Subgroups — C₄₁×#22602 #23798803

Order 10496.

780 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#433	C₂	1	2	yes	maximal
2	C₄₁×#2285	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#1940	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1917	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1916	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1818	C₂	1	2	yes	maximal
7	C₄₁×#1797	C₂	1	1	yes	maximal, characteristic
8	C₄₁×#1771	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1749	C₂	1	1	yes	maximal, characteristic
10	C₂×#117×C₄₁	C₂²	1	2	yes	—
11	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
12	C₄₁×#433	—	2	8	no	—
13	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
14	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#97×C₄₁	C₂²	1	2	yes	—
20	C₂×#97×C₄₁	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
22	C₄₁×#384	C₄	1	1	yes	characteristic
23	C₄₁×#384	C₄	1	1	yes	characteristic
24	C₄₁×#382	C₄	1	2	yes	—
25	C₄₁×#380	C₄	1	2	yes	—
26	C₄₁×#380	C₄	1	1	yes	characteristic
27	C₄₁×#380	C₄	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
31	C₄₁×#336	C₂²	1	2	yes	—
32	C₄₁×#336	C₂²	1	2	yes	—
33	C₄₁×#336	C₂²	1	1	yes	characteristic
34	C₄₁×#336	C₂²	1	1	yes	characteristic
35	C₄₁×#336	C₂²	1	2	yes	—
36	C₄₁×#336	C₂²	1	2	yes	—
37	C₄₁×#336	C₂²	1	2	yes	—
38	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
45	#117×C₄₁	—	2	4	no	—
46	#117×C₄₁	—	2	4	no	—
47	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₄₁	—	2	4	no	—
58	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
62	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
63	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
64	C₄⋊C₈×C₄₁	—	2	4	no	—
65	C₄⋊C₈×C₄₁	—	2	4	no	—
66	C₄⋊C₈×C₄₁	—	2	4	no	—
67	C₂²⋊C₈×C₄₁	—	2	4	no	—
68	C₂²⋊C₈×C₄₁	—	2	2	no	—
69	C₂²⋊C₈×C₄₁	D₄	1	4	yes	—
70	#97×C₄₁	—	2	4	no	—
71	#97×C₄₁	—	2	4	no	—
72	C₄×C₈×C₄₁	—	2	4	no	—
73	#95×C₄₁	C₂×C₄	1	2	yes	—
74	#95×C₄₁	C₂×C₄	1	2	yes	—
75	#95×C₄₁	C₂×C₄	1	2	yes	—
76	#95×C₄₁	C₂×C₄	1	2	yes	—
77	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₁	—	2	2	no	—
79	C₂²×C₄×C₄₁	—	2	2	no	—
80	C₂²×C₄×C₄₁	—	2	2	no	—
81	C₂²×C₄×C₄₁	—	2	2	no	—
82	C₂²×C₄×C₄₁	—	2	2	no	—
83	C₂²×C₄×C₄₁	—	4	1	no	—
84	C₂²×C₄×C₄₁	—	4	1	no	—
85	C₂²×C₄×C₄₁	—	4	1	no	—
86	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₁	#41	1	2	yes	—
97	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₄₁	—	2	2	no	—
99	C₂×C₈×C₄₁	—	2	2	no	—
100	C₂×C₈×C₄₁	—	2	2	no	—
101	C₂×C₈×C₄₁	—	2	2	no	—
102	C₂×C₈×C₄₁	—	2	2	no	—
103	C₂×C₈×C₄₁	—	2	2	no	—
104	C₂×C₈×C₄₁	—	2	2	no	—
105	C₂×C₈×C₄₁	—	2	2	no	—
106	C₂×C₈×C₄₁	—	2	2	no	—
107	C₂×C₈×C₄₁	—	2	2	no	—
108	C₂×C₈×C₄₁	—	2	2	no	—
109	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
110	C₄⋊C₄×C₄₁	—	2	4	no	—
111	C₄⋊C₄×C₄₁	—	2	4	no	—
112	C₄⋊C₄×C₄₁	—	2	4	no	—
113	C₄⋊C₄×C₄₁	—	4	1	no	—
114	C₄⋊C₄×C₄₁	—	4	1	no	—
115	C₄⋊C₄×C₄₁	—	4	1	no	—
116	C₄⋊C₄×C₄₁	—	4	1	no	—
117	C₄⋊C₄×C₄₁	—	4	2	no	—
118	C₂²⋊C₄×C₄₁	—	2	4	no	—
119	C₂²⋊C₄×C₄₁	—	2	4	no	—
120	C₄²×C₄₁	—	2	2	no	—
121	C₄²×C₄₁	—	2	2	no	—
122	C₄²×C₄₁	—	2	2	no	—
123	C₄²×C₄₁	—	2	2	no	—
124	C₄²×C₄₁	—	2	2	no	—
125	C₄²×C₄₁	—	2	2	no	—
126	C₄²×C₄₁	—	2	2	no	—
127	C₄²×C₄₁	#41	1	4	yes	—
128	C₂³×C₄₁	—	2	1	no	—
129	C₂³×C₄₁	—	2	1	no	—
130	C₂³×C₄₁	—	2	1	no	—
131	C₂³×C₄₁	—	2	1	no	—
132	C₂³×C₄₁	—	2	1	no	—
133	C₂³×C₄₁	—	2	1	no	—
134	C₂³×C₄₁	C₄×D₄	1	2	yes	—
135	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
136	C₂×C₄×C₄₁	—	2	1	no	—
137	C₂×C₄×C₄₁	—	2	1	no	—
138	C₂×C₄×C₄₁	—	2	1	no	—
139	C₂×C₄×C₄₁	—	2	1	no	—
140	C₂×C₄×C₄₁	—	2	1	no	—
141	C₂×C₄×C₄₁	—	2	1	no	—
142	C₂×C₄×C₄₁	—	2	1	no	—
143	C₂×C₄×C₄₁	—	2	1	no	—
144	C₂×C₄×C₄₁	—	2	4	no	—
145	C₂×C₄×C₄₁	—	2	4	no	—
146	C₂×C₄×C₄₁	—	2	1	no	—
147	C₂×C₄×C₄₁	—	2	2	no	—
148	C₂×C₄×C₄₁	—	2	2	no	—
149	C₂×C₄×C₄₁	—	2	2	no	—
150	C₂×C₄×C₄₁	—	2	2	no	—
151	C₂×C₄×C₄₁	—	2	2	no	—
152	C₂×C₄×C₄₁	—	2	2	no	—
153	C₂×C₄×C₄₁	—	2	2	no	—
154	C₂×C₄×C₄₁	—	2	2	no	—
155	C₂×C₄×C₄₁	—	2	2	no	—
156	C₂×C₄×C₄₁	—	2	2	no	—
157	C₂×C₄×C₄₁	—	2	2	no	—
158	C₂×C₄×C₄₁	—	2	2	no	—
159	C₂×C₄×C₄₁	—	2	1	no	—
160	C₂×C₄×C₄₁	—	2	1	no	—
161	C₂×C₄×C₄₁	—	4	4	no	—
162	C₂×C₄×C₄₁	—	4	4	no	—
163	C₂×C₄×C₄₁	#117	1	2	yes	—
164	C₂×C₄×C₄₁	#117	1	2	yes	—
165	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₄₁	#131	1	2	yes	—
167	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
169	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
171	C₈×C₄₁	—	2	4	no	—
172	C₈×C₄₁	—	4	2	no	—
173	C₈×C₄₁	—	4	2	no	—
174	C₈×C₄₁	—	4	2	no	—
175	#22602	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂²×C₄₁	—	2	2	no	—
177	C₂²×C₄₁	—	2	2	no	—
178	C₂²×C₄₁	—	2	2	no	—
179	C₂²×C₄₁	—	4	1	no	—
180	C₂²×C₄₁	—	4	1	no	—
181	C₂²×C₄₁	—	4	1	no	—
182	C₂²×C₄₁	—	4	1	no	—
183	C₂²×C₄₁	C₂×#117	1	1	yes	characteristic
184	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
185	C₂²×C₄₁	#519	1	1	yes	characteristic
186	C₂²×C₄₁	C₂×#131	1	1	yes	characteristic
187	C₂²×C₄₁	#568	1	1	yes	characteristic
188	C₂²×C₄₁	#568	1	1	yes	characteristic
189	C₂²×C₄₁	#568	1	1	yes	characteristic
190	C₄×C₄₁	—	2	2	no	—
191	C₄×C₄₁	—	2	2	no	—
192	C₄×C₄₁	—	2	2	no	—
193	C₄×C₄₁	—	2	2	no	—
194	C₄×C₄₁	—	4	1	no	—
195	C₄×C₄₁	—	4	2	no	—
196	C₄×C₄₁	—	4	2	no	—
197	C₄×C₄₁	—	4	2	no	—
198	C₄×C₄₁	—	4	2	no	—
199	C₄×C₄₁	#547	1	2	yes	—
200	C₄×C₄₁	#552	1	2	yes	—
201	C₂×#433	C₂×C₄₁	1	2	yes	—
202	#2285	C₂×C₄₁	1	1	yes	characteristic
203	#1940	C₂×C₄₁	1	2	yes	complemented
204	#1917	C₂×C₄₁	1	2	yes	complemented
205	#1916	C₂×C₄₁	1	2	yes	complemented
206	#1818	C₂×C₄₁	1	2	yes	—
207	#1797	C₂×C₄₁	1	1	yes	characteristic
208	#1771	C₂×C₄₁	1	2	yes	complemented
209	#1749	C₂×C₄₁	1	1	yes	characteristic
210	C₂×C₄₁	—	4	2	no	—
211	C₂×C₄₁	#2344	1	1	yes	characteristic
212	C₂×C₄₁	#2921	1	1	yes	characteristic
213	C₂×C₄₁	#2924	1	1	yes	characteristic
214	C₂×C₄₁	#2932	1	1	yes	characteristic
215	C₂×C₄₁	#2935	1	1	yes	characteristic
216	C₂×C₄₁	#2985	1	1	yes	characteristic
217	C₂×C₄₁	#2987	1	1	yes	characteristic
218	C₂×#117	C₂²×C₄₁	1	2	yes	—
219	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
220	#433	—	2	8	no	—
221	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
222	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
223	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
224	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
225	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
226	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
227	C₂×#97	C₂²×C₄₁	1	2	yes	—
228	C₂×#97	C₂²×C₄₁	1	2	yes	—
229	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
230	#384	C₄×C₄₁	1	1	yes	characteristic
231	#384	C₄×C₄₁	1	1	yes	characteristic
232	#382	C₄×C₄₁	1	2	yes	—
233	#380	C₄×C₄₁	1	2	yes	—
234	#380	C₄×C₄₁	1	1	yes	characteristic
235	#380	C₄×C₄₁	1	1	yes	characteristic
236	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
237	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
238	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
239	#336	C₂²×C₄₁	1	1	yes	characteristic
240	#336	C₂²×C₄₁	1	1	yes	characteristic
241	#336	C₂²×C₄₁	1	2	yes	—
242	#336	C₂²×C₄₁	1	2	yes	—
243	#336	C₂²×C₄₁	1	2	yes	—
244	#336	C₂²×C₄₁	1	2	yes	—
245	#336	C₂²×C₄₁	1	2	yes	—
246	C₄₁	#22602	1	1	yes	characteristic, direct product factor, Sylow
247	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
248	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
249	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
251	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
252	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
253	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
254	#117	—	2	4	no	—
255	#117	—	2	4	no	—
256	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
257	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
258	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
259	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
264	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
265	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
266	C₂×C₄²	—	2	4	no	—
267	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
268	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
270	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
271	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
273	C₄⋊C₈	—	2	4	no	—
274	C₄⋊C₈	—	2	4	no	—
275	C₄⋊C₈	—	2	4	no	—
276	C₂²⋊C₈	—	2	4	no	—
277	C₂²⋊C₈	—	2	2	no	—
278	C₂²⋊C₈	D₄×C₄₁	1	4	yes	—
279	#97	—	2	4	no	—
280	#97	—	2	4	no	—
281	C₄×C₈	—	2	4	no	—
282	#95	C₂×C₄×C₄₁	1	2	yes	—
283	#95	C₂×C₄×C₄₁	1	2	yes	—
284	#95	C₂×C₄×C₄₁	1	2	yes	—
285	#95	C₂×C₄×C₄₁	1	2	yes	—
286	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
297	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
301	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
305	C₂²×C₄	#41×C₄₁	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	#41×C₄₁	1	4	yes	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	C₄×D₄×C₄₁	1	2	yes	—
344	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	#117×C₄₁	1	2	yes	—
373	C₂×C₄	#117×C₄₁	1	2	yes	—
374	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
375	C₂×C₄	#131×C₄₁	1	2	yes	—
376	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
377	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
378	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
379	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
380	C₈	—	2	4	no	—
381	C₈	—	4	2	no	—
382	C₈	—	4	2	no	—
383	C₈	—	4	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	C₂×#117×C₄₁	1	1	yes	characteristic
392	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
393	C₂²	C₄₁×#519	1	1	yes	characteristic
394	C₂²	C₂×#131×C₄₁	1	1	yes	characteristic
395	C₂²	C₄₁×#568	1	1	yes	characteristic
396	C₂²	C₄₁×#568	1	1	yes	characteristic
397	C₂²	C₄₁×#568	1	1	yes	characteristic
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	C₄₁×#547	1	2	yes	—
408	C₄	C₄₁×#552	1	2	yes	—
409	C₂	—	4	2	no	—
410	C₂	C₄₁×#2344	1	1	yes	characteristic
411	C₂	C₄₁×#2921	1	1	yes	characteristic
412	C₂	C₄₁×#2924	1	1	yes	characteristic
413	C₂	C₄₁×#2932	1	1	yes	characteristic
414	C₂	C₄₁×#2935	1	1	yes	characteristic
415	C₂	C₄₁×#2985	1	1	yes	characteristic
416	C₂	C₄₁×#2987	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₄₁×#1940	C₂	semidirect
4. C₄₁×#1917	C₂	semidirect
5. C₄₁×#1916	C₂	semidirect
8. C₄₁×#1771	C₂	semidirect
175. #22602	C₄₁	direct (N × H)
203. #1940	C₂×C₄₁	semidirect
204. #1917	C₂×C₄₁	semidirect
205. #1916	C₂×C₄₁	semidirect
208. #1771	C₂×C₄₁	semidirect
246. C₄₁	#22602	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#433	2
C₄₁×#2285	2
C₄₁×#1940	2
C₄₁×#1917	2
C₄₁×#1916	2
C₄₁×#1818	2
C₄₁×#1797	2
C₄₁×#1771	2
C₄₁×#1749	2
#22602	41

Subgroups — C41×#22602 #23798803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#22602 #23798803