Subgroups — C₄₁×#62019 #23838220

Order 10496.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3558	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3400	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3371	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3311	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3310	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3300	C₂	1	2	yes	maximal, complemented
8	D₄×SD₁₆×C₄₁	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3270	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3266	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3258	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3222	C₂	1	2	yes	maximal, complemented
14	C₄₁×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3121	C₂	1	2	yes	maximal, complemented
16	C₄₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#3043	C₂	1	2	yes	maximal, complemented
18	C₂×C₄₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#137×C₄₁	C₂²	1	2	yes	complemented
21	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
22	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
24	C₄₁×#562	—	2	1	no	—
25	C₄₁×H(3,𝔽₄)	—	2	1	no	—
26	C₄₁×#559	C₂²	1	2	yes	—
27	C₄₁×#557	—	2	1	no	—
28	C₄₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₄₁×#557	C₂²	1	1	yes	characteristic, complemented
30	C₄₁×#556	—	2	1	no	—
31	C₄₁×#556	C₂²	1	1	yes	characteristic, complemented
32	C₄₁×#552	—	2	2	no	—
33	C₄₁×#552	C₂²	1	2	yes	complemented
34	D₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₄₁	C₂²	1	2	yes	complemented
36	C₄₁×#548	C₂²	1	2	yes	—
37	C₄₁×#546	—	2	2	no	—
38	C₄₁×#546	C₂²	1	2	yes	—
39	D₄²×C₄₁	C₂²	1	2	yes	—
40	C₄₁×#542	C₂²	1	2	yes	—
41	C₄₁×#541	—	2	2	no	—
42	C₄₁×#541	C₂²	1	2	yes	complemented
43	C₄₁×#538	—	2	2	no	—
44	C₄₁×#538	—	2	1	no	—
45	C₄₁×#535	C₂²	1	2	yes	—
46	C₄₁×#534	—	2	1	no	—
47	C₄₁×#533	—	2	1	no	—
48	C₄₁×#533	C₂²	1	1	yes	characteristic, complemented
49	C₄₁×#532	C₂²	1	1	yes	characteristic
50	C₄₁×#529	—	2	1	no	—
51	C₄₁×#529	C₂²	1	1	yes	characteristic
52	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
53	C₄₁×#519	C₂²	1	2	yes	complemented
54	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
55	C₄₁×#497	C₂²	1	2	yes	complemented
56	C₄₁×#497	C₂²	1	2	yes	complemented
57	C₄₁×#492	C₂²	1	2	yes	—
58	C₄₁×#490	C₂²	1	2	yes	—
59	C₄₁×#489	C₂²	1	2	yes	complemented
60	C₄₁×#488	C₂²	1	2	yes	complemented
61	C₄₁×#485	C₂²	1	2	yes	complemented
62	C₄₁×#482	C₂²	1	2	yes	—
63	C₄₁×#480	C₂²	1	2	yes	complemented
64	C₄₁×#479	C₂²	1	2	yes	complemented
65	C₄₁×#478	C₂²	1	2	yes	complemented
66	C₄₁×#477	C₂²	1	1	yes	characteristic, complemented
67	C₄₁×#477	C₂²	1	1	yes	characteristic, complemented
68	C₄₁×#476	C₂²	1	2	yes	complemented
69	C₄₁×#475	C₂²	1	2	yes	complemented
70	C₄₁×#470	C₂²	1	2	yes	complemented
71	C₄₁×#468	C₂²	1	2	yes	—
72	C₄₁×#467	C₂²	1	2	yes	complemented
73	C₄₁×#465	C₂²	1	2	yes	—
74	C₄₁×#465	C₂²	1	2	yes	complemented
75	C₄₁×#465	C₂²	1	2	yes	complemented
76	C₄₁×#464	C₂²	1	2	yes	complemented
77	C₄₁×#464	C₂²	1	2	yes	complemented
78	C₄₁×#464	C₂²	1	2	yes	complemented
79	C₄₁×#464	C₂²	1	2	yes	complemented
80	C₄₁×#464	C₂²	1	2	yes	complemented
81	C₄₁×#464	C₂²	1	2	yes	complemented
82	C₄₁×#464	C₂²	1	2	yes	complemented
83	C₄₁×#464	C₂²	1	2	yes	complemented
84	C₄₁×#462	C₂²	1	2	yes	complemented
85	C₄₁×#461	C₂²	1	2	yes	complemented
86	C₄₁×#461	C₂²	1	2	yes	complemented
87	C₄₁×#460	C₂²	1	2	yes	—
88	C₄₁×#460	C₂²	1	2	yes	—
89	C₄₁×#460	C₂²	1	1	yes	characteristic, complemented
90	C₄₁×#460	C₂²	1	2	yes	complemented
91	C₄₁×#460	C₂²	1	1	yes	characteristic, complemented
92	C₄₁×#452	C₂²	1	2	yes	complemented
93	C₄₁×#452	C₂²	1	2	yes	complemented
94	C₄₁×#451	C₂²	1	2	yes	complemented
95	C₄₁×#451	C₂²	1	2	yes	complemented
96	C₄₁×#450	C₂²	1	2	yes	—
97	C₄₁×#450	C₂²	1	2	yes	complemented
98	C₄₁×#450	C₂²	1	2	yes	complemented
99	C₄₁×#448	C₂²	1	2	yes	—
100	C₄₁×#448	C₂²	1	2	yes	complemented
101	C₄₁×#446	C₂²	1	2	yes	complemented
102	C₄₁×#441	C₂²	1	2	yes	complemented
103	C₄₁×#440	C₂²	1	2	yes	complemented
104	C₄₁×#440	C₂²	1	2	yes	complemented
105	C₄₁×#440	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
108	C₄₁×#435	C₂²	1	2	yes	complemented
109	C₄₁×#435	C₂²	1	2	yes	complemented
110	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
111	C₄₁×#433	C₂²	1	2	yes	complemented
112	C₄₁×#432	C₂²	1	1	yes	characteristic, complemented
113	C₄₁×#424	C₂²	1	2	yes	complemented
114	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
115	C₄₁×#418	C₂²	1	2	yes	complemented
116	C₄₁×#416	C₂²	1	2	yes	complemented
117	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
118	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
119	C₂×#41×C₄₁	—	2	1	no	—
120	C₂×#41×C₄₁	C₂³	1	2	yes	—
121	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
123	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₄₁	—	2	2	no	—
125	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
127	#137×C₄₁	—	4	4	no	—
128	C₂×Q₁₆×C₄₁	—	4	2	no	—
129	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
130	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
131	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
132	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
133	C₂×SD₁₆×C₄₁	—	4	2	no	—
134	C₂×SD₁₆×C₄₁	—	4	4	no	—
135	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
138	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
143	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
144	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
146	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
147	C₄⋊Q₈×C₄₁	—	2	1	no	—
148	C₄⋊Q₈×C₄₁	—	2	1	no	—
149	C₄⋊Q₈×C₄₁	—	2	2	no	—
150	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
154	#127×C₄₁	C₂³	1	1	yes	characteristic
155	#127×C₄₁	C₂³	1	2	yes	—
156	#126×C₄₁	—	2	2	no	—
157	#126×C₄₁	—	2	2	no	—
158	#126×C₄₁	—	2	2	no	—
159	#126×C₄₁	—	2	2	no	—
160	#126×C₄₁	—	2	2	no	—
161	#126×C₄₁	D₄	1	2	yes	—
162	#125×C₄₁	—	2	1	no	—
163	#125×C₄₁	—	2	2	no	—
164	#125×C₄₁	—	2	2	no	—
165	#125×C₄₁	—	2	2	no	—
166	#125×C₄₁	—	2	2	no	—
167	#125×C₄₁	—	2	2	no	—
168	#125×C₄₁	—	2	1	no	—
169	#125×C₄₁	D₄	1	1	yes	characteristic
170	#125×C₄₁	C₂³	1	2	yes	—
171	#124×C₄₁	—	2	2	no	—
172	#124×C₄₁	—	2	1	no	—
173	#124×C₄₁	—	2	2	no	—
174	#124×C₄₁	—	2	2	no	—
175	#124×C₄₁	—	2	1	no	—
176	#124×C₄₁	—	2	1	no	—
177	#124×C₄₁	—	2	1	no	—
178	#124×C₄₁	D₄	1	1	yes	characteristic
179	#124×C₄₁	C₂³	1	2	yes	—
180	#124×C₄₁	C₂³	1	2	yes	—
181	#124×C₄₁	C₂³	1	2	yes	—
182	#123×C₄₁	—	2	2	no	—
183	#123×C₄₁	—	2	2	no	—
184	#123×C₄₁	—	2	2	no	—
185	#123×C₄₁	—	2	2	no	—
186	#123×C₄₁	—	2	2	no	—
187	#123×C₄₁	D₄	1	2	yes	—
188	C₂²⋊Q₈×C₄₁	—	2	1	no	—
189	C₂²⋊Q₈×C₄₁	—	2	2	no	—
190	C₂²⋊Q₈×C₄₁	—	2	2	no	—
191	C₂²⋊Q₈×C₄₁	—	2	2	no	—
192	C₂²⋊Q₈×C₄₁	—	2	2	no	—
193	C₂²⋊Q₈×C₄₁	—	2	2	no	—
194	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
195	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
199	#121×C₄₁	—	2	2	no	—
200	#121×C₄₁	—	2	1	no	—
201	#121×C₄₁	—	2	2	no	—
202	#121×C₄₁	—	2	2	no	—
203	#121×C₄₁	—	2	2	no	—
204	#121×C₄₁	—	2	2	no	—
205	#121×C₄₁	D₄	1	1	yes	characteristic
206	#121×C₄₁	C₂³	1	2	yes	—
207	#121×C₄₁	C₂³	1	2	yes	—
208	#120×C₄₁	—	2	2	no	—
209	#120×C₄₁	—	2	2	no	—
210	#120×C₄₁	—	2	2	no	—
211	#120×C₄₁	—	2	2	no	—
212	#120×C₄₁	—	2	2	no	—
213	C₄×Q₈×C₄₁	—	2	1	no	—
214	C₄×Q₈×C₄₁	—	2	2	no	—
215	C₄×Q₈×C₄₁	—	2	2	no	—
216	C₄×Q₈×C₄₁	—	2	1	no	—
217	C₄×Q₈×C₄₁	—	2	1	no	—
218	C₄×Q₈×C₄₁	—	2	1	no	—
219	C₄×Q₈×C₄₁	—	2	1	no	—
220	C₄×Q₈×C₄₁	—	2	1	no	—
221	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
228	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₄₁	—	2	2	no	—
231	C₄×D₄×C₄₁	—	2	1	no	—
232	C₄×D₄×C₄₁	—	2	2	no	—
233	C₄×D₄×C₄₁	—	2	2	no	—
234	C₄×D₄×C₄₁	—	2	1	no	—
235	C₄×D₄×C₄₁	C₂³	1	2	yes	—
236	C₄×D₄×C₄₁	C₂³	1	2	yes	—
237	C₄×D₄×C₄₁	C₂³	1	2	yes	—
238	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
239	#117×C₄₁	—	2	1	no	—
240	#117×C₄₁	—	2	2	no	—
241	#117×C₄₁	—	2	2	no	—
242	#117×C₄₁	—	2	2	no	—
243	#117×C₄₁	C₂³	1	2	yes	—
244	#117×C₄₁	C₂³	1	2	yes	—
245	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
246	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
248	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
249	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
250	C₂×C₄²×C₄₁	—	2	1	no	—
251	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
252	#107×C₄₁	C₂³	1	2	yes	—
253	#107×C₄₁	C₂³	1	2	yes	—
254	#106×C₄₁	C₂³	1	2	yes	—
255	#106×C₄₁	C₂³	1	2	yes	—
256	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
257	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
258	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
259	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
260	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
261	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
262	#103×C₄₁	C₂³	1	2	yes	—
263	#103×C₄₁	C₂³	1	2	yes	—
264	#103×C₄₁	C₂³	1	2	yes	—
265	#103×C₄₁	C₂³	1	2	yes	—
266	#103×C₄₁	C₂³	1	2	yes	—
267	#103×C₄₁	C₂³	1	2	yes	—
268	#103×C₄₁	C₂³	1	2	yes	—
269	#103×C₄₁	C₂³	1	2	yes	—
270	#102×C₄₁	C₂³	1	2	yes	—
271	#102×C₄₁	C₂³	1	2	yes	—
272	#102×C₄₁	C₂³	1	2	yes	—
273	#102×C₄₁	C₂³	1	2	yes	—
274	#102×C₄₁	C₂³	1	2	yes	—
275	#102×C₄₁	C₂³	1	2	yes	—
276	#102×C₄₁	C₂³	1	2	yes	—
277	#102×C₄₁	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
279	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
280	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
281	#97×C₄₁	C₂³	1	2	yes	—
282	#97×C₄₁	C₂³	1	2	yes	—
283	C₄×C₈×C₄₁	C₂³	1	2	yes	—
284	C₂⁴×C₄₁	—	2	1	no	—
285	C₂⁴×C₄₁	—	2	2	no	—
286	#41×C₄₁	—	4	2	no	—
287	#41×C₄₁	—	4	2	no	—
288	#41×C₄₁	—	8	2	no	—
289	C₂×Q₈×C₄₁	—	2	1	no	—
290	C₂×Q₈×C₄₁	—	2	2	no	—
291	C₂×Q₈×C₄₁	—	2	1	no	—
292	C₂×Q₈×C₄₁	—	2	1	no	—
293	C₂×Q₈×C₄₁	—	2	1	no	—
294	C₂×Q₈×C₄₁	—	2	2	no	—
295	C₂×Q₈×C₄₁	—	2	4	no	—
296	C₂×Q₈×C₄₁	—	4	1	no	—
297	C₂×Q₈×C₄₁	—	4	2	no	—
298	C₂×Q₈×C₄₁	—	4	1	no	—
299	C₂×Q₈×C₄₁	—	4	1	no	—
300	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
301	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
302	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
303	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
304	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
305	C₂×D₄×C₄₁	—	2	2	no	—
306	C₂×D₄×C₄₁	—	2	2	no	—
307	C₂×D₄×C₄₁	—	2	2	no	—
308	C₂×D₄×C₄₁	—	2	2	no	—
309	C₂×D₄×C₄₁	—	2	1	no	—
310	C₂×D₄×C₄₁	—	2	1	no	—
311	C₂×D₄×C₄₁	—	2	1	no	—
312	C₂×D₄×C₄₁	—	2	2	no	—
313	C₂×D₄×C₄₁	—	2	2	no	—
314	C₂×D₄×C₄₁	—	4	1	no	—
315	C₂×D₄×C₄₁	—	4	2	no	—
316	C₂×D₄×C₄₁	—	4	1	no	—
317	C₂×D₄×C₄₁	—	4	2	no	—
318	C₂×D₄×C₄₁	—	8	4	no	—
319	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
320	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
321	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
322	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₄₁	—	2	1	no	—
324	C₂²×C₄×C₄₁	—	2	1	no	—
325	C₂²×C₄×C₄₁	—	2	2	no	—
326	C₂²×C₄×C₄₁	—	2	1	no	—
327	C₂²×C₄×C₄₁	—	2	2	no	—
328	C₂²×C₄×C₄₁	—	2	2	no	—
329	C₂²×C₄×C₄₁	—	2	2	no	—
330	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
334	Q₁₆×C₄₁	—	2	4	no	—
335	Q₁₆×C₄₁	—	4	2	no	—
336	Q₁₆×C₄₁	—	4	2	no	—
337	Q₁₆×C₄₁	—	4	2	no	—
338	SD₁₆×C₄₁	—	2	4	no	—
339	SD₁₆×C₄₁	—	2	4	no	—
340	SD₁₆×C₄₁	—	4	2	no	—
341	SD₁₆×C₄₁	—	4	2	no	—
342	SD₁₆×C₄₁	—	4	2	no	—
343	SD₁₆×C₄₁	—	4	2	no	—
344	SD₁₆×C₄₁	—	4	2	no	—
345	SD₁₆×C₄₁	—	4	2	no	—
346	M₁₆×C₄₁	—	4	2	no	—
347	C₂×C₈×C₄₁	—	4	1	no	—
348	C₂×C₈×C₄₁	—	4	2	no	—
349	C₂×C₈×C₄₁	—	4	1	no	—
350	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
351	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
352	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
353	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
354	C₄⋊C₄×C₄₁	—	2	1	no	—
355	C₄⋊C₄×C₄₁	—	2	1	no	—
356	C₄⋊C₄×C₄₁	—	2	1	no	—
357	C₄⋊C₄×C₄₁	—	2	1	no	—
358	C₄⋊C₄×C₄₁	—	2	1	no	—
359	C₄⋊C₄×C₄₁	—	2	2	no	—
360	C₄⋊C₄×C₄₁	—	2	2	no	—
361	C₄⋊C₄×C₄₁	—	2	2	no	—
362	C₄⋊C₄×C₄₁	—	2	1	no	—
363	C₄⋊C₄×C₄₁	—	2	2	no	—
364	C₄⋊C₄×C₄₁	—	2	1	no	—
365	C₄⋊C₄×C₄₁	—	2	2	no	—
366	C₄⋊C₄×C₄₁	—	2	1	no	—
367	C₄⋊C₄×C₄₁	—	2	2	no	—
368	C₄⋊C₄×C₄₁	—	2	1	no	—
369	C₄⋊C₄×C₄₁	—	2	2	no	—
370	C₄⋊C₄×C₄₁	—	2	2	no	—
371	C₄⋊C₄×C₄₁	—	2	2	no	—
372	C₄⋊C₄×C₄₁	—	2	2	no	—
373	C₄⋊C₄×C₄₁	—	2	2	no	—
374	C₄⋊C₄×C₄₁	—	2	2	no	—
375	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
377	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
380	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
382	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
385	C₂²⋊C₄×C₄₁	—	2	2	no	—
386	C₂²⋊C₄×C₄₁	—	2	2	no	—
387	C₂²⋊C₄×C₄₁	—	2	2	no	—
388	C₂²⋊C₄×C₄₁	—	2	2	no	—
389	C₂²⋊C₄×C₄₁	—	2	2	no	—
390	C₂²⋊C₄×C₄₁	—	2	2	no	—
391	C₂²⋊C₄×C₄₁	—	2	2	no	—
392	C₂²⋊C₄×C₄₁	—	2	2	no	—
393	C₂²⋊C₄×C₄₁	—	2	2	no	—
394	C₂²⋊C₄×C₄₁	—	2	2	no	—
395	C₂²⋊C₄×C₄₁	—	2	2	no	—
396	C₂²⋊C₄×C₄₁	—	2	2	no	—
397	C₂²⋊C₄×C₄₁	—	2	2	no	—
398	C₂²⋊C₄×C₄₁	—	2	2	no	—
399	C₂²⋊C₄×C₄₁	—	2	2	no	—
400	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
401	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
402	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
403	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
404	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
405	C₄²×C₄₁	—	2	1	no	—
406	C₄²×C₄₁	—	2	1	no	—
407	C₄²×C₄₁	—	2	1	no	—
408	C₄²×C₄₁	—	2	1	no	—
409	C₄²×C₄₁	—	2	2	no	—
410	C₄²×C₄₁	—	2	2	no	—
411	C₄²×C₄₁	—	2	2	no	—
412	C₄²×C₄₁	—	2	2	no	—
413	C₄²×C₄₁	—	2	2	no	—
414	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
415	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
416	C₄²×C₄₁	C₂⁴	1	2	yes	—
417	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
418	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
419	C₂³×C₄₁	—	2	2	no	—
420	C₂³×C₄₁	—	2	2	no	—
421	C₂³×C₄₁	—	4	2	no	—
422	C₂³×C₄₁	—	8	1	no	—
423	C₂³×C₄₁	—	8	2	no	—
424	C₂³×C₄₁	—	8	2	no	—
425	C₂³×C₄₁	—	8	1	no	—
426	C₂³×C₄₁	—	8	2	no	—
427	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
428	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
429	Q₈×C₄₁	—	2	1	no	—
430	Q₈×C₄₁	—	2	2	no	—
431	Q₈×C₄₁	—	2	1	no	—
432	Q₈×C₄₁	—	2	2	no	—
433	Q₈×C₄₁	—	2	1	no	—
434	Q₈×C₄₁	—	2	2	no	—
435	Q₈×C₄₁	—	2	2	no	—
436	Q₈×C₄₁	—	4	1	no	—
437	Q₈×C₄₁	—	4	4	no	—
438	Q₈×C₄₁	—	4	2	no	—
439	Q₈×C₄₁	—	4	2	no	—
440	Q₈×C₄₁	—	8	1	no	—
441	Q₈×C₄₁	—	8	1	no	—
442	Q₈×C₄₁	H(5,𝔽₂)	1	2	yes	—
443	D₄×C₄₁	—	2	4	no	—
444	D₄×C₄₁	—	2	2	no	—
445	D₄×C₄₁	—	2	2	no	—
446	D₄×C₄₁	—	2	2	no	—
447	D₄×C₄₁	—	2	2	no	—
448	D₄×C₄₁	—	4	1	no	—
449	D₄×C₄₁	—	4	4	no	—
450	D₄×C₄₁	—	8	1	no	—
451	D₄×C₄₁	—	8	2	no	—
452	D₄×C₄₁	—	8	2	no	—
453	D₄×C₄₁	—	8	1	no	—
454	D₄×C₄₁	—	8	2	no	—
455	D₄×C₄₁	—	8	1	no	—
456	D₄×C₄₁	—	8	2	no	—
457	D₄×C₄₁	—	8	2	no	—
458	C₂×C₄×C₄₁	—	2	2	no	—
459	C₂×C₄×C₄₁	—	2	1	no	—
460	C₂×C₄×C₄₁	—	2	1	no	—
461	C₂×C₄×C₄₁	—	2	2	no	—
462	C₂×C₄×C₄₁	—	2	1	no	—
463	C₂×C₄×C₄₁	—	2	2	no	—
464	C₂×C₄×C₄₁	—	2	1	no	—
465	C₂×C₄×C₄₁	—	2	2	no	—
466	C₂×C₄×C₄₁	—	2	1	no	—
467	C₂×C₄×C₄₁	—	2	1	no	—
468	C₂×C₄×C₄₁	—	2	2	no	—
469	C₂×C₄×C₄₁	—	2	2	no	—
470	C₂×C₄×C₄₁	—	2	2	no	—
471	C₂×C₄×C₄₁	—	4	1	no	—
472	C₂×C₄×C₄₁	—	4	2	no	—
473	C₂×C₄×C₄₁	—	4	4	no	—
474	C₂×C₄×C₄₁	—	4	2	no	—
475	C₂×C₄×C₄₁	—	8	2	no	—
476	C₂×C₄×C₄₁	—	8	2	no	—
477	C₂×C₄×C₄₁	—	8	2	no	—
478	C₂×C₄×C₄₁	—	8	1	no	—
479	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
488	C₈×C₄₁	—	2	2	no	—
489	C₈×C₄₁	—	2	2	no	—
490	C₈×C₄₁	—	2	2	no	—
491	C₈×C₄₁	—	2	2	no	—
492	#62019	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
493	C₂²×C₄₁	—	2	1	no	—
494	C₂²×C₄₁	—	2	1	no	—
495	C₂²×C₄₁	—	2	2	no	—
496	C₂²×C₄₁	—	2	2	no	—
497	C₂²×C₄₁	—	2	2	no	—
498	C₂²×C₄₁	—	4	2	no	—
499	C₂²×C₄₁	—	4	2	no	—
500	C₂²×C₄₁	—	4	2	no	—
501	C₂²×C₄₁	—	4	2	no	—
502	C₂²×C₄₁	—	4	2	no	—
503	C₂²×C₄₁	—	4	2	no	—
504	C₂²×C₄₁	—	16	2	no	—
505	C₂²×C₄₁	—	16	4	no	—
506	C₂²×C₄₁	#577	1	2	yes	—
507	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
508	C₄×C₄₁	—	2	1	no	—
509	C₄×C₄₁	—	2	1	no	—
510	C₄×C₄₁	—	2	2	no	—
511	C₄×C₄₁	—	2	2	no	—
512	C₄×C₄₁	—	2	1	no	—
513	C₄×C₄₁	—	2	2	no	—
514	C₄×C₄₁	—	2	1	no	—
515	C₄×C₄₁	—	2	1	no	—
516	C₄×C₄₁	—	2	2	no	—
517	C₄×C₄₁	—	4	2	no	—
518	C₄×C₄₁	—	4	2	no	—
519	C₄×C₄₁	—	4	1	no	—
520	C₄×C₄₁	—	4	2	no	—
521	C₄×C₄₁	—	4	1	no	—
522	C₄×C₄₁	—	4	1	no	—
523	C₄×C₄₁	—	4	2	no	—
524	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
525	C₄×C₄₁	#585	1	1	yes	characteristic
526	#3558	C₂×C₄₁	1	1	yes	characteristic
527	#3523	C₂×C₄₁	1	1	yes	characteristic, complemented
528	#3400	C₂×C₄₁	1	2	yes	complemented
529	#3371	C₂×C₄₁	1	2	yes	complemented
530	#3311	C₂×C₄₁	1	2	yes	complemented
531	#3310	C₂×C₄₁	1	2	yes	complemented
532	#3300	C₂×C₄₁	1	2	yes	complemented
533	D₄×SD₁₆	C₂×C₄₁	1	2	yes	complemented
534	#3270	C₂×C₄₁	1	2	yes	complemented
535	#3266	C₂×C₄₁	1	2	yes	complemented
536	#3258	C₂×C₄₁	1	2	yes	complemented
537	#3246	C₂×C₄₁	1	1	yes	characteristic, complemented
538	#3222	C₂×C₄₁	1	2	yes	complemented
539	#3215	C₂×C₄₁	1	1	yes	characteristic, complemented
540	#3121	C₂×C₄₁	1	2	yes	complemented
541	#3112	C₂×C₄₁	1	1	yes	characteristic, complemented
542	#3043	C₂×C₄₁	1	2	yes	complemented
543	C₂×#464	C₂×C₄₁	1	1	yes	characteristic, complemented
544	#2992	C₂×C₄₁	1	1	yes	characteristic, complemented
545	C₂×C₄₁	—	2	2	no	—
546	C₂×C₄₁	—	4	2	no	—
547	C₂×C₄₁	—	8	2	no	—
548	C₂×C₄₁	—	8	2	no	—
549	C₂×C₄₁	#3488	1	1	yes	characteristic
550	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
551	C₂×C₄₁	#3586	1	1	yes	characteristic
552	C₂×#137	C₂²×C₄₁	1	2	yes	complemented
553	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
554	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
555	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
556	#562	—	2	1	no	—
557	H(3,𝔽₄)	—	2	1	no	—
558	#559	C₂²×C₄₁	1	2	yes	—
559	#557	—	2	1	no	—
560	#557	C₂²×C₄₁	1	1	yes	characteristic, complemented
561	#557	C₂²×C₄₁	1	1	yes	characteristic, complemented
562	#556	—	2	1	no	—
563	#556	C₂²×C₄₁	1	1	yes	characteristic, complemented
564	#552	—	2	2	no	—
565	#552	C₂²×C₄₁	1	2	yes	complemented
566	D₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
567	D₄×Q₈	C₂²×C₄₁	1	2	yes	complemented
568	#548	C₂²×C₄₁	1	2	yes	—
569	#546	—	2	2	no	—
570	#546	C₂²×C₄₁	1	2	yes	—
571	D₄²	C₂²×C₄₁	1	2	yes	—
572	#542	C₂²×C₄₁	1	2	yes	—
573	#541	—	2	2	no	—
574	#541	C₂²×C₄₁	1	2	yes	complemented
575	#538	—	2	2	no	—
576	#538	—	2	1	no	—
577	#535	C₂²×C₄₁	1	2	yes	—
578	#534	—	2	1	no	—
579	#533	—	2	1	no	—
580	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
581	#532	C₂²×C₄₁	1	1	yes	characteristic
582	#529	—	2	1	no	—
583	#529	C₂²×C₄₁	1	1	yes	characteristic
584	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
585	#519	C₂²×C₄₁	1	2	yes	complemented
586	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
587	#497	C₂²×C₄₁	1	2	yes	complemented
588	#497	C₂²×C₄₁	1	2	yes	complemented
589	#492	C₂²×C₄₁	1	2	yes	—
590	#490	C₂²×C₄₁	1	2	yes	—
591	#489	C₂²×C₄₁	1	2	yes	complemented
592	#488	C₂²×C₄₁	1	2	yes	complemented
593	#485	C₂²×C₄₁	1	2	yes	complemented
594	#482	C₂²×C₄₁	1	2	yes	—
595	#480	C₂²×C₄₁	1	2	yes	complemented
596	#479	C₂²×C₄₁	1	2	yes	complemented
597	#478	C₂²×C₄₁	1	2	yes	complemented
598	#477	C₂²×C₄₁	1	1	yes	characteristic, complemented
599	#477	C₂²×C₄₁	1	1	yes	characteristic, complemented
600	#476	C₂²×C₄₁	1	2	yes	complemented
601	#475	C₂²×C₄₁	1	2	yes	complemented
602	#470	C₂²×C₄₁	1	2	yes	complemented
603	#468	C₂²×C₄₁	1	2	yes	—
604	#467	C₂²×C₄₁	1	2	yes	complemented
605	#465	C₂²×C₄₁	1	2	yes	—
606	#465	C₂²×C₄₁	1	2	yes	complemented
607	#465	C₂²×C₄₁	1	2	yes	complemented
608	#464	C₂²×C₄₁	1	2	yes	complemented
609	#464	C₂²×C₄₁	1	2	yes	complemented
610	#464	C₂²×C₄₁	1	2	yes	complemented
611	#464	C₂²×C₄₁	1	2	yes	complemented
612	#464	C₂²×C₄₁	1	2	yes	complemented
613	#464	C₂²×C₄₁	1	2	yes	complemented
614	#464	C₂²×C₄₁	1	2	yes	complemented
615	#464	C₂²×C₄₁	1	2	yes	complemented
616	#462	C₂²×C₄₁	1	2	yes	complemented
617	#461	C₂²×C₄₁	1	2	yes	complemented
618	#461	C₂²×C₄₁	1	2	yes	complemented
619	#460	C₂²×C₄₁	1	2	yes	—
620	#460	C₂²×C₄₁	1	2	yes	—
621	#460	C₂²×C₄₁	1	1	yes	characteristic, complemented
622	#460	C₂²×C₄₁	1	1	yes	characteristic, complemented
623	#460	C₂²×C₄₁	1	2	yes	complemented
624	#452	C₂²×C₄₁	1	2	yes	complemented
625	#452	C₂²×C₄₁	1	2	yes	complemented
626	#451	C₂²×C₄₁	1	2	yes	complemented
627	#451	C₂²×C₄₁	1	2	yes	complemented
628	#450	C₂²×C₄₁	1	2	yes	—
629	#450	C₂²×C₄₁	1	2	yes	complemented
630	#450	C₂²×C₄₁	1	2	yes	complemented
631	#448	C₂²×C₄₁	1	2	yes	—
632	#448	C₂²×C₄₁	1	2	yes	complemented
633	#446	C₂²×C₄₁	1	2	yes	complemented
634	#441	C₂²×C₄₁	1	2	yes	complemented
635	#440	C₂²×C₄₁	1	2	yes	complemented
636	#440	C₂²×C₄₁	1	2	yes	complemented
637	#440	C₂²×C₄₁	1	2	yes	complemented
638	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
639	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
640	#435	C₂²×C₄₁	1	2	yes	complemented
641	#435	C₂²×C₄₁	1	2	yes	complemented
642	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
643	#433	C₂²×C₄₁	1	2	yes	complemented
644	#432	C₂²×C₄₁	1	1	yes	characteristic, complemented
645	#424	C₂²×C₄₁	1	2	yes	complemented
646	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
647	#418	C₂²×C₄₁	1	2	yes	complemented
648	#416	C₂²×C₄₁	1	2	yes	complemented
649	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
650	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
651	C₄₁	#62019	1	1	yes	characteristic, direct product factor, Sylow
652	C₂×#41	—	2	1	no	—
653	C₂×#41	C₂³×C₄₁	1	2	yes	—
654	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
655	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
656	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
657	C₂²×D₄	—	2	2	no	—
658	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
659	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
660	#137	—	4	4	no	—
661	C₂×Q₁₆	—	4	2	no	—
662	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
663	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
664	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
665	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
666	C₂×SD₁₆	—	4	2	no	—
667	C₂×SD₁₆	—	4	4	no	—
668	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
669	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
670	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
671	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
672	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
673	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
674	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
675	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
676	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
677	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
678	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
679	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
680	C₄⋊Q₈	—	2	1	no	—
681	C₄⋊Q₈	—	2	1	no	—
682	C₄⋊Q₈	—	2	2	no	—
683	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
684	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
685	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
686	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
687	#127	C₂³×C₄₁	1	1	yes	characteristic
688	#127	C₂³×C₄₁	1	2	yes	—
689	#126	—	2	2	no	—
690	#126	—	2	2	no	—
691	#126	—	2	2	no	—
692	#126	—	2	2	no	—
693	#126	—	2	2	no	—
694	#126	D₄×C₄₁	1	2	yes	—
695	#125	—	2	1	no	—
696	#125	—	2	2	no	—
697	#125	—	2	2	no	—
698	#125	—	2	2	no	—
699	#125	—	2	2	no	—
700	#125	—	2	2	no	—
701	#125	—	2	1	no	—
702	#125	D₄×C₄₁	1	1	yes	characteristic
703	#125	C₂³×C₄₁	1	2	yes	—
704	#124	—	2	2	no	—
705	#124	—	2	1	no	—
706	#124	—	2	2	no	—
707	#124	—	2	2	no	—
708	#124	—	2	1	no	—
709	#124	—	2	1	no	—
710	#124	—	2	1	no	—
711	#124	D₄×C₄₁	1	1	yes	characteristic
712	#124	C₂³×C₄₁	1	2	yes	—
713	#124	C₂³×C₄₁	1	2	yes	—
714	#124	C₂³×C₄₁	1	2	yes	—
715	#123	—	2	2	no	—
716	#123	—	2	2	no	—
717	#123	—	2	2	no	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	#123	D₄×C₄₁	1	2	yes	—
721	C₂²⋊Q₈	—	2	1	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
728	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
729	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
730	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
731	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
732	#121	—	2	2	no	—
733	#121	—	2	1	no	—
734	#121	—	2	2	no	—
735	#121	—	2	2	no	—
736	#121	—	2	2	no	—
737	#121	—	2	2	no	—
738	#121	D₄×C₄₁	1	1	yes	characteristic
739	#121	C₂³×C₄₁	1	2	yes	—
740	#121	C₂³×C₄₁	1	2	yes	—
741	#120	—	2	2	no	—
742	#120	—	2	2	no	—
743	#120	—	2	2	no	—
744	#120	—	2	2	no	—
745	#120	—	2	2	no	—
746	C₄×Q₈	—	2	1	no	—
747	C₄×Q₈	—	2	2	no	—
748	C₄×Q₈	—	2	2	no	—
749	C₄×Q₈	—	2	1	no	—
750	C₄×Q₈	—	2	1	no	—
751	C₄×Q₈	—	2	1	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	—	2	1	no	—
754	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
755	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
756	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
757	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
758	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
759	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
760	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
761	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
762	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
763	C₄×D₄	—	2	2	no	—
764	C₄×D₄	—	2	1	no	—
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	—	2	1	no	—
768	C₄×D₄	C₂³×C₄₁	1	2	yes	—
769	C₄×D₄	C₂³×C₄₁	1	2	yes	—
770	C₄×D₄	C₂³×C₄₁	1	2	yes	—
771	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
772	#117	—	2	1	no	—
773	#117	—	2	2	no	—
774	#117	—	2	2	no	—
775	#117	—	2	2	no	—
776	#117	C₂³×C₄₁	1	2	yes	—
777	#117	C₂³×C₄₁	1	2	yes	—
778	C₂×C₄⋊C₄	—	2	1	no	—
779	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
780	C₂×C₂²⋊C₄	—	2	1	no	—
781	C₂×C₂²⋊C₄	—	2	1	no	—
782	C₂×C₂²⋊C₄	—	2	2	no	—
783	C₂×C₄²	—	2	1	no	—
784	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
785	#107	C₂³×C₄₁	1	2	yes	—
786	#107	C₂³×C₄₁	1	2	yes	—
787	#106	C₂³×C₄₁	1	2	yes	—
788	#106	C₂³×C₄₁	1	2	yes	—
789	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
790	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
791	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
792	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
793	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
794	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
795	#103	C₂³×C₄₁	1	2	yes	—
796	#103	C₂³×C₄₁	1	2	yes	—
797	#103	C₂³×C₄₁	1	2	yes	—
798	#103	C₂³×C₄₁	1	2	yes	—
799	#103	C₂³×C₄₁	1	2	yes	—
800	#103	C₂³×C₄₁	1	2	yes	—
801	#103	C₂³×C₄₁	1	2	yes	—
802	#103	C₂³×C₄₁	1	2	yes	—
803	#102	C₂³×C₄₁	1	2	yes	—
804	#102	C₂³×C₄₁	1	2	yes	—
805	#102	C₂³×C₄₁	1	2	yes	—
806	#102	C₂³×C₄₁	1	2	yes	—
807	#102	C₂³×C₄₁	1	2	yes	—
808	#102	C₂³×C₄₁	1	2	yes	—
809	#102	C₂³×C₄₁	1	2	yes	—
810	#102	C₂³×C₄₁	1	2	yes	—
811	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
812	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
813	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
814	#97	C₂³×C₄₁	1	2	yes	—
815	#97	C₂³×C₄₁	1	2	yes	—
816	C₄×C₈	C₂³×C₄₁	1	2	yes	—
817	C₂⁴	—	2	1	no	—
818	C₂⁴	—	2	2	no	—
819	#41	—	4	2	no	—
820	#41	—	4	2	no	—
821	#41	—	8	2	no	—
822	C₂×Q₈	—	2	1	no	—
823	C₂×Q₈	—	2	2	no	—
824	C₂×Q₈	—	2	1	no	—
825	C₂×Q₈	—	2	1	no	—
826	C₂×Q₈	—	2	1	no	—
827	C₂×Q₈	—	2	2	no	—
828	C₂×Q₈	—	2	4	no	—
829	C₂×Q₈	—	4	1	no	—
830	C₂×Q₈	—	4	2	no	—
831	C₂×Q₈	—	4	1	no	—
832	C₂×Q₈	—	4	1	no	—
833	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
834	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
835	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
836	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
837	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	2	2	no	—
841	C₂×D₄	—	2	2	no	—
842	C₂×D₄	—	2	1	no	—
843	C₂×D₄	—	2	1	no	—
844	C₂×D₄	—	2	1	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	4	1	no	—
848	C₂×D₄	—	4	2	no	—
849	C₂×D₄	—	4	1	no	—
850	C₂×D₄	—	4	2	no	—
851	C₂×D₄	—	8	4	no	—
852	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
853	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
854	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
855	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
864	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
867	Q₁₆	—	2	4	no	—
868	Q₁₆	—	4	2	no	—
869	Q₁₆	—	4	2	no	—
870	Q₁₆	—	4	2	no	—
871	SD₁₆	—	2	4	no	—
872	SD₁₆	—	2	4	no	—
873	SD₁₆	—	4	2	no	—
874	SD₁₆	—	4	2	no	—
875	SD₁₆	—	4	2	no	—
876	SD₁₆	—	4	2	no	—
877	SD₁₆	—	4	2	no	—
878	SD₁₆	—	4	2	no	—
879	M₁₆	—	4	2	no	—
880	C₂×C₈	—	4	1	no	—
881	C₂×C₈	—	4	2	no	—
882	C₂×C₈	—	4	1	no	—
883	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
884	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
885	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
886	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	1	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
909	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
910	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
911	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
912	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
913	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
914	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
915	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
916	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
917	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	2	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	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
934	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
935	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
936	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
937	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
938	C₄²	—	2	1	no	—
939	C₄²	—	2	1	no	—
940	C₄²	—	2	1	no	—
941	C₄²	—	2	1	no	—
942	C₄²	—	2	2	no	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	2	2	no	—
946	C₄²	—	2	2	no	—
947	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
948	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
949	C₄²	C₂⁴×C₄₁	1	2	yes	—
950	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
951	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
952	C₂³	—	2	2	no	—
953	C₂³	—	2	2	no	—
954	C₂³	—	4	2	no	—
955	C₂³	—	8	1	no	—
956	C₂³	—	8	2	no	—
957	C₂³	—	8	2	no	—
958	C₂³	—	8	1	no	—
959	C₂³	—	8	2	no	—
960	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
961	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
962	Q₈	—	2	1	no	—
963	Q₈	—	2	2	no	—
964	Q₈	—	2	1	no	—
965	Q₈	—	2	2	no	—
966	Q₈	—	2	1	no	—
967	Q₈	—	2	2	no	—
968	Q₈	—	2	2	no	—
969	Q₈	—	4	1	no	—
970	Q₈	—	4	4	no	—
971	Q₈	—	4	2	no	—
972	Q₈	—	4	2	no	—
973	Q₈	—	8	1	no	—
974	Q₈	—	8	1	no	—
975	Q₈	H(5,𝔽₂)×C₄₁	1	2	yes	—
976	D₄	—	2	4	no	—
977	D₄	—	2	2	no	—
978	D₄	—	2	2	no	—
979	D₄	—	2	2	no	—
980	D₄	—	2	2	no	—
981	D₄	—	4	1	no	—
982	D₄	—	4	4	no	—
983	D₄	—	8	2	no	—
984	D₄	—	8	1	no	—
985	D₄	—	8	2	no	—
986	D₄	—	8	1	no	—
987	D₄	—	8	1	no	—
988	D₄	—	8	2	no	—
989	D₄	—	8	2	no	—
990	D₄	—	8	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	4	1	no	—
1005	C₂×C₄	—	4	2	no	—
1006	C₂×C₄	—	4	4	no	—
1007	C₂×C₄	—	4	2	no	—
1008	C₂×C₄	—	8	2	no	—
1009	C₂×C₄	—	8	2	no	—
1010	C₂×C₄	—	8	2	no	—
1011	C₂×C₄	—	8	1	no	—
1012	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1013	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1014	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1015	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1016	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1017	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1018	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1019	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1020	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1021	C₈	—	2	2	no	—
1022	C₈	—	2	2	no	—
1023	C₈	—	2	2	no	—
1024	C₈	—	2	2	no	—
1025	C₂²	—	2	1	no	—
1026	C₂²	—	2	1	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	2	2	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	—	4	2	no	—
1033	C₂²	—	4	2	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	4	2	no	—
1036	C₂²	—	16	2	no	—
1037	C₂²	—	16	4	no	—
1038	C₂²	C₄₁×#577	1	2	yes	—
1039	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1040	C₄	—	2	1	no	—
1041	C₄	—	2	1	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	1	no	—
1044	C₄	—	2	1	no	—
1045	C₄	—	2	2	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	2	1	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	4	1	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	2	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	2	no	—
1056	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1057	C₄	C₄₁×#585	1	1	yes	characteristic
1058	C₂	—	2	2	no	—
1059	C₂	—	4	2	no	—
1060	C₂	—	8	2	no	—
1061	C₂	—	8	2	no	—
1062	C₂	C₄₁×#3488	1	1	yes	characteristic
1063	C₂	C₂×C₄₁×#577	1	1	yes	characteristic
1064	C₂	C₄₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₄₁×#3558	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#3523	C₂	semidirect
3. C₄₁×#3400	C₂	semidirect
4. C₄₁×#3371	C₂	semidirect
5. C₄₁×#3311	C₂	semidirect
6. C₄₁×#3310	C₂	semidirect
7. C₄₁×#3300	C₂	semidirect
8. D₄×SD₁₆×C₄₁	C₂	semidirect
9. C₄₁×#3270	C₂	semidirect
10. C₄₁×#3266	C₂	semidirect
11. C₄₁×#3258	C₂	semidirect
12. C₄₁×#3246	C₂	semidirect
13. C₄₁×#3222	C₂	semidirect
14. C₄₁×#3215	C₂	semidirect
15. C₄₁×#3121	C₂	semidirect
16. C₄₁×#3112	C₂	semidirect
17. C₄₁×#3043	C₂	semidirect
18. C₂×C₄₁×#464	C₂	semidirect
19. C₄₁×#2992	C₂	semidirect
20. C₂×#137×C₄₁	C₂²	semidirect
21. C₂²×Q₁₆×C₄₁	C₂²	semidirect
23. C₂²×SD₁₆×C₄₁	C₂²	semidirect
28. C₄₁×#557	C₂²	semidirect
29. C₄₁×#557	C₂²	semidirect
31. C₄₁×#556	C₂²	semidirect
33. C₄₁×#552	C₂²	semidirect
34. D₄×Q₈×C₄₁	C₂²	semidirect
35. D₄×Q₈×C₄₁	C₂²	semidirect
42. C₄₁×#541	C₂²	semidirect
48. C₄₁×#533	C₂²	semidirect
53. C₄₁×#519	C₂²	semidirect
54. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
55. C₄₁×#497	C₂²	semidirect
56. C₄₁×#497	C₂²	semidirect
59. C₄₁×#489	C₂²	semidirect
60. C₄₁×#488	C₂²	semidirect
61. C₄₁×#485	C₂²	semidirect
63. C₄₁×#480	C₂²	semidirect
64. C₄₁×#479	C₂²	semidirect
65. C₄₁×#478	C₂²	semidirect
66. C₄₁×#477	C₂²	semidirect
67. C₄₁×#477	C₂²	semidirect
68. C₄₁×#476	C₂²	semidirect
69. C₄₁×#475	C₂²	semidirect
70. C₄₁×#470	C₂²	semidirect
72. C₄₁×#467	C₂²	semidirect
74. C₄₁×#465	C₂²	semidirect
75. C₄₁×#465	C₂²	semidirect
76. C₄₁×#464	C₂²	semidirect
77. C₄₁×#464	C₂²	semidirect
78. C₄₁×#464	C₂²	semidirect
79. C₄₁×#464	C₂²	semidirect
80. C₄₁×#464	C₂²	semidirect
81. C₄₁×#464	C₂²	semidirect
82. C₄₁×#464	C₂²	semidirect
83. C₄₁×#464	C₂²	semidirect
84. C₄₁×#462	C₂²	semidirect
85. C₄₁×#461	C₂²	semidirect
86. C₄₁×#461	C₂²	semidirect
89. C₄₁×#460	C₂²	semidirect
90. C₄₁×#460	C₂²	semidirect
91. C₄₁×#460	C₂²	semidirect
92. C₄₁×#452	C₂²	semidirect
93. C₄₁×#452	C₂²	semidirect
94. C₄₁×#451	C₂²	semidirect
95. C₄₁×#451	C₂²	semidirect
97. C₄₁×#450	C₂²	semidirect
98. C₄₁×#450	C₂²	semidirect
100. C₄₁×#448	C₂²	semidirect
101. C₄₁×#446	C₂²	semidirect
102. C₄₁×#441	C₂²	semidirect
103. C₄₁×#440	C₂²	semidirect
104. C₄₁×#440	C₂²	semidirect
105. C₄₁×#440	C₂²	semidirect
106. C₄×Q₁₆×C₄₁	C₂²	semidirect
107. C₄×SD₁₆×C₄₁	C₂²	semidirect
108. C₄₁×#435	C₂²	semidirect
109. C₄₁×#435	C₂²	semidirect
110. C₈×D₄×C₄₁	C₂²	semidirect
111. C₄₁×#433	C₂²	semidirect
112. C₄₁×#432	C₂²	semidirect
113. C₄₁×#424	C₂²	semidirect
114. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
115. C₄₁×#418	C₂²	semidirect
116. C₄₁×#416	C₂²	semidirect
117. C₂×#103×C₄₁	C₂²	semidirect
492. #62019	C₄₁	direct (N × H)
527. #3523	C₂×C₄₁	semidirect
528. #3400	C₂×C₄₁	semidirect
529. #3371	C₂×C₄₁	semidirect
530. #3311	C₂×C₄₁	semidirect
531. #3310	C₂×C₄₁	semidirect
532. #3300	C₂×C₄₁	semidirect
533. D₄×SD₁₆	C₂×C₄₁	semidirect
534. #3270	C₂×C₄₁	semidirect
535. #3266	C₂×C₄₁	semidirect
536. #3258	C₂×C₄₁	semidirect
537. #3246	C₂×C₄₁	semidirect
538. #3222	C₂×C₄₁	semidirect
539. #3215	C₂×C₄₁	semidirect
540. #3121	C₂×C₄₁	semidirect
541. #3112	C₂×C₄₁	semidirect
542. #3043	C₂×C₄₁	semidirect
543. C₂×#464	C₂×C₄₁	semidirect
544. #2992	C₂×C₄₁	semidirect
552. C₂×#137	C₂²×C₄₁	semidirect
553. C₂²×Q₁₆	C₂²×C₄₁	semidirect
555. C₂²×SD₁₆	C₂²×C₄₁	semidirect
560. #557	C₂²×C₄₁	semidirect
561. #557	C₂²×C₄₁	semidirect
563. #556	C₂²×C₄₁	semidirect
565. #552	C₂²×C₄₁	semidirect
566. D₄×Q₈	C₂²×C₄₁	semidirect
567. D₄×Q₈	C₂²×C₄₁	semidirect
574. #541	C₂²×C₄₁	semidirect
580. #533	C₂²×C₄₁	semidirect
585. #519	C₂²×C₄₁	semidirect
586. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
587. #497	C₂²×C₄₁	semidirect
588. #497	C₂²×C₄₁	semidirect
591. #489	C₂²×C₄₁	semidirect
592. #488	C₂²×C₄₁	semidirect
593. #485	C₂²×C₄₁	semidirect
595. #480	C₂²×C₄₁	semidirect
596. #479	C₂²×C₄₁	semidirect
597. #478	C₂²×C₄₁	semidirect
598. #477	C₂²×C₄₁	semidirect
599. #477	C₂²×C₄₁	semidirect
600. #476	C₂²×C₄₁	semidirect
601. #475	C₂²×C₄₁	semidirect
602. #470	C₂²×C₄₁	semidirect
604. #467	C₂²×C₄₁	semidirect
606. #465	C₂²×C₄₁	semidirect
607. #465	C₂²×C₄₁	semidirect
608. #464	C₂²×C₄₁	semidirect
609. #464	C₂²×C₄₁	semidirect
610. #464	C₂²×C₄₁	semidirect
611. #464	C₂²×C₄₁	semidirect
612. #464	C₂²×C₄₁	semidirect
613. #464	C₂²×C₄₁	semidirect
614. #464	C₂²×C₄₁	semidirect
615. #464	C₂²×C₄₁	semidirect
616. #462	C₂²×C₄₁	semidirect
617. #461	C₂²×C₄₁	semidirect
618. #461	C₂²×C₄₁	semidirect
621. #460	C₂²×C₄₁	semidirect
622. #460	C₂²×C₄₁	semidirect
623. #460	C₂²×C₄₁	semidirect
624. #452	C₂²×C₄₁	semidirect
625. #452	C₂²×C₄₁	semidirect
626. #451	C₂²×C₄₁	semidirect
627. #451	C₂²×C₄₁	semidirect
629. #450	C₂²×C₄₁	semidirect
630. #450	C₂²×C₄₁	semidirect
632. #448	C₂²×C₄₁	semidirect
633. #446	C₂²×C₄₁	semidirect
634. #441	C₂²×C₄₁	semidirect
635. #440	C₂²×C₄₁	semidirect
636. #440	C₂²×C₄₁	semidirect
637. #440	C₂²×C₄₁	semidirect
638. C₄×Q₁₆	C₂²×C₄₁	semidirect
639. C₄×SD₁₆	C₂²×C₄₁	semidirect
640. #435	C₂²×C₄₁	semidirect
641. #435	C₂²×C₄₁	semidirect
642. C₈×D₄	C₂²×C₄₁	semidirect
643. #433	C₂²×C₄₁	semidirect
644. #432	C₂²×C₄₁	semidirect
645. #424	C₂²×C₄₁	semidirect
646. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
647. #418	C₂²×C₄₁	semidirect
648. #416	C₂²×C₄₁	semidirect
649. C₂×#103	C₂²×C₄₁	semidirect
651. C₄₁	#62019	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×#3558	2
C₄₁×#3523	2
C₄₁×#3400	2
C₄₁×#3371	2
C₄₁×#3311	2
C₄₁×#3310	2
C₄₁×#3300	2
D₄×SD₁₆×C₄₁	2
C₄₁×#3270	2
C₄₁×#3266	2
C₄₁×#3258	2
C₄₁×#3246	2
C₄₁×#3222	2
C₄₁×#3215	2
C₄₁×#3121	2
C₄₁×#3112	2
C₄₁×#3043	2
C₂×C₄₁×#464	2
C₄₁×#2992	2
#62019	41

Subgroups — C41×#62019 #23838220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#62019 #23838220