Subgroups — C₄₁×#61502 #23837703

Order 10496.

1788 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3524	C₂	1	2	yes	maximal, complemented
2	C₄₁×#3403	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3365	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3355	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#3348	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3305	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3301	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3300	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3277	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3271	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3179	C₂	1	2	yes	maximal, complemented
13	C₄₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3121	C₂	1	2	yes	maximal, complemented
15	C₄₁×#3119	C₂	1	2	yes	maximal, complemented
16	C₄₁×#3111	C₂	1	2	yes	maximal, complemented
17	C₄₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄₁×#2947	C₂	1	2	yes	maximal, complemented
19	C₄×#135×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#137×C₄₁	C₂²	1	2	yes	—
21	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
22	C₄₁×#559	—	2	2	no	—
23	C₄₁×#559	C₂²	1	2	yes	—
24	C₄₁×#557	C₂²	1	2	yes	—
25	C₄₁×#555	—	2	2	no	—
26	C₄₁×#555	C₂²	1	2	yes	—
27	C₄₁×#553	—	2	2	no	—
28	C₄₁×#553	C₂²	1	2	yes	—
29	C₄₁×#552	—	2	2	no	—
30	C₄₁×#552	C₂²	1	2	yes	—
31	C₄₁×#550	C₂²	1	2	yes	—
32	C₄₁×#548	C₂²	1	2	yes	—
33	C₄₁×#548	C₂²	1	2	yes	—
34	C₄₁×#542	—	2	2	no	—
35	C₄₁×#542	C₂²	1	2	yes	—
36	C₄₁×#540	—	2	2	no	—
37	C₄₁×#540	C₂²	1	2	yes	—
38	C₄₁×#529	—	2	2	no	—
39	C₄₁×#529	—	2	2	no	—
40	C₄₁×#529	C₂²	1	2	yes	—
41	C₄₁×#529	C₂²	1	1	yes	characteristic
42	C₄₁×#520	C₂²	1	2	yes	—
43	C₄₁×#519	C₂²	1	2	yes	—
44	C₄×#41×C₄₁	C₂²	1	2	yes	—
45	C₄₁×#501	C₂²	1	2	yes	—
46	C₄₁×#499	C₂²	1	1	yes	characteristic
47	C₄₁×#496	C₂²	1	2	yes	—
48	C₄₁×#495	C₂²	1	1	yes	characteristic
49	C₄₁×#488	C₂²	1	2	yes	—
50	C₄₁×#488	C₂²	1	2	yes	—
51	C₄₁×#486	C₂²	1	2	yes	—
52	C₄₁×#485	C₂²	1	2	yes	—
53	C₄₁×#485	C₂²	1	2	yes	—
54	C₄₁×#482	C₂²	1	2	yes	—
55	C₄₁×#482	C₂²	1	2	yes	—
56	C₄₁×#481	C₂²	1	2	yes	—
57	C₄₁×#480	C₂²	1	2	yes	—
58	C₄₁×#479	C₂²	1	2	yes	—
59	C₄₁×#479	C₂²	1	2	yes	—
60	C₄₁×#478	C₂²	1	2	yes	—
61	C₄₁×#478	C₂²	1	2	yes	—
62	C₄₁×#477	C₂²	1	2	yes	—
63	C₄₁×#475	C₂²	1	2	yes	—
64	C₄₁×#469	C₂²	1	2	yes	—
65	C₄₁×#468	C₂²	1	2	yes	—
66	C₄₁×#467	C₂²	1	1	yes	characteristic
67	C₄₁×#466	C₂²	1	2	yes	—
68	C₄₁×#466	C₂²	1	1	yes	characteristic
69	C₄₁×#465	C₂²	1	2	yes	—
70	C₄₁×#465	C₂²	1	2	yes	—
71	C₄₁×#464	C₂²	1	2	yes	—
72	C₄₁×#464	C₂²	1	2	yes	—
73	C₄₁×#464	C₂²	1	2	yes	—
74	C₄₁×#463	C₂²	1	2	yes	—
75	C₄₁×#460	C₂²	1	2	yes	—
76	C₄₁×#459	C₂²	1	2	yes	—
77	C₄₁×#452	C₂²	1	2	yes	—
78	C₄₁×#451	C₂²	1	2	yes	—
79	C₄₁×#449	C₂²	1	2	yes	—
80	C₄₁×#449	C₂²	1	2	yes	—
81	C₄₁×#449	C₂²	1	2	yes	—
82	C₄₁×#448	C₂²	1	2	yes	—
83	C₄₁×#446	C₂²	1	1	yes	characteristic
84	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
85	C₄₁×#442	C₂²	1	2	yes	—
86	C₄₁×#441	C₂²	1	2	yes	—
87	C₄₁×#441	C₂²	1	2	yes	—
88	C₄₁×#440	C₂²	1	2	yes	—
89	C₄₁×#440	C₂²	1	2	yes	—
90	C₄₁×#440	C₂²	1	2	yes	—
91	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	—
92	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
93	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
94	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
95	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
96	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
97	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
98	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
99	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
100	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
101	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
102	C₄₁×#436	C₂²	1	1	yes	characteristic
103	C₄₁×#435	C₂²	1	2	yes	—
104	C₈×D₄×C₄₁	C₂²	1	2	yes	—
105	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
106	C₄₁×#433	C₂²	1	2	yes	—
107	C₄₁×#432	C₂²	1	1	yes	characteristic
108	C₄₁×#428	C₂²	1	2	yes	—
109	C₄₁×#427	C₂²	1	1	yes	characteristic
110	C₄₁×#416	C₂²	1	2	yes	—
111	C₄₁×#416	C₂²	1	2	yes	—
112	C₂×#103×C₄₁	C₂²	1	2	yes	—
113	C₄₁×#405	C₂²	1	2	yes	—
114	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
115	C₂×#41×C₄₁	C₂³	1	2	yes	—
116	C₂×#41×C₄₁	C₂³	1	2	yes	—
117	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
118	#137×C₄₁	—	2	8	no	—
119	#135×C₄₁	—	2	4	no	—
120	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
121	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
122	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
123	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
127	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
128	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
129	C₂×D₈×C₄₁	C₂³	1	2	yes	—
130	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
131	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₄₁	—	2	2	no	—
135	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
136	#127×C₄₁	—	2	2	no	—
137	#127×C₄₁	C₂³	1	2	yes	—
138	#126×C₄₁	—	2	2	no	—
139	#126×C₄₁	—	2	2	no	—
140	#126×C₄₁	—	2	2	no	—
141	#126×C₄₁	—	2	2	no	—
142	#126×C₄₁	D₄	1	2	yes	—
143	#125×C₄₁	—	2	2	no	—
144	#125×C₄₁	—	2	2	no	—
145	#125×C₄₁	—	2	2	no	—
146	#125×C₄₁	D₄	1	1	yes	characteristic
147	#125×C₄₁	C₂³	1	2	yes	—
148	#125×C₄₁	C₂³	1	2	yes	—
149	#124×C₄₁	—	2	2	no	—
150	#124×C₄₁	—	2	2	no	—
151	#124×C₄₁	—	2	2	no	—
152	#124×C₄₁	—	2	2	no	—
153	#124×C₄₁	—	2	2	no	—
154	#124×C₄₁	—	2	2	no	—
155	#124×C₄₁	D₄	1	1	yes	characteristic
156	#124×C₄₁	C₂³	1	2	yes	—
157	#124×C₄₁	C₂³	1	2	yes	—
158	#123×C₄₁	—	2	2	no	—
159	#123×C₄₁	—	2	2	no	—
160	#123×C₄₁	—	2	2	no	—
161	#123×C₄₁	—	2	2	no	—
162	#123×C₄₁	—	2	2	no	—
163	#123×C₄₁	—	2	2	no	—
164	#123×C₄₁	—	2	2	no	—
165	#123×C₄₁	—	2	2	no	—
166	#123×C₄₁	D₄	1	2	yes	—
167	C₂²⋊Q₈×C₄₁	—	2	2	no	—
168	C₂²⋊Q₈×C₄₁	—	2	2	no	—
169	C₂²⋊Q₈×C₄₁	—	2	2	no	—
170	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
171	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
172	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
173	#121×C₄₁	—	2	2	no	—
174	#121×C₄₁	—	2	2	no	—
175	#121×C₄₁	—	2	2	no	—
176	#121×C₄₁	—	2	2	no	—
177	#121×C₄₁	—	2	2	no	—
178	#121×C₄₁	—	2	2	no	—
179	#121×C₄₁	—	2	2	no	—
180	#121×C₄₁	—	2	2	no	—
181	#121×C₄₁	D₄	1	1	yes	characteristic
182	#121×C₄₁	C₂³	1	2	yes	—
183	#121×C₄₁	C₂³	1	2	yes	—
184	#121×C₄₁	C₂³	1	2	yes	—
185	#121×C₄₁	C₂³	1	2	yes	—
186	C₄×Q₈×C₄₁	—	2	2	no	—
187	C₄×Q₈×C₄₁	—	2	2	no	—
188	C₄×Q₈×C₄₁	—	2	2	no	—
189	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
190	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
191	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
192	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
193	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
194	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
195	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
196	C₄×D₄×C₄₁	—	2	2	no	—
197	C₄×D₄×C₄₁	—	2	2	no	—
198	C₄×D₄×C₄₁	—	2	2	no	—
199	C₄×D₄×C₄₁	—	2	2	no	—
200	C₄×D₄×C₄₁	—	2	2	no	—
201	C₄×D₄×C₄₁	—	2	2	no	—
202	C₄×D₄×C₄₁	—	2	2	no	—
203	C₄×D₄×C₄₁	—	2	2	no	—
204	C₄×D₄×C₄₁	—	2	2	no	—
205	C₄×D₄×C₄₁	—	2	2	no	—
206	C₄×D₄×C₄₁	C₂³	1	2	yes	—
207	C₄×D₄×C₄₁	C₂³	1	2	yes	—
208	C₄×D₄×C₄₁	C₂³	1	2	yes	—
209	C₄×D₄×C₄₁	C₂³	1	2	yes	—
210	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
211	C₄×D₄×C₄₁	C₂³	1	2	yes	—
212	#117×C₄₁	—	2	2	no	—
213	#117×C₄₁	—	2	2	no	—
214	#117×C₄₁	—	2	2	no	—
215	#117×C₄₁	—	2	2	no	—
216	#117×C₄₁	—	2	2	no	—
217	#117×C₄₁	—	2	2	no	—
218	#117×C₄₁	—	2	2	no	—
219	#117×C₄₁	C₂³	1	2	yes	—
220	#117×C₄₁	C₂³	1	2	yes	—
221	#117×C₄₁	C₂³	1	2	yes	—
222	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
223	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
224	C₂×C₄²×C₄₁	—	2	2	no	—
225	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
226	#107×C₄₁	C₂³	1	1	yes	characteristic
227	#107×C₄₁	C₂³	1	2	yes	—
228	#107×C₄₁	C₂³	1	1	yes	characteristic
229	#107×C₄₁	C₂³	1	2	yes	—
230	#107×C₄₁	C₂³	1	1	yes	characteristic
231	#107×C₄₁	C₂³	1	1	yes	characteristic
232	#106×C₄₁	C₂³	1	2	yes	—
233	#106×C₄₁	C₂³	1	2	yes	—
234	#106×C₄₁	C₂³	1	2	yes	—
235	#106×C₄₁	C₂³	1	2	yes	—
236	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
237	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
238	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
239	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
240	#103×C₄₁	C₂³	1	2	yes	—
241	#103×C₄₁	C₂³	1	2	yes	—
242	#103×C₄₁	C₂³	1	2	yes	—
243	#103×C₄₁	C₂³	1	2	yes	—
244	#103×C₄₁	C₂³	1	2	yes	—
245	#103×C₄₁	C₂³	1	2	yes	—
246	#103×C₄₁	C₂³	1	2	yes	—
247	#103×C₄₁	C₂³	1	2	yes	—
248	#102×C₄₁	C₂³	1	2	yes	—
249	#102×C₄₁	C₂³	1	2	yes	—
250	#102×C₄₁	C₂³	1	2	yes	—
251	#102×C₄₁	C₂³	1	2	yes	—
252	#102×C₄₁	C₂³	1	2	yes	—
253	#102×C₄₁	C₂³	1	2	yes	—
254	#102×C₄₁	C₂³	1	2	yes	—
255	#102×C₄₁	C₂³	1	2	yes	—
256	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
257	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
258	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
259	#97×C₄₁	C₂³	1	2	yes	—
260	#97×C₄₁	C₂³	1	2	yes	—
261	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₄₁	C₂³	1	2	yes	—
266	#41×C₄₁	—	2	4	no	—
267	#41×C₄₁	—	2	4	no	—
268	#41×C₄₁	—	4	2	no	—
269	#41×C₄₁	—	4	2	no	—
270	C₂×Q₈×C₄₁	—	2	2	no	—
271	C₂×Q₈×C₄₁	—	2	2	no	—
272	C₂×Q₈×C₄₁	—	2	4	no	—
273	C₂×Q₈×C₄₁	—	4	2	no	—
274	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
275	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
276	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
277	C₂×D₄×C₄₁	—	2	2	no	—
278	C₂×D₄×C₄₁	—	2	2	no	—
279	C₂×D₄×C₄₁	—	2	2	no	—
280	C₂×D₄×C₄₁	—	2	2	no	—
281	C₂×D₄×C₄₁	—	2	2	no	—
282	C₂×D₄×C₄₁	—	2	2	no	—
283	C₂×D₄×C₄₁	—	2	2	no	—
284	C₂×D₄×C₄₁	—	2	2	no	—
285	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
286	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
287	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
288	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₄₁	—	2	2	no	—
290	C₂²×C₄×C₄₁	—	2	2	no	—
291	C₂²×C₄×C₄₁	—	2	2	no	—
292	C₂²×C₄×C₄₁	—	2	2	no	—
293	C₂²×C₄×C₄₁	—	2	2	no	—
294	C₂²×C₄×C₄₁	—	2	2	no	—
295	C₂²×C₄×C₄₁	—	2	2	no	—
296	C₂²×C₄×C₄₁	—	2	2	no	—
297	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
301	Q₁₆×C₄₁	—	2	4	no	—
302	Q₁₆×C₄₁	—	4	1	no	—
303	Q₁₆×C₄₁	#41	1	4	yes	—
304	SD₁₆×C₄₁	—	2	4	no	—
305	SD₁₆×C₄₁	—	2	4	no	—
306	SD₁₆×C₄₁	—	2	4	no	—
307	SD₁₆×C₄₁	—	4	2	no	—
308	D₈×C₄₁	—	2	2	no	—
309	D₈×C₄₁	—	4	2	no	—
310	D₈×C₄₁	—	4	1	no	—
311	M₁₆×C₄₁	—	2	4	no	—
312	C₂×C₈×C₄₁	—	2	2	no	—
313	C₂×C₈×C₄₁	—	4	2	no	—
314	C₂×C₈×C₄₁	—	4	1	no	—
315	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
316	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
317	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
318	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
319	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
320	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
321	C₄⋊C₄×C₄₁	—	2	2	no	—
322	C₄⋊C₄×C₄₁	—	2	2	no	—
323	C₄⋊C₄×C₄₁	—	2	2	no	—
324	C₄⋊C₄×C₄₁	—	2	2	no	—
325	C₄⋊C₄×C₄₁	—	2	2	no	—
326	C₄⋊C₄×C₄₁	—	2	2	no	—
327	C₄⋊C₄×C₄₁	—	2	2	no	—
328	C₄⋊C₄×C₄₁	—	2	2	no	—
329	C₄⋊C₄×C₄₁	—	2	2	no	—
330	C₄⋊C₄×C₄₁	—	2	2	no	—
331	C₄⋊C₄×C₄₁	—	2	2	no	—
332	C₄⋊C₄×C₄₁	—	2	2	no	—
333	C₄⋊C₄×C₄₁	—	2	2	no	—
334	C₄⋊C₄×C₄₁	—	2	2	no	—
335	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
336	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
337	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
338	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
339	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
340	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
341	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
343	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
345	C₂²⋊C₄×C₄₁	—	2	2	no	—
346	C₂²⋊C₄×C₄₁	—	2	2	no	—
347	C₂²⋊C₄×C₄₁	—	2	2	no	—
348	C₂²⋊C₄×C₄₁	—	2	2	no	—
349	C₂²⋊C₄×C₄₁	—	2	2	no	—
350	C₂²⋊C₄×C₄₁	—	2	2	no	—
351	C₂²⋊C₄×C₄₁	—	2	2	no	—
352	C₂²⋊C₄×C₄₁	—	2	2	no	—
353	C₂²⋊C₄×C₄₁	—	2	2	no	—
354	C₂²⋊C₄×C₄₁	—	2	2	no	—
355	C₂²⋊C₄×C₄₁	—	2	2	no	—
356	C₂²⋊C₄×C₄₁	—	2	2	no	—
357	C₂²⋊C₄×C₄₁	—	2	2	no	—
358	C₂²⋊C₄×C₄₁	—	2	2	no	—
359	C₂²⋊C₄×C₄₁	—	2	2	no	—
360	C₂²⋊C₄×C₄₁	—	2	2	no	—
361	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
362	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
363	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
364	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
365	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
366	C₄²×C₄₁	—	2	2	no	—
367	C₄²×C₄₁	—	2	2	no	—
368	C₄²×C₄₁	—	2	2	no	—
369	C₄²×C₄₁	—	2	2	no	—
370	C₄²×C₄₁	—	2	2	no	—
371	C₄²×C₄₁	—	2	2	no	—
372	C₄²×C₄₁	—	2	2	no	—
373	C₄²×C₄₁	—	2	2	no	—
374	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
377	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
378	C₄²×C₄₁	C₂⁴	1	2	yes	—
379	C₂³×C₄₁	—	2	2	no	—
380	C₂³×C₄₁	—	2	2	no	—
381	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
382	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
383	Q₈×C₄₁	—	2	2	no	—
384	Q₈×C₄₁	—	2	2	no	—
385	Q₈×C₄₁	—	2	2	no	—
386	Q₈×C₄₁	—	4	1	no	—
387	Q₈×C₄₁	—	4	4	no	—
388	Q₈×C₄₁	—	8	2	no	—
389	Q₈×C₄₁	C₂×#41	1	4	yes	—
390	D₄×C₄₁	—	2	2	no	—
391	D₄×C₄₁	—	2	2	no	—
392	D₄×C₄₁	—	2	2	no	—
393	D₄×C₄₁	—	2	2	no	—
394	D₄×C₄₁	—	4	1	no	—
395	D₄×C₄₁	—	4	2	no	—
396	D₄×C₄₁	—	4	4	no	—
397	D₄×C₄₁	—	4	4	no	—
398	D₄×C₄₁	—	8	2	no	—
399	D₄×C₄₁	—	8	2	no	—
400	D₄×C₄₁	—	8	2	no	—
401	D₄×C₄₁	—	8	2	no	—
402	D₄×C₄₁	—	8	2	no	—
403	D₄×C₄₁	—	8	2	no	—
404	C₂×C₄×C₄₁	—	2	2	no	—
405	C₂×C₄×C₄₁	—	2	1	no	—
406	C₂×C₄×C₄₁	—	2	2	no	—
407	C₂×C₄×C₄₁	—	2	2	no	—
408	C₂×C₄×C₄₁	—	2	1	no	—
409	C₂×C₄×C₄₁	—	2	2	no	—
410	C₂×C₄×C₄₁	—	2	2	no	—
411	C₂×C₄×C₄₁	—	2	2	no	—
412	C₂×C₄×C₄₁	—	2	2	no	—
413	C₂×C₄×C₄₁	—	2	2	no	—
414	C₂×C₄×C₄₁	—	4	1	no	—
415	C₂×C₄×C₄₁	—	4	1	no	—
416	C₂×C₄×C₄₁	—	4	4	no	—
417	C₂×C₄×C₄₁	—	4	4	no	—
418	C₂×C₄×C₄₁	—	4	4	no	—
419	C₂×C₄×C₄₁	—	8	2	no	—
420	C₂×C₄×C₄₁	—	8	2	no	—
421	C₂×C₄×C₄₁	—	8	2	no	—
422	C₂×C₄×C₄₁	—	8	2	no	—
423	C₂×C₄×C₄₁	—	8	2	no	—
424	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
429	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
433	C₈×C₄₁	—	2	1	no	—
434	C₈×C₄₁	—	2	2	no	—
435	C₈×C₄₁	—	2	1	no	—
436	C₈×C₄₁	—	2	2	no	—
437	C₈×C₄₁	—	2	1	no	—
438	C₈×C₄₁	C₂×#41	1	2	yes	—
439	#61502	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
440	C₂²×C₄₁	—	2	1	no	—
441	C₂²×C₄₁	—	2	1	no	—
442	C₂²×C₄₁	—	2	2	no	—
443	C₂²×C₄₁	—	2	2	no	—
444	C₂²×C₄₁	—	2	2	no	—
445	C₂²×C₄₁	—	2	1	no	—
446	C₂²×C₄₁	—	4	2	no	—
447	C₂²×C₄₁	—	4	2	no	—
448	C₂²×C₄₁	—	4	2	no	—
449	C₂²×C₄₁	—	4	2	no	—
450	C₂²×C₄₁	—	4	2	no	—
451	C₂²×C₄₁	—	4	2	no	—
452	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
453	C₄×C₄₁	—	2	1	no	—
454	C₄×C₄₁	—	2	1	no	—
455	C₄×C₄₁	—	2	1	no	—
456	C₄×C₄₁	—	2	1	no	—
457	C₄×C₄₁	—	2	2	no	—
458	C₄×C₄₁	—	2	2	no	—
459	C₄×C₄₁	—	2	1	no	—
460	C₄×C₄₁	—	2	2	no	—
461	C₄×C₄₁	—	2	4	no	—
462	C₄×C₄₁	—	4	2	no	—
463	C₄×C₄₁	—	4	2	no	—
464	C₄×C₄₁	—	4	2	no	—
465	C₄×C₄₁	—	4	2	no	—
466	C₄×C₄₁	—	4	2	no	—
467	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
468	C₄×C₄₁	#585	1	1	yes	characteristic
469	#3524	C₂×C₄₁	1	2	yes	complemented
470	#3403	C₂×C₄₁	1	1	yes	characteristic, complemented
471	#3390	C₂×C₄₁	1	1	yes	characteristic, complemented
472	#3365	C₂×C₄₁	1	2	yes	complemented
473	#3355	C₂×C₄₁	1	1	yes	characteristic, complemented
474	#3348	C₂×C₄₁	1	2	yes	complemented
475	#3305	C₂×C₄₁	1	2	yes	complemented
476	#3301	C₂×C₄₁	1	2	yes	complemented
477	#3300	C₂×C₄₁	1	2	yes	complemented
478	#3277	C₂×C₄₁	1	1	yes	characteristic, complemented
479	#3271	C₂×C₄₁	1	2	yes	complemented
480	#3179	C₂×C₄₁	1	2	yes	complemented
481	#3168	C₂×C₄₁	1	1	yes	characteristic, complemented
482	#3121	C₂×C₄₁	1	2	yes	complemented
483	#3119	C₂×C₄₁	1	2	yes	complemented
484	#3111	C₂×C₄₁	1	2	yes	complemented
485	#2966	C₂×C₄₁	1	1	yes	characteristic, complemented
486	#2947	C₂×C₄₁	1	2	yes	complemented
487	C₄×#135	C₂×C₄₁	1	1	yes	characteristic, complemented
488	C₂×C₄₁	—	4	1	no	—
489	C₂×C₄₁	—	4	2	no	—
490	C₂×C₄₁	—	8	2	no	—
491	C₂×C₄₁	—	8	2	no	—
492	C₂×C₄₁	D₄×#41	1	1	yes	characteristic
493	C₂×C₄₁	#3584	1	1	yes	characteristic
494	C₂×C₄₁	#3584	1	1	yes	characteristic
495	C₂×#137	C₂²×C₄₁	1	2	yes	—
496	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
497	#559	—	2	2	no	—
498	#559	C₂²×C₄₁	1	2	yes	—
499	#557	C₂²×C₄₁	1	2	yes	—
500	#555	—	2	2	no	—
501	#555	C₂²×C₄₁	1	2	yes	—
502	#553	—	2	2	no	—
503	#553	C₂²×C₄₁	1	2	yes	—
504	#552	—	2	2	no	—
505	#552	C₂²×C₄₁	1	2	yes	—
506	#550	C₂²×C₄₁	1	2	yes	—
507	#548	C₂²×C₄₁	1	2	yes	—
508	#548	C₂²×C₄₁	1	2	yes	—
509	#542	—	2	2	no	—
510	#542	C₂²×C₄₁	1	2	yes	—
511	#540	—	2	2	no	—
512	#540	C₂²×C₄₁	1	2	yes	—
513	#529	—	2	2	no	—
514	#529	—	2	2	no	—
515	#529	C₂²×C₄₁	1	2	yes	—
516	#529	C₂²×C₄₁	1	1	yes	characteristic
517	#520	C₂²×C₄₁	1	2	yes	—
518	#519	C₂²×C₄₁	1	2	yes	—
519	C₄×#41	C₂²×C₄₁	1	2	yes	—
520	#501	C₂²×C₄₁	1	2	yes	—
521	#499	C₂²×C₄₁	1	1	yes	characteristic
522	#496	C₂²×C₄₁	1	2	yes	—
523	#495	C₂²×C₄₁	1	1	yes	characteristic
524	#488	C₂²×C₄₁	1	2	yes	—
525	#488	C₂²×C₄₁	1	2	yes	—
526	#486	C₂²×C₄₁	1	2	yes	—
527	#485	C₂²×C₄₁	1	2	yes	—
528	#485	C₂²×C₄₁	1	2	yes	—
529	#482	C₂²×C₄₁	1	2	yes	—
530	#482	C₂²×C₄₁	1	2	yes	—
531	#481	C₂²×C₄₁	1	2	yes	—
532	#480	C₂²×C₄₁	1	2	yes	—
533	#479	C₂²×C₄₁	1	2	yes	—
534	#479	C₂²×C₄₁	1	2	yes	—
535	#478	C₂²×C₄₁	1	2	yes	—
536	#478	C₂²×C₄₁	1	2	yes	—
537	#477	C₂²×C₄₁	1	2	yes	—
538	#475	C₂²×C₄₁	1	2	yes	—
539	#469	C₂²×C₄₁	1	2	yes	—
540	#468	C₂²×C₄₁	1	2	yes	—
541	#467	C₂²×C₄₁	1	1	yes	characteristic
542	#466	C₂²×C₄₁	1	1	yes	characteristic
543	#466	C₂²×C₄₁	1	2	yes	—
544	#465	C₂²×C₄₁	1	2	yes	—
545	#465	C₂²×C₄₁	1	2	yes	—
546	#464	C₂²×C₄₁	1	2	yes	—
547	#464	C₂²×C₄₁	1	2	yes	—
548	#464	C₂²×C₄₁	1	2	yes	—
549	#463	C₂²×C₄₁	1	2	yes	—
550	#460	C₂²×C₄₁	1	2	yes	—
551	#459	C₂²×C₄₁	1	2	yes	—
552	#452	C₂²×C₄₁	1	2	yes	—
553	#451	C₂²×C₄₁	1	2	yes	—
554	#449	C₂²×C₄₁	1	2	yes	—
555	#449	C₂²×C₄₁	1	2	yes	—
556	#449	C₂²×C₄₁	1	2	yes	—
557	#448	C₂²×C₄₁	1	2	yes	—
558	#446	C₂²×C₄₁	1	1	yes	characteristic
559	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
560	#442	C₂²×C₄₁	1	2	yes	—
561	#441	C₂²×C₄₁	1	2	yes	—
562	#441	C₂²×C₄₁	1	2	yes	—
563	#440	C₂²×C₄₁	1	2	yes	—
564	#440	C₂²×C₄₁	1	2	yes	—
565	#440	C₂²×C₄₁	1	2	yes	—
566	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	—
567	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
568	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
569	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
570	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
571	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
572	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
573	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
574	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
575	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
576	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
577	#436	C₂²×C₄₁	1	1	yes	characteristic
578	#435	C₂²×C₄₁	1	2	yes	—
579	C₈×D₄	C₂²×C₄₁	1	2	yes	—
580	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
581	#433	C₂²×C₄₁	1	2	yes	—
582	#432	C₂²×C₄₁	1	1	yes	characteristic
583	#428	C₂²×C₄₁	1	2	yes	—
584	#427	C₂²×C₄₁	1	1	yes	characteristic
585	#416	C₂²×C₄₁	1	2	yes	—
586	#416	C₂²×C₄₁	1	2	yes	—
587	C₂×#103	C₂²×C₄₁	1	2	yes	—
588	#405	C₂²×C₄₁	1	2	yes	—
589	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
590	C₄₁	#61502	1	1	yes	characteristic, direct product factor, Sylow
591	C₂×#41	C₂³×C₄₁	1	2	yes	—
592	C₂×#41	C₂³×C₄₁	1	2	yes	—
593	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
594	#137	—	2	8	no	—
595	#135	—	2	4	no	—
596	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
597	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
598	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
599	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
600	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
601	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
602	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
603	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
604	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
605	C₂×D₈	C₂³×C₄₁	1	2	yes	—
606	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
607	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
608	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
609	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
610	C₄⋊Q₈	—	2	2	no	—
611	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
612	#127	—	2	2	no	—
613	#127	C₂³×C₄₁	1	2	yes	—
614	#126	—	2	2	no	—
615	#126	—	2	2	no	—
616	#126	—	2	2	no	—
617	#126	—	2	2	no	—
618	#126	D₄×C₄₁	1	2	yes	—
619	#125	—	2	2	no	—
620	#125	—	2	2	no	—
621	#125	—	2	2	no	—
622	#125	D₄×C₄₁	1	1	yes	characteristic
623	#125	C₂³×C₄₁	1	2	yes	—
624	#125	C₂³×C₄₁	1	2	yes	—
625	#124	—	2	2	no	—
626	#124	—	2	2	no	—
627	#124	—	2	2	no	—
628	#124	—	2	2	no	—
629	#124	—	2	2	no	—
630	#124	—	2	2	no	—
631	#124	D₄×C₄₁	1	1	yes	characteristic
632	#124	C₂³×C₄₁	1	2	yes	—
633	#124	C₂³×C₄₁	1	2	yes	—
634	#123	—	2	2	no	—
635	#123	—	2	2	no	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	#123	D₄×C₄₁	1	2	yes	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	—	2	2	no	—
646	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
647	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
648	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
649	#121	—	2	2	no	—
650	#121	—	2	2	no	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	2	no	—
655	#121	—	2	2	no	—
656	#121	—	2	2	no	—
657	#121	D₄×C₄₁	1	1	yes	characteristic
658	#121	C₂³×C₄₁	1	2	yes	—
659	#121	C₂³×C₄₁	1	2	yes	—
660	#121	C₂³×C₄₁	1	2	yes	—
661	#121	C₂³×C₄₁	1	2	yes	—
662	C₄×Q₈	—	2	2	no	—
663	C₄×Q₈	—	2	2	no	—
664	C₄×Q₈	—	2	2	no	—
665	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
666	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
667	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
668	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
669	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
670	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
671	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	2	no	—
680	C₄×D₄	—	2	2	no	—
681	C₄×D₄	—	2	2	no	—
682	C₄×D₄	C₂³×C₄₁	1	2	yes	—
683	C₄×D₄	C₂³×C₄₁	1	2	yes	—
684	C₄×D₄	C₂³×C₄₁	1	2	yes	—
685	C₄×D₄	C₂³×C₄₁	1	2	yes	—
686	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
687	C₄×D₄	C₂³×C₄₁	1	2	yes	—
688	#117	—	2	2	no	—
689	#117	—	2	2	no	—
690	#117	—	2	2	no	—
691	#117	—	2	2	no	—
692	#117	—	2	2	no	—
693	#117	—	2	2	no	—
694	#117	—	2	2	no	—
695	#117	C₂³×C₄₁	1	2	yes	—
696	#117	C₂³×C₄₁	1	2	yes	—
697	#117	C₂³×C₄₁	1	2	yes	—
698	C₂×C₄⋊C₄	—	2	2	no	—
699	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
700	C₂×C₄²	—	2	2	no	—
701	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
702	#107	C₂³×C₄₁	1	1	yes	characteristic
703	#107	C₂³×C₄₁	1	1	yes	characteristic
704	#107	C₂³×C₄₁	1	2	yes	—
705	#107	C₂³×C₄₁	1	1	yes	characteristic
706	#107	C₂³×C₄₁	1	1	yes	characteristic
707	#107	C₂³×C₄₁	1	2	yes	—
708	#106	C₂³×C₄₁	1	2	yes	—
709	#106	C₂³×C₄₁	1	2	yes	—
710	#106	C₂³×C₄₁	1	2	yes	—
711	#106	C₂³×C₄₁	1	2	yes	—
712	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
713	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
714	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
715	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
716	#103	C₂³×C₄₁	1	2	yes	—
717	#103	C₂³×C₄₁	1	2	yes	—
718	#103	C₂³×C₄₁	1	2	yes	—
719	#103	C₂³×C₄₁	1	2	yes	—
720	#103	C₂³×C₄₁	1	2	yes	—
721	#103	C₂³×C₄₁	1	2	yes	—
722	#103	C₂³×C₄₁	1	2	yes	—
723	#103	C₂³×C₄₁	1	2	yes	—
724	#102	C₂³×C₄₁	1	2	yes	—
725	#102	C₂³×C₄₁	1	2	yes	—
726	#102	C₂³×C₄₁	1	2	yes	—
727	#102	C₂³×C₄₁	1	2	yes	—
728	#102	C₂³×C₄₁	1	2	yes	—
729	#102	C₂³×C₄₁	1	2	yes	—
730	#102	C₂³×C₄₁	1	2	yes	—
731	#102	C₂³×C₄₁	1	2	yes	—
732	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
733	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
734	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
735	#97	C₂³×C₄₁	1	2	yes	—
736	#97	C₂³×C₄₁	1	2	yes	—
737	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
738	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
739	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
740	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
741	C₄×C₈	C₂³×C₄₁	1	2	yes	—
742	#41	—	2	4	no	—
743	#41	—	2	4	no	—
744	#41	—	4	2	no	—
745	#41	—	4	2	no	—
746	C₂×Q₈	—	2	2	no	—
747	C₂×Q₈	—	2	2	no	—
748	C₂×Q₈	—	2	4	no	—
749	C₂×Q₈	—	4	2	no	—
750	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
751	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
752	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
762	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
763	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
764	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
774	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
777	Q₁₆	—	2	4	no	—
778	Q₁₆	—	4	1	no	—
779	Q₁₆	#41×C₄₁	1	4	yes	—
780	SD₁₆	—	2	4	no	—
781	SD₁₆	—	2	4	no	—
782	SD₁₆	—	2	4	no	—
783	SD₁₆	—	4	2	no	—
784	D₈	—	2	2	no	—
785	D₈	—	4	2	no	—
786	D₈	—	4	1	no	—
787	M₁₆	—	2	4	no	—
788	C₂×C₈	—	2	2	no	—
789	C₂×C₈	—	4	2	no	—
790	C₂×C₈	—	4	1	no	—
791	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
792	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
793	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
794	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
795	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
796	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
812	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
813	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
814	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
815	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
816	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
817	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
818	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
819	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
820	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
838	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
839	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
840	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
841	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
842	C₄²	—	2	2	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	2	no	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
851	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
852	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
853	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
854	C₄²	C₂⁴×C₄₁	1	2	yes	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
858	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
859	Q₈	—	2	2	no	—
860	Q₈	—	2	2	no	—
861	Q₈	—	2	2	no	—
862	Q₈	—	4	1	no	—
863	Q₈	—	4	4	no	—
864	Q₈	—	8	2	no	—
865	Q₈	C₂×#41×C₄₁	1	4	yes	—
866	D₄	—	2	2	no	—
867	D₄	—	2	2	no	—
868	D₄	—	2	2	no	—
869	D₄	—	2	2	no	—
870	D₄	—	4	1	no	—
871	D₄	—	4	2	no	—
872	D₄	—	4	4	no	—
873	D₄	—	4	4	no	—
874	D₄	—	8	2	no	—
875	D₄	—	8	2	no	—
876	D₄	—	8	2	no	—
877	D₄	—	8	2	no	—
878	D₄	—	8	2	no	—
879	D₄	—	8	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	—	4	1	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	8	2	no	—
896	C₂×C₄	—	8	2	no	—
897	C₂×C₄	—	8	2	no	—
898	C₂×C₄	—	8	2	no	—
899	C₂×C₄	—	8	2	no	—
900	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
901	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
903	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
904	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
905	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
906	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
907	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
908	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
909	C₈	—	2	1	no	—
910	C₈	—	2	2	no	—
911	C₈	—	2	1	no	—
912	C₈	—	2	2	no	—
913	C₈	—	2	1	no	—
914	C₈	C₂×#41×C₄₁	1	2	yes	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	1	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
928	C₄	—	2	1	no	—
929	C₄	—	2	1	no	—
930	C₄	—	2	1	no	—
931	C₄	—	2	1	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	4	no	—
937	C₄	—	4	2	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	2	no	—
942	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
943	C₄	C₄₁×#585	1	1	yes	characteristic
944	C₂	—	4	1	no	—
945	C₂	—	4	2	no	—
946	C₂	—	8	2	no	—
947	C₂	—	8	2	no	—
948	C₂	D₄×#41×C₄₁	1	1	yes	characteristic
949	C₂	C₄₁×#3584	1	1	yes	characteristic
950	C₂	C₄₁×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3524	C₂	semidirect
2. C₄₁×#3403	C₂	semidirect
3. C₄₁×#3390	C₂	semidirect
4. C₄₁×#3365	C₂	semidirect
5. C₄₁×#3355	C₂	semidirect
6. C₄₁×#3348	C₂	semidirect
7. C₄₁×#3305	C₂	semidirect
8. C₄₁×#3301	C₂	semidirect
9. C₄₁×#3300	C₂	semidirect
10. C₄₁×#3277	C₂	semidirect
11. C₄₁×#3271	C₂	semidirect
12. C₄₁×#3179	C₂	semidirect
13. C₄₁×#3168	C₂	semidirect
14. C₄₁×#3121	C₂	semidirect
15. C₄₁×#3119	C₂	semidirect
16. C₄₁×#3111	C₂	semidirect
17. C₄₁×#2966	C₂	semidirect
18. C₄₁×#2947	C₂	semidirect
19. C₄×#135×C₄₁	C₂	semidirect
439. #61502	C₄₁	direct (N × H)
469. #3524	C₂×C₄₁	semidirect
470. #3403	C₂×C₄₁	semidirect
471. #3390	C₂×C₄₁	semidirect
472. #3365	C₂×C₄₁	semidirect
473. #3355	C₂×C₄₁	semidirect
474. #3348	C₂×C₄₁	semidirect
475. #3305	C₂×C₄₁	semidirect
476. #3301	C₂×C₄₁	semidirect
477. #3300	C₂×C₄₁	semidirect
478. #3277	C₂×C₄₁	semidirect
479. #3271	C₂×C₄₁	semidirect
480. #3179	C₂×C₄₁	semidirect
481. #3168	C₂×C₄₁	semidirect
482. #3121	C₂×C₄₁	semidirect
483. #3119	C₂×C₄₁	semidirect
484. #3111	C₂×C₄₁	semidirect
485. #2966	C₂×C₄₁	semidirect
486. #2947	C₂×C₄₁	semidirect
487. C₄×#135	C₂×C₄₁	semidirect
590. C₄₁	#61502	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×#3524	2
C₄₁×#3403	2
C₄₁×#3390	2
C₄₁×#3365	2
C₄₁×#3355	2
C₄₁×#3348	2
C₄₁×#3305	2
C₄₁×#3301	2
C₄₁×#3300	2
C₄₁×#3277	2
C₄₁×#3271	2
C₄₁×#3179	2
C₄₁×#3168	2
C₄₁×#3121	2
C₄₁×#3119	2
C₄₁×#3111	2
C₄₁×#2966	2
C₄₁×#2947	2
C₄×#135×C₄₁	2
#61502	41

Subgroups — C41×#61502 #23837703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61502 #23837703