Subgroups — C₄₁×#61255 #23837456

Order 10496.

1898 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#553	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3355	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3351	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3350	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3347	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3346	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3345	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3339	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3337	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3094	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3094	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3093	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3092	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#3080	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄₁×#3055	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#3055	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×AGL(1,ℤ/8)×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×M₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄₁×#2911	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#556	C₂²	1	1	yes	characteristic, complemented
28	C₄₁×#555	C₂²	1	1	yes	characteristic, complemented
29	C₄₁×#554	C₂²	1	1	yes	characteristic, complemented
30	C₄₁×#553	—	2	1	no	—
31	C₄₁×#553	—	2	1	no	—
32	C₄₁×#553	—	2	1	no	—
33	C₄₁×#553	—	2	1	no	—
34	C₄₁×#553	C₂²	1	2	yes	—
35	C₄₁×#553	C₂²	1	2	yes	—
36	C₄₁×#553	C₂²	1	2	yes	—
37	C₄₁×#553	C₂²	1	2	yes	—
38	C₄₁×#553	C₂²	1	1	yes	characteristic, complemented
39	C₄₁×#553	C₂²	1	1	yes	characteristic, complemented
40	C₄₁×#552	—	2	1	no	—
41	C₄₁×#552	C₂²	1	1	yes	characteristic, complemented
42	C₄₁×#552	C₂²	1	1	yes	characteristic, complemented
43	C₄₁×#551	—	2	1	no	—
44	C₄₁×#551	—	2	1	no	—
45	C₄₁×#547	C₂²	1	1	yes	characteristic, complemented
46	C₄₁×#546	—	2	1	no	—
47	C₄₁×#533	C₂²	1	1	yes	characteristic
48	C₄₁×#529	—	2	1	no	—
49	C₄₁×#529	—	2	1	no	—
50	C₄₁×#529	—	2	1	no	—
51	C₂×#126×C₄₁	—	2	1	no	—
52	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
53	C₄₁×#525	C₂²	1	1	yes	characteristic
54	C₄₁×#525	C₂²	1	1	yes	characteristic
55	C₂×#123×C₄₁	—	2	1	no	—
56	C₂×#121×C₄₁	—	2	1	no	—
57	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
58	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
59	C₄×#41×C₄₁	—	2	1	no	—
60	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
61	C₂×C₄×D₄×C₄₁	—	2	1	no	—
62	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
63	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
64	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
65	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
66	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
67	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
68	C₄₁×#501	C₂²	1	2	yes	complemented
69	C₄₁×#501	C₂²	1	2	yes	complemented
70	C₄₁×#499	C₂²	1	2	yes	complemented
71	C₄₁×#499	C₂²	1	2	yes	complemented
72	C₄₁×#485	C₂²	1	2	yes	complemented
73	C₄₁×#485	C₂²	1	2	yes	complemented
74	C₄₁×#484	C₂²	1	2	yes	complemented
75	C₄₁×#483	C₂²	1	2	yes	complemented
76	C₄₁×#482	C₂²	1	2	yes	complemented
77	C₄₁×#482	C₂²	1	2	yes	complemented
78	C₄₁×#482	C₂²	1	2	yes	complemented
79	C₄₁×#482	C₂²	1	2	yes	complemented
80	C₄₁×#482	C₂²	1	2	yes	complemented
81	C₄₁×#482	C₂²	1	2	yes	complemented
82	C₄₁×#481	C₂²	1	2	yes	complemented
83	C₄₁×#481	C₂²	1	2	yes	complemented
84	C₄₁×#481	C₂²	1	2	yes	complemented
85	C₄₁×#480	C₂²	1	2	yes	complemented
86	C₄₁×#480	C₂²	1	2	yes	complemented
87	C₄₁×#480	C₂²	1	2	yes	complemented
88	C₄₁×#479	C₂²	1	2	yes	complemented
89	C₄₁×#479	C₂²	1	2	yes	complemented
90	C₄₁×#478	C₂²	1	2	yes	complemented
91	C₄₁×#478	C₂²	1	2	yes	complemented
92	C₄₁×#478	C₂²	1	2	yes	complemented
93	C₄₁×#478	C₂²	1	2	yes	complemented
94	C₄₁×#476	C₂²	1	2	yes	complemented
95	C₄₁×#474	C₂²	1	2	yes	complemented
96	C₄₁×#469	C₂²	1	2	yes	complemented
97	C₄₁×#469	C₂²	1	2	yes	complemented
98	C₄₁×#468	C₂²	1	2	yes	complemented
99	C₄₁×#468	C₂²	1	2	yes	complemented
100	C₄₁×#466	C₂²	1	2	yes	complemented
101	C₄₁×#466	C₂²	1	2	yes	complemented
102	C₄₁×#465	C₂²	1	2	yes	complemented
103	C₄₁×#465	C₂²	1	2	yes	complemented
104	C₄₁×#442	C₂²	1	2	yes	complemented
105	C₄₁×#440	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
107	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
108	C₄₁×#436	C₂²	1	2	yes	complemented
109	C₄₁×#435	C₂²	1	2	yes	complemented
110	C₄₁×#435	C₂²	1	2	yes	complemented
111	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
112	C₄₁×#428	C₂²	1	1	yes	characteristic
113	C₄₁×#428	C₂²	1	1	yes	characteristic
114	C₄₁×#428	C₂²	1	1	yes	characteristic
115	C₄₁×#428	C₂²	1	1	yes	characteristic
116	C₄₁×#428	C₂²	1	1	yes	characteristic
117	C₄₁×#428	C₂²	1	1	yes	characteristic
118	C₄₁×#428	C₂²	1	1	yes	characteristic
119	C₄₁×#428	C₂²	1	1	yes	characteristic
120	C₄₁×#428	C₂²	1	1	yes	characteristic
121	C₄₁×#428	C₂²	1	2	yes	complemented
122	C₄₁×#428	C₂²	1	2	yes	complemented
123	C₄₁×#428	C₂²	1	2	yes	complemented
124	C₄₁×#428	C₂²	1	2	yes	complemented
125	C₄₁×#427	C₂²	1	2	yes	complemented
126	C₄₁×#427	C₂²	1	2	yes	complemented
127	C₂×#107×C₄₁	C₂²	1	2	yes	complemented
128	C₂×#106×C₄₁	C₂²	1	2	yes	complemented
129	C₄₁×#423	C₂²	1	1	yes	characteristic
130	C₄₁×#418	C₂²	1	1	yes	characteristic
131	C₄₁×#418	C₂²	1	1	yes	characteristic
132	C₄₁×#418	C₂²	1	1	yes	characteristic
133	C₄₁×#417	C₂²	1	1	yes	characteristic
134	C₄₁×#417	C₂²	1	1	yes	characteristic
135	C₄₁×#417	C₂²	1	1	yes	characteristic
136	C₄₁×#407	C₂²	1	1	yes	characteristic
137	C₄₁×#407	C₂²	1	1	yes	characteristic
138	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
139	C₂×#41×C₄₁	—	2	1	no	—
140	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₄₁	—	2	1	no	—
142	C₂²×D₄×C₄₁	—	2	1	no	—
143	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
144	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₄₁	—	2	1	no	—
146	C₂³×C₄×C₄₁	—	2	1	no	—
147	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
149	AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
150	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
151	C₂×D₈×C₄₁	C₂³	1	2	yes	—
152	C₂×M₁₆×C₄₁	—	2	4	no	—
153	C₂×M₁₆×C₄₁	—	2	4	no	—
154	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
157	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
158	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
159	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
164	#126×C₄₁	—	2	2	no	—
165	#126×C₄₁	—	2	2	no	—
166	#126×C₄₁	—	2	2	no	—
167	#126×C₄₁	—	2	2	no	—
168	#126×C₄₁	—	2	1	no	—
169	#126×C₄₁	—	2	1	no	—
170	#126×C₄₁	—	2	1	no	—
171	#126×C₄₁	—	2	1	no	—
172	#126×C₄₁	—	2	1	no	—
173	#126×C₄₁	—	2	1	no	—
174	#125×C₄₁	—	2	1	no	—
175	#125×C₄₁	—	2	1	no	—
176	#125×C₄₁	—	2	1	no	—
177	#125×C₄₁	—	2	1	no	—
178	#125×C₄₁	—	2	1	no	—
179	#125×C₄₁	C₂³	1	2	yes	—
180	#125×C₄₁	C₂³	1	2	yes	—
181	#125×C₄₁	C₂³	1	1	yes	characteristic
182	#125×C₄₁	C₂³	1	1	yes	characteristic
183	#124×C₄₁	—	2	1	no	—
184	#124×C₄₁	—	2	1	no	—
185	#124×C₄₁	—	2	1	no	—
186	#123×C₄₁	—	2	1	no	—
187	#123×C₄₁	—	2	1	no	—
188	#123×C₄₁	—	2	1	no	—
189	#123×C₄₁	—	2	1	no	—
190	#123×C₄₁	—	2	2	no	—
191	#123×C₄₁	—	2	2	no	—
192	#123×C₄₁	—	2	2	no	—
193	#123×C₄₁	—	2	2	no	—
194	#123×C₄₁	—	2	1	no	—
195	#123×C₄₁	—	2	1	no	—
196	#123×C₄₁	—	2	1	no	—
197	#123×C₄₁	—	2	1	no	—
198	C₂²⋊Q₈×C₄₁	—	2	1	no	—
199	C₂²⋊Q₈×C₄₁	—	2	1	no	—
200	C₂²⋊Q₈×C₄₁	—	2	1	no	—
201	C₂²⋊Q₈×C₄₁	—	2	1	no	—
202	C₂²⋊Q₈×C₄₁	—	2	1	no	—
203	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
204	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
205	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
206	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
207	#121×C₄₁	—	2	2	no	—
208	#121×C₄₁	—	2	2	no	—
209	#121×C₄₁	—	2	2	no	—
210	#121×C₄₁	—	2	2	no	—
211	#121×C₄₁	—	2	1	no	—
212	#121×C₄₁	—	2	1	no	—
213	#121×C₄₁	—	2	1	no	—
214	#121×C₄₁	—	2	1	no	—
215	#121×C₄₁	—	2	1	no	—
216	#121×C₄₁	—	2	1	no	—
217	#121×C₄₁	—	2	1	no	—
218	#121×C₄₁	C₂³	1	2	yes	—
219	#121×C₄₁	C₂³	1	2	yes	—
220	#121×C₄₁	C₂³	1	2	yes	—
221	#121×C₄₁	C₂³	1	2	yes	—
222	#121×C₄₁	C₂³	1	1	yes	characteristic
223	#121×C₄₁	C₂³	1	1	yes	characteristic
224	#121×C₄₁	C₂³	1	1	yes	characteristic
225	#121×C₄₁	C₂³	1	1	yes	characteristic
226	#120×C₄₁	—	2	1	no	—
227	#120×C₄₁	—	2	1	no	—
228	C₄×Q₈×C₄₁	—	2	1	no	—
229	C₄×Q₈×C₄₁	—	2	1	no	—
230	C₄×Q₈×C₄₁	—	2	1	no	—
231	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₄₁	—	2	1	no	—
234	C₄×D₄×C₄₁	—	2	1	no	—
235	C₄×D₄×C₄₁	—	2	1	no	—
236	C₄×D₄×C₄₁	—	2	1	no	—
237	C₄×D₄×C₄₁	—	2	1	no	—
238	C₄×D₄×C₄₁	—	2	1	no	—
239	C₄×D₄×C₄₁	—	2	1	no	—
240	C₄×D₄×C₄₁	—	2	2	no	—
241	C₄×D₄×C₄₁	—	2	2	no	—
242	C₄×D₄×C₄₁	—	2	2	no	—
243	C₄×D₄×C₄₁	—	2	2	no	—
244	C₄×D₄×C₄₁	—	2	1	no	—
245	C₄×D₄×C₄₁	—	2	1	no	—
246	C₄×D₄×C₄₁	—	2	1	no	—
247	C₄×D₄×C₄₁	—	2	1	no	—
248	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
249	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
250	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
251	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
252	C₄×D₄×C₄₁	C₂³	1	2	yes	—
253	C₄×D₄×C₄₁	C₂³	1	2	yes	—
254	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
260	#117×C₄₁	—	2	1	no	—
261	#117×C₄₁	—	2	1	no	—
262	#117×C₄₁	—	2	1	no	—
263	#117×C₄₁	—	2	1	no	—
264	#117×C₄₁	—	2	1	no	—
265	#117×C₄₁	—	2	1	no	—
266	#117×C₄₁	—	2	1	no	—
267	#117×C₄₁	—	2	1	no	—
268	#117×C₄₁	—	2	1	no	—
269	#117×C₄₁	—	2	1	no	—
270	#117×C₄₁	C₂³	1	1	yes	characteristic
271	#117×C₄₁	C₂³	1	1	yes	characteristic
272	#117×C₄₁	C₂³	1	1	yes	characteristic
273	#117×C₄₁	C₂³	1	1	yes	characteristic
274	#117×C₄₁	C₂³	1	1	yes	characteristic
275	#117×C₄₁	C₂³	1	2	yes	—
276	#117×C₄₁	C₂³	1	2	yes	—
277	#117×C₄₁	C₂³	1	1	yes	characteristic
278	#117×C₄₁	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
280	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
281	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
282	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
283	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
284	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
289	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
297	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
298	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
299	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
300	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
301	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
302	C₂×C₄²×C₄₁	—	2	1	no	—
303	C₂×C₄²×C₄₁	—	2	1	no	—
304	C₂×C₄²×C₄₁	—	2	1	no	—
305	C₂×C₄²×C₄₁	—	2	1	no	—
306	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
307	#107×C₄₁	C₂³	1	2	yes	—
308	#107×C₄₁	C₂³	1	2	yes	—
309	#107×C₄₁	C₂³	1	2	yes	—
310	#107×C₄₁	C₂³	1	2	yes	—
311	#107×C₄₁	C₂³	1	2	yes	—
312	#107×C₄₁	C₂³	1	2	yes	—
313	#107×C₄₁	C₂³	1	2	yes	—
314	#107×C₄₁	C₂³	1	2	yes	—
315	#107×C₄₁	C₂³	1	2	yes	—
316	#106×C₄₁	C₂³	1	2	yes	—
317	#106×C₄₁	C₂³	1	2	yes	—
318	#106×C₄₁	C₂³	1	2	yes	—
319	#106×C₄₁	C₂³	1	2	yes	—
320	#106×C₄₁	C₂³	1	2	yes	—
321	#106×C₄₁	C₂³	1	2	yes	—
322	#106×C₄₁	C₂³	1	2	yes	—
323	#106×C₄₁	C₂³	1	2	yes	—
324	#106×C₄₁	C₂³	1	2	yes	—
325	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
326	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
327	#103×C₄₁	C₂³	1	2	yes	—
328	#103×C₄₁	C₂³	1	2	yes	—
329	#103×C₄₁	C₂³	1	2	yes	—
330	#102×C₄₁	C₂³	1	2	yes	—
331	#102×C₄₁	C₂³	1	2	yes	—
332	#102×C₄₁	C₂³	1	2	yes	—
333	#102×C₄₁	C₂³	1	2	yes	—
334	#102×C₄₁	C₂³	1	2	yes	—
335	#102×C₄₁	C₂³	1	2	yes	—
336	#102×C₄₁	C₂³	1	2	yes	—
337	#102×C₄₁	C₂³	1	2	yes	—
338	#102×C₄₁	C₂³	1	2	yes	—
339	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
340	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
341	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
342	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
343	#97×C₄₁	C₂³	1	2	yes	—
344	C₄×C₈×C₄₁	C₂³	1	2	yes	—
345	C₂⁴×C₄₁	—	2	1	no	—
346	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
347	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
348	#41×C₄₁	—	2	2	no	—
349	#41×C₄₁	—	2	2	no	—
350	#41×C₄₁	—	4	4	no	—
351	C₂×Q₈×C₄₁	—	2	1	no	—
352	C₂×Q₈×C₄₁	—	2	1	no	—
353	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₄₁	—	2	1	no	—
355	C₂×D₄×C₄₁	—	2	1	no	—
356	C₂×D₄×C₄₁	—	2	1	no	—
357	C₂×D₄×C₄₁	—	2	2	no	—
358	C₂×D₄×C₄₁	—	2	2	no	—
359	C₂×D₄×C₄₁	—	2	1	no	—
360	C₂×D₄×C₄₁	—	2	1	no	—
361	C₂×D₄×C₄₁	—	2	2	no	—
362	C₂×D₄×C₄₁	—	2	2	no	—
363	C₂×D₄×C₄₁	—	2	1	no	—
364	C₂×D₄×C₄₁	—	2	2	no	—
365	C₂×D₄×C₄₁	—	2	2	no	—
366	C₂×D₄×C₄₁	—	4	2	no	—
367	C₂×D₄×C₄₁	—	4	4	no	—
368	C₂×D₄×C₄₁	—	8	2	no	—
369	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
370	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
371	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
372	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
373	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
374	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₄₁	—	2	2	no	—
376	C₂²×C₄×C₄₁	—	2	2	no	—
377	C₂²×C₄×C₄₁	—	2	2	no	—
378	C₂²×C₄×C₄₁	—	2	2	no	—
379	C₂²×C₄×C₄₁	—	2	1	no	—
380	C₂²×C₄×C₄₁	—	2	1	no	—
381	C₂²×C₄×C₄₁	—	2	1	no	—
382	C₂²×C₄×C₄₁	—	2	1	no	—
383	C₂²×C₄×C₄₁	—	2	1	no	—
384	C₂²×C₄×C₄₁	—	2	1	no	—
385	C₂²×C₄×C₄₁	—	2	1	no	—
386	C₂²×C₄×C₄₁	—	2	2	no	—
387	C₂²×C₄×C₄₁	—	2	2	no	—
388	C₂²×C₄×C₄₁	—	2	1	no	—
389	C₂²×C₄×C₄₁	—	2	1	no	—
390	C₂²×C₄×C₄₁	—	2	1	no	—
391	C₂²×C₄×C₄₁	—	2	2	no	—
392	C₂²×C₄×C₄₁	—	2	2	no	—
393	C₂²×C₄×C₄₁	—	8	2	no	—
394	C₂²×C₄×C₄₁	—	8	2	no	—
395	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
408	SD₁₆×C₄₁	—	2	4	no	—
409	D₈×C₄₁	—	2	4	no	—
410	M₁₆×C₄₁	—	2	2	no	—
411	M₁₆×C₄₁	—	2	2	no	—
412	M₁₆×C₄₁	—	2	2	no	—
413	M₁₆×C₄₁	—	2	4	no	—
414	M₁₆×C₄₁	—	2	4	no	—
415	M₁₆×C₄₁	#41	1	4	yes	complemented
416	C₂×C₈×C₄₁	—	2	4	no	—
417	C₂×C₈×C₄₁	—	2	4	no	—
418	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
419	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
420	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
421	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
422	C₄⋊C₄×C₄₁	—	2	1	no	—
423	C₄⋊C₄×C₄₁	—	2	1	no	—
424	C₄⋊C₄×C₄₁	—	2	2	no	—
425	C₄⋊C₄×C₄₁	—	2	2	no	—
426	C₄⋊C₄×C₄₁	—	2	2	no	—
427	C₄⋊C₄×C₄₁	—	2	2	no	—
428	C₄⋊C₄×C₄₁	—	2	2	no	—
429	C₄⋊C₄×C₄₁	—	2	2	no	—
430	C₄⋊C₄×C₄₁	—	2	1	no	—
431	C₄⋊C₄×C₄₁	—	2	1	no	—
432	C₄⋊C₄×C₄₁	—	2	1	no	—
433	C₄⋊C₄×C₄₁	—	2	1	no	—
434	C₄⋊C₄×C₄₁	—	2	1	no	—
435	C₄⋊C₄×C₄₁	—	2	1	no	—
436	C₄⋊C₄×C₄₁	—	2	1	no	—
437	C₄⋊C₄×C₄₁	—	2	1	no	—
438	C₄⋊C₄×C₄₁	—	2	1	no	—
439	C₄⋊C₄×C₄₁	—	2	1	no	—
440	C₄⋊C₄×C₄₁	—	2	1	no	—
441	C₄⋊C₄×C₄₁	—	2	1	no	—
442	C₄⋊C₄×C₄₁	—	2	1	no	—
443	C₄⋊C₄×C₄₁	—	2	1	no	—
444	C₄⋊C₄×C₄₁	—	2	1	no	—
445	C₄⋊C₄×C₄₁	—	2	1	no	—
446	C₄⋊C₄×C₄₁	—	2	1	no	—
447	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
456	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
457	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
458	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
459	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
460	C₂²⋊C₄×C₄₁	—	2	1	no	—
461	C₂²⋊C₄×C₄₁	—	2	1	no	—
462	C₂²⋊C₄×C₄₁	—	2	1	no	—
463	C₂²⋊C₄×C₄₁	—	2	2	no	—
464	C₂²⋊C₄×C₄₁	—	2	2	no	—
465	C₂²⋊C₄×C₄₁	—	2	1	no	—
466	C₂²⋊C₄×C₄₁	—	2	1	no	—
467	C₂²⋊C₄×C₄₁	—	2	1	no	—
468	C₂²⋊C₄×C₄₁	—	2	1	no	—
469	C₂²⋊C₄×C₄₁	—	2	1	no	—
470	C₂²⋊C₄×C₄₁	—	2	1	no	—
471	C₂²⋊C₄×C₄₁	—	2	1	no	—
472	C₂²⋊C₄×C₄₁	—	2	1	no	—
473	C₂²⋊C₄×C₄₁	—	2	2	no	—
474	C₂²⋊C₄×C₄₁	—	2	2	no	—
475	C₂²⋊C₄×C₄₁	—	2	2	no	—
476	C₂²⋊C₄×C₄₁	—	2	2	no	—
477	C₂²⋊C₄×C₄₁	—	2	2	no	—
478	C₂²⋊C₄×C₄₁	—	2	2	no	—
479	C₂²⋊C₄×C₄₁	—	2	1	no	—
480	C₂²⋊C₄×C₄₁	—	2	1	no	—
481	C₂²⋊C₄×C₄₁	—	2	1	no	—
482	C₂²⋊C₄×C₄₁	—	2	1	no	—
483	C₂²⋊C₄×C₄₁	—	2	1	no	—
484	C₂²⋊C₄×C₄₁	—	2	1	no	—
485	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
486	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
487	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
488	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
489	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
490	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
491	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
492	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₄₁	—	2	1	no	—
494	C₄²×C₄₁	—	2	1	no	—
495	C₄²×C₄₁	—	2	1	no	—
496	C₄²×C₄₁	—	2	1	no	—
497	C₄²×C₄₁	—	2	1	no	—
498	C₄²×C₄₁	—	2	1	no	—
499	C₄²×C₄₁	—	2	2	no	—
500	C₄²×C₄₁	—	2	2	no	—
501	C₄²×C₄₁	—	2	1	no	—
502	C₄²×C₄₁	—	2	1	no	—
503	C₄²×C₄₁	—	2	1	no	—
504	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
505	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
506	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
507	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
508	C₂³×C₄₁	—	2	2	no	—
509	C₂³×C₄₁	—	2	2	no	—
510	C₂³×C₄₁	—	2	2	no	—
511	C₂³×C₄₁	—	2	1	no	—
512	C₂³×C₄₁	—	2	2	no	—
513	C₂³×C₄₁	—	4	1	no	—
514	C₂³×C₄₁	—	4	1	no	—
515	C₂³×C₄₁	—	4	1	no	—
516	C₂³×C₄₁	—	4	2	no	—
517	C₂³×C₄₁	—	4	2	no	—
518	C₂³×C₄₁	—	4	2	no	—
519	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
520	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
521	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
522	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
523	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
524	Q₈×C₄₁	—	2	1	no	—
525	Q₈×C₄₁	—	2	1	no	—
526	Q₈×C₄₁	—	4	2	no	—
527	Q₈×C₄₁	—	8	1	no	—
528	D₄×C₄₁	—	2	2	no	—
529	D₄×C₄₁	—	2	2	no	—
530	D₄×C₄₁	—	2	1	no	—
531	D₄×C₄₁	—	2	2	no	—
532	D₄×C₄₁	—	2	2	no	—
533	D₄×C₄₁	—	2	1	no	—
534	D₄×C₄₁	—	4	1	no	—
535	D₄×C₄₁	—	4	1	no	—
536	D₄×C₄₁	—	4	4	no	—
537	D₄×C₄₁	—	4	2	no	—
538	D₄×C₄₁	—	4	2	no	—
539	D₄×C₄₁	—	4	4	no	—
540	D₄×C₄₁	—	4	2	no	—
541	D₄×C₄₁	—	4	2	no	—
542	D₄×C₄₁	—	8	1	no	—
543	D₄×C₄₁	—	8	1	no	—
544	D₄×C₄₁	—	8	2	no	—
545	D₄×C₄₁	—	8	2	no	—
546	C₂×C₄×C₄₁	—	2	2	no	—
547	C₂×C₄×C₄₁	—	2	2	no	—
548	C₂×C₄×C₄₁	—	2	2	no	—
549	C₂×C₄×C₄₁	—	2	2	no	—
550	C₂×C₄×C₄₁	—	2	2	no	—
551	C₂×C₄×C₄₁	—	2	2	no	—
552	C₂×C₄×C₄₁	—	2	1	no	—
553	C₂×C₄×C₄₁	—	2	1	no	—
554	C₂×C₄×C₄₁	—	2	1	no	—
555	C₂×C₄×C₄₁	—	2	1	no	—
556	C₂×C₄×C₄₁	—	2	1	no	—
557	C₂×C₄×C₄₁	—	2	1	no	—
558	C₂×C₄×C₄₁	—	2	1	no	—
559	C₂×C₄×C₄₁	—	2	1	no	—
560	C₂×C₄×C₄₁	—	2	1	no	—
561	C₂×C₄×C₄₁	—	2	1	no	—
562	C₂×C₄×C₄₁	—	2	1	no	—
563	C₂×C₄×C₄₁	—	2	2	no	—
564	C₂×C₄×C₄₁	—	2	1	no	—
565	C₂×C₄×C₄₁	—	2	1	no	—
566	C₂×C₄×C₄₁	—	2	1	no	—
567	C₂×C₄×C₄₁	—	2	1	no	—
568	C₂×C₄×C₄₁	—	2	2	no	—
569	C₂×C₄×C₄₁	—	2	2	no	—
570	C₂×C₄×C₄₁	—	4	1	no	—
571	C₂×C₄×C₄₁	—	4	1	no	—
572	C₂×C₄×C₄₁	—	4	2	no	—
573	C₂×C₄×C₄₁	—	4	2	no	—
574	C₂×C₄×C₄₁	—	4	2	no	—
575	C₂×C₄×C₄₁	—	4	2	no	—
576	C₂×C₄×C₄₁	—	4	2	no	—
577	C₂×C₄×C₄₁	—	4	2	no	—
578	C₂×C₄×C₄₁	—	4	2	no	—
579	C₂×C₄×C₄₁	—	8	1	no	—
580	C₂×C₄×C₄₁	—	8	2	no	—
581	C₂×C₄×C₄₁	—	8	2	no	—
582	C₂×C₄×C₄₁	—	8	1	no	—
583	C₂×C₄×C₄₁	—	8	1	no	—
584	C₂×C₄×C₄₁	—	8	2	no	—
585	C₂×C₄×C₄₁	—	8	2	no	—
586	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
587	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
588	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
589	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
591	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
592	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
593	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
594	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
595	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
596	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
597	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
598	C₈×C₄₁	—	2	2	no	—
599	C₈×C₄₁	—	2	2	no	—
600	C₈×C₄₁	—	2	2	no	—
601	C₈×C₄₁	C₂×#41	1	4	yes	—
602	#61255	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
603	C₂²×C₄₁	—	2	1	no	—
604	C₂²×C₄₁	—	2	1	no	—
605	C₂²×C₄₁	—	2	1	no	—
606	C₂²×C₄₁	—	2	1	no	—
607	C₂²×C₄₁	—	2	1	no	—
608	C₂²×C₄₁	—	2	1	no	—
609	C₂²×C₄₁	—	2	1	no	—
610	C₂²×C₄₁	—	2	1	no	—
611	C₂²×C₄₁	—	2	1	no	—
612	C₂²×C₄₁	—	2	1	no	—
613	C₂²×C₄₁	—	2	1	no	—
614	C₂²×C₄₁	—	2	1	no	—
615	C₂²×C₄₁	—	2	1	no	—
616	C₂²×C₄₁	—	4	4	no	—
617	C₂²×C₄₁	—	4	2	no	—
618	C₂²×C₄₁	—	4	1	no	—
619	C₂²×C₄₁	—	4	1	no	—
620	C₂²×C₄₁	—	4	2	no	—
621	C₂²×C₄₁	—	4	1	no	—
622	C₂²×C₄₁	—	4	2	no	—
623	C₂²×C₄₁	—	8	2	no	—
624	C₂²×C₄₁	—	8	4	no	—
625	C₂²×C₄₁	#547	1	2	yes	—
626	C₂²×C₄₁	#575	1	2	yes	—
627	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
628	C₄×C₄₁	—	2	1	no	—
629	C₄×C₄₁	—	2	1	no	—
630	C₄×C₄₁	—	2	1	no	—
631	C₄×C₄₁	—	2	1	no	—
632	C₄×C₄₁	—	2	1	no	—
633	C₄×C₄₁	—	2	1	no	—
634	C₄×C₄₁	—	2	1	no	—
635	C₄×C₄₁	—	2	1	no	—
636	C₄×C₄₁	—	4	2	no	—
637	C₄×C₄₁	—	4	2	no	—
638	C₄×C₄₁	—	4	1	no	—
639	C₄×C₄₁	—	4	1	no	—
640	C₄×C₄₁	—	4	1	no	—
641	C₄×C₄₁	—	4	1	no	—
642	C₄×C₄₁	—	4	1	no	—
643	C₄×C₄₁	—	4	2	no	—
644	C₄×C₄₁	—	4	1	no	—
645	C₄×C₄₁	—	4	1	no	—
646	C₄×C₄₁	#547	1	2	yes	—
647	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
648	C₄×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
649	#3475	C₂×C₄₁	1	1	yes	characteristic, complemented
650	C₂×#553	C₂×C₄₁	1	1	yes	characteristic, complemented
651	#3355	C₂×C₄₁	1	2	yes	complemented
652	#3351	C₂×C₄₁	1	2	yes	complemented
653	#3350	C₂×C₄₁	1	2	yes	complemented
654	#3347	C₂×C₄₁	1	2	yes	complemented
655	#3346	C₂×C₄₁	1	2	yes	complemented
656	#3345	C₂×C₄₁	1	2	yes	complemented
657	#3339	C₂×C₄₁	1	2	yes	complemented
658	#3337	C₂×C₄₁	1	2	yes	complemented
659	#3166	C₂×C₄₁	1	1	yes	characteristic, complemented
660	#3094	C₂×C₄₁	1	1	yes	characteristic, complemented
661	#3094	C₂×C₄₁	1	1	yes	characteristic, complemented
662	#3093	C₂×C₄₁	1	1	yes	characteristic, complemented
663	#3092	C₂×C₄₁	1	1	yes	characteristic, complemented
664	#3080	C₂×C₄₁	1	1	yes	characteristic, complemented
665	#3077	C₂×C₄₁	1	1	yes	characteristic, complemented
666	#3055	C₂×C₄₁	1	1	yes	characteristic, complemented
667	#3055	C₂×C₄₁	1	1	yes	characteristic, complemented
668	C₄×AGL(1,ℤ/8)	C₂×C₄₁	1	1	yes	characteristic, complemented
669	D₄×M₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
670	#2911	C₂×C₄₁	1	1	yes	characteristic, complemented
671	C₂×#428	C₂×C₄₁	1	1	yes	characteristic, complemented
672	C₂×C₄₁	—	2	2	no	—
673	C₂×C₄₁	—	2	2	no	—
674	C₂×C₄₁	—	4	1	no	—
675	C₂×C₄₁	—	4	1	no	—
676	C₂×C₄₁	—	4	1	no	—
677	C₂×C₄₁	—	8	1	no	—
678	C₂×C₄₁	—	8	2	no	—
679	C₂×C₄₁	C₂×#547	1	1	yes	characteristic
680	C₂×C₄₁	C₂×#575	1	1	yes	characteristic
681	C₂×C₄₁	#3585	1	1	yes	characteristic
682	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	1	yes	characteristic
683	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
684	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
685	#556	C₂²×C₄₁	1	1	yes	characteristic, complemented
686	#555	C₂²×C₄₁	1	1	yes	characteristic, complemented
687	#554	C₂²×C₄₁	1	1	yes	characteristic, complemented
688	#553	—	2	1	no	—
689	#553	—	2	1	no	—
690	#553	—	2	1	no	—
691	#553	—	2	1	no	—
692	#553	C₂²×C₄₁	1	2	yes	—
693	#553	C₂²×C₄₁	1	2	yes	—
694	#553	C₂²×C₄₁	1	2	yes	—
695	#553	C₂²×C₄₁	1	2	yes	—
696	#553	C₂²×C₄₁	1	1	yes	characteristic, complemented
697	#553	C₂²×C₄₁	1	1	yes	characteristic, complemented
698	#552	—	2	1	no	—
699	#552	C₂²×C₄₁	1	1	yes	characteristic, complemented
700	#552	C₂²×C₄₁	1	1	yes	characteristic, complemented
701	#551	—	2	1	no	—
702	#551	—	2	1	no	—
703	#547	C₂²×C₄₁	1	1	yes	characteristic, complemented
704	#546	—	2	1	no	—
705	#533	C₂²×C₄₁	1	1	yes	characteristic
706	#529	—	2	1	no	—
707	#529	—	2	1	no	—
708	#529	—	2	1	no	—
709	C₂×#126	—	2	1	no	—
710	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
711	#525	C₂²×C₄₁	1	1	yes	characteristic
712	#525	C₂²×C₄₁	1	1	yes	characteristic
713	C₂×#123	—	2	1	no	—
714	C₂×#121	—	2	1	no	—
715	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
716	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
717	C₄×#41	—	2	1	no	—
718	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
719	C₂×C₄×D₄	—	2	1	no	—
720	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
721	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
722	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
723	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
724	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
725	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
726	#501	C₂²×C₄₁	1	2	yes	complemented
727	#501	C₂²×C₄₁	1	2	yes	complemented
728	#499	C₂²×C₄₁	1	2	yes	complemented
729	#499	C₂²×C₄₁	1	2	yes	complemented
730	#485	C₂²×C₄₁	1	2	yes	complemented
731	#485	C₂²×C₄₁	1	2	yes	complemented
732	#484	C₂²×C₄₁	1	2	yes	complemented
733	#483	C₂²×C₄₁	1	2	yes	complemented
734	#482	C₂²×C₄₁	1	2	yes	complemented
735	#482	C₂²×C₄₁	1	2	yes	complemented
736	#482	C₂²×C₄₁	1	2	yes	complemented
737	#482	C₂²×C₄₁	1	2	yes	complemented
738	#482	C₂²×C₄₁	1	2	yes	complemented
739	#482	C₂²×C₄₁	1	2	yes	complemented
740	#481	C₂²×C₄₁	1	2	yes	complemented
741	#481	C₂²×C₄₁	1	2	yes	complemented
742	#481	C₂²×C₄₁	1	2	yes	complemented
743	#480	C₂²×C₄₁	1	2	yes	complemented
744	#480	C₂²×C₄₁	1	2	yes	complemented
745	#480	C₂²×C₄₁	1	2	yes	complemented
746	#479	C₂²×C₄₁	1	2	yes	complemented
747	#479	C₂²×C₄₁	1	2	yes	complemented
748	#478	C₂²×C₄₁	1	2	yes	complemented
749	#478	C₂²×C₄₁	1	2	yes	complemented
750	#478	C₂²×C₄₁	1	2	yes	complemented
751	#478	C₂²×C₄₁	1	2	yes	complemented
752	#476	C₂²×C₄₁	1	2	yes	complemented
753	#474	C₂²×C₄₁	1	2	yes	complemented
754	#469	C₂²×C₄₁	1	2	yes	complemented
755	#469	C₂²×C₄₁	1	2	yes	complemented
756	#468	C₂²×C₄₁	1	2	yes	complemented
757	#468	C₂²×C₄₁	1	2	yes	complemented
758	#466	C₂²×C₄₁	1	2	yes	complemented
759	#466	C₂²×C₄₁	1	2	yes	complemented
760	#465	C₂²×C₄₁	1	2	yes	complemented
761	#465	C₂²×C₄₁	1	2	yes	complemented
762	#442	C₂²×C₄₁	1	2	yes	complemented
763	#440	C₂²×C₄₁	1	2	yes	complemented
764	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
765	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
766	#436	C₂²×C₄₁	1	2	yes	complemented
767	#435	C₂²×C₄₁	1	2	yes	complemented
768	#435	C₂²×C₄₁	1	2	yes	complemented
769	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
770	#428	C₂²×C₄₁	1	1	yes	characteristic
771	#428	C₂²×C₄₁	1	1	yes	characteristic
772	#428	C₂²×C₄₁	1	1	yes	characteristic
773	#428	C₂²×C₄₁	1	1	yes	characteristic
774	#428	C₂²×C₄₁	1	1	yes	characteristic
775	#428	C₂²×C₄₁	1	1	yes	characteristic
776	#428	C₂²×C₄₁	1	1	yes	characteristic
777	#428	C₂²×C₄₁	1	1	yes	characteristic
778	#428	C₂²×C₄₁	1	1	yes	characteristic
779	#428	C₂²×C₄₁	1	2	yes	complemented
780	#428	C₂²×C₄₁	1	2	yes	complemented
781	#428	C₂²×C₄₁	1	2	yes	complemented
782	#428	C₂²×C₄₁	1	2	yes	complemented
783	#427	C₂²×C₄₁	1	2	yes	complemented
784	#427	C₂²×C₄₁	1	2	yes	complemented
785	C₂×#107	C₂²×C₄₁	1	2	yes	complemented
786	C₂×#106	C₂²×C₄₁	1	2	yes	complemented
787	#423	C₂²×C₄₁	1	1	yes	characteristic
788	#418	C₂²×C₄₁	1	1	yes	characteristic
789	#418	C₂²×C₄₁	1	1	yes	characteristic
790	#418	C₂²×C₄₁	1	1	yes	characteristic
791	#417	C₂²×C₄₁	1	1	yes	characteristic
792	#417	C₂²×C₄₁	1	1	yes	characteristic
793	#417	C₂²×C₄₁	1	1	yes	characteristic
794	#407	C₂²×C₄₁	1	1	yes	characteristic
795	#407	C₂²×C₄₁	1	1	yes	characteristic
796	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
797	C₄₁	#61255	1	1	yes	characteristic, direct product factor, Sylow
798	C₂×#41	—	2	1	no	—
799	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
800	C₂²×D₄	—	2	1	no	—
801	C₂²×D₄	—	2	1	no	—
802	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
803	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
804	C₂³×C₄	—	2	1	no	—
805	C₂³×C₄	—	2	1	no	—
806	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
807	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
808	AGL(1,ℤ/8)	—	2	4	no	—
809	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
810	C₂×D₈	C₂³×C₄₁	1	2	yes	—
811	C₂×M₁₆	—	2	4	no	—
812	C₂×M₁₆	—	2	4	no	—
813	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
814	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
815	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
816	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
817	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
818	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
819	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
820	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
821	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
822	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
823	#126	—	2	2	no	—
824	#126	—	2	2	no	—
825	#126	—	2	2	no	—
826	#126	—	2	2	no	—
827	#126	—	2	1	no	—
828	#126	—	2	1	no	—
829	#126	—	2	1	no	—
830	#126	—	2	1	no	—
831	#126	—	2	1	no	—
832	#126	—	2	1	no	—
833	#125	—	2	1	no	—
834	#125	—	2	1	no	—
835	#125	—	2	1	no	—
836	#125	—	2	1	no	—
837	#125	—	2	1	no	—
838	#125	C₂³×C₄₁	1	2	yes	—
839	#125	C₂³×C₄₁	1	2	yes	—
840	#125	C₂³×C₄₁	1	1	yes	characteristic
841	#125	C₂³×C₄₁	1	1	yes	characteristic
842	#124	—	2	1	no	—
843	#124	—	2	1	no	—
844	#124	—	2	1	no	—
845	#123	—	2	1	no	—
846	#123	—	2	1	no	—
847	#123	—	2	1	no	—
848	#123	—	2	1	no	—
849	#123	—	2	2	no	—
850	#123	—	2	2	no	—
851	#123	—	2	2	no	—
852	#123	—	2	2	no	—
853	#123	—	2	1	no	—
854	#123	—	2	1	no	—
855	#123	—	2	1	no	—
856	#123	—	2	1	no	—
857	C₂²⋊Q₈	—	2	1	no	—
858	C₂²⋊Q₈	—	2	1	no	—
859	C₂²⋊Q₈	—	2	1	no	—
860	C₂²⋊Q₈	—	2	1	no	—
861	C₂²⋊Q₈	—	2	1	no	—
862	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
863	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
864	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
865	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
866	#121	—	2	2	no	—
867	#121	—	2	2	no	—
868	#121	—	2	2	no	—
869	#121	—	2	2	no	—
870	#121	—	2	1	no	—
871	#121	—	2	1	no	—
872	#121	—	2	1	no	—
873	#121	—	2	1	no	—
874	#121	—	2	1	no	—
875	#121	—	2	1	no	—
876	#121	—	2	1	no	—
877	#121	C₂³×C₄₁	1	2	yes	—
878	#121	C₂³×C₄₁	1	2	yes	—
879	#121	C₂³×C₄₁	1	2	yes	—
880	#121	C₂³×C₄₁	1	2	yes	—
881	#121	C₂³×C₄₁	1	1	yes	characteristic
882	#121	C₂³×C₄₁	1	1	yes	characteristic
883	#121	C₂³×C₄₁	1	1	yes	characteristic
884	#121	C₂³×C₄₁	1	1	yes	characteristic
885	#120	—	2	1	no	—
886	#120	—	2	1	no	—
887	C₄×Q₈	—	2	1	no	—
888	C₄×Q₈	—	2	1	no	—
889	C₄×Q₈	—	2	1	no	—
890	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
891	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	—	2	1	no	—
897	C₄×D₄	—	2	1	no	—
898	C₄×D₄	—	2	1	no	—
899	C₄×D₄	—	2	2	no	—
900	C₄×D₄	—	2	2	no	—
901	C₄×D₄	—	2	2	no	—
902	C₄×D₄	—	2	2	no	—
903	C₄×D₄	—	2	1	no	—
904	C₄×D₄	—	2	1	no	—
905	C₄×D₄	—	2	1	no	—
906	C₄×D₄	—	2	1	no	—
907	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
908	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
909	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
910	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
911	C₄×D₄	C₂³×C₄₁	1	2	yes	—
912	C₄×D₄	C₂³×C₄₁	1	2	yes	—
913	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
914	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
915	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
916	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
917	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
918	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
919	#117	—	2	1	no	—
920	#117	—	2	1	no	—
921	#117	—	2	1	no	—
922	#117	—	2	1	no	—
923	#117	—	2	1	no	—
924	#117	—	2	1	no	—
925	#117	—	2	1	no	—
926	#117	—	2	1	no	—
927	#117	—	2	1	no	—
928	#117	—	2	1	no	—
929	#117	C₂³×C₄₁	1	1	yes	characteristic
930	#117	C₂³×C₄₁	1	1	yes	characteristic
931	#117	C₂³×C₄₁	1	1	yes	characteristic
932	#117	C₂³×C₄₁	1	1	yes	characteristic
933	#117	C₂³×C₄₁	1	1	yes	characteristic
934	#117	C₂³×C₄₁	1	2	yes	—
935	#117	C₂³×C₄₁	1	2	yes	—
936	#117	C₂³×C₄₁	1	1	yes	characteristic
937	#117	C₂³×C₄₁	1	1	yes	characteristic
938	C₂×C₄⋊C₄	—	2	1	no	—
939	C₂×C₄⋊C₄	—	2	1	no	—
940	C₂×C₄⋊C₄	—	2	1	no	—
941	C₂×C₄⋊C₄	—	2	1	no	—
942	C₂×C₄⋊C₄	—	2	1	no	—
943	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
946	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
947	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
948	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
949	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
950	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
951	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
952	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
953	C₂×C₂²⋊C₄	—	2	1	no	—
954	C₂×C₂²⋊C₄	—	2	1	no	—
955	C₂×C₂²⋊C₄	—	2	1	no	—
956	C₂×C₂²⋊C₄	—	2	1	no	—
957	C₂×C₂²⋊C₄	—	2	1	no	—
958	C₂×C₂²⋊C₄	—	2	1	no	—
959	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
960	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
961	C₂×C₄²	—	2	1	no	—
962	C₂×C₄²	—	2	1	no	—
963	C₂×C₄²	—	2	1	no	—
964	C₂×C₄²	—	2	1	no	—
965	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
966	#107	C₂³×C₄₁	1	2	yes	—
967	#107	C₂³×C₄₁	1	2	yes	—
968	#107	C₂³×C₄₁	1	2	yes	—
969	#107	C₂³×C₄₁	1	2	yes	—
970	#107	C₂³×C₄₁	1	2	yes	—
971	#107	C₂³×C₄₁	1	2	yes	—
972	#107	C₂³×C₄₁	1	2	yes	—
973	#107	C₂³×C₄₁	1	2	yes	—
974	#107	C₂³×C₄₁	1	2	yes	—
975	#106	C₂³×C₄₁	1	2	yes	—
976	#106	C₂³×C₄₁	1	2	yes	—
977	#106	C₂³×C₄₁	1	2	yes	—
978	#106	C₂³×C₄₁	1	2	yes	—
979	#106	C₂³×C₄₁	1	2	yes	—
980	#106	C₂³×C₄₁	1	2	yes	—
981	#106	C₂³×C₄₁	1	2	yes	—
982	#106	C₂³×C₄₁	1	2	yes	—
983	#106	C₂³×C₄₁	1	2	yes	—
984	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
985	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
986	#103	C₂³×C₄₁	1	2	yes	—
987	#103	C₂³×C₄₁	1	2	yes	—
988	#103	C₂³×C₄₁	1	2	yes	—
989	#102	C₂³×C₄₁	1	2	yes	—
990	#102	C₂³×C₄₁	1	2	yes	—
991	#102	C₂³×C₄₁	1	2	yes	—
992	#102	C₂³×C₄₁	1	2	yes	—
993	#102	C₂³×C₄₁	1	2	yes	—
994	#102	C₂³×C₄₁	1	2	yes	—
995	#102	C₂³×C₄₁	1	2	yes	—
996	#102	C₂³×C₄₁	1	2	yes	—
997	#102	C₂³×C₄₁	1	2	yes	—
998	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
999	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
1000	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
1001	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
1002	#97	C₂³×C₄₁	1	2	yes	—
1003	C₄×C₈	C₂³×C₄₁	1	2	yes	—
1004	C₂⁴	—	2	1	no	—
1005	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
1006	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
1007	#41	—	2	2	no	—
1008	#41	—	2	2	no	—
1009	#41	—	4	4	no	—
1010	C₂×Q₈	—	2	1	no	—
1011	C₂×Q₈	—	2	1	no	—
1012	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
1013	C₂×D₄	—	2	1	no	—
1014	C₂×D₄	—	2	1	no	—
1015	C₂×D₄	—	2	1	no	—
1016	C₂×D₄	—	2	2	no	—
1017	C₂×D₄	—	2	2	no	—
1018	C₂×D₄	—	2	1	no	—
1019	C₂×D₄	—	2	1	no	—
1020	C₂×D₄	—	2	2	no	—
1021	C₂×D₄	—	2	2	no	—
1022	C₂×D₄	—	2	1	no	—
1023	C₂×D₄	—	2	2	no	—
1024	C₂×D₄	—	2	2	no	—
1025	C₂×D₄	—	4	2	no	—
1026	C₂×D₄	—	4	4	no	—
1027	C₂×D₄	—	8	2	no	—
1028	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1029	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1030	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1031	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1032	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
1033	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
1034	C₂²×C₄	—	2	2	no	—
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	2	2	no	—
1038	C₂²×C₄	—	2	1	no	—
1039	C₂²×C₄	—	2	1	no	—
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	1	no	—
1042	C₂²×C₄	—	2	1	no	—
1043	C₂²×C₄	—	2	1	no	—
1044	C₂²×C₄	—	2	1	no	—
1045	C₂²×C₄	—	2	2	no	—
1046	C₂²×C₄	—	2	2	no	—
1047	C₂²×C₄	—	2	1	no	—
1048	C₂²×C₄	—	2	1	no	—
1049	C₂²×C₄	—	2	1	no	—
1050	C₂²×C₄	—	2	2	no	—
1051	C₂²×C₄	—	2	2	no	—
1052	C₂²×C₄	—	8	2	no	—
1053	C₂²×C₄	—	8	2	no	—
1054	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1055	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1056	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1057	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1058	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1059	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1060	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1061	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1062	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1063	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1064	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1065	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1066	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1067	SD₁₆	—	2	4	no	—
1068	D₈	—	2	4	no	—
1069	M₁₆	—	2	2	no	—
1070	M₁₆	—	2	2	no	—
1071	M₁₆	—	2	2	no	—
1072	M₁₆	—	2	4	no	—
1073	M₁₆	—	2	4	no	—
1074	M₁₆	#41×C₄₁	1	4	yes	complemented
1075	C₂×C₈	—	2	4	no	—
1076	C₂×C₈	—	2	4	no	—
1077	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1078	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1079	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1080	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	2	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	2	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	1	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	—	2	1	no	—
1093	C₄⋊C₄	—	2	1	no	—
1094	C₄⋊C₄	—	2	1	no	—
1095	C₄⋊C₄	—	2	1	no	—
1096	C₄⋊C₄	—	2	1	no	—
1097	C₄⋊C₄	—	2	1	no	—
1098	C₄⋊C₄	—	2	1	no	—
1099	C₄⋊C₄	—	2	1	no	—
1100	C₄⋊C₄	—	2	1	no	—
1101	C₄⋊C₄	—	2	1	no	—
1102	C₄⋊C₄	—	2	1	no	—
1103	C₄⋊C₄	—	2	1	no	—
1104	C₄⋊C₄	—	2	1	no	—
1105	C₄⋊C₄	—	2	1	no	—
1106	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1107	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1108	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1109	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1110	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1111	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1112	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1113	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1114	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1115	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1116	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1117	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1118	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1119	C₂²⋊C₄	—	2	1	no	—
1120	C₂²⋊C₄	—	2	1	no	—
1121	C₂²⋊C₄	—	2	1	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	2	no	—
1124	C₂²⋊C₄	—	2	1	no	—
1125	C₂²⋊C₄	—	2	1	no	—
1126	C₂²⋊C₄	—	2	1	no	—
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	—	2	1	no	—
1129	C₂²⋊C₄	—	2	1	no	—
1130	C₂²⋊C₄	—	2	1	no	—
1131	C₂²⋊C₄	—	2	1	no	—
1132	C₂²⋊C₄	—	2	2	no	—
1133	C₂²⋊C₄	—	2	2	no	—
1134	C₂²⋊C₄	—	2	2	no	—
1135	C₂²⋊C₄	—	2	2	no	—
1136	C₂²⋊C₄	—	2	2	no	—
1137	C₂²⋊C₄	—	2	2	no	—
1138	C₂²⋊C₄	—	2	1	no	—
1139	C₂²⋊C₄	—	2	1	no	—
1140	C₂²⋊C₄	—	2	1	no	—
1141	C₂²⋊C₄	—	2	1	no	—
1142	C₂²⋊C₄	—	2	1	no	—
1143	C₂²⋊C₄	—	2	1	no	—
1144	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1145	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1146	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1147	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1148	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1149	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1150	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1151	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1152	C₄²	—	2	1	no	—
1153	C₄²	—	2	1	no	—
1154	C₄²	—	2	1	no	—
1155	C₄²	—	2	1	no	—
1156	C₄²	—	2	1	no	—
1157	C₄²	—	2	1	no	—
1158	C₄²	—	2	2	no	—
1159	C₄²	—	2	2	no	—
1160	C₄²	—	2	1	no	—
1161	C₄²	—	2	1	no	—
1162	C₄²	—	2	1	no	—
1163	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1164	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1165	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1166	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1167	C₂³	—	2	2	no	—
1168	C₂³	—	2	2	no	—
1169	C₂³	—	2	2	no	—
1170	C₂³	—	2	1	no	—
1171	C₂³	—	2	2	no	—
1172	C₂³	—	4	1	no	—
1173	C₂³	—	4	1	no	—
1174	C₂³	—	4	1	no	—
1175	C₂³	—	4	2	no	—
1176	C₂³	—	4	2	no	—
1177	C₂³	—	4	2	no	—
1178	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1179	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1180	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1181	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1182	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1183	Q₈	—	2	1	no	—
1184	Q₈	—	2	1	no	—
1185	Q₈	—	4	2	no	—
1186	Q₈	—	8	1	no	—
1187	D₄	—	2	2	no	—
1188	D₄	—	2	2	no	—
1189	D₄	—	2	1	no	—
1190	D₄	—	2	2	no	—
1191	D₄	—	2	2	no	—
1192	D₄	—	2	1	no	—
1193	D₄	—	4	1	no	—
1194	D₄	—	4	1	no	—
1195	D₄	—	4	4	no	—
1196	D₄	—	4	2	no	—
1197	D₄	—	4	2	no	—
1198	D₄	—	4	4	no	—
1199	D₄	—	4	2	no	—
1200	D₄	—	4	2	no	—
1201	D₄	—	8	2	no	—
1202	D₄	—	8	2	no	—
1203	D₄	—	8	1	no	—
1204	D₄	—	8	1	no	—
1205	C₂×C₄	—	2	2	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	2	no	—
1209	C₂×C₄	—	2	2	no	—
1210	C₂×C₄	—	2	2	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	1	no	—
1215	C₂×C₄	—	2	1	no	—
1216	C₂×C₄	—	2	1	no	—
1217	C₂×C₄	—	2	1	no	—
1218	C₂×C₄	—	2	1	no	—
1219	C₂×C₄	—	2	1	no	—
1220	C₂×C₄	—	2	1	no	—
1221	C₂×C₄	—	2	1	no	—
1222	C₂×C₄	—	2	2	no	—
1223	C₂×C₄	—	2	1	no	—
1224	C₂×C₄	—	2	1	no	—
1225	C₂×C₄	—	2	1	no	—
1226	C₂×C₄	—	2	1	no	—
1227	C₂×C₄	—	2	2	no	—
1228	C₂×C₄	—	2	2	no	—
1229	C₂×C₄	—	4	1	no	—
1230	C₂×C₄	—	4	1	no	—
1231	C₂×C₄	—	4	2	no	—
1232	C₂×C₄	—	4	2	no	—
1233	C₂×C₄	—	4	2	no	—
1234	C₂×C₄	—	4	2	no	—
1235	C₂×C₄	—	4	2	no	—
1236	C₂×C₄	—	4	2	no	—
1237	C₂×C₄	—	4	2	no	—
1238	C₂×C₄	—	8	2	no	—
1239	C₂×C₄	—	8	2	no	—
1240	C₂×C₄	—	8	1	no	—
1241	C₂×C₄	—	8	2	no	—
1242	C₂×C₄	—	8	2	no	—
1243	C₂×C₄	—	8	1	no	—
1244	C₂×C₄	—	8	1	no	—
1245	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1246	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1247	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1248	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1249	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1250	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1251	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1252	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1253	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1254	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
1255	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
1256	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1257	C₈	—	2	2	no	—
1258	C₈	—	2	2	no	—
1259	C₈	—	2	2	no	—
1260	C₈	C₂×#41×C₄₁	1	4	yes	—
1261	C₂²	—	2	1	no	—
1262	C₂²	—	2	1	no	—
1263	C₂²	—	2	1	no	—
1264	C₂²	—	2	1	no	—
1265	C₂²	—	2	1	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	1	no	—
1269	C₂²	—	2	1	no	—
1270	C₂²	—	2	1	no	—
1271	C₂²	—	2	1	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	4	4	no	—
1275	C₂²	—	4	1	no	—
1276	C₂²	—	4	2	no	—
1277	C₂²	—	4	2	no	—
1278	C₂²	—	4	1	no	—
1279	C₂²	—	4	1	no	—
1280	C₂²	—	4	2	no	—
1281	C₂²	—	8	2	no	—
1282	C₂²	—	8	4	no	—
1283	C₂²	C₄₁×#547	1	2	yes	—
1284	C₂²	C₄₁×#575	1	2	yes	—
1285	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1286	C₄	—	2	1	no	—
1287	C₄	—	2	1	no	—
1288	C₄	—	2	1	no	—
1289	C₄	—	2	1	no	—
1290	C₄	—	2	1	no	—
1291	C₄	—	2	1	no	—
1292	C₄	—	2	1	no	—
1293	C₄	—	2	1	no	—
1294	C₄	—	4	1	no	—
1295	C₄	—	4	2	no	—
1296	C₄	—	4	1	no	—
1297	C₄	—	4	1	no	—
1298	C₄	—	4	2	no	—
1299	C₄	—	4	2	no	—
1300	C₄	—	4	1	no	—
1301	C₄	—	4	1	no	—
1302	C₄	—	4	1	no	—
1303	C₄	—	4	1	no	—
1304	C₄	C₄₁×#547	1	2	yes	—
1305	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
1306	C₄	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
1307	C₂	—	2	2	no	—
1308	C₂	—	2	2	no	—
1309	C₂	—	4	1	no	—
1310	C₂	—	4	1	no	—
1311	C₂	—	4	1	no	—
1312	C₂	—	8	2	no	—
1313	C₂	—	8	1	no	—
1314	C₂	C₂×C₄₁×#547	1	1	yes	characteristic
1315	C₂	C₂×C₄₁×#575	1	1	yes	characteristic
1316	C₂	C₄₁×#3585	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 ◁ C₂×C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3475	C₂	semidirect
2. C₂×C₄₁×#553	C₂	semidirect
3. C₄₁×#3355	C₂	semidirect
4. C₄₁×#3351	C₂	semidirect
5. C₄₁×#3350	C₂	semidirect
6. C₄₁×#3347	C₂	semidirect
7. C₄₁×#3346	C₂	semidirect
8. C₄₁×#3345	C₂	semidirect
9. C₄₁×#3339	C₂	semidirect
10. C₄₁×#3337	C₂	semidirect
11. C₄₁×#3166	C₂	semidirect
12. C₄₁×#3094	C₂	semidirect
13. C₄₁×#3094	C₂	semidirect
14. C₄₁×#3093	C₂	semidirect
15. C₄₁×#3092	C₂	semidirect
16. C₄₁×#3080	C₂	semidirect
17. C₄₁×#3077	C₂	semidirect
18. C₄₁×#3055	C₂	semidirect
19. C₄₁×#3055	C₂	semidirect
20. C₄×AGL(1,ℤ/8)×C₄₁	C₂	semidirect
21. D₄×M₁₆×C₄₁	C₂	semidirect
22. C₄₁×#2911	C₂	semidirect
23. C₂×C₄₁×#428	C₂	semidirect
27. C₄₁×#556	C₂²	semidirect
28. C₄₁×#555	C₂²	semidirect
29. C₄₁×#554	C₂²	semidirect
38. C₄₁×#553	C₂²	semidirect
39. C₄₁×#553	C₂²	semidirect
41. C₄₁×#552	C₂²	semidirect
42. C₄₁×#552	C₂²	semidirect
45. C₄₁×#547	C₂²	semidirect
68. C₄₁×#501	C₂²	semidirect
69. C₄₁×#501	C₂²	semidirect
70. C₄₁×#499	C₂²	semidirect
71. C₄₁×#499	C₂²	semidirect
72. C₄₁×#485	C₂²	semidirect
73. C₄₁×#485	C₂²	semidirect
74. C₄₁×#484	C₂²	semidirect
75. C₄₁×#483	C₂²	semidirect
76. C₄₁×#482	C₂²	semidirect
77. C₄₁×#482	C₂²	semidirect
78. C₄₁×#482	C₂²	semidirect
79. C₄₁×#482	C₂²	semidirect
80. C₄₁×#482	C₂²	semidirect
81. C₄₁×#482	C₂²	semidirect
82. C₄₁×#481	C₂²	semidirect
83. C₄₁×#481	C₂²	semidirect
84. C₄₁×#481	C₂²	semidirect
85. C₄₁×#480	C₂²	semidirect
86. C₄₁×#480	C₂²	semidirect
87. C₄₁×#480	C₂²	semidirect
88. C₄₁×#479	C₂²	semidirect
89. C₄₁×#479	C₂²	semidirect
90. C₄₁×#478	C₂²	semidirect
91. C₄₁×#478	C₂²	semidirect
92. C₄₁×#478	C₂²	semidirect
93. C₄₁×#478	C₂²	semidirect
94. C₄₁×#476	C₂²	semidirect
95. C₄₁×#474	C₂²	semidirect
96. C₄₁×#469	C₂²	semidirect
97. C₄₁×#469	C₂²	semidirect
98. C₄₁×#468	C₂²	semidirect
99. C₄₁×#468	C₂²	semidirect
100. C₄₁×#466	C₂²	semidirect
101. C₄₁×#466	C₂²	semidirect
102. C₄₁×#465	C₂²	semidirect
103. C₄₁×#465	C₂²	semidirect
104. C₄₁×#442	C₂²	semidirect
105. C₄₁×#440	C₂²	semidirect
106. C₄×SD₁₆×C₄₁	C₂²	semidirect
107. C₄×D₈×C₄₁	C₂²	semidirect
108. C₄₁×#436	C₂²	semidirect
109. C₄₁×#435	C₂²	semidirect
110. C₄₁×#435	C₂²	semidirect
111. C₈×D₄×C₄₁	C₂²	semidirect
121. C₄₁×#428	C₂²	semidirect
122. C₄₁×#428	C₂²	semidirect
123. C₄₁×#428	C₂²	semidirect
124. C₄₁×#428	C₂²	semidirect
125. C₄₁×#427	C₂²	semidirect
126. C₄₁×#427	C₂²	semidirect
127. C₂×#107×C₄₁	C₂²	semidirect
128. C₂×#106×C₄₁	C₂²	semidirect
415. M₁₆×C₄₁	#41	semidirect
602. #61255	C₄₁	direct (N × H)
649. #3475	C₂×C₄₁	semidirect
650. C₂×#553	C₂×C₄₁	semidirect
651. #3355	C₂×C₄₁	semidirect
652. #3351	C₂×C₄₁	semidirect
653. #3350	C₂×C₄₁	semidirect
654. #3347	C₂×C₄₁	semidirect
655. #3346	C₂×C₄₁	semidirect
656. #3345	C₂×C₄₁	semidirect
657. #3339	C₂×C₄₁	semidirect
658. #3337	C₂×C₄₁	semidirect
659. #3166	C₂×C₄₁	semidirect
660. #3094	C₂×C₄₁	semidirect
661. #3094	C₂×C₄₁	semidirect
662. #3093	C₂×C₄₁	semidirect
663. #3092	C₂×C₄₁	semidirect
664. #3080	C₂×C₄₁	semidirect
665. #3077	C₂×C₄₁	semidirect
666. #3055	C₂×C₄₁	semidirect
667. #3055	C₂×C₄₁	semidirect
668. C₄×AGL(1,ℤ/8)	C₂×C₄₁	semidirect
669. D₄×M₁₆	C₂×C₄₁	semidirect
670. #2911	C₂×C₄₁	semidirect
671. C₂×#428	C₂×C₄₁	semidirect
685. #556	C₂²×C₄₁	semidirect
686. #555	C₂²×C₄₁	semidirect
687. #554	C₂²×C₄₁	semidirect
696. #553	C₂²×C₄₁	semidirect
697. #553	C₂²×C₄₁	semidirect
699. #552	C₂²×C₄₁	semidirect
700. #552	C₂²×C₄₁	semidirect
703. #547	C₂²×C₄₁	semidirect
726. #501	C₂²×C₄₁	semidirect
727. #501	C₂²×C₄₁	semidirect
728. #499	C₂²×C₄₁	semidirect
729. #499	C₂²×C₄₁	semidirect
730. #485	C₂²×C₄₁	semidirect
731. #485	C₂²×C₄₁	semidirect
732. #484	C₂²×C₄₁	semidirect
733. #483	C₂²×C₄₁	semidirect
734. #482	C₂²×C₄₁	semidirect
735. #482	C₂²×C₄₁	semidirect
736. #482	C₂²×C₄₁	semidirect
737. #482	C₂²×C₄₁	semidirect
738. #482	C₂²×C₄₁	semidirect
739. #482	C₂²×C₄₁	semidirect
740. #481	C₂²×C₄₁	semidirect
741. #481	C₂²×C₄₁	semidirect
742. #481	C₂²×C₄₁	semidirect
743. #480	C₂²×C₄₁	semidirect
744. #480	C₂²×C₄₁	semidirect
745. #480	C₂²×C₄₁	semidirect
746. #479	C₂²×C₄₁	semidirect
747. #479	C₂²×C₄₁	semidirect
748. #478	C₂²×C₄₁	semidirect
749. #478	C₂²×C₄₁	semidirect
750. #478	C₂²×C₄₁	semidirect
751. #478	C₂²×C₄₁	semidirect
752. #476	C₂²×C₄₁	semidirect
753. #474	C₂²×C₄₁	semidirect
754. #469	C₂²×C₄₁	semidirect
755. #469	C₂²×C₄₁	semidirect
756. #468	C₂²×C₄₁	semidirect
757. #468	C₂²×C₄₁	semidirect
758. #466	C₂²×C₄₁	semidirect
759. #466	C₂²×C₄₁	semidirect
760. #465	C₂²×C₄₁	semidirect
761. #465	C₂²×C₄₁	semidirect
762. #442	C₂²×C₄₁	semidirect
763. #440	C₂²×C₄₁	semidirect
764. C₄×SD₁₆	C₂²×C₄₁	semidirect
765. C₄×D₈	C₂²×C₄₁	semidirect
766. #436	C₂²×C₄₁	semidirect
767. #435	C₂²×C₄₁	semidirect
768. #435	C₂²×C₄₁	semidirect
769. C₈×D₄	C₂²×C₄₁	semidirect
779. #428	C₂²×C₄₁	semidirect
780. #428	C₂²×C₄₁	semidirect
781. #428	C₂²×C₄₁	semidirect
782. #428	C₂²×C₄₁	semidirect
783. #427	C₂²×C₄₁	semidirect
784. #427	C₂²×C₄₁	semidirect
785. C₂×#107	C₂²×C₄₁	semidirect
786. C₂×#106	C₂²×C₄₁	semidirect
797. C₄₁	#61255	direct (N × H)
1074. M₁₆	#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×#3475	2
C₂×C₄₁×#553	2
C₄₁×#3355	2
C₄₁×#3351	2
C₄₁×#3350	2
C₄₁×#3347	2
C₄₁×#3346	2
C₄₁×#3345	2
C₄₁×#3339	2
C₄₁×#3337	2
C₄₁×#3166	2
C₄₁×#3094	2
C₄₁×#3093	2
C₄₁×#3092	2
C₄₁×#3080	2
C₄₁×#3077	2
C₄₁×#3055	2
C₄×AGL(1,ℤ/8)×C₄₁	2
D₄×M₁₆×C₄₁	2
C₄₁×#2911	2
C₂×C₄₁×#428	2
#61255	41

Subgroups — C41×#61255 #23837456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61255 #23837456