Subgroups — C₄₁×#61480 #23837681

Order 10496.

2010 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3519	C₂	1	2	yes	maximal, complemented
2	C₄₁×#3391	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3366	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#3339	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3325	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3318	C₂	1	4	yes	maximal, complemented
9	D₄×D₈×C₄₁	C₂	1	2	yes	maximal, complemented
10	D₄×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3176	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3122	C₂	1	4	yes	maximal, complemented
14	C₄₁×#3109	C₂	1	2	yes	maximal, complemented
15	C₄₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#2948	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₄₁	C₂²	1	2	yes	—
20	C₄₁×#555	C₂²	1	2	yes	complemented
21	C₄₁×#554	C₂²	1	2	yes	complemented
22	C₄₁×#553	—	2	2	no	—
23	C₄₁×#553	C₂²	1	4	yes	complemented
24	C₄₁×#550	C₂²	1	2	yes	complemented
25	C₄₁×#546	—	2	2	no	—
26	C₄₁×#546	—	2	4	no	—
27	D₄²×C₄₁	C₂²	1	4	yes	complemented
28	D₄²×C₄₁	C₂²	1	2	yes	complemented
29	C₄₁×#540	C₂²	1	4	yes	complemented
30	C₄₁×#538	—	2	4	no	—
31	C₄₁×#532	C₂²	1	2	yes	complemented
32	C₄₁×#529	C₂²	1	1	yes	characteristic
33	C₄₁×#525	—	2	2	no	—
34	C₂×#121×C₄₁	—	2	2	no	—
35	C₄₁×#518	C₂²	1	4	yes	complemented
36	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
37	C₄₁×#500	C₂²	1	1	yes	characteristic, complemented
38	C₄₁×#499	C₂²	1	2	yes	complemented
39	C₄₁×#493	C₂²	1	1	yes	characteristic, complemented
40	C₄₁×#493	C₂²	1	2	yes	complemented
41	C₄₁×#490	C₂²	1	4	yes	complemented
42	C₄₁×#486	C₂²	1	2	yes	complemented
43	C₄₁×#482	C₂²	1	4	yes	complemented
44	C₄₁×#482	C₂²	1	4	yes	complemented
45	C₄₁×#481	C₂²	1	4	yes	complemented
46	C₄₁×#478	C₂²	1	4	yes	complemented
47	C₄₁×#478	C₂²	1	4	yes	complemented
48	C₄₁×#476	C₂²	1	2	yes	complemented
49	C₄₁×#476	C₂²	1	2	yes	complemented
50	C₄₁×#469	C₂²	1	4	yes	complemented
51	C₄₁×#466	C₂²	1	2	yes	complemented
52	C₄₁×#466	C₂²	1	2	yes	complemented
53	C₄₁×#466	C₂²	1	2	yes	complemented
54	C₄₁×#466	C₂²	1	2	yes	complemented
55	C₄₁×#459	C₂²	1	4	yes	complemented
56	C₄₁×#459	C₂²	1	2	yes	complemented
57	C₄₁×#459	C₂²	1	2	yes	complemented
58	C₄₁×#459	C₂²	1	4	yes	complemented
59	C₄₁×#447	C₂²	1	4	yes	complemented
60	C₄₁×#447	C₂²	1	4	yes	complemented
61	C₄₁×#447	C₂²	1	4	yes	complemented
62	C₄₁×#446	C₂²	1	1	yes	characteristic, complemented
63	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
64	C₄₁×#442	C₂²	1	4	yes	complemented
65	C₄₁×#442	C₂²	1	4	yes	complemented
66	C₄₁×#442	C₂²	1	4	yes	complemented
67	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
68	C₄×D₈×C₄₁	C₂²	1	2	yes	—
69	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
70	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
71	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
72	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
73	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
74	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
75	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
76	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
77	C₄₁×#436	C₂²	1	1	yes	characteristic, complemented
78	C₄₁×#435	C₂²	1	2	yes	complemented
79	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
80	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
81	C₄₁×#433	C₂²	1	2	yes	complemented
82	C₄₁×#432	C₂²	1	1	yes	characteristic, complemented
83	C₄₁×#427	C₂²	1	2	yes	complemented
84	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic, complemented
85	C₄₁×#418	C₂²	1	4	yes	complemented
86	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
87	C₄₁×#405	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
89	C₂×#41×C₄₁	—	2	2	no	—
90	C₂×#41×C₄₁	—	2	2	no	—
91	C₂²×D₄×C₄₁	—	2	2	no	—
92	C₂²×D₄×C₄₁	—	2	4	no	—
93	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
94	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
95	C₂³×C₄×C₄₁	—	2	2	no	—
96	C₂×D₈×C₄₁	—	2	4	no	—
97	C₂×D₈×C₄₁	—	2	8	no	—
98	C₂×D₈×C₄₁	C₂³	1	2	yes	—
99	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
100	C₂×D₈×C₄₁	C₂³	1	2	yes	—
101	C₂×D₈×C₄₁	C₂³	1	4	yes	—
102	C₂×D₈×C₄₁	C₂³	1	2	yes	—
103	C₂×D₈×C₄₁	C₂³	1	4	yes	—
104	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
105	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
106	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
108	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
109	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
110	#127×C₄₁	C₂³	1	2	yes	—
111	#127×C₄₁	C₂³	1	4	yes	—
112	#126×C₄₁	—	2	4	no	—
113	#126×C₄₁	D₄	1	2	yes	—
114	#125×C₄₁	D₄	1	1	yes	characteristic
115	#125×C₄₁	C₂³	1	4	yes	—
116	#124×C₄₁	—	2	4	no	—
117	#124×C₄₁	—	2	2	no	—
118	#124×C₄₁	D₄	1	1	yes	characteristic
119	#123×C₄₁	—	2	4	no	—
120	#123×C₄₁	—	2	4	no	—
121	#123×C₄₁	—	2	4	no	—
122	#123×C₄₁	D₄	1	2	yes	—
123	C₂²⋊Q₈×C₄₁	—	2	2	no	—
124	C₂²⋊Q₈×C₄₁	—	2	4	no	—
125	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
126	#121×C₄₁	—	2	4	no	—
127	#121×C₄₁	—	2	2	no	—
128	#121×C₄₁	—	2	2	no	—
129	#121×C₄₁	—	2	2	no	—
130	#121×C₄₁	—	2	2	no	—
131	#121×C₄₁	—	2	4	no	—
132	#121×C₄₁	—	2	4	no	—
133	#121×C₄₁	—	2	4	no	—
134	#121×C₄₁	—	2	4	no	—
135	#121×C₄₁	D₄	1	1	yes	characteristic
136	#121×C₄₁	C₂³	1	4	yes	—
137	#121×C₄₁	C₂³	1	4	yes	—
138	#121×C₄₁	C₂³	1	4	yes	—
139	#120×C₄₁	—	2	4	no	—
140	#120×C₄₁	—	2	4	no	—
141	#120×C₄₁	—	2	4	no	—
142	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
143	C₄×D₄×C₄₁	—	2	4	no	—
144	C₄×D₄×C₄₁	—	2	4	no	—
145	C₄×D₄×C₄₁	—	2	4	no	—
146	C₄×D₄×C₄₁	—	2	2	no	—
147	C₄×D₄×C₄₁	—	2	2	no	—
148	C₄×D₄×C₄₁	—	2	2	no	—
149	C₄×D₄×C₄₁	C₂³	1	2	yes	—
150	C₄×D₄×C₄₁	C₂³	1	2	yes	—
151	C₄×D₄×C₄₁	C₂³	1	2	yes	—
152	C₄×D₄×C₄₁	C₂³	1	2	yes	—
153	C₄×D₄×C₄₁	C₂³	1	4	yes	—
154	C₄×D₄×C₄₁	C₂³	1	4	yes	—
155	C₄×D₄×C₄₁	C₂³	1	4	yes	—
156	C₄×D₄×C₄₁	C₂³	1	2	yes	—
157	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
158	#117×C₄₁	—	2	2	no	—
159	#117×C₄₁	C₂³	1	4	yes	—
160	#117×C₄₁	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
162	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
164	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
165	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
166	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
167	#107×C₄₁	C₂³	1	2	yes	—
168	#107×C₄₁	C₂³	1	2	yes	—
169	#107×C₄₁	C₂³	1	1	yes	characteristic
170	#107×C₄₁	C₂³	1	1	yes	characteristic
171	#107×C₄₁	C₂³	1	2	yes	—
172	#106×C₄₁	C₂³	1	4	yes	—
173	#106×C₄₁	C₂³	1	4	yes	—
174	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
175	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
176	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
177	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
178	#102×C₄₁	C₂³	1	2	yes	—
179	#102×C₄₁	C₂³	1	2	yes	—
180	#102×C₄₁	C₂³	1	2	yes	—
181	#102×C₄₁	C₂³	1	2	yes	—
182	#102×C₄₁	C₂³	1	4	yes	—
183	#102×C₄₁	C₂³	1	4	yes	—
184	#102×C₄₁	C₂³	1	4	yes	—
185	#102×C₄₁	C₂³	1	4	yes	—
186	#102×C₄₁	C₂³	1	4	yes	—
187	#102×C₄₁	C₂³	1	4	yes	—
188	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
191	#97×C₄₁	C₂³	1	2	yes	—
192	#97×C₄₁	C₂³	1	2	yes	—
193	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₄₁	C₂³	1	2	yes	—
198	C₂⁴×C₄₁	—	2	2	no	—
199	C₂⁴×C₄₁	—	2	4	no	—
200	#41×C₄₁	—	8	4	no	—
201	#41×C₄₁	—	8	4	no	—
202	C₂×Q₈×C₄₁	—	2	2	no	—
203	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
204	C₂×D₄×C₄₁	—	2	4	no	—
205	C₂×D₄×C₄₁	—	2	8	no	—
206	C₂×D₄×C₄₁	—	2	4	no	—
207	C₂×D₄×C₄₁	—	2	4	no	—
208	C₂×D₄×C₄₁	—	2	4	no	—
209	C₂×D₄×C₄₁	—	2	4	no	—
210	C₂×D₄×C₄₁	—	2	2	no	—
211	C₂×D₄×C₄₁	—	2	2	no	—
212	C₂×D₄×C₄₁	—	2	4	no	—
213	C₂×D₄×C₄₁	—	2	2	no	—
214	C₂×D₄×C₄₁	—	2	4	no	—
215	C₂×D₄×C₄₁	—	4	2	no	—
216	C₂×D₄×C₄₁	—	4	4	no	—
217	C₂×D₄×C₄₁	—	8	4	no	—
218	C₂×D₄×C₄₁	—	8	8	no	—
219	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
221	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
222	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
223	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₄₁	—	2	2	no	—
225	C₂²×C₄×C₄₁	—	2	2	no	—
226	C₂²×C₄×C₄₁	—	2	2	no	—
227	C₂²×C₄×C₄₁	—	2	2	no	—
228	C₂²×C₄×C₄₁	—	2	4	no	—
229	C₂²×C₄×C₄₁	—	2	4	no	—
230	C₂²×C₄×C₄₁	—	2	4	no	—
231	C₂²×C₄×C₄₁	—	2	2	no	—
232	C₂²×C₄×C₄₁	—	8	4	no	—
233	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
237	D₈×C₄₁	—	2	4	no	—
238	D₈×C₄₁	—	2	8	no	—
239	D₈×C₄₁	—	2	2	no	—
240	D₈×C₄₁	—	2	4	no	—
241	D₈×C₄₁	—	4	2	no	—
242	D₈×C₄₁	—	4	4	no	—
243	D₈×C₄₁	#41	1	4	yes	complemented
244	M₁₆×C₄₁	—	4	2	no	—
245	C₂×C₈×C₄₁	—	2	2	no	—
246	C₂×C₈×C₄₁	—	2	4	no	—
247	C₂×C₈×C₄₁	—	4	1	no	—
248	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
249	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
252	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
253	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
254	C₄⋊C₄×C₄₁	—	2	2	no	—
255	C₄⋊C₄×C₄₁	—	2	4	no	—
256	C₄⋊C₄×C₄₁	—	2	2	no	—
257	C₄⋊C₄×C₄₁	—	2	4	no	—
258	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
259	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
260	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
263	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
264	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
267	C₂²⋊C₄×C₄₁	—	2	4	no	—
268	C₂²⋊C₄×C₄₁	—	2	2	no	—
269	C₂²⋊C₄×C₄₁	—	2	4	no	—
270	C₂²⋊C₄×C₄₁	—	2	2	no	—
271	C₂²⋊C₄×C₄₁	—	2	4	no	—
272	C₂²⋊C₄×C₄₁	—	2	2	no	—
273	C₂²⋊C₄×C₄₁	—	2	4	no	—
274	C₂²⋊C₄×C₄₁	—	2	2	no	—
275	C₂²⋊C₄×C₄₁	—	2	4	no	—
276	C₂²⋊C₄×C₄₁	—	2	4	no	—
277	C₂²⋊C₄×C₄₁	—	2	4	no	—
278	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
279	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
280	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
281	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
282	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
283	C₄²×C₄₁	—	2	4	no	—
284	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
287	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
288	C₄²×C₄₁	C₂⁴	1	2	yes	—
289	C₂³×C₄₁	—	2	2	no	—
290	C₂³×C₄₁	—	2	2	no	—
291	C₂³×C₄₁	—	2	4	no	—
292	C₂³×C₄₁	—	4	4	no	—
293	C₂³×C₄₁	—	4	8	no	—
294	C₂³×C₄₁	—	4	4	no	—
295	C₂³×C₄₁	—	8	2	no	—
296	C₂³×C₄₁	—	8	4	no	—
297	C₂³×C₄₁	—	8	4	no	—
298	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
299	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
300	Q₈×C₄₁	—	2	2	no	—
301	Q₈×C₄₁	—	8	2	no	—
302	D₄×C₄₁	—	2	4	no	—
303	D₄×C₄₁	—	2	2	no	—
304	D₄×C₄₁	—	2	2	no	—
305	D₄×C₄₁	—	2	4	no	—
306	D₄×C₄₁	—	2	2	no	—
307	D₄×C₄₁	—	2	2	no	—
308	D₄×C₄₁	—	2	4	no	—
309	D₄×C₄₁	—	4	4	no	—
310	D₄×C₄₁	—	4	8	no	—
311	D₄×C₄₁	—	4	8	no	—
312	D₄×C₄₁	—	4	4	no	—
313	D₄×C₄₁	—	8	4	no	—
314	D₄×C₄₁	—	8	2	no	—
315	D₄×C₄₁	—	8	4	no	—
316	D₄×C₄₁	—	8	4	no	—
317	D₄×C₄₁	—	8	4	no	—
318	D₄×C₄₁	C₂×#41	1	4	yes	—
319	C₂×C₄×C₄₁	—	2	2	no	—
320	C₂×C₄×C₄₁	—	2	2	no	—
321	C₂×C₄×C₄₁	—	2	1	no	—
322	C₂×C₄×C₄₁	—	2	2	no	—
323	C₂×C₄×C₄₁	—	2	1	no	—
324	C₂×C₄×C₄₁	—	2	2	no	—
325	C₂×C₄×C₄₁	—	2	2	no	—
326	C₂×C₄×C₄₁	—	2	4	no	—
327	C₂×C₄×C₄₁	—	2	2	no	—
328	C₂×C₄×C₄₁	—	4	4	no	—
329	C₂×C₄×C₄₁	—	4	4	no	—
330	C₂×C₄×C₄₁	—	8	2	no	—
331	C₂×C₄×C₄₁	—	8	2	no	—
332	C₂×C₄×C₄₁	—	8	4	no	—
333	C₂×C₄×C₄₁	—	8	4	no	—
334	C₂×C₄×C₄₁	—	8	4	no	—
335	C₂×C₄×C₄₁	—	8	2	no	—
336	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
345	C₈×C₄₁	—	2	1	no	—
346	C₈×C₄₁	—	2	2	no	—
347	C₈×C₄₁	—	2	1	no	—
348	C₈×C₄₁	—	2	1	no	—
349	C₈×C₄₁	—	2	2	no	—
350	C₈×C₄₁	C₂×#41	1	2	yes	—
351	#61480	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
352	C₂²×C₄₁	—	2	1	no	—
353	C₂²×C₄₁	—	2	1	no	—
354	C₂²×C₄₁	—	2	2	no	—
355	C₂²×C₄₁	—	2	4	no	—
356	C₂²×C₄₁	—	2	2	no	—
357	C₂²×C₄₁	—	2	2	no	—
358	C₂²×C₄₁	—	4	2	no	—
359	C₂²×C₄₁	—	4	2	no	—
360	C₂²×C₄₁	—	4	2	no	—
361	C₂²×C₄₁	—	4	4	no	—
362	C₂²×C₄₁	—	4	2	no	—
363	C₂²×C₄₁	—	4	4	no	—
364	C₂²×C₄₁	—	4	4	no	—
365	C₂²×C₄₁	—	4	2	no	—
366	C₂²×C₄₁	—	8	8	no	—
367	C₂²×C₄₁	—	16	8	no	—
368	C₂²×C₄₁	#576	1	2	yes	—
369	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
370	C₄×C₄₁	—	2	1	no	—
371	C₄×C₄₁	—	2	2	no	—
372	C₄×C₄₁	—	2	1	no	—
373	C₄×C₄₁	—	2	1	no	—
374	C₄×C₄₁	—	2	1	no	—
375	C₄×C₄₁	—	2	2	no	—
376	C₄×C₄₁	—	2	2	no	—
377	C₄×C₄₁	—	4	2	no	—
378	C₄×C₄₁	—	4	2	no	—
379	C₄×C₄₁	—	4	4	no	—
380	C₄×C₄₁	#576	1	2	yes	—
381	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
382	C₄×C₄₁	#585	1	1	yes	characteristic
383	#3519	C₂×C₄₁	1	2	yes	complemented
384	#3391	C₂×C₄₁	1	1	yes	characteristic, complemented
385	#3380	C₂×C₄₁	1	1	yes	characteristic, complemented
386	#3366	C₂×C₄₁	1	2	yes	complemented
387	#3341	C₂×C₄₁	1	1	yes	characteristic, complemented
388	#3339	C₂×C₄₁	1	2	yes	complemented
389	#3325	C₂×C₄₁	1	2	yes	complemented
390	#3318	C₂×C₄₁	1	4	yes	complemented
391	D₄×D₈	C₂×C₄₁	1	2	yes	complemented
392	D₄×D₈	C₂×C₄₁	1	1	yes	characteristic, complemented
393	#3176	C₂×C₄₁	1	2	yes	complemented
394	#3169	C₂×C₄₁	1	1	yes	characteristic, complemented
395	#3122	C₂×C₄₁	1	4	yes	complemented
396	#3109	C₂×C₄₁	1	2	yes	complemented
397	#2966	C₂×C₄₁	1	1	yes	characteristic, complemented
398	#2948	C₂×C₄₁	1	2	yes	complemented
399	C₂×C₄×D₈	C₂×C₄₁	1	1	yes	characteristic, complemented
400	C₂×C₄₁	—	2	2	no	—
401	C₂×C₄₁	—	4	2	no	—
402	C₂×C₄₁	—	4	4	no	—
403	C₂×C₄₁	—	8	2	no	—
404	C₂×C₄₁	—	8	4	no	—
405	C₂×C₄₁	D₄×#41	1	1	yes	characteristic
406	C₂×C₄₁	C₂×#576	1	1	yes	characteristic
407	C₂×C₄₁	C₂×#576	1	1	yes	characteristic
408	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
409	C₂²×D₈	C₂²×C₄₁	1	2	yes	—
410	#555	C₂²×C₄₁	1	2	yes	complemented
411	#554	C₂²×C₄₁	1	2	yes	complemented
412	#553	—	2	2	no	—
413	#553	C₂²×C₄₁	1	4	yes	complemented
414	#550	C₂²×C₄₁	1	2	yes	complemented
415	#546	—	2	2	no	—
416	#546	—	2	4	no	—
417	D₄²	C₂²×C₄₁	1	4	yes	complemented
418	D₄²	C₂²×C₄₁	1	2	yes	complemented
419	#540	C₂²×C₄₁	1	4	yes	complemented
420	#538	—	2	4	no	—
421	#532	C₂²×C₄₁	1	2	yes	complemented
422	#529	C₂²×C₄₁	1	1	yes	characteristic
423	#525	—	2	2	no	—
424	C₂×#121	—	2	2	no	—
425	#518	C₂²×C₄₁	1	4	yes	complemented
426	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
427	#500	C₂²×C₄₁	1	1	yes	characteristic, complemented
428	#499	C₂²×C₄₁	1	2	yes	complemented
429	#493	C₂²×C₄₁	1	1	yes	characteristic, complemented
430	#493	C₂²×C₄₁	1	2	yes	complemented
431	#490	C₂²×C₄₁	1	4	yes	complemented
432	#486	C₂²×C₄₁	1	2	yes	complemented
433	#482	C₂²×C₄₁	1	4	yes	complemented
434	#482	C₂²×C₄₁	1	4	yes	complemented
435	#481	C₂²×C₄₁	1	4	yes	complemented
436	#478	C₂²×C₄₁	1	4	yes	complemented
437	#478	C₂²×C₄₁	1	4	yes	complemented
438	#476	C₂²×C₄₁	1	2	yes	complemented
439	#476	C₂²×C₄₁	1	2	yes	complemented
440	#469	C₂²×C₄₁	1	4	yes	complemented
441	#466	C₂²×C₄₁	1	2	yes	complemented
442	#466	C₂²×C₄₁	1	2	yes	complemented
443	#466	C₂²×C₄₁	1	2	yes	complemented
444	#466	C₂²×C₄₁	1	2	yes	complemented
445	#459	C₂²×C₄₁	1	2	yes	complemented
446	#459	C₂²×C₄₁	1	2	yes	complemented
447	#459	C₂²×C₄₁	1	4	yes	complemented
448	#459	C₂²×C₄₁	1	4	yes	complemented
449	#447	C₂²×C₄₁	1	4	yes	complemented
450	#447	C₂²×C₄₁	1	4	yes	complemented
451	#447	C₂²×C₄₁	1	4	yes	complemented
452	#446	C₂²×C₄₁	1	1	yes	characteristic, complemented
453	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
454	#442	C₂²×C₄₁	1	4	yes	complemented
455	#442	C₂²×C₄₁	1	4	yes	complemented
456	#442	C₂²×C₄₁	1	4	yes	complemented
457	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
458	C₄×D₈	C₂²×C₄₁	1	2	yes	—
459	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
460	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
461	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
462	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
463	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
464	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
465	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
466	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
467	#436	C₂²×C₄₁	1	1	yes	characteristic, complemented
468	#435	C₂²×C₄₁	1	2	yes	complemented
469	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
470	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
471	#433	C₂²×C₄₁	1	2	yes	complemented
472	#432	C₂²×C₄₁	1	1	yes	characteristic, complemented
473	#427	C₂²×C₄₁	1	2	yes	complemented
474	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic, complemented
475	#418	C₂²×C₄₁	1	4	yes	complemented
476	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
477	#405	C₂²×C₄₁	1	2	yes	complemented
478	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
479	C₄₁	#61480	1	1	yes	characteristic, direct product factor, Sylow
480	C₂×#41	—	2	2	no	—
481	C₂×#41	—	2	2	no	—
482	C₂²×D₄	—	2	2	no	—
483	C₂²×D₄	—	2	4	no	—
484	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
485	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
486	C₂³×C₄	—	2	2	no	—
487	C₂×D₈	—	2	4	no	—
488	C₂×D₈	—	2	8	no	—
489	C₂×D₈	C₂³×C₄₁	1	2	yes	—
490	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
491	C₂×D₈	C₂³×C₄₁	1	2	yes	—
492	C₂×D₈	C₂³×C₄₁	1	4	yes	—
493	C₂×D₈	C₂³×C₄₁	1	2	yes	—
494	C₂×D₈	C₂³×C₄₁	1	4	yes	—
495	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
496	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
497	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
498	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
499	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
500	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
501	#127	C₂³×C₄₁	1	2	yes	—
502	#127	C₂³×C₄₁	1	4	yes	—
503	#126	—	2	4	no	—
504	#126	D₄×C₄₁	1	2	yes	—
505	#125	D₄×C₄₁	1	1	yes	characteristic
506	#125	C₂³×C₄₁	1	4	yes	—
507	#124	—	2	4	no	—
508	#124	—	2	2	no	—
509	#124	D₄×C₄₁	1	1	yes	characteristic
510	#123	—	2	4	no	—
511	#123	—	2	4	no	—
512	#123	—	2	4	no	—
513	#123	D₄×C₄₁	1	2	yes	—
514	C₂²⋊Q₈	—	2	2	no	—
515	C₂²⋊Q₈	—	2	4	no	—
516	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
517	#121	—	2	4	no	—
518	#121	—	2	2	no	—
519	#121	—	2	2	no	—
520	#121	—	2	2	no	—
521	#121	—	2	2	no	—
522	#121	—	2	4	no	—
523	#121	—	2	4	no	—
524	#121	—	2	4	no	—
525	#121	—	2	4	no	—
526	#121	D₄×C₄₁	1	1	yes	characteristic
527	#121	C₂³×C₄₁	1	4	yes	—
528	#121	C₂³×C₄₁	1	4	yes	—
529	#121	C₂³×C₄₁	1	4	yes	—
530	#120	—	2	4	no	—
531	#120	—	2	4	no	—
532	#120	—	2	4	no	—
533	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
534	C₄×D₄	—	2	4	no	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	—	2	4	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	C₂³×C₄₁	1	2	yes	—
541	C₄×D₄	C₂³×C₄₁	1	2	yes	—
542	C₄×D₄	C₂³×C₄₁	1	2	yes	—
543	C₄×D₄	C₂³×C₄₁	1	2	yes	—
544	C₄×D₄	C₂³×C₄₁	1	4	yes	—
545	C₄×D₄	C₂³×C₄₁	1	4	yes	—
546	C₄×D₄	C₂³×C₄₁	1	4	yes	—
547	C₄×D₄	C₂³×C₄₁	1	2	yes	—
548	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
549	#117	—	2	2	no	—
550	#117	C₂³×C₄₁	1	4	yes	—
551	#117	C₂³×C₄₁	1	2	yes	—
552	C₂×C₄⋊C₄	—	2	2	no	—
553	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
554	C₂×C₂²⋊C₄	—	2	2	no	—
555	C₂×C₂²⋊C₄	—	2	4	no	—
556	C₂×C₂²⋊C₄	—	2	4	no	—
557	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
558	#107	C₂³×C₄₁	1	1	yes	characteristic
559	#107	C₂³×C₄₁	1	1	yes	characteristic
560	#107	C₂³×C₄₁	1	2	yes	—
561	#107	C₂³×C₄₁	1	2	yes	—
562	#107	C₂³×C₄₁	1	2	yes	—
563	#106	C₂³×C₄₁	1	4	yes	—
564	#106	C₂³×C₄₁	1	4	yes	—
565	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
566	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
567	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
568	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
569	#102	C₂³×C₄₁	1	2	yes	—
570	#102	C₂³×C₄₁	1	2	yes	—
571	#102	C₂³×C₄₁	1	2	yes	—
572	#102	C₂³×C₄₁	1	2	yes	—
573	#102	C₂³×C₄₁	1	4	yes	—
574	#102	C₂³×C₄₁	1	4	yes	—
575	#102	C₂³×C₄₁	1	4	yes	—
576	#102	C₂³×C₄₁	1	4	yes	—
577	#102	C₂³×C₄₁	1	4	yes	—
578	#102	C₂³×C₄₁	1	4	yes	—
579	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
580	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
581	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
582	#97	C₂³×C₄₁	1	2	yes	—
583	#97	C₂³×C₄₁	1	2	yes	—
584	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
585	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
586	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
587	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
588	C₄×C₈	C₂³×C₄₁	1	2	yes	—
589	C₂⁴	—	2	2	no	—
590	C₂⁴	—	2	4	no	—
591	#41	—	8	4	no	—
592	#41	—	8	4	no	—
593	C₂×Q₈	—	2	2	no	—
594	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	8	4	no	—
609	C₂×D₄	—	8	8	no	—
610	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
611	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
612	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
613	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
614	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	8	4	no	—
624	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
628	D₈	—	2	4	no	—
629	D₈	—	2	8	no	—
630	D₈	—	2	2	no	—
631	D₈	—	2	4	no	—
632	D₈	—	4	2	no	—
633	D₈	—	4	4	no	—
634	D₈	#41×C₄₁	1	4	yes	complemented
635	M₁₆	—	4	2	no	—
636	C₂×C₈	—	2	2	no	—
637	C₂×C₈	—	2	4	no	—
638	C₂×C₈	—	4	1	no	—
639	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
640	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
641	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
642	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
643	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
644	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
650	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
651	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
652	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
653	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
654	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
655	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
656	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
657	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
670	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
671	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
672	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
673	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
674	C₄²	—	2	4	no	—
675	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
676	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
677	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
678	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
679	C₄²	C₂⁴×C₄₁	1	2	yes	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	4	no	—
683	C₂³	—	4	4	no	—
684	C₂³	—	4	8	no	—
685	C₂³	—	4	4	no	—
686	C₂³	—	8	2	no	—
687	C₂³	—	8	4	no	—
688	C₂³	—	8	4	no	—
689	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
690	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
691	Q₈	—	2	2	no	—
692	Q₈	—	8	2	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	4	no	—
697	D₄	—	2	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	4	no	—
700	D₄	—	4	4	no	—
701	D₄	—	4	8	no	—
702	D₄	—	4	8	no	—
703	D₄	—	4	4	no	—
704	D₄	—	8	4	no	—
705	D₄	—	8	2	no	—
706	D₄	—	8	4	no	—
707	D₄	—	8	4	no	—
708	D₄	—	8	4	no	—
709	D₄	C₂×#41×C₄₁	1	4	yes	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	4	4	no	—
721	C₂×C₄	—	8	2	no	—
722	C₂×C₄	—	8	2	no	—
723	C₂×C₄	—	8	4	no	—
724	C₂×C₄	—	8	4	no	—
725	C₂×C₄	—	8	4	no	—
726	C₂×C₄	—	8	2	no	—
727	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
731	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
733	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
734	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
735	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
736	C₈	—	2	1	no	—
737	C₈	—	2	2	no	—
738	C₈	—	2	1	no	—
739	C₈	—	2	1	no	—
740	C₈	—	2	2	no	—
741	C₈	C₂×#41×C₄₁	1	2	yes	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	4	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	4	4	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	8	8	no	—
757	C₂²	—	16	8	no	—
758	C₂²	C₄₁×#576	1	2	yes	—
759	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
760	C₄	—	2	1	no	—
761	C₄	—	2	1	no	—
762	C₄	—	2	1	no	—
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	2	1	no	—
766	C₄	—	2	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	4	no	—
770	C₄	C₄₁×#576	1	2	yes	—
771	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
772	C₄	C₄₁×#585	1	1	yes	characteristic
773	C₂	—	2	2	no	—
774	C₂	—	4	2	no	—
775	C₂	—	4	4	no	—
776	C₂	—	8	2	no	—
777	C₂	—	8	4	no	—
778	C₂	D₄×#41×C₄₁	1	1	yes	characteristic
779	C₂	C₂×C₄₁×#576	1	1	yes	characteristic
780	C₂	C₂×C₄₁×#576	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×#3519	C₂	semidirect
2. C₄₁×#3391	C₂	semidirect
3. C₄₁×#3380	C₂	semidirect
4. C₄₁×#3366	C₂	semidirect
5. C₄₁×#3341	C₂	semidirect
6. C₄₁×#3339	C₂	semidirect
7. C₄₁×#3325	C₂	semidirect
8. C₄₁×#3318	C₂	semidirect
9. D₄×D₈×C₄₁	C₂	semidirect
10. D₄×D₈×C₄₁	C₂	semidirect
11. C₄₁×#3176	C₂	semidirect
12. C₄₁×#3169	C₂	semidirect
13. C₄₁×#3122	C₂	semidirect
14. C₄₁×#3109	C₂	semidirect
15. C₄₁×#2966	C₂	semidirect
16. C₄₁×#2948	C₂	semidirect
17. C₂×C₄×D₈×C₄₁	C₂	semidirect
20. C₄₁×#555	C₂²	semidirect
21. C₄₁×#554	C₂²	semidirect
23. C₄₁×#553	C₂²	semidirect
24. C₄₁×#550	C₂²	semidirect
27. D₄²×C₄₁	C₂²	semidirect
28. D₄²×C₄₁	C₂²	semidirect
29. C₄₁×#540	C₂²	semidirect
31. C₄₁×#532	C₂²	semidirect
35. C₄₁×#518	C₂²	semidirect
36. C₂×C₄×D₄×C₄₁	C₂²	semidirect
37. C₄₁×#500	C₂²	semidirect
38. C₄₁×#499	C₂²	semidirect
39. C₄₁×#493	C₂²	semidirect
40. C₄₁×#493	C₂²	semidirect
41. C₄₁×#490	C₂²	semidirect
42. C₄₁×#486	C₂²	semidirect
43. C₄₁×#482	C₂²	semidirect
44. C₄₁×#482	C₂²	semidirect
45. C₄₁×#481	C₂²	semidirect
46. C₄₁×#478	C₂²	semidirect
47. C₄₁×#478	C₂²	semidirect
48. C₄₁×#476	C₂²	semidirect
49. C₄₁×#476	C₂²	semidirect
50. C₄₁×#469	C₂²	semidirect
51. C₄₁×#466	C₂²	semidirect
52. C₄₁×#466	C₂²	semidirect
53. C₄₁×#466	C₂²	semidirect
54. C₄₁×#466	C₂²	semidirect
55. C₄₁×#459	C₂²	semidirect
56. C₄₁×#459	C₂²	semidirect
57. C₄₁×#459	C₂²	semidirect
58. C₄₁×#459	C₂²	semidirect
59. C₄₁×#447	C₂²	semidirect
60. C₄₁×#447	C₂²	semidirect
61. C₄₁×#447	C₂²	semidirect
62. C₄₁×#446	C₂²	semidirect
63. C₈×Q₈×C₄₁	C₂²	semidirect
64. C₄₁×#442	C₂²	semidirect
65. C₄₁×#442	C₂²	semidirect
66. C₄₁×#442	C₂²	semidirect
70. C₄×D₈×C₄₁	C₂²	semidirect
71. C₄×D₈×C₄₁	C₂²	semidirect
72. C₄×D₈×C₄₁	C₂²	semidirect
73. C₄×D₈×C₄₁	C₂²	semidirect
74. C₄×D₈×C₄₁	C₂²	semidirect
75. C₄×D₈×C₄₁	C₂²	semidirect
76. C₄×D₈×C₄₁	C₂²	semidirect
77. C₄₁×#436	C₂²	semidirect
78. C₄₁×#435	C₂²	semidirect
79. C₈×D₄×C₄₁	C₂²	semidirect
80. C₈×D₄×C₄₁	C₂²	semidirect
81. C₄₁×#433	C₂²	semidirect
82. C₄₁×#432	C₂²	semidirect
83. C₄₁×#427	C₂²	semidirect
84. C₂×#107×C₄₁	C₂²	semidirect
85. C₄₁×#418	C₂²	semidirect
86. C₂×#102×C₄₁	C₂²	semidirect
87. C₄₁×#405	C₂²	semidirect
88. C₂×C₄×C₈×C₄₁	C₂²	semidirect
243. D₈×C₄₁	#41	semidirect
351. #61480	C₄₁	direct (N × H)
383. #3519	C₂×C₄₁	semidirect
384. #3391	C₂×C₄₁	semidirect
385. #3380	C₂×C₄₁	semidirect
386. #3366	C₂×C₄₁	semidirect
387. #3341	C₂×C₄₁	semidirect
388. #3339	C₂×C₄₁	semidirect
389. #3325	C₂×C₄₁	semidirect
390. #3318	C₂×C₄₁	semidirect
391. D₄×D₈	C₂×C₄₁	semidirect
392. D₄×D₈	C₂×C₄₁	semidirect
393. #3176	C₂×C₄₁	semidirect
394. #3169	C₂×C₄₁	semidirect
395. #3122	C₂×C₄₁	semidirect
396. #3109	C₂×C₄₁	semidirect
397. #2966	C₂×C₄₁	semidirect
398. #2948	C₂×C₄₁	semidirect
399. C₂×C₄×D₈	C₂×C₄₁	semidirect
410. #555	C₂²×C₄₁	semidirect
411. #554	C₂²×C₄₁	semidirect
413. #553	C₂²×C₄₁	semidirect
414. #550	C₂²×C₄₁	semidirect
417. D₄²	C₂²×C₄₁	semidirect
418. D₄²	C₂²×C₄₁	semidirect
419. #540	C₂²×C₄₁	semidirect
421. #532	C₂²×C₄₁	semidirect
425. #518	C₂²×C₄₁	semidirect
426. C₂×C₄×D₄	C₂²×C₄₁	semidirect
427. #500	C₂²×C₄₁	semidirect
428. #499	C₂²×C₄₁	semidirect
429. #493	C₂²×C₄₁	semidirect
430. #493	C₂²×C₄₁	semidirect
431. #490	C₂²×C₄₁	semidirect
432. #486	C₂²×C₄₁	semidirect
433. #482	C₂²×C₄₁	semidirect
434. #482	C₂²×C₄₁	semidirect
435. #481	C₂²×C₄₁	semidirect
436. #478	C₂²×C₄₁	semidirect
437. #478	C₂²×C₄₁	semidirect
438. #476	C₂²×C₄₁	semidirect
439. #476	C₂²×C₄₁	semidirect
440. #469	C₂²×C₄₁	semidirect
441. #466	C₂²×C₄₁	semidirect
442. #466	C₂²×C₄₁	semidirect
443. #466	C₂²×C₄₁	semidirect
444. #466	C₂²×C₄₁	semidirect
445. #459	C₂²×C₄₁	semidirect
446. #459	C₂²×C₄₁	semidirect
447. #459	C₂²×C₄₁	semidirect
448. #459	C₂²×C₄₁	semidirect
449. #447	C₂²×C₄₁	semidirect
450. #447	C₂²×C₄₁	semidirect
451. #447	C₂²×C₄₁	semidirect
452. #446	C₂²×C₄₁	semidirect
453. C₈×Q₈	C₂²×C₄₁	semidirect
454. #442	C₂²×C₄₁	semidirect
455. #442	C₂²×C₄₁	semidirect
456. #442	C₂²×C₄₁	semidirect
460. C₄×D₈	C₂²×C₄₁	semidirect
461. C₄×D₈	C₂²×C₄₁	semidirect
462. C₄×D₈	C₂²×C₄₁	semidirect
463. C₄×D₈	C₂²×C₄₁	semidirect
464. C₄×D₈	C₂²×C₄₁	semidirect
465. C₄×D₈	C₂²×C₄₁	semidirect
466. C₄×D₈	C₂²×C₄₁	semidirect
467. #436	C₂²×C₄₁	semidirect
468. #435	C₂²×C₄₁	semidirect
469. C₈×D₄	C₂²×C₄₁	semidirect
470. C₈×D₄	C₂²×C₄₁	semidirect
471. #433	C₂²×C₄₁	semidirect
472. #432	C₂²×C₄₁	semidirect
473. #427	C₂²×C₄₁	semidirect
474. C₂×#107	C₂²×C₄₁	semidirect
475. #418	C₂²×C₄₁	semidirect
476. C₂×#102	C₂²×C₄₁	semidirect
477. #405	C₂²×C₄₁	semidirect
478. C₂×C₄×C₈	C₂²×C₄₁	semidirect
479. C₄₁	#61480	direct (N × H)
634. D₈	#41×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3519	2
C₄₁×#3391	2
C₄₁×#3380	2
C₄₁×#3366	2
C₄₁×#3341	2
C₄₁×#3339	2
C₄₁×#3325	2
C₄₁×#3318	2
D₄×D₈×C₄₁	2
C₄₁×#3176	2
C₄₁×#3169	2
C₄₁×#3122	2
C₄₁×#3109	2
C₄₁×#2966	2
C₄₁×#2948	2
C₂×C₄×D₈×C₄₁	2
#61480	41

Subgroups — C41×#61480 #23837681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61480 #23837681