26	C₄₁×#553	—	2	2	no	—
27	C₄₁×#552	—	2	1	no	—
28	C₄₁×#552	—	2	2	no	—
29	D₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₄₁×#548	—	2	1	no	—
31	C₄₁×#548	C₂²	1	4	yes	—
32	C₄₁×#547	C₂²	1	2	yes	—
33	C₄₁×#547	C₂²	1	2	yes	—
34	C₄₁×#547	C₂²	1	1	yes	characteristic
35	C₄₁×#542	—	2	2	no	—
36	C₄₁×#537	—	2	1	no	—
37	C₄₁×#533	C₂²	1	2	yes	—
38	C₄₁×#533	C₂²	1	1	yes	characteristic
39	C₄₁×#533	C₂²	1	2	yes	—
40	C₄₁×#532	C₂²	1	2	yes	—
41	C₄₁×#532	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
43	C₄₁×#529	—	2	2	no	—
44	C₄₁×#529	—	2	1	no	—
45	C₄₁×#520	—	2	1	no	—
46	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
47	C₄×#41×C₄₁	C₂²	1	2	yes	—
48	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
50	C₄₁×#497	C₂²	1	4	yes	—
51	C₄₁×#494	C₂²	1	2	yes	—
52	C₄₁×#489	C₂²	1	4	yes	—
53	C₄₁×#487	C₂²	1	2	yes	—
54	C₄₁×#485	C₂²	1	4	yes	—
55	C₄₁×#482	C₂²	1	2	yes	—
56	C₄₁×#477	C₂²	1	4	yes	—
57	C₄₁×#477	C₂²	1	1	yes	characteristic
58	C₄₁×#477	C₂²	1	2	yes	—
59	C₄₁×#476	C₂²	1	1	yes	characteristic
60	C₄₁×#474	C₂²	1	2	yes	—
61	C₄₁×#468	C₂²	1	4	yes	—
62	C₄₁×#467	C₂²	1	4	yes	—
63	C₄₁×#467	C₂²	1	4	yes	—
64	C₄₁×#464	C₂²	1	4	yes	—
65	C₄₁×#463	C₂²	1	4	yes	—
66	C₄₁×#462	C₂²	1	2	yes	—
67	C₄₁×#462	C₂²	1	2	yes	—
68	C₄₁×#462	C₂²	1	2	yes	—
69	C₄₁×#462	C₂²	1	4	yes	—
70	C₄₁×#462	C₂²	1	2	yes	—
71	C₄₁×#461	C₂²	1	2	yes	—
72	C₄₁×#461	C₂²	1	2	yes	—
73	C₄₁×#461	C₂²	1	2	yes	—
74	C₄₁×#460	C₂²	1	1	yes	characteristic
75	C₄₁×#460	C₂²	1	2	yes	—
76	C₄₁×#459	C₂²	1	1	yes	characteristic
77	C₄₁×#452	C₂²	1	4	yes	—
78	C₄₁×#452	C₂²	1	4	yes	—
79	C₄₁×#452	C₂²	1	4	yes	—
80	C₄₁×#451	C₂²	1	4	yes	—
81	C₄₁×#449	C₂²	1	2	yes	—
82	C₄₁×#446	C₂²	1	2	yes	—
83	C₄₁×#441	C₂²	1	4	yes	—
84	C₄₁×#440	C₂²	1	4	yes	—
85	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
86	C₄×D₈×C₄₁	C₂²	1	2	yes	—
87	C₄₁×#435	C₂²	1	4	yes	—
88	C₈×D₄×C₄₁	C₂²	1	2	yes	—
89	C₄₁×#432	C₂²	1	2	yes	—
90	C₄₁×#431	C₂²	1	1	yes	characteristic
91	C₄₁×#423	C₂²	1	1	yes	characteristic
92	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
93	C₄₁×#419	C₂²	1	2	yes	—
94	C₄₁×#416	C₂²	1	4	yes	—
95	C₂×#41×C₄₁	—	2	1	no	—
96	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
97	C₂×#41×C₄₁	C₂³	1	2	yes	—
98	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
99	C₂×#41×C₄₁	C₂³	1	4	yes	—
100	C₂²×Q₈×C₄₁	—	2	1	no	—
101	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
102	#137×C₄₁	—	4	4	no	—
103	#135×C₄₁	—	4	8	no	—
104	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
105	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
106	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
110	C₂×D₈×C₄₁	C₂³	1	2	yes	—
111	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
112	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
113	C₄⋊Q₈×C₄₁	—	2	1	no	—
114	C₄⋊Q₈×C₄₁	—	2	1	no	—
115	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
116	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
117	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
119	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
122	#127×C₄₁	C₂³	1	1	yes	characteristic
123	#126×C₄₁	—	2	4	no	—
124	#126×C₄₁	—	2	2	no	—
125	#126×C₄₁	—	2	2	no	—
126	#126×C₄₁	—	2	2	no	—
127	#125×C₄₁	—	2	1	no	—
128	#125×C₄₁	—	2	2	no	—
129	#125×C₄₁	—	2	2	no	—
130	#125×C₄₁	—	2	1	no	—
131	#125×C₄₁	—	2	2	no	—
132	#124×C₄₁	—	2	1	no	—
133	#124×C₄₁	—	2	2	no	—
134	#124×C₄₁	—	2	4	no	—
135	#124×C₄₁	—	2	1	no	—
136	#124×C₄₁	C₂³	1	4	yes	—
137	#123×C₄₁	—	2	2	no	—
138	#123×C₄₁	—	2	2	no	—
139	#123×C₄₁	—	2	2	no	—
140	#123×C₄₁	—	2	4	no	—
141	C₂²⋊Q₈×C₄₁	—	2	2	no	—
142	C₂²⋊Q₈×C₄₁	—	2	2	no	—
143	C₂²⋊Q₈×C₄₁	—	2	1	no	—
144	C₂²⋊Q₈×C₄₁	—	2	2	no	—
145	C₂²⋊Q₈×C₄₁	—	2	1	no	—
146	C₂²⋊Q₈×C₄₁	—	2	2	no	—
147	C₂²⋊Q₈×C₄₁	—	2	4	no	—
148	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
149	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
150	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
151	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
152	#121×C₄₁	—	2	1	no	—
153	#121×C₄₁	—	2	2	no	—
154	#121×C₄₁	—	2	2	no	—
155	#121×C₄₁	—	2	4	no	—
156	#121×C₄₁	—	2	2	no	—
157	#121×C₄₁	—	2	1	no	—
158	#121×C₄₁	—	2	2	no	—
159	#121×C₄₁	C₂³	1	2	yes	—
160	C₄×Q₈×C₄₁	—	2	1	no	—
161	C₄×Q₈×C₄₁	—	2	1	no	—
162	C₄×Q₈×C₄₁	—	2	2	no	—
163	C₄×Q₈×C₄₁	—	2	2	no	—
164	C₄×Q₈×C₄₁	—	2	1	no	—
165	C₄×Q₈×C₄₁	—	2	2	no	—
166	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
169	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
171	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
172	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₄₁	—	2	1	no	—
174	C₄×D₄×C₄₁	—	2	2	no	—
175	C₄×D₄×C₄₁	—	2	1	no	—
176	C₄×D₄×C₄₁	—	2	2	no	—
177	C₄×D₄×C₄₁	—	2	4	no	—
178	C₄×D₄×C₄₁	—	2	2	no	—
179	C₄×D₄×C₄₁	—	2	2	no	—
180	C₄×D₄×C₄₁	—	2	1	no	—
181	C₄×D₄×C₄₁	D₄	1	2	yes	—
182	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
183	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₄₁	C₂³	1	2	yes	—
186	C₄×D₄×C₄₁	C₂³	1	2	yes	—
187	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₄₁	C₂³	1	2	yes	—
189	#117×C₄₁	—	2	1	no	—
190	#117×C₄₁	—	2	2	no	—
191	#117×C₄₁	—	2	2	no	—
192	#117×C₄₁	—	2	2	no	—
193	#117×C₄₁	—	2	2	no	—
194	#117×C₄₁	—	2	1	no	—
195	#117×C₄₁	D₄	1	1	yes	characteristic
196	#117×C₄₁	D₄	1	2	yes	—
197	#117×C₄₁	C₂³	1	2	yes	—
198	#117×C₄₁	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
200	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
201	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
202	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
203	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
204	C₂×C₄²×C₄₁	—	2	2	no	—
205	C₂×C₄²×C₄₁	—	2	1	no	—
206	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
208	#107×C₄₁	C₂³	1	2	yes	—
209	#107×C₄₁	C₂³	1	4	yes	—
210	#106×C₄₁	C₂³	1	2	yes	—
211	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
212	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
213	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
214	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
215	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
216	#103×C₄₁	C₂³	1	4	yes	—
217	#103×C₄₁	C₂³	1	4	yes	—
218	#103×C₄₁	C₂³	1	4	yes	—
219	#103×C₄₁	C₂³	1	2	yes	—
220	#103×C₄₁	C₂³	1	4	yes	—
221	#103×C₄₁	C₂³	1	4	yes	—
222	#102×C₄₁	C₂³	1	2	yes	—
223	#102×C₄₁	C₂³	1	4	yes	—
224	#102×C₄₁	C₂³	1	2	yes	—
225	#102×C₄₁	C₂³	1	2	yes	—
226	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
227	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
228	#97×C₄₁	C₂³	1	4	yes	—
229	C₄×C₈×C₄₁	C₂³	1	2	yes	—
230	#41×C₄₁	—	2	4	no	—
231	#41×C₄₁	—	2	2	no	—
232	#41×C₄₁	—	4	2	no	—
233	#41×C₄₁	—	4	1	no	—
234	#41×C₄₁	—	4	2	no	—
235	#41×C₄₁	—	4	4	no	—
236	#41×C₄₁	—	4	4	no	—
237	#41×C₄₁	—	4	4	no	—
238	C₂×Q₈×C₄₁	—	2	2	no	—
239	C₂×Q₈×C₄₁	—	2	1	no	—
240	C₂×Q₈×C₄₁	—	2	1	no	—
241	C₂×Q₈×C₄₁	—	2	2	no	—
242	C₂×Q₈×C₄₁	—	4	2	no	—
243	C₂×Q₈×C₄₁	—	4	2	no	—
244	C₂×Q₈×C₄₁	—	4	4	no	—
245	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
247	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
248	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
249	C₂×D₄×C₄₁	—	2	2	no	—
250	C₂×D₄×C₄₁	—	2	2	no	—
251	C₂×D₄×C₄₁	—	2	1	no	—
252	C₂×D₄×C₄₁	—	2	4	no	—
253	C₂×D₄×C₄₁	—	2	1	no	—
254	C₂×D₄×C₄₁	—	2	1	no	—
255	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
258	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₄₁	—	2	2	no	—
260	C₂²×C₄×C₄₁	—	2	1	no	—
261	C₂²×C₄×C₄₁	—	2	1	no	—
262	C₂²×C₄×C₄₁	—	2	2	no	—
263	C₂²×C₄×C₄₁	—	2	2	no	—
264	C₂²×C₄×C₄₁	—	2	1	no	—
265	C₂²×C₄×C₄₁	—	2	2	no	—
266	C₂²×C₄×C₄₁	—	2	4	no	—
267	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
273	Q₁₆×C₄₁	—	4	4	no	—
274	Q₁₆×C₄₁	—	4	4	no	—
275	Q₁₆×C₄₁	—	4	4	no	—
276	SD₁₆×C₄₁	—	2	8	no	—
277	SD₁₆×C₄₁	—	4	2	no	—
278	SD₁₆×C₄₁	—	4	4	no	—
279	D₈×C₄₁	—	2	4	no	—
280	M₁₆×C₄₁	—	4	2	no	—
281	C₂×C₈×C₄₁	—	4	4	no	—
282	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
283	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
284	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
285	C₄⋊C₄×C₄₁	—	2	2	no	—
286	C₄⋊C₄×C₄₁	—	2	2	no	—
287	C₄⋊C₄×C₄₁	—	2	2	no	—
288	C₄⋊C₄×C₄₁	—	2	4	no	—
289	C₄⋊C₄×C₄₁	—	2	2	no	—
290	C₄⋊C₄×C₄₁	—	2	1	no	—
291	C₄⋊C₄×C₄₁	—	2	2	no	—
292	C₄⋊C₄×C₄₁	—	2	2	no	—
293	C₄⋊C₄×C₄₁	—	2	2	no	—
294	C₄⋊C₄×C₄₁	—	2	2	no	—
295	C₄⋊C₄×C₄₁	—	2	1	no	—
296	C₄⋊C₄×C₄₁	—	2	2	no	—
297	C₄⋊C₄×C₄₁	—	2	1	no	—
298	C₄⋊C₄×C₄₁	—	2	2	no	—
299	C₄⋊C₄×C₄₁	—	2	1	no	—
300	C₄⋊C₄×C₄₁	—	2	2	no	—
301	C₄⋊C₄×C₄₁	—	2	1	no	—
302	C₄⋊C₄×C₄₁	—	2	2	no	—
303	C₄⋊C₄×C₄₁	—	2	1	no	—
304	C₄⋊C₄×C₄₁	—	2	4	no	—
305	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
306	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
307	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
308	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
311	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
313	C₂²⋊C₄×C₄₁	—	2	4	no	—
314	C₂²⋊C₄×C₄₁	—	2	2	no	—
315	C₂²⋊C₄×C₄₁	—	2	2	no	—
316	C₂²⋊C₄×C₄₁	—	2	2	no	—
317	C₂²⋊C₄×C₄₁	—	2	2	no	—
318	C₂²⋊C₄×C₄₁	—	2	1	no	—
319	C₂²⋊C₄×C₄₁	—	2	1	no	—
320	C₂²⋊C₄×C₄₁	—	2	4	no	—
321	C₂²⋊C₄×C₄₁	—	2	2	no	—
322	C₂²⋊C₄×C₄₁	—	2	1	no	—
323	C₂²⋊C₄×C₄₁	—	2	4	no	—
324	C₂²⋊C₄×C₄₁	—	2	2	no	—
325	C₂²⋊C₄×C₄₁	—	2	2	no	—
326	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
327	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
328	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
329	C₄²×C₄₁	—	2	2	no	—
330	C₄²×C₄₁	—	2	1	no	—
331	C₄²×C₄₁	—	2	1	no	—
332	C₄²×C₄₁	—	2	2	no	—
333	C₄²×C₄₁	—	2	2	no	—
334	C₄²×C₄₁	—	2	1	no	—
335	C₄²×C₄₁	—	2	4	no	—
336	C₄²×C₄₁	C₂×D₄	1	2	yes	—
337	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₄₁	C₂×D₄	1	2	yes	—
339	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
341	C₄²×C₄₁	C₂⁴	1	2	yes	—
342	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
343	C₂³×C₄₁	—	2	1	no	—
344	C₂³×C₄₁	—	2	2	no	—
345	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
346	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
347	Q₈×C₄₁	—	2	2	no	—
348	Q₈×C₄₁	—	2	4	no	—
349	Q₈×C₄₁	—	2	2	no	—
350	Q₈×C₄₁	—	2	1	no	—
351	Q₈×C₄₁	—	2	1	no	—
352	Q₈×C₄₁	—	2	2	no	—
353	Q₈×C₄₁	—	2	4	no	—
354	Q₈×C₄₁	—	4	4	no	—
355	Q₈×C₄₁	—	4	2	no	—
356	Q₈×C₄₁	—	4	2	no	—
357	Q₈×C₄₁	—	8	2	no	—
358	D₄×C₄₁	—	2	2	no	—
359	D₄×C₄₁	—	2	2	no	—
360	D₄×C₄₁	—	2	1	no	—
361	D₄×C₄₁	—	2	2	no	—
362	D₄×C₄₁	—	4	2	no	—
363	D₄×C₄₁	—	4	2	no	—
364	D₄×C₄₁	—	4	2	no	—
365	D₄×C₄₁	—	4	4	no	—
366	D₄×C₄₁	—	4	4	no	—
367	D₄×C₄₁	—	4	2	no	—
368	D₄×C₄₁	—	8	4	no	—
369	D₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
370	C₂×C₄×C₄₁	—	2	2	no	—
371	C₂×C₄×C₄₁	—	2	2	no	—
372	C₂×C₄×C₄₁	—	2	4	no	—
373	C₂×C₄×C₄₁	—	2	2	no	—
374	C₂×C₄×C₄₁	—	2	1	no	—
375	C₂×C₄×C₄₁	—	2	1	no	—
376	C₂×C₄×C₄₁	—	2	2	no	—
377	C₂×C₄×C₄₁	—	2	1	no	—
378	C₂×C₄×C₄₁	—	2	2	no	—
379	C₂×C₄×C₄₁	—	2	2	no	—
380	C₂×C₄×C₄₁	—	2	1	no	—
381	C₂×C₄×C₄₁	—	2	2	no	—
382	C₂×C₄×C₄₁	—	2	1	no	—
383	C₂×C₄×C₄₁	—	2	4	no	—
384	C₂×C₄×C₄₁	—	4	2	no	—
385	C₂×C₄×C₄₁	—	4	4	no	—
386	C₂×C₄×C₄₁	—	4	2	no	—
387	C₂×C₄×C₄₁	—	4	4	no	—
388	C₂×C₄×C₄₁	—	4	2	no	—
389	C₂×C₄×C₄₁	—	4	4	no	—
390	C₂×C₄×C₄₁	—	4	2	no	—
391	C₂×C₄×C₄₁	—	8	4	no	—
392	C₂×C₄×C₄₁	—	8	2	no	—
393	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
402	C₈×C₄₁	—	2	2	no	—
403	C₈×C₄₁	—	2	4	no	—
404	C₈×C₄₁	—	2	2	no	—
405	#61985	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
406	C₂²×C₄₁	—	2	1	no	—
407	C₂²×C₄₁	—	2	2	no	—
408	C₂²×C₄₁	—	2	2	no	—
409	C₂²×C₄₁	—	2	1	no	—
410	C₂²×C₄₁	—	2	2	no	—
411	C₂²×C₄₁	—	2	2	no	—
412	C₂²×C₄₁	—	2	1	no	—
413	C₂²×C₄₁	—	4	1	no	—
414	C₂²×C₄₁	—	4	1	no	—
415	C₂²×C₄₁	—	4	2	no	—
416	C₂²×C₄₁	—	4	2	no	—
417	C₂²×C₄₁	—	4	2	no	—
418	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
419	C₄×C₄₁	—	2	2	no	—
420	C₄×C₄₁	—	2	1	no	—
421	C₄×C₄₁	—	2	1	no	—
422	C₄×C₄₁	—	2	2	no	—
423	C₄×C₄₁	—	2	2	no	—
424	C₄×C₄₁	—	2	1	no	—
425	C₄×C₄₁	—	4	2	no	—
426	C₄×C₄₁	—	4	1	no	—
427	C₄×C₄₁	—	4	4	no	—
428	C₄×C₄₁	—	4	2	no	—
429	C₄×C₄₁	—	4	2	no	—
430	C₄×C₄₁	—	4	1	no	—
431	C₄×C₄₁	—	4	1	no	—
432	C₄×C₄₁	#575	1	2	yes	—
433	C₄×C₄₁	#578	1	2	yes	—
434	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
435	C₄×C₄₁	#585	1	1	yes	characteristic
436	#3511	C₂×C₄₁	1	1	yes	characteristic, complemented
437	#3482	C₂×C₄₁	1	1	yes	characteristic, complemented
438	#3398	C₂×C₄₁	1	2	yes	complemented
439	#3367	C₂×C₄₁	1	2	yes	complemented
440	#3313	C₂×C₄₁	1	4	yes	complemented
441	#3302	C₂×C₄₁	1	2	yes	complemented
442	#3283	C₂×C₄₁	1	2	yes	complemented
443	#3269	C₂×C₄₁	1	4	yes	complemented
444	#3254	C₂×C₄₁	1	1	yes	characteristic, complemented
445	#3249	C₂×C₄₁	1	2	yes	complemented
446	#3216	C₂×C₄₁	1	2	yes	complemented
447	#3209	C₂×C₄₁	1	1	yes	characteristic, complemented
448	#3116	C₂×C₄₁	1	2	yes	complemented
449	#3106	C₂×C₄₁	1	1	yes	characteristic, complemented
450	#3039	C₂×C₄₁	1	1	yes	characteristic, complemented
451	#3035	C₂×C₄₁	1	2	yes	complemented
452	#2990	C₂×C₄₁	1	1	yes	characteristic, complemented
453	C₂×C₄₁	—	4	1	no	—
454	C₂×C₄₁	—	4	2	no	—
455	C₂×C₄₁	—	4	2	no	—
456	C₂×C₄₁	—	8	2	no	—
457	C₂×C₄₁	#3488	1	1	yes	characteristic
458	C₂×C₄₁	C₂×#575	1	1	yes	characteristic
459	C₂×C₄₁	C₂×#578	1	1	yes	characteristic
460	C₂×#137	C₂²×C₄₁	1	2	yes	—
461	C₂×#135	C₂²×C₄₁	1	4	yes	—
462	#557	C₂²×C₄₁	1	1	yes	characteristic
463	#556	C₂²×C₄₁	1	2	yes	—
464	#556	C₂²×C₄₁	1	1	yes	characteristic
465	#556	C₂²×C₄₁	1	2	yes	—
466	#555	—	2	1	no	—
467	#554	—	2	1	no	—
468	#553	—	2	2	no	—
469	#552	—	2	1	no	—
470	#552	—	2	2	no	—
471	D₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
472	#548	—	2	1	no	—
473	#548	C₂²×C₄₁	1	4	yes	—
474	#547	C₂²×C₄₁	1	2	yes	—
475	#547	C₂²×C₄₁	1	1	yes	characteristic
476	#547	C₂²×C₄₁	1	2	yes	—
477	#542	—	2	2	no	—
478	#537	—	2	1	no	—
479	#533	C₂²×C₄₁	1	2	yes	—
480	#533	C₂²×C₄₁	1	1	yes	characteristic
481	#533	C₂²×C₄₁	1	2	yes	—
482	#532	C₂²×C₄₁	1	2	yes	—
483	#532	C₂²×C₄₁	1	1	yes	characteristic
484	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
485	#529	—	2	2	no	—
486	#529	—	2	1	no	—
487	#520	—	2	1	no	—
488	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
489	C₄×#41	C₂²×C₄₁	1	2	yes	—
490	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
491	C₂×C₄×Q₈	—	2	1	no	—
492	#497	C₂²×C₄₁	1	4	yes	—
493	#494	C₂²×C₄₁	1	2	yes	—
494	#489	C₂²×C₄₁	1	4	yes	—
495	#487	C₂²×C₄₁	1	2	yes	—
496	#485	C₂²×C₄₁	1	4	yes	—
497	#482	C₂²×C₄₁	1	2	yes	—
498	#477	C₂²×C₄₁	1	1	yes	characteristic
499	#477	C₂²×C₄₁	1	4	yes	—
500	#477	C₂²×C₄₁	1	2	yes	—
501	#476	C₂²×C₄₁	1	1	yes	characteristic
502	#474	C₂²×C₄₁	1	2	yes	—
503	#468	C₂²×C₄₁	1	4	yes	—
504	#467	C₂²×C₄₁	1	4	yes	—
505	#467	C₂²×C₄₁	1	4	yes	—
506	#464	C₂²×C₄₁	1	4	yes	—
507	#463	C₂²×C₄₁	1	4	yes	—
508	#462	C₂²×C₄₁	1	2	yes	—
509	#462	C₂²×C₄₁	1	4	yes	—
510	#462	C₂²×C₄₁	1	2	yes	—
511	#462	C₂²×C₄₁	1	2	yes	—
512	#462	C₂²×C₄₁	1	2	yes	—
513	#461	C₂²×C₄₁	1	2	yes	—
514	#461	C₂²×C₄₁	1	2	yes	—
515	#461	C₂²×C₄₁	1	2	yes	—
516	#460	C₂²×C₄₁	1	1	yes	characteristic
517	#460	C₂²×C₄₁	1	2	yes	—
518	#459	C₂²×C₄₁	1	1	yes	characteristic
519	#452	C₂²×C₄₁	1	4	yes	—
520	#452	C₂²×C₄₁	1	4	yes	—
521	#452	C₂²×C₄₁	1	4	yes	—
522	#451	C₂²×C₄₁	1	4	yes	—
523	#449	C₂²×C₄₁	1	2	yes	—
524	#446	C₂²×C₄₁	1	2	yes	—
525	#441	C₂²×C₄₁	1	4	yes	—
526	#440	C₂²×C₄₁	1	4	yes	—
527	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
528	C₄×D₈	C₂²×C₄₁	1	2	yes	—
529	#435	C₂²×C₄₁	1	4	yes	—
530	C₈×D₄	C₂²×C₄₁	1	2	yes	—
531	#432	C₂²×C₄₁	1	2	yes	—
532	#431	C₂²×C₄₁	1	1	yes	characteristic
533	#423	C₂²×C₄₁	1	1	yes	characteristic
534	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
535	#419	C₂²×C₄₁	1	2	yes	—
536	#416	C₂²×C₄₁	1	4	yes	—
537	C₄₁	#61985	1	1	yes	characteristic, direct product factor, Sylow
538	C₂×#41	—	2	1	no	—
539	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
540	C₂×#41	C₂³×C₄₁	1	2	yes	—
541	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
542	C₂×#41	C₂³×C₄₁	1	4	yes	—
543	C₂²×Q₈	—	2	1	no	—
544	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
545	#137	—	4	4	no	—
546	#135	—	4	8	no	—
547	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
548	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
549	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
550	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
551	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
552	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
553	C₂×D₈	C₂³×C₄₁	1	2	yes	—
554	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
555	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
556	C₄⋊Q₈	—	2	1	no	—
557	C₄⋊Q₈	—	2	1	no	—
558	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
559	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
560	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
561	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
562	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
563	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
564	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
565	#127	C₂³×C₄₁	1	1	yes	characteristic
566	#126	—	2	4	no	—
567	#126	—	2	2	no	—
568	#126	—	2	2	no	—
569	#126	—	2	2	no	—
570	#125	—	2	1	no	—
571	#125	—	2	2	no	—
572	#125	—	2	2	no	—
573	#125	—	2	1	no	—
574	#125	—	2	2	no	—
575	#124	—	2	1	no	—
576	#124	—	2	2	no	—
577	#124	—	2	4	no	—
578	#124	—	2	1	no	—
579	#124	C₂³×C₄₁	1	4	yes	—
580	#123	—	2	2	no	—
581	#123	—	2	2	no	—
582	#123	—	2	2	no	—
583	#123	—	2	4	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	1	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	—	2	1	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	2	4	no	—
591	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
592	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
593	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
594	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
595	#121	—	2	1	no	—
596	#121	—	2	2	no	—
597	#121	—	2	2	no	—
598	#121	—	2	4	no	—
599	#121	—	2	2	no	—
600	#121	—	2	1	no	—
601	#121	—	2	2	no	—
602	#121	C₂³×C₄₁	1	2	yes	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	—	2	2	no	—
606	C₄×Q₈	—	2	2	no	—
607	C₄×Q₈	—	2	1	no	—
608	C₄×Q₈	—	2	2	no	—
609	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
610	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
611	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
612	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
613	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
614	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
615	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	4	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	D₄×C₄₁	1	2	yes	—
625	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
626	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
627	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
628	C₄×D₄	C₂³×C₄₁	1	2	yes	—
629	C₄×D₄	C₂³×C₄₁	1	2	yes	—
630	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
631	C₄×D₄	C₂³×C₄₁	1	2	yes	—
632	#117	—	2	1	no	—
633	#117	—	2	2	no	—
634	#117	—	2	2	no	—
635	#117	—	2	2	no	—
636	#117	—	2	2	no	—
637	#117	—	2	1	no	—
638	#117	D₄×C₄₁	1	1	yes	characteristic
639	#117	D₄×C₄₁	1	2	yes	—
640	#117	C₂³×C₄₁	1	2	yes	—
641	#117	C₂³×C₄₁	1	1	yes	characteristic
642	C₂×C₄⋊C₄	—	2	1	no	—
643	C₂×C₄⋊C₄	—	2	1	no	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	2	no	—
646	C₂×C₄⋊C₄	—	2	2	no	—
647	C₂×C₄²	—	2	2	no	—
648	C₂×C₄²	—	2	1	no	—
649	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
651	#107	C₂³×C₄₁	1	2	yes	—
652	#107	C₂³×C₄₁	1	4	yes	—
653	#106	C₂³×C₄₁	1	2	yes	—
654	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
655	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
656	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
657	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
658	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
659	#103	C₂³×C₄₁	1	4	yes	—
660	#103	C₂³×C₄₁	1	4	yes	—
661	#103	C₂³×C₄₁	1	4	yes	—
662	#103	C₂³×C₄₁	1	2	yes	—
663	#103	C₂³×C₄₁	1	4	yes	—
664	#103	C₂³×C₄₁	1	4	yes	—
665	#102	C₂³×C₄₁	1	2	yes	—
666	#102	C₂³×C₄₁	1	4	yes	—
667	#102	C₂³×C₄₁	1	2	yes	—
668	#102	C₂³×C₄₁	1	2	yes	—
669	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
670	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
671	#97	C₂³×C₄₁	1	4	yes	—
672	C₄×C₈	C₂³×C₄₁	1	2	yes	—
673	#41	—	2	4	no	—
674	#41	—	2	2	no	—
675	#41	—	4	2	no	—
676	#41	—	4	1	no	—
677	#41	—	4	2	no	—
678	#41	—	4	4	no	—
679	#41	—	4	4	no	—
680	#41	—	4	4	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	—	2	1	no	—
683	C₂×Q₈	—	2	1	no	—
684	C₂×Q₈	—	2	2	no	—
685	C₂×Q₈	—	4	2	no	—
686	C₂×Q₈	—	4	2	no	—
687	C₂×Q₈	—	4	4	no	—
688	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
689	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
690	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
691	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
699	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
700	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
701	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
713	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
716	Q₁₆	—	4	4	no	—
717	Q₁₆	—	4	4	no	—
718	Q₁₆	—	4	4	no	—
719	SD₁₆	—	2	8	no	—
720	SD₁₆	—	4	2	no	—
721	SD₁₆	—	4	4	no	—
722	D₈	—	2	4	no	—
723	M₁₆	—	4	2	no	—
724	C₂×C₈	—	4	4	no	—
725	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
726	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
727	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
749	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
750	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
751	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
752	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
753	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
754	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
755	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	2	1	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	1	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
770	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
771	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	1	no	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	1	no	—
778	C₄²	—	2	4	no	—
779	C₄²	C₂×D₄×C₄₁	1	2	yes	—
780	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
781	C₄²	C₂×D₄×C₄₁	1	2	yes	—
782	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
783	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
784	C₄²	C₂⁴×C₄₁	1	2	yes	—
785	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
786	C₂³	—	2	1	no	—
787	C₂³	—	2	2	no	—
788	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
789	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
790	Q₈	—	2	2	no	—
791	Q₈	—	2	4	no	—
792	Q₈	—	2	2	no	—
793	Q₈	—	2	1	no	—
794	Q₈	—	2	1	no	—
795	Q₈	—	2	2	no	—
796	Q₈	—	2	4	no	—
797	Q₈	—	4	4	no	—
798	Q₈	—	4	2	no	—
799	Q₈	—	4	2	no	—
800	Q₈	—	8	2	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	1	no	—
804	D₄	—	2	2	no	—
805	D₄	—	4	2	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	2	no	—
808	D₄	—	4	4	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	2	no	—
811	D₄	—	8	4	no	—
812	D₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	8	4	no	—
835	C₂×C₄	—	8	2	no	—
836	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
837	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
839	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
840	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
844	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
845	C₈	—	2	2	no	—
846	C₈	—	2	4	no	—
847	C₈	—	2	2	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
861	C₄	—	2	1	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	1	no	—
865	C₄	—	2	2	no	—
866	C₄	—	2	1	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	4	no	—
874	C₄	C₄₁×#575	1	2	yes	—
875	C₄	C₄₁×#578	1	2	yes	—
876	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
877	C₄	C₄₁×#585	1	1	yes	characteristic
878	C₂	—	4	1	no	—
879	C₂	—	4	2	no	—
880	C₂	—	4	2	no	—
881	C₂	—	8	2	no	—
882	C₂	C₄₁×#3488	1	1	yes	characteristic
883	C₂	C₂×C₄₁×#575	1	1	yes	characteristic
884	C₂	C₂×C₄₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3511	C₂	semidirect
2. C₄₁×#3482	C₂	semidirect
3. C₄₁×#3398	C₂	semidirect
4. C₄₁×#3367	C₂	semidirect
5. C₄₁×#3313	C₂	semidirect
6. C₄₁×#3302	C₂	semidirect
7. C₄₁×#3283	C₂	semidirect
8. C₄₁×#3269	C₂	semidirect
9. C₄₁×#3254	C₂	semidirect
10. C₄₁×#3249	C₂	semidirect
11. C₄₁×#3216	C₂	semidirect
12. C₄₁×#3209	C₂	semidirect
13. C₄₁×#3116	C₂	semidirect
14. C₄₁×#3106	C₂	semidirect
15. C₄₁×#3039	C₂	semidirect
16. C₄₁×#3035	C₂	semidirect
17. C₄₁×#2990	C₂	semidirect
405. #61985	C₄₁	direct (N × H)
436. #3511	C₂×C₄₁	semidirect
437. #3482	C₂×C₄₁	semidirect
438. #3398	C₂×C₄₁	semidirect
439. #3367	C₂×C₄₁	semidirect
440. #3313	C₂×C₄₁	semidirect
441. #3302	C₂×C₄₁	semidirect
442. #3283	C₂×C₄₁	semidirect
443. #3269	C₂×C₄₁	semidirect
444. #3254	C₂×C₄₁	semidirect
445. #3249	C₂×C₄₁	semidirect
446. #3216	C₂×C₄₁	semidirect
447. #3209	C₂×C₄₁	semidirect
448. #3116	C₂×C₄₁	semidirect
449. #3106	C₂×C₄₁	semidirect
450. #3039	C₂×C₄₁	semidirect
451. #3035	C₂×C₄₁	semidirect
452. #2990	C₂×C₄₁	semidirect
537. C₄₁	#61985	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×#3511	2
C₄₁×#3482	2
C₄₁×#3398	2
C₄₁×#3367	2
C₄₁×#3313	2
C₄₁×#3302	2
C₄₁×#3283	2
C₄₁×#3269	2
C₄₁×#3254	2
C₄₁×#3249	2
C₄₁×#3216	2
C₄₁×#3209	2
C₄₁×#3116	2
C₄₁×#3106	2
C₄₁×#3039	2
C₄₁×#3035	2
C₄₁×#2990	2
#61985	41

Subgroups — C41×#61985 #23838186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61985 #23838186