Subgroups — C₄₁×#61831 #23838032

Order 10496.

1750 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3389	C₂	1	4	yes	maximal, complemented
4	C₄₁×#3388	C₂	1	4	yes	maximal, complemented
5	C₄₁×#3376	C₂	1	4	yes	maximal, complemented
6	C₄₁×#3370	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3239	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3236	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#3234	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3232	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3114	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3109	C₂	1	1	yes	maximal, characteristic
14	C₄₁×#3105	C₂	1	2	yes	maximal, complemented
15	C₄₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#559	C₂²	1	2	yes	complemented
17	C₄₁×#557	C₂²	1	2	yes	complemented
18	C₄₁×#556	—	2	2	no	—
19	C₄₁×#556	C₂²	1	2	yes	complemented
20	C₄₁×#554	—	2	2	no	—
21	C₄₁×#554	—	2	2	no	—
22	C₄₁×#554	C₂²	1	4	yes	—
23	C₄₁×#554	C₂²	1	4	yes	—
24	C₄₁×#554	C₂²	1	2	yes	complemented
25	C₄₁×#552	—	2	2	no	—
26	C₄₁×#539	—	2	1	no	—
27	C₄₁×#539	—	2	1	no	—
28	C₄₁×#536	—	2	1	no	—
29	C₄₁×#533	C₂²	1	1	yes	characteristic
30	C₄₁×#532	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₄₁×#529	C₂²	1	2	yes	—
33	C₄₁×#529	C₂²	1	2	yes	—
34	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
37	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
38	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
39	C₄₁×#520	—	2	1	no	—
40	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
45	C₄₁×#501	C₂²	1	2	yes	complemented
46	C₄₁×#501	C₂²	1	4	yes	complemented
47	C₄₁×#501	C₂²	1	2	yes	complemented
48	C₄₁×#499	C₂²	1	4	yes	complemented
49	C₄₁×#491	C₂²	1	2	yes	complemented
50	C₄₁×#490	C₂²	1	2	yes	complemented
51	C₄₁×#489	C₂²	1	4	yes	complemented
52	C₄₁×#488	C₂²	1	4	yes	complemented
53	C₄₁×#484	C₂²	1	2	yes	—
54	C₄₁×#484	C₂²	1	2	yes	—
55	C₄₁×#483	C₂²	1	2	yes	—
56	C₄₁×#481	C₂²	1	2	yes	—
57	C₄₁×#481	C₂²	1	2	yes	—
58	C₄₁×#480	C₂²	1	2	yes	—
59	C₄₁×#479	C₂²	1	4	yes	complemented
60	C₄₁×#479	C₂²	1	4	yes	complemented
61	C₄₁×#478	C₂²	1	4	yes	—
62	C₄₁×#478	C₂²	1	4	yes	—
63	C₄₁×#478	C₂²	1	4	yes	complemented
64	C₄₁×#478	C₂²	1	4	yes	complemented
65	C₄₁×#476	C₂²	1	2	yes	—
66	C₄₁×#475	C₂²	1	4	yes	complemented
67	C₄₁×#474	C₂²	1	2	yes	—
68	C₄₁×#474	C₂²	1	4	yes	complemented
69	C₄₁×#463	C₂²	1	4	yes	—
70	C₄₁×#463	C₂²	1	4	yes	—
71	C₄₁×#461	C₂²	1	2	yes	—
72	C₄₁×#459	C₂²	1	2	yes	—
73	C₄₁×#450	C₂²	1	2	yes	—
74	C₄₁×#447	C₂²	1	2	yes	—
75	C₄₁×#446	C₂²	1	4	yes	complemented
76	C₄₁×#446	C₂²	1	4	yes	complemented
77	C₄₁×#442	C₂²	1	4	yes	—
78	C₄₁×#442	C₂²	1	4	yes	—
79	C₄₁×#440	C₂²	1	4	yes	—
80	C₄₁×#440	C₂²	1	4	yes	—
81	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	—
82	C₄×D₈×C₄₁	C₂²	1	4	yes	—
83	C₄₁×#432	C₂²	1	1	yes	characteristic
84	C₄₁×#432	C₂²	1	1	yes	characteristic
85	C₄₁×#432	C₂²	1	2	yes	—
86	C₄₁×#431	C₂²	1	2	yes	—
87	C₂×#41×C₄₁	—	2	1	no	—
88	C₂²×Q₈×C₄₁	—	2	1	no	—
89	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
90	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₄₁	—	2	1	no	—
92	C₂³×C₄×C₄₁	—	2	1	no	—
93	C₂³×C₄×C₄₁	—	2	1	no	—
94	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
95	C₂×D₈×C₄₁	C₂³	1	4	yes	—
96	C₄⋊Q₈×C₄₁	—	2	2	no	—
97	C₄⋊Q₈×C₄₁	—	2	2	no	—
98	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
99	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
102	#127×C₄₁	C₂³	1	1	yes	characteristic
103	#126×C₄₁	—	2	2	no	—
104	#126×C₄₁	—	2	2	no	—
105	#126×C₄₁	—	2	2	no	—
106	#126×C₄₁	—	2	2	no	—
107	#125×C₄₁	—	2	2	no	—
108	#125×C₄₁	—	2	2	no	—
109	#125×C₄₁	—	2	2	no	—
110	#125×C₄₁	—	2	1	no	—
111	#125×C₄₁	—	2	1	no	—
112	#125×C₄₁	—	2	1	no	—
113	#125×C₄₁	C₂³	1	2	yes	—
114	#125×C₄₁	C₂³	1	2	yes	—
115	#125×C₄₁	C₂³	1	2	yes	—
116	#125×C₄₁	C₂³	1	4	yes	—
117	#125×C₄₁	C₂³	1	2	yes	—
118	#124×C₄₁	—	2	2	no	—
119	#124×C₄₁	—	2	1	no	—
120	#124×C₄₁	C₂³	1	2	yes	—
121	#124×C₄₁	C₂³	1	2	yes	—
122	#123×C₄₁	—	2	2	no	—
123	#123×C₄₁	—	2	2	no	—
124	#123×C₄₁	—	2	2	no	—
125	#123×C₄₁	—	2	2	no	—
126	C₂²⋊Q₈×C₄₁	—	2	4	no	—
127	C₂²⋊Q₈×C₄₁	—	2	4	no	—
128	C₂²⋊Q₈×C₄₁	—	2	2	no	—
129	C₂²⋊Q₈×C₄₁	—	2	2	no	—
130	C₂²⋊Q₈×C₄₁	—	2	1	no	—
131	C₂²⋊Q₈×C₄₁	—	2	4	no	—
132	C₂²⋊Q₈×C₄₁	—	2	4	no	—
133	C₂²⋊Q₈×C₄₁	—	2	4	no	—
134	C₂²⋊Q₈×C₄₁	—	2	4	no	—
135	C₂²⋊Q₈×C₄₁	—	2	2	no	—
136	C₂²⋊Q₈×C₄₁	—	2	2	no	—
137	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
138	#121×C₄₁	—	2	1	no	—
139	#121×C₄₁	C₂³	1	2	yes	—
140	C₄×Q₈×C₄₁	—	2	2	no	—
141	C₄×Q₈×C₄₁	—	2	1	no	—
142	C₄×Q₈×C₄₁	D₄	1	2	yes	—
143	C₄×Q₈×C₄₁	D₄	1	2	yes	—
144	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
145	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
146	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
147	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
148	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
149	C₄×D₄×C₄₁	—	2	2	no	—
150	C₄×D₄×C₄₁	—	2	2	no	—
151	C₄×D₄×C₄₁	—	2	2	no	—
152	C₄×D₄×C₄₁	—	2	2	no	—
153	C₄×D₄×C₄₁	—	2	2	no	—
154	C₄×D₄×C₄₁	—	2	1	no	—
155	C₄×D₄×C₄₁	—	2	1	no	—
156	C₄×D₄×C₄₁	—	2	1	no	—
157	C₄×D₄×C₄₁	C₂³	1	4	yes	—
158	C₄×D₄×C₄₁	C₂³	1	2	yes	—
159	C₄×D₄×C₄₁	C₂³	1	4	yes	—
160	C₄×D₄×C₄₁	C₂³	1	2	yes	—
161	C₄×D₄×C₄₁	C₂³	1	2	yes	—
162	C₄×D₄×C₄₁	C₂³	1	2	yes	—
163	C₄×D₄×C₄₁	C₂³	1	2	yes	—
164	#117×C₄₁	—	2	1	no	—
165	#117×C₄₁	—	2	2	no	—
166	#117×C₄₁	—	2	2	no	—
167	#117×C₄₁	—	2	2	no	—
168	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
169	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
170	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
171	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
172	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
173	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
174	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
175	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
176	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
185	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
188	#107×C₄₁	C₂³	1	4	yes	—
189	#107×C₄₁	C₂³	1	4	yes	—
190	#107×C₄₁	C₂³	1	4	yes	—
191	#106×C₄₁	C₂³	1	4	yes	—
192	#106×C₄₁	C₂³	1	4	yes	—
193	#106×C₄₁	C₂³	1	4	yes	—
194	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
195	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
196	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
197	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
198	#103×C₄₁	C₂³	1	4	yes	—
199	#103×C₄₁	C₂³	1	4	yes	—
200	#103×C₄₁	C₂³	1	4	yes	—
201	#102×C₄₁	C₂³	1	4	yes	—
202	#102×C₄₁	C₂³	1	4	yes	—
203	#102×C₄₁	C₂³	1	4	yes	—
204	#102×C₄₁	C₂³	1	4	yes	—
205	#102×C₄₁	C₂³	1	4	yes	—
206	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
207	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
208	#97×C₄₁	C₂³	1	2	yes	—
209	#97×C₄₁	C₂³	1	4	yes	—
210	#97×C₄₁	C₂³	1	2	yes	—
211	C₄×C₈×C₄₁	C₂³	1	4	yes	—
212	C₂⁴×C₄₁	—	2	1	no	—
213	#41×C₄₁	—	4	4	no	—
214	C₂×Q₈×C₄₁	—	2	1	no	—
215	C₂×Q₈×C₄₁	—	2	1	no	—
216	C₂×Q₈×C₄₁	—	2	4	no	—
217	C₂×Q₈×C₄₁	—	4	2	no	—
218	C₂×Q₈×C₄₁	—	8	2	no	—
219	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
220	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
221	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
222	C₂×D₄×C₄₁	—	2	4	no	—
223	C₂×D₄×C₄₁	—	2	2	no	—
224	C₂×D₄×C₄₁	—	2	1	no	—
225	C₂×D₄×C₄₁	—	2	1	no	—
226	C₂×D₄×C₄₁	—	2	1	no	—
227	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
228	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₄₁	—	2	1	no	—
230	C₂²×C₄×C₄₁	—	2	1	no	—
231	C₂²×C₄×C₄₁	—	2	1	no	—
232	C₂²×C₄×C₄₁	—	2	4	no	—
233	C₂²×C₄×C₄₁	—	2	2	no	—
234	C₂²×C₄×C₄₁	—	2	4	no	—
235	C₂²×C₄×C₄₁	—	2	2	no	—
236	C₂²×C₄×C₄₁	—	2	2	no	—
237	C₂²×C₄×C₄₁	—	2	2	no	—
238	C₂²×C₄×C₄₁	—	2	2	no	—
239	C₂²×C₄×C₄₁	—	4	4	no	—
240	C₂²×C₄×C₄₁	—	8	2	no	—
241	C₂²×C₄×C₄₁	—	8	2	no	—
242	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
249	SD₁₆×C₄₁	—	2	8	no	—
250	D₈×C₄₁	—	2	8	no	—
251	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
252	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
253	C₄⋊C₄×C₄₁	—	2	4	no	—
254	C₄⋊C₄×C₄₁	—	2	2	no	—
255	C₄⋊C₄×C₄₁	—	2	2	no	—
256	C₄⋊C₄×C₄₁	—	2	4	no	—
257	C₄⋊C₄×C₄₁	—	2	1	no	—
258	C₄⋊C₄×C₄₁	—	2	2	no	—
259	C₄⋊C₄×C₄₁	—	2	2	no	—
260	C₄⋊C₄×C₄₁	—	2	2	no	—
261	C₄⋊C₄×C₄₁	—	2	4	no	—
262	C₄⋊C₄×C₄₁	—	2	2	no	—
263	C₄⋊C₄×C₄₁	—	2	1	no	—
264	C₄⋊C₄×C₄₁	—	2	1	no	—
265	C₄⋊C₄×C₄₁	—	2	1	no	—
266	C₄⋊C₄×C₄₁	—	2	1	no	—
267	C₄⋊C₄×C₄₁	—	2	2	no	—
268	C₄⋊C₄×C₄₁	—	2	2	no	—
269	C₄⋊C₄×C₄₁	—	2	2	no	—
270	C₄⋊C₄×C₄₁	—	2	1	no	—
271	C₄⋊C₄×C₄₁	—	2	1	no	—
272	C₄⋊C₄×C₄₁	—	2	2	no	—
273	C₄⋊C₄×C₄₁	—	2	2	no	—
274	C₄⋊C₄×C₄₁	—	2	2	no	—
275	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
286	C₂²⋊C₄×C₄₁	—	2	2	no	—
287	C₂²⋊C₄×C₄₁	—	2	4	no	—
288	C₂²⋊C₄×C₄₁	—	2	2	no	—
289	C₂²⋊C₄×C₄₁	—	2	4	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	—	2	2	no	—
298	C₂²⋊C₄×C₄₁	—	2	2	no	—
299	C₄²×C₄₁	—	2	2	no	—
300	C₄²×C₄₁	—	2	2	no	—
301	C₄²×C₄₁	—	2	2	no	—
302	C₄²×C₄₁	C₂×D₄	1	2	yes	—
303	C₄²×C₄₁	C₂×D₄	1	2	yes	—
304	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₄₁	C₂⁴	1	2	yes	—
307	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
308	C₄²×C₄₁	C₂⁴	1	2	yes	—
309	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
310	C₂³×C₄₁	—	2	4	no	—
311	C₂³×C₄₁	—	2	2	no	—
312	C₂³×C₄₁	—	2	2	no	—
313	C₂³×C₄₁	—	4	2	no	—
314	C₂³×C₄₁	—	4	2	no	—
315	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
316	Q₈×C₄₁	—	2	4	no	—
317	Q₈×C₄₁	—	4	2	no	—
318	Q₈×C₄₁	—	4	2	no	—
319	Q₈×C₄₁	—	4	2	no	—
320	Q₈×C₄₁	—	8	1	no	—
321	Q₈×C₄₁	—	8	4	no	—
322	D₄×C₄₁	—	2	4	no	—
323	D₄×C₄₁	—	2	2	no	—
324	D₄×C₄₁	—	2	4	no	—
325	D₄×C₄₁	—	4	2	no	—
326	D₄×C₄₁	—	4	4	no	—
327	D₄×C₄₁	—	8	1	no	—
328	D₄×C₄₁	2₋¹⁺⁴	1	4	yes	—
329	C₂×C₄×C₄₁	—	2	2	no	—
330	C₂×C₄×C₄₁	—	2	2	no	—
331	C₂×C₄×C₄₁	—	2	2	no	—
332	C₂×C₄×C₄₁	—	2	2	no	—
333	C₂×C₄×C₄₁	—	2	2	no	—
334	C₂×C₄×C₄₁	—	2	2	no	—
335	C₂×C₄×C₄₁	—	2	2	no	—
336	C₂×C₄×C₄₁	—	2	2	no	—
337	C₂×C₄×C₄₁	—	2	2	no	—
338	C₂×C₄×C₄₁	—	2	2	no	—
339	C₂×C₄×C₄₁	—	4	1	no	—
340	C₂×C₄×C₄₁	—	4	1	no	—
341	C₂×C₄×C₄₁	—	4	1	no	—
342	C₂×C₄×C₄₁	—	4	8	no	—
343	C₂×C₄×C₄₁	—	4	4	no	—
344	C₂×C₄×C₄₁	—	4	2	no	—
345	C₂×C₄×C₄₁	—	4	2	no	—
346	C₂×C₄×C₄₁	—	4	2	no	—
347	C₂×C₄×C₄₁	—	8	2	no	—
348	C₂×C₄×C₄₁	—	8	2	no	—
349	C₂×C₄×C₄₁	—	8	4	no	—
350	C₂×C₄×C₄₁	—	8	2	no	—
351	C₂×C₄×C₄₁	—	8	2	no	—
352	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
354	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
355	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
362	C₈×C₄₁	—	2	4	no	—
363	C₈×C₄₁	—	2	4	no	—
364	#61831	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
365	C₂²×C₄₁	—	2	1	no	—
366	C₂²×C₄₁	—	2	1	no	—
367	C₂²×C₄₁	—	2	4	no	—
368	C₂²×C₄₁	—	4	8	no	—
369	C₂²×C₄₁	—	4	2	no	—
370	C₂²×C₄₁	—	4	2	no	—
371	C₂²×C₄₁	—	4	2	no	—
372	C₂²×C₄₁	—	4	2	no	—
373	C₂²×C₄₁	—	4	2	no	—
374	C₂²×C₄₁	#575	1	2	yes	—
375	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
376	C₄×C₄₁	—	2	2	no	—
377	C₄×C₄₁	—	2	1	no	—
378	C₄×C₄₁	—	2	1	no	—
379	C₄×C₄₁	—	2	2	no	—
380	C₄×C₄₁	—	2	1	no	—
381	C₄×C₄₁	—	2	2	no	—
382	C₄×C₄₁	—	2	1	no	—
383	C₄×C₄₁	—	2	1	no	—
384	C₄×C₄₁	—	2	2	no	—
385	C₄×C₄₁	—	4	2	no	—
386	C₄×C₄₁	—	4	2	no	—
387	C₄×C₄₁	—	4	2	no	—
388	C₄×C₄₁	—	4	2	no	—
389	C₄×C₄₁	—	4	2	no	—
390	C₄×C₄₁	—	4	2	no	—
391	C₄×C₄₁	C₂×2₋¹⁺⁴	1	2	yes	—
392	#3507	C₂×C₄₁	1	1	yes	characteristic, complemented
393	C₂×#554	C₂×C₄₁	1	1	yes	characteristic, complemented
394	#3389	C₂×C₄₁	1	4	yes	complemented
395	#3388	C₂×C₄₁	1	4	yes	complemented
396	#3376	C₂×C₄₁	1	4	yes	complemented
397	#3370	C₂×C₄₁	1	4	yes	complemented
398	#3239	C₂×C₄₁	1	2	yes	complemented
399	#3236	C₂×C₄₁	1	1	yes	characteristic, complemented
400	#3234	C₂×C₄₁	1	1	yes	characteristic, complemented
401	#3232	C₂×C₄₁	1	2	yes	complemented
402	#3114	C₂×C₄₁	1	2	yes	complemented
403	#3110	C₂×C₄₁	1	1	yes	characteristic, complemented
404	#3109	C₂×C₄₁	1	1	yes	characteristic
405	#3105	C₂×C₄₁	1	2	yes	complemented
406	#2983	C₂×C₄₁	1	1	yes	characteristic, complemented
407	C₂×C₄₁	—	2	2	no	—
408	C₂×C₄₁	—	4	4	no	—
409	C₂×C₄₁	—	8	2	no	—
410	C₂×C₄₁	#3486	1	1	yes	characteristic
411	C₂×C₄₁	C₂×#575	1	1	yes	characteristic
412	C₂×C₄₁	#3585	1	1	yes	characteristic
413	#559	C₂²×C₄₁	1	2	yes	complemented
414	#557	C₂²×C₄₁	1	2	yes	complemented
415	#556	—	2	2	no	—
416	#556	C₂²×C₄₁	1	2	yes	complemented
417	#554	—	2	2	no	—
418	#554	—	2	2	no	—
419	#554	C₂²×C₄₁	1	4	yes	—
420	#554	C₂²×C₄₁	1	4	yes	—
421	#554	C₂²×C₄₁	1	2	yes	complemented
422	#552	—	2	2	no	—
423	#539	—	2	1	no	—
424	#539	—	2	1	no	—
425	#536	—	2	1	no	—
426	#533	C₂²×C₄₁	1	1	yes	characteristic
427	#532	C₂²×C₄₁	1	1	yes	characteristic
428	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
429	#529	C₂²×C₄₁	1	2	yes	—
430	#529	C₂²×C₄₁	1	2	yes	—
431	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
432	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
433	C₂×C₂²⋊Q₈	—	2	1	no	—
434	C₂×C₂²⋊Q₈	—	2	1	no	—
435	C₂×C₂²⋊Q₈	—	2	1	no	—
436	#520	—	2	1	no	—
437	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
438	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
439	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
440	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
441	C₂²×C₄⋊C₄	—	2	1	no	—
442	#501	C₂²×C₄₁	1	2	yes	complemented
443	#501	C₂²×C₄₁	1	4	yes	complemented
444	#501	C₂²×C₄₁	1	2	yes	complemented
445	#499	C₂²×C₄₁	1	4	yes	complemented
446	#491	C₂²×C₄₁	1	2	yes	complemented
447	#490	C₂²×C₄₁	1	2	yes	complemented
448	#489	C₂²×C₄₁	1	4	yes	complemented
449	#488	C₂²×C₄₁	1	4	yes	complemented
450	#484	C₂²×C₄₁	1	2	yes	—
451	#484	C₂²×C₄₁	1	2	yes	—
452	#483	C₂²×C₄₁	1	2	yes	—
453	#481	C₂²×C₄₁	1	2	yes	—
454	#481	C₂²×C₄₁	1	2	yes	—
455	#480	C₂²×C₄₁	1	2	yes	—
456	#479	C₂²×C₄₁	1	4	yes	complemented
457	#479	C₂²×C₄₁	1	4	yes	complemented
458	#478	C₂²×C₄₁	1	4	yes	—
459	#478	C₂²×C₄₁	1	4	yes	—
460	#478	C₂²×C₄₁	1	4	yes	complemented
461	#478	C₂²×C₄₁	1	4	yes	complemented
462	#476	C₂²×C₄₁	1	2	yes	—
463	#475	C₂²×C₄₁	1	4	yes	complemented
464	#474	C₂²×C₄₁	1	2	yes	—
465	#474	C₂²×C₄₁	1	4	yes	complemented
466	#463	C₂²×C₄₁	1	4	yes	—
467	#463	C₂²×C₄₁	1	4	yes	—
468	#461	C₂²×C₄₁	1	2	yes	—
469	#459	C₂²×C₄₁	1	2	yes	—
470	#450	C₂²×C₄₁	1	2	yes	—
471	#447	C₂²×C₄₁	1	2	yes	—
472	#446	C₂²×C₄₁	1	4	yes	complemented
473	#446	C₂²×C₄₁	1	4	yes	complemented
474	#442	C₂²×C₄₁	1	4	yes	—
475	#442	C₂²×C₄₁	1	4	yes	—
476	#440	C₂²×C₄₁	1	4	yes	—
477	#440	C₂²×C₄₁	1	4	yes	—
478	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	—
479	C₄×D₈	C₂²×C₄₁	1	4	yes	—
480	#432	C₂²×C₄₁	1	1	yes	characteristic
481	#432	C₂²×C₄₁	1	1	yes	characteristic
482	#432	C₂²×C₄₁	1	2	yes	—
483	#431	C₂²×C₄₁	1	2	yes	—
484	C₄₁	#61831	1	1	yes	characteristic, direct product factor, Sylow
485	C₂×#41	—	2	1	no	—
486	C₂²×Q₈	—	2	1	no	—
487	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
488	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
489	C₂³×C₄	—	2	1	no	—
490	C₂³×C₄	—	2	1	no	—
491	C₂³×C₄	—	2	1	no	—
492	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
493	C₂×D₈	C₂³×C₄₁	1	4	yes	—
494	C₄⋊Q₈	—	2	2	no	—
495	C₄⋊Q₈	—	2	2	no	—
496	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
497	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
498	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
499	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
500	#127	C₂³×C₄₁	1	1	yes	characteristic
501	#126	—	2	2	no	—
502	#126	—	2	2	no	—
503	#126	—	2	2	no	—
504	#126	—	2	2	no	—
505	#125	—	2	2	no	—
506	#125	—	2	2	no	—
507	#125	—	2	2	no	—
508	#125	—	2	1	no	—
509	#125	—	2	1	no	—
510	#125	—	2	1	no	—
511	#125	C₂³×C₄₁	1	2	yes	—
512	#125	C₂³×C₄₁	1	4	yes	—
513	#125	C₂³×C₄₁	1	2	yes	—
514	#125	C₂³×C₄₁	1	2	yes	—
515	#125	C₂³×C₄₁	1	2	yes	—
516	#124	—	2	2	no	—
517	#124	—	2	1	no	—
518	#124	C₂³×C₄₁	1	2	yes	—
519	#124	C₂³×C₄₁	1	2	yes	—
520	#123	—	2	2	no	—
521	#123	—	2	2	no	—
522	#123	—	2	2	no	—
523	#123	—	2	2	no	—
524	C₂²⋊Q₈	—	2	4	no	—
525	C₂²⋊Q₈	—	2	4	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	C₂²⋊Q₈	—	2	1	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	—	2	4	no	—
532	C₂²⋊Q₈	—	2	4	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
536	#121	—	2	1	no	—
537	#121	C₂³×C₄₁	1	2	yes	—
538	C₄×Q₈	—	2	2	no	—
539	C₄×Q₈	—	2	1	no	—
540	C₄×Q₈	D₄×C₄₁	1	2	yes	—
541	C₄×Q₈	D₄×C₄₁	1	2	yes	—
542	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
543	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
544	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
545	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
546	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	2	2	no	—
552	C₄×D₄	—	2	1	no	—
553	C₄×D₄	—	2	1	no	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	C₂³×C₄₁	1	4	yes	—
556	C₄×D₄	C₂³×C₄₁	1	2	yes	—
557	C₄×D₄	C₂³×C₄₁	1	4	yes	—
558	C₄×D₄	C₂³×C₄₁	1	2	yes	—
559	C₄×D₄	C₂³×C₄₁	1	2	yes	—
560	C₄×D₄	C₂³×C₄₁	1	2	yes	—
561	C₄×D₄	C₂³×C₄₁	1	2	yes	—
562	#117	—	2	1	no	—
563	#117	—	2	2	no	—
564	#117	—	2	2	no	—
565	#117	—	2	2	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	4	no	—
572	C₂×C₄⋊C₄	—	2	4	no	—
573	C₂×C₄⋊C₄	—	2	2	no	—
574	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
575	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
576	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₂²⋊C₄	—	2	1	no	—
582	C₂×C₂²⋊C₄	—	2	1	no	—
583	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
586	#107	C₂³×C₄₁	1	4	yes	—
587	#107	C₂³×C₄₁	1	4	yes	—
588	#107	C₂³×C₄₁	1	4	yes	—
589	#106	C₂³×C₄₁	1	4	yes	—
590	#106	C₂³×C₄₁	1	4	yes	—
591	#106	C₂³×C₄₁	1	4	yes	—
592	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
593	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
594	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
595	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
596	#103	C₂³×C₄₁	1	4	yes	—
597	#103	C₂³×C₄₁	1	4	yes	—
598	#103	C₂³×C₄₁	1	4	yes	—
599	#102	C₂³×C₄₁	1	4	yes	—
600	#102	C₂³×C₄₁	1	4	yes	—
601	#102	C₂³×C₄₁	1	4	yes	—
602	#102	C₂³×C₄₁	1	4	yes	—
603	#102	C₂³×C₄₁	1	4	yes	—
604	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
605	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
606	#97	C₂³×C₄₁	1	2	yes	—
607	#97	C₂³×C₄₁	1	4	yes	—
608	#97	C₂³×C₄₁	1	2	yes	—
609	C₄×C₈	C₂³×C₄₁	1	4	yes	—
610	C₂⁴	—	2	1	no	—
611	#41	—	4	4	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	4	no	—
615	C₂×Q₈	—	4	2	no	—
616	C₂×Q₈	—	8	2	no	—
617	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
618	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
619	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
626	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	4	4	no	—
638	C₂²×C₄	—	8	2	no	—
639	C₂²×C₄	—	8	2	no	—
640	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
647	SD₁₆	—	2	8	no	—
648	D₈	—	2	8	no	—
649	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
650	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
674	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
675	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
676	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
677	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
678	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
679	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
681	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
682	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₄²	—	2	2	no	—
698	C₄²	—	2	2	no	—
699	C₄²	—	2	2	no	—
700	C₄²	C₂×D₄×C₄₁	1	2	yes	—
701	C₄²	C₂×D₄×C₄₁	1	2	yes	—
702	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
703	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
704	C₄²	C₂⁴×C₄₁	1	2	yes	—
705	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
706	C₄²	C₂⁴×C₄₁	1	2	yes	—
707	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
708	C₂³	—	2	4	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	4	2	no	—
712	C₂³	—	4	2	no	—
713	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
714	Q₈	—	2	4	no	—
715	Q₈	—	4	2	no	—
716	Q₈	—	4	2	no	—
717	Q₈	—	4	2	no	—
718	Q₈	—	8	4	no	—
719	Q₈	—	8	1	no	—
720	D₄	—	2	4	no	—
721	D₄	—	2	2	no	—
722	D₄	—	2	4	no	—
723	D₄	—	4	2	no	—
724	D₄	—	4	4	no	—
725	D₄	—	8	1	no	—
726	D₄	2₋¹⁺⁴×C₄₁	1	4	yes	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	8	no	—
741	C₂×C₄	—	4	4	no	—
742	C₂×C₄	—	4	2	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	4	2	no	—
745	C₂×C₄	—	8	4	no	—
746	C₂×C₄	—	8	2	no	—
747	C₂×C₄	—	8	2	no	—
748	C₂×C₄	—	8	2	no	—
749	C₂×C₄	—	8	2	no	—
750	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
751	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
752	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
753	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
754	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
755	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
756	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
757	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
759	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
760	C₈	—	2	4	no	—
761	C₈	—	2	4	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	4	8	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	C₄₁×#575	1	2	yes	—
772	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
773	C₄	—	2	2	no	—
774	C₄	—	2	1	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	1	no	—
779	C₄	—	2	1	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	1	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	C₂×2₋¹⁺⁴×C₄₁	1	2	yes	—
789	C₂	—	2	2	no	—
790	C₂	—	4	4	no	—
791	C₂	—	8	2	no	—
792	C₂	C₄₁×#3486	1	1	yes	characteristic
793	C₂	C₂×C₄₁×#575	1	1	yes	characteristic
794	C₂	C₄₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₄₁×#3109	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄×Q₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3507	C₂	semidirect
2. C₂×C₄₁×#554	C₂	semidirect
3. C₄₁×#3389	C₂	semidirect
4. C₄₁×#3388	C₂	semidirect
5. C₄₁×#3376	C₂	semidirect
6. C₄₁×#3370	C₂	semidirect
7. C₄₁×#3239	C₂	semidirect
8. C₄₁×#3236	C₂	semidirect
9. C₄₁×#3234	C₂	semidirect
10. C₄₁×#3232	C₂	semidirect
11. C₄₁×#3114	C₂	semidirect
12. C₄₁×#3110	C₂	semidirect
14. C₄₁×#3105	C₂	semidirect
15. C₄₁×#2983	C₂	semidirect
16. C₄₁×#559	C₂²	semidirect
17. C₄₁×#557	C₂²	semidirect
19. C₄₁×#556	C₂²	semidirect
24. C₄₁×#554	C₂²	semidirect
45. C₄₁×#501	C₂²	semidirect
46. C₄₁×#501	C₂²	semidirect
47. C₄₁×#501	C₂²	semidirect
48. C₄₁×#499	C₂²	semidirect
49. C₄₁×#491	C₂²	semidirect
50. C₄₁×#490	C₂²	semidirect
51. C₄₁×#489	C₂²	semidirect
52. C₄₁×#488	C₂²	semidirect
59. C₄₁×#479	C₂²	semidirect
60. C₄₁×#479	C₂²	semidirect
63. C₄₁×#478	C₂²	semidirect
64. C₄₁×#478	C₂²	semidirect
66. C₄₁×#475	C₂²	semidirect
68. C₄₁×#474	C₂²	semidirect
75. C₄₁×#446	C₂²	semidirect
76. C₄₁×#446	C₂²	semidirect
364. #61831	C₄₁	direct (N × H)
392. #3507	C₂×C₄₁	semidirect
393. C₂×#554	C₂×C₄₁	semidirect
394. #3389	C₂×C₄₁	semidirect
395. #3388	C₂×C₄₁	semidirect
396. #3376	C₂×C₄₁	semidirect
397. #3370	C₂×C₄₁	semidirect
398. #3239	C₂×C₄₁	semidirect
399. #3236	C₂×C₄₁	semidirect
400. #3234	C₂×C₄₁	semidirect
401. #3232	C₂×C₄₁	semidirect
402. #3114	C₂×C₄₁	semidirect
403. #3110	C₂×C₄₁	semidirect
405. #3105	C₂×C₄₁	semidirect
406. #2983	C₂×C₄₁	semidirect
413. #559	C₂²×C₄₁	semidirect
414. #557	C₂²×C₄₁	semidirect
416. #556	C₂²×C₄₁	semidirect
421. #554	C₂²×C₄₁	semidirect
442. #501	C₂²×C₄₁	semidirect
443. #501	C₂²×C₄₁	semidirect
444. #501	C₂²×C₄₁	semidirect
445. #499	C₂²×C₄₁	semidirect
446. #491	C₂²×C₄₁	semidirect
447. #490	C₂²×C₄₁	semidirect
448. #489	C₂²×C₄₁	semidirect
449. #488	C₂²×C₄₁	semidirect
456. #479	C₂²×C₄₁	semidirect
457. #479	C₂²×C₄₁	semidirect
460. #478	C₂²×C₄₁	semidirect
461. #478	C₂²×C₄₁	semidirect
463. #475	C₂²×C₄₁	semidirect
465. #474	C₂²×C₄₁	semidirect
472. #446	C₂²×C₄₁	semidirect
473. #446	C₂²×C₄₁	semidirect
484. C₄₁	#61831	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×#3507	2
C₂×C₄₁×#554	2
C₄₁×#3389	2
C₄₁×#3388	2
C₄₁×#3376	2
C₄₁×#3370	2
C₄₁×#3239	2
C₄₁×#3236	2
C₄₁×#3234	2
C₄₁×#3232	2
C₄₁×#3114	2
C₄₁×#3110	2
C₄₁×#3109	2
C₄₁×#3105	2
C₄₁×#2983	2
#61831	41

Subgroups — C41×#61831 #23838032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61831 #23838032