Subgroups — C₄₁×#20865 #23797066

Order 10496.

1394 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3428	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#421	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#417	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2317	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1860	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1859	C₂	1	4	yes	maximal, complemented
8	C₄₁×#1742	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1733	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₄₁×#520	—	2	1	no	—
14	C₄₁×#520	—	2	1	no	—
15	C₄₁×#520	C₂²	1	2	yes	—
16	C₄₁×#520	C₂²	1	2	yes	—
17	C₄₁×#519	—	2	1	no	—
18	C₄₁×#518	—	2	1	no	—
19	C₄₁×#518	—	2	2	no	—
20	C₄×#41×C₄₁	—	2	2	no	—
21	C₄×#41×C₄₁	—	2	2	no	—
22	C₂×#117×C₄₁	—	2	2	no	—
23	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#428	—	2	2	no	—
28	C₄₁×#428	C₂²	1	4	yes	complemented
29	C₂×#107×C₄₁	—	2	1	no	—
30	C₂×#106×C₄₁	—	2	1	no	—
31	C₄₁×#421	C₄	1	8	yes	complemented
32	C₂×#104×C₄₁	C₂²	1	4	yes	—
33	C₄₁×#417	—	2	2	no	—
34	C₄₁×#417	C₂²	1	4	yes	—
35	C₂×#103×C₄₁	—	2	1	no	—
36	C₂×#102×C₄₁	—	2	1	no	—
37	C₄₁×#389	—	2	2	no	—
38	C₄₁×#385	—	2	2	no	—
39	C₄₁×#384	C₂²	1	2	yes	complemented
40	C₄₁×#382	C₂²	1	2	yes	complemented
41	C₄₁×#343	C₂²	1	2	yes	complemented
42	C₄₁×#343	C₂²	1	2	yes	complemented
43	C₄₁×#339	C₂²	1	4	yes	complemented
44	C₂×#41×C₄₁	—	2	1	no	—
45	C₂×#41×C₄₁	—	2	1	no	—
46	C₂×#41×C₄₁	—	2	2	no	—
47	C₂×#41×C₄₁	—	2	2	no	—
48	C₂×#41×C₄₁	C₂×C₄	1	4	yes	—
49	C₂×#41×C₄₁	D₄	1	2	yes	—
50	C₂×#41×C₄₁	Q₈	1	4	yes	—
51	C₂×#41×C₄₁	C₂³	1	2	yes	—
52	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
53	C₂²×D₄×C₄₁	—	2	1	no	—
54	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₁	—	2	1	no	—
56	C₂³×C₄×C₄₁	—	2	1	no	—
57	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₄₁	—	2	1	no	—
59	C₂×M₁₆×C₄₁	—	2	2	no	—
60	C₂×M₁₆×C₄₁	—	2	1	no	—
61	C₂×M₁₆×C₄₁	—	2	2	no	—
62	C₂×M₁₆×C₄₁	—	2	2	no	—
63	C₂×M₁₆×C₄₁	C₂×C₄	1	4	yes	complemented
64	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
65	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
66	C₂²×C₈×C₄₁	—	2	1	no	—
67	C₂²×C₈×C₄₁	—	2	1	no	—
68	C₄×Q₈×C₄₁	—	2	2	no	—
69	C₄×Q₈×C₄₁	—	2	2	no	—
70	C₄×Q₈×C₄₁	—	2	2	no	—
71	C₄×Q₈×C₄₁	—	2	2	no	—
72	C₄×D₄×C₄₁	—	2	4	no	—
73	C₄×D₄×C₄₁	—	2	4	no	—
74	C₄×D₄×C₄₁	—	2	2	no	—
75	C₄×D₄×C₄₁	—	2	2	no	—
76	C₄×D₄×C₄₁	—	2	2	no	—
77	C₄×D₄×C₄₁	—	2	2	no	—
78	C₄×D₄×C₄₁	—	2	4	no	—
79	C₄×D₄×C₄₁	—	2	4	no	—
80	#117×C₄₁	—	2	4	no	—
81	#117×C₄₁	—	2	4	no	—
82	#117×C₄₁	—	2	1	no	—
83	#117×C₄₁	—	2	1	no	—
84	#117×C₄₁	—	2	1	no	—
85	#117×C₄₁	—	2	1	no	—
86	#117×C₄₁	—	2	1	no	—
87	#117×C₄₁	—	2	1	no	—
88	#117×C₄₁	—	2	2	no	—
89	#117×C₄₁	—	2	2	no	—
90	#117×C₄₁	—	2	2	no	—
91	#117×C₄₁	C₂×C₄	1	4	yes	complemented
92	#117×C₄₁	D₄	1	2	yes	—
93	#117×C₄₁	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
96	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
97	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
98	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
99	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
100	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
101	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
102	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
103	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
109	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
112	C₂×C₄²×C₄₁	—	2	4	no	—
113	C₂×C₄²×C₄₁	—	2	1	no	—
114	C₂×C₄²×C₄₁	D₄	1	2	yes	—
115	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
116	#107×C₄₁	—	2	4	no	—
117	#106×C₄₁	—	2	4	no	—
118	#104×C₄₁	C₂×C₄	1	16	yes	complemented
119	#103×C₄₁	—	2	4	no	—
120	#102×C₄₁	—	2	4	no	—
121	#95×C₄₁	—	2	4	no	—
122	C₂⁴×C₄₁	—	2	1	no	—
123	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
124	#41×C₄₁	—	2	4	no	—
125	#41×C₄₁	—	2	4	no	—
126	#41×C₄₁	—	2	4	no	—
127	#41×C₄₁	—	2	4	no	—
128	#41×C₄₁	—	2	4	no	—
129	#41×C₄₁	—	2	2	no	—
130	#41×C₄₁	—	2	2	no	—
131	#41×C₄₁	C₄⋊C₄	1	8	yes	complemented
132	#41×C₄₁	C₂²×C₄	1	4	yes	—
133	#41×C₄₁	C₂×Q₈	1	4	yes	—
134	C₂×Q₈×C₄₁	—	2	1	no	—
135	C₂×Q₈×C₄₁	—	2	2	no	—
136	C₂×Q₈×C₄₁	C₄⋊C₄	1	4	yes	complemented
137	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₄₁	—	2	4	no	—
139	C₂×D₄×C₄₁	—	2	2	no	—
140	C₂×D₄×C₄₁	—	2	4	no	—
141	C₂×D₄×C₄₁	—	2	2	no	—
142	C₂×D₄×C₄₁	—	2	1	no	—
143	C₂×D₄×C₄₁	—	2	2	no	—
144	C₂×D₄×C₄₁	C₄⋊C₄	1	4	yes	complemented
145	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₄₁	—	2	1	no	—
147	C₂²×C₄×C₄₁	—	2	4	no	—
148	C₂²×C₄×C₄₁	—	2	2	no	—
149	C₂²×C₄×C₄₁	—	2	4	no	—
150	C₂²×C₄×C₄₁	—	2	2	no	—
151	C₂²×C₄×C₄₁	—	2	2	no	—
152	C₂²×C₄×C₄₁	—	2	4	no	—
153	C₂²×C₄×C₄₁	—	2	4	no	—
154	C₂²×C₄×C₄₁	—	2	1	no	—
155	C₂²×C₄×C₄₁	—	2	1	no	—
156	C₂²×C₄×C₄₁	—	2	2	no	—
157	C₂²×C₄×C₄₁	—	4	1	no	—
158	C₂²×C₄×C₄₁	—	4	1	no	—
159	C₂²×C₄×C₄₁	—	8	2	no	—
160	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
169	C₂²×C₄×C₄₁	#41	1	2	yes	—
170	C₂²×C₄×C₄₁	#41	1	2	yes	—
171	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
172	M₁₆×C₄₁	—	2	4	no	—
173	M₁₆×C₄₁	—	2	2	no	—
174	M₁₆×C₄₁	—	2	2	no	—
175	M₁₆×C₄₁	—	2	2	no	—
176	M₁₆×C₄₁	—	4	2	no	—
177	M₁₆×C₄₁	C₂²×C₄	1	4	yes	—
178	C₂×C₈×C₄₁	—	2	4	no	—
179	C₂×C₈×C₄₁	—	2	2	no	—
180	C₂×C₈×C₄₁	—	2	2	no	—
181	C₂×C₈×C₄₁	—	4	2	no	—
182	C₄⋊C₄×C₄₁	—	2	4	no	—
183	C₄⋊C₄×C₄₁	—	2	4	no	—
184	C₄⋊C₄×C₄₁	—	2	4	no	—
185	C₄⋊C₄×C₄₁	—	2	1	no	—
186	C₄⋊C₄×C₄₁	—	2	1	no	—
187	C₄⋊C₄×C₄₁	—	2	1	no	—
188	C₄⋊C₄×C₄₁	—	2	1	no	—
189	C₄⋊C₄×C₄₁	—	2	1	no	—
190	C₄⋊C₄×C₄₁	—	2	1	no	—
191	C₄⋊C₄×C₄₁	—	2	2	no	—
192	C₄⋊C₄×C₄₁	—	2	2	no	—
193	C₄⋊C₄×C₄₁	—	4	1	no	—
194	C₄⋊C₄×C₄₁	—	4	1	no	—
195	C₄⋊C₄×C₄₁	—	8	4	no	—
196	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
197	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
198	C₂²⋊C₄×C₄₁	—	2	4	no	—
199	C₂²⋊C₄×C₄₁	—	2	4	no	—
200	C₂²⋊C₄×C₄₁	—	2	4	no	—
201	C₂²⋊C₄×C₄₁	—	2	2	no	—
202	C₂²⋊C₄×C₄₁	—	2	2	no	—
203	C₂²⋊C₄×C₄₁	—	2	2	no	—
204	C₂²⋊C₄×C₄₁	—	2	2	no	—
205	C₄²×C₄₁	—	2	4	no	—
206	C₄²×C₄₁	—	2	4	no	—
207	C₄²×C₄₁	—	2	2	no	—
208	C₄²×C₄₁	—	2	2	no	—
209	C₄²×C₄₁	—	2	2	no	—
210	C₄²×C₄₁	—	2	2	no	—
211	C₄²×C₄₁	—	2	2	no	—
212	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
213	C₂³×C₄₁	—	2	2	no	—
214	C₂³×C₄₁	—	2	4	no	—
215	C₂³×C₄₁	—	4	1	no	—
216	C₂³×C₄₁	—	4	1	no	—
217	C₂³×C₄₁	—	8	1	no	—
218	C₂³×C₄₁	—	8	1	no	—
219	C₂³×C₄₁	C₄×D₄	1	2	yes	—
220	C₂³×C₄₁	#120	1	1	yes	characteristic
221	C₂³×C₄₁	#120	1	1	yes	characteristic
222	C₂³×C₄₁	C₂²⋊Q₈	1	2	yes	—
223	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₄₁	—	2	2	no	—
225	Q₈×C₄₁	—	2	4	no	—
226	Q₈×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
227	D₄×C₄₁	—	2	4	no	—
228	D₄×C₄₁	—	2	4	no	—
229	D₄×C₄₁	—	2	8	no	—
230	D₄×C₄₁	—	2	2	no	—
231	D₄×C₄₁	—	2	4	no	—
232	D₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
233	C₂×C₄×C₄₁	—	2	2	no	—
234	C₂×C₄×C₄₁	—	2	4	no	—
235	C₂×C₄×C₄₁	—	2	4	no	—
236	C₂×C₄×C₄₁	—	2	4	no	—
237	C₂×C₄×C₄₁	—	2	8	no	—
238	C₂×C₄×C₄₁	—	2	4	no	—
239	C₂×C₄×C₄₁	—	2	2	no	—
240	C₂×C₄×C₄₁	—	2	2	no	—
241	C₂×C₄×C₄₁	—	2	2	no	—
242	C₂×C₄×C₄₁	—	2	2	no	—
243	C₂×C₄×C₄₁	—	4	2	no	—
244	C₂×C₄×C₄₁	—	4	2	no	—
245	C₂×C₄×C₄₁	—	4	2	no	—
246	C₂×C₄×C₄₁	—	4	2	no	—
247	C₂×C₄×C₄₁	—	4	4	no	—
248	C₂×C₄×C₄₁	—	4	2	no	—
249	C₂×C₄×C₄₁	—	8	1	no	—
250	C₂×C₄×C₄₁	—	8	1	no	—
251	C₂×C₄×C₄₁	—	8	4	no	—
252	C₂×C₄×C₄₁	—	8	4	no	—
253	C₂×C₄×C₄₁	—	8	2	no	—
254	C₂×C₄×C₄₁	—	8	2	no	—
255	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
256	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
257	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
258	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
259	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
260	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
261	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
262	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
263	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
264	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
265	C₂×C₄×C₄₁	#123	1	2	yes	—
266	C₂×C₄×C₄₁	#123	1	2	yes	—
267	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
268	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
271	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
273	C₈×C₄₁	—	2	4	no	—
274	C₈×C₄₁	—	4	2	no	—
275	#20865	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂²×C₄₁	—	2	1	no	—
277	C₂²×C₄₁	—	2	1	no	—
278	C₂²×C₄₁	—	2	1	no	—
279	C₂²×C₄₁	—	2	1	no	—
280	C₂²×C₄₁	—	2	1	no	—
281	C₂²×C₄₁	—	2	1	no	—
282	C₂²×C₄₁	—	2	4	no	—
283	C₂²×C₄₁	—	4	2	no	—
284	C₂²×C₄₁	—	4	2	no	—
285	C₂²×C₄₁	—	4	2	no	—
286	C₂²×C₄₁	—	4	2	no	—
287	C₂²×C₄₁	—	8	4	no	—
288	C₂²×C₄₁	#385	1	2	yes	—
289	C₂²×C₄₁	#385	1	2	yes	—
290	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
292	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
293	C₄×C₄₁	—	2	4	no	—
294	C₄×C₄₁	—	4	4	no	—
295	C₄×C₄₁	—	4	2	no	—
296	C₄×C₄₁	—	4	2	no	—
297	C₄×C₄₁	—	4	2	no	—
298	C₄×C₄₁	—	4	2	no	—
299	C₄×C₄₁	—	8	2	no	—
300	C₄×C₄₁	#385	1	2	yes	—
301	C₄×C₄₁	#385	1	2	yes	—
302	C₄×C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
303	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
304	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
305	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
306	#3428	C₂×C₄₁	1	1	yes	characteristic
307	C₂×#428	C₂×C₄₁	1	1	yes	characteristic, complemented
308	C₂×#421	C₂×C₄₁	1	1	yes	characteristic
309	C₂×#417	C₂×C₄₁	1	1	yes	characteristic
310	#2317	C₂×C₄₁	1	1	yes	characteristic, complemented
311	#1860	C₂×C₄₁	1	4	yes	complemented
312	#1859	C₂×C₄₁	1	4	yes	complemented
313	#1742	C₂×C₄₁	1	1	yes	characteristic, complemented
314	#1733	C₂×C₄₁	1	1	yes	characteristic, complemented
315	C₂×C₄₁	—	2	1	no	—
316	C₂×C₄₁	—	2	2	no	—
317	C₂×C₄₁	—	2	1	no	—
318	C₂×C₄₁	—	2	2	no	—
319	C₂×C₄₁	—	4	4	no	—
320	C₂×C₄₁	C₂×#385	1	1	yes	characteristic
321	C₂×C₄₁	#3021	1	1	yes	characteristic
322	C₂×C₄₁	#3022	1	1	yes	characteristic
323	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
324	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
325	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
326	#520	—	2	1	no	—
327	#520	—	2	1	no	—
328	#520	C₂²×C₄₁	1	2	yes	—
329	#520	C₂²×C₄₁	1	2	yes	—
330	#519	—	2	1	no	—
331	#518	—	2	1	no	—
332	#518	—	2	2	no	—
333	C₄×#41	—	2	2	no	—
334	C₄×#41	—	2	2	no	—
335	C₂×#117	—	2	2	no	—
336	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
337	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
338	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
339	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
340	#428	—	2	2	no	—
341	#428	C₂²×C₄₁	1	4	yes	complemented
342	C₂×#107	—	2	1	no	—
343	C₂×#106	—	2	1	no	—
344	#421	C₄×C₄₁	1	8	yes	complemented
345	C₂×#104	C₂²×C₄₁	1	4	yes	—
346	#417	—	2	2	no	—
347	#417	C₂²×C₄₁	1	4	yes	—
348	C₂×#103	—	2	1	no	—
349	C₂×#102	—	2	1	no	—
350	#389	—	2	2	no	—
351	#385	—	2	2	no	—
352	#384	C₂²×C₄₁	1	2	yes	complemented
353	#382	C₂²×C₄₁	1	2	yes	complemented
354	#343	C₂²×C₄₁	1	2	yes	complemented
355	#343	C₂²×C₄₁	1	2	yes	complemented
356	#339	C₂²×C₄₁	1	4	yes	complemented
357	C₄₁	#20865	1	1	yes	characteristic, direct product factor, Sylow
358	C₂×#41	—	2	1	no	—
359	C₂×#41	—	2	1	no	—
360	C₂×#41	—	2	2	no	—
361	C₂×#41	—	2	2	no	—
362	C₂×#41	C₂×C₄×C₄₁	1	4	yes	—
363	C₂×#41	D₄×C₄₁	1	2	yes	—
364	C₂×#41	Q₈×C₄₁	1	4	yes	—
365	C₂×#41	C₂³×C₄₁	1	2	yes	—
366	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
367	C₂²×D₄	—	2	1	no	—
368	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
369	C₂³×C₄	—	2	1	no	—
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	2	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	2	no	—
376	C₂×M₁₆	—	2	2	no	—
377	C₂×M₁₆	C₂×C₄×C₄₁	1	4	yes	complemented
378	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
379	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	2	1	no	—
382	C₄×Q₈	—	2	2	no	—
383	C₄×Q₈	—	2	2	no	—
384	C₄×Q₈	—	2	2	no	—
385	C₄×Q₈	—	2	2	no	—
386	C₄×D₄	—	2	4	no	—
387	C₄×D₄	—	2	4	no	—
388	C₄×D₄	—	2	2	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	4	no	—
393	C₄×D₄	—	2	4	no	—
394	#117	—	2	4	no	—
395	#117	—	2	4	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	—	2	1	no	—
401	#117	—	2	1	no	—
402	#117	—	2	2	no	—
403	#117	—	2	2	no	—
404	#117	—	2	2	no	—
405	#117	C₂×C₄×C₄₁	1	4	yes	complemented
406	#117	D₄×C₄₁	1	2	yes	—
407	#117	C₂³×C₄₁	1	2	yes	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	2	no	—
410	C₂×C₄⋊C₄	—	2	2	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	4	no	—
417	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
418	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	—	2	4	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
426	C₂×C₄²	—	2	4	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	D₄×C₄₁	1	2	yes	—
429	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
430	#107	—	2	4	no	—
431	#106	—	2	4	no	—
432	#104	C₂×C₄×C₄₁	1	16	yes	complemented
433	#103	—	2	4	no	—
434	#102	—	2	4	no	—
435	#95	—	2	4	no	—
436	C₂⁴	—	2	1	no	—
437	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
438	#41	—	2	4	no	—
439	#41	—	2	4	no	—
440	#41	—	2	4	no	—
441	#41	—	2	4	no	—
442	#41	—	2	4	no	—
443	#41	—	2	2	no	—
444	#41	—	2	2	no	—
445	#41	C₄⋊C₄×C₄₁	1	8	yes	complemented
446	#41	C₂²×C₄×C₄₁	1	4	yes	—
447	#41	C₂×Q₈×C₄₁	1	4	yes	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	C₄⋊C₄×C₄₁	1	4	yes	complemented
451	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	C₄⋊C₄×C₄₁	1	4	yes	complemented
459	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	8	2	no	—
474	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
475	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
476	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
477	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
482	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
483	C₂²×C₄	#41×C₄₁	1	2	yes	—
484	C₂²×C₄	#41×C₄₁	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
486	M₁₆	—	2	4	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	2	2	no	—
489	M₁₆	—	2	2	no	—
490	M₁₆	—	4	2	no	—
491	M₁₆	C₂²×C₄×C₄₁	1	4	yes	—
492	C₂×C₈	—	2	4	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	4	2	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	4	1	no	—
508	C₄⋊C₄	—	4	1	no	—
509	C₄⋊C₄	—	8	4	no	—
510	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
511	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₄²	—	2	4	no	—
520	C₄²	—	2	4	no	—
521	C₄²	—	2	2	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	2	2	no	—
525	C₄²	—	2	2	no	—
526	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	4	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	8	1	no	—
532	C₂³	—	8	1	no	—
533	C₂³	C₄×D₄×C₄₁	1	2	yes	—
534	C₂³	#120×C₄₁	1	1	yes	characteristic
535	C₂³	#120×C₄₁	1	1	yes	characteristic
536	C₂³	C₂²⋊Q₈×C₄₁	1	2	yes	—
537	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
538	Q₈	—	2	2	no	—
539	Q₈	—	2	4	no	—
540	Q₈	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
541	D₄	—	2	4	no	—
542	D₄	—	2	4	no	—
543	D₄	—	2	8	no	—
544	D₄	—	2	2	no	—
545	D₄	—	2	4	no	—
546	D₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	8	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	8	1	no	—
564	C₂×C₄	—	8	1	no	—
565	C₂×C₄	—	8	4	no	—
566	C₂×C₄	—	8	4	no	—
567	C₂×C₄	—	8	2	no	—
568	C₂×C₄	—	8	2	no	—
569	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
570	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
571	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
572	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
573	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
574	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
575	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
576	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
577	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
578	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
579	C₂×C₄	#123×C₄₁	1	2	yes	—
580	C₂×C₄	#123×C₄₁	1	2	yes	—
581	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
582	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
583	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
584	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
585	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
586	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
587	C₈	—	2	4	no	—
588	C₈	—	4	2	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	8	4	no	—
601	C₂²	C₄₁×#385	1	2	yes	—
602	C₂²	C₄₁×#385	1	2	yes	—
603	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
604	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
605	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
606	C₄	—	2	4	no	—
607	C₄	—	4	4	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	2	no	—
612	C₄	—	8	2	no	—
613	C₄	C₄₁×#385	1	2	yes	—
614	C₄	C₄₁×#385	1	2	yes	—
615	C₄	C₂²×C₄⋊C₄×C₄₁	1	1	yes	characteristic
616	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
617	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
618	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
619	C₂	—	2	1	no	—
620	C₂	—	2	2	no	—
621	C₂	—	2	1	no	—
622	C₂	—	2	2	no	—
623	C₂	—	4	4	no	—
624	C₂	C₂×C₄₁×#385	1	1	yes	characteristic
625	C₂	C₄₁×#3021	1	1	yes	characteristic
626	C₂	C₄₁×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#428	C₂	semidirect
5. C₄₁×#2317	C₂	semidirect
6. C₄₁×#1860	C₂	semidirect
7. C₄₁×#1859	C₂	semidirect
8. C₄₁×#1742	C₂	semidirect
9. C₄₁×#1733	C₂	semidirect
28. C₄₁×#428	C₂²	semidirect
31. C₄₁×#421	C₄	semidirect
39. C₄₁×#384	C₂²	semidirect
40. C₄₁×#382	C₂²	semidirect
41. C₄₁×#343	C₂²	semidirect
42. C₄₁×#343	C₂²	semidirect
43. C₄₁×#339	C₂²	semidirect
63. C₂×M₁₆×C₄₁	C₂×C₄	semidirect
91. #117×C₄₁	C₂×C₄	semidirect
118. #104×C₄₁	C₂×C₄	semidirect
131. #41×C₄₁	C₄⋊C₄	semidirect
136. C₂×Q₈×C₄₁	C₄⋊C₄	semidirect
144. C₂×D₄×C₄₁	C₄⋊C₄	semidirect
275. #20865	C₄₁	direct (N × H)
307. C₂×#428	C₂×C₄₁	semidirect
310. #2317	C₂×C₄₁	semidirect
311. #1860	C₂×C₄₁	semidirect
312. #1859	C₂×C₄₁	semidirect
313. #1742	C₂×C₄₁	semidirect
314. #1733	C₂×C₄₁	semidirect
341. #428	C₂²×C₄₁	semidirect
344. #421	C₄×C₄₁	semidirect
352. #384	C₂²×C₄₁	semidirect
353. #382	C₂²×C₄₁	semidirect
354. #343	C₂²×C₄₁	semidirect
355. #343	C₂²×C₄₁	semidirect
356. #339	C₂²×C₄₁	semidirect
357. C₄₁	#20865	direct (N × H)
377. C₂×M₁₆	C₂×C₄×C₄₁	semidirect
405. #117	C₂×C₄×C₄₁	semidirect
432. #104	C₂×C₄×C₄₁	semidirect
445. #41	C₄⋊C₄×C₄₁	semidirect
450. C₂×Q₈	C₄⋊C₄×C₄₁	semidirect
458. C₂×D₄	C₄⋊C₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3428	2
C₂×C₄₁×#428	2
C₂×C₄₁×#421	2
C₂×C₄₁×#417	2
C₄₁×#2317	2
C₄₁×#1860	2
C₄₁×#1859	2
C₄₁×#1742	2
C₄₁×#1733	2
#20865	41

Subgroups — C41×#20865 #23797066

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#20865 #23797066