Subgroups — C₄₁×#62051 #23838252

Order 10496.

2020 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#3325	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#3318	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3305	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3297	C₂	1	2	yes	maximal, complemented
11	D₄×D₈×C₄₁	C₂	1	2	yes	maximal, complemented
12	D₄×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3264	C₂	1	2	yes	maximal, complemented
15	C₄₁×#3259	C₂	1	2	yes	maximal, complemented
16	C₄₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#3220	C₂	1	2	yes	maximal, complemented
18	C₄₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#3122	C₂	1	2	yes	maximal, complemented
20	C₄₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄₁×#3041	C₂	1	2	yes	maximal, complemented
22	C₂×C₄₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	2	yes	complemented
25	C₂²×D₈×C₄₁	C₂²	1	2	yes	complemented
26	C₂²×D₈×C₄₁	C₂²	1	2	yes	complemented
27	C₄₁×#560	—	2	2	no	—
28	C₄₁×#559	C₂²	1	1	yes	characteristic, complemented
29	C₄₁×#555	C₂²	1	1	yes	characteristic, complemented
30	C₄₁×#554	C₂²	1	1	yes	characteristic, complemented
31	C₄₁×#553	—	2	1	no	—
32	C₄₁×#553	C₂²	1	2	yes	complemented
33	C₄₁×#550	C₂²	1	1	yes	characteristic, complemented
34	C₄₁×#550	C₂²	1	1	yes	characteristic, complemented
35	C₄₁×#550	C₂²	1	1	yes	characteristic, complemented
36	C₄₁×#546	—	2	1	no	—
37	C₄₁×#546	—	2	2	no	—
38	C₄₁×#546	—	2	1	no	—
39	C₄₁×#546	C₂²	1	2	yes	complemented
40	D₄²×C₄₁	—	2	1	no	—
41	D₄²×C₄₁	C₂²	1	2	yes	complemented
42	D₄²×C₄₁	C₂²	1	1	yes	characteristic, complemented
43	D₄²×C₄₁	C₂²	1	2	yes	complemented
44	D₄²×C₄₁	C₂²	1	1	yes	characteristic, complemented
45	C₄₁×#540	—	2	1	no	—
46	C₄₁×#540	C₂²	1	2	yes	complemented
47	C₄₁×#540	C₂²	1	2	yes	complemented
48	C₄₁×#538	—	2	2	no	—
49	C₄₁×#535	—	2	1	no	—
50	C₄₁×#535	C₂²	1	2	yes	complemented
51	C₄₁×#534	—	2	2	no	—
52	C₄₁×#532	C₂²	1	1	yes	characteristic, complemented
53	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic, complemented
54	C₄₁×#529	C₂²	1	1	yes	characteristic
55	C₄₁×#529	C₂²	1	1	yes	characteristic, complemented
56	C₄₁×#525	—	2	1	no	—
57	C₂×#121×C₄₁	—	2	1	no	—
58	C₄₁×#518	C₂²	1	2	yes	complemented
59	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
60	C₄₁×#496	C₂²	1	2	yes	complemented
61	C₄₁×#493	C₂²	1	1	yes	characteristic, complemented
62	C₄₁×#493	C₂²	1	2	yes	complemented
63	C₄₁×#493	C₂²	1	1	yes	characteristic, complemented
64	C₄₁×#490	C₂²	1	2	yes	complemented
65	C₄₁×#488	C₂²	1	2	yes	complemented
66	C₄₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₄₁×#486	C₂²	1	1	yes	characteristic, complemented
68	C₄₁×#484	C₂²	1	1	yes	characteristic, complemented
69	C₄₁×#482	C₂²	1	2	yes	complemented
70	C₄₁×#482	C₂²	1	2	yes	complemented
71	C₄₁×#481	C₂²	1	1	yes	characteristic, complemented
72	C₄₁×#478	C₂²	1	2	yes	complemented
73	C₄₁×#478	C₂²	1	2	yes	complemented
74	C₄₁×#478	C₂²	1	1	yes	characteristic, complemented
75	C₄₁×#478	C₂²	1	1	yes	characteristic, complemented
76	C₄₁×#478	C₂²	1	2	yes	complemented
77	C₄₁×#477	C₂²	1	1	yes	characteristic, complemented
78	C₄₁×#476	C₂²	1	1	yes	characteristic, complemented
79	C₄₁×#469	C₂²	1	2	yes	complemented
80	C₄₁×#469	C₂²	1	2	yes	complemented
81	C₄₁×#466	C₂²	1	2	yes	complemented
82	C₄₁×#466	C₂²	1	2	yes	complemented
83	C₄₁×#466	C₂²	1	2	yes	complemented
84	C₄₁×#465	C₂²	1	2	yes	complemented
85	C₄₁×#463	C₂²	1	1	yes	characteristic, complemented
86	C₄₁×#463	C₂²	1	2	yes	complemented
87	C₄₁×#463	C₂²	1	2	yes	complemented
88	C₄₁×#463	C₂²	1	2	yes	complemented
89	C₄₁×#463	C₂²	1	1	yes	characteristic, complemented
90	C₄₁×#460	C₂²	1	1	yes	characteristic, complemented
91	C₄₁×#459	C₂²	1	1	yes	characteristic
92	C₄₁×#459	C₂²	1	2	yes	complemented
93	C₄₁×#459	C₂²	1	2	yes	complemented
94	C₄₁×#459	C₂²	1	2	yes	complemented
95	C₄₁×#459	C₂²	1	2	yes	complemented
96	C₄₁×#459	C₂²	1	1	yes	characteristic, complemented
97	C₄₁×#459	C₂²	1	1	yes	characteristic, complemented
98	C₄₁×#459	C₂²	1	1	yes	characteristic, complemented
99	C₄₁×#459	C₂²	1	2	yes	complemented
100	C₄₁×#459	C₂²	1	1	yes	characteristic, complemented
101	C₄₁×#459	C₂²	1	2	yes	complemented
102	C₄₁×#459	C₂²	1	2	yes	complemented
103	C₄₁×#459	C₂²	1	2	yes	complemented
104	C₄₁×#450	C₂²	1	1	yes	characteristic, complemented
105	C₄₁×#449	C₂²	1	2	yes	complemented
106	C₄₁×#449	C₂²	1	2	yes	complemented
107	C₄₁×#447	C₂²	1	1	yes	characteristic
108	C₄₁×#447	C₂²	1	2	yes	complemented
109	C₄₁×#447	C₂²	1	2	yes	complemented
110	C₄₁×#447	C₂²	1	2	yes	complemented
111	C₄₁×#447	C₂²	1	2	yes	complemented
112	C₄₁×#447	C₂²	1	2	yes	complemented
113	C₄₁×#447	C₂²	1	2	yes	complemented
114	C₄₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
116	C₄₁×#442	C₂²	1	2	yes	complemented
117	C₄₁×#442	C₂²	1	2	yes	complemented
118	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
121	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
124	C₄₁×#436	C₂²	1	1	yes	characteristic, complemented
125	C₄₁×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
127	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
128	C₄₁×#433	C₂²	1	2	yes	complemented
129	C₄₁×#431	C₂²	1	1	yes	characteristic, complemented
130	C₄₁×#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
132	C₄₁×#418	C₂²	1	2	yes	complemented
133	C₄₁×#416	C₂²	1	2	yes	complemented
134	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
135	C₂×#41×C₄₁	—	2	1	no	—
136	C₂×#41×C₄₁	—	2	1	no	—
137	C₂×#41×C₄₁	—	2	1	no	—
138	C₂×#41×C₄₁	C₂³	1	2	yes	—
139	C₂²×D₄×C₄₁	—	2	1	no	—
140	C₂²×D₄×C₄₁	—	2	2	no	—
141	C₂²×D₄×C₄₁	—	2	2	no	—
142	C₂²×D₄×C₄₁	—	2	1	no	—
143	C₂²×D₄×C₄₁	—	2	1	no	—
144	C₂²×D₄×C₄₁	—	2	1	no	—
145	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
147	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
148	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
149	C₂³×C₄×C₄₁	—	2	1	no	—
150	AGL(1,ℤ/8)×C₄₁	—	4	4	no	—
151	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₄₁	—	4	4	no	—
155	C₂×D₈×C₄₁	—	4	4	no	—
156	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
157	C₂×D₈×C₄₁	C₂³	1	2	yes	—
158	C₂×D₈×C₄₁	C₂³	1	2	yes	—
159	C₂×D₈×C₄₁	C₂³	1	2	yes	—
160	C₂×D₈×C₄₁	C₂³	1	2	yes	—
161	C₂×D₈×C₄₁	C₂³	1	2	yes	—
162	C₂×D₈×C₄₁	C₂³	1	2	yes	—
163	C₂×D₈×C₄₁	C₂³	1	2	yes	—
164	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
165	C₂×D₈×C₄₁	C₂³	1	2	yes	—
166	C₂×D₈×C₄₁	C₂³	1	2	yes	—
167	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
168	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
169	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
170	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
171	#127×C₄₁	—	2	1	no	—
172	#127×C₄₁	—	2	1	no	—
173	#127×C₄₁	—	2	1	no	—
174	#127×C₄₁	C₂³	1	2	yes	—
175	#127×C₄₁	C₂³	1	1	yes	characteristic
176	#127×C₄₁	C₂³	1	1	yes	characteristic
177	#127×C₄₁	C₂³	1	1	yes	characteristic
178	#127×C₄₁	C₂³	1	2	yes	—
179	#127×C₄₁	C₂³	1	2	yes	—
180	#126×C₄₁	—	2	2	no	—
181	#126×C₄₁	—	2	1	no	—
182	#126×C₄₁	D₄	1	2	yes	—
183	#125×C₄₁	D₄	1	1	yes	characteristic
184	#125×C₄₁	C₂³	1	1	yes	characteristic
185	#125×C₄₁	C₂³	1	2	yes	—
186	#124×C₄₁	—	2	1	no	—
187	#124×C₄₁	—	2	2	no	—
188	#124×C₄₁	—	2	1	no	—
189	#124×C₄₁	D₄	1	1	yes	characteristic
190	#124×C₄₁	C₂³	1	1	yes	characteristic
191	#124×C₄₁	C₂³	1	2	yes	—
192	#123×C₄₁	—	2	1	no	—
193	#123×C₄₁	—	2	2	no	—
194	#123×C₄₁	—	2	2	no	—
195	#123×C₄₁	—	2	2	no	—
196	#123×C₄₁	—	2	2	no	—
197	#123×C₄₁	—	2	2	no	—
198	#123×C₄₁	—	2	2	no	—
199	#123×C₄₁	—	2	2	no	—
200	#123×C₄₁	D₄	1	2	yes	—
201	C₂²⋊Q₈×C₄₁	—	2	1	no	—
202	C₂²⋊Q₈×C₄₁	—	2	2	no	—
203	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
204	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
205	#121×C₄₁	—	2	2	no	—
206	#121×C₄₁	—	2	1	no	—
207	#121×C₄₁	—	2	1	no	—
208	#121×C₄₁	—	2	1	no	—
209	#121×C₄₁	—	2	1	no	—
210	#121×C₄₁	—	2	2	no	—
211	#121×C₄₁	—	2	2	no	—
212	#121×C₄₁	—	2	2	no	—
213	#121×C₄₁	—	2	2	no	—
214	#121×C₄₁	—	2	2	no	—
215	#121×C₄₁	—	2	1	no	—
216	#121×C₄₁	—	2	1	no	—
217	#121×C₄₁	—	2	2	no	—
218	#121×C₄₁	—	2	2	no	—
219	#121×C₄₁	—	2	2	no	—
220	#121×C₄₁	—	2	2	no	—
221	#121×C₄₁	—	2	2	no	—
222	#121×C₄₁	—	2	2	no	—
223	#121×C₄₁	—	2	2	no	—
224	#121×C₄₁	D₄	1	1	yes	characteristic
225	#121×C₄₁	C₂³	1	1	yes	characteristic
226	#121×C₄₁	C₂³	1	2	yes	—
227	#121×C₄₁	C₂³	1	2	yes	—
228	#121×C₄₁	C₂³	1	2	yes	—
229	#121×C₄₁	C₂³	1	2	yes	—
230	#121×C₄₁	C₂³	1	2	yes	—
231	#120×C₄₁	—	2	2	no	—
232	#120×C₄₁	—	2	2	no	—
233	#120×C₄₁	—	2	2	no	—
234	#120×C₄₁	—	2	2	no	—
235	#120×C₄₁	—	2	2	no	—
236	#120×C₄₁	—	2	2	no	—
237	#120×C₄₁	—	2	2	no	—
238	#120×C₄₁	—	2	2	no	—
239	#120×C₄₁	—	2	2	no	—
240	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₄₁	—	2	1	no	—
243	C₄×D₄×C₄₁	—	2	2	no	—
244	C₄×D₄×C₄₁	—	2	2	no	—
245	C₄×D₄×C₄₁	—	2	1	no	—
246	C₄×D₄×C₄₁	—	2	1	no	—
247	C₄×D₄×C₄₁	—	2	2	no	—
248	C₄×D₄×C₄₁	—	2	1	no	—
249	C₄×D₄×C₄₁	—	2	1	no	—
250	C₄×D₄×C₄₁	—	2	1	no	—
251	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₄₁	C₂³	1	2	yes	—
256	C₄×D₄×C₄₁	C₂³	1	2	yes	—
257	C₄×D₄×C₄₁	C₂³	1	2	yes	—
258	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₄₁	C₂³	1	2	yes	—
260	C₄×D₄×C₄₁	C₂³	1	2	yes	—
261	C₄×D₄×C₄₁	C₂³	1	2	yes	—
262	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
263	#117×C₄₁	—	2	1	no	—
264	#117×C₄₁	—	2	1	no	—
265	#117×C₄₁	C₂³	1	2	yes	—
266	#117×C₄₁	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
268	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
270	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
272	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
273	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
274	#107×C₄₁	C₂³	1	1	yes	characteristic
275	#107×C₄₁	C₂³	1	2	yes	—
276	#107×C₄₁	C₂³	1	1	yes	characteristic
277	#106×C₄₁	C₂³	1	1	yes	characteristic
278	#106×C₄₁	C₂³	1	1	yes	characteristic
279	#106×C₄₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
285	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
286	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
287	#103×C₄₁	C₂³	1	1	yes	characteristic
288	#103×C₄₁	C₂³	1	2	yes	—
289	#103×C₄₁	C₂³	1	1	yes	characteristic
290	#102×C₄₁	C₂³	1	2	yes	—
291	#102×C₄₁	C₂³	1	2	yes	—
292	#102×C₄₁	C₂³	1	2	yes	—
293	#102×C₄₁	C₂³	1	2	yes	—
294	#102×C₄₁	C₂³	1	2	yes	—
295	#102×C₄₁	C₂³	1	1	yes	characteristic
296	#102×C₄₁	C₂³	1	2	yes	—
297	#102×C₄₁	C₂³	1	2	yes	—
298	#102×C₄₁	C₂³	1	1	yes	characteristic
299	#102×C₄₁	C₂³	1	1	yes	characteristic
300	#102×C₄₁	C₂³	1	2	yes	—
301	#102×C₄₁	C₂³	1	1	yes	characteristic
302	#102×C₄₁	C₂³	1	2	yes	—
303	#102×C₄₁	C₂³	1	1	yes	characteristic
304	#102×C₄₁	C₂³	1	1	yes	characteristic
305	#102×C₄₁	C₂³	1	2	yes	—
306	#102×C₄₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
311	#97×C₄₁	C₂³	1	2	yes	—
312	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₄₁	C₂³	1	2	yes	—
315	C₂⁴×C₄₁	—	2	1	no	—
316	C₂⁴×C₄₁	—	2	2	no	—
317	C₂⁴×C₄₁	—	2	2	no	—
318	C₂⁴×C₄₁	—	2	2	no	—
319	#41×C₄₁	—	4	2	no	—
320	#41×C₄₁	—	4	2	no	—
321	#41×C₄₁	—	8	2	no	—
322	#41×C₄₁	—	8	2	no	—
323	#41×C₄₁	—	8	2	no	—
324	C₂×Q₈×C₄₁	—	2	1	no	—
325	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₄₁	—	2	2	no	—
328	C₂×D₄×C₄₁	—	2	4	no	—
329	C₂×D₄×C₄₁	—	2	1	no	—
330	C₂×D₄×C₄₁	—	2	2	no	—
331	C₂×D₄×C₄₁	—	2	2	no	—
332	C₂×D₄×C₄₁	—	2	2	no	—
333	C₂×D₄×C₄₁	—	2	2	no	—
334	C₂×D₄×C₄₁	—	2	2	no	—
335	C₂×D₄×C₄₁	—	2	2	no	—
336	C₂×D₄×C₄₁	—	2	2	no	—
337	C₂×D₄×C₄₁	—	2	1	no	—
338	C₂×D₄×C₄₁	—	2	1	no	—
339	C₂×D₄×C₄₁	—	2	1	no	—
340	C₂×D₄×C₄₁	—	2	1	no	—
341	C₂×D₄×C₄₁	—	2	2	no	—
342	C₂×D₄×C₄₁	—	2	2	no	—
343	C₂×D₄×C₄₁	—	2	2	no	—
344	C₂×D₄×C₄₁	—	2	1	no	—
345	C₂×D₄×C₄₁	—	2	1	no	—
346	C₂×D₄×C₄₁	—	2	2	no	—
347	C₂×D₄×C₄₁	—	2	2	no	—
348	C₂×D₄×C₄₁	—	2	2	no	—
349	C₂×D₄×C₄₁	—	2	2	no	—
350	C₂×D₄×C₄₁	—	2	2	no	—
351	C₂×D₄×C₄₁	—	2	1	no	—
352	C₂×D₄×C₄₁	—	4	1	no	—
353	C₂×D₄×C₄₁	—	4	2	no	—
354	C₂×D₄×C₄₁	—	4	2	no	—
355	C₂×D₄×C₄₁	—	4	2	no	—
356	C₂×D₄×C₄₁	—	4	2	no	—
357	C₂×D₄×C₄₁	—	4	2	no	—
358	C₂×D₄×C₄₁	—	8	2	no	—
359	C₂×D₄×C₄₁	—	8	2	no	—
360	C₂×D₄×C₄₁	—	8	2	no	—
361	C₂×D₄×C₄₁	—	8	2	no	—
362	C₂×D₄×C₄₁	—	8	4	no	—
363	C₂×D₄×C₄₁	—	8	4	no	—
364	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
365	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
367	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
368	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
369	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
370	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
371	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₄₁	—	2	1	no	—
373	C₂²×C₄×C₄₁	—	2	1	no	—
374	C₂²×C₄×C₄₁	—	2	1	no	—
375	C₂²×C₄×C₄₁	—	2	1	no	—
376	C₂²×C₄×C₄₁	—	2	1	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	1	no	—
383	C₂²×C₄×C₄₁	—	2	2	no	—
384	C₂²×C₄×C₄₁	—	8	2	no	—
385	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
389	SD₁₆×C₄₁	—	2	2	no	—
390	SD₁₆×C₄₁	—	4	1	no	—
391	SD₁₆×C₄₁	—	4	2	no	—
392	D₈×C₄₁	—	2	2	no	—
393	D₈×C₄₁	—	2	4	no	—
394	D₈×C₄₁	—	2	4	no	—
395	D₈×C₄₁	—	4	2	no	—
396	D₈×C₄₁	—	4	2	no	—
397	D₈×C₄₁	—	4	2	no	—
398	D₈×C₄₁	—	4	2	no	—
399	D₈×C₄₁	—	4	2	no	—
400	D₈×C₄₁	—	4	1	no	—
401	D₈×C₄₁	—	4	2	no	—
402	D₈×C₄₁	—	4	2	no	—
403	M₁₆×C₄₁	—	4	2	no	—
404	C₂×C₈×C₄₁	—	4	2	no	—
405	C₂×C₈×C₄₁	—	4	2	no	—
406	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
410	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
411	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₄₁	—	2	1	no	—
413	C₄⋊C₄×C₄₁	—	2	2	no	—
414	C₄⋊C₄×C₄₁	—	2	1	no	—
415	C₄⋊C₄×C₄₁	—	2	1	no	—
416	C₄⋊C₄×C₄₁	—	2	1	no	—
417	C₄⋊C₄×C₄₁	—	2	1	no	—
418	C₄⋊C₄×C₄₁	—	2	2	no	—
419	C₄⋊C₄×C₄₁	—	2	1	no	—
420	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
422	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
423	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
424	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
425	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
426	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
429	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
430	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
431	C₂²⋊C₄×C₄₁	—	2	2	no	—
432	C₂²⋊C₄×C₄₁	—	2	1	no	—
433	C₂²⋊C₄×C₄₁	—	2	1	no	—
434	C₂²⋊C₄×C₄₁	—	2	2	no	—
435	C₂²⋊C₄×C₄₁	—	2	1	no	—
436	C₂²⋊C₄×C₄₁	—	2	2	no	—
437	C₂²⋊C₄×C₄₁	—	2	1	no	—
438	C₂²⋊C₄×C₄₁	—	2	2	no	—
439	C₂²⋊C₄×C₄₁	—	2	1	no	—
440	C₂²⋊C₄×C₄₁	—	2	2	no	—
441	C₂²⋊C₄×C₄₁	—	2	2	no	—
442	C₂²⋊C₄×C₄₁	—	2	1	no	—
443	C₂²⋊C₄×C₄₁	—	2	1	no	—
444	C₂²⋊C₄×C₄₁	—	2	2	no	—
445	C₂²⋊C₄×C₄₁	—	2	1	no	—
446	C₂²⋊C₄×C₄₁	—	2	2	no	—
447	C₂²⋊C₄×C₄₁	—	2	2	no	—
448	C₂²⋊C₄×C₄₁	—	2	2	no	—
449	C₂²⋊C₄×C₄₁	—	2	2	no	—
450	C₂²⋊C₄×C₄₁	—	2	1	no	—
451	C₂²⋊C₄×C₄₁	—	2	2	no	—
452	C₂²⋊C₄×C₄₁	—	2	2	no	—
453	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
454	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
455	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
456	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
457	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
458	C₄²×C₄₁	—	2	2	no	—
459	C₄²×C₄₁	—	2	1	no	—
460	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
461	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
462	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
463	C₄²×C₄₁	C₂⁴	1	2	yes	—
464	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
465	C₂³×C₄₁	—	2	1	no	—
466	C₂³×C₄₁	—	2	1	no	—
467	C₂³×C₄₁	—	2	2	no	—
468	C₂³×C₄₁	—	2	1	no	—
469	C₂³×C₄₁	—	2	2	no	—
470	C₂³×C₄₁	—	2	2	no	—
471	C₂³×C₄₁	—	4	2	no	—
472	C₂³×C₄₁	—	4	4	no	—
473	C₂³×C₄₁	—	4	2	no	—
474	C₂³×C₄₁	—	4	4	no	—
475	C₂³×C₄₁	—	8	1	no	—
476	C₂³×C₄₁	—	8	2	no	—
477	C₂³×C₄₁	—	8	2	no	—
478	C₂³×C₄₁	—	8	2	no	—
479	C₂³×C₄₁	—	8	2	no	—
480	C₂³×C₄₁	—	8	2	no	—
481	C₂³×C₄₁	—	8	2	no	—
482	C₂³×C₄₁	—	8	2	no	—
483	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
484	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
485	Q₈×C₄₁	—	2	2	no	—
486	Q₈×C₄₁	—	2	1	no	—
487	Q₈×C₄₁	—	2	1	no	—
488	Q₈×C₄₁	—	8	1	no	—
489	D₄×C₄₁	—	2	4	no	—
490	D₄×C₄₁	—	2	2	no	—
491	D₄×C₄₁	—	2	1	no	—
492	D₄×C₄₁	—	2	2	no	—
493	D₄×C₄₁	—	2	2	no	—
494	D₄×C₄₁	—	2	1	no	—
495	D₄×C₄₁	—	2	2	no	—
496	D₄×C₄₁	—	2	1	no	—
497	D₄×C₄₁	—	2	2	no	—
498	D₄×C₄₁	—	2	1	no	—
499	D₄×C₄₁	—	2	1	no	—
500	D₄×C₄₁	—	2	2	no	—
501	D₄×C₄₁	—	2	2	no	—
502	D₄×C₄₁	—	4	4	no	—
503	D₄×C₄₁	—	4	2	no	—
504	D₄×C₄₁	—	4	2	no	—
505	D₄×C₄₁	—	4	4	no	—
506	D₄×C₄₁	—	4	2	no	—
507	D₄×C₄₁	—	4	2	no	—
508	D₄×C₄₁	—	4	2	no	—
509	D₄×C₄₁	—	8	2	no	—
510	D₄×C₄₁	—	8	2	no	—
511	D₄×C₄₁	—	8	2	no	—
512	D₄×C₄₁	—	8	2	no	—
513	D₄×C₄₁	—	8	1	no	—
514	D₄×C₄₁	—	8	1	no	—
515	D₄×C₄₁	—	8	2	no	—
516	D₄×C₄₁	—	8	2	no	—
517	D₄×C₄₁	—	8	1	no	—
518	D₄×C₄₁	—	8	2	no	—
519	D₄×C₄₁	—	8	2	no	—
520	D₄×C₄₁	—	8	2	no	—
521	D₄×C₄₁	—	8	2	no	—
522	D₄×C₄₁	—	8	2	no	—
523	D₄×C₄₁	—	8	2	no	—
524	D₄×C₄₁	—	8	2	no	—
525	D₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
526	C₂×C₄×C₄₁	—	2	2	no	—
527	C₂×C₄×C₄₁	—	2	2	no	—
528	C₂×C₄×C₄₁	—	2	1	no	—
529	C₂×C₄×C₄₁	—	2	2	no	—
530	C₂×C₄×C₄₁	—	2	1	no	—
531	C₂×C₄×C₄₁	—	2	2	no	—
532	C₂×C₄×C₄₁	—	2	1	no	—
533	C₂×C₄×C₄₁	—	2	1	no	—
534	C₂×C₄×C₄₁	—	2	1	no	—
535	C₂×C₄×C₄₁	—	2	2	no	—
536	C₂×C₄×C₄₁	—	2	1	no	—
537	C₂×C₄×C₄₁	—	2	1	no	—
538	C₂×C₄×C₄₁	—	4	2	no	—
539	C₂×C₄×C₄₁	—	4	2	no	—
540	C₂×C₄×C₄₁	—	4	2	no	—
541	C₂×C₄×C₄₁	—	8	1	no	—
542	C₂×C₄×C₄₁	—	8	1	no	—
543	C₂×C₄×C₄₁	—	8	2	no	—
544	C₂×C₄×C₄₁	—	8	2	no	—
545	C₂×C₄×C₄₁	—	8	2	no	—
546	C₂×C₄×C₄₁	—	8	2	no	—
547	C₂×C₄×C₄₁	—	8	2	no	—
548	C₂×C₄×C₄₁	—	8	2	no	—
549	C₂×C₄×C₄₁	—	8	1	no	—
550	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
551	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
556	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
557	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
559	C₈×C₄₁	—	2	1	no	—
560	C₈×C₄₁	—	2	2	no	—
561	C₈×C₄₁	—	2	2	no	—
562	C₈×C₄₁	—	2	1	no	—
563	C₈×C₄₁	—	2	1	no	—
564	C₈×C₄₁	—	2	1	no	—
565	#62051	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
566	C₂²×C₄₁	—	2	1	no	—
567	C₂²×C₄₁	—	2	1	no	—
568	C₂²×C₄₁	—	2	2	no	—
569	C₂²×C₄₁	—	2	2	no	—
570	C₂²×C₄₁	—	2	2	no	—
571	C₂²×C₄₁	—	2	2	no	—
572	C₂²×C₄₁	—	4	1	no	—
573	C₂²×C₄₁	—	4	1	no	—
574	C₂²×C₄₁	—	4	2	no	—
575	C₂²×C₄₁	—	4	1	no	—
576	C₂²×C₄₁	—	4	2	no	—
577	C₂²×C₄₁	—	4	1	no	—
578	C₂²×C₄₁	—	4	2	no	—
579	C₂²×C₄₁	—	4	1	no	—
580	C₂²×C₄₁	—	4	1	no	—
581	C₂²×C₄₁	—	4	2	no	—
582	C₂²×C₄₁	—	4	2	no	—
583	C₂²×C₄₁	—	4	2	no	—
584	C₂²×C₄₁	—	4	2	no	—
585	C₂²×C₄₁	—	4	1	no	—
586	C₂²×C₄₁	—	4	2	no	—
587	C₂²×C₄₁	—	4	1	no	—
588	C₂²×C₄₁	—	4	2	no	—
589	C₂²×C₄₁	—	8	4	no	—
590	C₂²×C₄₁	—	16	4	no	—
591	C₂²×C₄₁	—	16	4	no	—
592	C₂²×C₄₁	—	16	4	no	—
593	C₂²×C₄₁	#576	1	2	yes	—
594	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
595	C₄×C₄₁	—	2	2	no	—
596	C₄×C₄₁	—	2	1	no	—
597	C₄×C₄₁	—	2	1	no	—
598	C₄×C₄₁	—	2	1	no	—
599	C₄×C₄₁	—	2	1	no	—
600	C₄×C₄₁	—	2	2	no	—
601	C₄×C₄₁	—	2	2	no	—
602	C₄×C₄₁	—	4	1	no	—
603	C₄×C₄₁	—	4	1	no	—
604	C₄×C₄₁	—	4	1	no	—
605	C₄×C₄₁	—	4	1	no	—
606	C₄×C₄₁	—	4	1	no	—
607	C₄×C₄₁	—	4	2	no	—
608	C₄×C₄₁	#576	1	2	yes	—
609	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
610	C₄×C₄₁	#585	1	1	yes	characteristic
611	#3543	C₂×C₄₁	1	1	yes	characteristic, complemented
612	#3519	C₂×C₄₁	1	1	yes	characteristic, complemented
613	#3399	C₂×C₄₁	1	1	yes	characteristic, complemented
614	#3391	C₂×C₄₁	1	1	yes	characteristic, complemented
615	#3366	C₂×C₄₁	1	1	yes	characteristic, complemented
616	#3361	C₂×C₄₁	1	1	yes	characteristic, complemented
617	#3325	C₂×C₄₁	1	1	yes	characteristic, complemented
618	#3318	C₂×C₄₁	1	2	yes	complemented
619	#3305	C₂×C₄₁	1	1	yes	characteristic, complemented
620	#3297	C₂×C₄₁	1	2	yes	complemented
621	D₄×D₈	C₂×C₄₁	1	2	yes	complemented
622	D₄×D₈	C₂×C₄₁	1	1	yes	characteristic, complemented
623	#3274	C₂×C₄₁	1	1	yes	characteristic, complemented
624	#3264	C₂×C₄₁	1	2	yes	complemented
625	#3259	C₂×C₄₁	1	2	yes	complemented
626	#3247	C₂×C₄₁	1	1	yes	characteristic, complemented
627	#3220	C₂×C₄₁	1	2	yes	complemented
628	#3205	C₂×C₄₁	1	1	yes	characteristic, complemented
629	#3122	C₂×C₄₁	1	2	yes	complemented
630	#3105	C₂×C₄₁	1	1	yes	characteristic, complemented
631	#3041	C₂×C₄₁	1	2	yes	complemented
632	C₂×#459	C₂×C₄₁	1	1	yes	characteristic, complemented
633	#2994	C₂×C₄₁	1	1	yes	characteristic, complemented
634	C₂×C₄₁	—	2	2	no	—
635	C₂×C₄₁	—	4	2	no	—
636	C₂×C₄₁	—	4	2	no	—
637	C₂×C₄₁	—	8	1	no	—
638	C₂×C₄₁	—	8	2	no	—
639	C₂×C₄₁	—	8	2	no	—
640	C₂×C₄₁	—	8	1	no	—
641	C₂×C₄₁	—	8	2	no	—
642	C₂×C₄₁	#3488	1	1	yes	characteristic
643	C₂×C₄₁	C₂×#576	1	1	yes	characteristic
644	C₂×C₄₁	C₂×#576	1	1	yes	characteristic
645	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	2	yes	complemented
646	C₂²×D₈	C₂²×C₄₁	1	2	yes	complemented
647	C₂²×D₈	C₂²×C₄₁	1	2	yes	complemented
648	#560	—	2	2	no	—
649	#559	C₂²×C₄₁	1	1	yes	characteristic, complemented
650	#555	C₂²×C₄₁	1	1	yes	characteristic, complemented
651	#554	C₂²×C₄₁	1	1	yes	characteristic, complemented
652	#553	—	2	1	no	—
653	#553	C₂²×C₄₁	1	2	yes	complemented
654	#550	C₂²×C₄₁	1	1	yes	characteristic, complemented
655	#550	C₂²×C₄₁	1	1	yes	characteristic, complemented
656	#550	C₂²×C₄₁	1	1	yes	characteristic, complemented
657	#546	—	2	1	no	—
658	#546	—	2	2	no	—
659	#546	—	2	1	no	—
660	#546	C₂²×C₄₁	1	2	yes	complemented
661	D₄²	—	2	1	no	—
662	D₄²	C₂²×C₄₁	1	2	yes	complemented
663	D₄²	C₂²×C₄₁	1	1	yes	characteristic, complemented
664	D₄²	C₂²×C₄₁	1	2	yes	complemented
665	D₄²	C₂²×C₄₁	1	1	yes	characteristic, complemented
666	#540	—	2	1	no	—
667	#540	C₂²×C₄₁	1	2	yes	complemented
668	#540	C₂²×C₄₁	1	2	yes	complemented
669	#538	—	2	2	no	—
670	#535	—	2	1	no	—
671	#535	C₂²×C₄₁	1	2	yes	complemented
672	#534	—	2	2	no	—
673	#532	C₂²×C₄₁	1	1	yes	characteristic, complemented
674	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic, complemented
675	#529	C₂²×C₄₁	1	1	yes	characteristic
676	#529	C₂²×C₄₁	1	1	yes	characteristic, complemented
677	#525	—	2	1	no	—
678	C₂×#121	—	2	1	no	—
679	#518	C₂²×C₄₁	1	2	yes	complemented
680	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
681	#496	C₂²×C₄₁	1	2	yes	complemented
682	#493	C₂²×C₄₁	1	1	yes	characteristic, complemented
683	#493	C₂²×C₄₁	1	2	yes	complemented
684	#493	C₂²×C₄₁	1	1	yes	characteristic, complemented
685	#490	C₂²×C₄₁	1	2	yes	complemented
686	#488	C₂²×C₄₁	1	2	yes	complemented
687	#486	C₂²×C₄₁	1	1	yes	characteristic, complemented
688	#486	C₂²×C₄₁	1	1	yes	characteristic, complemented
689	#484	C₂²×C₄₁	1	1	yes	characteristic, complemented
690	#482	C₂²×C₄₁	1	2	yes	complemented
691	#482	C₂²×C₄₁	1	2	yes	complemented
692	#481	C₂²×C₄₁	1	1	yes	characteristic, complemented
693	#478	C₂²×C₄₁	1	1	yes	characteristic, complemented
694	#478	C₂²×C₄₁	1	1	yes	characteristic, complemented
695	#478	C₂²×C₄₁	1	2	yes	complemented
696	#478	C₂²×C₄₁	1	2	yes	complemented
697	#478	C₂²×C₄₁	1	2	yes	complemented
698	#477	C₂²×C₄₁	1	1	yes	characteristic, complemented
699	#476	C₂²×C₄₁	1	1	yes	characteristic, complemented
700	#469	C₂²×C₄₁	1	2	yes	complemented
701	#469	C₂²×C₄₁	1	2	yes	complemented
702	#466	C₂²×C₄₁	1	2	yes	complemented
703	#466	C₂²×C₄₁	1	2	yes	complemented
704	#466	C₂²×C₄₁	1	2	yes	complemented
705	#465	C₂²×C₄₁	1	2	yes	complemented
706	#463	C₂²×C₄₁	1	1	yes	characteristic, complemented
707	#463	C₂²×C₄₁	1	1	yes	characteristic, complemented
708	#463	C₂²×C₄₁	1	2	yes	complemented
709	#463	C₂²×C₄₁	1	2	yes	complemented
710	#463	C₂²×C₄₁	1	2	yes	complemented
711	#460	C₂²×C₄₁	1	1	yes	characteristic, complemented
712	#459	C₂²×C₄₁	1	1	yes	characteristic
713	#459	C₂²×C₄₁	1	1	yes	characteristic, complemented
714	#459	C₂²×C₄₁	1	2	yes	complemented
715	#459	C₂²×C₄₁	1	2	yes	complemented
716	#459	C₂²×C₄₁	1	2	yes	complemented
717	#459	C₂²×C₄₁	1	1	yes	characteristic, complemented
718	#459	C₂²×C₄₁	1	2	yes	complemented
719	#459	C₂²×C₄₁	1	1	yes	characteristic, complemented
720	#459	C₂²×C₄₁	1	2	yes	complemented
721	#459	C₂²×C₄₁	1	2	yes	complemented
722	#459	C₂²×C₄₁	1	1	yes	characteristic, complemented
723	#459	C₂²×C₄₁	1	2	yes	complemented
724	#459	C₂²×C₄₁	1	2	yes	complemented
725	#450	C₂²×C₄₁	1	1	yes	characteristic, complemented
726	#449	C₂²×C₄₁	1	2	yes	complemented
727	#449	C₂²×C₄₁	1	2	yes	complemented
728	#447	C₂²×C₄₁	1	1	yes	characteristic
729	#447	C₂²×C₄₁	1	2	yes	complemented
730	#447	C₂²×C₄₁	1	2	yes	complemented
731	#447	C₂²×C₄₁	1	2	yes	complemented
732	#447	C₂²×C₄₁	1	2	yes	complemented
733	#447	C₂²×C₄₁	1	2	yes	complemented
734	#447	C₂²×C₄₁	1	2	yes	complemented
735	#446	C₂²×C₄₁	1	1	yes	characteristic, complemented
736	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
737	#442	C₂²×C₄₁	1	2	yes	complemented
738	#442	C₂²×C₄₁	1	2	yes	complemented
739	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
740	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
741	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
742	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
743	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
744	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
745	#436	C₂²×C₄₁	1	1	yes	characteristic, complemented
746	#435	C₂²×C₄₁	1	2	yes	complemented
747	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
748	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
749	#433	C₂²×C₄₁	1	2	yes	complemented
750	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
751	#424	C₂²×C₄₁	1	2	yes	complemented
752	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
753	#418	C₂²×C₄₁	1	2	yes	complemented
754	#416	C₂²×C₄₁	1	2	yes	complemented
755	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
756	C₄₁	#62051	1	1	yes	characteristic, direct product factor, Sylow
757	C₂×#41	—	2	1	no	—
758	C₂×#41	—	2	1	no	—
759	C₂×#41	—	2	1	no	—
760	C₂×#41	C₂³×C₄₁	1	2	yes	—
761	C₂²×D₄	—	2	1	no	—
762	C₂²×D₄	—	2	2	no	—
763	C₂²×D₄	—	2	2	no	—
764	C₂²×D₄	—	2	1	no	—
765	C₂²×D₄	—	2	1	no	—
766	C₂²×D₄	—	2	1	no	—
767	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
768	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
769	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
770	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
771	C₂³×C₄	—	2	1	no	—
772	AGL(1,ℤ/8)	—	4	4	no	—
773	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
774	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
776	C₂×D₈	—	4	4	no	—
777	C₂×D₈	—	4	4	no	—
778	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
779	C₂×D₈	C₂³×C₄₁	1	2	yes	—
780	C₂×D₈	C₂³×C₄₁	1	2	yes	—
781	C₂×D₈	C₂³×C₄₁	1	2	yes	—
782	C₂×D₈	C₂³×C₄₁	1	2	yes	—
783	C₂×D₈	C₂³×C₄₁	1	2	yes	—
784	C₂×D₈	C₂³×C₄₁	1	2	yes	—
785	C₂×D₈	C₂³×C₄₁	1	2	yes	—
786	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
787	C₂×D₈	C₂³×C₄₁	1	2	yes	—
788	C₂×D₈	C₂³×C₄₁	1	2	yes	—
789	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
790	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
791	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
792	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
793	#127	—	2	1	no	—
794	#127	—	2	1	no	—
795	#127	—	2	1	no	—
796	#127	C₂³×C₄₁	1	2	yes	—
797	#127	C₂³×C₄₁	1	1	yes	characteristic
798	#127	C₂³×C₄₁	1	1	yes	characteristic
799	#127	C₂³×C₄₁	1	1	yes	characteristic
800	#127	C₂³×C₄₁	1	2	yes	—
801	#127	C₂³×C₄₁	1	2	yes	—
802	#126	—	2	2	no	—
803	#126	—	2	1	no	—
804	#126	D₄×C₄₁	1	2	yes	—
805	#125	D₄×C₄₁	1	1	yes	characteristic
806	#125	C₂³×C₄₁	1	1	yes	characteristic
807	#125	C₂³×C₄₁	1	2	yes	—
808	#124	—	2	1	no	—
809	#124	—	2	2	no	—
810	#124	—	2	1	no	—
811	#124	D₄×C₄₁	1	1	yes	characteristic
812	#124	C₂³×C₄₁	1	1	yes	characteristic
813	#124	C₂³×C₄₁	1	2	yes	—
814	#123	—	2	1	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	2	no	—
822	#123	D₄×C₄₁	1	2	yes	—
823	C₂²⋊Q₈	—	2	1	no	—
824	C₂²⋊Q₈	—	2	2	no	—
825	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
826	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
827	#121	—	2	2	no	—
828	#121	—	2	1	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	1	no	—
832	#121	—	2	2	no	—
833	#121	—	2	2	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	1	no	—
838	#121	—	2	1	no	—
839	#121	—	2	2	no	—
840	#121	—	2	2	no	—
841	#121	—	2	2	no	—
842	#121	—	2	2	no	—
843	#121	—	2	2	no	—
844	#121	—	2	2	no	—
845	#121	—	2	2	no	—
846	#121	D₄×C₄₁	1	1	yes	characteristic
847	#121	C₂³×C₄₁	1	1	yes	characteristic
848	#121	C₂³×C₄₁	1	2	yes	—
849	#121	C₂³×C₄₁	1	2	yes	—
850	#121	C₂³×C₄₁	1	2	yes	—
851	#121	C₂³×C₄₁	1	2	yes	—
852	#121	C₂³×C₄₁	1	2	yes	—
853	#120	—	2	2	no	—
854	#120	—	2	2	no	—
855	#120	—	2	2	no	—
856	#120	—	2	2	no	—
857	#120	—	2	2	no	—
858	#120	—	2	2	no	—
859	#120	—	2	2	no	—
860	#120	—	2	2	no	—
861	#120	—	2	2	no	—
862	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
863	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	1	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	—	2	1	no	—
873	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
874	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
875	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
876	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
877	C₄×D₄	C₂³×C₄₁	1	2	yes	—
878	C₄×D₄	C₂³×C₄₁	1	2	yes	—
879	C₄×D₄	C₂³×C₄₁	1	2	yes	—
880	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
881	C₄×D₄	C₂³×C₄₁	1	2	yes	—
882	C₄×D₄	C₂³×C₄₁	1	2	yes	—
883	C₄×D₄	C₂³×C₄₁	1	2	yes	—
884	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
885	#117	—	2	1	no	—
886	#117	—	2	1	no	—
887	#117	C₂³×C₄₁	1	2	yes	—
888	#117	C₂³×C₄₁	1	2	yes	—
889	C₂×C₄⋊C₄	—	2	1	no	—
890	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
891	C₂×C₂²⋊C₄	—	2	1	no	—
892	C₂×C₂²⋊C₄	—	2	2	no	—
893	C₂×C₂²⋊C₄	—	2	2	no	—
894	C₂×C₂²⋊C₄	—	2	2	no	—
895	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
896	#107	C₂³×C₄₁	1	1	yes	characteristic
897	#107	C₂³×C₄₁	1	2	yes	—
898	#107	C₂³×C₄₁	1	1	yes	characteristic
899	#106	C₂³×C₄₁	1	1	yes	characteristic
900	#106	C₂³×C₄₁	1	1	yes	characteristic
901	#106	C₂³×C₄₁	1	2	yes	—
902	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
903	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
904	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
905	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
906	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
907	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
908	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
909	#103	C₂³×C₄₁	1	1	yes	characteristic
910	#103	C₂³×C₄₁	1	2	yes	—
911	#103	C₂³×C₄₁	1	1	yes	characteristic
912	#102	C₂³×C₄₁	1	2	yes	—
913	#102	C₂³×C₄₁	1	2	yes	—
914	#102	C₂³×C₄₁	1	2	yes	—
915	#102	C₂³×C₄₁	1	2	yes	—
916	#102	C₂³×C₄₁	1	2	yes	—
917	#102	C₂³×C₄₁	1	1	yes	characteristic
918	#102	C₂³×C₄₁	1	2	yes	—
919	#102	C₂³×C₄₁	1	2	yes	—
920	#102	C₂³×C₄₁	1	1	yes	characteristic
921	#102	C₂³×C₄₁	1	1	yes	characteristic
922	#102	C₂³×C₄₁	1	2	yes	—
923	#102	C₂³×C₄₁	1	1	yes	characteristic
924	#102	C₂³×C₄₁	1	2	yes	—
925	#102	C₂³×C₄₁	1	1	yes	characteristic
926	#102	C₂³×C₄₁	1	1	yes	characteristic
927	#102	C₂³×C₄₁	1	2	yes	—
928	#102	C₂³×C₄₁	1	2	yes	—
929	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
930	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
931	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
932	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
933	#97	C₂³×C₄₁	1	2	yes	—
934	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
935	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
936	C₄×C₈	C₂³×C₄₁	1	2	yes	—
937	C₂⁴	—	2	1	no	—
938	C₂⁴	—	2	2	no	—
939	C₂⁴	—	2	2	no	—
940	C₂⁴	—	2	2	no	—
941	#41	—	4	2	no	—
942	#41	—	4	2	no	—
943	#41	—	8	2	no	—
944	#41	—	8	2	no	—
945	#41	—	8	2	no	—
946	C₂×Q₈	—	2	1	no	—
947	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
948	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	4	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	1	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	1	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	1	no	—
974	C₂×D₄	—	4	1	no	—
975	C₂×D₄	—	4	2	no	—
976	C₂×D₄	—	4	2	no	—
977	C₂×D₄	—	4	2	no	—
978	C₂×D₄	—	4	2	no	—
979	C₂×D₄	—	4	2	no	—
980	C₂×D₄	—	8	2	no	—
981	C₂×D₄	—	8	2	no	—
982	C₂×D₄	—	8	2	no	—
983	C₂×D₄	—	8	2	no	—
984	C₂×D₄	—	8	4	no	—
985	C₂×D₄	—	8	4	no	—
986	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
987	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
988	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
989	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
990	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
991	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
992	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
993	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	1	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	—	2	2	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	8	2	no	—
1007	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1008	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1009	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1010	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
1011	SD₁₆	—	2	2	no	—
1012	SD₁₆	—	4	1	no	—
1013	SD₁₆	—	4	2	no	—
1014	D₈	—	2	2	no	—
1015	D₈	—	2	4	no	—
1016	D₈	—	2	4	no	—
1017	D₈	—	4	2	no	—
1018	D₈	—	4	2	no	—
1019	D₈	—	4	2	no	—
1020	D₈	—	4	2	no	—
1021	D₈	—	4	2	no	—
1022	D₈	—	4	1	no	—
1023	D₈	—	4	2	no	—
1024	D₈	—	4	2	no	—
1025	M₁₆	—	4	2	no	—
1026	C₂×C₈	—	4	2	no	—
1027	C₂×C₈	—	4	2	no	—
1028	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1029	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1030	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1031	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1032	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1033	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1043	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1044	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1045	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1046	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1047	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1048	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1049	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1050	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1051	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1052	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	1	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	1	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	1	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1076	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1077	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1078	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1079	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1080	C₄²	—	2	2	no	—
1081	C₄²	—	2	1	no	—
1082	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1083	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1084	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1085	C₄²	C₂⁴×C₄₁	1	2	yes	—
1086	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1087	C₂³	—	2	1	no	—
1088	C₂³	—	2	1	no	—
1089	C₂³	—	2	2	no	—
1090	C₂³	—	2	1	no	—
1091	C₂³	—	2	2	no	—
1092	C₂³	—	2	2	no	—
1093	C₂³	—	4	2	no	—
1094	C₂³	—	4	4	no	—
1095	C₂³	—	4	2	no	—
1096	C₂³	—	4	4	no	—
1097	C₂³	—	8	1	no	—
1098	C₂³	—	8	2	no	—
1099	C₂³	—	8	2	no	—
1100	C₂³	—	8	2	no	—
1101	C₂³	—	8	2	no	—
1102	C₂³	—	8	2	no	—
1103	C₂³	—	8	2	no	—
1104	C₂³	—	8	2	no	—
1105	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1106	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1107	Q₈	—	2	2	no	—
1108	Q₈	—	2	1	no	—
1109	Q₈	—	2	1	no	—
1110	Q₈	—	8	1	no	—
1111	D₄	—	2	4	no	—
1112	D₄	—	2	2	no	—
1113	D₄	—	2	1	no	—
1114	D₄	—	2	2	no	—
1115	D₄	—	2	2	no	—
1116	D₄	—	2	1	no	—
1117	D₄	—	2	2	no	—
1118	D₄	—	2	1	no	—
1119	D₄	—	2	2	no	—
1120	D₄	—	2	1	no	—
1121	D₄	—	2	1	no	—
1122	D₄	—	2	2	no	—
1123	D₄	—	2	2	no	—
1124	D₄	—	4	4	no	—
1125	D₄	—	4	2	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	4	no	—
1128	D₄	—	4	2	no	—
1129	D₄	—	4	2	no	—
1130	D₄	—	4	2	no	—
1131	D₄	—	8	2	no	—
1132	D₄	—	8	2	no	—
1133	D₄	—	8	2	no	—
1134	D₄	—	8	2	no	—
1135	D₄	—	8	1	no	—
1136	D₄	—	8	1	no	—
1137	D₄	—	8	2	no	—
1138	D₄	—	8	2	no	—
1139	D₄	—	8	1	no	—
1140	D₄	—	8	2	no	—
1141	D₄	—	8	2	no	—
1142	D₄	—	8	2	no	—
1143	D₄	—	8	2	no	—
1144	D₄	—	8	2	no	—
1145	D₄	—	8	2	no	—
1146	D₄	—	8	2	no	—
1147	D₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	4	2	no	—
1161	C₂×C₄	—	4	2	no	—
1162	C₂×C₄	—	4	2	no	—
1163	C₂×C₄	—	8	1	no	—
1164	C₂×C₄	—	8	1	no	—
1165	C₂×C₄	—	8	2	no	—
1166	C₂×C₄	—	8	2	no	—
1167	C₂×C₄	—	8	2	no	—
1168	C₂×C₄	—	8	2	no	—
1169	C₂×C₄	—	8	2	no	—
1170	C₂×C₄	—	8	2	no	—
1171	C₂×C₄	—	8	1	no	—
1172	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1173	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1174	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1175	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1176	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1177	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1178	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1179	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1180	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1181	C₈	—	2	1	no	—
1182	C₈	—	2	2	no	—
1183	C₈	—	2	2	no	—
1184	C₈	—	2	1	no	—
1185	C₈	—	2	1	no	—
1186	C₈	—	2	1	no	—
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	2	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	2	no	—
1198	C₂²	—	4	2	no	—
1199	C₂²	—	4	2	no	—
1200	C₂²	—	4	2	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	4	2	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	2	no	—
1205	C₂²	—	4	2	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	2	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	2	no	—
1210	C₂²	—	8	4	no	—
1211	C₂²	—	16	4	no	—
1212	C₂²	—	16	4	no	—
1213	C₂²	—	16	4	no	—
1214	C₂²	C₄₁×#576	1	2	yes	—
1215	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1216	C₄	—	2	1	no	—
1217	C₄	—	2	1	no	—
1218	C₄	—	2	1	no	—
1219	C₄	—	2	2	no	—
1220	C₄	—	2	2	no	—
1221	C₄	—	2	2	no	—
1222	C₄	—	2	1	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	1	no	—
1227	C₄	—	4	2	no	—
1228	C₄	—	4	1	no	—
1229	C₄	C₄₁×#576	1	2	yes	—
1230	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1231	C₄	C₄₁×#585	1	1	yes	characteristic
1232	C₂	—	2	2	no	—
1233	C₂	—	4	2	no	—
1234	C₂	—	4	2	no	—
1235	C₂	—	8	1	no	—
1236	C₂	—	8	1	no	—
1237	C₂	—	8	2	no	—
1238	C₂	—	8	2	no	—
1239	C₂	—	8	2	no	—
1240	C₂	C₄₁×#3488	1	1	yes	characteristic
1241	C₂	C₂×C₄₁×#576	1	1	yes	characteristic
1242	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×#3543	C₂	semidirect
2. C₄₁×#3519	C₂	semidirect
3. C₄₁×#3399	C₂	semidirect
4. C₄₁×#3391	C₂	semidirect
5. C₄₁×#3366	C₂	semidirect
6. C₄₁×#3361	C₂	semidirect
7. C₄₁×#3325	C₂	semidirect
8. C₄₁×#3318	C₂	semidirect
9. C₄₁×#3305	C₂	semidirect
10. C₄₁×#3297	C₂	semidirect
11. D₄×D₈×C₄₁	C₂	semidirect
12. D₄×D₈×C₄₁	C₂	semidirect
13. C₄₁×#3274	C₂	semidirect
14. C₄₁×#3264	C₂	semidirect
15. C₄₁×#3259	C₂	semidirect
16. C₄₁×#3247	C₂	semidirect
17. C₄₁×#3220	C₂	semidirect
18. C₄₁×#3205	C₂	semidirect
19. C₄₁×#3122	C₂	semidirect
20. C₄₁×#3105	C₂	semidirect
21. C₄₁×#3041	C₂	semidirect
22. C₂×C₄₁×#459	C₂	semidirect
23. C₄₁×#2994	C₂	semidirect
24. C₂×AGL(1,ℤ/8)×C₄₁	C₂²	semidirect
25. C₂²×D₈×C₄₁	C₂²	semidirect
26. C₂²×D₈×C₄₁	C₂²	semidirect
28. C₄₁×#559	C₂²	semidirect
29. C₄₁×#555	C₂²	semidirect
30. C₄₁×#554	C₂²	semidirect
32. C₄₁×#553	C₂²	semidirect
33. C₄₁×#550	C₂²	semidirect
34. C₄₁×#550	C₂²	semidirect
35. C₄₁×#550	C₂²	semidirect
39. C₄₁×#546	C₂²	semidirect
41. D₄²×C₄₁	C₂²	semidirect
42. D₄²×C₄₁	C₂²	semidirect
43. D₄²×C₄₁	C₂²	semidirect
44. D₄²×C₄₁	C₂²	semidirect
46. C₄₁×#540	C₂²	semidirect
47. C₄₁×#540	C₂²	semidirect
50. C₄₁×#535	C₂²	semidirect
52. C₄₁×#532	C₂²	semidirect
53. C₂×#127×C₄₁	C₂²	semidirect
55. C₄₁×#529	C₂²	semidirect
58. C₄₁×#518	C₂²	semidirect
59. C₂×C₄×D₄×C₄₁	C₂²	semidirect
60. C₄₁×#496	C₂²	semidirect
61. C₄₁×#493	C₂²	semidirect
62. C₄₁×#493	C₂²	semidirect
63. C₄₁×#493	C₂²	semidirect
64. C₄₁×#490	C₂²	semidirect
65. C₄₁×#488	C₂²	semidirect
66. C₄₁×#486	C₂²	semidirect
67. C₄₁×#486	C₂²	semidirect
68. C₄₁×#484	C₂²	semidirect
69. C₄₁×#482	C₂²	semidirect
70. C₄₁×#482	C₂²	semidirect
71. C₄₁×#481	C₂²	semidirect
72. C₄₁×#478	C₂²	semidirect
73. C₄₁×#478	C₂²	semidirect
74. C₄₁×#478	C₂²	semidirect
75. C₄₁×#478	C₂²	semidirect
76. C₄₁×#478	C₂²	semidirect
77. C₄₁×#477	C₂²	semidirect
78. C₄₁×#476	C₂²	semidirect
79. C₄₁×#469	C₂²	semidirect
80. C₄₁×#469	C₂²	semidirect
81. C₄₁×#466	C₂²	semidirect
82. C₄₁×#466	C₂²	semidirect
83. C₄₁×#466	C₂²	semidirect
84. C₄₁×#465	C₂²	semidirect
85. C₄₁×#463	C₂²	semidirect
86. C₄₁×#463	C₂²	semidirect
87. C₄₁×#463	C₂²	semidirect
88. C₄₁×#463	C₂²	semidirect
89. C₄₁×#463	C₂²	semidirect
90. C₄₁×#460	C₂²	semidirect
92. C₄₁×#459	C₂²	semidirect
93. C₄₁×#459	C₂²	semidirect
94. C₄₁×#459	C₂²	semidirect
95. C₄₁×#459	C₂²	semidirect
96. C₄₁×#459	C₂²	semidirect
97. C₄₁×#459	C₂²	semidirect
98. C₄₁×#459	C₂²	semidirect
99. C₄₁×#459	C₂²	semidirect
100. C₄₁×#459	C₂²	semidirect
101. C₄₁×#459	C₂²	semidirect
102. C₄₁×#459	C₂²	semidirect
103. C₄₁×#459	C₂²	semidirect
104. C₄₁×#450	C₂²	semidirect
105. C₄₁×#449	C₂²	semidirect
106. C₄₁×#449	C₂²	semidirect
108. C₄₁×#447	C₂²	semidirect
109. C₄₁×#447	C₂²	semidirect
110. C₄₁×#447	C₂²	semidirect
111. C₄₁×#447	C₂²	semidirect
112. C₄₁×#447	C₂²	semidirect
113. C₄₁×#447	C₂²	semidirect
114. C₄₁×#446	C₂²	semidirect
115. C₈×Q₈×C₄₁	C₂²	semidirect
116. C₄₁×#442	C₂²	semidirect
117. C₄₁×#442	C₂²	semidirect
118. C₄×SD₁₆×C₄₁	C₂²	semidirect
119. C₄×SD₁₆×C₄₁	C₂²	semidirect
120. C₄×D₈×C₄₁	C₂²	semidirect
121. C₄×D₈×C₄₁	C₂²	semidirect
122. C₄×D₈×C₄₁	C₂²	semidirect
123. C₄×D₈×C₄₁	C₂²	semidirect
124. C₄₁×#436	C₂²	semidirect
125. C₄₁×#435	C₂²	semidirect
126. C₈×D₄×C₄₁	C₂²	semidirect
127. C₈×D₄×C₄₁	C₂²	semidirect
128. C₄₁×#433	C₂²	semidirect
129. C₄₁×#431	C₂²	semidirect
130. C₄₁×#424	C₂²	semidirect
131. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
132. C₄₁×#418	C₂²	semidirect
133. C₄₁×#416	C₂²	semidirect
134. C₂×#102×C₄₁	C₂²	semidirect
565. #62051	C₄₁	direct (N × H)
611. #3543	C₂×C₄₁	semidirect
612. #3519	C₂×C₄₁	semidirect
613. #3399	C₂×C₄₁	semidirect
614. #3391	C₂×C₄₁	semidirect
615. #3366	C₂×C₄₁	semidirect
616. #3361	C₂×C₄₁	semidirect
617. #3325	C₂×C₄₁	semidirect
618. #3318	C₂×C₄₁	semidirect
619. #3305	C₂×C₄₁	semidirect
620. #3297	C₂×C₄₁	semidirect
621. D₄×D₈	C₂×C₄₁	semidirect
622. D₄×D₈	C₂×C₄₁	semidirect
623. #3274	C₂×C₄₁	semidirect
624. #3264	C₂×C₄₁	semidirect
625. #3259	C₂×C₄₁	semidirect
626. #3247	C₂×C₄₁	semidirect
627. #3220	C₂×C₄₁	semidirect
628. #3205	C₂×C₄₁	semidirect
629. #3122	C₂×C₄₁	semidirect
630. #3105	C₂×C₄₁	semidirect
631. #3041	C₂×C₄₁	semidirect
632. C₂×#459	C₂×C₄₁	semidirect
633. #2994	C₂×C₄₁	semidirect
645. C₂×AGL(1,ℤ/8)	C₂²×C₄₁	semidirect
646. C₂²×D₈	C₂²×C₄₁	semidirect
647. C₂²×D₈	C₂²×C₄₁	semidirect
649. #559	C₂²×C₄₁	semidirect
650. #555	C₂²×C₄₁	semidirect
651. #554	C₂²×C₄₁	semidirect
653. #553	C₂²×C₄₁	semidirect
654. #550	C₂²×C₄₁	semidirect
655. #550	C₂²×C₄₁	semidirect
656. #550	C₂²×C₄₁	semidirect
660. #546	C₂²×C₄₁	semidirect
662. D₄²	C₂²×C₄₁	semidirect
663. D₄²	C₂²×C₄₁	semidirect
664. D₄²	C₂²×C₄₁	semidirect
665. D₄²	C₂²×C₄₁	semidirect
667. #540	C₂²×C₄₁	semidirect
668. #540	C₂²×C₄₁	semidirect
671. #535	C₂²×C₄₁	semidirect
673. #532	C₂²×C₄₁	semidirect
674. C₂×#127	C₂²×C₄₁	semidirect
676. #529	C₂²×C₄₁	semidirect
679. #518	C₂²×C₄₁	semidirect
680. C₂×C₄×D₄	C₂²×C₄₁	semidirect
681. #496	C₂²×C₄₁	semidirect
682. #493	C₂²×C₄₁	semidirect
683. #493	C₂²×C₄₁	semidirect
684. #493	C₂²×C₄₁	semidirect
685. #490	C₂²×C₄₁	semidirect
686. #488	C₂²×C₄₁	semidirect
687. #486	C₂²×C₄₁	semidirect
688. #486	C₂²×C₄₁	semidirect
689. #484	C₂²×C₄₁	semidirect
690. #482	C₂²×C₄₁	semidirect
691. #482	C₂²×C₄₁	semidirect
692. #481	C₂²×C₄₁	semidirect
693. #478	C₂²×C₄₁	semidirect
694. #478	C₂²×C₄₁	semidirect
695. #478	C₂²×C₄₁	semidirect
696. #478	C₂²×C₄₁	semidirect
697. #478	C₂²×C₄₁	semidirect
698. #477	C₂²×C₄₁	semidirect
699. #476	C₂²×C₄₁	semidirect
700. #469	C₂²×C₄₁	semidirect
701. #469	C₂²×C₄₁	semidirect
702. #466	C₂²×C₄₁	semidirect
703. #466	C₂²×C₄₁	semidirect
704. #466	C₂²×C₄₁	semidirect
705. #465	C₂²×C₄₁	semidirect
706. #463	C₂²×C₄₁	semidirect
707. #463	C₂²×C₄₁	semidirect
708. #463	C₂²×C₄₁	semidirect
709. #463	C₂²×C₄₁	semidirect
710. #463	C₂²×C₄₁	semidirect
711. #460	C₂²×C₄₁	semidirect
713. #459	C₂²×C₄₁	semidirect
714. #459	C₂²×C₄₁	semidirect
715. #459	C₂²×C₄₁	semidirect
716. #459	C₂²×C₄₁	semidirect
717. #459	C₂²×C₄₁	semidirect
718. #459	C₂²×C₄₁	semidirect
719. #459	C₂²×C₄₁	semidirect
720. #459	C₂²×C₄₁	semidirect
721. #459	C₂²×C₄₁	semidirect
722. #459	C₂²×C₄₁	semidirect
723. #459	C₂²×C₄₁	semidirect
724. #459	C₂²×C₄₁	semidirect
725. #450	C₂²×C₄₁	semidirect
726. #449	C₂²×C₄₁	semidirect
727. #449	C₂²×C₄₁	semidirect
729. #447	C₂²×C₄₁	semidirect
730. #447	C₂²×C₄₁	semidirect
731. #447	C₂²×C₄₁	semidirect
732. #447	C₂²×C₄₁	semidirect
733. #447	C₂²×C₄₁	semidirect
734. #447	C₂²×C₄₁	semidirect
735. #446	C₂²×C₄₁	semidirect
736. C₈×Q₈	C₂²×C₄₁	semidirect
737. #442	C₂²×C₄₁	semidirect
738. #442	C₂²×C₄₁	semidirect
739. C₄×SD₁₆	C₂²×C₄₁	semidirect
740. C₄×SD₁₆	C₂²×C₄₁	semidirect
741. C₄×D₈	C₂²×C₄₁	semidirect
742. C₄×D₈	C₂²×C₄₁	semidirect
743. C₄×D₈	C₂²×C₄₁	semidirect
744. C₄×D₈	C₂²×C₄₁	semidirect
745. #436	C₂²×C₄₁	semidirect
746. #435	C₂²×C₄₁	semidirect
747. C₈×D₄	C₂²×C₄₁	semidirect
748. C₈×D₄	C₂²×C₄₁	semidirect
749. #433	C₂²×C₄₁	semidirect
750. #431	C₂²×C₄₁	semidirect
751. #424	C₂²×C₄₁	semidirect
752. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
753. #418	C₂²×C₄₁	semidirect
754. #416	C₂²×C₄₁	semidirect
755. C₂×#102	C₂²×C₄₁	semidirect
756. C₄₁	#62051	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×#3543	2
C₄₁×#3519	2
C₄₁×#3399	2
C₄₁×#3391	2
C₄₁×#3366	2
C₄₁×#3361	2
C₄₁×#3325	2
C₄₁×#3318	2
C₄₁×#3305	2
C₄₁×#3297	2
D₄×D₈×C₄₁	2
C₄₁×#3274	2
C₄₁×#3264	2
C₄₁×#3259	2
C₄₁×#3247	2
C₄₁×#3220	2
C₄₁×#3205	2
C₄₁×#3122	2
C₄₁×#3105	2
C₄₁×#3041	2
C₂×C₄₁×#459	2
C₄₁×#2994	2
#62051	41

Subgroups — C41×#62051 #23838252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#62051 #23838252