Subgroups — C₂×C₄₁×#2504 #23810982

Order 10496.

3438 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2504	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₁×#397	C₂	1	4	yes	maximal, complemented
5	C₂×C₄₁×#390	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₁×#386	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₁×#382	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₄₁	C₂²	1	2	yes	—
10	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₄₁	C₂²	1	2	yes	—
13	C₂×#121×C₄₁	—	2	8	no	—
14	C₂×#121×C₄₁	C₂²	1	8	yes	—
15	C₂²×C₄⋊C₄×C₄₁	—	2	8	no	—
16	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₄₁	C₂²	1	8	yes	complemented
20	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	8	yes	—
23	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
24	C₄₁×#397	C₂²	1	32	yes	complemented
25	C₄₁×#390	C₂²	1	16	yes	complemented
26	C₄₁×#386	C₂²	1	32	yes	complemented
27	C₄₁×#382	C₂²	1	16	yes	complemented
28	C₄×C₂²⋊C₄×C₄₁	C₂²	1	8	yes	complemented
29	C₂×#95×C₄₁	C₂²	1	2	yes	—
30	C₂×#95×C₄₁	C₂²	1	8	yes	—
31	C₂⁵×C₄₁	C₂³	1	2	yes	—
32	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
33	C₂²×D₄×C₄₁	—	2	8	no	—
34	C₂²×D₄×C₄₁	—	2	16	no	—
35	C₂²×D₄×C₄₁	—	2	4	no	—
36	C₂²×D₄×C₄₁	—	2	8	no	—
37	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
38	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
39	C₂³×C₄×C₄₁	—	2	8	no	—
40	C₂³×C₄×C₄₁	—	2	8	no	—
41	C₂³×C₄×C₄₁	—	4	8	no	—
42	C₂³×C₄×C₄₁	D₄	1	8	yes	—
43	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
44	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
45	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
46	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
47	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₁	C₂³	1	8	yes	—
49	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
50	#121×C₄₁	—	2	32	no	—
51	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
52	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	32	no	—
54	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
56	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
57	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
58	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
59	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
60	C₂×C₂²⋊C₄×C₄₁	—	4	16	no	—
61	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
62	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
63	C₂×C₂²⋊C₄×C₄₁	C₂³	1	32	yes	—
64	C₂×C₄²×C₄₁	—	2	8	no	—
65	C₂×C₄²×C₄₁	C₂³	1	8	yes	—
66	#95×C₄₁	C₂³	1	8	yes	—
67	#95×C₄₁	C₂³	1	32	yes	—
68	C₂⁴×C₄₁	—	2	4	no	—
69	C₂⁴×C₄₁	—	2	4	no	—
70	C₂⁴×C₄₁	—	2	4	no	—
71	C₂⁴×C₄₁	—	2	8	no	—
72	C₂⁴×C₄₁	—	2	8	no	—
73	C₂⁴×C₄₁	—	2	8	no	—
74	C₂⁴×C₄₁	C₂×D₄	1	4	yes	—
75	C₂⁴×C₄₁	#41	1	8	yes	—
76	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
77	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
78	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
79	C₂×D₄×C₄₁	—	2	16	no	—
80	C₂×D₄×C₄₁	—	2	32	no	—
81	C₂×D₄×C₄₁	—	2	8	no	—
82	C₂×D₄×C₄₁	—	2	16	no	—
83	C₂×D₄×C₄₁	—	4	32	no	—
84	C₂×D₄×C₄₁	—	4	16	no	—
85	C₂²×C₄×C₄₁	—	2	4	no	—
86	C₂²×C₄×C₄₁	—	2	32	no	—
87	C₂²×C₄×C₄₁	—	2	16	no	—
88	C₂²×C₄×C₄₁	—	2	4	no	—
89	C₂²×C₄×C₄₁	—	2	16	no	—
90	C₂²×C₄×C₄₁	—	2	8	no	—
91	C₂²×C₄×C₄₁	—	2	8	no	—
92	C₂²×C₄×C₄₁	—	2	8	no	—
93	C₂²×C₄×C₄₁	—	2	8	no	—
94	C₂²×C₄×C₄₁	—	2	8	no	—
95	C₂²×C₄×C₄₁	—	2	16	no	—
96	C₂²×C₄×C₄₁	—	4	16	no	—
97	C₂²×C₄×C₄₁	—	4	32	no	—
98	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₄₁	C₂×D₄	1	16	yes	—
100	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₄₁	#41	1	8	yes	—
102	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
104	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
105	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
106	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
107	C₄⋊C₄×C₄₁	—	2	16	no	—
108	C₄⋊C₄×C₄₁	—	2	16	no	—
109	C₄⋊C₄×C₄₁	—	2	8	no	—
110	C₂²⋊C₄×C₄₁	—	2	16	no	—
111	C₂²⋊C₄×C₄₁	—	2	16	no	—
112	C₂²⋊C₄×C₄₁	—	4	32	no	—
113	C₄²×C₄₁	—	2	16	no	—
114	C₂³×C₄₁	—	2	8	no	—
115	C₂³×C₄₁	—	2	8	no	—
116	C₂³×C₄₁	—	2	32	no	—
117	C₂³×C₄₁	—	2	4	no	—
118	C₂³×C₄₁	—	2	4	no	—
119	C₂³×C₄₁	—	2	4	no	—
120	C₂³×C₄₁	—	2	8	no	—
121	C₂³×C₄₁	—	2	8	no	—
122	C₂³×C₄₁	—	2	8	no	—
123	C₂³×C₄₁	—	4	8	no	—
124	C₂³×C₄₁	—	4	8	no	—
125	C₂³×C₄₁	—	4	8	no	—
126	C₂³×C₄₁	—	4	32	no	—
127	C₂³×C₄₁	#124	1	16	yes	—
128	C₂³×C₄₁	C₂²×D₄	1	4	yes	—
129	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
130	C₂³×C₄₁	C₂×#41	1	8	yes	—
131	C₂³×C₄₁	C₂×#41	1	4	yes	—
132	C₂³×C₄₁	C₂×#41	1	4	yes	—
133	C₂³×C₄₁	H(5,𝔽₂)	1	4	yes	—
134	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
135	D₄×C₄₁	—	4	32	no	—
136	D₄×C₄₁	—	4	16	no	—
137	C₂×C₄×C₄₁	—	2	8	no	—
138	C₂×C₄×C₄₁	—	2	4	no	—
139	C₂×C₄×C₄₁	—	2	32	no	—
140	C₂×C₄×C₄₁	—	2	4	no	—
141	C₂×C₄×C₄₁	—	2	8	no	—
142	C₂×C₄×C₄₁	—	2	8	no	—
143	C₂×C₄×C₄₁	—	2	8	no	—
144	C₂×C₄×C₄₁	—	2	8	no	—
145	C₂×C₄×C₄₁	—	2	8	no	—
146	C₂×C₄×C₄₁	—	2	16	no	—
147	C₂×C₄×C₄₁	—	4	32	no	—
148	C₂×C₄×C₄₁	—	4	8	no	—
149	C₂×C₄×C₄₁	—	4	16	no	—
150	C₂×C₄×C₄₁	—	4	16	no	—
151	C₂×C₄×C₄₁	#123	1	16	yes	—
152	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
153	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
154	C₂×C₄×C₄₁	C₂×#41	1	8	yes	—
155	C₂×#2504	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂²×C₄₁	—	2	4	no	—
157	C₂²×C₄₁	—	2	4	no	—
158	C₂²×C₄₁	—	2	16	no	—
159	C₂²×C₄₁	—	2	32	no	—
160	C₂²×C₄₁	—	4	4	no	—
161	C₂²×C₄₁	—	4	4	no	—
162	C₂²×C₄₁	—	4	4	no	—
163	C₂²×C₄₁	—	4	16	no	—
164	C₂²×C₄₁	—	8	16	no	—
165	C₂²×C₄₁	C₂×#123	1	4	yes	—
166	C₂²×C₄₁	C₂×#124	1	8	yes	—
167	C₂²×C₄₁	C₂×#124	1	4	yes	—
168	C₂²×C₄₁	#535	1	4	yes	—
169	C₂²×C₄₁	#553	1	16	yes	—
170	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
171	C₂²×C₄₁	C₂²×#41	1	2	yes	—
172	C₂²×C₄₁	C₂²×#41	1	2	yes	—
173	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
174	C₄×C₄₁	—	2	4	no	—
175	C₄×C₄₁	—	4	4	no	—
176	C₄×C₄₁	—	4	8	no	—
177	C₄×C₄₁	—	4	8	no	—
178	C₄×C₄₁	C₂×#123	1	8	yes	—
179	C₂²×#121	C₂×C₄₁	1	1	yes	characteristic
180	C₂³×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
181	#2504	C₂×C₄₁	1	16	yes	direct product factor
182	C₂×#397	C₂×C₄₁	1	4	yes	complemented
183	C₂×#390	C₂×C₄₁	1	2	yes	complemented
184	C₂×#386	C₂×C₄₁	1	4	yes	complemented
185	C₂×#382	C₂×C₄₁	1	2	yes	complemented
186	C₂×C₄×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
187	C₂×C₄₁	—	2	8	no	—
188	C₂×C₄₁	—	8	4	no	—
189	C₂×C₄₁	#2504	1	8	yes	direct product factor
190	C₂×C₄₁	C₂²×#123	1	1	yes	characteristic
191	C₂×C₄₁	C₂²×#124	1	1	yes	characteristic
192	C₂×C₄₁	C₂×#535	1	1	yes	characteristic
193	C₂×C₄₁	C₂×#553	1	4	yes	—
194	C₂³×D₄	C₂²×C₄₁	1	2	yes	—
195	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
196	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
197	C₂⁴×C₄	C₂²×C₄₁	1	2	yes	—
198	C₂×#121	—	2	8	no	—
199	C₂×#121	C₂²×C₄₁	1	8	yes	—
200	C₂²×C₄⋊C₄	—	2	8	no	—
201	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
202	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
203	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
204	C₂²×C₄⋊C₄	C₂²×C₄₁	1	8	yes	complemented
205	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
206	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
207	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	8	yes	—
208	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
209	#397	C₂²×C₄₁	1	32	yes	complemented
210	#390	C₂²×C₄₁	1	16	yes	complemented
211	#386	C₂²×C₄₁	1	32	yes	complemented
212	#382	C₂²×C₄₁	1	16	yes	complemented
213	C₄×C₂²⋊C₄	C₂²×C₄₁	1	8	yes	complemented
214	C₂×#95	C₂²×C₄₁	1	2	yes	—
215	C₂×#95	C₂²×C₄₁	1	8	yes	—
216	C₄₁	C₂×#2504	1	1	yes	characteristic, direct product factor, Sylow
217	C₂⁵	C₂³×C₄₁	1	2	yes	—
218	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
219	C₂²×D₄	—	2	8	no	—
220	C₂²×D₄	—	2	16	no	—
221	C₂²×D₄	—	2	4	no	—
222	C₂²×D₄	—	2	8	no	—
223	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
224	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
225	C₂³×C₄	—	2	8	no	—
226	C₂³×C₄	—	2	8	no	—
227	C₂³×C₄	—	4	8	no	—
228	C₂³×C₄	D₄×C₄₁	1	8	yes	—
229	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
230	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
231	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
232	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
233	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
234	C₂³×C₄	C₂³×C₄₁	1	8	yes	—
235	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
236	#121	—	2	32	no	—
237	C₂×C₄⋊C₄	—	2	8	no	—
238	C₂×C₄⋊C₄	—	2	8	no	—
239	C₂×C₄⋊C₄	—	2	32	no	—
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
242	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
243	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
244	C₂×C₂²⋊C₄	—	2	8	no	—
245	C₂×C₂²⋊C₄	—	2	8	no	—
246	C₂×C₂²⋊C₄	—	4	16	no	—
247	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
248	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
249	C₂×C₂²⋊C₄	C₂³×C₄₁	1	32	yes	—
250	C₂×C₄²	—	2	8	no	—
251	C₂×C₄²	C₂³×C₄₁	1	8	yes	—
252	#95	C₂³×C₄₁	1	8	yes	—
253	#95	C₂³×C₄₁	1	32	yes	—
254	C₂⁴	—	2	4	no	—
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	2	8	no	—
258	C₂⁴	—	2	8	no	—
259	C₂⁴	—	2	8	no	—
260	C₂⁴	C₂×D₄×C₄₁	1	4	yes	—
261	C₂⁴	#41×C₄₁	1	8	yes	—
262	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
263	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
264	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
265	C₂×D₄	—	2	16	no	—
266	C₂×D₄	—	2	32	no	—
267	C₂×D₄	—	2	8	no	—
268	C₂×D₄	—	2	16	no	—
269	C₂×D₄	—	4	32	no	—
270	C₂×D₄	—	4	16	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	32	no	—
273	C₂²×C₄	—	2	16	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	16	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	2	8	no	—
279	C₂²×C₄	—	2	8	no	—
280	C₂²×C₄	—	2	8	no	—
281	C₂²×C₄	—	2	16	no	—
282	C₂²×C₄	—	4	16	no	—
283	C₂²×C₄	—	4	32	no	—
284	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
285	C₂²×C₄	C₂×D₄×C₄₁	1	16	yes	—
286	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
287	C₂²×C₄	#41×C₄₁	1	8	yes	—
288	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
289	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
290	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
291	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
292	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
293	C₄⋊C₄	—	2	16	no	—
294	C₄⋊C₄	—	2	16	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₂²⋊C₄	—	2	16	no	—
297	C₂²⋊C₄	—	2	16	no	—
298	C₂²⋊C₄	—	4	32	no	—
299	C₄²	—	2	16	no	—
300	C₂³	—	2	8	no	—
301	C₂³	—	2	8	no	—
302	C₂³	—	2	32	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	2	8	no	—
307	C₂³	—	2	8	no	—
308	C₂³	—	2	8	no	—
309	C₂³	—	4	8	no	—
310	C₂³	—	4	8	no	—
311	C₂³	—	4	8	no	—
312	C₂³	—	4	32	no	—
313	C₂³	#124×C₄₁	1	16	yes	—
314	C₂³	C₂²×D₄×C₄₁	1	4	yes	—
315	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
316	C₂³	C₂×#41×C₄₁	1	8	yes	—
317	C₂³	C₂×#41×C₄₁	1	4	yes	—
318	C₂³	C₂×#41×C₄₁	1	4	yes	—
319	C₂³	H(5,𝔽₂)×C₄₁	1	4	yes	—
320	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
321	D₄	—	4	32	no	—
322	D₄	—	4	16	no	—
323	C₂×C₄	—	2	8	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	32	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	16	no	—
333	C₂×C₄	—	4	32	no	—
334	C₂×C₄	—	4	8	no	—
335	C₂×C₄	—	4	16	no	—
336	C₂×C₄	—	4	16	no	—
337	C₂×C₄	#123×C₄₁	1	16	yes	—
338	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
339	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
340	C₂×C₄	C₂×#41×C₄₁	1	8	yes	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	16	no	—
344	C₂²	—	2	32	no	—
345	C₂²	—	4	4	no	—
346	C₂²	—	4	4	no	—
347	C₂²	—	4	4	no	—
348	C₂²	—	4	16	no	—
349	C₂²	—	8	16	no	—
350	C₂²	C₂×#123×C₄₁	1	4	yes	—
351	C₂²	C₂×#124×C₄₁	1	8	yes	—
352	C₂²	C₂×#124×C₄₁	1	4	yes	—
353	C₂²	C₄₁×#535	1	4	yes	—
354	C₂²	C₄₁×#553	1	16	yes	—
355	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
356	C₂²	C₂²×#41×C₄₁	1	2	yes	—
357	C₂²	C₂²×#41×C₄₁	1	2	yes	—
358	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
359	C₄	—	2	4	no	—
360	C₄	—	4	4	no	—
361	C₄	—	4	8	no	—
362	C₄	—	4	8	no	—
363	C₄	C₂×#123×C₄₁	1	8	yes	—
364	C₂	—	2	8	no	—
365	C₂	—	8	4	no	—
366	C₂	C₄₁×#2504	1	8	yes	direct product factor
367	C₂	C₂²×#123×C₄₁	1	1	yes	characteristic
368	C₂	C₂²×#124×C₄₁	1	1	yes	characteristic
369	C₂	C₂×C₄₁×#535	1	1	yes	characteristic
370	C₂	C₂×C₄₁×#553	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂²×#121×C₄₁	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄⋊C₄×C₄₁	C₂	semidirect
3. C₄₁×#2504	C₂	direct (N × H)
4. C₂×C₄₁×#397	C₂	semidirect
5. C₂×C₄₁×#390	C₂	semidirect
6. C₂×C₄₁×#386	C₂	semidirect
7. C₂×C₄₁×#382	C₂	semidirect
8. C₂×C₄×C₂²⋊C₄×C₄₁	C₂	semidirect
19. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
24. C₄₁×#397	C₂²	semidirect
25. C₄₁×#390	C₂²	semidirect
26. C₄₁×#386	C₂²	semidirect
27. C₄₁×#382	C₂²	semidirect
28. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
155. C₂×#2504	C₄₁	direct (N × H)
180. C₂³×C₄⋊C₄	C₂×C₄₁	semidirect
181. #2504	C₂×C₄₁	direct (N × H)
182. C₂×#397	C₂×C₄₁	semidirect
183. C₂×#390	C₂×C₄₁	semidirect
184. C₂×#386	C₂×C₄₁	semidirect
185. C₂×#382	C₂×C₄₁	semidirect
186. C₂×C₄×C₂²⋊C₄	C₂×C₄₁	semidirect
189. C₂×C₄₁	#2504	direct (N × H)
204. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
209. #397	C₂²×C₄₁	semidirect
210. #390	C₂²×C₄₁	semidirect
211. #386	C₂²×C₄₁	semidirect
212. #382	C₂²×C₄₁	semidirect
213. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
216. C₄₁	C₂×#2504	direct (N × H)
366. C₂	C₄₁×#2504	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#121×C₄₁	2
C₂³×C₄⋊C₄×C₄₁	2
C₄₁×#2504	2
C₂×C₄₁×#397	2
C₂×C₄₁×#390	2
C₂×C₄₁×#386	2
C₂×C₄₁×#382	2
C₂×C₄×C₂²⋊C₄×C₄₁	2
C₂×#2504	41

Subgroups — C2×C41×#2504 #23810982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2504 #23810982