Subgroups — C₄₁×#62170 #23838371

Order 10496.

1740 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3385	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3370	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3346	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3345	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3334	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3309	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3308	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3301	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3257	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3245	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3243	C₂	1	2	yes	maximal, complemented
14	C₄₁×#3234	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3119	C₂	1	2	yes	maximal, complemented
16	C₄₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#3083	C₂	1	2	yes	maximal, complemented
18	C₂×C₄₁×#479	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄₁×#563	—	2	1	no	—
21	C₄₁×#562	—	2	1	no	—
22	C₄₁×#559	—	2	1	no	—
23	C₄₁×#559	C₂²	1	1	yes	characteristic
24	Q₈²×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#554	—	2	1	no	—
26	C₄₁×#554	C₂²	1	2	yes	—
27	C₄₁×#554	C₂²	1	1	yes	characteristic
28	C₄₁×#553	C₂²	1	2	yes	—
29	C₄₁×#553	C₂²	1	2	yes	—
30	C₄₁×#550	C₂²	1	1	yes	characteristic
31	C₄₁×#548	C₂²	1	2	yes	—
32	C₄₁×#547	—	2	2	no	—
33	C₄₁×#547	—	2	2	no	—
34	C₄₁×#547	C₂²	1	2	yes	—
35	C₄₁×#547	C₂²	1	2	yes	—
36	C₄₁×#544	C₂²	1	2	yes	—
37	C₄₁×#542	—	2	2	no	—
38	C₄₁×#542	C₂²	1	2	yes	—
39	C₄₁×#540	C₂²	1	2	yes	—
40	C₄₁×#539	—	2	2	no	—
41	C₄₁×#539	—	2	1	no	—
42	C₄₁×#537	—	2	1	no	—
43	C₄₁×#532	—	2	1	no	—
44	C₄₁×#532	C₂²	1	1	yes	characteristic
45	C₄₁×#532	C₂²	1	1	yes	characteristic
46	C₄₁×#529	—	2	1	no	—
47	C₄₁×#529	C₂²	1	1	yes	characteristic
48	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
49	C₄₁×#520	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
51	C₄₁×#501	C₂²	1	2	yes	—
52	C₄₁×#501	C₂²	1	2	yes	—
53	C₄₁×#500	C₂²	1	2	yes	—
54	C₄₁×#490	C₂²	1	2	yes	—
55	C₄₁×#489	C₂²	1	2	yes	—
56	C₄₁×#488	C₂²	1	2	yes	—
57	C₄₁×#485	C₂²	1	2	yes	—
58	C₄₁×#484	C₂²	1	2	yes	—
59	C₄₁×#482	C₂²	1	2	yes	—
60	C₄₁×#481	C₂²	1	2	yes	—
61	C₄₁×#481	C₂²	1	2	yes	—
62	C₄₁×#480	C₂²	1	2	yes	—
63	C₄₁×#480	C₂²	1	2	yes	—
64	C₄₁×#480	C₂²	1	2	yes	—
65	C₄₁×#480	C₂²	1	2	yes	—
66	C₄₁×#479	C₂²	1	2	yes	—
67	C₄₁×#479	C₂²	1	2	yes	—
68	C₄₁×#479	C₂²	1	2	yes	—
69	C₄₁×#479	C₂²	1	2	yes	—
70	C₄₁×#479	C₂²	1	2	yes	—
71	C₄₁×#478	C₂²	1	2	yes	—
72	C₄₁×#478	C₂²	1	2	yes	—
73	C₄₁×#478	C₂²	1	2	yes	—
74	C₄₁×#477	C₂²	1	2	yes	—
75	C₄₁×#477	C₂²	1	1	yes	characteristic
76	C₄₁×#477	C₂²	1	1	yes	characteristic
77	C₄₁×#476	C₂²	1	2	yes	—
78	C₄₁×#474	C₂²	1	2	yes	—
79	C₄₁×#474	C₂²	1	2	yes	—
80	C₄₁×#474	C₂²	1	2	yes	—
81	C₄₁×#474	C₂²	1	2	yes	—
82	C₄₁×#469	C₂²	1	2	yes	—
83	C₄₁×#468	C₂²	1	2	yes	—
84	C₄₁×#466	C₂²	1	2	yes	—
85	C₄₁×#466	C₂²	1	2	yes	—
86	C₄₁×#466	C₂²	1	2	yes	—
87	C₄₁×#465	C₂²	1	2	yes	—
88	C₄₁×#463	C₂²	1	2	yes	—
89	C₄₁×#463	C₂²	1	2	yes	—
90	C₄₁×#460	C₂²	1	1	yes	characteristic
91	C₄₁×#460	C₂²	1	1	yes	characteristic
92	C₄₁×#459	C₂²	1	2	yes	—
93	C₄₁×#459	C₂²	1	2	yes	—
94	C₄₁×#449	C₂²	1	2	yes	—
95	C₄₁×#449	C₂²	1	2	yes	—
96	C₄₁×#448	C₂²	1	2	yes	—
97	C₄₁×#446	C₂²	1	2	yes	—
98	C₄₁×#442	C₂²	1	2	yes	—
99	C₄₁×#440	C₂²	1	2	yes	—
100	C₄₁×#440	C₂²	1	2	yes	—
101	C₄₁×#440	C₂²	1	2	yes	—
102	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
103	C₄×D₈×C₄₁	C₂²	1	2	yes	—
104	C₄₁×#435	C₂²	1	2	yes	—
105	C₄₁×#435	C₂²	1	2	yes	—
106	C₈×D₄×C₄₁	C₂²	1	2	yes	—
107	C₄₁×#433	C₂²	1	2	yes	—
108	C₄₁×#432	C₂²	1	1	yes	characteristic
109	C₄₁×#428	C₂²	1	2	yes	—
110	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
111	C₂×#107×C₄₁	C₂²	1	2	yes	—
112	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
113	C₄₁×#424	C₂²	1	2	yes	—
114	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
115	C₄₁×#417	C₂²	1	2	yes	—
116	C₄₁×#416	C₂²	1	2	yes	—
117	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
118	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
119	C₂×#41×C₄₁	—	2	2	no	—
120	C₂×#41×C₄₁	—	2	2	no	—
121	C₂×#41×C₄₁	—	2	1	no	—
122	C₂×#41×C₄₁	—	2	1	no	—
123	C₂×#41×C₄₁	C₂³	1	2	yes	—
124	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
125	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
127	C₂×D₈×C₄₁	C₂³	1	2	yes	—
128	C₂×D₈×C₄₁	C₂³	1	2	yes	—
129	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
130	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₄₁	—	2	1	no	—
134	C₄⋊Q₈×C₄₁	—	2	2	no	—
135	C₄⋊Q₈×C₄₁	—	2	2	no	—
136	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
138	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
139	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
140	#127×C₄₁	—	2	1	no	—
141	#127×C₄₁	C₂³	1	1	yes	characteristic
142	#127×C₄₁	C₂³	1	1	yes	characteristic
143	#126×C₄₁	—	2	2	no	—
144	#126×C₄₁	—	2	2	no	—
145	#126×C₄₁	—	2	2	no	—
146	#126×C₄₁	D₄	1	2	yes	—
147	#125×C₄₁	—	2	1	no	—
148	#125×C₄₁	—	2	2	no	—
149	#125×C₄₁	—	2	1	no	—
150	#125×C₄₁	—	2	1	no	—
151	#125×C₄₁	D₄	1	1	yes	characteristic
152	#125×C₄₁	C₂³	1	2	yes	—
153	#125×C₄₁	C₂³	1	2	yes	—
154	#125×C₄₁	C₂³	1	2	yes	—
155	#124×C₄₁	—	2	1	no	—
156	#124×C₄₁	—	2	2	no	—
157	#124×C₄₁	—	2	2	no	—
158	#124×C₄₁	—	2	1	no	—
159	#124×C₄₁	—	2	1	no	—
160	#124×C₄₁	D₄	1	1	yes	characteristic
161	#124×C₄₁	C₂³	1	2	yes	—
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	—	2	2	no	—
167	#123×C₄₁	—	2	2	no	—
168	#123×C₄₁	—	2	2	no	—
169	#123×C₄₁	—	2	2	no	—
170	#123×C₄₁	—	2	2	no	—
171	#123×C₄₁	—	2	2	no	—
172	#123×C₄₁	D₄	1	2	yes	—
173	C₂²⋊Q₈×C₄₁	—	2	2	no	—
174	C₂²⋊Q₈×C₄₁	—	2	2	no	—
175	C₂²⋊Q₈×C₄₁	—	2	2	no	—
176	C₂²⋊Q₈×C₄₁	—	2	2	no	—
177	C₂²⋊Q₈×C₄₁	—	2	2	no	—
178	C₂²⋊Q₈×C₄₁	—	2	2	no	—
179	C₂²⋊Q₈×C₄₁	—	2	2	no	—
180	C₂²⋊Q₈×C₄₁	—	2	2	no	—
181	C₂²⋊Q₈×C₄₁	—	2	2	no	—
182	C₂²⋊Q₈×C₄₁	—	2	2	no	—
183	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
184	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
185	#121×C₄₁	—	2	2	no	—
186	#121×C₄₁	—	2	2	no	—
187	#121×C₄₁	—	2	2	no	—
188	#121×C₄₁	—	2	1	no	—
189	#121×C₄₁	—	2	1	no	—
190	#121×C₄₁	—	2	2	no	—
191	#121×C₄₁	—	2	2	no	—
192	#121×C₄₁	—	2	2	no	—
193	#121×C₄₁	D₄	1	1	yes	characteristic
194	#121×C₄₁	C₂³	1	2	yes	—
195	#121×C₄₁	C₂³	1	2	yes	—
196	#121×C₄₁	C₂³	1	2	yes	—
197	#121×C₄₁	C₂³	1	2	yes	—
198	#121×C₄₁	C₂³	1	2	yes	—
199	C₄×Q₈×C₄₁	—	2	1	no	—
200	C₄×Q₈×C₄₁	—	2	1	no	—
201	C₄×Q₈×C₄₁	—	2	1	no	—
202	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
203	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
204	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
205	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
207	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
208	C₄×D₄×C₄₁	—	2	1	no	—
209	C₄×D₄×C₄₁	—	2	1	no	—
210	C₄×D₄×C₄₁	—	2	1	no	—
211	C₄×D₄×C₄₁	—	2	2	no	—
212	C₄×D₄×C₄₁	—	2	2	no	—
213	C₄×D₄×C₄₁	—	2	2	no	—
214	C₄×D₄×C₄₁	—	2	2	no	—
215	C₄×D₄×C₄₁	—	2	2	no	—
216	C₄×D₄×C₄₁	—	2	1	no	—
217	C₄×D₄×C₄₁	—	2	1	no	—
218	C₄×D₄×C₄₁	C₂³	1	2	yes	—
219	C₄×D₄×C₄₁	C₂³	1	2	yes	—
220	C₄×D₄×C₄₁	C₂³	1	2	yes	—
221	C₄×D₄×C₄₁	C₂³	1	2	yes	—
222	C₄×D₄×C₄₁	C₂³	1	2	yes	—
223	C₄×D₄×C₄₁	C₂³	1	2	yes	—
224	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
225	#117×C₄₁	—	2	2	no	—
226	#117×C₄₁	C₂³	1	2	yes	—
227	#117×C₄₁	C₂³	1	2	yes	—
228	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
229	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
230	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
231	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
232	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
233	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
238	C₂×C₄²×C₄₁	—	2	1	no	—
239	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
240	#107×C₄₁	C₂³	1	2	yes	—
241	#107×C₄₁	C₂³	1	2	yes	—
242	#107×C₄₁	C₂³	1	2	yes	—
243	#107×C₄₁	C₂³	1	2	yes	—
244	#107×C₄₁	C₂³	1	2	yes	—
245	#107×C₄₁	C₂³	1	2	yes	—
246	#107×C₄₁	C₂³	1	2	yes	—
247	#107×C₄₁	C₂³	1	2	yes	—
248	#106×C₄₁	C₂³	1	2	yes	—
249	#106×C₄₁	C₂³	1	2	yes	—
250	#106×C₄₁	C₂³	1	2	yes	—
251	#106×C₄₁	C₂³	1	2	yes	—
252	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
253	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
254	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
255	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
256	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
257	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
258	#103×C₄₁	C₂³	1	2	yes	—
259	#103×C₄₁	C₂³	1	2	yes	—
260	#103×C₄₁	C₂³	1	2	yes	—
261	#103×C₄₁	C₂³	1	2	yes	—
262	#103×C₄₁	C₂³	1	2	yes	—
263	#103×C₄₁	C₂³	1	2	yes	—
264	#102×C₄₁	C₂³	1	2	yes	—
265	#102×C₄₁	C₂³	1	2	yes	—
266	#102×C₄₁	C₂³	1	2	yes	—
267	#102×C₄₁	C₂³	1	2	yes	—
268	#102×C₄₁	C₂³	1	2	yes	—
269	#102×C₄₁	C₂³	1	2	yes	—
270	#102×C₄₁	C₂³	1	2	yes	—
271	#102×C₄₁	C₂³	1	2	yes	—
272	#102×C₄₁	C₂³	1	2	yes	—
273	#102×C₄₁	C₂³	1	2	yes	—
274	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
277	#97×C₄₁	C₂³	1	2	yes	—
278	#97×C₄₁	C₂³	1	2	yes	—
279	C₄×C₈×C₄₁	C₂³	1	2	yes	—
280	#41×C₄₁	—	2	4	no	—
281	#41×C₄₁	—	4	2	no	—
282	#41×C₄₁	—	8	2	no	—
283	#41×C₄₁	—	8	2	no	—
284	#41×C₄₁	—	8	4	no	—
285	#41×C₄₁	—	8	4	no	—
286	C₂×Q₈×C₄₁	—	2	1	no	—
287	C₂×Q₈×C₄₁	—	2	2	no	—
288	C₂×Q₈×C₄₁	—	2	2	no	—
289	C₂×Q₈×C₄₁	—	2	1	no	—
290	C₂×Q₈×C₄₁	—	2	1	no	—
291	C₂×Q₈×C₄₁	—	2	2	no	—
292	C₂×Q₈×C₄₁	—	4	1	no	—
293	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
294	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
295	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
296	C₂×D₄×C₄₁	—	2	2	no	—
297	C₂×D₄×C₄₁	—	2	2	no	—
298	C₂×D₄×C₄₁	—	2	2	no	—
299	C₂×D₄×C₄₁	—	2	2	no	—
300	C₂×D₄×C₄₁	—	2	2	no	—
301	C₂×D₄×C₄₁	—	2	2	no	—
302	C₂×D₄×C₄₁	—	2	1	no	—
303	C₂×D₄×C₄₁	—	2	1	no	—
304	C₂×D₄×C₄₁	—	2	1	no	—
305	C₂×D₄×C₄₁	—	2	1	no	—
306	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
307	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
308	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
309	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₄₁	—	2	1	no	—
311	C₂²×C₄×C₄₁	—	2	1	no	—
312	C₂²×C₄×C₄₁	—	2	1	no	—
313	C₂²×C₄×C₄₁	—	2	1	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	2	no	—
319	C₂²×C₄×C₄₁	—	2	2	no	—
320	C₂²×C₄×C₄₁	—	2	2	no	—
321	C₂²×C₄×C₄₁	—	2	2	no	—
322	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
326	SD₁₆×C₄₁	—	2	4	no	—
327	SD₁₆×C₄₁	—	4	2	no	—
328	D₈×C₄₁	—	4	2	no	—
329	D₈×C₄₁	—	4	2	no	—
330	M₁₆×C₄₁	—	4	2	no	—
331	C₂×C₈×C₄₁	—	4	1	no	—
332	C₂×C₈×C₄₁	—	4	2	no	—
333	C₂×C₈×C₄₁	—	4	1	no	—
334	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
335	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
336	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
337	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₄₁	—	2	1	no	—
339	C₄⋊C₄×C₄₁	—	2	2	no	—
340	C₄⋊C₄×C₄₁	—	2	2	no	—
341	C₄⋊C₄×C₄₁	—	2	2	no	—
342	C₄⋊C₄×C₄₁	—	2	1	no	—
343	C₄⋊C₄×C₄₁	—	2	1	no	—
344	C₄⋊C₄×C₄₁	—	2	1	no	—
345	C₄⋊C₄×C₄₁	—	2	2	no	—
346	C₄⋊C₄×C₄₁	—	2	2	no	—
347	C₄⋊C₄×C₄₁	—	2	2	no	—
348	C₄⋊C₄×C₄₁	—	2	2	no	—
349	C₄⋊C₄×C₄₁	—	2	2	no	—
350	C₄⋊C₄×C₄₁	—	2	1	no	—
351	C₄⋊C₄×C₄₁	—	2	1	no	—
352	C₄⋊C₄×C₄₁	—	2	2	no	—
353	C₄⋊C₄×C₄₁	—	2	1	no	—
354	C₄⋊C₄×C₄₁	—	2	1	no	—
355	C₄⋊C₄×C₄₁	—	2	1	no	—
356	C₄⋊C₄×C₄₁	—	2	2	no	—
357	C₄⋊C₄×C₄₁	—	2	2	no	—
358	C₄⋊C₄×C₄₁	—	2	2	no	—
359	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
364	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
365	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
370	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
371	C₂²⋊C₄×C₄₁	—	2	2	no	—
372	C₂²⋊C₄×C₄₁	—	2	2	no	—
373	C₂²⋊C₄×C₄₁	—	2	2	no	—
374	C₂²⋊C₄×C₄₁	—	2	2	no	—
375	C₂²⋊C₄×C₄₁	—	2	2	no	—
376	C₂²⋊C₄×C₄₁	—	2	2	no	—
377	C₂²⋊C₄×C₄₁	—	2	2	no	—
378	C₂²⋊C₄×C₄₁	—	2	2	no	—
379	C₂²⋊C₄×C₄₁	—	2	2	no	—
380	C₂²⋊C₄×C₄₁	—	2	2	no	—
381	C₂²⋊C₄×C₄₁	—	2	2	no	—
382	C₂²⋊C₄×C₄₁	—	2	2	no	—
383	C₂²⋊C₄×C₄₁	—	2	2	no	—
384	C₂²⋊C₄×C₄₁	—	2	2	no	—
385	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
386	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
387	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
390	C₄²×C₄₁	—	2	1	no	—
391	C₄²×C₄₁	—	2	1	no	—
392	C₄²×C₄₁	—	2	1	no	—
393	C₄²×C₄₁	—	2	1	no	—
394	C₄²×C₄₁	—	2	2	no	—
395	C₄²×C₄₁	—	2	2	no	—
396	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₄₁	C₂⁴	1	2	yes	—
399	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
400	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
401	C₂³×C₄₁	—	2	2	no	—
402	C₂³×C₄₁	—	2	2	no	—
403	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
404	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
405	Q₈×C₄₁	—	2	1	no	—
406	Q₈×C₄₁	—	2	1	no	—
407	Q₈×C₄₁	—	2	1	no	—
408	Q₈×C₄₁	—	4	1	no	—
409	Q₈×C₄₁	—	4	2	no	—
410	Q₈×C₄₁	—	8	1	no	—
411	Q₈×C₄₁	—	8	1	no	—
412	Q₈×C₄₁	—	8	2	no	—
413	Q₈×C₄₁	—	8	2	no	—
414	Q₈×C₄₁	2₋¹⁺⁴	1	2	yes	—
415	D₄×C₄₁	—	2	4	no	—
416	D₄×C₄₁	—	2	2	no	—
417	D₄×C₄₁	—	2	2	no	—
418	D₄×C₄₁	—	2	2	no	—
419	D₄×C₄₁	—	2	2	no	—
420	D₄×C₄₁	—	4	1	no	—
421	D₄×C₄₁	—	4	4	no	—
422	D₄×C₄₁	—	4	2	no	—
423	D₄×C₄₁	—	4	4	no	—
424	D₄×C₄₁	—	4	4	no	—
425	D₄×C₄₁	—	8	1	no	—
426	D₄×C₄₁	—	8	1	no	—
427	D₄×C₄₁	—	8	1	no	—
428	D₄×C₄₁	—	8	2	no	—
429	D₄×C₄₁	—	8	2	no	—
430	D₄×C₄₁	—	8	2	no	—
431	C₂×C₄×C₄₁	—	2	2	no	—
432	C₂×C₄×C₄₁	—	2	1	no	—
433	C₂×C₄×C₄₁	—	2	1	no	—
434	C₂×C₄×C₄₁	—	2	2	no	—
435	C₂×C₄×C₄₁	—	2	1	no	—
436	C₂×C₄×C₄₁	—	2	2	no	—
437	C₂×C₄×C₄₁	—	2	1	no	—
438	C₂×C₄×C₄₁	—	2	1	no	—
439	C₂×C₄×C₄₁	—	2	1	no	—
440	C₂×C₄×C₄₁	—	2	2	no	—
441	C₂×C₄×C₄₁	—	2	2	no	—
442	C₂×C₄×C₄₁	—	2	2	no	—
443	C₂×C₄×C₄₁	—	2	2	no	—
444	C₂×C₄×C₄₁	—	4	1	no	—
445	C₂×C₄×C₄₁	—	4	4	no	—
446	C₂×C₄×C₄₁	—	4	2	no	—
447	C₂×C₄×C₄₁	—	4	2	no	—
448	C₂×C₄×C₄₁	—	4	2	no	—
449	C₂×C₄×C₄₁	—	8	2	no	—
450	C₂×C₄×C₄₁	—	8	2	no	—
451	C₂×C₄×C₄₁	—	8	2	no	—
452	C₂×C₄×C₄₁	—	8	2	no	—
453	C₂×C₄×C₄₁	—	8	2	no	—
454	C₂×C₄×C₄₁	—	8	1	no	—
455	C₂×C₄×C₄₁	—	8	2	no	—
456	C₂×C₄×C₄₁	—	8	2	no	—
457	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
466	C₈×C₄₁	—	2	2	no	—
467	C₈×C₄₁	—	2	2	no	—
468	C₈×C₄₁	—	2	2	no	—
469	C₈×C₄₁	—	2	2	no	—
470	#62170	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
471	C₂²×C₄₁	—	2	1	no	—
472	C₂²×C₄₁	—	2	1	no	—
473	C₂²×C₄₁	—	2	2	no	—
474	C₂²×C₄₁	—	2	2	no	—
475	C₂²×C₄₁	—	2	2	no	—
476	C₂²×C₄₁	—	4	2	no	—
477	C₂²×C₄₁	—	4	2	no	—
478	C₂²×C₄₁	—	4	2	no	—
479	C₂²×C₄₁	—	4	2	no	—
480	C₂²×C₄₁	—	4	2	no	—
481	C₂²×C₄₁	—	4	2	no	—
482	C₂²×C₄₁	#576	1	2	yes	—
483	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
484	C₄×C₄₁	—	2	1	no	—
485	C₄×C₄₁	—	2	1	no	—
486	C₄×C₄₁	—	2	2	no	—
487	C₄×C₄₁	—	2	2	no	—
488	C₄×C₄₁	—	2	1	no	—
489	C₄×C₄₁	—	2	2	no	—
490	C₄×C₄₁	—	2	1	no	—
491	C₄×C₄₁	—	2	1	no	—
492	C₄×C₄₁	—	2	2	no	—
493	C₄×C₄₁	—	4	2	no	—
494	C₄×C₄₁	—	4	1	no	—
495	C₄×C₄₁	—	4	1	no	—
496	C₄×C₄₁	—	4	2	no	—
497	C₄×C₄₁	—	4	1	no	—
498	C₄×C₄₁	—	4	2	no	—
499	C₄×C₄₁	—	4	2	no	—
500	C₄×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
501	C₄×C₄₁	#585	1	1	yes	characteristic
502	#3559	C₂×C₄₁	1	1	yes	characteristic, complemented
503	#3522	C₂×C₄₁	1	1	yes	characteristic, complemented
504	#3385	C₂×C₄₁	1	2	yes	complemented
505	#3370	C₂×C₄₁	1	2	yes	complemented
506	#3346	C₂×C₄₁	1	2	yes	complemented
507	#3345	C₂×C₄₁	1	2	yes	complemented
508	#3334	C₂×C₄₁	1	2	yes	complemented
509	#3309	C₂×C₄₁	1	2	yes	complemented
510	#3308	C₂×C₄₁	1	2	yes	complemented
511	#3301	C₂×C₄₁	1	2	yes	complemented
512	#3257	C₂×C₄₁	1	2	yes	complemented
513	#3245	C₂×C₄₁	1	1	yes	characteristic, complemented
514	#3243	C₂×C₄₁	1	2	yes	complemented
515	#3234	C₂×C₄₁	1	1	yes	characteristic, complemented
516	#3119	C₂×C₄₁	1	2	yes	complemented
517	#3112	C₂×C₄₁	1	1	yes	characteristic, complemented
518	#3083	C₂×C₄₁	1	2	yes	complemented
519	C₂×#479	C₂×C₄₁	1	1	yes	characteristic, complemented
520	#2992	C₂×C₄₁	1	1	yes	characteristic, complemented
521	C₂×C₄₁	—	2	2	no	—
522	C₂×C₄₁	—	4	2	no	—
523	C₂×C₄₁	—	8	2	no	—
524	C₂×C₄₁	—	8	2	no	—
525	C₂×C₄₁	#3489	1	1	yes	characteristic
526	C₂×C₄₁	C₂×#576	1	1	yes	characteristic
527	C₂×C₄₁	#3586	1	1	yes	characteristic
528	#563	—	2	1	no	—
529	#562	—	2	1	no	—
530	#559	—	2	1	no	—
531	#559	C₂²×C₄₁	1	1	yes	characteristic
532	Q₈²	C₂²×C₄₁	1	1	yes	characteristic
533	#554	—	2	1	no	—
534	#554	C₂²×C₄₁	1	2	yes	—
535	#554	C₂²×C₄₁	1	1	yes	characteristic
536	#553	C₂²×C₄₁	1	2	yes	—
537	#553	C₂²×C₄₁	1	2	yes	—
538	#550	C₂²×C₄₁	1	1	yes	characteristic
539	#548	C₂²×C₄₁	1	2	yes	—
540	#547	—	2	2	no	—
541	#547	—	2	2	no	—
542	#547	C₂²×C₄₁	1	2	yes	—
543	#547	C₂²×C₄₁	1	2	yes	—
544	#544	C₂²×C₄₁	1	2	yes	—
545	#542	—	2	2	no	—
546	#542	C₂²×C₄₁	1	2	yes	—
547	#540	C₂²×C₄₁	1	2	yes	—
548	#539	—	2	2	no	—
549	#539	—	2	1	no	—
550	#537	—	2	1	no	—
551	#532	—	2	1	no	—
552	#532	C₂²×C₄₁	1	1	yes	characteristic
553	#532	C₂²×C₄₁	1	1	yes	characteristic
554	#529	—	2	1	no	—
555	#529	C₂²×C₄₁	1	1	yes	characteristic
556	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
557	#520	C₂²×C₄₁	1	2	yes	—
558	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
559	#501	C₂²×C₄₁	1	2	yes	—
560	#501	C₂²×C₄₁	1	2	yes	—
561	#500	C₂²×C₄₁	1	2	yes	—
562	#490	C₂²×C₄₁	1	2	yes	—
563	#489	C₂²×C₄₁	1	2	yes	—
564	#488	C₂²×C₄₁	1	2	yes	—
565	#485	C₂²×C₄₁	1	2	yes	—
566	#484	C₂²×C₄₁	1	2	yes	—
567	#482	C₂²×C₄₁	1	2	yes	—
568	#481	C₂²×C₄₁	1	2	yes	—
569	#481	C₂²×C₄₁	1	2	yes	—
570	#480	C₂²×C₄₁	1	2	yes	—
571	#480	C₂²×C₄₁	1	2	yes	—
572	#480	C₂²×C₄₁	1	2	yes	—
573	#480	C₂²×C₄₁	1	2	yes	—
574	#479	C₂²×C₄₁	1	2	yes	—
575	#479	C₂²×C₄₁	1	2	yes	—
576	#479	C₂²×C₄₁	1	2	yes	—
577	#479	C₂²×C₄₁	1	2	yes	—
578	#479	C₂²×C₄₁	1	2	yes	—
579	#478	C₂²×C₄₁	1	2	yes	—
580	#478	C₂²×C₄₁	1	2	yes	—
581	#478	C₂²×C₄₁	1	2	yes	—
582	#477	C₂²×C₄₁	1	1	yes	characteristic
583	#477	C₂²×C₄₁	1	2	yes	—
584	#477	C₂²×C₄₁	1	1	yes	characteristic
585	#476	C₂²×C₄₁	1	2	yes	—
586	#474	C₂²×C₄₁	1	2	yes	—
587	#474	C₂²×C₄₁	1	2	yes	—
588	#474	C₂²×C₄₁	1	2	yes	—
589	#474	C₂²×C₄₁	1	2	yes	—
590	#469	C₂²×C₄₁	1	2	yes	—
591	#468	C₂²×C₄₁	1	2	yes	—
592	#466	C₂²×C₄₁	1	2	yes	—
593	#466	C₂²×C₄₁	1	2	yes	—
594	#466	C₂²×C₄₁	1	2	yes	—
595	#465	C₂²×C₄₁	1	2	yes	—
596	#463	C₂²×C₄₁	1	2	yes	—
597	#463	C₂²×C₄₁	1	2	yes	—
598	#460	C₂²×C₄₁	1	1	yes	characteristic
599	#460	C₂²×C₄₁	1	1	yes	characteristic
600	#459	C₂²×C₄₁	1	2	yes	—
601	#459	C₂²×C₄₁	1	2	yes	—
602	#449	C₂²×C₄₁	1	2	yes	—
603	#449	C₂²×C₄₁	1	2	yes	—
604	#448	C₂²×C₄₁	1	2	yes	—
605	#446	C₂²×C₄₁	1	2	yes	—
606	#442	C₂²×C₄₁	1	2	yes	—
607	#440	C₂²×C₄₁	1	2	yes	—
608	#440	C₂²×C₄₁	1	2	yes	—
609	#440	C₂²×C₄₁	1	2	yes	—
610	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
611	C₄×D₈	C₂²×C₄₁	1	2	yes	—
612	#435	C₂²×C₄₁	1	2	yes	—
613	#435	C₂²×C₄₁	1	2	yes	—
614	C₈×D₄	C₂²×C₄₁	1	2	yes	—
615	#433	C₂²×C₄₁	1	2	yes	—
616	#432	C₂²×C₄₁	1	1	yes	characteristic
617	#428	C₂²×C₄₁	1	2	yes	—
618	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
619	C₂×#107	C₂²×C₄₁	1	2	yes	—
620	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
621	#424	C₂²×C₄₁	1	2	yes	—
622	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
623	#417	C₂²×C₄₁	1	2	yes	—
624	#416	C₂²×C₄₁	1	2	yes	—
625	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
626	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
627	C₄₁	#62170	1	1	yes	characteristic, direct product factor, Sylow
628	C₂×#41	—	2	2	no	—
629	C₂×#41	—	2	2	no	—
630	C₂×#41	—	2	1	no	—
631	C₂×#41	—	2	1	no	—
632	C₂×#41	C₂³×C₄₁	1	2	yes	—
633	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
634	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
635	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
636	C₂×D₈	C₂³×C₄₁	1	2	yes	—
637	C₂×D₈	C₂³×C₄₁	1	2	yes	—
638	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
639	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
640	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
641	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
642	C₄⋊Q₈	—	2	1	no	—
643	C₄⋊Q₈	—	2	2	no	—
644	C₄⋊Q₈	—	2	2	no	—
645	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
646	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
647	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
648	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
649	#127	—	2	1	no	—
650	#127	C₂³×C₄₁	1	1	yes	characteristic
651	#127	C₂³×C₄₁	1	1	yes	characteristic
652	#126	—	2	2	no	—
653	#126	—	2	2	no	—
654	#126	—	2	2	no	—
655	#126	D₄×C₄₁	1	2	yes	—
656	#125	—	2	1	no	—
657	#125	—	2	2	no	—
658	#125	—	2	1	no	—
659	#125	—	2	1	no	—
660	#125	D₄×C₄₁	1	1	yes	characteristic
661	#125	C₂³×C₄₁	1	2	yes	—
662	#125	C₂³×C₄₁	1	2	yes	—
663	#125	C₂³×C₄₁	1	2	yes	—
664	#124	—	2	1	no	—
665	#124	—	2	2	no	—
666	#124	—	2	2	no	—
667	#124	—	2	1	no	—
668	#124	—	2	1	no	—
669	#124	D₄×C₄₁	1	1	yes	characteristic
670	#124	C₂³×C₄₁	1	2	yes	—
671	#123	—	2	2	no	—
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	D₄×C₄₁	1	2	yes	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
693	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
694	#121	—	2	2	no	—
695	#121	—	2	2	no	—
696	#121	—	2	2	no	—
697	#121	—	2	1	no	—
698	#121	—	2	1	no	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	D₄×C₄₁	1	1	yes	characteristic
703	#121	C₂³×C₄₁	1	2	yes	—
704	#121	C₂³×C₄₁	1	2	yes	—
705	#121	C₂³×C₄₁	1	2	yes	—
706	#121	C₂³×C₄₁	1	2	yes	—
707	#121	C₂³×C₄₁	1	2	yes	—
708	C₄×Q₈	—	2	1	no	—
709	C₄×Q₈	—	2	1	no	—
710	C₄×Q₈	—	2	1	no	—
711	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
712	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
713	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
714	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
715	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
716	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
717	C₄×D₄	—	2	1	no	—
718	C₄×D₄	—	2	1	no	—
719	C₄×D₄	—	2	1	no	—
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	—	2	1	no	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	C₂³×C₄₁	1	2	yes	—
728	C₄×D₄	C₂³×C₄₁	1	2	yes	—
729	C₄×D₄	C₂³×C₄₁	1	2	yes	—
730	C₄×D₄	C₂³×C₄₁	1	2	yes	—
731	C₄×D₄	C₂³×C₄₁	1	2	yes	—
732	C₄×D₄	C₂³×C₄₁	1	2	yes	—
733	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
734	#117	—	2	2	no	—
735	#117	C₂³×C₄₁	1	2	yes	—
736	#117	C₂³×C₄₁	1	2	yes	—
737	C₂×C₄⋊C₄	—	2	1	no	—
738	C₂×C₄⋊C₄	—	2	1	no	—
739	C₂×C₄⋊C₄	—	2	1	no	—
740	C₂×C₄⋊C₄	—	2	2	no	—
741	C₂×C₄⋊C₄	—	2	2	no	—
742	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
743	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
744	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
747	C₂×C₄²	—	2	1	no	—
748	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
749	#107	C₂³×C₄₁	1	2	yes	—
750	#107	C₂³×C₄₁	1	2	yes	—
751	#107	C₂³×C₄₁	1	2	yes	—
752	#107	C₂³×C₄₁	1	2	yes	—
753	#107	C₂³×C₄₁	1	2	yes	—
754	#107	C₂³×C₄₁	1	2	yes	—
755	#107	C₂³×C₄₁	1	2	yes	—
756	#107	C₂³×C₄₁	1	2	yes	—
757	#106	C₂³×C₄₁	1	2	yes	—
758	#106	C₂³×C₄₁	1	2	yes	—
759	#106	C₂³×C₄₁	1	2	yes	—
760	#106	C₂³×C₄₁	1	2	yes	—
761	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
762	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
763	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
764	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
765	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
766	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
767	#103	C₂³×C₄₁	1	2	yes	—
768	#103	C₂³×C₄₁	1	2	yes	—
769	#103	C₂³×C₄₁	1	2	yes	—
770	#103	C₂³×C₄₁	1	2	yes	—
771	#103	C₂³×C₄₁	1	2	yes	—
772	#103	C₂³×C₄₁	1	2	yes	—
773	#102	C₂³×C₄₁	1	2	yes	—
774	#102	C₂³×C₄₁	1	2	yes	—
775	#102	C₂³×C₄₁	1	2	yes	—
776	#102	C₂³×C₄₁	1	2	yes	—
777	#102	C₂³×C₄₁	1	2	yes	—
778	#102	C₂³×C₄₁	1	2	yes	—
779	#102	C₂³×C₄₁	1	2	yes	—
780	#102	C₂³×C₄₁	1	2	yes	—
781	#102	C₂³×C₄₁	1	2	yes	—
782	#102	C₂³×C₄₁	1	2	yes	—
783	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
784	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
785	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
786	#97	C₂³×C₄₁	1	2	yes	—
787	#97	C₂³×C₄₁	1	2	yes	—
788	C₄×C₈	C₂³×C₄₁	1	2	yes	—
789	#41	—	2	4	no	—
790	#41	—	4	2	no	—
791	#41	—	8	2	no	—
792	#41	—	8	2	no	—
793	#41	—	8	4	no	—
794	#41	—	8	4	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	2	no	—
797	C₂×Q₈	—	2	2	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	2	no	—
801	C₂×Q₈	—	4	1	no	—
802	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
803	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
804	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	1	no	—
813	C₂×D₄	—	2	1	no	—
814	C₂×D₄	—	2	1	no	—
815	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
816	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
817	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
818	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	1	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	C₂×D₄×C₄₁	1	1	yes	characteristic
832	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
835	SD₁₆	—	2	4	no	—
836	SD₁₆	—	4	2	no	—
837	D₈	—	4	2	no	—
838	D₈	—	4	2	no	—
839	M₁₆	—	4	2	no	—
840	C₂×C₈	—	4	1	no	—
841	C₂×C₈	—	4	2	no	—
842	C₂×C₈	—	4	1	no	—
843	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
844	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
845	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
846	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
847	C₄⋊C₄	—	2	1	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	1	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	1	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
869	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
870	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
871	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
872	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
873	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
874	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
875	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
876	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
877	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
878	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
879	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
880	C₂²⋊C₄	—	2	2	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	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
895	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
896	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
897	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
898	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
899	C₄²	—	2	1	no	—
900	C₄²	—	2	1	no	—
901	C₄²	—	2	1	no	—
902	C₄²	—	2	1	no	—
903	C₄²	—	2	2	no	—
904	C₄²	—	2	2	no	—
905	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
906	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
907	C₄²	C₂⁴×C₄₁	1	2	yes	—
908	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
909	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
910	C₂³	—	2	2	no	—
911	C₂³	—	2	2	no	—
912	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
913	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
914	Q₈	—	2	1	no	—
915	Q₈	—	2	1	no	—
916	Q₈	—	2	1	no	—
917	Q₈	—	4	1	no	—
918	Q₈	—	4	2	no	—
919	Q₈	—	8	1	no	—
920	Q₈	—	8	1	no	—
921	Q₈	—	8	2	no	—
922	Q₈	—	8	2	no	—
923	Q₈	2₋¹⁺⁴×C₄₁	1	2	yes	—
924	D₄	—	2	4	no	—
925	D₄	—	2	2	no	—
926	D₄	—	2	2	no	—
927	D₄	—	2	2	no	—
928	D₄	—	2	2	no	—
929	D₄	—	4	1	no	—
930	D₄	—	4	4	no	—
931	D₄	—	4	2	no	—
932	D₄	—	4	4	no	—
933	D₄	—	4	4	no	—
934	D₄	—	8	1	no	—
935	D₄	—	8	1	no	—
936	D₄	—	8	1	no	—
937	D₄	—	8	2	no	—
938	D₄	—	8	2	no	—
939	D₄	—	8	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	4	1	no	—
954	C₂×C₄	—	4	4	no	—
955	C₂×C₄	—	4	2	no	—
956	C₂×C₄	—	4	2	no	—
957	C₂×C₄	—	4	2	no	—
958	C₂×C₄	—	8	2	no	—
959	C₂×C₄	—	8	2	no	—
960	C₂×C₄	—	8	2	no	—
961	C₂×C₄	—	8	2	no	—
962	C₂×C₄	—	8	2	no	—
963	C₂×C₄	—	8	2	no	—
964	C₂×C₄	—	8	2	no	—
965	C₂×C₄	—	8	1	no	—
966	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
967	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
968	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
969	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
970	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
971	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
972	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
973	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
974	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
975	C₈	—	2	2	no	—
976	C₈	—	2	2	no	—
977	C₈	—	2	2	no	—
978	C₈	—	2	2	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	2	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	2	no	—
990	C₂²	C₄₁×#576	1	2	yes	—
991	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
992	C₄	—	2	1	no	—
993	C₄	—	2	1	no	—
994	C₄	—	2	2	no	—
995	C₄	—	2	1	no	—
996	C₄	—	2	1	no	—
997	C₄	—	2	2	no	—
998	C₄	—	2	2	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	2	no	—
1001	C₄	—	4	1	no	—
1002	C₄	—	4	2	no	—
1003	C₄	—	4	1	no	—
1004	C₄	—	4	2	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	2	no	—
1007	C₄	—	4	1	no	—
1008	C₄	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
1009	C₄	C₄₁×#585	1	1	yes	characteristic
1010	C₂	—	2	2	no	—
1011	C₂	—	4	2	no	—
1012	C₂	—	8	2	no	—
1013	C₂	—	8	2	no	—
1014	C₂	C₄₁×#3489	1	1	yes	characteristic
1015	C₂	C₂×C₄₁×#576	1	1	yes	characteristic
1016	C₂	C₄₁×#3586	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×#3559	C₂	semidirect
2. C₄₁×#3522	C₂	semidirect
3. C₄₁×#3385	C₂	semidirect
4. C₄₁×#3370	C₂	semidirect
5. C₄₁×#3346	C₂	semidirect
6. C₄₁×#3345	C₂	semidirect
7. C₄₁×#3334	C₂	semidirect
8. C₄₁×#3309	C₂	semidirect
9. C₄₁×#3308	C₂	semidirect
10. C₄₁×#3301	C₂	semidirect
11. C₄₁×#3257	C₂	semidirect
12. C₄₁×#3245	C₂	semidirect
13. C₄₁×#3243	C₂	semidirect
14. C₄₁×#3234	C₂	semidirect
15. C₄₁×#3119	C₂	semidirect
16. C₄₁×#3112	C₂	semidirect
17. C₄₁×#3083	C₂	semidirect
18. C₂×C₄₁×#479	C₂	semidirect
19. C₄₁×#2992	C₂	semidirect
470. #62170	C₄₁	direct (N × H)
502. #3559	C₂×C₄₁	semidirect
503. #3522	C₂×C₄₁	semidirect
504. #3385	C₂×C₄₁	semidirect
505. #3370	C₂×C₄₁	semidirect
506. #3346	C₂×C₄₁	semidirect
507. #3345	C₂×C₄₁	semidirect
508. #3334	C₂×C₄₁	semidirect
509. #3309	C₂×C₄₁	semidirect
510. #3308	C₂×C₄₁	semidirect
511. #3301	C₂×C₄₁	semidirect
512. #3257	C₂×C₄₁	semidirect
513. #3245	C₂×C₄₁	semidirect
514. #3243	C₂×C₄₁	semidirect
515. #3234	C₂×C₄₁	semidirect
516. #3119	C₂×C₄₁	semidirect
517. #3112	C₂×C₄₁	semidirect
518. #3083	C₂×C₄₁	semidirect
519. C₂×#479	C₂×C₄₁	semidirect
520. #2992	C₂×C₄₁	semidirect
627. C₄₁	#62170	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄₁×#3559	2
C₄₁×#3522	2
C₄₁×#3385	2
C₄₁×#3370	2
C₄₁×#3346	2
C₄₁×#3345	2
C₄₁×#3334	2
C₄₁×#3309	2
C₄₁×#3308	2
C₄₁×#3301	2
C₄₁×#3257	2
C₄₁×#3245	2
C₄₁×#3243	2
C₄₁×#3234	2
C₄₁×#3119	2
C₄₁×#3112	2
C₄₁×#3083	2
C₂×C₄₁×#479	2
C₄₁×#2992	2
#62170	41

Subgroups — C41×#62170 #23838371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#62170 #23838371