Subgroups — C₄₁×#61581 #23837782

Order 10496.

2258 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3323	C₂	1	4	yes	maximal, complemented
4	C₄₁×#3322	C₂	1	4	yes	maximal, complemented
5	C₄₁×#3275	C₂	1	4	yes	maximal, complemented
6	C₄₁×#3273	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3211	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3196	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3193	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3192	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3105	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3007	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3003	C₂	1	2	yes	maximal, complemented
15	C₄₁×#2975	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
18	C₂×#137×C₄₁	C₂²	1	2	yes	complemented
19	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	4	yes	complemented
20	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	2	yes	complemented
21	C₄₁×#553	—	2	2	no	—
22	C₄₁×#553	C₂²	1	2	yes	complemented
23	C₄₁×#552	C₂²	1	2	yes	complemented
24	C₄₁×#551	—	2	2	no	—
25	C₄₁×#548	C₂²	1	2	yes	complemented
26	C₄₁×#546	—	2	2	no	—
27	C₄₁×#546	—	2	2	no	—
28	C₄₁×#546	C₂²	1	4	yes	—
29	C₄₁×#546	C₂²	1	4	yes	complemented
30	C₄₁×#546	C₂²	1	2	yes	complemented
31	C₄₁×#539	—	2	1	no	—
32	C₄₁×#538	—	2	1	no	—
33	C₄₁×#534	—	2	1	no	—
34	C₄₁×#529	C₂²	1	2	yes	complemented
35	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic, complemented
36	C₄₁×#525	C₂²	1	2	yes	—
37	C₂×#123×C₄₁	—	2	1	no	—
38	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
40	C₂×#121×C₄₁	—	2	1	no	—
41	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
42	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic, complemented
43	C₂×#120×C₄₁	—	2	1	no	—
44	C₄₁×#518	—	2	1	no	—
45	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₂²⋊C₄×C₄₁	—	2	1	no	—
48	C₄₁×#495	C₂²	1	4	yes	complemented
49	C₄₁×#488	C₂²	1	4	yes	complemented
50	C₄₁×#485	C₂²	1	4	yes	complemented
51	C₄₁×#484	C₂²	1	2	yes	complemented
52	C₄₁×#481	C₂²	1	2	yes	complemented
53	C₄₁×#481	C₂²	1	2	yes	complemented
54	C₄₁×#480	C₂²	1	2	yes	complemented
55	C₄₁×#478	C₂²	1	4	yes	complemented
56	C₄₁×#470	C₂²	1	4	yes	complemented
57	C₄₁×#469	C₂²	1	4	yes	complemented
58	C₄₁×#468	C₂²	1	4	yes	complemented
59	C₄₁×#468	C₂²	1	4	yes	complemented
60	C₄₁×#464	C₂²	1	4	yes	complemented
61	C₄₁×#463	C₂²	1	4	yes	complemented
62	C₄₁×#463	C₂²	1	4	yes	complemented
63	C₄₁×#452	C₂²	1	4	yes	complemented
64	C₄₁×#452	C₂²	1	4	yes	complemented
65	C₄₁×#451	C₂²	1	2	yes	complemented
66	C₄₁×#450	C₂²	1	4	yes	complemented
67	C₄₁×#450	C₂²	1	2	yes	complemented
68	C₄₁×#450	C₂²	1	2	yes	complemented
69	C₄₁×#449	C₂²	1	4	yes	complemented
70	C₄₁×#448	C₂²	1	2	yes	complemented
71	C₄₁×#448	C₂²	1	2	yes	complemented
72	C₄₁×#447	C₂²	1	2	yes	—
73	C₄₁×#447	C₂²	1	2	yes	—
74	C₄₁×#447	C₂²	1	4	yes	complemented
75	C₄₁×#447	C₂²	1	2	yes	complemented
76	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	complemented
77	C₄×D₈×C₄₁	C₂²	1	4	yes	complemented
78	C₄₁×#436	C₂²	1	4	yes	complemented
79	C₄₁×#436	C₂²	1	4	yes	complemented
80	C₄₁×#431	C₂²	1	2	yes	complemented
81	C₄₁×#418	C₂²	1	4	yes	complemented
82	C₄₁×#417	C₂²	1	2	yes	complemented
83	C₄₁×#417	C₂²	1	2	yes	complemented
84	C₄₁×#407	C₂²	1	2	yes	complemented
85	C₄₁×#407	C₂²	1	1	yes	characteristic, complemented
86	C₄₁×#407	C₂²	1	1	yes	characteristic, complemented
87	C₂⁵×C₄₁	—	2	1	no	—
88	C₂×#41×C₄₁	—	2	1	no	—
89	C₂×#41×C₄₁	—	2	1	no	—
90	C₂×#41×C₄₁	—	4	4	no	—
91	C₂×#41×C₄₁	C₂³	1	2	yes	—
92	C₂×#41×C₄₁	C₂³	1	2	yes	—
93	C₂×#41×C₄₁	C₂³	1	2	yes	—
94	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic, complemented
96	C₂²×D₄×C₄₁	—	2	1	no	—
97	C₂²×D₄×C₄₁	—	2	1	no	—
98	C₂²×D₄×C₄₁	—	2	1	no	—
99	C₂²×D₄×C₄₁	—	2	1	no	—
100	C₂²×D₄×C₄₁	—	2	2	no	—
101	C₂²×D₄×C₄₁	—	4	4	no	—
102	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
103	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
105	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic, complemented
107	C₂³×C₄×C₄₁	—	2	1	no	—
108	C₂³×C₄×C₄₁	—	2	1	no	—
109	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
111	#137×C₄₁	—	4	4	no	—
112	AGL(1,ℤ/8)×C₄₁	—	4	4	no	—
113	AGL(1,ℤ/8)×C₄₁	—	4	8	no	—
114	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	complemented
115	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	complemented
118	C₂×D₈×C₄₁	C₂³	1	4	yes	—
119	C₂×D₈×C₄₁	C₂³	1	4	yes	—
120	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
121	C₂×M₁₆×C₄₁	C₂³	1	2	yes	complemented
122	C₂×M₁₆×C₄₁	C₂³	1	2	yes	complemented
123	#126×C₄₁	—	2	2	no	—
124	#126×C₄₁	—	2	2	no	—
125	#126×C₄₁	—	2	2	no	—
126	#125×C₄₁	—	2	2	no	—
127	#125×C₄₁	C₂³	1	2	yes	complemented
128	#124×C₄₁	—	2	2	no	—
129	#124×C₄₁	—	2	2	no	—
130	#124×C₄₁	C₂³	1	4	yes	—
131	#124×C₄₁	C₂³	1	2	yes	complemented
132	#123×C₄₁	—	2	2	no	—
133	#123×C₄₁	—	2	2	no	—
134	#123×C₄₁	—	2	2	no	—
135	#123×C₄₁	—	2	4	no	—
136	#123×C₄₁	—	2	4	no	—
137	#123×C₄₁	—	2	2	no	—
138	#123×C₄₁	—	2	2	no	—
139	C₂²⋊Q₈×C₄₁	—	2	1	no	—
140	C₂²⋊Q₈×C₄₁	—	2	2	no	—
141	C₂²⋊Q₈×C₄₁	—	2	1	no	—
142	C₂²⋊Q₈×C₄₁	—	2	2	no	—
143	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
144	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
145	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
146	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	complemented
147	#121×C₄₁	—	2	2	no	—
148	#121×C₄₁	—	2	2	no	—
149	#121×C₄₁	—	2	1	no	—
150	#121×C₄₁	—	2	1	no	—
151	#121×C₄₁	—	2	1	no	—
152	#121×C₄₁	—	2	1	no	—
153	#121×C₄₁	—	2	4	no	—
154	#121×C₄₁	—	2	4	no	—
155	#121×C₄₁	—	2	2	no	—
156	#121×C₄₁	C₂³	1	2	yes	—
157	#121×C₄₁	C₂³	1	2	yes	—
158	#121×C₄₁	C₂³	1	2	yes	—
159	#121×C₄₁	C₂³	1	2	yes	—
160	#121×C₄₁	C₂³	1	2	yes	complemented
161	#120×C₄₁	—	2	2	no	—
162	#120×C₄₁	—	2	4	no	—
163	#120×C₄₁	—	2	4	no	—
164	#120×C₄₁	—	2	2	no	—
165	C₄×Q₈×C₄₁	C₂³	1	2	yes	complemented
166	C₄×D₄×C₄₁	—	2	2	no	—
167	C₄×D₄×C₄₁	—	2	2	no	—
168	C₄×D₄×C₄₁	—	2	2	no	—
169	C₄×D₄×C₄₁	—	2	2	no	—
170	C₄×D₄×C₄₁	—	2	2	no	—
171	C₄×D₄×C₄₁	—	2	2	no	—
172	C₄×D₄×C₄₁	D₄	1	2	yes	—
173	C₄×D₄×C₄₁	D₄	1	2	yes	—
174	C₄×D₄×C₄₁	C₂³	1	4	yes	—
175	C₄×D₄×C₄₁	C₂³	1	2	yes	—
176	C₄×D₄×C₄₁	C₂³	1	2	yes	—
177	C₄×D₄×C₄₁	C₂³	1	2	yes	complemented
178	#117×C₄₁	—	2	2	no	—
179	#117×C₄₁	—	2	2	no	—
180	#117×C₄₁	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
182	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
183	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic, complemented
186	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic, complemented
187	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
188	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
189	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
190	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
191	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
192	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
193	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
195	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
196	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
197	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
199	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
200	#107×C₄₁	C₂³	1	4	yes	complemented
201	#106×C₄₁	C₂³	1	4	yes	complemented
202	C₄⋊C₈×C₄₁	C₂³	1	4	yes	complemented
203	#103×C₄₁	C₂³	1	4	yes	complemented
204	#103×C₄₁	C₂³	1	4	yes	complemented
205	#103×C₄₁	C₂³	1	4	yes	complemented
206	#102×C₄₁	C₂³	1	4	yes	—
207	#102×C₄₁	C₂³	1	4	yes	—
208	#102×C₄₁	C₂³	1	4	yes	—
209	#102×C₄₁	C₂³	1	4	yes	—
210	#102×C₄₁	C₂³	1	4	yes	complemented
211	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
212	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
213	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
214	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	complemented
215	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	complemented
216	C₄×C₈×C₄₁	C₂³	1	4	yes	complemented
217	C₂⁴×C₄₁	—	2	1	no	—
218	C₂⁴×C₄₁	—	2	1	no	—
219	C₂⁴×C₄₁	—	2	4	no	—
220	C₂⁴×C₄₁	—	2	1	no	—
221	C₂⁴×C₄₁	—	4	4	no	—
222	C₂⁴×C₄₁	—	4	4	no	—
223	C₂⁴×C₄₁	—	8	2	no	—
224	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
225	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
226	#41×C₄₁	—	2	4	no	—
227	#41×C₄₁	—	2	4	no	—
228	#41×C₄₁	—	4	2	no	—
229	#41×C₄₁	—	4	2	no	—
230	#41×C₄₁	—	4	4	no	—
231	#41×C₄₁	—	4	4	no	—
232	#41×C₄₁	—	4	4	no	—
233	C₂×Q₈×C₄₁	—	2	1	no	—
234	C₂×Q₈×C₄₁	—	2	1	no	—
235	C₂×Q₈×C₄₁	—	4	2	no	—
236	C₂×Q₈×C₄₁	—	4	2	no	—
237	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
239	C₂×D₄×C₄₁	—	2	4	no	—
240	C₂×D₄×C₄₁	—	2	8	no	—
241	C₂×D₄×C₄₁	—	2	2	no	—
242	C₂×D₄×C₄₁	—	2	2	no	—
243	C₂×D₄×C₄₁	—	2	2	no	—
244	C₂×D₄×C₄₁	—	2	2	no	—
245	C₂×D₄×C₄₁	—	2	2	no	—
246	C₂×D₄×C₄₁	—	2	2	no	—
247	C₂×D₄×C₄₁	—	2	2	no	—
248	C₂×D₄×C₄₁	—	2	2	no	—
249	C₂×D₄×C₄₁	—	2	1	no	—
250	C₂×D₄×C₄₁	—	2	4	no	—
251	C₂×D₄×C₄₁	—	2	1	no	—
252	C₂×D₄×C₄₁	—	2	1	no	—
253	C₂×D₄×C₄₁	—	4	4	no	—
254	C₂×D₄×C₄₁	—	4	2	no	—
255	C₂×D₄×C₄₁	—	4	2	no	—
256	C₂×D₄×C₄₁	—	4	2	no	—
257	C₂×D₄×C₄₁	—	4	8	no	—
258	C₂×D₄×C₄₁	—	4	4	no	—
259	C₂×D₄×C₄₁	—	4	4	no	—
260	C₂×D₄×C₄₁	—	4	4	no	—
261	C₂×D₄×C₄₁	—	8	2	no	—
262	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
263	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
265	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
266	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₄₁	—	2	1	no	—
268	C₂²×C₄×C₄₁	—	2	1	no	—
269	C₂²×C₄×C₄₁	—	2	1	no	—
270	C₂²×C₄×C₄₁	—	2	1	no	—
271	C₂²×C₄×C₄₁	—	2	1	no	—
272	C₂²×C₄×C₄₁	—	2	2	no	—
273	C₂²×C₄×C₄₁	—	2	2	no	—
274	C₂²×C₄×C₄₁	—	2	4	no	—
275	C₂²×C₄×C₄₁	—	2	2	no	—
276	C₂²×C₄×C₄₁	—	2	2	no	—
277	C₂²×C₄×C₄₁	—	4	2	no	—
278	C₂²×C₄×C₄₁	—	4	2	no	—
279	C₂²×C₄×C₄₁	—	4	4	no	—
280	C₂²×C₄×C₄₁	—	8	2	no	—
281	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
288	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
292	Q₁₆×C₄₁	—	4	4	no	—
293	SD₁₆×C₄₁	—	2	8	no	—
294	SD₁₆×C₄₁	—	4	4	no	—
295	SD₁₆×C₄₁	—	4	4	no	—
296	D₈×C₄₁	—	2	8	no	—
297	D₈×C₄₁	—	4	4	no	—
298	M₁₆×C₄₁	—	4	4	no	—
299	M₁₆×C₄₁	—	4	2	no	—
300	M₁₆×C₄₁	—	4	2	no	—
301	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
302	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
303	C₄⋊C₄×C₄₁	—	2	2	no	—
304	C₄⋊C₄×C₄₁	—	2	4	no	—
305	C₄⋊C₄×C₄₁	—	2	2	no	—
306	C₄⋊C₄×C₄₁	—	2	1	no	—
307	C₄⋊C₄×C₄₁	—	2	1	no	—
308	C₄⋊C₄×C₄₁	—	2	1	no	—
309	C₄⋊C₄×C₄₁	—	2	2	no	—
310	C₄⋊C₄×C₄₁	—	2	2	no	—
311	C₄⋊C₄×C₄₁	—	2	2	no	—
312	C₄⋊C₄×C₄₁	—	2	2	no	—
313	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
314	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
315	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
317	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
318	C₂²⋊C₄×C₄₁	—	2	4	no	—
319	C₂²⋊C₄×C₄₁	—	2	2	no	—
320	C₂²⋊C₄×C₄₁	—	2	2	no	—
321	C₂²⋊C₄×C₄₁	—	2	2	no	—
322	C₂²⋊C₄×C₄₁	—	2	2	no	—
323	C₂²⋊C₄×C₄₁	—	2	4	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	2	no	—
329	C₂²⋊C₄×C₄₁	—	2	4	no	—
330	C₂²⋊C₄×C₄₁	—	2	4	no	—
331	C₂²⋊C₄×C₄₁	—	2	2	no	—
332	C₂²⋊C₄×C₄₁	—	2	2	no	—
333	C₂²⋊C₄×C₄₁	—	2	2	no	—
334	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
335	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
336	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
337	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
338	C₄²×C₄₁	—	2	2	no	—
339	C₄²×C₄₁	—	2	2	no	—
340	C₄²×C₄₁	C₂×D₄	1	2	yes	—
341	C₄²×C₄₁	C₂⁴	1	2	yes	—
342	C₂³×C₄₁	—	2	4	no	—
343	C₂³×C₄₁	—	2	2	no	—
344	C₂³×C₄₁	—	2	2	no	—
345	C₂³×C₄₁	—	2	2	no	—
346	C₂³×C₄₁	—	2	2	no	—
347	C₂³×C₄₁	—	2	2	no	—
348	C₂³×C₄₁	—	4	1	no	—
349	C₂³×C₄₁	—	4	1	no	—
350	C₂³×C₄₁	—	4	1	no	—
351	C₂³×C₄₁	—	4	1	no	—
352	C₂³×C₄₁	—	4	8	no	—
353	C₂³×C₄₁	—	4	2	no	—
354	C₂³×C₄₁	—	4	2	no	—
355	C₂³×C₄₁	—	4	2	no	—
356	C₂³×C₄₁	—	4	8	no	—
357	C₂³×C₄₁	—	4	2	no	—
358	C₂³×C₄₁	—	4	2	no	—
359	C₂³×C₄₁	—	4	2	no	—
360	C₂³×C₄₁	—	8	4	no	—
361	C₂³×C₄₁	—	8	1	no	—
362	C₂³×C₄₁	—	8	1	no	—
363	C₂³×C₄₁	—	8	16	no	—
364	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
365	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
366	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
367	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
368	Q₈×C₄₁	—	2	4	no	—
369	Q₈×C₄₁	—	2	2	no	—
370	Q₈×C₄₁	—	2	2	no	—
371	Q₈×C₄₁	—	4	2	no	—
372	Q₈×C₄₁	—	8	1	no	—
373	D₄×C₄₁	—	2	4	no	—
374	D₄×C₄₁	—	2	2	no	—
375	D₄×C₄₁	—	2	4	no	—
376	D₄×C₄₁	—	2	4	no	—
377	D₄×C₄₁	—	4	2	no	—
378	D₄×C₄₁	—	4	2	no	—
379	D₄×C₄₁	—	4	8	no	—
380	D₄×C₄₁	—	4	2	no	—
381	D₄×C₄₁	—	4	4	no	—
382	D₄×C₄₁	—	4	4	no	—
383	D₄×C₄₁	—	4	4	no	—
384	D₄×C₄₁	—	4	4	no	—
385	D₄×C₄₁	—	8	1	no	—
386	D₄×C₄₁	—	8	2	no	—
387	D₄×C₄₁	—	8	2	no	—
388	D₄×C₄₁	—	8	2	no	—
389	D₄×C₄₁	—	8	2	no	—
390	D₄×C₄₁	H(5,𝔽₂)	1	4	yes	—
391	C₂×C₄×C₄₁	—	2	2	no	—
392	C₂×C₄×C₄₁	—	2	4	no	—
393	C₂×C₄×C₄₁	—	2	2	no	—
394	C₂×C₄×C₄₁	—	2	2	no	—
395	C₂×C₄×C₄₁	—	2	2	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	—	2	2	no	—
400	C₂×C₄×C₄₁	—	2	2	no	—
401	C₂×C₄×C₄₁	—	4	1	no	—
402	C₂×C₄×C₄₁	—	4	2	no	—
403	C₂×C₄×C₄₁	—	4	1	no	—
404	C₂×C₄×C₄₁	—	4	1	no	—
405	C₂×C₄×C₄₁	—	4	1	no	—
406	C₂×C₄×C₄₁	—	4	1	no	—
407	C₂×C₄×C₄₁	—	4	4	no	—
408	C₂×C₄×C₄₁	—	4	4	no	—
409	C₂×C₄×C₄₁	—	4	2	no	—
410	C₂×C₄×C₄₁	—	4	2	no	—
411	C₂×C₄×C₄₁	—	4	2	no	—
412	C₂×C₄×C₄₁	—	8	2	no	—
413	C₂×C₄×C₄₁	—	8	4	no	—
414	C₂×C₄×C₄₁	—	8	2	no	—
415	C₂×C₄×C₄₁	—	8	1	no	—
416	C₂×C₄×C₄₁	—	8	1	no	—
417	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
424	C₈×C₄₁	—	2	4	no	—
425	C₈×C₄₁	—	2	4	no	—
426	#61581	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
427	C₂²×C₄₁	—	2	1	no	—
428	C₂²×C₄₁	—	2	1	no	—
429	C₂²×C₄₁	—	2	1	no	—
430	C₂²×C₄₁	—	2	1	no	—
431	C₂²×C₄₁	—	2	2	no	—
432	C₂²×C₄₁	—	2	1	no	—
433	C₂²×C₄₁	—	2	1	no	—
434	C₂²×C₄₁	—	2	2	no	—
435	C₂²×C₄₁	—	2	4	no	—
436	C₂²×C₄₁	—	2	1	no	—
437	C₂²×C₄₁	—	2	1	no	—
438	C₂²×C₄₁	—	2	2	no	—
439	C₂²×C₄₁	—	4	8	no	—
440	C₂²×C₄₁	—	4	4	no	—
441	C₂²×C₄₁	—	4	2	no	—
442	C₂²×C₄₁	—	4	2	no	—
443	C₂²×C₄₁	—	4	2	no	—
444	C₂²×C₄₁	—	4	2	no	—
445	C₂²×C₄₁	—	4	2	no	—
446	C₂²×C₄₁	—	4	2	no	—
447	C₂²×C₄₁	—	4	2	no	—
448	C₂²×C₄₁	—	4	2	no	—
449	C₂²×C₄₁	—	8	2	no	—
450	C₂²×C₄₁	—	8	4	no	—
451	C₂²×C₄₁	—	8	16	no	—
452	C₂²×C₄₁	—	16	2	no	—
453	C₂²×C₄₁	#575	1	2	yes	—
454	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
455	C₄×C₄₁	—	2	2	no	—
456	C₄×C₄₁	—	2	1	no	—
457	C₄×C₄₁	—	2	1	no	—
458	C₄×C₄₁	—	2	1	no	—
459	C₄×C₄₁	—	2	2	no	—
460	C₄×C₄₁	—	2	2	no	—
461	C₄×C₄₁	—	4	2	no	—
462	C₄×C₄₁	—	4	2	no	—
463	C₄×C₄₁	—	4	2	no	—
464	C₄×C₄₁	—	4	2	no	—
465	C₄×C₄₁	—	4	2	no	—
466	C₄×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
467	#3505	C₂×C₄₁	1	1	yes	characteristic, complemented
468	C₂×#546	C₂×C₄₁	1	1	yes	characteristic, complemented
469	#3323	C₂×C₄₁	1	4	yes	complemented
470	#3322	C₂×C₄₁	1	4	yes	complemented
471	#3275	C₂×C₄₁	1	4	yes	complemented
472	#3273	C₂×C₄₁	1	4	yes	complemented
473	#3211	C₂×C₄₁	1	2	yes	complemented
474	#3196	C₂×C₄₁	1	2	yes	complemented
475	#3193	C₂×C₄₁	1	1	yes	characteristic, complemented
476	#3192	C₂×C₄₁	1	1	yes	characteristic, complemented
477	#3105	C₂×C₄₁	1	2	yes	complemented
478	#3007	C₂×C₄₁	1	1	yes	characteristic, complemented
479	#3006	C₂×C₄₁	1	1	yes	characteristic, complemented
480	#3003	C₂×C₄₁	1	2	yes	complemented
481	#2975	C₂×C₄₁	1	1	yes	characteristic, complemented
482	C₂×C₄₁	—	2	2	no	—
483	C₂×C₄₁	—	4	2	no	—
484	C₂×C₄₁	—	4	1	no	—
485	C₂×C₄₁	—	4	1	no	—
486	C₂×C₄₁	—	4	4	no	—
487	C₂×C₄₁	—	8	2	no	—
488	C₂×C₄₁	—	8	2	no	—
489	C₂×C₄₁	#3484	1	1	yes	characteristic
490	C₂×C₄₁	C₂×#575	1	1	yes	characteristic
491	C₂×C₄₁	#3585	1	1	yes	characteristic
492	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
493	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
494	C₂×#137	C₂²×C₄₁	1	2	yes	complemented
495	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	4	yes	complemented
496	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	2	yes	complemented
497	#553	—	2	2	no	—
498	#553	C₂²×C₄₁	1	2	yes	complemented
499	#552	C₂²×C₄₁	1	2	yes	complemented
500	#551	—	2	2	no	—
501	#548	C₂²×C₄₁	1	2	yes	complemented
502	#546	—	2	2	no	—
503	#546	—	2	2	no	—
504	#546	C₂²×C₄₁	1	4	yes	—
505	#546	C₂²×C₄₁	1	4	yes	complemented
506	#546	C₂²×C₄₁	1	2	yes	complemented
507	#539	—	2	1	no	—
508	#538	—	2	1	no	—
509	#534	—	2	1	no	—
510	#529	C₂²×C₄₁	1	2	yes	complemented
511	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic, complemented
512	#525	C₂²×C₄₁	1	2	yes	—
513	C₂×#123	—	2	1	no	—
514	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
515	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
516	C₂×#121	—	2	1	no	—
517	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
518	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic, complemented
519	C₂×#120	—	2	1	no	—
520	#518	—	2	1	no	—
521	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
522	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
523	C₂²×C₂²⋊C₄	—	2	1	no	—
524	#495	C₂²×C₄₁	1	4	yes	complemented
525	#488	C₂²×C₄₁	1	4	yes	complemented
526	#485	C₂²×C₄₁	1	4	yes	complemented
527	#484	C₂²×C₄₁	1	2	yes	complemented
528	#481	C₂²×C₄₁	1	2	yes	complemented
529	#481	C₂²×C₄₁	1	2	yes	complemented
530	#480	C₂²×C₄₁	1	2	yes	complemented
531	#478	C₂²×C₄₁	1	4	yes	complemented
532	#470	C₂²×C₄₁	1	4	yes	complemented
533	#469	C₂²×C₄₁	1	4	yes	complemented
534	#468	C₂²×C₄₁	1	4	yes	complemented
535	#468	C₂²×C₄₁	1	4	yes	complemented
536	#464	C₂²×C₄₁	1	4	yes	complemented
537	#463	C₂²×C₄₁	1	4	yes	complemented
538	#463	C₂²×C₄₁	1	4	yes	complemented
539	#452	C₂²×C₄₁	1	4	yes	complemented
540	#452	C₂²×C₄₁	1	4	yes	complemented
541	#451	C₂²×C₄₁	1	2	yes	complemented
542	#450	C₂²×C₄₁	1	2	yes	complemented
543	#450	C₂²×C₄₁	1	2	yes	complemented
544	#450	C₂²×C₄₁	1	4	yes	complemented
545	#449	C₂²×C₄₁	1	4	yes	complemented
546	#448	C₂²×C₄₁	1	2	yes	complemented
547	#448	C₂²×C₄₁	1	2	yes	complemented
548	#447	C₂²×C₄₁	1	2	yes	—
549	#447	C₂²×C₄₁	1	2	yes	—
550	#447	C₂²×C₄₁	1	4	yes	complemented
551	#447	C₂²×C₄₁	1	2	yes	complemented
552	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	complemented
553	C₄×D₈	C₂²×C₄₁	1	4	yes	complemented
554	#436	C₂²×C₄₁	1	4	yes	complemented
555	#436	C₂²×C₄₁	1	4	yes	complemented
556	#431	C₂²×C₄₁	1	2	yes	complemented
557	#418	C₂²×C₄₁	1	4	yes	complemented
558	#417	C₂²×C₄₁	1	2	yes	complemented
559	#417	C₂²×C₄₁	1	2	yes	complemented
560	#407	C₂²×C₄₁	1	2	yes	complemented
561	#407	C₂²×C₄₁	1	1	yes	characteristic, complemented
562	#407	C₂²×C₄₁	1	1	yes	characteristic, complemented
563	C₄₁	#61581	1	1	yes	characteristic, direct product factor, Sylow
564	C₂⁵	—	2	1	no	—
565	C₂×#41	—	2	1	no	—
566	C₂×#41	—	2	1	no	—
567	C₂×#41	—	4	4	no	—
568	C₂×#41	C₂³×C₄₁	1	2	yes	—
569	C₂×#41	C₂³×C₄₁	1	2	yes	—
570	C₂×#41	C₂³×C₄₁	1	2	yes	—
571	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
572	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic, complemented
573	C₂²×D₄	—	2	1	no	—
574	C₂²×D₄	—	2	1	no	—
575	C₂²×D₄	—	2	1	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	—	2	2	no	—
578	C₂²×D₄	—	4	4	no	—
579	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
580	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
581	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
582	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
583	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic, complemented
584	C₂³×C₄	—	2	1	no	—
585	C₂³×C₄	—	2	1	no	—
586	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
588	#137	—	4	4	no	—
589	AGL(1,ℤ/8)	—	4	4	no	—
590	AGL(1,ℤ/8)	—	4	8	no	—
591	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	complemented
592	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
593	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
594	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	complemented
595	C₂×D₈	C₂³×C₄₁	1	4	yes	—
596	C₂×D₈	C₂³×C₄₁	1	4	yes	—
597	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
598	C₂×M₁₆	C₂³×C₄₁	1	2	yes	complemented
599	C₂×M₁₆	C₂³×C₄₁	1	2	yes	complemented
600	#126	—	2	2	no	—
601	#126	—	2	2	no	—
602	#126	—	2	2	no	—
603	#125	—	2	2	no	—
604	#125	C₂³×C₄₁	1	2	yes	complemented
605	#124	—	2	2	no	—
606	#124	—	2	2	no	—
607	#124	C₂³×C₄₁	1	4	yes	—
608	#124	C₂³×C₄₁	1	2	yes	complemented
609	#123	—	2	2	no	—
610	#123	—	2	2	no	—
611	#123	—	2	2	no	—
612	#123	—	2	4	no	—
613	#123	—	2	4	no	—
614	#123	—	2	2	no	—
615	#123	—	2	2	no	—
616	C₂²⋊Q₈	—	2	1	no	—
617	C₂²⋊Q₈	—	2	2	no	—
618	C₂²⋊Q₈	—	2	1	no	—
619	C₂²⋊Q₈	—	2	2	no	—
620	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
621	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
622	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
623	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	complemented
624	#121	—	2	2	no	—
625	#121	—	2	2	no	—
626	#121	—	2	1	no	—
627	#121	—	2	1	no	—
628	#121	—	2	1	no	—
629	#121	—	2	1	no	—
630	#121	—	2	4	no	—
631	#121	—	2	4	no	—
632	#121	—	2	2	no	—
633	#121	C₂³×C₄₁	1	2	yes	—
634	#121	C₂³×C₄₁	1	2	yes	—
635	#121	C₂³×C₄₁	1	2	yes	—
636	#121	C₂³×C₄₁	1	2	yes	—
637	#121	C₂³×C₄₁	1	2	yes	complemented
638	#120	—	2	2	no	—
639	#120	—	2	4	no	—
640	#120	—	2	4	no	—
641	#120	—	2	2	no	—
642	C₄×Q₈	C₂³×C₄₁	1	2	yes	complemented
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	—	2	2	no	—
649	C₄×D₄	D₄×C₄₁	1	2	yes	—
650	C₄×D₄	D₄×C₄₁	1	2	yes	—
651	C₄×D₄	C₂³×C₄₁	1	4	yes	—
652	C₄×D₄	C₂³×C₄₁	1	2	yes	—
653	C₄×D₄	C₂³×C₄₁	1	2	yes	—
654	C₄×D₄	C₂³×C₄₁	1	2	yes	complemented
655	#117	—	2	2	no	—
656	#117	—	2	2	no	—
657	#117	C₂³×C₄₁	1	2	yes	—
658	C₂×C₄⋊C₄	—	2	1	no	—
659	C₂×C₄⋊C₄	—	2	1	no	—
660	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic, complemented
663	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic, complemented
664	C₂×C₂²⋊C₄	—	2	1	no	—
665	C₂×C₂²⋊C₄	—	2	1	no	—
666	C₂×C₂²⋊C₄	—	2	1	no	—
667	C₂×C₂²⋊C₄	—	2	1	no	—
668	C₂×C₂²⋊C₄	—	2	1	no	—
669	C₂×C₂²⋊C₄	—	2	1	no	—
670	C₂×C₂²⋊C₄	—	2	1	no	—
671	C₂×C₂²⋊C₄	—	2	4	no	—
672	C₂×C₂²⋊C₄	—	2	4	no	—
673	C₂×C₂²⋊C₄	—	2	2	no	—
674	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
677	#107	C₂³×C₄₁	1	4	yes	complemented
678	#106	C₂³×C₄₁	1	4	yes	complemented
679	C₄⋊C₈	C₂³×C₄₁	1	4	yes	complemented
680	#103	C₂³×C₄₁	1	4	yes	complemented
681	#103	C₂³×C₄₁	1	4	yes	complemented
682	#103	C₂³×C₄₁	1	4	yes	complemented
683	#102	C₂³×C₄₁	1	4	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	4	yes	complemented
688	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
689	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
690	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
691	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	complemented
692	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	complemented
693	C₄×C₈	C₂³×C₄₁	1	4	yes	complemented
694	C₂⁴	—	2	1	no	—
695	C₂⁴	—	2	1	no	—
696	C₂⁴	—	2	4	no	—
697	C₂⁴	—	2	1	no	—
698	C₂⁴	—	4	4	no	—
699	C₂⁴	—	4	4	no	—
700	C₂⁴	—	8	2	no	—
701	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
702	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
703	#41	—	2	4	no	—
704	#41	—	2	4	no	—
705	#41	—	4	2	no	—
706	#41	—	4	2	no	—
707	#41	—	4	4	no	—
708	#41	—	4	4	no	—
709	#41	—	4	4	no	—
710	C₂×Q₈	—	2	1	no	—
711	C₂×Q₈	—	2	1	no	—
712	C₂×Q₈	—	4	2	no	—
713	C₂×Q₈	—	4	2	no	—
714	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
715	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	8	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	4	4	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	2	no	—
734	C₂×D₄	—	4	8	no	—
735	C₂×D₄	—	4	4	no	—
736	C₂×D₄	—	4	4	no	—
737	C₂×D₄	—	4	4	no	—
738	C₂×D₄	—	8	2	no	—
739	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
740	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
741	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
742	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
743	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	4	no	—
757	C₂²×C₄	—	8	2	no	—
758	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
759	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
760	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
761	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
762	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
763	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
764	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
769	Q₁₆	—	4	4	no	—
770	SD₁₆	—	2	8	no	—
771	SD₁₆	—	4	4	no	—
772	SD₁₆	—	4	4	no	—
773	D₈	—	2	8	no	—
774	D₈	—	4	4	no	—
775	M₁₆	—	4	4	no	—
776	M₁₆	—	4	2	no	—
777	M₁₆	—	4	2	no	—
778	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
779	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	—	2	1	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
791	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
792	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
794	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
812	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
813	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
814	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	C₂×D₄×C₄₁	1	2	yes	—
818	C₄²	C₂⁴×C₄₁	1	2	yes	—
819	C₂³	—	2	4	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	4	1	no	—
826	C₂³	—	4	1	no	—
827	C₂³	—	4	1	no	—
828	C₂³	—	4	1	no	—
829	C₂³	—	4	8	no	—
830	C₂³	—	4	2	no	—
831	C₂³	—	4	2	no	—
832	C₂³	—	4	2	no	—
833	C₂³	—	4	8	no	—
834	C₂³	—	4	2	no	—
835	C₂³	—	4	2	no	—
836	C₂³	—	4	2	no	—
837	C₂³	—	8	4	no	—
838	C₂³	—	8	1	no	—
839	C₂³	—	8	1	no	—
840	C₂³	—	8	16	no	—
841	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
842	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
843	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
844	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
845	Q₈	—	2	4	no	—
846	Q₈	—	2	2	no	—
847	Q₈	—	2	2	no	—
848	Q₈	—	4	2	no	—
849	Q₈	—	8	1	no	—
850	D₄	—	2	4	no	—
851	D₄	—	2	2	no	—
852	D₄	—	2	4	no	—
853	D₄	—	2	4	no	—
854	D₄	—	4	2	no	—
855	D₄	—	4	2	no	—
856	D₄	—	4	8	no	—
857	D₄	—	4	2	no	—
858	D₄	—	4	4	no	—
859	D₄	—	4	4	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	4	no	—
862	D₄	—	8	1	no	—
863	D₄	—	8	2	no	—
864	D₄	—	8	2	no	—
865	D₄	—	8	2	no	—
866	D₄	—	8	2	no	—
867	D₄	H(5,𝔽₂)×C₄₁	1	4	yes	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	4	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	2	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	—	4	1	no	—
884	C₂×C₄	—	4	4	no	—
885	C₂×C₄	—	4	4	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	4	2	no	—
888	C₂×C₄	—	4	2	no	—
889	C₂×C₄	—	8	4	no	—
890	C₂×C₄	—	8	2	no	—
891	C₂×C₄	—	8	2	no	—
892	C₂×C₄	—	8	1	no	—
893	C₂×C₄	—	8	1	no	—
894	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
895	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
896	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
897	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
899	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
900	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
901	C₈	—	2	4	no	—
902	C₈	—	2	4	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	4	no	—
915	C₂²	—	4	4	no	—
916	C₂²	—	4	8	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	8	2	no	—
926	C₂²	—	8	4	no	—
927	C₂²	—	8	16	no	—
928	C₂²	—	16	2	no	—
929	C₂²	C₄₁×#575	1	2	yes	—
930	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	2	no	—
937	C₄	—	4	2	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	2	no	—
942	C₄	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
943	C₂	—	2	2	no	—
944	C₂	—	4	2	no	—
945	C₂	—	4	1	no	—
946	C₂	—	4	1	no	—
947	C₂	—	4	4	no	—
948	C₂	—	8	2	no	—
949	C₂	—	8	2	no	—
950	C₂	C₄₁×#3484	1	1	yes	characteristic
951	C₂	C₂×C₄₁×#575	1	1	yes	characteristic
952	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×#3505	C₂	semidirect
2. C₂×C₄₁×#546	C₂	semidirect
3. C₄₁×#3323	C₂	semidirect
4. C₄₁×#3322	C₂	semidirect
5. C₄₁×#3275	C₂	semidirect
6. C₄₁×#3273	C₂	semidirect
7. C₄₁×#3211	C₂	semidirect
8. C₄₁×#3196	C₂	semidirect
9. C₄₁×#3193	C₂	semidirect
10. C₄₁×#3192	C₂	semidirect
11. C₄₁×#3105	C₂	semidirect
12. C₄₁×#3007	C₂	semidirect
13. C₄₁×#3006	C₂	semidirect
14. C₄₁×#3003	C₂	semidirect
15. C₄₁×#2975	C₂	semidirect
17. C₂³×D₄×C₄₁	C₂²	semidirect
18. C₂×#137×C₄₁	C₂²	semidirect
19. C₂×AGL(1,ℤ/8)×C₄₁	C₂²	semidirect
20. C₂×AGL(1,ℤ/8)×C₄₁	C₂²	semidirect
22. C₄₁×#553	C₂²	semidirect
23. C₄₁×#552	C₂²	semidirect
25. C₄₁×#548	C₂²	semidirect
29. C₄₁×#546	C₂²	semidirect
30. C₄₁×#546	C₂²	semidirect
34. C₄₁×#529	C₂²	semidirect
35. C₂×#124×C₄₁	C₂²	semidirect
38. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
39. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
42. C₂×#121×C₄₁	C₂²	semidirect
46. C₂×C₄×D₄×C₄₁	C₂²	semidirect
48. C₄₁×#495	C₂²	semidirect
49. C₄₁×#488	C₂²	semidirect
50. C₄₁×#485	C₂²	semidirect
51. C₄₁×#484	C₂²	semidirect
52. C₄₁×#481	C₂²	semidirect
53. C₄₁×#481	C₂²	semidirect
54. C₄₁×#480	C₂²	semidirect
55. C₄₁×#478	C₂²	semidirect
56. C₄₁×#470	C₂²	semidirect
57. C₄₁×#469	C₂²	semidirect
58. C₄₁×#468	C₂²	semidirect
59. C₄₁×#468	C₂²	semidirect
60. C₄₁×#464	C₂²	semidirect
61. C₄₁×#463	C₂²	semidirect
62. C₄₁×#463	C₂²	semidirect
63. C₄₁×#452	C₂²	semidirect
64. C₄₁×#452	C₂²	semidirect
65. C₄₁×#451	C₂²	semidirect
66. C₄₁×#450	C₂²	semidirect
67. C₄₁×#450	C₂²	semidirect
68. C₄₁×#450	C₂²	semidirect
69. C₄₁×#449	C₂²	semidirect
70. C₄₁×#448	C₂²	semidirect
71. C₄₁×#448	C₂²	semidirect
74. C₄₁×#447	C₂²	semidirect
75. C₄₁×#447	C₂²	semidirect
76. C₄×SD₁₆×C₄₁	C₂²	semidirect
77. C₄×D₈×C₄₁	C₂²	semidirect
78. C₄₁×#436	C₂²	semidirect
79. C₄₁×#436	C₂²	semidirect
80. C₄₁×#431	C₂²	semidirect
81. C₄₁×#418	C₂²	semidirect
82. C₄₁×#417	C₂²	semidirect
83. C₄₁×#417	C₂²	semidirect
84. C₄₁×#407	C₂²	semidirect
85. C₄₁×#407	C₂²	semidirect
86. C₄₁×#407	C₂²	semidirect
95. C₂²×Q₈×C₄₁	C₂³	semidirect
106. C₂²×D₄×C₄₁	C₂³	semidirect
114. C₂×Q₁₆×C₄₁	C₂³	semidirect
117. C₂×SD₁₆×C₄₁	C₂³	semidirect
121. C₂×M₁₆×C₄₁	C₂³	semidirect
122. C₂×M₁₆×C₄₁	C₂³	semidirect
127. #125×C₄₁	C₂³	semidirect
131. #124×C₄₁	C₂³	semidirect
146. C₂²⋊Q₈×C₄₁	C₂³	semidirect
160. #121×C₄₁	C₂³	semidirect
165. C₄×Q₈×C₄₁	C₂³	semidirect
177. C₄×D₄×C₄₁	C₂³	semidirect
185. C₂×C₄⋊C₄×C₄₁	C₂³	semidirect
186. C₂×C₄⋊C₄×C₄₁	C₂³	semidirect
200. #107×C₄₁	C₂³	semidirect
201. #106×C₄₁	C₂³	semidirect
202. C₄⋊C₈×C₄₁	C₂³	semidirect
203. #103×C₄₁	C₂³	semidirect
204. #103×C₄₁	C₂³	semidirect
205. #103×C₄₁	C₂³	semidirect
210. #102×C₄₁	C₂³	semidirect
214. C₂²⋊C₈×C₄₁	C₂³	semidirect
215. C₂²⋊C₈×C₄₁	C₂³	semidirect
216. C₄×C₈×C₄₁	C₂³	semidirect
426. #61581	C₄₁	direct (N × H)
467. #3505	C₂×C₄₁	semidirect
468. C₂×#546	C₂×C₄₁	semidirect
469. #3323	C₂×C₄₁	semidirect
470. #3322	C₂×C₄₁	semidirect
471. #3275	C₂×C₄₁	semidirect
472. #3273	C₂×C₄₁	semidirect
473. #3211	C₂×C₄₁	semidirect
474. #3196	C₂×C₄₁	semidirect
475. #3193	C₂×C₄₁	semidirect
476. #3192	C₂×C₄₁	semidirect
477. #3105	C₂×C₄₁	semidirect
478. #3007	C₂×C₄₁	semidirect
479. #3006	C₂×C₄₁	semidirect
480. #3003	C₂×C₄₁	semidirect
481. #2975	C₂×C₄₁	semidirect
493. C₂³×D₄	C₂²×C₄₁	semidirect
494. C₂×#137	C₂²×C₄₁	semidirect
495. C₂×AGL(1,ℤ/8)	C₂²×C₄₁	semidirect
496. C₂×AGL(1,ℤ/8)	C₂²×C₄₁	semidirect
498. #553	C₂²×C₄₁	semidirect
499. #552	C₂²×C₄₁	semidirect
501. #548	C₂²×C₄₁	semidirect
505. #546	C₂²×C₄₁	semidirect
506. #546	C₂²×C₄₁	semidirect
510. #529	C₂²×C₄₁	semidirect
511. C₂×#124	C₂²×C₄₁	semidirect
514. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
515. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
518. C₂×#121	C₂²×C₄₁	semidirect
522. C₂×C₄×D₄	C₂²×C₄₁	semidirect
524. #495	C₂²×C₄₁	semidirect
525. #488	C₂²×C₄₁	semidirect
526. #485	C₂²×C₄₁	semidirect
527. #484	C₂²×C₄₁	semidirect
528. #481	C₂²×C₄₁	semidirect
529. #481	C₂²×C₄₁	semidirect
530. #480	C₂²×C₄₁	semidirect
531. #478	C₂²×C₄₁	semidirect
532. #470	C₂²×C₄₁	semidirect
533. #469	C₂²×C₄₁	semidirect
534. #468	C₂²×C₄₁	semidirect
535. #468	C₂²×C₄₁	semidirect
536. #464	C₂²×C₄₁	semidirect
537. #463	C₂²×C₄₁	semidirect
538. #463	C₂²×C₄₁	semidirect
539. #452	C₂²×C₄₁	semidirect
540. #452	C₂²×C₄₁	semidirect
541. #451	C₂²×C₄₁	semidirect
542. #450	C₂²×C₄₁	semidirect
543. #450	C₂²×C₄₁	semidirect
544. #450	C₂²×C₄₁	semidirect
545. #449	C₂²×C₄₁	semidirect
546. #448	C₂²×C₄₁	semidirect
547. #448	C₂²×C₄₁	semidirect
550. #447	C₂²×C₄₁	semidirect
551. #447	C₂²×C₄₁	semidirect
552. C₄×SD₁₆	C₂²×C₄₁	semidirect
553. C₄×D₈	C₂²×C₄₁	semidirect
554. #436	C₂²×C₄₁	semidirect
555. #436	C₂²×C₄₁	semidirect
556. #431	C₂²×C₄₁	semidirect
557. #418	C₂²×C₄₁	semidirect
558. #417	C₂²×C₄₁	semidirect
559. #417	C₂²×C₄₁	semidirect
560. #407	C₂²×C₄₁	semidirect
561. #407	C₂²×C₄₁	semidirect
562. #407	C₂²×C₄₁	semidirect
563. C₄₁	#61581	direct (N × H)
572. C₂²×Q₈	C₂³×C₄₁	semidirect
583. C₂²×D₄	C₂³×C₄₁	semidirect
591. C₂×Q₁₆	C₂³×C₄₁	semidirect
594. C₂×SD₁₆	C₂³×C₄₁	semidirect
598. C₂×M₁₆	C₂³×C₄₁	semidirect
599. C₂×M₁₆	C₂³×C₄₁	semidirect
604. #125	C₂³×C₄₁	semidirect
608. #124	C₂³×C₄₁	semidirect
623. C₂²⋊Q₈	C₂³×C₄₁	semidirect
637. #121	C₂³×C₄₁	semidirect
642. C₄×Q₈	C₂³×C₄₁	semidirect
654. C₄×D₄	C₂³×C₄₁	semidirect
662. C₂×C₄⋊C₄	C₂³×C₄₁	semidirect
663. C₂×C₄⋊C₄	C₂³×C₄₁	semidirect
677. #107	C₂³×C₄₁	semidirect
678. #106	C₂³×C₄₁	semidirect
679. C₄⋊C₈	C₂³×C₄₁	semidirect
680. #103	C₂³×C₄₁	semidirect
681. #103	C₂³×C₄₁	semidirect
682. #103	C₂³×C₄₁	semidirect
687. #102	C₂³×C₄₁	semidirect
691. C₂²⋊C₈	C₂³×C₄₁	semidirect
692. C₂²⋊C₈	C₂³×C₄₁	semidirect
693. C₄×C₈	C₂³×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3505	2
C₂×C₄₁×#546	2
C₄₁×#3323	2
C₄₁×#3322	2
C₄₁×#3275	2
C₄₁×#3273	2
C₄₁×#3211	2
C₄₁×#3196	2
C₄₁×#3193	2
C₄₁×#3192	2
C₄₁×#3105	2
C₄₁×#3007	2
C₄₁×#3006	2
C₄₁×#3003	2
C₄₁×#2975	2
#61581	41

Subgroups — C41×#61581 #23837782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61581 #23837782