Subgroups — C₄₁×#61921 #23838122

Order 10496.

1760 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3401	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#3397	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#3392	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#3375	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3371	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3368	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3362	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3224	C₂	1	2	yes	maximal, complemented
16	C₄₁×#3222	C₂	1	2	yes	maximal, complemented
17	C₄₁×#3217	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#3123	C₂	1	2	yes	maximal, complemented
20	C₄₁×#3118	C₂	1	2	yes	maximal, complemented
21	C₄₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄₁×#563	—	2	2	no	—
25	C₄₁×#559	C₂²	1	1	yes	characteristic
26	C₄₁×#559	C₂²	1	2	yes	—
27	C₄₁×#559	C₂²	1	1	yes	characteristic
28	Q₈²×C₄₁	C₂²	1	1	yes	characteristic, complemented
29	C₄₁×#557	C₂²	1	1	yes	characteristic, complemented
30	C₄₁×#557	C₂²	1	2	yes	complemented
31	C₄₁×#556	—	2	1	no	—
32	C₄₁×#556	C₂²	1	1	yes	characteristic, complemented
33	C₄₁×#556	C₂²	1	2	yes	complemented
34	C₄₁×#554	C₂²	1	1	yes	characteristic, complemented
35	C₄₁×#552	—	2	1	no	—
36	C₄₁×#550	C₂²	1	1	yes	characteristic
37	C₄₁×#550	C₂²	1	1	yes	characteristic
38	C₄₁×#550	C₂²	1	2	yes	—
39	C₄₁×#546	—	2	1	no	—
40	C₄₁×#546	—	2	1	no	—
41	C₄₁×#546	—	2	2	no	—
42	C₄₁×#544	—	2	1	no	—
43	C₄₁×#542	C₂²	1	2	yes	—
44	C₄₁×#541	—	2	1	no	—
45	C₄₁×#541	—	2	2	no	—
46	C₄₁×#541	C₂²	1	2	yes	—
47	C₄₁×#540	—	2	2	no	—
48	C₄₁×#535	C₂²	1	2	yes	—
49	C₄₁×#533	C₂²	1	1	yes	characteristic
50	C₄₁×#533	C₂²	1	1	yes	characteristic
51	C₄₁×#532	—	2	1	no	—
52	C₄₁×#532	—	2	1	no	—
53	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
54	C₄₁×#529	C₂²	1	1	yes	characteristic
55	C₄₁×#518	C₂²	1	2	yes	—
56	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
57	C₄₁×#497	C₂²	1	2	yes	complemented
58	C₄₁×#496	C₂²	1	2	yes	—
59	C₄₁×#496	C₂²	1	2	yes	complemented
60	C₄₁×#495	C₂²	1	2	yes	complemented
61	C₄₁×#492	C₂²	1	1	yes	characteristic
62	C₄₁×#492	C₂²	1	1	yes	characteristic
63	C₄₁×#492	C₂²	1	2	yes	complemented
64	C₄₁×#490	C₂²	1	2	yes	—
65	C₄₁×#490	C₂²	1	2	yes	complemented
66	C₄₁×#489	C₂²	1	2	yes	complemented
67	C₄₁×#488	C₂²	1	2	yes	complemented
68	C₄₁×#486	C₂²	1	1	yes	characteristic
69	C₄₁×#486	C₂²	1	1	yes	characteristic
70	C₄₁×#486	C₂²	1	2	yes	complemented
71	C₄₁×#485	C₂²	1	1	yes	characteristic
72	C₄₁×#485	C₂²	1	2	yes	—
73	C₄₁×#482	C₂²	1	1	yes	characteristic
74	C₄₁×#479	C₂²	1	1	yes	characteristic, complemented
75	C₄₁×#478	C₂²	1	1	yes	characteristic, complemented
76	C₄₁×#478	C₂²	1	2	yes	complemented
77	C₄₁×#478	C₂²	1	2	yes	complemented
78	C₄₁×#477	C₂²	1	1	yes	characteristic, complemented
79	C₄₁×#476	C₂²	1	1	yes	characteristic, complemented
80	C₄₁×#476	C₂²	1	2	yes	complemented
81	C₄₁×#474	C₂²	1	2	yes	complemented
82	C₄₁×#464	C₂²	1	1	yes	characteristic, complemented
83	C₄₁×#464	C₂²	1	2	yes	complemented
84	C₄₁×#464	C₂²	1	2	yes	complemented
85	C₄₁×#464	C₂²	1	2	yes	complemented
86	C₄₁×#463	C₂²	1	1	yes	characteristic, complemented
87	C₄₁×#463	C₂²	1	2	yes	complemented
88	C₄₁×#463	C₂²	1	2	yes	complemented
89	C₄₁×#463	C₂²	1	2	yes	complemented
90	C₄₁×#462	C₂²	1	1	yes	characteristic, complemented
91	C₄₁×#461	C₂²	1	1	yes	characteristic, complemented
92	C₄₁×#461	C₂²	1	2	yes	complemented
93	C₄₁×#461	C₂²	1	2	yes	complemented
94	C₄₁×#460	C₂²	1	1	yes	characteristic
95	C₄₁×#460	C₂²	1	2	yes	—
96	C₄₁×#460	C₂²	1	2	yes	—
97	C₄₁×#460	C₂²	1	1	yes	characteristic
98	C₄₁×#460	C₂²	1	2	yes	complemented
99	C₄₁×#460	C₂²	1	2	yes	complemented
100	C₄₁×#460	C₂²	1	2	yes	complemented
101	C₄₁×#459	C₂²	1	1	yes	characteristic
102	C₄₁×#459	C₂²	1	1	yes	characteristic
103	C₄₁×#459	C₂²	1	2	yes	complemented
104	C₄₁×#452	C₂²	1	1	yes	characteristic
105	C₄₁×#452	C₂²	1	2	yes	—
106	C₄₁×#450	C₂²	1	2	yes	—
107	C₄₁×#450	C₂²	1	2	yes	—
108	C₄₁×#450	C₂²	1	2	yes	—
109	C₄₁×#449	C₂²	1	1	yes	characteristic
110	C₄₁×#447	C₂²	1	2	yes	—
111	C₄₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₄₁×#446	C₂²	1	2	yes	complemented
113	C₄₁×#446	C₂²	1	2	yes	complemented
114	C₄₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
116	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
117	C₄₁×#442	C₂²	1	2	yes	complemented
118	C₄₁×#441	C₂²	1	2	yes	complemented
119	C₄₁×#440	C₂²	1	2	yes	complemented
120	C₄₁×#440	C₂²	1	2	yes	complemented
121	C₄₁×#440	C₂²	1	2	yes	complemented
122	C₄₁×#440	C₂²	1	2	yes	complemented
123	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
124	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
125	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
126	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
127	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
128	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
129	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
130	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
131	C₄₁×#433	C₂²	1	2	yes	—
132	C₄₁×#433	C₂²	1	2	yes	—
133	C₄₁×#432	C₂²	1	1	yes	characteristic
134	C₄₁×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₄₁	—	2	1	no	—
136	C₂×#41×C₄₁	—	2	1	no	—
137	C₂×#41×C₄₁	—	2	2	no	—
138	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₄₁	—	2	1	no	—
140	C₂²×D₄×C₄₁	—	2	1	no	—
141	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
153	C₂×D₈×C₄₁	C₂³	1	2	yes	—
154	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₄₁	C₂³	1	2	yes	—
156	C₄⋊Q₈×C₄₁	—	2	2	no	—
157	C₄⋊Q₈×C₄₁	—	2	2	no	—
158	C₄⋊Q₈×C₄₁	—	2	1	no	—
159	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
160	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
161	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
165	#127×C₄₁	—	2	1	no	—
166	#127×C₄₁	—	2	1	no	—
167	#127×C₄₁	C₂³	1	1	yes	characteristic
168	#127×C₄₁	C₂³	1	1	yes	characteristic
169	#127×C₄₁	C₂³	1	2	yes	—
170	#127×C₄₁	C₂³	1	2	yes	—
171	#127×C₄₁	C₂³	1	2	yes	—
172	#126×C₄₁	—	2	2	no	—
173	#126×C₄₁	—	2	2	no	—
174	#126×C₄₁	—	2	2	no	—
175	#126×C₄₁	—	2	2	no	—
176	#126×C₄₁	—	2	2	no	—
177	#126×C₄₁	—	2	2	no	—
178	#126×C₄₁	—	2	1	no	—
179	#125×C₄₁	—	2	2	no	—
180	#125×C₄₁	—	2	2	no	—
181	#125×C₄₁	—	2	2	no	—
182	#125×C₄₁	—	2	2	no	—
183	#125×C₄₁	—	2	2	no	—
184	#125×C₄₁	—	2	1	no	—
185	#125×C₄₁	—	2	1	no	—
186	#125×C₄₁	D₄	1	2	yes	—
187	#125×C₄₁	C₂³	1	1	yes	characteristic
188	#125×C₄₁	C₂³	1	2	yes	—
189	#124×C₄₁	—	2	1	no	—
190	#124×C₄₁	—	2	1	no	—
191	#124×C₄₁	—	2	2	no	—
192	#124×C₄₁	—	2	2	no	—
193	#124×C₄₁	C₂³	1	1	yes	characteristic
194	#124×C₄₁	C₂³	1	2	yes	—
195	#124×C₄₁	C₂³	1	2	yes	—
196	#124×C₄₁	C₂³	1	2	yes	—
197	#123×C₄₁	—	2	1	no	—
198	#123×C₄₁	—	2	2	no	—
199	#123×C₄₁	—	2	2	no	—
200	#123×C₄₁	—	2	2	no	—
201	#123×C₄₁	—	2	2	no	—
202	#123×C₄₁	—	2	2	no	—
203	C₂²⋊Q₈×C₄₁	—	2	1	no	—
204	C₂²⋊Q₈×C₄₁	—	2	1	no	—
205	C₂²⋊Q₈×C₄₁	—	2	2	no	—
206	C₂²⋊Q₈×C₄₁	—	2	1	no	—
207	C₂²⋊Q₈×C₄₁	—	2	2	no	—
208	C₂²⋊Q₈×C₄₁	—	2	2	no	—
209	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
211	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
212	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
214	#121×C₄₁	—	2	2	no	—
215	#121×C₄₁	—	2	2	no	—
216	#121×C₄₁	—	2	1	no	—
217	#121×C₄₁	—	2	1	no	—
218	#121×C₄₁	—	2	2	no	—
219	#121×C₄₁	—	2	2	no	—
220	#121×C₄₁	—	2	2	no	—
221	#121×C₄₁	—	2	2	no	—
222	#121×C₄₁	—	2	2	no	—
223	#121×C₄₁	C₂³	1	1	yes	characteristic
224	#120×C₄₁	—	2	2	no	—
225	#120×C₄₁	—	2	2	no	—
226	C₄×Q₈×C₄₁	—	2	1	no	—
227	C₄×Q₈×C₄₁	—	2	1	no	—
228	C₄×Q₈×C₄₁	—	2	2	no	—
229	C₄×Q₈×C₄₁	—	2	1	no	—
230	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
234	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
235	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
236	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
237	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
239	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₄₁	—	2	1	no	—
241	C₄×D₄×C₄₁	—	2	1	no	—
242	C₄×D₄×C₄₁	—	2	1	no	—
243	C₄×D₄×C₄₁	—	2	2	no	—
244	C₄×D₄×C₄₁	—	2	2	no	—
245	C₄×D₄×C₄₁	—	2	1	no	—
246	C₄×D₄×C₄₁	—	2	1	no	—
247	C₄×D₄×C₄₁	—	2	2	no	—
248	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₄₁	C₂³	1	2	yes	—
251	C₄×D₄×C₄₁	C₂³	1	2	yes	—
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	2	yes	—
256	#117×C₄₁	—	2	1	no	—
257	#117×C₄₁	—	2	2	no	—
258	#117×C₄₁	—	2	1	no	—
259	#117×C₄₁	—	2	1	no	—
260	#117×C₄₁	—	2	1	no	—
261	#117×C₄₁	C₂³	1	1	yes	characteristic
262	#117×C₄₁	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
266	C₂×C₄²×C₄₁	—	2	1	no	—
267	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
268	#107×C₄₁	C₂³	1	2	yes	—
269	#107×C₄₁	C₂³	1	1	yes	characteristic
270	#107×C₄₁	C₂³	1	1	yes	characteristic
271	#106×C₄₁	C₂³	1	1	yes	characteristic
272	#106×C₄₁	C₂³	1	1	yes	characteristic
273	#106×C₄₁	C₂³	1	2	yes	—
274	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
279	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
282	#103×C₄₁	C₂³	1	1	yes	characteristic
283	#103×C₄₁	C₂³	1	2	yes	—
284	#103×C₄₁	C₂³	1	2	yes	—
285	#103×C₄₁	C₂³	1	1	yes	characteristic
286	#103×C₄₁	C₂³	1	1	yes	characteristic
287	#103×C₄₁	C₂³	1	1	yes	characteristic
288	#103×C₄₁	C₂³	1	2	yes	—
289	#102×C₄₁	C₂³	1	1	yes	characteristic
290	#102×C₄₁	C₂³	1	1	yes	characteristic
291	#102×C₄₁	C₂³	1	2	yes	—
292	#102×C₄₁	C₂³	1	1	yes	characteristic
293	#102×C₄₁	C₂³	1	2	yes	—
294	#102×C₄₁	C₂³	1	1	yes	characteristic
295	#102×C₄₁	C₂³	1	2	yes	—
296	#102×C₄₁	C₂³	1	2	yes	—
297	#102×C₄₁	C₂³	1	2	yes	—
298	#102×C₄₁	C₂³	1	2	yes	—
299	#102×C₄₁	C₂³	1	2	yes	—
300	#102×C₄₁	C₂³	1	2	yes	—
301	#102×C₄₁	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
305	#97×C₄₁	C₂³	1	2	yes	—
306	#97×C₄₁	C₂³	1	2	yes	—
307	#97×C₄₁	C₂³	1	2	yes	—
308	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₄₁	C₂³	1	2	yes	—
311	C₄×C₈×C₄₁	C₂³	1	2	yes	—
312	C₂⁴×C₄₁	—	2	2	no	—
313	#41×C₄₁	—	4	1	no	—
314	#41×C₄₁	—	4	1	no	—
315	#41×C₄₁	—	8	2	no	—
316	#41×C₄₁	—	8	2	no	—
317	#41×C₄₁	—	8	4	no	—
318	C₂×Q₈×C₄₁	—	2	1	no	—
319	C₂×Q₈×C₄₁	—	2	2	no	—
320	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
323	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
326	C₂×D₄×C₄₁	—	2	1	no	—
327	C₂×D₄×C₄₁	—	2	1	no	—
328	C₂×D₄×C₄₁	—	2	2	no	—
329	C₂×D₄×C₄₁	—	2	2	no	—
330	C₂×D₄×C₄₁	—	2	1	no	—
331	C₂×D₄×C₄₁	—	2	1	no	—
332	C₂×D₄×C₄₁	—	2	2	no	—
333	C₂×D₄×C₄₁	—	2	2	no	—
334	C₂×D₄×C₄₁	—	2	2	no	—
335	C₂×D₄×C₄₁	—	2	2	no	—
336	C₂×D₄×C₄₁	—	2	2	no	—
337	C₂×D₄×C₄₁	—	2	1	no	—
338	C₂×D₄×C₄₁	—	2	1	no	—
339	C₂×D₄×C₄₁	—	4	2	no	—
340	C₂×D₄×C₄₁	—	4	2	no	—
341	C₂×D₄×C₄₁	—	8	2	no	—
342	C₂×D₄×C₄₁	—	8	2	no	—
343	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
344	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
345	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₄₁	—	2	1	no	—
348	C₂²×C₄×C₄₁	—	2	1	no	—
349	C₂²×C₄×C₄₁	—	2	1	no	—
350	C₂²×C₄×C₄₁	—	2	1	no	—
351	C₂²×C₄×C₄₁	—	2	2	no	—
352	C₂²×C₄×C₄₁	—	2	2	no	—
353	C₂²×C₄×C₄₁	—	2	2	no	—
354	C₂²×C₄×C₄₁	—	2	2	no	—
355	C₂²×C₄×C₄₁	—	2	2	no	—
356	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
359	Q₁₆×C₄₁	—	4	2	no	—
360	Q₁₆×C₄₁	—	4	1	no	—
361	SD₁₆×C₄₁	—	4	2	no	—
362	SD₁₆×C₄₁	—	4	2	no	—
363	SD₁₆×C₄₁	—	4	2	no	—
364	SD₁₆×C₄₁	—	4	2	no	—
365	SD₁₆×C₄₁	—	4	1	no	—
366	SD₁₆×C₄₁	—	4	2	no	—
367	SD₁₆×C₄₁	—	4	1	no	—
368	SD₁₆×C₄₁	—	4	2	no	—
369	SD₁₆×C₄₁	—	4	2	no	—
370	D₈×C₄₁	—	4	1	no	—
371	D₈×C₄₁	—	4	2	no	—
372	D₈×C₄₁	—	4	2	no	—
373	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
377	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
379	C₄⋊C₄×C₄₁	—	2	1	no	—
380	C₄⋊C₄×C₄₁	—	2	2	no	—
381	C₄⋊C₄×C₄₁	—	2	1	no	—
382	C₄⋊C₄×C₄₁	—	2	1	no	—
383	C₄⋊C₄×C₄₁	—	2	1	no	—
384	C₄⋊C₄×C₄₁	—	2	2	no	—
385	C₄⋊C₄×C₄₁	—	2	1	no	—
386	C₄⋊C₄×C₄₁	—	2	1	no	—
387	C₄⋊C₄×C₄₁	—	2	1	no	—
388	C₄⋊C₄×C₄₁	—	2	2	no	—
389	C₄⋊C₄×C₄₁	—	2	2	no	—
390	C₄⋊C₄×C₄₁	—	2	1	no	—
391	C₄⋊C₄×C₄₁	—	2	2	no	—
392	C₄⋊C₄×C₄₁	—	2	2	no	—
393	C₄⋊C₄×C₄₁	—	2	2	no	—
394	C₄⋊C₄×C₄₁	—	2	2	no	—
395	C₄⋊C₄×C₄₁	—	2	2	no	—
396	C₄⋊C₄×C₄₁	—	2	2	no	—
397	C₄⋊C₄×C₄₁	—	2	1	no	—
398	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄×C₄₁	—	2	1	no	—
413	C₂²⋊C₄×C₄₁	—	2	2	no	—
414	C₂²⋊C₄×C₄₁	—	2	1	no	—
415	C₂²⋊C₄×C₄₁	—	2	2	no	—
416	C₂²⋊C₄×C₄₁	—	2	2	no	—
417	C₂²⋊C₄×C₄₁	—	2	2	no	—
418	C₂²⋊C₄×C₄₁	—	2	2	no	—
419	C₂²⋊C₄×C₄₁	—	2	1	no	—
420	C₂²⋊C₄×C₄₁	—	2	1	no	—
421	C₂²⋊C₄×C₄₁	—	2	1	no	—
422	C₂²⋊C₄×C₄₁	—	2	1	no	—
423	C₂²⋊C₄×C₄₁	—	2	1	no	—
424	C₂²⋊C₄×C₄₁	—	2	2	no	—
425	C₂²⋊C₄×C₄₁	—	2	2	no	—
426	C₂²⋊C₄×C₄₁	—	2	2	no	—
427	C₂²⋊C₄×C₄₁	—	2	2	no	—
428	C₂²⋊C₄×C₄₁	—	2	2	no	—
429	C₂²⋊C₄×C₄₁	—	2	2	no	—
430	C₂²⋊C₄×C₄₁	—	2	1	no	—
431	C₂²⋊C₄×C₄₁	—	2	2	no	—
432	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
434	C₄²×C₄₁	—	2	1	no	—
435	C₄²×C₄₁	—	2	1	no	—
436	C₄²×C₄₁	—	2	1	no	—
437	C₄²×C₄₁	—	2	2	no	—
438	C₄²×C₄₁	—	2	1	no	—
439	C₄²×C₄₁	—	2	2	no	—
440	C₄²×C₄₁	—	2	2	no	—
441	C₄²×C₄₁	—	2	2	no	—
442	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
445	C₄²×C₄₁	C₂⁴	1	2	yes	—
446	C₄²×C₄₁	C₂⁴	1	2	yes	—
447	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
448	C₂³×C₄₁	—	2	1	no	—
449	C₂³×C₄₁	—	2	2	no	—
450	C₂³×C₄₁	—	2	2	no	—
451	C₂³×C₄₁	—	2	1	no	—
452	C₂³×C₄₁	—	4	4	no	—
453	C₂³×C₄₁	—	8	2	no	—
454	C₂³×C₄₁	—	8	2	no	—
455	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
456	Q₈×C₄₁	—	2	2	no	—
457	Q₈×C₄₁	—	2	2	no	—
458	Q₈×C₄₁	—	2	2	no	—
459	Q₈×C₄₁	—	2	1	no	—
460	Q₈×C₄₁	—	2	1	no	—
461	Q₈×C₄₁	—	2	2	no	—
462	Q₈×C₄₁	—	2	1	no	—
463	Q₈×C₄₁	—	2	1	no	—
464	Q₈×C₄₁	—	4	2	no	—
465	Q₈×C₄₁	—	8	1	no	—
466	Q₈×C₄₁	—	8	2	no	—
467	D₄×C₄₁	—	2	1	no	—
468	D₄×C₄₁	—	2	1	no	—
469	D₄×C₄₁	—	2	2	no	—
470	D₄×C₄₁	—	2	2	no	—
471	D₄×C₄₁	—	2	1	no	—
472	D₄×C₄₁	—	2	2	no	—
473	D₄×C₄₁	—	2	2	no	—
474	D₄×C₄₁	—	2	1	no	—
475	D₄×C₄₁	—	4	4	no	—
476	D₄×C₄₁	—	4	4	no	—
477	D₄×C₄₁	—	4	2	no	—
478	D₄×C₄₁	—	4	2	no	—
479	D₄×C₄₁	—	4	2	no	—
480	D₄×C₄₁	—	8	1	no	—
481	D₄×C₄₁	—	8	1	no	—
482	D₄×C₄₁	—	8	2	no	—
483	D₄×C₄₁	—	8	2	no	—
484	D₄×C₄₁	—	8	2	no	—
485	D₄×C₄₁	—	8	2	no	—
486	D₄×C₄₁	—	8	2	no	—
487	D₄×C₄₁	—	8	1	no	—
488	C₂×C₄×C₄₁	—	2	2	no	—
489	C₂×C₄×C₄₁	—	2	1	no	—
490	C₂×C₄×C₄₁	—	2	1	no	—
491	C₂×C₄×C₄₁	—	2	2	no	—
492	C₂×C₄×C₄₁	—	2	1	no	—
493	C₂×C₄×C₄₁	—	2	1	no	—
494	C₂×C₄×C₄₁	—	2	1	no	—
495	C₂×C₄×C₄₁	—	2	1	no	—
496	C₂×C₄×C₄₁	—	2	1	no	—
497	C₂×C₄×C₄₁	—	2	1	no	—
498	C₂×C₄×C₄₁	—	2	2	no	—
499	C₂×C₄×C₄₁	—	4	1	no	—
500	C₂×C₄×C₄₁	—	4	2	no	—
501	C₂×C₄×C₄₁	—	4	2	no	—
502	C₂×C₄×C₄₁	—	4	2	no	—
503	C₂×C₄×C₄₁	—	4	2	no	—
504	C₂×C₄×C₄₁	—	8	2	no	—
505	C₂×C₄×C₄₁	—	8	2	no	—
506	C₂×C₄×C₄₁	—	8	2	no	—
507	C₂×C₄×C₄₁	—	8	2	no	—
508	C₂×C₄×C₄₁	—	8	2	no	—
509	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
519	C₈×C₄₁	—	2	2	no	—
520	C₈×C₄₁	—	2	1	no	—
521	C₈×C₄₁	—	2	2	no	—
522	C₈×C₄₁	—	2	1	no	—
523	C₈×C₄₁	—	2	1	no	—
524	C₈×C₄₁	—	2	1	no	—
525	#61921	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
526	C₂²×C₄₁	—	2	1	no	—
527	C₂²×C₄₁	—	2	1	no	—
528	C₂²×C₄₁	—	2	1	no	—
529	C₂²×C₄₁	—	4	1	no	—
530	C₂²×C₄₁	—	4	1	no	—
531	C₂²×C₄₁	—	4	2	no	—
532	C₂²×C₄₁	—	4	2	no	—
533	C₂²×C₄₁	—	4	1	no	—
534	C₂²×C₄₁	—	4	2	no	—
535	C₂²×C₄₁	—	4	2	no	—
536	C₂²×C₄₁	—	4	1	no	—
537	C₂²×C₄₁	—	4	1	no	—
538	C₂²×C₄₁	—	4	1	no	—
539	C₂²×C₄₁	—	4	2	no	—
540	C₂²×C₄₁	—	4	2	no	—
541	C₂²×C₄₁	—	16	4	no	—
542	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
543	C₄×C₄₁	—	2	1	no	—
544	C₄×C₄₁	—	2	1	no	—
545	C₄×C₄₁	—	2	2	no	—
546	C₄×C₄₁	—	2	2	no	—
547	C₄×C₄₁	—	2	1	no	—
548	C₄×C₄₁	—	2	1	no	—
549	C₄×C₄₁	—	2	2	no	—
550	C₄×C₄₁	—	2	2	no	—
551	C₄×C₄₁	—	4	1	no	—
552	C₄×C₄₁	—	4	2	no	—
553	C₄×C₄₁	—	4	1	no	—
554	C₄×C₄₁	—	4	1	no	—
555	C₄×C₄₁	—	4	2	no	—
556	C₄×C₄₁	—	4	1	no	—
557	C₄×C₄₁	—	4	1	no	—
558	C₄×C₄₁	—	4	1	no	—
559	C₄×C₄₁	#577	1	2	yes	—
560	C₄×C₄₁	#585	1	1	yes	characteristic
561	C₄×C₄₁	#585	1	1	yes	characteristic
562	#3555	C₂×C₄₁	1	1	yes	characteristic, complemented
563	#3508	C₂×C₄₁	1	1	yes	characteristic, complemented
564	#3401	C₂×C₄₁	1	2	yes	complemented
565	#3400	C₂×C₄₁	1	1	yes	characteristic, complemented
566	#3397	C₂×C₄₁	1	1	yes	characteristic, complemented
567	#3397	C₂×C₄₁	1	2	yes	complemented
568	#3394	C₂×C₄₁	1	1	yes	characteristic, complemented
569	#3392	C₂×C₄₁	1	1	yes	characteristic, complemented
570	#3375	C₂×C₄₁	1	1	yes	characteristic, complemented
571	#3371	C₂×C₄₁	1	2	yes	complemented
572	#3368	C₂×C₄₁	1	2	yes	complemented
573	#3366	C₂×C₄₁	1	1	yes	characteristic, complemented
574	#3362	C₂×C₄₁	1	1	yes	characteristic, complemented
575	#3361	C₂×C₄₁	1	1	yes	characteristic, complemented
576	#3224	C₂×C₄₁	1	2	yes	complemented
577	#3222	C₂×C₄₁	1	2	yes	complemented
578	#3217	C₂×C₄₁	1	1	yes	characteristic, complemented
579	#3208	C₂×C₄₁	1	1	yes	characteristic, complemented
580	#3123	C₂×C₄₁	1	2	yes	complemented
581	#3118	C₂×C₄₁	1	2	yes	complemented
582	#3116	C₂×C₄₁	1	1	yes	characteristic, complemented
583	#3102	C₂×C₄₁	1	1	yes	characteristic, complemented
584	#2985	C₂×C₄₁	1	1	yes	characteristic, complemented
585	C₂×C₄₁	—	4	1	no	—
586	C₂×C₄₁	—	8	1	no	—
587	C₂×C₄₁	—	8	1	no	—
588	C₂×C₄₁	—	8	2	no	—
589	C₂×C₄₁	—	8	2	no	—
590	C₂×C₄₁	#3487	1	1	yes	characteristic
591	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
592	C₂×C₄₁	#3585	1	1	yes	characteristic
593	#563	—	2	2	no	—
594	#559	C₂²×C₄₁	1	1	yes	characteristic
595	#559	C₂²×C₄₁	1	2	yes	—
596	#559	C₂²×C₄₁	1	1	yes	characteristic
597	Q₈²	C₂²×C₄₁	1	1	yes	characteristic, complemented
598	#557	C₂²×C₄₁	1	1	yes	characteristic, complemented
599	#557	C₂²×C₄₁	1	2	yes	complemented
600	#556	—	2	1	no	—
601	#556	C₂²×C₄₁	1	1	yes	characteristic, complemented
602	#556	C₂²×C₄₁	1	2	yes	complemented
603	#554	C₂²×C₄₁	1	1	yes	characteristic, complemented
604	#552	—	2	1	no	—
605	#550	C₂²×C₄₁	1	1	yes	characteristic
606	#550	C₂²×C₄₁	1	1	yes	characteristic
607	#550	C₂²×C₄₁	1	2	yes	—
608	#546	—	2	1	no	—
609	#546	—	2	1	no	—
610	#546	—	2	2	no	—
611	#544	—	2	1	no	—
612	#542	C₂²×C₄₁	1	2	yes	—
613	#541	—	2	1	no	—
614	#541	—	2	2	no	—
615	#541	C₂²×C₄₁	1	2	yes	—
616	#540	—	2	2	no	—
617	#535	C₂²×C₄₁	1	2	yes	—
618	#533	C₂²×C₄₁	1	1	yes	characteristic
619	#533	C₂²×C₄₁	1	1	yes	characteristic
620	#532	—	2	1	no	—
621	#532	—	2	1	no	—
622	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
623	#529	C₂²×C₄₁	1	1	yes	characteristic
624	#518	C₂²×C₄₁	1	2	yes	—
625	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
626	#497	C₂²×C₄₁	1	2	yes	complemented
627	#496	C₂²×C₄₁	1	2	yes	—
628	#496	C₂²×C₄₁	1	2	yes	complemented
629	#495	C₂²×C₄₁	1	2	yes	complemented
630	#492	C₂²×C₄₁	1	1	yes	characteristic
631	#492	C₂²×C₄₁	1	1	yes	characteristic
632	#492	C₂²×C₄₁	1	2	yes	complemented
633	#490	C₂²×C₄₁	1	2	yes	—
634	#490	C₂²×C₄₁	1	2	yes	complemented
635	#489	C₂²×C₄₁	1	2	yes	complemented
636	#488	C₂²×C₄₁	1	2	yes	complemented
637	#486	C₂²×C₄₁	1	1	yes	characteristic
638	#486	C₂²×C₄₁	1	1	yes	characteristic
639	#486	C₂²×C₄₁	1	2	yes	complemented
640	#485	C₂²×C₄₁	1	1	yes	characteristic
641	#485	C₂²×C₄₁	1	2	yes	—
642	#482	C₂²×C₄₁	1	1	yes	characteristic
643	#479	C₂²×C₄₁	1	1	yes	characteristic, complemented
644	#478	C₂²×C₄₁	1	1	yes	characteristic, complemented
645	#478	C₂²×C₄₁	1	2	yes	complemented
646	#478	C₂²×C₄₁	1	2	yes	complemented
647	#477	C₂²×C₄₁	1	1	yes	characteristic, complemented
648	#476	C₂²×C₄₁	1	1	yes	characteristic, complemented
649	#476	C₂²×C₄₁	1	2	yes	complemented
650	#474	C₂²×C₄₁	1	2	yes	complemented
651	#464	C₂²×C₄₁	1	1	yes	characteristic, complemented
652	#464	C₂²×C₄₁	1	2	yes	complemented
653	#464	C₂²×C₄₁	1	2	yes	complemented
654	#464	C₂²×C₄₁	1	2	yes	complemented
655	#463	C₂²×C₄₁	1	1	yes	characteristic, complemented
656	#463	C₂²×C₄₁	1	2	yes	complemented
657	#463	C₂²×C₄₁	1	2	yes	complemented
658	#463	C₂²×C₄₁	1	2	yes	complemented
659	#462	C₂²×C₄₁	1	1	yes	characteristic, complemented
660	#461	C₂²×C₄₁	1	1	yes	characteristic, complemented
661	#461	C₂²×C₄₁	1	2	yes	complemented
662	#461	C₂²×C₄₁	1	2	yes	complemented
663	#460	C₂²×C₄₁	1	1	yes	characteristic
664	#460	C₂²×C₄₁	1	2	yes	—
665	#460	C₂²×C₄₁	1	2	yes	—
666	#460	C₂²×C₄₁	1	1	yes	characteristic
667	#460	C₂²×C₄₁	1	2	yes	complemented
668	#460	C₂²×C₄₁	1	2	yes	complemented
669	#460	C₂²×C₄₁	1	2	yes	complemented
670	#459	C₂²×C₄₁	1	1	yes	characteristic
671	#459	C₂²×C₄₁	1	1	yes	characteristic
672	#459	C₂²×C₄₁	1	2	yes	complemented
673	#452	C₂²×C₄₁	1	1	yes	characteristic
674	#452	C₂²×C₄₁	1	2	yes	—
675	#450	C₂²×C₄₁	1	2	yes	—
676	#450	C₂²×C₄₁	1	2	yes	—
677	#450	C₂²×C₄₁	1	2	yes	—
678	#449	C₂²×C₄₁	1	1	yes	characteristic
679	#447	C₂²×C₄₁	1	2	yes	—
680	#446	C₂²×C₄₁	1	1	yes	characteristic, complemented
681	#446	C₂²×C₄₁	1	2	yes	complemented
682	#446	C₂²×C₄₁	1	2	yes	complemented
683	#446	C₂²×C₄₁	1	1	yes	characteristic, complemented
684	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
685	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
686	#442	C₂²×C₄₁	1	2	yes	complemented
687	#441	C₂²×C₄₁	1	2	yes	complemented
688	#440	C₂²×C₄₁	1	2	yes	complemented
689	#440	C₂²×C₄₁	1	2	yes	complemented
690	#440	C₂²×C₄₁	1	2	yes	complemented
691	#440	C₂²×C₄₁	1	2	yes	complemented
692	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
693	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
694	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
695	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
696	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
697	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
698	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
699	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
700	#433	C₂²×C₄₁	1	2	yes	—
701	#433	C₂²×C₄₁	1	2	yes	—
702	#432	C₂²×C₄₁	1	1	yes	characteristic
703	#431	C₂²×C₄₁	1	1	yes	characteristic
704	C₄₁	#61921	1	1	yes	characteristic, direct product factor, Sylow
705	C₂×#41	—	2	1	no	—
706	C₂×#41	—	2	1	no	—
707	C₂×#41	—	2	2	no	—
708	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
709	C₂²×D₄	—	2	1	no	—
710	C₂²×D₄	—	2	1	no	—
711	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
712	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
713	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
715	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
716	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
717	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
719	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
723	C₂×D₈	C₂³×C₄₁	1	2	yes	—
724	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
725	C₂×D₈	C₂³×C₄₁	1	2	yes	—
726	C₄⋊Q₈	—	2	2	no	—
727	C₄⋊Q₈	—	2	2	no	—
728	C₄⋊Q₈	—	2	1	no	—
729	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
730	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
731	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
732	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
733	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
734	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
735	#127	—	2	1	no	—
736	#127	—	2	1	no	—
737	#127	C₂³×C₄₁	1	1	yes	characteristic
738	#127	C₂³×C₄₁	1	1	yes	characteristic
739	#127	C₂³×C₄₁	1	2	yes	—
740	#127	C₂³×C₄₁	1	2	yes	—
741	#127	C₂³×C₄₁	1	2	yes	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#126	—	2	1	no	—
749	#125	—	2	2	no	—
750	#125	—	2	2	no	—
751	#125	—	2	2	no	—
752	#125	—	2	2	no	—
753	#125	—	2	2	no	—
754	#125	—	2	1	no	—
755	#125	—	2	1	no	—
756	#125	D₄×C₄₁	1	2	yes	—
757	#125	C₂³×C₄₁	1	1	yes	characteristic
758	#125	C₂³×C₄₁	1	2	yes	—
759	#124	—	2	1	no	—
760	#124	—	2	1	no	—
761	#124	—	2	2	no	—
762	#124	—	2	2	no	—
763	#124	C₂³×C₄₁	1	1	yes	characteristic
764	#124	C₂³×C₄₁	1	2	yes	—
765	#124	C₂³×C₄₁	1	2	yes	—
766	#124	C₂³×C₄₁	1	2	yes	—
767	#123	—	2	1	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	C₂²⋊Q₈	—	2	1	no	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
780	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
781	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
782	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	—	2	1	no	—
787	#121	—	2	1	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	2	no	—
793	#121	C₂³×C₄₁	1	1	yes	characteristic
794	#120	—	2	2	no	—
795	#120	—	2	2	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	—	2	2	no	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
803	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
804	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
805	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
806	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
807	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
809	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₄₁	1	2	yes	—
821	C₄×D₄	C₂³×C₄₁	1	2	yes	—
822	C₄×D₄	C₂³×C₄₁	1	2	yes	—
823	C₄×D₄	C₂³×C₄₁	1	2	yes	—
824	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₄₁	1	2	yes	—
826	#117	—	2	1	no	—
827	#117	—	2	2	no	—
828	#117	—	2	1	no	—
829	#117	—	2	1	no	—
830	#117	—	2	1	no	—
831	#117	C₂³×C₄₁	1	1	yes	characteristic
832	#117	C₂³×C₄₁	1	2	yes	—
833	C₂×C₄⋊C₄	—	2	1	no	—
834	C₂×C₂²⋊C₄	—	2	2	no	—
835	C₂×C₂²⋊C₄	—	2	2	no	—
836	C₂×C₄²	—	2	1	no	—
837	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
838	#107	C₂³×C₄₁	1	2	yes	—
839	#107	C₂³×C₄₁	1	1	yes	characteristic
840	#107	C₂³×C₄₁	1	1	yes	characteristic
841	#106	C₂³×C₄₁	1	1	yes	characteristic
842	#106	C₂³×C₄₁	1	1	yes	characteristic
843	#106	C₂³×C₄₁	1	2	yes	—
844	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
845	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
849	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
850	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
851	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
852	#103	C₂³×C₄₁	1	1	yes	characteristic
853	#103	C₂³×C₄₁	1	2	yes	—
854	#103	C₂³×C₄₁	1	2	yes	—
855	#103	C₂³×C₄₁	1	1	yes	characteristic
856	#103	C₂³×C₄₁	1	1	yes	characteristic
857	#103	C₂³×C₄₁	1	1	yes	characteristic
858	#103	C₂³×C₄₁	1	2	yes	—
859	#102	C₂³×C₄₁	1	1	yes	characteristic
860	#102	C₂³×C₄₁	1	1	yes	characteristic
861	#102	C₂³×C₄₁	1	2	yes	—
862	#102	C₂³×C₄₁	1	1	yes	characteristic
863	#102	C₂³×C₄₁	1	2	yes	—
864	#102	C₂³×C₄₁	1	1	yes	characteristic
865	#102	C₂³×C₄₁	1	2	yes	—
866	#102	C₂³×C₄₁	1	2	yes	—
867	#102	C₂³×C₄₁	1	2	yes	—
868	#102	C₂³×C₄₁	1	2	yes	—
869	#102	C₂³×C₄₁	1	2	yes	—
870	#102	C₂³×C₄₁	1	2	yes	—
871	#102	C₂³×C₄₁	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
874	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
875	#97	C₂³×C₄₁	1	2	yes	—
876	#97	C₂³×C₄₁	1	2	yes	—
877	#97	C₂³×C₄₁	1	2	yes	—
878	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
879	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
880	C₄×C₈	C₂³×C₄₁	1	2	yes	—
881	C₄×C₈	C₂³×C₄₁	1	2	yes	—
882	C₂⁴	—	2	2	no	—
883	#41	—	4	1	no	—
884	#41	—	4	1	no	—
885	#41	—	8	2	no	—
886	#41	—	8	2	no	—
887	#41	—	8	4	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
891	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
892	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
893	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
894	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
895	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	4	2	no	—
910	C₂×D₄	—	4	2	no	—
911	C₂×D₄	—	8	2	no	—
912	C₂×D₄	—	8	2	no	—
913	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
914	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
915	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
916	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
927	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
928	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
929	Q₁₆	—	4	2	no	—
930	Q₁₆	—	4	1	no	—
931	SD₁₆	—	4	2	no	—
932	SD₁₆	—	4	2	no	—
933	SD₁₆	—	4	2	no	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	—	4	1	no	—
936	SD₁₆	—	4	2	no	—
937	SD₁₆	—	4	1	no	—
938	SD₁₆	—	4	2	no	—
939	SD₁₆	—	4	2	no	—
940	D₈	—	4	1	no	—
941	D₈	—	4	2	no	—
942	D₈	—	4	2	no	—
943	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
944	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
945	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
946	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
947	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
973	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
974	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
975	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
976	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
979	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
980	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1003	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1013	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1015	C₄²	C₂⁴×C₄₁	1	2	yes	—
1016	C₄²	C₂⁴×C₄₁	1	2	yes	—
1017	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	2	no	—
1020	C₂³	—	2	2	no	—
1021	C₂³	—	2	1	no	—
1022	C₂³	—	4	4	no	—
1023	C₂³	—	8	2	no	—
1024	C₂³	—	8	2	no	—
1025	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1026	Q₈	—	2	2	no	—
1027	Q₈	—	2	2	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	2	1	no	—
1030	Q₈	—	2	1	no	—
1031	Q₈	—	2	2	no	—
1032	Q₈	—	2	1	no	—
1033	Q₈	—	2	1	no	—
1034	Q₈	—	4	2	no	—
1035	Q₈	—	8	1	no	—
1036	Q₈	—	8	2	no	—
1037	D₄	—	2	1	no	—
1038	D₄	—	2	1	no	—
1039	D₄	—	2	2	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	2	1	no	—
1042	D₄	—	2	2	no	—
1043	D₄	—	2	2	no	—
1044	D₄	—	2	1	no	—
1045	D₄	—	4	4	no	—
1046	D₄	—	4	4	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	2	no	—
1050	D₄	—	8	2	no	—
1051	D₄	—	8	1	no	—
1052	D₄	—	8	1	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	2	no	—
1057	D₄	—	8	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	2	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	2	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1084	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1085	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1087	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1088	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1089	C₈	—	2	2	no	—
1090	C₈	—	2	1	no	—
1091	C₈	—	2	2	no	—
1092	C₈	—	2	1	no	—
1093	C₈	—	2	1	no	—
1094	C₈	—	2	1	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	1	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	2	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	16	4	no	—
1111	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1112	C₄	—	2	1	no	—
1113	C₄	—	2	2	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	1	no	—
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	2	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	1	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	2	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	C₄₁×#577	1	2	yes	—
1129	C₄	C₄₁×#585	1	1	yes	characteristic
1130	C₄	C₄₁×#585	1	1	yes	characteristic
1131	C₂	—	4	1	no	—
1132	C₂	—	8	2	no	—
1133	C₂	—	8	2	no	—
1134	C₂	—	8	1	no	—
1135	C₂	—	8	1	no	—
1136	C₂	C₄₁×#3487	1	1	yes	characteristic
1137	C₂	C₂×C₄₁×#577	1	1	yes	characteristic
1138	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 ◁ C₄₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3555	C₂	semidirect
2. C₄₁×#3508	C₂	semidirect
3. C₄₁×#3401	C₂	semidirect
4. C₄₁×#3400	C₂	semidirect
5. C₄₁×#3397	C₂	semidirect
6. C₄₁×#3397	C₂	semidirect
7. C₄₁×#3394	C₂	semidirect
8. C₄₁×#3392	C₂	semidirect
9. C₄₁×#3375	C₂	semidirect
10. C₄₁×#3371	C₂	semidirect
11. C₄₁×#3368	C₂	semidirect
12. C₄₁×#3366	C₂	semidirect
13. C₄₁×#3362	C₂	semidirect
14. C₄₁×#3361	C₂	semidirect
15. C₄₁×#3224	C₂	semidirect
16. C₄₁×#3222	C₂	semidirect
17. C₄₁×#3217	C₂	semidirect
18. C₄₁×#3208	C₂	semidirect
19. C₄₁×#3123	C₂	semidirect
20. C₄₁×#3118	C₂	semidirect
21. C₄₁×#3116	C₂	semidirect
22. C₄₁×#3102	C₂	semidirect
23. C₄₁×#2985	C₂	semidirect
28. Q₈²×C₄₁	C₂²	semidirect
29. C₄₁×#557	C₂²	semidirect
30. C₄₁×#557	C₂²	semidirect
32. C₄₁×#556	C₂²	semidirect
33. C₄₁×#556	C₂²	semidirect
34. C₄₁×#554	C₂²	semidirect
57. C₄₁×#497	C₂²	semidirect
59. C₄₁×#496	C₂²	semidirect
60. C₄₁×#495	C₂²	semidirect
63. C₄₁×#492	C₂²	semidirect
65. C₄₁×#490	C₂²	semidirect
66. C₄₁×#489	C₂²	semidirect
67. C₄₁×#488	C₂²	semidirect
70. C₄₁×#486	C₂²	semidirect
74. C₄₁×#479	C₂²	semidirect
75. C₄₁×#478	C₂²	semidirect
76. C₄₁×#478	C₂²	semidirect
77. C₄₁×#478	C₂²	semidirect
78. C₄₁×#477	C₂²	semidirect
79. C₄₁×#476	C₂²	semidirect
80. C₄₁×#476	C₂²	semidirect
81. C₄₁×#474	C₂²	semidirect
82. C₄₁×#464	C₂²	semidirect
83. C₄₁×#464	C₂²	semidirect
84. C₄₁×#464	C₂²	semidirect
85. C₄₁×#464	C₂²	semidirect
86. C₄₁×#463	C₂²	semidirect
87. C₄₁×#463	C₂²	semidirect
88. C₄₁×#463	C₂²	semidirect
89. C₄₁×#463	C₂²	semidirect
90. C₄₁×#462	C₂²	semidirect
91. C₄₁×#461	C₂²	semidirect
92. C₄₁×#461	C₂²	semidirect
93. C₄₁×#461	C₂²	semidirect
98. C₄₁×#460	C₂²	semidirect
99. C₄₁×#460	C₂²	semidirect
100. C₄₁×#460	C₂²	semidirect
103. C₄₁×#459	C₂²	semidirect
111. C₄₁×#446	C₂²	semidirect
112. C₄₁×#446	C₂²	semidirect
113. C₄₁×#446	C₂²	semidirect
114. C₄₁×#446	C₂²	semidirect
115. C₈×Q₈×C₄₁	C₂²	semidirect
116. C₈×Q₈×C₄₁	C₂²	semidirect
117. C₄₁×#442	C₂²	semidirect
118. C₄₁×#441	C₂²	semidirect
119. C₄₁×#440	C₂²	semidirect
120. C₄₁×#440	C₂²	semidirect
121. C₄₁×#440	C₂²	semidirect
122. C₄₁×#440	C₂²	semidirect
123. C₄×Q₁₆×C₄₁	C₂²	semidirect
124. C₄×SD₁₆×C₄₁	C₂²	semidirect
125. C₄×SD₁₆×C₄₁	C₂²	semidirect
126. C₄×SD₁₆×C₄₁	C₂²	semidirect
127. C₄×SD₁₆×C₄₁	C₂²	semidirect
128. C₄×SD₁₆×C₄₁	C₂²	semidirect
129. C₄×D₈×C₄₁	C₂²	semidirect
130. C₄×D₈×C₄₁	C₂²	semidirect
525. #61921	C₄₁	direct (N × H)
562. #3555	C₂×C₄₁	semidirect
563. #3508	C₂×C₄₁	semidirect
564. #3401	C₂×C₄₁	semidirect
565. #3400	C₂×C₄₁	semidirect
566. #3397	C₂×C₄₁	semidirect
567. #3397	C₂×C₄₁	semidirect
568. #3394	C₂×C₄₁	semidirect
569. #3392	C₂×C₄₁	semidirect
570. #3375	C₂×C₄₁	semidirect
571. #3371	C₂×C₄₁	semidirect
572. #3368	C₂×C₄₁	semidirect
573. #3366	C₂×C₄₁	semidirect
574. #3362	C₂×C₄₁	semidirect
575. #3361	C₂×C₄₁	semidirect
576. #3224	C₂×C₄₁	semidirect
577. #3222	C₂×C₄₁	semidirect
578. #3217	C₂×C₄₁	semidirect
579. #3208	C₂×C₄₁	semidirect
580. #3123	C₂×C₄₁	semidirect
581. #3118	C₂×C₄₁	semidirect
582. #3116	C₂×C₄₁	semidirect
583. #3102	C₂×C₄₁	semidirect
584. #2985	C₂×C₄₁	semidirect
597. Q₈²	C₂²×C₄₁	semidirect
598. #557	C₂²×C₄₁	semidirect
599. #557	C₂²×C₄₁	semidirect
601. #556	C₂²×C₄₁	semidirect
602. #556	C₂²×C₄₁	semidirect
603. #554	C₂²×C₄₁	semidirect
626. #497	C₂²×C₄₁	semidirect
628. #496	C₂²×C₄₁	semidirect
629. #495	C₂²×C₄₁	semidirect
632. #492	C₂²×C₄₁	semidirect
634. #490	C₂²×C₄₁	semidirect
635. #489	C₂²×C₄₁	semidirect
636. #488	C₂²×C₄₁	semidirect
639. #486	C₂²×C₄₁	semidirect
643. #479	C₂²×C₄₁	semidirect
644. #478	C₂²×C₄₁	semidirect
645. #478	C₂²×C₄₁	semidirect
646. #478	C₂²×C₄₁	semidirect
647. #477	C₂²×C₄₁	semidirect
648. #476	C₂²×C₄₁	semidirect
649. #476	C₂²×C₄₁	semidirect
650. #474	C₂²×C₄₁	semidirect
651. #464	C₂²×C₄₁	semidirect
652. #464	C₂²×C₄₁	semidirect
653. #464	C₂²×C₄₁	semidirect
654. #464	C₂²×C₄₁	semidirect
655. #463	C₂²×C₄₁	semidirect
656. #463	C₂²×C₄₁	semidirect
657. #463	C₂²×C₄₁	semidirect
658. #463	C₂²×C₄₁	semidirect
659. #462	C₂²×C₄₁	semidirect
660. #461	C₂²×C₄₁	semidirect
661. #461	C₂²×C₄₁	semidirect
662. #461	C₂²×C₄₁	semidirect
667. #460	C₂²×C₄₁	semidirect
668. #460	C₂²×C₄₁	semidirect
669. #460	C₂²×C₄₁	semidirect
672. #459	C₂²×C₄₁	semidirect
680. #446	C₂²×C₄₁	semidirect
681. #446	C₂²×C₄₁	semidirect
682. #446	C₂²×C₄₁	semidirect
683. #446	C₂²×C₄₁	semidirect
684. C₈×Q₈	C₂²×C₄₁	semidirect
685. C₈×Q₈	C₂²×C₄₁	semidirect
686. #442	C₂²×C₄₁	semidirect
687. #441	C₂²×C₄₁	semidirect
688. #440	C₂²×C₄₁	semidirect
689. #440	C₂²×C₄₁	semidirect
690. #440	C₂²×C₄₁	semidirect
691. #440	C₂²×C₄₁	semidirect
692. C₄×Q₁₆	C₂²×C₄₁	semidirect
693. C₄×SD₁₆	C₂²×C₄₁	semidirect
694. C₄×SD₁₆	C₂²×C₄₁	semidirect
695. C₄×SD₁₆	C₂²×C₄₁	semidirect
696. C₄×SD₁₆	C₂²×C₄₁	semidirect
697. C₄×SD₁₆	C₂²×C₄₁	semidirect
698. C₄×D₈	C₂²×C₄₁	semidirect
699. C₄×D₈	C₂²×C₄₁	semidirect
704. C₄₁	#61921	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×#3555	2
C₄₁×#3508	2
C₄₁×#3401	2
C₄₁×#3400	2
C₄₁×#3397	2
C₄₁×#3394	2
C₄₁×#3392	2
C₄₁×#3375	2
C₄₁×#3371	2
C₄₁×#3368	2
C₄₁×#3366	2
C₄₁×#3362	2
C₄₁×#3361	2
C₄₁×#3224	2
C₄₁×#3222	2
C₄₁×#3217	2
C₄₁×#3208	2
C₄₁×#3123	2
C₄₁×#3118	2
C₄₁×#3116	2
C₄₁×#3102	2
C₄₁×#2985	2
#61921	41

Subgroups — C41×#61921 #23838122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61921 #23838122