Subgroups — C₄₁×#61995 #23838196

Order 10496.

1978 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3396	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3361	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3333	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3322	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3274	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3273	C₂	1	4	yes	maximal, complemented
9	C₄₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3251	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3212	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3100	C₂	1	2	yes	maximal, complemented
15	C₄₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#3036	C₂	1	2	yes	maximal, complemented
17	C₄₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	4	yes	complemented
20	C₄₁×#559	—	2	1	no	—
21	C₄₁×#559	C₂²	1	2	yes	complemented
22	C₄₁×#559	C₂²	1	1	yes	characteristic, complemented
23	C₄₁×#554	C₂²	1	1	yes	characteristic, complemented
24	C₄₁×#554	C₂²	1	1	yes	characteristic, complemented
25	C₄₁×#553	—	2	1	no	—
26	C₄₁×#553	C₂²	1	2	yes	—
27	C₄₁×#551	—	2	2	no	—
28	C₄₁×#550	—	2	1	no	—
29	C₄₁×#550	C₂²	1	2	yes	—
30	C₄₁×#546	—	2	1	no	—
31	C₄₁×#546	—	2	2	no	—
32	C₄₁×#546	C₂²	1	2	yes	—
33	C₄₁×#546	C₂²	1	4	yes	complemented
34	D₄²×C₄₁	C₂²	1	1	yes	characteristic, complemented
35	C₄₁×#540	—	2	2	no	—
36	C₄₁×#535	—	2	1	no	—
37	C₄₁×#533	C₂²	1	1	yes	characteristic, complemented
38	C₄₁×#532	C₂²	1	1	yes	characteristic
39	C₄₁×#532	C₂²	1	2	yes	complemented
40	C₄₁×#532	C₂²	1	2	yes	complemented
41	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic, complemented
42	C₄₁×#529	—	2	1	no	—
43	C₄₁×#529	C₂²	1	2	yes	complemented
44	C₄₁×#525	—	2	2	no	—
45	C₄₁×#518	—	2	1	no	—
46	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
47	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₄₁	—	2	1	no	—
49	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
50	C₄₁×#495	C₂²	1	4	yes	complemented
51	C₄₁×#493	C₂²	1	2	yes	—
52	C₄₁×#488	C₂²	1	4	yes	complemented
53	C₄₁×#486	C₂²	1	2	yes	complemented
54	C₄₁×#485	C₂²	1	2	yes	complemented
55	C₄₁×#480	C₂²	1	4	yes	complemented
56	C₄₁×#478	C₂²	1	4	yes	complemented
57	C₄₁×#477	C₂²	1	2	yes	complemented
58	C₄₁×#475	C₂²	1	1	yes	characteristic, complemented
59	C₄₁×#474	C₂²	1	1	yes	characteristic, complemented
60	C₄₁×#474	C₂²	1	2	yes	complemented
61	C₄₁×#469	C₂²	1	4	yes	complemented
62	C₄₁×#468	C₂²	1	4	yes	complemented
63	C₄₁×#468	C₂²	1	4	yes	complemented
64	C₄₁×#463	C₂²	1	4	yes	complemented
65	C₄₁×#463	C₂²	1	4	yes	complemented
66	C₄₁×#463	C₂²	1	4	yes	complemented
67	C₄₁×#462	C₂²	1	1	yes	characteristic, complemented
68	C₄₁×#461	C₂²	1	1	yes	characteristic, complemented
69	C₄₁×#461	C₂²	1	2	yes	complemented
70	C₄₁×#460	C₂²	1	2	yes	complemented
71	C₄₁×#460	C₂²	1	2	yes	complemented
72	C₄₁×#460	C₂²	1	2	yes	complemented
73	C₄₁×#459	C₂²	1	2	yes	—
74	C₄₁×#459	C₂²	1	2	yes	—
75	C₄₁×#459	C₂²	1	2	yes	complemented
76	C₄₁×#459	C₂²	1	2	yes	complemented
77	C₄₁×#452	C₂²	1	2	yes	—
78	C₄₁×#452	C₂²	1	4	yes	complemented
79	C₄₁×#449	C₂²	1	4	yes	complemented
80	C₄₁×#447	C₂²	1	4	yes	complemented
81	C₄₁×#447	C₂²	1	4	yes	complemented
82	C₈×Q₈×C₄₁	C₂²	1	2	yes	complemented
83	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
84	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
85	C₄×D₈×C₄₁	C₂²	1	4	yes	complemented
86	C₄×D₈×C₄₁	C₂²	1	4	yes	complemented
87	C₄₁×#436	C₂²	1	4	yes	complemented
88	C₄₁×#436	C₂²	1	2	yes	complemented
89	C₄₁×#431	C₂²	1	2	yes	complemented
90	C₄₁×#431	C₂²	1	1	yes	characteristic, complemented
91	C₄₁×#423	C₂²	1	2	yes	complemented
92	C₄₁×#423	C₂²	1	1	yes	characteristic, complemented
93	C₄₁×#418	C₂²	1	2	yes	complemented
94	C₄₁×#417	C₂²	1	4	yes	complemented
95	C₂×#41×C₄₁	—	2	1	no	—
96	C₂×#41×C₄₁	—	2	2	no	—
97	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
98	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
99	C₂×#41×C₄₁	C₂³	1	4	yes	—
100	C₂²×D₄×C₄₁	—	2	1	no	—
101	C₂²×D₄×C₄₁	—	2	1	no	—
102	C₂²×D₄×C₄₁	—	2	1	no	—
103	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
104	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
105	C₂³×C₄×C₄₁	—	2	2	no	—
106	AGL(1,ℤ/8)×C₄₁	—	4	4	no	—
107	AGL(1,ℤ/8)×C₄₁	—	4	8	no	—
108	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
112	C₂×D₈×C₄₁	C₂³	1	4	yes	—
113	C₂×D₈×C₄₁	C₂³	1	4	yes	—
114	C₂×D₈×C₄₁	C₂³	1	4	yes	—
115	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
116	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
117	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
120	#127×C₄₁	—	2	2	no	—
121	#127×C₄₁	—	2	1	no	—
122	#127×C₄₁	—	2	1	no	—
123	#127×C₄₁	C₂³	1	2	yes	—
124	#127×C₄₁	C₂³	1	2	yes	—
125	#127×C₄₁	C₂³	1	1	yes	characteristic
126	#126×C₄₁	—	2	2	no	—
127	#126×C₄₁	—	2	2	no	—
128	#125×C₄₁	—	2	1	no	—
129	#125×C₄₁	—	2	1	no	—
130	#125×C₄₁	C₂³	1	2	yes	—
131	#124×C₄₁	—	2	1	no	—
132	#124×C₄₁	—	2	2	no	—
133	#124×C₄₁	—	2	1	no	—
134	#124×C₄₁	—	2	2	no	—
135	#124×C₄₁	C₂³	1	2	yes	—
136	#124×C₄₁	C₂³	1	4	yes	—
137	#123×C₄₁	—	2	2	no	—
138	#123×C₄₁	—	2	2	no	—
139	#123×C₄₁	—	2	2	no	—
140	#123×C₄₁	—	2	4	no	—
141	#123×C₄₁	—	2	4	no	—
142	#123×C₄₁	—	2	2	no	—
143	C₂²⋊Q₈×C₄₁	—	2	1	no	—
144	C₂²⋊Q₈×C₄₁	—	2	1	no	—
145	C₂²⋊Q₈×C₄₁	—	2	2	no	—
146	C₂²⋊Q₈×C₄₁	—	2	2	no	—
147	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
148	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
149	#121×C₄₁	—	2	2	no	—
150	#121×C₄₁	—	2	1	no	—
151	#121×C₄₁	—	2	2	no	—
152	#121×C₄₁	—	2	2	no	—
153	#121×C₄₁	—	2	2	no	—
154	#121×C₄₁	—	2	1	no	—
155	#121×C₄₁	—	2	2	no	—
156	#121×C₄₁	—	2	4	no	—
157	#121×C₄₁	—	2	4	no	—
158	#121×C₄₁	C₂³	1	2	yes	—
159	#121×C₄₁	C₂³	1	2	yes	—
160	#121×C₄₁	C₂³	1	4	yes	—
161	#120×C₄₁	—	2	2	no	—
162	#120×C₄₁	—	2	4	no	—
163	#120×C₄₁	—	2	2	no	—
164	C₄×Q₈×C₄₁	—	2	1	no	—
165	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
169	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₄₁	—	2	1	no	—
171	C₄×D₄×C₄₁	—	2	2	no	—
172	C₄×D₄×C₄₁	—	2	1	no	—
173	C₄×D₄×C₄₁	—	2	1	no	—
174	C₄×D₄×C₄₁	—	2	1	no	—
175	C₄×D₄×C₄₁	—	2	2	no	—
176	C₄×D₄×C₄₁	—	2	2	no	—
177	C₄×D₄×C₄₁	—	2	2	no	—
178	C₄×D₄×C₄₁	—	2	1	no	—
179	C₄×D₄×C₄₁	—	2	2	no	—
180	C₄×D₄×C₄₁	—	2	2	no	—
181	C₄×D₄×C₄₁	—	2	2	no	—
182	C₄×D₄×C₄₁	—	2	2	no	—
183	C₄×D₄×C₄₁	—	2	2	no	—
184	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
185	C₄×D₄×C₄₁	D₄	1	2	yes	—
186	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₄₁	C₂³	1	2	yes	—
188	C₄×D₄×C₄₁	C₂³	1	2	yes	—
189	C₄×D₄×C₄₁	C₂³	1	2	yes	—
190	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₄₁	C₂³	1	4	yes	—
192	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₄₁	C₂³	1	2	yes	—
194	#117×C₄₁	—	2	1	no	—
195	#117×C₄₁	—	2	1	no	—
196	#117×C₄₁	—	2	2	no	—
197	#117×C₄₁	D₄	1	1	yes	characteristic
198	#117×C₄₁	D₄	1	2	yes	—
199	#117×C₄₁	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
201	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
203	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
204	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
205	C₂×C₄²×C₄₁	—	2	1	no	—
206	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
208	#107×C₄₁	C₂³	1	2	yes	—
209	#107×C₄₁	C₂³	1	4	yes	—
210	#106×C₄₁	C₂³	1	2	yes	—
211	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
212	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
213	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
214	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
215	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
216	#103×C₄₁	C₂³	1	2	yes	—
217	#103×C₄₁	C₂³	1	4	yes	—
218	#103×C₄₁	C₂³	1	2	yes	—
219	#103×C₄₁	C₂³	1	2	yes	—
220	#102×C₄₁	C₂³	1	4	yes	—
221	#102×C₄₁	C₂³	1	4	yes	—
222	#102×C₄₁	C₂³	1	4	yes	—
223	#102×C₄₁	C₂³	1	2	yes	—
224	#102×C₄₁	C₂³	1	4	yes	—
225	#102×C₄₁	C₂³	1	4	yes	—
226	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
227	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
228	C₄×C₈×C₄₁	C₂³	1	4	yes	—
229	C₄×C₈×C₄₁	C₂³	1	2	yes	—
230	C₂⁴×C₄₁	—	2	2	no	—
231	C₂⁴×C₄₁	—	2	2	no	—
232	#41×C₄₁	—	2	2	no	—
233	#41×C₄₁	—	4	2	no	—
234	#41×C₄₁	—	4	1	no	—
235	#41×C₄₁	—	4	4	no	—
236	#41×C₄₁	—	4	4	no	—
237	#41×C₄₁	—	8	2	no	—
238	#41×C₄₁	—	8	4	no	—
239	C₂×Q₈×C₄₁	—	2	1	no	—
240	C₂×Q₈×C₄₁	—	2	1	no	—
241	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
242	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
243	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₄₁	—	2	4	no	—
245	C₂×D₄×C₄₁	—	2	1	no	—
246	C₂×D₄×C₄₁	—	2	2	no	—
247	C₂×D₄×C₄₁	—	2	4	no	—
248	C₂×D₄×C₄₁	—	2	2	no	—
249	C₂×D₄×C₄₁	—	2	4	no	—
250	C₂×D₄×C₄₁	—	2	2	no	—
251	C₂×D₄×C₄₁	—	2	1	no	—
252	C₂×D₄×C₄₁	—	2	2	no	—
253	C₂×D₄×C₄₁	—	2	2	no	—
254	C₂×D₄×C₄₁	—	2	2	no	—
255	C₂×D₄×C₄₁	—	2	1	no	—
256	C₂×D₄×C₄₁	—	2	2	no	—
257	C₂×D₄×C₄₁	—	2	2	no	—
258	C₂×D₄×C₄₁	—	4	2	no	—
259	C₂×D₄×C₄₁	—	4	2	no	—
260	C₂×D₄×C₄₁	—	4	2	no	—
261	C₂×D₄×C₄₁	—	4	4	no	—
262	C₂×D₄×C₄₁	—	4	4	no	—
263	C₂×D₄×C₄₁	—	8	2	no	—
264	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
265	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
266	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
267	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
268	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₄₁	—	2	2	no	—
270	C₂²×C₄×C₄₁	—	2	1	no	—
271	C₂²×C₄×C₄₁	—	2	1	no	—
272	C₂²×C₄×C₄₁	—	2	1	no	—
273	C₂²×C₄×C₄₁	—	2	2	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	2	no	—
278	C₂²×C₄×C₄₁	—	8	4	no	—
279	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
285	Q₁₆×C₄₁	—	4	2	no	—
286	SD₁₆×C₄₁	—	2	4	no	—
287	SD₁₆×C₄₁	—	4	4	no	—
288	SD₁₆×C₄₁	—	4	4	no	—
289	D₈×C₄₁	—	2	8	no	—
290	D₈×C₄₁	—	4	4	no	—
291	D₈×C₄₁	—	4	4	no	—
292	M₁₆×C₄₁	—	4	2	no	—
293	M₁₆×C₄₁	—	4	4	no	—
294	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
295	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
296	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₄₁	—	2	1	no	—
298	C₄⋊C₄×C₄₁	—	2	2	no	—
299	C₄⋊C₄×C₄₁	—	2	2	no	—
300	C₄⋊C₄×C₄₁	—	2	1	no	—
301	C₄⋊C₄×C₄₁	—	2	1	no	—
302	C₄⋊C₄×C₄₁	—	2	1	no	—
303	C₄⋊C₄×C₄₁	—	2	1	no	—
304	C₄⋊C₄×C₄₁	—	2	2	no	—
305	C₄⋊C₄×C₄₁	—	2	2	no	—
306	C₄⋊C₄×C₄₁	—	2	1	no	—
307	C₄⋊C₄×C₄₁	—	2	2	no	—
308	C₄⋊C₄×C₄₁	—	2	2	no	—
309	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
311	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
315	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
317	C₂²⋊C₄×C₄₁	—	2	2	no	—
318	C₂²⋊C₄×C₄₁	—	2	2	no	—
319	C₂²⋊C₄×C₄₁	—	2	1	no	—
320	C₂²⋊C₄×C₄₁	—	2	1	no	—
321	C₂²⋊C₄×C₄₁	—	2	4	no	—
322	C₂²⋊C₄×C₄₁	—	2	4	no	—
323	C₂²⋊C₄×C₄₁	—	2	2	no	—
324	C₂²⋊C₄×C₄₁	—	2	2	no	—
325	C₂²⋊C₄×C₄₁	—	2	2	no	—
326	C₂²⋊C₄×C₄₁	—	2	2	no	—
327	C₂²⋊C₄×C₄₁	—	2	2	no	—
328	C₂²⋊C₄×C₄₁	—	2	1	no	—
329	C₂²⋊C₄×C₄₁	—	2	2	no	—
330	C₂²⋊C₄×C₄₁	—	2	2	no	—
331	C₂²⋊C₄×C₄₁	—	2	4	no	—
332	C₂²⋊C₄×C₄₁	—	2	4	no	—
333	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
334	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
335	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
336	C₄²×C₄₁	—	2	1	no	—
337	C₄²×C₄₁	—	2	1	no	—
338	C₄²×C₄₁	—	2	1	no	—
339	C₄²×C₄₁	—	2	2	no	—
340	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₄₁	C₂×D₄	1	2	yes	—
343	C₄²×C₄₁	C₂×D₄	1	2	yes	—
344	C₄²×C₄₁	C₂⁴	1	2	yes	—
345	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
346	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
347	C₂³×C₄₁	—	2	1	no	—
348	C₂³×C₄₁	—	2	2	no	—
349	C₂³×C₄₁	—	2	4	no	—
350	C₂³×C₄₁	—	4	4	no	—
351	C₂³×C₄₁	—	4	4	no	—
352	C₂³×C₄₁	—	4	4	no	—
353	C₂³×C₄₁	—	8	2	no	—
354	C₂³×C₄₁	—	8	2	no	—
355	C₂³×C₄₁	—	8	2	no	—
356	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
357	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
358	Q₈×C₄₁	—	2	2	no	—
359	Q₈×C₄₁	—	2	2	no	—
360	Q₈×C₄₁	—	2	1	no	—
361	Q₈×C₄₁	—	2	1	no	—
362	Q₈×C₄₁	—	2	2	no	—
363	Q₈×C₄₁	—	4	2	no	—
364	Q₈×C₄₁	—	8	1	no	—
365	D₄×C₄₁	—	2	2	no	—
366	D₄×C₄₁	—	2	4	no	—
367	D₄×C₄₁	—	2	2	no	—
368	D₄×C₄₁	—	2	1	no	—
369	D₄×C₄₁	—	2	2	no	—
370	D₄×C₄₁	—	2	4	no	—
371	D₄×C₄₁	—	4	2	no	—
372	D₄×C₄₁	—	4	4	no	—
373	D₄×C₄₁	—	4	4	no	—
374	D₄×C₄₁	—	4	2	no	—
375	D₄×C₄₁	—	4	4	no	—
376	D₄×C₄₁	—	4	2	no	—
377	D₄×C₄₁	—	4	4	no	—
378	D₄×C₄₁	—	4	4	no	—
379	D₄×C₄₁	—	8	2	no	—
380	D₄×C₄₁	—	8	2	no	—
381	D₄×C₄₁	—	8	1	no	—
382	D₄×C₄₁	—	8	4	no	—
383	D₄×C₄₁	—	8	2	no	—
384	D₄×C₄₁	—	8	4	no	—
385	D₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
386	C₂×C₄×C₄₁	—	2	2	no	—
387	C₂×C₄×C₄₁	—	2	4	no	—
388	C₂×C₄×C₄₁	—	2	2	no	—
389	C₂×C₄×C₄₁	—	2	2	no	—
390	C₂×C₄×C₄₁	—	2	1	no	—
391	C₂×C₄×C₄₁	—	2	1	no	—
392	C₂×C₄×C₄₁	—	2	2	no	—
393	C₂×C₄×C₄₁	—	2	1	no	—
394	C₂×C₄×C₄₁	—	2	1	no	—
395	C₂×C₄×C₄₁	—	2	1	no	—
396	C₂×C₄×C₄₁	—	2	2	no	—
397	C₂×C₄×C₄₁	—	2	2	no	—
398	C₂×C₄×C₄₁	—	2	2	no	—
399	C₂×C₄×C₄₁	—	4	2	no	—
400	C₂×C₄×C₄₁	—	4	2	no	—
401	C₂×C₄×C₄₁	—	4	2	no	—
402	C₂×C₄×C₄₁	—	4	2	no	—
403	C₂×C₄×C₄₁	—	4	4	no	—
404	C₂×C₄×C₄₁	—	8	2	no	—
405	C₂×C₄×C₄₁	—	8	2	no	—
406	C₂×C₄×C₄₁	—	8	4	no	—
407	C₂×C₄×C₄₁	—	8	4	no	—
408	C₂×C₄×C₄₁	—	8	2	no	—
409	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
418	C₈×C₄₁	—	2	4	no	—
419	C₈×C₄₁	—	2	2	no	—
420	C₈×C₄₁	—	2	2	no	—
421	#61995	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
422	C₂²×C₄₁	—	2	1	no	—
423	C₂²×C₄₁	—	2	2	no	—
424	C₂²×C₄₁	—	2	2	no	—
425	C₂²×C₄₁	—	2	1	no	—
426	C₂²×C₄₁	—	2	2	no	—
427	C₂²×C₄₁	—	2	2	no	—
428	C₂²×C₄₁	—	2	1	no	—
429	C₂²×C₄₁	—	4	1	no	—
430	C₂²×C₄₁	—	4	1	no	—
431	C₂²×C₄₁	—	4	4	no	—
432	C₂²×C₄₁	—	4	2	no	—
433	C₂²×C₄₁	—	4	2	no	—
434	C₂²×C₄₁	—	4	4	no	—
435	C₂²×C₄₁	—	4	2	no	—
436	C₂²×C₄₁	—	4	4	no	—
437	C₂²×C₄₁	—	8	8	no	—
438	C₂²×C₄₁	—	16	4	no	—
439	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
440	C₄×C₄₁	—	2	1	no	—
441	C₄×C₄₁	—	2	2	no	—
442	C₄×C₄₁	—	2	1	no	—
443	C₄×C₄₁	—	2	2	no	—
444	C₄×C₄₁	—	2	2	no	—
445	C₄×C₄₁	—	2	1	no	—
446	C₄×C₄₁	—	4	1	no	—
447	C₄×C₄₁	—	4	2	no	—
448	C₄×C₄₁	—	4	1	no	—
449	C₄×C₄₁	—	4	1	no	—
450	C₄×C₄₁	—	4	2	no	—
451	C₄×C₄₁	—	4	2	no	—
452	C₄×C₄₁	#575	1	2	yes	—
453	C₄×C₄₁	#576	1	2	yes	—
454	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
455	C₄×C₄₁	#585	1	1	yes	characteristic
456	#3508	C₂×C₄₁	1	1	yes	characteristic, complemented
457	#3481	C₂×C₄₁	1	1	yes	characteristic, complemented
458	#3396	C₂×C₄₁	1	2	yes	complemented
459	#3361	C₂×C₄₁	1	2	yes	complemented
460	#3333	C₂×C₄₁	1	2	yes	complemented
461	#3322	C₂×C₄₁	1	4	yes	complemented
462	#3274	C₂×C₄₁	1	2	yes	complemented
463	#3273	C₂×C₄₁	1	4	yes	complemented
464	#3254	C₂×C₄₁	1	1	yes	characteristic, complemented
465	#3251	C₂×C₄₁	1	2	yes	complemented
466	#3212	C₂×C₄₁	1	2	yes	complemented
467	#3205	C₂×C₄₁	1	1	yes	characteristic, complemented
468	#3107	C₂×C₄₁	1	1	yes	characteristic, complemented
469	#3100	C₂×C₄₁	1	2	yes	complemented
470	#3038	C₂×C₄₁	1	1	yes	characteristic, complemented
471	#3036	C₂×C₄₁	1	2	yes	complemented
472	#2991	C₂×C₄₁	1	1	yes	characteristic, complemented
473	C₂×C₄₁	—	4	2	no	—
474	C₂×C₄₁	—	4	1	no	—
475	C₂×C₄₁	—	4	2	no	—
476	C₂×C₄₁	—	8	2	no	—
477	C₂×C₄₁	—	8	4	no	—
478	C₂×C₄₁	#3488	1	1	yes	characteristic
479	C₂×C₄₁	C₂×#575	1	1	yes	characteristic
480	C₂×C₄₁	C₂×#576	1	1	yes	characteristic
481	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	2	yes	—
482	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	4	yes	complemented
483	#559	—	2	1	no	—
484	#559	C₂²×C₄₁	1	2	yes	complemented
485	#559	C₂²×C₄₁	1	1	yes	characteristic, complemented
486	#554	C₂²×C₄₁	1	1	yes	characteristic, complemented
487	#554	C₂²×C₄₁	1	1	yes	characteristic, complemented
488	#553	—	2	1	no	—
489	#553	C₂²×C₄₁	1	2	yes	—
490	#551	—	2	2	no	—
491	#550	—	2	1	no	—
492	#550	C₂²×C₄₁	1	2	yes	—
493	#546	—	2	1	no	—
494	#546	—	2	2	no	—
495	#546	C₂²×C₄₁	1	2	yes	—
496	#546	C₂²×C₄₁	1	4	yes	complemented
497	D₄²	C₂²×C₄₁	1	1	yes	characteristic, complemented
498	#540	—	2	2	no	—
499	#535	—	2	1	no	—
500	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
501	#532	C₂²×C₄₁	1	1	yes	characteristic
502	#532	C₂²×C₄₁	1	2	yes	complemented
503	#532	C₂²×C₄₁	1	2	yes	complemented
504	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic, complemented
505	#529	—	2	1	no	—
506	#529	C₂²×C₄₁	1	2	yes	complemented
507	#525	—	2	2	no	—
508	#518	—	2	1	no	—
509	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
510	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
511	C₂×C₄×D₄	—	2	1	no	—
512	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
513	#495	C₂²×C₄₁	1	4	yes	complemented
514	#493	C₂²×C₄₁	1	2	yes	—
515	#488	C₂²×C₄₁	1	4	yes	complemented
516	#486	C₂²×C₄₁	1	2	yes	complemented
517	#485	C₂²×C₄₁	1	2	yes	complemented
518	#480	C₂²×C₄₁	1	4	yes	complemented
519	#478	C₂²×C₄₁	1	4	yes	complemented
520	#477	C₂²×C₄₁	1	2	yes	complemented
521	#475	C₂²×C₄₁	1	1	yes	characteristic, complemented
522	#474	C₂²×C₄₁	1	1	yes	characteristic, complemented
523	#474	C₂²×C₄₁	1	2	yes	complemented
524	#469	C₂²×C₄₁	1	4	yes	complemented
525	#468	C₂²×C₄₁	1	4	yes	complemented
526	#468	C₂²×C₄₁	1	4	yes	complemented
527	#463	C₂²×C₄₁	1	4	yes	complemented
528	#463	C₂²×C₄₁	1	4	yes	complemented
529	#463	C₂²×C₄₁	1	4	yes	complemented
530	#462	C₂²×C₄₁	1	1	yes	characteristic, complemented
531	#461	C₂²×C₄₁	1	1	yes	characteristic, complemented
532	#461	C₂²×C₄₁	1	2	yes	complemented
533	#460	C₂²×C₄₁	1	2	yes	complemented
534	#460	C₂²×C₄₁	1	2	yes	complemented
535	#460	C₂²×C₄₁	1	2	yes	complemented
536	#459	C₂²×C₄₁	1	2	yes	—
537	#459	C₂²×C₄₁	1	2	yes	—
538	#459	C₂²×C₄₁	1	2	yes	complemented
539	#459	C₂²×C₄₁	1	2	yes	complemented
540	#452	C₂²×C₄₁	1	2	yes	—
541	#452	C₂²×C₄₁	1	4	yes	complemented
542	#449	C₂²×C₄₁	1	4	yes	complemented
543	#447	C₂²×C₄₁	1	4	yes	complemented
544	#447	C₂²×C₄₁	1	4	yes	complemented
545	C₈×Q₈	C₂²×C₄₁	1	2	yes	complemented
546	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
547	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
548	C₄×D₈	C₂²×C₄₁	1	4	yes	complemented
549	C₄×D₈	C₂²×C₄₁	1	4	yes	complemented
550	#436	C₂²×C₄₁	1	2	yes	complemented
551	#436	C₂²×C₄₁	1	4	yes	complemented
552	#431	C₂²×C₄₁	1	2	yes	complemented
553	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
554	#423	C₂²×C₄₁	1	2	yes	complemented
555	#423	C₂²×C₄₁	1	1	yes	characteristic, complemented
556	#418	C₂²×C₄₁	1	2	yes	complemented
557	#417	C₂²×C₄₁	1	4	yes	complemented
558	C₄₁	#61995	1	1	yes	characteristic, direct product factor, Sylow
559	C₂×#41	—	2	1	no	—
560	C₂×#41	—	2	2	no	—
561	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
562	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
563	C₂×#41	C₂³×C₄₁	1	4	yes	—
564	C₂²×D₄	—	2	1	no	—
565	C₂²×D₄	—	2	1	no	—
566	C₂²×D₄	—	2	1	no	—
567	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
568	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
569	C₂³×C₄	—	2	2	no	—
570	AGL(1,ℤ/8)	—	4	4	no	—
571	AGL(1,ℤ/8)	—	4	8	no	—
572	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
573	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
574	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
575	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
576	C₂×D₈	C₂³×C₄₁	1	4	yes	—
577	C₂×D₈	C₂³×C₄₁	1	4	yes	—
578	C₂×D₈	C₂³×C₄₁	1	4	yes	—
579	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
580	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
581	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
582	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
583	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
584	#127	—	2	2	no	—
585	#127	—	2	1	no	—
586	#127	—	2	1	no	—
587	#127	C₂³×C₄₁	1	2	yes	—
588	#127	C₂³×C₄₁	1	2	yes	—
589	#127	C₂³×C₄₁	1	1	yes	characteristic
590	#126	—	2	2	no	—
591	#126	—	2	2	no	—
592	#125	—	2	1	no	—
593	#125	—	2	1	no	—
594	#125	C₂³×C₄₁	1	2	yes	—
595	#124	—	2	1	no	—
596	#124	—	2	2	no	—
597	#124	—	2	1	no	—
598	#124	—	2	2	no	—
599	#124	C₂³×C₄₁	1	2	yes	—
600	#124	C₂³×C₄₁	1	4	yes	—
601	#123	—	2	2	no	—
602	#123	—	2	2	no	—
603	#123	—	2	2	no	—
604	#123	—	2	4	no	—
605	#123	—	2	4	no	—
606	#123	—	2	2	no	—
607	C₂²⋊Q₈	—	2	1	no	—
608	C₂²⋊Q₈	—	2	1	no	—
609	C₂²⋊Q₈	—	2	2	no	—
610	C₂²⋊Q₈	—	2	2	no	—
611	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
612	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
613	#121	—	2	2	no	—
614	#121	—	2	1	no	—
615	#121	—	2	2	no	—
616	#121	—	2	2	no	—
617	#121	—	2	2	no	—
618	#121	—	2	1	no	—
619	#121	—	2	2	no	—
620	#121	—	2	4	no	—
621	#121	—	2	4	no	—
622	#121	C₂³×C₄₁	1	2	yes	—
623	#121	C₂³×C₄₁	1	2	yes	—
624	#121	C₂³×C₄₁	1	4	yes	—
625	#120	—	2	2	no	—
626	#120	—	2	4	no	—
627	#120	—	2	2	no	—
628	C₄×Q₈	—	2	1	no	—
629	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
630	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
631	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
632	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
633	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
634	C₄×D₄	—	2	1	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	1	no	—
637	C₄×D₄	—	2	1	no	—
638	C₄×D₄	—	2	1	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	1	no	—
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
649	C₄×D₄	D₄×C₄₁	1	2	yes	—
650	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
651	C₄×D₄	C₂³×C₄₁	1	2	yes	—
652	C₄×D₄	C₂³×C₄₁	1	2	yes	—
653	C₄×D₄	C₂³×C₄₁	1	2	yes	—
654	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
655	C₄×D₄	C₂³×C₄₁	1	4	yes	—
656	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
657	C₄×D₄	C₂³×C₄₁	1	2	yes	—
658	#117	—	2	1	no	—
659	#117	—	2	1	no	—
660	#117	—	2	2	no	—
661	#117	D₄×C₄₁	1	1	yes	characteristic
662	#117	D₄×C₄₁	1	2	yes	—
663	#117	C₂³×C₄₁	1	1	yes	characteristic
664	C₂×C₄⋊C₄	—	2	1	no	—
665	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
666	C₂×C₂²⋊C₄	—	2	2	no	—
667	C₂×C₂²⋊C₄	—	2	2	no	—
668	C₂×C₂²⋊C₄	—	2	4	no	—
669	C₂×C₄²	—	2	1	no	—
670	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
671	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
672	#107	C₂³×C₄₁	1	2	yes	—
673	#107	C₂³×C₄₁	1	4	yes	—
674	#106	C₂³×C₄₁	1	2	yes	—
675	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
676	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
677	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
678	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
679	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
680	#103	C₂³×C₄₁	1	2	yes	—
681	#103	C₂³×C₄₁	1	4	yes	—
682	#103	C₂³×C₄₁	1	2	yes	—
683	#103	C₂³×C₄₁	1	2	yes	—
684	#102	C₂³×C₄₁	1	4	yes	—
685	#102	C₂³×C₄₁	1	4	yes	—
686	#102	C₂³×C₄₁	1	4	yes	—
687	#102	C₂³×C₄₁	1	2	yes	—
688	#102	C₂³×C₄₁	1	4	yes	—
689	#102	C₂³×C₄₁	1	4	yes	—
690	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
691	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
692	C₄×C₈	C₂³×C₄₁	1	4	yes	—
693	C₄×C₈	C₂³×C₄₁	1	2	yes	—
694	C₂⁴	—	2	2	no	—
695	C₂⁴	—	2	2	no	—
696	#41	—	2	2	no	—
697	#41	—	4	2	no	—
698	#41	—	4	1	no	—
699	#41	—	4	4	no	—
700	#41	—	4	4	no	—
701	#41	—	8	2	no	—
702	#41	—	8	4	no	—
703	C₂×Q₈	—	2	1	no	—
704	C₂×Q₈	—	2	1	no	—
705	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
706	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
707	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	4	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	4	2	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	2	no	—
725	C₂×D₄	—	4	4	no	—
726	C₂×D₄	—	4	4	no	—
727	C₂×D₄	—	8	2	no	—
728	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
729	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
730	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
731	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
732	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	4	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	8	4	no	—
743	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
744	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
745	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
746	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
749	Q₁₆	—	4	2	no	—
750	SD₁₆	—	2	4	no	—
751	SD₁₆	—	4	4	no	—
752	SD₁₆	—	4	4	no	—
753	D₈	—	2	8	no	—
754	D₈	—	4	4	no	—
755	D₈	—	4	4	no	—
756	M₁₆	—	4	2	no	—
757	M₁₆	—	4	4	no	—
758	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
759	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
760	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
761	C₄⋊C₄	—	2	1	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
774	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
775	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
776	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
777	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
778	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
779	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
780	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	1	no	—
784	C₂²⋊C₄	—	2	1	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
798	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
799	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
800	C₄²	—	2	1	no	—
801	C₄²	—	2	1	no	—
802	C₄²	—	2	1	no	—
803	C₄²	—	2	2	no	—
804	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
805	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
806	C₄²	C₂×D₄×C₄₁	1	2	yes	—
807	C₄²	C₂×D₄×C₄₁	1	2	yes	—
808	C₄²	C₂⁴×C₄₁	1	2	yes	—
809	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
810	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
811	C₂³	—	2	1	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	4	4	no	—
815	C₂³	—	4	4	no	—
816	C₂³	—	4	4	no	—
817	C₂³	—	8	2	no	—
818	C₂³	—	8	2	no	—
819	C₂³	—	8	2	no	—
820	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
821	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
822	Q₈	—	2	2	no	—
823	Q₈	—	2	2	no	—
824	Q₈	—	2	1	no	—
825	Q₈	—	2	1	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	4	2	no	—
828	Q₈	—	8	1	no	—
829	D₄	—	2	2	no	—
830	D₄	—	2	4	no	—
831	D₄	—	2	2	no	—
832	D₄	—	2	1	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	4	no	—
835	D₄	—	4	2	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	2	no	—
839	D₄	—	4	4	no	—
840	D₄	—	4	2	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	4	no	—
843	D₄	—	8	2	no	—
844	D₄	—	8	2	no	—
845	D₄	—	8	1	no	—
846	D₄	—	8	4	no	—
847	D₄	—	8	2	no	—
848	D₄	—	8	4	no	—
849	D₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	—	8	2	no	—
870	C₂×C₄	—	8	4	no	—
871	C₂×C₄	—	8	4	no	—
872	C₂×C₄	—	8	2	no	—
873	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
875	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
876	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
877	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
878	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
880	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
881	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
882	C₈	—	2	4	no	—
883	C₈	—	2	2	no	—
884	C₈	—	2	2	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	1	no	—
889	C₂²	—	2	1	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	4	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	4	no	—
898	C₂²	—	4	4	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	8	8	no	—
901	C₂²	—	16	4	no	—
902	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
903	C₄	—	2	1	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	1	no	—
907	C₄	—	2	1	no	—
908	C₄	—	2	2	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	1	no	—
914	C₄	—	4	2	no	—
915	C₄	C₄₁×#575	1	2	yes	—
916	C₄	C₄₁×#576	1	2	yes	—
917	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
918	C₄	C₄₁×#585	1	1	yes	characteristic
919	C₂	—	4	2	no	—
920	C₂	—	4	1	no	—
921	C₂	—	4	2	no	—
922	C₂	—	8	2	no	—
923	C₂	—	8	4	no	—
924	C₂	C₄₁×#3488	1	1	yes	characteristic
925	C₂	C₂×C₄₁×#575	1	1	yes	characteristic
926	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 ◁ C₄×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3508	C₂	semidirect
2. C₄₁×#3481	C₂	semidirect
3. C₄₁×#3396	C₂	semidirect
4. C₄₁×#3361	C₂	semidirect
5. C₄₁×#3333	C₂	semidirect
6. C₄₁×#3322	C₂	semidirect
7. C₄₁×#3274	C₂	semidirect
8. C₄₁×#3273	C₂	semidirect
9. C₄₁×#3254	C₂	semidirect
10. C₄₁×#3251	C₂	semidirect
11. C₄₁×#3212	C₂	semidirect
12. C₄₁×#3205	C₂	semidirect
13. C₄₁×#3107	C₂	semidirect
14. C₄₁×#3100	C₂	semidirect
15. C₄₁×#3038	C₂	semidirect
16. C₄₁×#3036	C₂	semidirect
17. C₄₁×#2991	C₂	semidirect
19. C₂×AGL(1,ℤ/8)×C₄₁	C₂²	semidirect
21. C₄₁×#559	C₂²	semidirect
22. C₄₁×#559	C₂²	semidirect
23. C₄₁×#554	C₂²	semidirect
24. C₄₁×#554	C₂²	semidirect
33. C₄₁×#546	C₂²	semidirect
34. D₄²×C₄₁	C₂²	semidirect
37. C₄₁×#533	C₂²	semidirect
39. C₄₁×#532	C₂²	semidirect
40. C₄₁×#532	C₂²	semidirect
41. C₂×#127×C₄₁	C₂²	semidirect
43. C₄₁×#529	C₂²	semidirect
49. C₂×C₄×D₄×C₄₁	C₂²	semidirect
50. C₄₁×#495	C₂²	semidirect
52. C₄₁×#488	C₂²	semidirect
53. C₄₁×#486	C₂²	semidirect
54. C₄₁×#485	C₂²	semidirect
55. C₄₁×#480	C₂²	semidirect
56. C₄₁×#478	C₂²	semidirect
57. C₄₁×#477	C₂²	semidirect
58. C₄₁×#475	C₂²	semidirect
59. C₄₁×#474	C₂²	semidirect
60. C₄₁×#474	C₂²	semidirect
61. C₄₁×#469	C₂²	semidirect
62. C₄₁×#468	C₂²	semidirect
63. C₄₁×#468	C₂²	semidirect
64. C₄₁×#463	C₂²	semidirect
65. C₄₁×#463	C₂²	semidirect
66. C₄₁×#463	C₂²	semidirect
67. C₄₁×#462	C₂²	semidirect
68. C₄₁×#461	C₂²	semidirect
69. C₄₁×#461	C₂²	semidirect
70. C₄₁×#460	C₂²	semidirect
71. C₄₁×#460	C₂²	semidirect
72. C₄₁×#460	C₂²	semidirect
75. C₄₁×#459	C₂²	semidirect
76. C₄₁×#459	C₂²	semidirect
78. C₄₁×#452	C₂²	semidirect
79. C₄₁×#449	C₂²	semidirect
80. C₄₁×#447	C₂²	semidirect
81. C₄₁×#447	C₂²	semidirect
82. C₈×Q₈×C₄₁	C₂²	semidirect
83. C₄×Q₁₆×C₄₁	C₂²	semidirect
84. C₄×SD₁₆×C₄₁	C₂²	semidirect
85. C₄×D₈×C₄₁	C₂²	semidirect
86. C₄×D₈×C₄₁	C₂²	semidirect
87. C₄₁×#436	C₂²	semidirect
88. C₄₁×#436	C₂²	semidirect
89. C₄₁×#431	C₂²	semidirect
90. C₄₁×#431	C₂²	semidirect
91. C₄₁×#423	C₂²	semidirect
92. C₄₁×#423	C₂²	semidirect
93. C₄₁×#418	C₂²	semidirect
94. C₄₁×#417	C₂²	semidirect
421. #61995	C₄₁	direct (N × H)
456. #3508	C₂×C₄₁	semidirect
457. #3481	C₂×C₄₁	semidirect
458. #3396	C₂×C₄₁	semidirect
459. #3361	C₂×C₄₁	semidirect
460. #3333	C₂×C₄₁	semidirect
461. #3322	C₂×C₄₁	semidirect
462. #3274	C₂×C₄₁	semidirect
463. #3273	C₂×C₄₁	semidirect
464. #3254	C₂×C₄₁	semidirect
465. #3251	C₂×C₄₁	semidirect
466. #3212	C₂×C₄₁	semidirect
467. #3205	C₂×C₄₁	semidirect
468. #3107	C₂×C₄₁	semidirect
469. #3100	C₂×C₄₁	semidirect
470. #3038	C₂×C₄₁	semidirect
471. #3036	C₂×C₄₁	semidirect
472. #2991	C₂×C₄₁	semidirect
482. C₂×AGL(1,ℤ/8)	C₂²×C₄₁	semidirect
484. #559	C₂²×C₄₁	semidirect
485. #559	C₂²×C₄₁	semidirect
486. #554	C₂²×C₄₁	semidirect
487. #554	C₂²×C₄₁	semidirect
496. #546	C₂²×C₄₁	semidirect
497. D₄²	C₂²×C₄₁	semidirect
500. #533	C₂²×C₄₁	semidirect
502. #532	C₂²×C₄₁	semidirect
503. #532	C₂²×C₄₁	semidirect
504. C₂×#127	C₂²×C₄₁	semidirect
506. #529	C₂²×C₄₁	semidirect
512. C₂×C₄×D₄	C₂²×C₄₁	semidirect
513. #495	C₂²×C₄₁	semidirect
515. #488	C₂²×C₄₁	semidirect
516. #486	C₂²×C₄₁	semidirect
517. #485	C₂²×C₄₁	semidirect
518. #480	C₂²×C₄₁	semidirect
519. #478	C₂²×C₄₁	semidirect
520. #477	C₂²×C₄₁	semidirect
521. #475	C₂²×C₄₁	semidirect
522. #474	C₂²×C₄₁	semidirect
523. #474	C₂²×C₄₁	semidirect
524. #469	C₂²×C₄₁	semidirect
525. #468	C₂²×C₄₁	semidirect
526. #468	C₂²×C₄₁	semidirect
527. #463	C₂²×C₄₁	semidirect
528. #463	C₂²×C₄₁	semidirect
529. #463	C₂²×C₄₁	semidirect
530. #462	C₂²×C₄₁	semidirect
531. #461	C₂²×C₄₁	semidirect
532. #461	C₂²×C₄₁	semidirect
533. #460	C₂²×C₄₁	semidirect
534. #460	C₂²×C₄₁	semidirect
535. #460	C₂²×C₄₁	semidirect
538. #459	C₂²×C₄₁	semidirect
539. #459	C₂²×C₄₁	semidirect
541. #452	C₂²×C₄₁	semidirect
542. #449	C₂²×C₄₁	semidirect
543. #447	C₂²×C₄₁	semidirect
544. #447	C₂²×C₄₁	semidirect
545. C₈×Q₈	C₂²×C₄₁	semidirect
546. C₄×Q₁₆	C₂²×C₄₁	semidirect
547. C₄×SD₁₆	C₂²×C₄₁	semidirect
548. C₄×D₈	C₂²×C₄₁	semidirect
549. C₄×D₈	C₂²×C₄₁	semidirect
550. #436	C₂²×C₄₁	semidirect
551. #436	C₂²×C₄₁	semidirect
552. #431	C₂²×C₄₁	semidirect
553. #431	C₂²×C₄₁	semidirect
554. #423	C₂²×C₄₁	semidirect
555. #423	C₂²×C₄₁	semidirect
556. #418	C₂²×C₄₁	semidirect
557. #417	C₂²×C₄₁	semidirect
558. C₄₁	#61995	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×#3508	2
C₄₁×#3481	2
C₄₁×#3396	2
C₄₁×#3361	2
C₄₁×#3333	2
C₄₁×#3322	2
C₄₁×#3274	2
C₄₁×#3273	2
C₄₁×#3254	2
C₄₁×#3251	2
C₄₁×#3212	2
C₄₁×#3205	2
C₄₁×#3107	2
C₄₁×#3100	2
C₄₁×#3038	2
C₄₁×#3036	2
C₄₁×#2991	2
#61995	41

Subgroups — C41×#61995 #23838196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61995 #23838196