Subgroups — C₄₁×#61986 #23838187

Order 10496.

1906 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3400	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3373	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3311	C₂	1	4	yes	maximal, complemented
6	C₄₁×#3304	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3284	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3267	C₂	1	4	yes	maximal, complemented
9	C₄₁×#3255	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3246	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3216	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3115	C₂	1	2	yes	maximal, complemented
14	C₄₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#3035	C₂	1	2	yes	maximal, complemented
17	C₄₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	2	yes	—
19	C₂×#135×C₄₁	C₂²	1	4	yes	complemented
20	C₄₁×#559	—	2	1	no	—
21	C₄₁×#559	C₂²	1	2	yes	—
22	C₄₁×#557	C₂²	1	1	yes	characteristic, complemented
23	C₄₁×#556	C₂²	1	2	yes	—
24	C₄₁×#556	C₂²	1	1	yes	characteristic, complemented
25	C₄₁×#552	—	2	2	no	—
26	C₄₁×#552	—	2	1	no	—
27	C₄₁×#550	—	2	1	no	—
28	C₄₁×#550	C₂²	1	2	yes	—
29	D₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
30	C₄₁×#548	—	2	1	no	—
31	C₄₁×#547	C₂²	1	2	yes	—
32	C₄₁×#547	C₂²	1	1	yes	characteristic, complemented
33	C₄₁×#546	—	2	2	no	—
34	C₄₁×#546	C₂²	1	4	yes	—
35	C₄₁×#540	—	2	2	no	—
36	C₄₁×#535	—	2	1	no	—
37	C₄₁×#533	C₂²	1	1	yes	characteristic
38	C₄₁×#533	C₂²	1	1	yes	characteristic
39	C₄₁×#533	C₂²	1	2	yes	complemented
40	C₄₁×#532	C₂²	1	2	yes	—
41	C₄₁×#532	C₂²	1	2	yes	—
42	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
43	C₄₁×#529	—	2	1	no	—
44	C₄₁×#529	—	2	2	no	—
45	C₄₁×#518	—	2	1	no	—
46	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
47	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
48	C₄×#41×C₄₁	C₂²	1	2	yes	complemented
49	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
50	C₄₁×#497	C₂²	1	4	yes	complemented
51	C₄₁×#492	C₂²	1	2	yes	—
52	C₄₁×#489	C₂²	1	4	yes	complemented
53	C₄₁×#486	C₂²	1	2	yes	—
54	C₄₁×#485	C₂²	1	2	yes	—
55	C₄₁×#482	C₂²	1	4	yes	complemented
56	C₄₁×#476	C₂²	1	4	yes	complemented
57	C₄₁×#475	C₂²	1	2	yes	complemented
58	C₄₁×#475	C₂²	1	1	yes	characteristic, complemented
59	C₄₁×#475	C₂²	1	2	yes	complemented
60	C₄₁×#474	C₂²	1	1	yes	characteristic, complemented
61	C₄₁×#470	C₂²	1	4	yes	—
62	C₄₁×#465	C₂²	1	4	yes	complemented
63	C₄₁×#465	C₂²	1	4	yes	complemented
64	C₄₁×#464	C₂²	1	4	yes	complemented
65	C₄₁×#463	C₂²	1	4	yes	complemented
66	C₄₁×#462	C₂²	1	1	yes	characteristic, complemented
67	C₄₁×#462	C₂²	1	2	yes	complemented
68	C₄₁×#462	C₂²	1	2	yes	complemented
69	C₄₁×#461	C₂²	1	1	yes	characteristic, complemented
70	C₄₁×#461	C₂²	1	4	yes	complemented
71	C₄₁×#460	C₂²	1	2	yes	—
72	C₄₁×#460	C₂²	1	2	yes	—
73	C₄₁×#460	C₂²	1	2	yes	—
74	C₄₁×#460	C₂²	1	2	yes	—
75	C₄₁×#459	C₂²	1	2	yes	—
76	C₄₁×#459	C₂²	1	2	yes	—
77	C₄₁×#452	C₂²	1	2	yes	—
78	C₄₁×#452	C₂²	1	4	yes	complemented
79	C₄₁×#452	C₂²	1	4	yes	complemented
80	C₄₁×#450	C₂²	1	4	yes	—
81	C₄₁×#449	C₂²	1	4	yes	complemented
82	C₄₁×#446	C₂²	1	2	yes	complemented
83	C₄₁×#442	C₂²	1	4	yes	complemented
84	C₄₁×#440	C₂²	1	4	yes	complemented
85	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
86	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
87	C₄₁×#435	C₂²	1	4	yes	—
88	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
89	C₄₁×#432	C₂²	1	2	yes	complemented
90	C₄₁×#431	C₂²	1	1	yes	characteristic
91	C₄₁×#423	C₂²	1	1	yes	characteristic
92	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	complemented
93	C₄₁×#418	C₂²	1	2	yes	—
94	C₄₁×#416	C₂²	1	4	yes	complemented
95	C₂×#41×C₄₁	—	2	2	no	—
96	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
97	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
98	C₂×#41×C₄₁	C₂³	1	2	yes	—
99	C₂×#41×C₄₁	C₂³	1	4	yes	—
100	C₂²×Q₈×C₄₁	—	2	1	no	—
101	C₂²×D₄×C₄₁	—	2	1	no	—
102	C₂²×D₄×C₄₁	—	2	1	no	—
103	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
104	AGL(1,ℤ/8)×C₄₁	—	4	4	no	—
105	#135×C₄₁	—	4	8	no	—
106	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
107	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
112	C₂×D₈×C₄₁	C₂³	1	4	yes	—
113	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
114	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
115	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
117	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
118	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
121	#127×C₄₁	—	2	2	no	—
122	#127×C₄₁	—	2	1	no	—
123	#127×C₄₁	—	2	1	no	—
124	#127×C₄₁	C₂³	1	2	yes	—
125	#127×C₄₁	C₂³	1	2	yes	—
126	#126×C₄₁	—	2	2	no	—
127	#126×C₄₁	—	2	2	no	—
128	#126×C₄₁	—	2	2	no	—
129	#125×C₄₁	—	2	1	no	—
130	#125×C₄₁	—	2	2	no	—
131	#125×C₄₁	—	2	1	no	—
132	#125×C₄₁	—	2	1	no	—
133	#125×C₄₁	—	2	2	no	—
134	#124×C₄₁	—	2	2	no	—
135	#124×C₄₁	—	2	2	no	—
136	#124×C₄₁	—	2	1	no	—
137	#124×C₄₁	—	2	2	no	—
138	#124×C₄₁	C₂³	1	4	yes	—
139	#123×C₄₁	—	2	4	no	—
140	#123×C₄₁	—	2	4	no	—
141	#123×C₄₁	—	2	2	no	—
142	#123×C₄₁	—	2	2	no	—
143	#123×C₄₁	—	2	2	no	—
144	C₂²⋊Q₈×C₄₁	—	2	1	no	—
145	C₂²⋊Q₈×C₄₁	—	2	1	no	—
146	C₂²⋊Q₈×C₄₁	—	2	2	no	—
147	C₂²⋊Q₈×C₄₁	—	2	1	no	—
148	C₂²⋊Q₈×C₄₁	—	2	2	no	—
149	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
150	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
151	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
152	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
153	#121×C₄₁	—	2	2	no	—
154	#121×C₄₁	—	2	1	no	—
155	#121×C₄₁	—	2	2	no	—
156	#121×C₄₁	—	2	2	no	—
157	#121×C₄₁	—	2	2	no	—
158	#121×C₄₁	—	2	4	no	—
159	#121×C₄₁	—	2	4	no	—
160	#121×C₄₁	C₂³	1	4	yes	—
161	#120×C₄₁	—	2	4	no	—
162	C₄×Q₈×C₄₁	—	2	1	no	—
163	C₄×Q₈×C₄₁	—	2	2	no	—
164	C₄×Q₈×C₄₁	—	2	1	no	—
165	C₄×Q₈×C₄₁	—	2	1	no	—
166	C₄×Q₈×C₄₁	—	2	2	no	—
167	C₄×Q₈×C₄₁	—	2	1	no	—
168	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
169	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
172	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
173	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
174	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₄₁	—	2	1	no	—
176	C₄×D₄×C₄₁	—	2	1	no	—
177	C₄×D₄×C₄₁	—	2	2	no	—
178	C₄×D₄×C₄₁	—	2	2	no	—
179	C₄×D₄×C₄₁	—	2	2	no	—
180	C₄×D₄×C₄₁	—	2	2	no	—
181	C₄×D₄×C₄₁	—	2	2	no	—
182	C₄×D₄×C₄₁	—	2	2	no	—
183	C₄×D₄×C₄₁	—	2	2	no	—
184	C₄×D₄×C₄₁	D₄	1	2	yes	—
185	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
186	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₄₁	C₂³	1	2	yes	—
189	C₄×D₄×C₄₁	C₂³	1	4	yes	—
190	C₄×D₄×C₄₁	C₂³	1	2	yes	—
191	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
192	#117×C₄₁	—	2	1	no	—
193	#117×C₄₁	—	2	1	no	—
194	#117×C₄₁	—	2	2	no	—
195	#117×C₄₁	—	2	1	no	—
196	#117×C₄₁	—	2	2	no	—
197	#117×C₄₁	D₄	1	1	yes	characteristic
198	#117×C₄₁	D₄	1	2	yes	—
199	#117×C₄₁	C₂³	1	1	yes	characteristic
200	#117×C₄₁	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
202	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
203	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
204	C₂×C₄²×C₄₁	—	2	1	no	—
205	C₂×C₄²×C₄₁	—	2	2	no	—
206	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
208	#107×C₄₁	C₂³	1	2	yes	—
209	#106×C₄₁	C₂³	1	2	yes	—
210	#106×C₄₁	C₂³	1	4	yes	—
211	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
212	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
213	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
214	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
215	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
216	#103×C₄₁	C₂³	1	2	yes	—
217	#103×C₄₁	C₂³	1	4	yes	—
218	#103×C₄₁	C₂³	1	2	yes	—
219	#103×C₄₁	C₂³	1	2	yes	—
220	#103×C₄₁	C₂³	1	4	yes	—
221	#102×C₄₁	C₂³	1	4	yes	—
222	#102×C₄₁	C₂³	1	4	yes	—
223	#102×C₄₁	C₂³	1	4	yes	—
224	#102×C₄₁	C₂³	1	2	yes	—
225	#102×C₄₁	C₂³	1	4	yes	—
226	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
227	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
228	#97×C₄₁	C₂³	1	4	yes	—
229	C₄×C₈×C₄₁	C₂³	1	2	yes	—
230	C₂⁴×C₄₁	—	2	2	no	—
231	#41×C₄₁	—	2	4	no	—
232	#41×C₄₁	—	2	2	no	—
233	#41×C₄₁	—	4	2	no	—
234	#41×C₄₁	—	4	1	no	—
235	#41×C₄₁	—	4	2	no	—
236	#41×C₄₁	—	4	4	no	—
237	#41×C₄₁	—	4	4	no	—
238	#41×C₄₁	—	8	4	no	—
239	C₂×Q₈×C₄₁	—	2	2	no	—
240	C₂×Q₈×C₄₁	—	2	1	no	—
241	C₂×Q₈×C₄₁	—	2	1	no	—
242	C₂×Q₈×C₄₁	—	4	4	no	—
243	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
246	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
247	C₂×D₄×C₄₁	—	2	1	no	—
248	C₂×D₄×C₄₁	—	2	2	no	—
249	C₂×D₄×C₄₁	—	2	4	no	—
250	C₂×D₄×C₄₁	—	2	4	no	—
251	C₂×D₄×C₄₁	—	2	2	no	—
252	C₂×D₄×C₄₁	—	2	2	no	—
253	C₂×D₄×C₄₁	—	2	2	no	—
254	C₂×D₄×C₄₁	—	2	2	no	—
255	C₂×D₄×C₄₁	—	2	2	no	—
256	C₂×D₄×C₄₁	—	4	2	no	—
257	C₂×D₄×C₄₁	—	4	2	no	—
258	C₂×D₄×C₄₁	—	4	4	no	—
259	C₂×D₄×C₄₁	—	8	2	no	—
260	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
261	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
262	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
263	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₄₁	—	2	1	no	—
265	C₂²×C₄×C₄₁	—	2	2	no	—
266	C₂²×C₄×C₄₁	—	2	1	no	—
267	C₂²×C₄×C₄₁	—	2	2	no	—
268	C₂²×C₄×C₄₁	—	2	1	no	—
269	C₂²×C₄×C₄₁	—	2	4	no	—
270	C₂²×C₄×C₄₁	—	2	4	no	—
271	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
277	Q₁₆×C₄₁	—	4	2	no	—
278	Q₁₆×C₄₁	—	4	4	no	—
279	SD₁₆×C₄₁	—	2	4	no	—
280	SD₁₆×C₄₁	—	4	4	no	—
281	SD₁₆×C₄₁	—	4	4	no	—
282	SD₁₆×C₄₁	—	4	4	no	—
283	D₈×C₄₁	—	2	8	no	—
284	M₁₆×C₄₁	—	4	2	no	—
285	C₂×C₈×C₄₁	—	4	4	no	—
286	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
287	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
288	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
289	C₄⋊C₄×C₄₁	—	2	2	no	—
290	C₄⋊C₄×C₄₁	—	2	1	no	—
291	C₄⋊C₄×C₄₁	—	2	2	no	—
292	C₄⋊C₄×C₄₁	—	2	2	no	—
293	C₄⋊C₄×C₄₁	—	2	2	no	—
294	C₄⋊C₄×C₄₁	—	2	1	no	—
295	C₄⋊C₄×C₄₁	—	2	1	no	—
296	C₄⋊C₄×C₄₁	—	2	1	no	—
297	C₄⋊C₄×C₄₁	—	2	2	no	—
298	C₄⋊C₄×C₄₁	—	2	2	no	—
299	C₄⋊C₄×C₄₁	—	2	1	no	—
300	C₄⋊C₄×C₄₁	—	2	2	no	—
301	C₄⋊C₄×C₄₁	—	2	1	no	—
302	C₄⋊C₄×C₄₁	—	2	2	no	—
303	C₄⋊C₄×C₄₁	—	2	1	no	—
304	C₄⋊C₄×C₄₁	—	2	1	no	—
305	C₄⋊C₄×C₄₁	—	2	2	no	—
306	C₄⋊C₄×C₄₁	—	2	2	no	—
307	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
308	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
315	C₂²⋊C₄×C₄₁	—	2	2	no	—
316	C₂²⋊C₄×C₄₁	—	2	2	no	—
317	C₂²⋊C₄×C₄₁	—	2	2	no	—
318	C₂²⋊C₄×C₄₁	—	2	2	no	—
319	C₂²⋊C₄×C₄₁	—	2	1	no	—
320	C₂²⋊C₄×C₄₁	—	2	2	no	—
321	C₂²⋊C₄×C₄₁	—	2	4	no	—
322	C₂²⋊C₄×C₄₁	—	2	4	no	—
323	C₂²⋊C₄×C₄₁	—	2	1	no	—
324	C₂²⋊C₄×C₄₁	—	2	2	no	—
325	C₂²⋊C₄×C₄₁	—	2	1	no	—
326	C₂²⋊C₄×C₄₁	—	2	4	no	—
327	C₂²⋊C₄×C₄₁	—	2	4	no	—
328	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
329	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
331	C₄²×C₄₁	—	2	1	no	—
332	C₄²×C₄₁	—	2	2	no	—
333	C₄²×C₄₁	—	2	2	no	—
334	C₄²×C₄₁	—	2	1	no	—
335	C₄²×C₄₁	—	2	2	no	—
336	C₄²×C₄₁	—	2	1	no	—
337	C₄²×C₄₁	—	2	2	no	—
338	C₄²×C₄₁	C₂×D₄	1	2	yes	—
339	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₄₁	C₂×D₄	1	2	yes	—
341	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
343	C₄²×C₄₁	C₂⁴	1	2	yes	—
344	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
345	C₂³×C₄₁	—	2	1	no	—
346	C₂³×C₄₁	—	2	4	no	—
347	C₂³×C₄₁	—	4	4	no	—
348	C₂³×C₄₁	—	8	2	no	—
349	C₂³×C₄₁	—	8	2	no	—
350	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
351	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
352	Q₈×C₄₁	—	2	2	no	—
353	Q₈×C₄₁	—	2	2	no	—
354	Q₈×C₄₁	—	2	1	no	—
355	Q₈×C₄₁	—	2	2	no	—
356	Q₈×C₄₁	—	2	2	no	—
357	Q₈×C₄₁	—	2	1	no	—
358	Q₈×C₄₁	—	2	2	no	—
359	Q₈×C₄₁	—	4	4	no	—
360	Q₈×C₄₁	—	4	2	no	—
361	Q₈×C₄₁	—	4	2	no	—
362	D₄×C₄₁	—	2	2	no	—
363	D₄×C₄₁	—	2	4	no	—
364	D₄×C₄₁	—	2	1	no	—
365	D₄×C₄₁	—	2	4	no	—
366	D₄×C₄₁	—	4	2	no	—
367	D₄×C₄₁	—	4	4	no	—
368	D₄×C₄₁	—	4	4	no	—
369	D₄×C₄₁	—	4	2	no	—
370	D₄×C₄₁	—	4	4	no	—
371	D₄×C₄₁	—	4	4	no	—
372	D₄×C₄₁	—	8	2	no	—
373	D₄×C₄₁	—	8	2	no	—
374	D₄×C₄₁	—	8	4	no	—
375	D₄×C₄₁	—	8	4	no	—
376	D₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
377	C₂×C₄×C₄₁	—	2	2	no	—
378	C₂×C₄×C₄₁	—	2	2	no	—
379	C₂×C₄×C₄₁	—	2	4	no	—
380	C₂×C₄×C₄₁	—	2	2	no	—
381	C₂×C₄×C₄₁	—	2	1	no	—
382	C₂×C₄×C₄₁	—	2	1	no	—
383	C₂×C₄×C₄₁	—	2	2	no	—
384	C₂×C₄×C₄₁	—	2	1	no	—
385	C₂×C₄×C₄₁	—	2	2	no	—
386	C₂×C₄×C₄₁	—	2	1	no	—
387	C₂×C₄×C₄₁	—	2	1	no	—
388	C₂×C₄×C₄₁	—	2	2	no	—
389	C₂×C₄×C₄₁	—	2	2	no	—
390	C₂×C₄×C₄₁	—	2	2	no	—
391	C₂×C₄×C₄₁	—	4	2	no	—
392	C₂×C₄×C₄₁	—	4	4	no	—
393	C₂×C₄×C₄₁	—	4	2	no	—
394	C₂×C₄×C₄₁	—	4	4	no	—
395	C₂×C₄×C₄₁	—	4	2	no	—
396	C₂×C₄×C₄₁	—	4	2	no	—
397	C₂×C₄×C₄₁	—	8	4	no	—
398	C₂×C₄×C₄₁	—	8	4	no	—
399	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
408	C₈×C₄₁	—	2	2	no	—
409	C₈×C₄₁	—	2	4	no	—
410	C₈×C₄₁	—	2	2	no	—
411	#61986	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
412	C₂²×C₄₁	—	2	2	no	—
413	C₂²×C₄₁	—	2	1	no	—
414	C₂²×C₄₁	—	2	2	no	—
415	C₂²×C₄₁	—	2	1	no	—
416	C₂²×C₄₁	—	2	2	no	—
417	C₂²×C₄₁	—	2	2	no	—
418	C₂²×C₄₁	—	2	1	no	—
419	C₂²×C₄₁	—	4	1	no	—
420	C₂²×C₄₁	—	4	1	no	—
421	C₂²×C₄₁	—	4	4	no	—
422	C₂²×C₄₁	—	4	4	no	—
423	C₂²×C₄₁	—	4	4	no	—
424	C₂²×C₄₁	—	16	4	no	—
425	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
426	C₄×C₄₁	—	2	2	no	—
427	C₄×C₄₁	—	2	1	no	—
428	C₄×C₄₁	—	2	1	no	—
429	C₄×C₄₁	—	2	2	no	—
430	C₄×C₄₁	—	2	2	no	—
431	C₄×C₄₁	—	2	1	no	—
432	C₄×C₄₁	—	4	1	no	—
433	C₄×C₄₁	—	4	2	no	—
434	C₄×C₄₁	—	4	2	no	—
435	C₄×C₄₁	—	4	2	no	—
436	C₄×C₄₁	—	4	1	no	—
437	C₄×C₄₁	—	4	1	no	—
438	C₄×C₄₁	—	4	2	no	—
439	C₄×C₄₁	#575	1	2	yes	—
440	C₄×C₄₁	#577	1	2	yes	—
441	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
442	C₄×C₄₁	#585	1	1	yes	characteristic
443	#3508	C₂×C₄₁	1	1	yes	characteristic, complemented
444	#3482	C₂×C₄₁	1	1	yes	characteristic, complemented
445	#3400	C₂×C₄₁	1	2	yes	complemented
446	#3373	C₂×C₄₁	1	2	yes	complemented
447	#3311	C₂×C₄₁	1	4	yes	complemented
448	#3304	C₂×C₄₁	1	2	yes	complemented
449	#3284	C₂×C₄₁	1	2	yes	complemented
450	#3267	C₂×C₄₁	1	4	yes	complemented
451	#3255	C₂×C₄₁	1	1	yes	characteristic, complemented
452	#3246	C₂×C₄₁	1	2	yes	complemented
453	#3216	C₂×C₄₁	1	2	yes	complemented
454	#3208	C₂×C₄₁	1	1	yes	characteristic, complemented
455	#3115	C₂×C₄₁	1	2	yes	complemented
456	#3107	C₂×C₄₁	1	1	yes	characteristic, complemented
457	#3038	C₂×C₄₁	1	1	yes	characteristic, complemented
458	#3035	C₂×C₄₁	1	2	yes	complemented
459	#2990	C₂×C₄₁	1	1	yes	characteristic, complemented
460	C₂×C₄₁	—	4	2	no	—
461	C₂×C₄₁	—	4	1	no	—
462	C₂×C₄₁	—	4	2	no	—
463	C₂×C₄₁	—	8	4	no	—
464	C₂×C₄₁	#3488	1	1	yes	characteristic
465	C₂×C₄₁	C₂×#575	1	1	yes	characteristic
466	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
467	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	2	yes	—
468	C₂×#135	C₂²×C₄₁	1	4	yes	complemented
469	#559	—	2	1	no	—
470	#559	C₂²×C₄₁	1	2	yes	—
471	#557	C₂²×C₄₁	1	1	yes	characteristic, complemented
472	#556	C₂²×C₄₁	1	2	yes	—
473	#556	C₂²×C₄₁	1	1	yes	characteristic, complemented
474	#552	—	2	2	no	—
475	#552	—	2	1	no	—
476	#550	—	2	1	no	—
477	#550	C₂²×C₄₁	1	2	yes	—
478	D₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
479	#548	—	2	1	no	—
480	#547	C₂²×C₄₁	1	2	yes	—
481	#547	C₂²×C₄₁	1	1	yes	characteristic, complemented
482	#546	—	2	2	no	—
483	#546	C₂²×C₄₁	1	4	yes	—
484	#540	—	2	2	no	—
485	#535	—	2	1	no	—
486	#533	C₂²×C₄₁	1	1	yes	characteristic
487	#533	C₂²×C₄₁	1	1	yes	characteristic
488	#533	C₂²×C₄₁	1	2	yes	complemented
489	#532	C₂²×C₄₁	1	2	yes	—
490	#532	C₂²×C₄₁	1	2	yes	—
491	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
492	#529	—	2	1	no	—
493	#529	—	2	2	no	—
494	#518	—	2	1	no	—
495	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
496	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
497	C₄×#41	C₂²×C₄₁	1	2	yes	complemented
498	C₂×C₄×Q₈	—	2	1	no	—
499	#497	C₂²×C₄₁	1	4	yes	complemented
500	#492	C₂²×C₄₁	1	2	yes	—
501	#489	C₂²×C₄₁	1	4	yes	complemented
502	#486	C₂²×C₄₁	1	2	yes	—
503	#485	C₂²×C₄₁	1	2	yes	—
504	#482	C₂²×C₄₁	1	4	yes	complemented
505	#476	C₂²×C₄₁	1	4	yes	complemented
506	#475	C₂²×C₄₁	1	1	yes	characteristic, complemented
507	#475	C₂²×C₄₁	1	2	yes	complemented
508	#475	C₂²×C₄₁	1	2	yes	complemented
509	#474	C₂²×C₄₁	1	1	yes	characteristic, complemented
510	#470	C₂²×C₄₁	1	4	yes	—
511	#465	C₂²×C₄₁	1	4	yes	complemented
512	#465	C₂²×C₄₁	1	4	yes	complemented
513	#464	C₂²×C₄₁	1	4	yes	complemented
514	#463	C₂²×C₄₁	1	4	yes	complemented
515	#462	C₂²×C₄₁	1	1	yes	characteristic, complemented
516	#462	C₂²×C₄₁	1	2	yes	complemented
517	#462	C₂²×C₄₁	1	2	yes	complemented
518	#461	C₂²×C₄₁	1	1	yes	characteristic, complemented
519	#461	C₂²×C₄₁	1	4	yes	complemented
520	#460	C₂²×C₄₁	1	2	yes	—
521	#460	C₂²×C₄₁	1	2	yes	—
522	#460	C₂²×C₄₁	1	2	yes	—
523	#460	C₂²×C₄₁	1	2	yes	—
524	#459	C₂²×C₄₁	1	2	yes	—
525	#459	C₂²×C₄₁	1	2	yes	—
526	#452	C₂²×C₄₁	1	2	yes	—
527	#452	C₂²×C₄₁	1	4	yes	complemented
528	#452	C₂²×C₄₁	1	4	yes	complemented
529	#450	C₂²×C₄₁	1	4	yes	—
530	#449	C₂²×C₄₁	1	4	yes	complemented
531	#446	C₂²×C₄₁	1	2	yes	complemented
532	#442	C₂²×C₄₁	1	4	yes	complemented
533	#440	C₂²×C₄₁	1	4	yes	complemented
534	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
535	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
536	#435	C₂²×C₄₁	1	4	yes	—
537	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
538	#432	C₂²×C₄₁	1	2	yes	complemented
539	#431	C₂²×C₄₁	1	1	yes	characteristic
540	#423	C₂²×C₄₁	1	1	yes	characteristic
541	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
542	#418	C₂²×C₄₁	1	2	yes	—
543	#416	C₂²×C₄₁	1	4	yes	complemented
544	C₄₁	#61986	1	1	yes	characteristic, direct product factor, Sylow
545	C₂×#41	—	2	2	no	—
546	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
547	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
548	C₂×#41	C₂³×C₄₁	1	2	yes	—
549	C₂×#41	C₂³×C₄₁	1	4	yes	—
550	C₂²×Q₈	—	2	1	no	—
551	C₂²×D₄	—	2	1	no	—
552	C₂²×D₄	—	2	1	no	—
553	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
554	AGL(1,ℤ/8)	—	4	4	no	—
555	#135	—	4	8	no	—
556	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
557	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
558	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
559	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
560	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
561	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
562	C₂×D₈	C₂³×C₄₁	1	4	yes	—
563	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
564	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
565	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
566	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
567	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
568	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
569	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
570	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
571	#127	—	2	2	no	—
572	#127	—	2	1	no	—
573	#127	—	2	1	no	—
574	#127	C₂³×C₄₁	1	2	yes	—
575	#127	C₂³×C₄₁	1	2	yes	—
576	#126	—	2	2	no	—
577	#126	—	2	2	no	—
578	#126	—	2	2	no	—
579	#125	—	2	1	no	—
580	#125	—	2	2	no	—
581	#125	—	2	1	no	—
582	#125	—	2	1	no	—
583	#125	—	2	2	no	—
584	#124	—	2	2	no	—
585	#124	—	2	2	no	—
586	#124	—	2	1	no	—
587	#124	—	2	2	no	—
588	#124	C₂³×C₄₁	1	4	yes	—
589	#123	—	2	4	no	—
590	#123	—	2	4	no	—
591	#123	—	2	2	no	—
592	#123	—	2	2	no	—
593	#123	—	2	2	no	—
594	C₂²⋊Q₈	—	2	1	no	—
595	C₂²⋊Q₈	—	2	1	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	—	2	1	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
600	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
601	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
602	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
603	#121	—	2	2	no	—
604	#121	—	2	1	no	—
605	#121	—	2	2	no	—
606	#121	—	2	2	no	—
607	#121	—	2	2	no	—
608	#121	—	2	4	no	—
609	#121	—	2	4	no	—
610	#121	C₂³×C₄₁	1	4	yes	—
611	#120	—	2	4	no	—
612	C₄×Q₈	—	2	1	no	—
613	C₄×Q₈	—	2	2	no	—
614	C₄×Q₈	—	2	1	no	—
615	C₄×Q₈	—	2	1	no	—
616	C₄×Q₈	—	2	2	no	—
617	C₄×Q₈	—	2	1	no	—
618	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
619	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
620	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
621	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
622	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
623	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
624	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	D₄×C₄₁	1	2	yes	—
635	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
636	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
637	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
638	C₄×D₄	C₂³×C₄₁	1	2	yes	—
639	C₄×D₄	C₂³×C₄₁	1	4	yes	—
640	C₄×D₄	C₂³×C₄₁	1	2	yes	—
641	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
642	#117	—	2	1	no	—
643	#117	—	2	1	no	—
644	#117	—	2	2	no	—
645	#117	—	2	1	no	—
646	#117	—	2	2	no	—
647	#117	D₄×C₄₁	1	1	yes	characteristic
648	#117	D₄×C₄₁	1	2	yes	—
649	#117	C₂³×C₄₁	1	1	yes	characteristic
650	#117	C₂³×C₄₁	1	2	yes	—
651	C₂×C₄⋊C₄	—	2	2	no	—
652	C₂×C₄⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	2	4	no	—
654	C₂×C₄²	—	2	1	no	—
655	C₂×C₄²	—	2	2	no	—
656	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
658	#107	C₂³×C₄₁	1	2	yes	—
659	#106	C₂³×C₄₁	1	2	yes	—
660	#106	C₂³×C₄₁	1	4	yes	—
661	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
662	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
663	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
664	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
665	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
666	#103	C₂³×C₄₁	1	2	yes	—
667	#103	C₂³×C₄₁	1	4	yes	—
668	#103	C₂³×C₄₁	1	2	yes	—
669	#103	C₂³×C₄₁	1	2	yes	—
670	#103	C₂³×C₄₁	1	4	yes	—
671	#102	C₂³×C₄₁	1	4	yes	—
672	#102	C₂³×C₄₁	1	4	yes	—
673	#102	C₂³×C₄₁	1	4	yes	—
674	#102	C₂³×C₄₁	1	2	yes	—
675	#102	C₂³×C₄₁	1	4	yes	—
676	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
677	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
678	#97	C₂³×C₄₁	1	4	yes	—
679	C₄×C₈	C₂³×C₄₁	1	2	yes	—
680	C₂⁴	—	2	2	no	—
681	#41	—	2	4	no	—
682	#41	—	2	2	no	—
683	#41	—	4	2	no	—
684	#41	—	4	1	no	—
685	#41	—	4	2	no	—
686	#41	—	4	4	no	—
687	#41	—	4	4	no	—
688	#41	—	8	4	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	2	1	no	—
691	C₂×Q₈	—	2	1	no	—
692	C₂×Q₈	—	4	4	no	—
693	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
694	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
695	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
696	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂×D₄	—	4	4	no	—
709	C₂×D₄	—	8	2	no	—
710	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
711	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
712	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
713	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
722	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
723	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
724	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
727	Q₁₆	—	4	2	no	—
728	Q₁₆	—	4	4	no	—
729	SD₁₆	—	2	4	no	—
730	SD₁₆	—	4	4	no	—
731	SD₁₆	—	4	4	no	—
732	SD₁₆	—	4	4	no	—
733	D₈	—	2	8	no	—
734	M₁₆	—	4	2	no	—
735	C₂×C₈	—	4	4	no	—
736	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
737	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
738	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	1	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
758	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
759	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
760	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
761	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
762	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
763	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
764	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	1	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
779	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
780	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
781	C₄²	—	2	1	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	1	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	1	no	—
787	C₄²	—	2	2	no	—
788	C₄²	C₂×D₄×C₄₁	1	2	yes	—
789	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
790	C₄²	C₂×D₄×C₄₁	1	2	yes	—
791	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
792	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
793	C₄²	C₂⁴×C₄₁	1	2	yes	—
794	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
795	C₂³	—	2	1	no	—
796	C₂³	—	2	4	no	—
797	C₂³	—	4	4	no	—
798	C₂³	—	8	2	no	—
799	C₂³	—	8	2	no	—
800	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
801	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
802	Q₈	—	2	2	no	—
803	Q₈	—	2	2	no	—
804	Q₈	—	2	1	no	—
805	Q₈	—	2	2	no	—
806	Q₈	—	2	2	no	—
807	Q₈	—	2	1	no	—
808	Q₈	—	2	2	no	—
809	Q₈	—	4	4	no	—
810	Q₈	—	4	2	no	—
811	Q₈	—	4	2	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	4	no	—
814	D₄	—	2	1	no	—
815	D₄	—	2	4	no	—
816	D₄	—	4	2	no	—
817	D₄	—	4	4	no	—
818	D₄	—	4	4	no	—
819	D₄	—	4	2	no	—
820	D₄	—	4	4	no	—
821	D₄	—	4	4	no	—
822	D₄	—	8	2	no	—
823	D₄	—	8	2	no	—
824	D₄	—	8	4	no	—
825	D₄	—	8	4	no	—
826	D₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	4	2	no	—
842	C₂×C₄	—	4	4	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	4	4	no	—
845	C₂×C₄	—	4	2	no	—
846	C₂×C₄	—	4	2	no	—
847	C₂×C₄	—	8	4	no	—
848	C₂×C₄	—	8	4	no	—
849	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
850	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
851	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
852	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
853	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
854	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
855	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
856	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
857	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
858	C₈	—	2	2	no	—
859	C₈	—	2	4	no	—
860	C₈	—	2	2	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	1	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	4	no	—
871	C₂²	—	4	4	no	—
872	C₂²	—	4	4	no	—
873	C₂²	—	16	4	no	—
874	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
875	C₄	—	2	1	no	—
876	C₄	—	2	2	no	—
877	C₄	—	2	2	no	—
878	C₄	—	2	1	no	—
879	C₄	—	2	2	no	—
880	C₄	—	2	1	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	2	no	—
887	C₄	—	4	2	no	—
888	C₄	C₄₁×#575	1	2	yes	—
889	C₄	C₄₁×#577	1	2	yes	—
890	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
891	C₄	C₄₁×#585	1	1	yes	characteristic
892	C₂	—	4	1	no	—
893	C₂	—	4	2	no	—
894	C₂	—	4	2	no	—
895	C₂	—	8	4	no	—
896	C₂	C₄₁×#3488	1	1	yes	characteristic
897	C₂	C₂×C₄₁×#575	1	1	yes	characteristic
898	C₂	C₂×C₄₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3508	C₂	semidirect
2. C₄₁×#3482	C₂	semidirect
3. C₄₁×#3400	C₂	semidirect
4. C₄₁×#3373	C₂	semidirect
5. C₄₁×#3311	C₂	semidirect
6. C₄₁×#3304	C₂	semidirect
7. C₄₁×#3284	C₂	semidirect
8. C₄₁×#3267	C₂	semidirect
9. C₄₁×#3255	C₂	semidirect
10. C₄₁×#3246	C₂	semidirect
11. C₄₁×#3216	C₂	semidirect
12. C₄₁×#3208	C₂	semidirect
13. C₄₁×#3115	C₂	semidirect
14. C₄₁×#3107	C₂	semidirect
15. C₄₁×#3038	C₂	semidirect
16. C₄₁×#3035	C₂	semidirect
17. C₄₁×#2990	C₂	semidirect
19. C₂×#135×C₄₁	C₂²	semidirect
22. C₄₁×#557	C₂²	semidirect
24. C₄₁×#556	C₂²	semidirect
29. D₄×Q₈×C₄₁	C₂²	semidirect
32. C₄₁×#547	C₂²	semidirect
39. C₄₁×#533	C₂²	semidirect
48. C₄×#41×C₄₁	C₂²	semidirect
50. C₄₁×#497	C₂²	semidirect
52. C₄₁×#489	C₂²	semidirect
55. C₄₁×#482	C₂²	semidirect
56. C₄₁×#476	C₂²	semidirect
57. C₄₁×#475	C₂²	semidirect
58. C₄₁×#475	C₂²	semidirect
59. C₄₁×#475	C₂²	semidirect
60. C₄₁×#474	C₂²	semidirect
62. C₄₁×#465	C₂²	semidirect
63. C₄₁×#465	C₂²	semidirect
64. C₄₁×#464	C₂²	semidirect
65. C₄₁×#463	C₂²	semidirect
66. C₄₁×#462	C₂²	semidirect
67. C₄₁×#462	C₂²	semidirect
68. C₄₁×#462	C₂²	semidirect
69. C₄₁×#461	C₂²	semidirect
70. C₄₁×#461	C₂²	semidirect
78. C₄₁×#452	C₂²	semidirect
79. C₄₁×#452	C₂²	semidirect
81. C₄₁×#449	C₂²	semidirect
82. C₄₁×#446	C₂²	semidirect
83. C₄₁×#442	C₂²	semidirect
84. C₄₁×#440	C₂²	semidirect
85. C₄×Q₁₆×C₄₁	C₂²	semidirect
86. C₄×SD₁₆×C₄₁	C₂²	semidirect
88. C₈×D₄×C₄₁	C₂²	semidirect
89. C₄₁×#432	C₂²	semidirect
92. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
94. C₄₁×#416	C₂²	semidirect
411. #61986	C₄₁	direct (N × H)
443. #3508	C₂×C₄₁	semidirect
444. #3482	C₂×C₄₁	semidirect
445. #3400	C₂×C₄₁	semidirect
446. #3373	C₂×C₄₁	semidirect
447. #3311	C₂×C₄₁	semidirect
448. #3304	C₂×C₄₁	semidirect
449. #3284	C₂×C₄₁	semidirect
450. #3267	C₂×C₄₁	semidirect
451. #3255	C₂×C₄₁	semidirect
452. #3246	C₂×C₄₁	semidirect
453. #3216	C₂×C₄₁	semidirect
454. #3208	C₂×C₄₁	semidirect
455. #3115	C₂×C₄₁	semidirect
456. #3107	C₂×C₄₁	semidirect
457. #3038	C₂×C₄₁	semidirect
458. #3035	C₂×C₄₁	semidirect
459. #2990	C₂×C₄₁	semidirect
468. C₂×#135	C₂²×C₄₁	semidirect
471. #557	C₂²×C₄₁	semidirect
473. #556	C₂²×C₄₁	semidirect
478. D₄×Q₈	C₂²×C₄₁	semidirect
481. #547	C₂²×C₄₁	semidirect
488. #533	C₂²×C₄₁	semidirect
497. C₄×#41	C₂²×C₄₁	semidirect
499. #497	C₂²×C₄₁	semidirect
501. #489	C₂²×C₄₁	semidirect
504. #482	C₂²×C₄₁	semidirect
505. #476	C₂²×C₄₁	semidirect
506. #475	C₂²×C₄₁	semidirect
507. #475	C₂²×C₄₁	semidirect
508. #475	C₂²×C₄₁	semidirect
509. #474	C₂²×C₄₁	semidirect
511. #465	C₂²×C₄₁	semidirect
512. #465	C₂²×C₄₁	semidirect
513. #464	C₂²×C₄₁	semidirect
514. #463	C₂²×C₄₁	semidirect
515. #462	C₂²×C₄₁	semidirect
516. #462	C₂²×C₄₁	semidirect
517. #462	C₂²×C₄₁	semidirect
518. #461	C₂²×C₄₁	semidirect
519. #461	C₂²×C₄₁	semidirect
527. #452	C₂²×C₄₁	semidirect
528. #452	C₂²×C₄₁	semidirect
530. #449	C₂²×C₄₁	semidirect
531. #446	C₂²×C₄₁	semidirect
532. #442	C₂²×C₄₁	semidirect
533. #440	C₂²×C₄₁	semidirect
534. C₄×Q₁₆	C₂²×C₄₁	semidirect
535. C₄×SD₁₆	C₂²×C₄₁	semidirect
537. C₈×D₄	C₂²×C₄₁	semidirect
538. #432	C₂²×C₄₁	semidirect
541. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
543. #416	C₂²×C₄₁	semidirect
544. C₄₁	#61986	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3508	2
C₄₁×#3482	2
C₄₁×#3400	2
C₄₁×#3373	2
C₄₁×#3311	2
C₄₁×#3304	2
C₄₁×#3284	2
C₄₁×#3267	2
C₄₁×#3255	2
C₄₁×#3246	2
C₄₁×#3216	2
C₄₁×#3208	2
C₄₁×#3115	2
C₄₁×#3107	2
C₄₁×#3038	2
C₄₁×#3035	2
C₄₁×#2990	2
#61986	41

Subgroups — C41×#61986 #23838187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61986 #23838187