Subgroups — C₄₁×#61920 #23838121

Order 10496.

1816 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3403	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3399	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#3391	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3370	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3366	C₂	1	2	yes	maximal, complemented
13	C₄₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3358	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3224	C₂	1	2	yes	maximal, complemented
16	C₄₁×#3220	C₂	1	2	yes	maximal, complemented
17	C₄₁×#3217	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#3122	C₂	1	2	yes	maximal, complemented
20	C₄₁×#3118	C₂	1	2	yes	maximal, complemented
21	C₄₁×#3115	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×#562	—	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	C₄₁×#559	C₂²	1	1	yes	characteristic, complemented
29	C₄₁×#559	C₂²	1	2	yes	complemented
30	C₄₁×#557	C₂²	1	1	yes	characteristic, complemented
31	C₄₁×#554	C₂²	1	2	yes	complemented
32	C₄₁×#550	C₂²	1	1	yes	characteristic
33	C₄₁×#550	C₂²	1	2	yes	—
34	C₄₁×#550	C₂²	1	1	yes	characteristic
35	C₄₁×#550	C₂²	1	1	yes	characteristic, complemented
36	D₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
37	C₄₁×#548	—	2	1	no	—
38	C₄₁×#547	—	2	1	no	—
39	C₄₁×#546	—	2	1	no	—
40	C₄₁×#546	—	2	1	no	—
41	C₄₁×#546	—	2	2	no	—
42	C₄₁×#542	—	2	1	no	—
43	C₄₁×#542	C₂²	1	2	yes	—
44	C₄₁×#540	—	2	2	no	—
45	C₄₁×#540	C₂²	1	2	yes	—
46	C₄₁×#539	—	2	2	no	—
47	C₄₁×#536	—	2	1	no	—
48	C₄₁×#535	C₂²	1	2	yes	—
49	C₄₁×#533	C₂²	1	1	yes	characteristic
50	C₄₁×#532	—	2	1	no	—
51	C₄₁×#532	—	2	1	no	—
52	C₄₁×#532	C₂²	1	1	yes	characteristic
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×#496	C₂²	1	2	yes	—
58	C₄₁×#496	C₂²	1	2	yes	complemented
59	C₄₁×#496	C₂²	1	2	yes	complemented
60	C₄₁×#495	C₂²	1	2	yes	complemented
61	C₄₁×#493	C₂²	1	1	yes	characteristic
62	C₄₁×#493	C₂²	1	1	yes	characteristic
63	C₄₁×#493	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×#482	C₂²	1	1	yes	characteristic
73	C₄₁×#482	C₂²	1	2	yes	—
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×#476	C₂²	1	2	yes	complemented
79	C₄₁×#475	C₂²	1	1	yes	characteristic, complemented
80	C₄₁×#474	C₂²	1	1	yes	characteristic, 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×#463	C₂²	1	1	yes	characteristic, complemented
85	C₄₁×#463	C₂²	1	2	yes	complemented
86	C₄₁×#463	C₂²	1	2	yes	complemented
87	C₄₁×#463	C₂²	1	2	yes	complemented
88	C₄₁×#463	C₂²	1	2	yes	complemented
89	C₄₁×#463	C₂²	1	2	yes	complemented
90	C₄₁×#460	C₂²	1	1	yes	characteristic
91	C₄₁×#460	C₂²	1	1	yes	characteristic
92	C₄₁×#460	C₂²	1	2	yes	complemented
93	C₄₁×#460	C₂²	1	1	yes	characteristic, complemented
94	C₄₁×#459	C₂²	1	1	yes	characteristic
95	C₄₁×#459	C₂²	1	2	yes	—
96	C₄₁×#459	C₂²	1	2	yes	—
97	C₄₁×#459	C₂²	1	1	yes	characteristic
98	C₄₁×#459	C₂²	1	2	yes	complemented
99	C₄₁×#459	C₂²	1	2	yes	complemented
100	C₄₁×#459	C₂²	1	2	yes	complemented
101	C₄₁×#459	C₂²	1	1	yes	characteristic, complemented
102	C₄₁×#459	C₂²	1	2	yes	complemented
103	C₄₁×#459	C₂²	1	2	yes	complemented
104	C₄₁×#452	C₂²	1	1	yes	characteristic
105	C₄₁×#450	C₂²	1	2	yes	—
106	C₄₁×#449	C₂²	1	1	yes	characteristic
107	C₄₁×#449	C₂²	1	2	yes	—
108	C₄₁×#447	C₂²	1	2	yes	—
109	C₄₁×#447	C₂²	1	2	yes	—
110	C₄₁×#447	C₂²	1	2	yes	—
111	C₄₁×#446	C₂²	1	2	yes	complemented
112	C₄₁×#446	C₂²	1	1	yes	characteristic, 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×#442	C₂²	1	2	yes	complemented
119	C₄₁×#442	C₂²	1	2	yes	complemented
120	C₄₁×#442	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×D₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
128	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
129	C₄×D₈×C₄₁	C₂²	1	2	yes	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	—	2	1	no	—
139	C₂×#41×C₄₁	—	2	1	no	—
140	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
141	C₂²×Q₈×C₄₁	—	2	1	no	—
142	C₂²×D₄×C₄₁	—	2	1	no	—
143	C₂²×D₄×C₄₁	—	2	1	no	—
144	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
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×D₈×C₄₁	C₂³	1	2	yes	—
152	C₂×D₈×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	C₂×D₈×C₄₁	C₂³	1	2	yes	—
157	C₂×D₈×C₄₁	C₂³	1	2	yes	—
158	C₂×D₈×C₄₁	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₄₁	—	2	1	no	—
160	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
161	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
162	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
164	#127×C₄₁	—	2	1	no	—
165	#127×C₄₁	—	2	1	no	—
166	#127×C₄₁	C₂³	1	2	yes	—
167	#127×C₄₁	C₂³	1	1	yes	characteristic
168	#127×C₄₁	C₂³	1	1	yes	characteristic
169	#127×C₄₁	C₂³	1	1	yes	characteristic
170	#127×C₄₁	C₂³	1	2	yes	—
171	#127×C₄₁	C₂³	1	2	yes	—
172	#127×C₄₁	C₂³	1	2	yes	—
173	#126×C₄₁	—	2	2	no	—
174	#126×C₄₁	—	2	1	no	—
175	#125×C₄₁	—	2	2	no	—
176	#125×C₄₁	D₄	1	2	yes	—
177	#125×C₄₁	C₂³	1	1	yes	characteristic
178	#125×C₄₁	C₂³	1	2	yes	—
179	#124×C₄₁	—	2	1	no	—
180	#124×C₄₁	—	2	1	no	—
181	#124×C₄₁	—	2	2	no	—
182	#124×C₄₁	—	2	1	no	—
183	#124×C₄₁	—	2	2	no	—
184	#124×C₄₁	—	2	2	no	—
185	#124×C₄₁	—	2	1	no	—
186	#124×C₄₁	C₂³	1	1	yes	characteristic
187	#124×C₄₁	C₂³	1	2	yes	—
188	#124×C₄₁	C₂³	1	2	yes	—
189	#124×C₄₁	C₂³	1	2	yes	—
190	#123×C₄₁	—	2	1	no	—
191	#123×C₄₁	—	2	2	no	—
192	#123×C₄₁	—	2	2	no	—
193	#123×C₄₁	—	2	2	no	—
194	#123×C₄₁	—	2	2	no	—
195	#123×C₄₁	—	2	2	no	—
196	#123×C₄₁	—	2	2	no	—
197	#123×C₄₁	—	2	2	no	—
198	#123×C₄₁	—	2	2	no	—
199	#123×C₄₁	—	2	2	no	—
200	#123×C₄₁	—	2	2	no	—
201	C₂²⋊Q₈×C₄₁	—	2	2	no	—
202	C₂²⋊Q₈×C₄₁	—	2	2	no	—
203	C₂²⋊Q₈×C₄₁	—	2	2	no	—
204	C₂²⋊Q₈×C₄₁	—	2	2	no	—
205	C₂²⋊Q₈×C₄₁	—	2	2	no	—
206	C₂²⋊Q₈×C₄₁	—	2	1	no	—
207	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
210	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
211	#121×C₄₁	—	2	1	no	—
212	#121×C₄₁	—	2	2	no	—
213	#121×C₄₁	—	2	2	no	—
214	#121×C₄₁	—	2	1	no	—
215	#121×C₄₁	—	2	1	no	—
216	#121×C₄₁	—	2	2	no	—
217	#121×C₄₁	—	2	2	no	—
218	#121×C₄₁	—	2	2	no	—
219	#121×C₄₁	—	2	2	no	—
220	#121×C₄₁	—	2	2	no	—
221	#121×C₄₁	—	2	2	no	—
222	#121×C₄₁	—	2	1	no	—
223	#121×C₄₁	—	2	2	no	—
224	#121×C₄₁	—	2	2	no	—
225	#121×C₄₁	C₂³	1	1	yes	characteristic
226	#121×C₄₁	C₂³	1	2	yes	—
227	#120×C₄₁	—	2	2	no	—
228	#120×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	1	yes	characteristic
235	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
237	C₄×D₄×C₄₁	—	2	1	no	—
238	C₄×D₄×C₄₁	—	2	1	no	—
239	C₄×D₄×C₄₁	—	2	1	no	—
240	C₄×D₄×C₄₁	—	2	2	no	—
241	C₄×D₄×C₄₁	—	2	2	no	—
242	C₄×D₄×C₄₁	—	2	1	no	—
243	C₄×D₄×C₄₁	—	2	1	no	—
244	C₄×D₄×C₄₁	—	2	2	no	—
245	C₄×D₄×C₄₁	—	2	2	no	—
246	C₄×D₄×C₄₁	—	2	1	no	—
247	C₄×D₄×C₄₁	—	2	1	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	C₄×D₄×C₄₁	C₂³	1	2	yes	—
257	C₄×D₄×C₄₁	C₂³	1	2	yes	—
258	C₄×D₄×C₄₁	C₂³	1	2	yes	—
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	2	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	1	yes	characteristic
269	#107×C₄₁	C₂³	1	1	yes	characteristic
270	#107×C₄₁	C₂³	1	2	yes	—
271	#106×C₄₁	C₂³	1	2	yes	—
272	#106×C₄₁	C₂³	1	1	yes	characteristic
273	#106×C₄₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
284	#103×C₄₁	C₂³	1	1	yes	characteristic
285	#103×C₄₁	C₂³	1	1	yes	characteristic
286	#103×C₄₁	C₂³	1	2	yes	—
287	#102×C₄₁	C₂³	1	1	yes	characteristic
288	#102×C₄₁	C₂³	1	2	yes	—
289	#102×C₄₁	C₂³	1	2	yes	—
290	#102×C₄₁	C₂³	1	2	yes	—
291	#102×C₄₁	C₂³	1	2	yes	—
292	#102×C₄₁	C₂³	1	2	yes	—
293	#102×C₄₁	C₂³	1	1	yes	characteristic
294	#102×C₄₁	C₂³	1	1	yes	characteristic
295	#102×C₄₁	C₂³	1	2	yes	—
296	#102×C₄₁	C₂³	1	1	yes	characteristic
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	2	no	—
318	#41×C₄₁	—	8	2	no	—
319	#41×C₄₁	—	8	4	no	—
320	C₂×Q₈×C₄₁	—	2	1	no	—
321	C₂×Q₈×C₄₁	—	2	2	no	—
322	C₂×Q₈×C₄₁	—	8	2	no	—
323	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₄₁	—	2	1	no	—
329	C₂×D₄×C₄₁	—	2	1	no	—
330	C₂×D₄×C₄₁	—	2	2	no	—
331	C₂×D₄×C₄₁	—	2	2	no	—
332	C₂×D₄×C₄₁	—	2	1	no	—
333	C₂×D₄×C₄₁	—	2	2	no	—
334	C₂×D₄×C₄₁	—	2	1	no	—
335	C₂×D₄×C₄₁	—	2	1	no	—
336	C₂×D₄×C₄₁	—	2	1	no	—
337	C₂×D₄×C₄₁	—	2	2	no	—
338	C₂×D₄×C₄₁	—	2	2	no	—
339	C₂×D₄×C₄₁	—	2	2	no	—
340	C₂×D₄×C₄₁	—	2	2	no	—
341	C₂×D₄×C₄₁	—	2	2	no	—
342	C₂×D₄×C₄₁	—	2	2	no	—
343	C₂×D₄×C₄₁	—	2	1	no	—
344	C₂×D₄×C₄₁	—	2	1	no	—
345	C₂×D₄×C₄₁	—	2	2	no	—
346	C₂×D₄×C₄₁	—	4	2	no	—
347	C₂×D₄×C₄₁	—	4	2	no	—
348	C₂×D₄×C₄₁	—	8	2	no	—
349	C₂×D₄×C₄₁	—	8	2	no	—
350	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
351	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
352	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₄₁	—	2	1	no	—
356	C₂²×C₄×C₄₁	—	2	1	no	—
357	C₂²×C₄×C₄₁	—	2	1	no	—
358	C₂²×C₄×C₄₁	—	2	1	no	—
359	C₂²×C₄×C₄₁	—	2	2	no	—
360	C₂²×C₄×C₄₁	—	2	2	no	—
361	C₂²×C₄×C₄₁	—	2	2	no	—
362	C₂²×C₄×C₄₁	—	2	2	no	—
363	C₂²×C₄×C₄₁	—	2	2	no	—
364	C₂²×C₄×C₄₁	—	2	2	no	—
365	C₂²×C₄×C₄₁	—	2	2	no	—
366	C₂²×C₄×C₄₁	—	2	2	no	—
367	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
370	Q₁₆×C₄₁	—	4	1	no	—
371	SD₁₆×C₄₁	—	4	1	no	—
372	SD₁₆×C₄₁	—	4	2	no	—
373	SD₁₆×C₄₁	—	4	1	no	—
374	SD₁₆×C₄₁	—	4	2	no	—
375	SD₁₆×C₄₁	—	4	2	no	—
376	D₈×C₄₁	—	4	1	no	—
377	D₈×C₄₁	—	4	2	no	—
378	D₈×C₄₁	—	4	2	no	—
379	D₈×C₄₁	—	4	2	no	—
380	D₈×C₄₁	—	4	2	no	—
381	D₈×C₄₁	—	4	2	no	—
382	D₈×C₄₁	—	4	2	no	—
383	D₈×C₄₁	—	4	2	no	—
384	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
387	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
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	1	no	—
394	C₄⋊C₄×C₄₁	—	2	1	no	—
395	C₄⋊C₄×C₄₁	—	2	1	no	—
396	C₄⋊C₄×C₄₁	—	2	1	no	—
397	C₄⋊C₄×C₄₁	—	2	1	no	—
398	C₄⋊C₄×C₄₁	—	2	2	no	—
399	C₄⋊C₄×C₄₁	—	2	2	no	—
400	C₄⋊C₄×C₄₁	—	2	1	no	—
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	1	yes	characteristic
405	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
415	C₂²⋊C₄×C₄₁	—	2	1	no	—
416	C₂²⋊C₄×C₄₁	—	2	1	no	—
417	C₂²⋊C₄×C₄₁	—	2	2	no	—
418	C₂²⋊C₄×C₄₁	—	2	2	no	—
419	C₂²⋊C₄×C₄₁	—	2	2	no	—
420	C₂²⋊C₄×C₄₁	—	2	2	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	1	no	—
425	C₂²⋊C₄×C₄₁	—	2	1	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	2	no	—
431	C₂²⋊C₄×C₄₁	—	2	2	no	—
432	C₂²⋊C₄×C₄₁	—	2	2	no	—
433	C₂²⋊C₄×C₄₁	—	2	1	no	—
434	C₂²⋊C₄×C₄₁	—	2	2	no	—
435	C₂²⋊C₄×C₄₁	—	2	2	no	—
436	C₂²⋊C₄×C₄₁	—	2	2	no	—
437	C₂²⋊C₄×C₄₁	—	2	2	no	—
438	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
440	C₄²×C₄₁	—	2	1	no	—
441	C₄²×C₄₁	—	2	1	no	—
442	C₄²×C₄₁	—	2	1	no	—
443	C₄²×C₄₁	—	2	1	no	—
444	C₄²×C₄₁	—	2	2	no	—
445	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
448	C₄²×C₄₁	C₂⁴	1	2	yes	—
449	C₄²×C₄₁	C₂⁴	1	2	yes	—
450	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
451	C₂³×C₄₁	—	2	2	no	—
452	C₂³×C₄₁	—	2	1	no	—
453	C₂³×C₄₁	—	2	2	no	—
454	C₂³×C₄₁	—	2	2	no	—
455	C₂³×C₄₁	—	2	1	no	—
456	C₂³×C₄₁	—	4	4	no	—
457	C₂³×C₄₁	—	8	2	no	—
458	C₂³×C₄₁	—	8	2	no	—
459	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
460	Q₈×C₄₁	—	2	2	no	—
461	Q₈×C₄₁	—	2	2	no	—
462	Q₈×C₄₁	—	2	1	no	—
463	Q₈×C₄₁	—	2	1	no	—
464	Q₈×C₄₁	—	2	1	no	—
465	Q₈×C₄₁	—	2	1	no	—
466	Q₈×C₄₁	—	4	2	no	—
467	Q₈×C₄₁	—	4	2	no	—
468	Q₈×C₄₁	—	8	2	no	—
469	D₄×C₄₁	—	2	1	no	—
470	D₄×C₄₁	—	2	2	no	—
471	D₄×C₄₁	—	2	2	no	—
472	D₄×C₄₁	—	2	1	no	—
473	D₄×C₄₁	—	2	2	no	—
474	D₄×C₄₁	—	2	2	no	—
475	D₄×C₄₁	—	2	1	no	—
476	D₄×C₄₁	—	2	2	no	—
477	D₄×C₄₁	—	2	2	no	—
478	D₄×C₄₁	—	2	1	no	—
479	D₄×C₄₁	—	4	4	no	—
480	D₄×C₄₁	—	4	4	no	—
481	D₄×C₄₁	—	4	2	no	—
482	D₄×C₄₁	—	4	2	no	—
483	D₄×C₄₁	—	4	2	no	—
484	D₄×C₄₁	—	4	2	no	—
485	D₄×C₄₁	—	8	1	no	—
486	D₄×C₄₁	—	8	2	no	—
487	D₄×C₄₁	—	8	1	no	—
488	D₄×C₄₁	—	8	1	no	—
489	D₄×C₄₁	—	8	2	no	—
490	D₄×C₄₁	—	8	2	no	—
491	D₄×C₄₁	—	8	2	no	—
492	D₄×C₄₁	—	8	2	no	—
493	D₄×C₄₁	—	8	2	no	—
494	D₄×C₄₁	—	8	2	no	—
495	D₄×C₄₁	—	8	1	no	—
496	D₄×C₄₁	—	8	2	no	—
497	C₂×C₄×C₄₁	—	2	2	no	—
498	C₂×C₄×C₄₁	—	2	1	no	—
499	C₂×C₄×C₄₁	—	2	1	no	—
500	C₂×C₄×C₄₁	—	2	1	no	—
501	C₂×C₄×C₄₁	—	2	1	no	—
502	C₂×C₄×C₄₁	—	2	1	no	—
503	C₂×C₄×C₄₁	—	2	1	no	—
504	C₂×C₄×C₄₁	—	2	1	no	—
505	C₂×C₄×C₄₁	—	2	2	no	—
506	C₂×C₄×C₄₁	—	2	1	no	—
507	C₂×C₄×C₄₁	—	4	1	no	—
508	C₂×C₄×C₄₁	—	4	2	no	—
509	C₂×C₄×C₄₁	—	4	2	no	—
510	C₂×C₄×C₄₁	—	4	2	no	—
511	C₂×C₄×C₄₁	—	4	2	no	—
512	C₂×C₄×C₄₁	—	8	2	no	—
513	C₂×C₄×C₄₁	—	8	2	no	—
514	C₂×C₄×C₄₁	—	8	2	no	—
515	C₂×C₄×C₄₁	—	8	2	no	—
516	C₂×C₄×C₄₁	—	8	2	no	—
517	C₂×C₄×C₄₁	—	8	2	no	—
518	C₂×C₄×C₄₁	—	8	2	no	—
519	C₂×C₄×C₄₁	—	8	2	no	—
520	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
530	C₈×C₄₁	—	2	1	no	—
531	C₈×C₄₁	—	2	1	no	—
532	C₈×C₄₁	—	2	1	no	—
533	C₈×C₄₁	—	2	2	no	—
534	C₈×C₄₁	—	2	1	no	—
535	C₈×C₄₁	—	2	2	no	—
536	#61920	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
537	C₂²×C₄₁	—	2	1	no	—
538	C₂²×C₄₁	—	2	1	no	—
539	C₂²×C₄₁	—	2	1	no	—
540	C₂²×C₄₁	—	4	1	no	—
541	C₂²×C₄₁	—	4	2	no	—
542	C₂²×C₄₁	—	4	2	no	—
543	C₂²×C₄₁	—	4	2	no	—
544	C₂²×C₄₁	—	4	1	no	—
545	C₂²×C₄₁	—	4	1	no	—
546	C₂²×C₄₁	—	4	2	no	—
547	C₂²×C₄₁	—	4	2	no	—
548	C₂²×C₄₁	—	4	2	no	—
549	C₂²×C₄₁	—	4	1	no	—
550	C₂²×C₄₁	—	4	1	no	—
551	C₂²×C₄₁	—	4	1	no	—
552	C₂²×C₄₁	—	4	2	no	—
553	C₂²×C₄₁	—	4	2	no	—
554	C₂²×C₄₁	—	4	2	no	—
555	C₂²×C₄₁	—	16	4	no	—
556	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
557	C₄×C₄₁	—	2	1	no	—
558	C₄×C₄₁	—	2	1	no	—
559	C₄×C₄₁	—	2	2	no	—
560	C₄×C₄₁	—	2	2	no	—
561	C₄×C₄₁	—	2	1	no	—
562	C₄×C₄₁	—	2	1	no	—
563	C₄×C₄₁	—	2	2	no	—
564	C₄×C₄₁	—	2	2	no	—
565	C₄×C₄₁	—	4	1	no	—
566	C₄×C₄₁	—	4	1	no	—
567	C₄×C₄₁	—	4	1	no	—
568	C₄×C₄₁	—	4	1	no	—
569	C₄×C₄₁	—	4	1	no	—
570	C₄×C₄₁	—	4	1	no	—
571	C₄×C₄₁	—	4	2	no	—
572	C₄×C₄₁	#576	1	2	yes	—
573	C₄×C₄₁	#585	1	1	yes	characteristic
574	C₄×C₄₁	#585	1	1	yes	characteristic
575	#3554	C₂×C₄₁	1	1	yes	characteristic, complemented
576	#3508	C₂×C₄₁	1	1	yes	characteristic, complemented
577	#3403	C₂×C₄₁	1	2	yes	complemented
578	#3399	C₂×C₄₁	1	2	yes	complemented
579	#3399	C₂×C₄₁	1	1	yes	characteristic, complemented
580	#3399	C₂×C₄₁	1	1	yes	characteristic, complemented
581	#3396	C₂×C₄₁	1	1	yes	characteristic, complemented
582	#3391	C₂×C₄₁	1	1	yes	characteristic, complemented
583	#3373	C₂×C₄₁	1	1	yes	characteristic, complemented
584	#3370	C₂×C₄₁	1	2	yes	complemented
585	#3368	C₂×C₄₁	1	1	yes	characteristic, complemented
586	#3366	C₂×C₄₁	1	2	yes	complemented
587	#3365	C₂×C₄₁	1	1	yes	characteristic, complemented
588	#3358	C₂×C₄₁	1	1	yes	characteristic, complemented
589	#3224	C₂×C₄₁	1	2	yes	complemented
590	#3220	C₂×C₄₁	1	2	yes	complemented
591	#3217	C₂×C₄₁	1	1	yes	characteristic, complemented
592	#3205	C₂×C₄₁	1	1	yes	characteristic, complemented
593	#3122	C₂×C₄₁	1	2	yes	complemented
594	#3118	C₂×C₄₁	1	2	yes	complemented
595	#3115	C₂×C₄₁	1	1	yes	characteristic, complemented
596	#3102	C₂×C₄₁	1	1	yes	characteristic, complemented
597	#2985	C₂×C₄₁	1	1	yes	characteristic, complemented
598	C₂×C₄₁	—	4	1	no	—
599	C₂×C₄₁	—	8	1	no	—
600	C₂×C₄₁	—	8	2	no	—
601	C₂×C₄₁	—	8	1	no	—
602	C₂×C₄₁	—	8	2	no	—
603	C₂×C₄₁	—	8	2	no	—
604	C₂×C₄₁	#3487	1	1	yes	characteristic
605	C₂×C₄₁	C₂×#576	1	1	yes	characteristic
606	C₂×C₄₁	#3585	1	1	yes	characteristic
607	#562	—	2	2	no	—
608	#559	C₂²×C₄₁	1	1	yes	characteristic
609	#559	C₂²×C₄₁	1	2	yes	—
610	#559	C₂²×C₄₁	1	1	yes	characteristic
611	#559	C₂²×C₄₁	1	1	yes	characteristic, complemented
612	#559	C₂²×C₄₁	1	2	yes	complemented
613	#557	C₂²×C₄₁	1	1	yes	characteristic, complemented
614	#554	C₂²×C₄₁	1	2	yes	complemented
615	#550	C₂²×C₄₁	1	1	yes	characteristic
616	#550	C₂²×C₄₁	1	2	yes	—
617	#550	C₂²×C₄₁	1	1	yes	characteristic
618	#550	C₂²×C₄₁	1	1	yes	characteristic, complemented
619	D₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
620	#548	—	2	1	no	—
621	#547	—	2	1	no	—
622	#546	—	2	1	no	—
623	#546	—	2	1	no	—
624	#546	—	2	2	no	—
625	#542	—	2	1	no	—
626	#542	C₂²×C₄₁	1	2	yes	—
627	#540	—	2	2	no	—
628	#540	C₂²×C₄₁	1	2	yes	—
629	#539	—	2	2	no	—
630	#536	—	2	1	no	—
631	#535	C₂²×C₄₁	1	2	yes	—
632	#533	C₂²×C₄₁	1	1	yes	characteristic
633	#532	—	2	1	no	—
634	#532	—	2	1	no	—
635	#532	C₂²×C₄₁	1	1	yes	characteristic
636	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
637	#529	C₂²×C₄₁	1	1	yes	characteristic
638	#518	C₂²×C₄₁	1	2	yes	—
639	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
640	#496	C₂²×C₄₁	1	2	yes	—
641	#496	C₂²×C₄₁	1	2	yes	complemented
642	#496	C₂²×C₄₁	1	2	yes	complemented
643	#495	C₂²×C₄₁	1	2	yes	complemented
644	#493	C₂²×C₄₁	1	1	yes	characteristic
645	#493	C₂²×C₄₁	1	1	yes	characteristic
646	#493	C₂²×C₄₁	1	2	yes	complemented
647	#490	C₂²×C₄₁	1	2	yes	—
648	#490	C₂²×C₄₁	1	2	yes	complemented
649	#489	C₂²×C₄₁	1	2	yes	complemented
650	#488	C₂²×C₄₁	1	2	yes	complemented
651	#486	C₂²×C₄₁	1	1	yes	characteristic
652	#486	C₂²×C₄₁	1	1	yes	characteristic
653	#486	C₂²×C₄₁	1	2	yes	complemented
654	#485	C₂²×C₄₁	1	1	yes	characteristic
655	#482	C₂²×C₄₁	1	1	yes	characteristic
656	#482	C₂²×C₄₁	1	2	yes	—
657	#479	C₂²×C₄₁	1	1	yes	characteristic, complemented
658	#478	C₂²×C₄₁	1	1	yes	characteristic, complemented
659	#478	C₂²×C₄₁	1	2	yes	complemented
660	#478	C₂²×C₄₁	1	2	yes	complemented
661	#476	C₂²×C₄₁	1	2	yes	complemented
662	#475	C₂²×C₄₁	1	1	yes	characteristic, complemented
663	#474	C₂²×C₄₁	1	1	yes	characteristic, complemented
664	#474	C₂²×C₄₁	1	2	yes	complemented
665	#464	C₂²×C₄₁	1	1	yes	characteristic, complemented
666	#464	C₂²×C₄₁	1	2	yes	complemented
667	#463	C₂²×C₄₁	1	1	yes	characteristic, complemented
668	#463	C₂²×C₄₁	1	2	yes	complemented
669	#463	C₂²×C₄₁	1	2	yes	complemented
670	#463	C₂²×C₄₁	1	2	yes	complemented
671	#463	C₂²×C₄₁	1	2	yes	complemented
672	#463	C₂²×C₄₁	1	2	yes	complemented
673	#460	C₂²×C₄₁	1	1	yes	characteristic
674	#460	C₂²×C₄₁	1	1	yes	characteristic
675	#460	C₂²×C₄₁	1	2	yes	complemented
676	#460	C₂²×C₄₁	1	1	yes	characteristic, complemented
677	#459	C₂²×C₄₁	1	1	yes	characteristic
678	#459	C₂²×C₄₁	1	2	yes	—
679	#459	C₂²×C₄₁	1	2	yes	—
680	#459	C₂²×C₄₁	1	1	yes	characteristic
681	#459	C₂²×C₄₁	1	2	yes	complemented
682	#459	C₂²×C₄₁	1	2	yes	complemented
683	#459	C₂²×C₄₁	1	2	yes	complemented
684	#459	C₂²×C₄₁	1	1	yes	characteristic, complemented
685	#459	C₂²×C₄₁	1	2	yes	complemented
686	#459	C₂²×C₄₁	1	2	yes	complemented
687	#452	C₂²×C₄₁	1	1	yes	characteristic
688	#450	C₂²×C₄₁	1	2	yes	—
689	#449	C₂²×C₄₁	1	1	yes	characteristic
690	#449	C₂²×C₄₁	1	2	yes	—
691	#447	C₂²×C₄₁	1	2	yes	—
692	#447	C₂²×C₄₁	1	2	yes	—
693	#447	C₂²×C₄₁	1	2	yes	—
694	#446	C₂²×C₄₁	1	2	yes	complemented
695	#446	C₂²×C₄₁	1	1	yes	characteristic, complemented
696	#446	C₂²×C₄₁	1	2	yes	complemented
697	#446	C₂²×C₄₁	1	1	yes	characteristic, complemented
698	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
699	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
700	#442	C₂²×C₄₁	1	2	yes	complemented
701	#442	C₂²×C₄₁	1	2	yes	complemented
702	#442	C₂²×C₄₁	1	2	yes	complemented
703	#442	C₂²×C₄₁	1	2	yes	complemented
704	#440	C₂²×C₄₁	1	2	yes	complemented
705	#440	C₂²×C₄₁	1	2	yes	complemented
706	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
707	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
708	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
709	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
710	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
711	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
712	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
713	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
714	#433	C₂²×C₄₁	1	2	yes	—
715	#433	C₂²×C₄₁	1	2	yes	—
716	#432	C₂²×C₄₁	1	1	yes	characteristic
717	#431	C₂²×C₄₁	1	1	yes	characteristic
718	C₄₁	#61920	1	1	yes	characteristic, direct product factor, Sylow
719	C₂×#41	—	2	1	no	—
720	C₂×#41	—	2	1	no	—
721	C₂×#41	—	2	2	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	—	2	1	no	—
724	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
725	C₂²×Q₈	—	2	1	no	—
726	C₂²×D₄	—	2	1	no	—
727	C₂²×D₄	—	2	1	no	—
728	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
729	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
730	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
731	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
733	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
735	C₂×D₈	C₂³×C₄₁	1	2	yes	—
736	C₂×D₈	C₂³×C₄₁	1	2	yes	—
737	C₂×D₈	C₂³×C₄₁	1	2	yes	—
738	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
739	C₂×D₈	C₂³×C₄₁	1	2	yes	—
740	C₂×D₈	C₂³×C₄₁	1	2	yes	—
741	C₂×D₈	C₂³×C₄₁	1	2	yes	—
742	C₂×D₈	C₂³×C₄₁	1	2	yes	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
745	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
746	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
748	#127	—	2	1	no	—
749	#127	—	2	1	no	—
750	#127	C₂³×C₄₁	1	2	yes	—
751	#127	C₂³×C₄₁	1	1	yes	characteristic
752	#127	C₂³×C₄₁	1	1	yes	characteristic
753	#127	C₂³×C₄₁	1	1	yes	characteristic
754	#127	C₂³×C₄₁	1	2	yes	—
755	#127	C₂³×C₄₁	1	2	yes	—
756	#127	C₂³×C₄₁	1	2	yes	—
757	#126	—	2	2	no	—
758	#126	—	2	1	no	—
759	#125	—	2	2	no	—
760	#125	D₄×C₄₁	1	2	yes	—
761	#125	C₂³×C₄₁	1	1	yes	characteristic
762	#125	C₂³×C₄₁	1	2	yes	—
763	#124	—	2	1	no	—
764	#124	—	2	1	no	—
765	#124	—	2	2	no	—
766	#124	—	2	1	no	—
767	#124	—	2	2	no	—
768	#124	—	2	2	no	—
769	#124	—	2	1	no	—
770	#124	C₂³×C₄₁	1	1	yes	characteristic
771	#124	C₂³×C₄₁	1	2	yes	—
772	#124	C₂³×C₄₁	1	2	yes	—
773	#124	C₂³×C₄₁	1	2	yes	—
774	#123	—	2	1	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
792	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
793	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	1	no	—
799	#121	—	2	1	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	C₂³×C₄₁	1	1	yes	characteristic
810	#121	C₂³×C₄₁	1	2	yes	—
811	#120	—	2	2	no	—
812	#120	—	2	2	no	—
813	C₄×Q₈	—	2	1	no	—
814	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
815	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
816	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
817	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
818	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
819	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
820	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₄₁	1	2	yes	—
835	C₄×D₄	C₂³×C₄₁	1	2	yes	—
836	C₄×D₄	C₂³×C₄₁	1	2	yes	—
837	C₄×D₄	C₂³×C₄₁	1	2	yes	—
838	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₄₁	1	2	yes	—
840	C₄×D₄	C₂³×C₄₁	1	2	yes	—
841	C₄×D₄	C₂³×C₄₁	1	2	yes	—
842	C₄×D₄	C₂³×C₄₁	1	2	yes	—
843	#117	—	2	1	no	—
844	#117	—	2	1	no	—
845	#117	C₂³×C₄₁	1	1	yes	characteristic
846	#117	C₂³×C₄₁	1	2	yes	—
847	C₂×C₄⋊C₄	—	2	2	no	—
848	C₂×C₂²⋊C₄	—	2	2	no	—
849	C₂×C₂²⋊C₄	—	2	2	no	—
850	C₂×C₄²	—	2	1	no	—
851	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
852	#107	C₂³×C₄₁	1	1	yes	characteristic
853	#107	C₂³×C₄₁	1	1	yes	characteristic
854	#107	C₂³×C₄₁	1	2	yes	—
855	#106	C₂³×C₄₁	1	2	yes	—
856	#106	C₂³×C₄₁	1	1	yes	characteristic
857	#106	C₂³×C₄₁	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
863	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
864	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
865	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
866	#103	C₂³×C₄₁	1	1	yes	characteristic
867	#103	C₂³×C₄₁	1	1	yes	characteristic
868	#103	C₂³×C₄₁	1	1	yes	characteristic
869	#103	C₂³×C₄₁	1	1	yes	characteristic
870	#103	C₂³×C₄₁	1	2	yes	—
871	#102	C₂³×C₄₁	1	1	yes	characteristic
872	#102	C₂³×C₄₁	1	2	yes	—
873	#102	C₂³×C₄₁	1	2	yes	—
874	#102	C₂³×C₄₁	1	2	yes	—
875	#102	C₂³×C₄₁	1	2	yes	—
876	#102	C₂³×C₄₁	1	2	yes	—
877	#102	C₂³×C₄₁	1	1	yes	characteristic
878	#102	C₂³×C₄₁	1	1	yes	characteristic
879	#102	C₂³×C₄₁	1	2	yes	—
880	#102	C₂³×C₄₁	1	1	yes	characteristic
881	#102	C₂³×C₄₁	1	2	yes	—
882	#102	C₂³×C₄₁	1	2	yes	—
883	#102	C₂³×C₄₁	1	2	yes	—
884	#102	C₂³×C₄₁	1	2	yes	—
885	#102	C₂³×C₄₁	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
887	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
888	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
889	#97	C₂³×C₄₁	1	2	yes	—
890	#97	C₂³×C₄₁	1	2	yes	—
891	#97	C₂³×C₄₁	1	2	yes	—
892	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₄₁	1	2	yes	—
895	C₄×C₈	C₂³×C₄₁	1	2	yes	—
896	C₂⁴	—	2	2	no	—
897	#41	—	4	1	no	—
898	#41	—	4	1	no	—
899	#41	—	8	2	no	—
900	#41	—	8	2	no	—
901	#41	—	8	2	no	—
902	#41	—	8	2	no	—
903	#41	—	8	4	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	8	2	no	—
907	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
908	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
909	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
910	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	1	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	4	2	no	—
931	C₂×D₄	—	4	2	no	—
932	C₂×D₄	—	8	2	no	—
933	C₂×D₄	—	8	2	no	—
934	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
935	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
936	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
937	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
938	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
952	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
953	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
954	Q₁₆	—	4	1	no	—
955	SD₁₆	—	4	1	no	—
956	SD₁₆	—	4	2	no	—
957	SD₁₆	—	4	1	no	—
958	SD₁₆	—	4	2	no	—
959	SD₁₆	—	4	2	no	—
960	D₈	—	4	1	no	—
961	D₈	—	4	2	no	—
962	D₈	—	4	2	no	—
963	D₈	—	4	2	no	—
964	D₈	—	4	2	no	—
965	D₈	—	4	2	no	—
966	D₈	—	4	2	no	—
967	D₈	—	4	2	no	—
968	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
971	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
986	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
987	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
988	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
989	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
991	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
992	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
994	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
995	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
997	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1030	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1031	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₄₁	1	2	yes	—
1033	C₄²	C₂⁴×C₄₁	1	2	yes	—
1034	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	4	4	no	—
1041	C₂³	—	8	2	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1044	Q₈	—	2	2	no	—
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	4	2	no	—
1051	Q₈	—	4	2	no	—
1052	Q₈	—	8	2	no	—
1053	D₄	—	2	1	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	2	2	no	—
1056	D₄	—	2	1	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	4	4	no	—
1064	D₄	—	4	4	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	1	no	—
1071	D₄	—	8	1	no	—
1072	D₄	—	8	2	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	1	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1105	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1107	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1108	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1109	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1110	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1111	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1112	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1113	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1114	C₈	—	2	1	no	—
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	2	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	2	no	—
1120	C₂²	—	2	1	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	16	4	no	—
1139	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1140	C₄	—	2	1	no	—
1141	C₄	—	2	2	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	2	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	2	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	C₄₁×#576	1	2	yes	—
1156	C₄	C₄₁×#585	1	1	yes	characteristic
1157	C₄	C₄₁×#585	1	1	yes	characteristic
1158	C₂	—	4	1	no	—
1159	C₂	—	8	2	no	—
1160	C₂	—	8	2	no	—
1161	C₂	—	8	1	no	—
1162	C₂	—	8	1	no	—
1163	C₂	—	8	2	no	—
1164	C₂	C₄₁×#3487	1	1	yes	characteristic
1165	C₂	C₂×C₄₁×#576	1	1	yes	characteristic
1166	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×#3554	C₂	semidirect
2. C₄₁×#3508	C₂	semidirect
3. C₄₁×#3403	C₂	semidirect
4. C₄₁×#3399	C₂	semidirect
5. C₄₁×#3399	C₂	semidirect
6. C₄₁×#3399	C₂	semidirect
7. C₄₁×#3396	C₂	semidirect
8. C₄₁×#3391	C₂	semidirect
9. C₄₁×#3373	C₂	semidirect
10. C₄₁×#3370	C₂	semidirect
11. C₄₁×#3368	C₂	semidirect
12. C₄₁×#3366	C₂	semidirect
13. C₄₁×#3365	C₂	semidirect
14. C₄₁×#3358	C₂	semidirect
15. C₄₁×#3224	C₂	semidirect
16. C₄₁×#3220	C₂	semidirect
17. C₄₁×#3217	C₂	semidirect
18. C₄₁×#3205	C₂	semidirect
19. C₄₁×#3122	C₂	semidirect
20. C₄₁×#3118	C₂	semidirect
21. C₄₁×#3115	C₂	semidirect
22. C₄₁×#3102	C₂	semidirect
23. C₄₁×#2985	C₂	semidirect
28. C₄₁×#559	C₂²	semidirect
29. C₄₁×#559	C₂²	semidirect
30. C₄₁×#557	C₂²	semidirect
31. C₄₁×#554	C₂²	semidirect
35. C₄₁×#550	C₂²	semidirect
36. D₄×Q₈×C₄₁	C₂²	semidirect
58. C₄₁×#496	C₂²	semidirect
59. C₄₁×#496	C₂²	semidirect
60. C₄₁×#495	C₂²	semidirect
63. C₄₁×#493	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×#476	C₂²	semidirect
79. C₄₁×#475	C₂²	semidirect
80. C₄₁×#474	C₂²	semidirect
81. C₄₁×#474	C₂²	semidirect
82. C₄₁×#464	C₂²	semidirect
83. C₄₁×#464	C₂²	semidirect
84. C₄₁×#463	C₂²	semidirect
85. C₄₁×#463	C₂²	semidirect
86. C₄₁×#463	C₂²	semidirect
87. C₄₁×#463	C₂²	semidirect
88. C₄₁×#463	C₂²	semidirect
89. C₄₁×#463	C₂²	semidirect
92. C₄₁×#460	C₂²	semidirect
93. C₄₁×#460	C₂²	semidirect
98. C₄₁×#459	C₂²	semidirect
99. C₄₁×#459	C₂²	semidirect
100. C₄₁×#459	C₂²	semidirect
101. C₄₁×#459	C₂²	semidirect
102. C₄₁×#459	C₂²	semidirect
103. C₄₁×#459	C₂²	semidirect
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×#442	C₂²	semidirect
119. C₄₁×#442	C₂²	semidirect
120. C₄₁×#442	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×D₈×C₄₁	C₂²	semidirect
128. C₄×D₈×C₄₁	C₂²	semidirect
129. C₄×D₈×C₄₁	C₂²	semidirect
130. C₄×D₈×C₄₁	C₂²	semidirect
536. #61920	C₄₁	direct (N × H)
575. #3554	C₂×C₄₁	semidirect
576. #3508	C₂×C₄₁	semidirect
577. #3403	C₂×C₄₁	semidirect
578. #3399	C₂×C₄₁	semidirect
579. #3399	C₂×C₄₁	semidirect
580. #3399	C₂×C₄₁	semidirect
581. #3396	C₂×C₄₁	semidirect
582. #3391	C₂×C₄₁	semidirect
583. #3373	C₂×C₄₁	semidirect
584. #3370	C₂×C₄₁	semidirect
585. #3368	C₂×C₄₁	semidirect
586. #3366	C₂×C₄₁	semidirect
587. #3365	C₂×C₄₁	semidirect
588. #3358	C₂×C₄₁	semidirect
589. #3224	C₂×C₄₁	semidirect
590. #3220	C₂×C₄₁	semidirect
591. #3217	C₂×C₄₁	semidirect
592. #3205	C₂×C₄₁	semidirect
593. #3122	C₂×C₄₁	semidirect
594. #3118	C₂×C₄₁	semidirect
595. #3115	C₂×C₄₁	semidirect
596. #3102	C₂×C₄₁	semidirect
597. #2985	C₂×C₄₁	semidirect
611. #559	C₂²×C₄₁	semidirect
612. #559	C₂²×C₄₁	semidirect
613. #557	C₂²×C₄₁	semidirect
614. #554	C₂²×C₄₁	semidirect
618. #550	C₂²×C₄₁	semidirect
619. D₄×Q₈	C₂²×C₄₁	semidirect
641. #496	C₂²×C₄₁	semidirect
642. #496	C₂²×C₄₁	semidirect
643. #495	C₂²×C₄₁	semidirect
646. #493	C₂²×C₄₁	semidirect
648. #490	C₂²×C₄₁	semidirect
649. #489	C₂²×C₄₁	semidirect
650. #488	C₂²×C₄₁	semidirect
653. #486	C₂²×C₄₁	semidirect
657. #479	C₂²×C₄₁	semidirect
658. #478	C₂²×C₄₁	semidirect
659. #478	C₂²×C₄₁	semidirect
660. #478	C₂²×C₄₁	semidirect
661. #476	C₂²×C₄₁	semidirect
662. #475	C₂²×C₄₁	semidirect
663. #474	C₂²×C₄₁	semidirect
664. #474	C₂²×C₄₁	semidirect
665. #464	C₂²×C₄₁	semidirect
666. #464	C₂²×C₄₁	semidirect
667. #463	C₂²×C₄₁	semidirect
668. #463	C₂²×C₄₁	semidirect
669. #463	C₂²×C₄₁	semidirect
670. #463	C₂²×C₄₁	semidirect
671. #463	C₂²×C₄₁	semidirect
672. #463	C₂²×C₄₁	semidirect
675. #460	C₂²×C₄₁	semidirect
676. #460	C₂²×C₄₁	semidirect
681. #459	C₂²×C₄₁	semidirect
682. #459	C₂²×C₄₁	semidirect
683. #459	C₂²×C₄₁	semidirect
684. #459	C₂²×C₄₁	semidirect
685. #459	C₂²×C₄₁	semidirect
686. #459	C₂²×C₄₁	semidirect
694. #446	C₂²×C₄₁	semidirect
695. #446	C₂²×C₄₁	semidirect
696. #446	C₂²×C₄₁	semidirect
697. #446	C₂²×C₄₁	semidirect
698. C₈×Q₈	C₂²×C₄₁	semidirect
699. C₈×Q₈	C₂²×C₄₁	semidirect
700. #442	C₂²×C₄₁	semidirect
701. #442	C₂²×C₄₁	semidirect
702. #442	C₂²×C₄₁	semidirect
703. #442	C₂²×C₄₁	semidirect
704. #440	C₂²×C₄₁	semidirect
705. #440	C₂²×C₄₁	semidirect
706. C₄×Q₁₆	C₂²×C₄₁	semidirect
707. C₄×SD₁₆	C₂²×C₄₁	semidirect
708. C₄×SD₁₆	C₂²×C₄₁	semidirect
709. C₄×SD₁₆	C₂²×C₄₁	semidirect
710. C₄×D₈	C₂²×C₄₁	semidirect
711. C₄×D₈	C₂²×C₄₁	semidirect
712. C₄×D₈	C₂²×C₄₁	semidirect
713. C₄×D₈	C₂²×C₄₁	semidirect
718. C₄₁	#61920	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×#3554	2
C₄₁×#3508	2
C₄₁×#3403	2
C₄₁×#3399	2
C₄₁×#3396	2
C₄₁×#3391	2
C₄₁×#3373	2
C₄₁×#3370	2
C₄₁×#3368	2
C₄₁×#3366	2
C₄₁×#3365	2
C₄₁×#3358	2
C₄₁×#3224	2
C₄₁×#3220	2
C₄₁×#3217	2
C₄₁×#3205	2
C₄₁×#3122	2
C₄₁×#3118	2
C₄₁×#3115	2
C₄₁×#3102	2
C₄₁×#2985	2
#61920	41

Subgroups — C41×#61920 #23838121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61920 #23838121