Subgroups — C₄₁×#21925 #23798126

Order 10496.

648 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2298	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#1924	C₂	1	2	yes	maximal
3	C₄₁×#1923	C₂	1	2	yes	maximal
4	C₄₁×#1917	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1916	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1843	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1832	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1798	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1798	C₂	1	1	yes	maximal, characteristic
10	C₄₁×#1767	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₄⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
21	C₂×#97×C₄₁	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
23	C₄₁×#388	C₄	1	2	yes	—
24	C₄₁×#388	C₄	1	2	yes	—
25	C₄₁×#387	C₄	1	2	yes	—
26	C₄₁×#387	C₄	1	2	yes	—
27	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
31	C₄₁×#376	C₂²	1	1	yes	characteristic
32	C₄³×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#336	C₂²	1	2	yes	—
34	C₄₁×#336	C₂²	1	2	yes	—
35	C₄₁×#336	C₂²	1	2	yes	—
36	C₄₁×#336	C₂²	1	2	yes	—
37	C₄₁×#336	C₂²	1	2	yes	—
38	C₄₁×#336	C₂²	1	2	yes	—
39	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
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	#117×C₄₁	—	2	2	no	—
45	#117×C₄₁	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
50	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
62	C₄⋊C₈×C₄₁	—	2	2	no	—
63	C₄⋊C₈×C₄₁	—	2	2	no	—
64	C₄⋊C₈×C₄₁	—	2	2	no	—
65	C₄⋊C₈×C₄₁	—	2	2	no	—
66	C₄⋊C₈×C₄₁	—	4	2	no	—
67	C₄⋊C₈×C₄₁	—	4	2	no	—
68	C₂²⋊C₈×C₄₁	—	4	2	no	—
69	C₂²⋊C₈×C₄₁	—	4	2	no	—
70	#97×C₄₁	—	4	2	no	—
71	C₄×C₈×C₄₁	—	4	2	no	—
72	#95×C₄₁	C₂×C₄	1	2	yes	—
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	#95×C₄₁	C₂×C₄	1	2	yes	—
78	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₁	—	2	1	no	—
80	C₂²×C₄×C₄₁	—	2	1	no	—
81	C₂²×C₄×C₄₁	—	2	1	no	—
82	C₂²×C₄×C₄₁	—	2	1	no	—
83	C₂²×C₄×C₄₁	—	2	1	no	—
84	C₂²×C₄×C₄₁	—	2	1	no	—
85	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
94	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
95	C₂×C₈×C₄₁	—	2	2	no	—
96	C₂×C₈×C₄₁	—	2	2	no	—
97	C₂×C₈×C₄₁	—	2	2	no	—
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	C₄⋊C₄×C₄₁	—	2	2	no	—
108	C₄⋊C₄×C₄₁	—	2	2	no	—
109	C₄⋊C₄×C₄₁	—	2	4	no	—
110	C₄⋊C₄×C₄₁	—	4	2	no	—
111	C₂²⋊C₄×C₄₁	—	2	2	no	—
112	C₂²⋊C₄×C₄₁	—	2	2	no	—
113	C₂²⋊C₄×C₄₁	—	2	4	no	—
114	C₂²⋊C₄×C₄₁	—	4	2	no	—
115	C₄²×C₄₁	—	2	4	no	—
116	C₄²×C₄₁	—	2	1	no	—
117	C₄²×C₄₁	—	2	1	no	—
118	C₄²×C₄₁	—	2	1	no	—
119	C₄²×C₄₁	—	2	1	no	—
120	C₄²×C₄₁	—	2	1	no	—
121	C₄²×C₄₁	—	2	1	no	—
122	C₄²×C₄₁	—	2	1	no	—
123	C₄²×C₄₁	—	2	1	no	—
124	C₄²×C₄₁	—	2	1	no	—
125	C₄²×C₄₁	—	2	1	no	—
126	C₄²×C₄₁	—	4	2	no	—
127	C₄²×C₄₁	#41	1	2	yes	—
128	C₄²×C₄₁	#41	1	2	yes	—
129	C₂³×C₄₁	—	2	1	no	—
130	C₂³×C₄₁	—	2	1	no	—
131	C₂³×C₄₁	—	2	1	no	—
132	C₂³×C₄₁	—	2	2	no	—
133	C₂³×C₄₁	—	2	2	no	—
134	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₄₁	—	2	2	no	—
136	C₂×C₄×C₄₁	—	2	2	no	—
137	C₂×C₄×C₄₁	—	2	2	no	—
138	C₂×C₄×C₄₁	—	2	2	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	2	no	—
143	C₂×C₄×C₄₁	—	2	2	no	—
144	C₂×C₄×C₄₁	—	2	2	no	—
145	C₂×C₄×C₄₁	—	2	1	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	—	4	1	no	—
156	C₂×C₄×C₄₁	—	4	1	no	—
157	C₂×C₄×C₄₁	—	4	1	no	—
158	C₂×C₄×C₄₁	—	4	1	no	—
159	C₂×C₄×C₄₁	#117	1	2	yes	—
160	C₂×C₄×C₄₁	#117	1	2	yes	—
161	C₂×C₄×C₄₁	#131	1	4	yes	—
162	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
167	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
168	C₈×C₄₁	—	4	2	no	—
169	C₈×C₄₁	—	4	2	no	—
170	C₈×C₄₁	—	4	2	no	—
171	C₈×C₄₁	—	4	2	no	—
172	#21925	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₄₁	—	4	1	no	—
174	C₂²×C₄₁	—	4	1	no	—
175	C₂²×C₄₁	—	4	1	no	—
176	C₂²×C₄₁	—	4	2	no	—
177	C₂²×C₄₁	—	4	2	no	—
178	C₂²×C₄₁	C₂×#117	1	1	yes	characteristic
179	C₂²×C₄₁	#520	1	1	yes	characteristic
180	C₂²×C₄₁	#520	1	1	yes	characteristic
181	C₂²×C₄₁	C₂×#131	1	2	yes	—
182	C₂²×C₄₁	#568	1	2	yes	—
183	C₄×C₄₁	—	2	2	no	—
184	C₄×C₄₁	—	2	2	no	—
185	C₄×C₄₁	—	2	4	no	—
186	C₄×C₄₁	—	4	1	no	—
187	C₄×C₄₁	—	4	1	no	—
188	C₄×C₄₁	—	4	1	no	—
189	C₄×C₄₁	—	4	2	no	—
190	C₄×C₄₁	—	4	2	no	—
191	C₄×C₄₁	—	4	2	no	—
192	C₄×C₄₁	#540	1	1	yes	characteristic
193	C₄×C₄₁	#541	1	1	yes	characteristic
194	C₄×C₄₁	#542	1	1	yes	characteristic
195	C₄×C₄₁	#542	1	1	yes	characteristic
196	#2298	C₂×C₄₁	1	1	yes	characteristic
197	#1924	C₂×C₄₁	1	2	yes	—
198	#1923	C₂×C₄₁	1	2	yes	—
199	#1917	C₂×C₄₁	1	2	yes	complemented
200	#1916	C₂×C₄₁	1	2	yes	complemented
201	#1843	C₂×C₄₁	1	1	yes	characteristic, complemented
202	#1832	C₂×C₄₁	1	1	yes	characteristic, complemented
203	#1798	C₂×C₄₁	1	1	yes	characteristic
204	#1798	C₂×C₄₁	1	1	yes	characteristic
205	#1767	C₂×C₄₁	1	1	yes	characteristic, complemented
206	C₄×C₄⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
207	C₂×C₄₁	—	8	1	no	—
208	C₂×C₄₁	#2314	1	1	yes	characteristic
209	C₂×C₄₁	#2922	1	1	yes	characteristic
210	C₂×C₄₁	#2923	1	1	yes	characteristic
211	C₂×C₄₁	#2992	1	2	yes	—
212	C₂×C₄₁	#2993	1	2	yes	—
213	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
215	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
218	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
219	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
220	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
221	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
222	C₂×#97	C₂²×C₄₁	1	2	yes	—
223	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
224	#388	C₄×C₄₁	1	2	yes	—
225	#388	C₄×C₄₁	1	2	yes	—
226	#387	C₄×C₄₁	1	2	yes	—
227	#387	C₄×C₄₁	1	2	yes	—
228	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
229	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
230	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
231	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
232	#376	C₂²×C₄₁	1	1	yes	characteristic
233	C₄³	C₂²×C₄₁	1	1	yes	characteristic
234	#336	C₂²×C₄₁	1	2	yes	—
235	#336	C₂²×C₄₁	1	2	yes	—
236	#336	C₂²×C₄₁	1	2	yes	—
237	#336	C₂²×C₄₁	1	2	yes	—
238	#336	C₂²×C₄₁	1	2	yes	—
239	#336	C₂²×C₄₁	1	2	yes	—
240	C₄₁	#21925	1	1	yes	characteristic, direct product factor, Sylow
241	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
243	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
244	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
245	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
246	#117	—	2	2	no	—
247	#117	—	2	2	no	—
248	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
251	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
252	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
255	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
256	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
257	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
258	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	4	2	no	—
269	C₄⋊C₈	—	4	2	no	—
270	C₂²⋊C₈	—	4	2	no	—
271	C₂²⋊C₈	—	4	2	no	—
272	#97	—	4	2	no	—
273	C₄×C₈	—	4	2	no	—
274	#95	C₂×C₄×C₄₁	1	2	yes	—
275	#95	C₂×C₄×C₄₁	1	2	yes	—
276	#95	C₂×C₄×C₄₁	1	2	yes	—
277	#95	C₂×C₄×C₄₁	1	2	yes	—
278	#95	C₂×C₄×C₄₁	1	2	yes	—
279	#95	C₂×C₄×C₄₁	1	2	yes	—
280	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
289	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
291	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
292	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
295	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
296	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	4	no	—
316	C₂²⋊C₄	—	4	2	no	—
317	C₄²	—	2	4	no	—
318	C₄²	—	2	1	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	4	2	no	—
329	C₄²	#41×C₄₁	1	2	yes	—
330	C₄²	#41×C₄₁	1	2	yes	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	#117×C₄₁	1	2	yes	—
362	C₂×C₄	#117×C₄₁	1	2	yes	—
363	C₂×C₄	#131×C₄₁	1	4	yes	—
364	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
365	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
366	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
367	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
368	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
369	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
370	C₈	—	4	2	no	—
371	C₈	—	4	2	no	—
372	C₈	—	4	2	no	—
373	C₈	—	4	2	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	C₂×#117×C₄₁	1	1	yes	characteristic
380	C₂²	C₄₁×#520	1	1	yes	characteristic
381	C₂²	C₄₁×#520	1	1	yes	characteristic
382	C₂²	C₂×#131×C₄₁	1	2	yes	—
383	C₂²	C₄₁×#568	1	2	yes	—
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	2	4	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	4	1	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	C₄₁×#540	1	1	yes	characteristic
394	C₄	C₄₁×#541	1	1	yes	characteristic
395	C₄	C₄₁×#542	1	1	yes	characteristic
396	C₄	C₄₁×#542	1	1	yes	characteristic
397	C₂	—	8	1	no	—
398	C₂	C₄₁×#2314	1	1	yes	characteristic
399	C₂	C₄₁×#2922	1	1	yes	characteristic
400	C₂	C₄₁×#2923	1	1	yes	characteristic
401	C₂	C₄₁×#2992	1	2	yes	—
402	C₂	C₄₁×#2993	1	2	yes	—

	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
4. C₄₁×#1917	C₂	semidirect
5. C₄₁×#1916	C₂	semidirect
6. C₄₁×#1843	C₂	semidirect
7. C₄₁×#1832	C₂	semidirect
10. C₄₁×#1767	C₂	semidirect
11. C₄×C₄⋊C₈×C₄₁	C₂	semidirect
172. #21925	C₄₁	direct (N × H)
199. #1917	C₂×C₄₁	semidirect
200. #1916	C₂×C₄₁	semidirect
201. #1843	C₂×C₄₁	semidirect
202. #1832	C₂×C₄₁	semidirect
205. #1767	C₂×C₄₁	semidirect
206. C₄×C₄⋊C₈	C₂×C₄₁	semidirect
240. C₄₁	#21925	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×#2298	2
C₄₁×#1924	2
C₄₁×#1923	2
C₄₁×#1917	2
C₄₁×#1916	2
C₄₁×#1843	2
C₄₁×#1832	2
C₄₁×#1798	2
C₄₁×#1767	2
C₄×C₄⋊C₈×C₄₁	2
#21925	41

Subgroups — C41×#21925 #23798126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21925 #23798126