Subgroups — C₂×C₄₁×#2406 #23810934

Order 10496.

5718 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×#123×C₄₁	C₂	1	2	yes	maximal, complemented
3	C₂³×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2406	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₄₁×#395	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₁×#394	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₁×#386	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₁×#385	C₂	1	4	yes	maximal, complemented
9	C₂×C₄₁×#381	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₁	—	2	16	no	—
11	C₂²×#41×C₄₁	—	2	8	no	—
12	C₂²×#41×C₄₁	C₂²	1	8	yes	—
13	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₄₁	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₄₁	C₂²	1	2	yes	—
17	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#123×C₄₁	—	2	16	no	—
21	C₂×#123×C₄₁	C₂²	1	16	yes	complemented
22	C₂²×C₄⋊C₄×C₄₁	—	2	8	no	—
23	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
25	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
26	C₂²×C₄⋊C₄×C₄₁	C₂²	1	8	yes	complemented
27	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
29	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
30	C₄₁×#395	C₂²	1	16	yes	complemented
31	C₄₁×#394	C₂²	1	16	yes	complemented
32	C₄₁×#386	C₂²	1	16	yes	complemented
33	C₄₁×#385	C₂²	1	32	yes	complemented
34	C₄₁×#381	C₂²	1	8	yes	complemented
35	C₂×#95×C₄₁	C₂²	1	2	yes	—
36	C₂×#95×C₄₁	C₂²	1	2	yes	—
37	C₂×#95×C₄₁	C₂²	1	4	yes	—
38	C₂⁵×C₄₁	C₂³	1	2	yes	—
39	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
40	C₂×#41×C₄₁	—	2	128	no	—
41	C₂×#41×C₄₁	—	2	64	no	—
42	C₂×#41×C₄₁	—	2	32	no	—
43	C₂²×Q₈×C₄₁	—	2	8	no	—
44	C₂²×Q₈×C₄₁	—	2	4	no	—
45	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
46	C₂²×D₄×C₄₁	—	2	8	no	—
47	C₂²×D₄×C₄₁	—	2	8	no	—
48	C₂²×D₄×C₄₁	—	2	8	no	—
49	C₂²×D₄×C₄₁	—	2	4	no	—
50	C₂²×D₄×C₄₁	D₄	1	16	yes	—
51	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
52	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
53	C₂³×C₄×C₄₁	—	2	4	no	—
54	C₂³×C₄×C₄₁	—	2	8	no	—
55	C₂³×C₄×C₄₁	—	2	8	no	—
56	C₂³×C₄×C₄₁	—	2	8	no	—
57	C₂³×C₄×C₄₁	—	2	8	no	—
58	C₂³×C₄×C₄₁	—	2	8	no	—
59	C₂³×C₄×C₄₁	—	2	4	no	—
60	C₂³×C₄×C₄₁	—	2	8	no	—
61	C₂³×C₄×C₄₁	D₄	1	8	yes	—
62	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
63	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
64	C₂³×C₄×C₄₁	C₂³	1	8	yes	—
65	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
66	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
67	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
68	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
70	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
72	#123×C₄₁	—	2	64	no	—
73	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
74	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
75	C₂×C₄⋊C₄×C₄₁	—	2	32	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	16	no	—
77	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
78	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
79	C₂×C₄⋊C₄×C₄₁	C₂³	1	16	yes	—
80	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
81	C₂×C₂²⋊C₄×C₄₁	—	2	16	no	—
82	C₂×C₂²⋊C₄×C₄₁	—	2	16	no	—
83	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
84	C₂×C₂²⋊C₄×C₄₁	C₂³	1	16	yes	—
85	C₂×C₂²⋊C₄×C₄₁	C₂³	1	16	yes	—
86	#95×C₄₁	C₂³	1	8	yes	—
87	#95×C₄₁	C₂³	1	8	yes	—
88	#95×C₄₁	C₂³	1	16	yes	—
89	C₂⁴×C₄₁	—	2	4	no	—
90	C₂⁴×C₄₁	—	2	4	no	—
91	C₂⁴×C₄₁	—	2	4	no	—
92	C₂⁴×C₄₁	—	2	4	no	—
93	C₂⁴×C₄₁	—	2	8	no	—
94	C₂⁴×C₄₁	—	2	8	no	—
95	C₂⁴×C₄₁	C₂×D₄	1	8	yes	—
96	C₂⁴×C₄₁	C₂×D₄	1	8	yes	—
97	C₂⁴×C₄₁	C₂×D₄	1	4	yes	—
98	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
99	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
100	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
101	#41×C₄₁	—	2	256	no	—
102	C₂×Q₈×C₄₁	—	2	32	no	—
103	C₂×Q₈×C₄₁	—	2	16	no	—
104	C₂×Q₈×C₄₁	—	2	8	no	—
105	C₂×D₄×C₄₁	—	2	32	no	—
106	C₂×D₄×C₄₁	—	2	64	no	—
107	C₂×D₄×C₄₁	—	2	16	no	—
108	C₂×D₄×C₄₁	—	2	16	no	—
109	C₂×D₄×C₄₁	—	2	16	no	—
110	C₂×D₄×C₄₁	—	2	8	no	—
111	C₂×D₄×C₄₁	C₂×D₄	1	32	yes	—
112	C₂²×C₄×C₄₁	—	2	32	no	—
113	C₂²×C₄×C₄₁	—	2	64	no	—
114	C₂²×C₄×C₄₁	—	2	32	no	—
115	C₂²×C₄×C₄₁	—	2	8	no	—
116	C₂²×C₄×C₄₁	—	2	4	no	—
117	C₂²×C₄×C₄₁	—	2	4	no	—
118	C₂²×C₄×C₄₁	—	2	4	no	—
119	C₂²×C₄×C₄₁	—	2	4	no	—
120	C₂²×C₄×C₄₁	—	2	4	no	—
121	C₂²×C₄×C₄₁	—	2	16	no	—
122	C₂²×C₄×C₄₁	—	2	16	no	—
123	C₂²×C₄×C₄₁	—	2	4	no	—
124	C₂²×C₄×C₄₁	—	2	16	no	—
125	C₂²×C₄×C₄₁	—	2	16	no	—
126	C₂²×C₄×C₄₁	—	2	16	no	—
127	C₂²×C₄×C₄₁	—	2	8	no	—
128	C₂²×C₄×C₄₁	—	2	8	no	—
129	C₂²×C₄×C₄₁	—	2	8	no	—
130	C₂²×C₄×C₄₁	—	2	4	no	—
131	C₂²×C₄×C₄₁	—	2	16	no	—
132	C₂²×C₄×C₄₁	—	2	8	no	—
133	C₂²×C₄×C₄₁	—	2	8	no	—
134	C₂²×C₄×C₄₁	—	4	16	no	—
135	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
137	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₄₁	C₂×D₄	1	16	yes	—
139	C₂²×C₄×C₄₁	#41	1	8	yes	complemented
140	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
141	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
146	C₄⋊C₄×C₄₁	—	2	16	no	—
147	C₄⋊C₄×C₄₁	—	2	16	no	—
148	C₄⋊C₄×C₄₁	—	2	32	no	—
149	C₂²⋊C₄×C₄₁	—	2	16	no	—
150	C₂²⋊C₄×C₄₁	—	2	32	no	—
151	C₂²⋊C₄×C₄₁	—	2	32	no	—
152	C₂³×C₄₁	—	2	8	no	—
153	C₂³×C₄₁	—	2	8	no	—
154	C₂³×C₄₁	—	2	32	no	—
155	C₂³×C₄₁	—	2	4	no	—
156	C₂³×C₄₁	—	2	4	no	—
157	C₂³×C₄₁	—	2	16	no	—
158	C₂³×C₄₁	—	2	32	no	—
159	C₂³×C₄₁	—	2	4	no	—
160	C₂³×C₄₁	—	2	4	no	—
161	C₂³×C₄₁	—	2	8	no	—
162	C₂³×C₄₁	—	2	8	no	—
163	C₂³×C₄₁	—	4	8	no	—
164	C₂³×C₄₁	—	4	8	no	—
165	C₂³×C₄₁	—	4	16	no	—
166	C₂³×C₄₁	#120	1	16	yes	—
167	C₂³×C₄₁	C₂²×D₄	1	8	yes	—
168	C₂³×C₄₁	C₂²×D₄	1	8	yes	—
169	C₂³×C₄₁	C₂²×D₄	1	4	yes	—
170	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
171	C₂³×C₄₁	C₂²×D₄	1	4	yes	—
172	C₂³×C₄₁	C₂×#41	1	4	yes	—
173	C₂³×C₄₁	2₋¹⁺⁴	1	4	yes	—
174	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
175	Q₈×C₄₁	—	2	32	no	—
176	D₄×C₄₁	—	2	32	no	—
177	D₄×C₄₁	—	2	64	no	—
178	C₂×C₄×C₄₁	—	2	32	no	—
179	C₂×C₄×C₄₁	—	2	64	no	—
180	C₂×C₄×C₄₁	—	2	8	no	—
181	C₂×C₄×C₄₁	—	2	16	no	—
182	C₂×C₄×C₄₁	—	2	8	no	—
183	C₂×C₄×C₄₁	—	2	32	no	—
184	C₂×C₄×C₄₁	—	2	16	no	—
185	C₂×C₄×C₄₁	—	2	4	no	—
186	C₂×C₄×C₄₁	—	2	4	no	—
187	C₂×C₄×C₄₁	—	2	4	no	—
188	C₂×C₄×C₄₁	—	2	4	no	—
189	C₂×C₄×C₄₁	—	2	4	no	—
190	C₂×C₄×C₄₁	—	2	4	no	—
191	C₂×C₄×C₄₁	—	2	8	no	—
192	C₂×C₄×C₄₁	—	2	8	no	—
193	C₂×C₄×C₄₁	—	2	4	no	—
194	C₂×C₄×C₄₁	—	2	8	no	—
195	C₂×C₄×C₄₁	—	2	8	no	—
196	C₂×C₄×C₄₁	—	4	16	no	—
197	C₂×C₄×C₄₁	—	4	8	no	—
198	C₂×C₄×C₄₁	—	4	16	no	—
199	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
200	C₂×C₄×C₄₁	C₂²×D₄	1	8	yes	—
201	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
202	C₂×C₄×C₄₁	C₂×#41	1	8	yes	complemented
203	C₂×#2406	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂²×C₄₁	—	2	32	no	—
205	C₂²×C₄₁	—	2	4	no	—
206	C₂²×C₄₁	—	2	4	no	—
207	C₂²×C₄₁	—	2	16	no	—
208	C₂²×C₄₁	—	2	8	no	—
209	C₂²×C₄₁	—	2	16	no	—
210	C₂²×C₄₁	—	4	32	no	—
211	C₂²×C₄₁	—	4	4	no	—
212	C₂²×C₄₁	—	4	4	no	—
213	C₂²×C₄₁	—	4	8	no	—
214	C₂²×C₄₁	C₂×#120	1	8	yes	—
215	C₂²×C₄₁	C₂×#120	1	4	yes	—
216	C₂²×C₄₁	#525	1	4	yes	—
217	C₂²×C₄₁	#536	1	4	yes	—
218	C₂²×C₄₁	#547	1	16	yes	—
219	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
220	C₂²×C₄₁	C₂³×D₄	1	2	yes	—
221	C₂²×C₄₁	C₂²×#41	1	2	yes	—
222	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	2	yes	—
223	C₄×C₄₁	—	2	4	no	—
224	C₄×C₄₁	—	2	8	no	—
225	C₄×C₄₁	—	2	4	no	—
226	C₄×C₄₁	—	2	8	no	—
227	C₄×C₄₁	—	4	4	no	—
228	C₄×C₄₁	—	4	8	no	—
229	C₂³×#41	C₂×C₄₁	1	1	yes	characteristic
230	C₂²×#123	C₂×C₄₁	1	2	yes	complemented
231	C₂³×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
232	#2406	C₂×C₄₁	1	16	yes	direct product factor
233	C₂×#395	C₂×C₄₁	1	2	yes	complemented
234	C₂×#394	C₂×C₄₁	1	2	yes	complemented
235	C₂×#386	C₂×C₄₁	1	2	yes	complemented
236	C₂×#385	C₂×C₄₁	1	4	yes	complemented
237	C₂×#381	C₂×C₄₁	1	1	yes	characteristic, complemented
238	C₂×C₄₁	—	2	8	no	—
239	C₂×C₄₁	—	4	8	no	—
240	C₂×C₄₁	#2406	1	8	yes	direct product factor
241	C₂×C₄₁	C₂²×#120	1	1	yes	characteristic
242	C₂×C₄₁	C₂×#525	1	1	yes	characteristic
243	C₂×C₄₁	C₂×#536	1	1	yes	characteristic
244	C₂×C₄₁	C₂×#547	1	4	yes	—
245	C₂²×#41	—	2	16	no	—
246	C₂²×#41	—	2	8	no	—
247	C₂²×#41	C₂²×C₄₁	1	8	yes	—
248	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
249	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
250	C₂³×D₄	C₂²×C₄₁	1	2	yes	—
251	C₂⁴×C₄	C₂²×C₄₁	1	2	yes	—
252	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
253	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
254	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
255	C₂×#123	—	2	16	no	—
256	C₂×#123	C₂²×C₄₁	1	16	yes	complemented
257	C₂²×C₄⋊C₄	—	2	8	no	—
258	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
259	C₂²×C₄⋊C₄	C₂²×C₄₁	1	4	yes	—
260	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
261	C₂²×C₄⋊C₄	C₂²×C₄₁	1	8	yes	complemented
262	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
263	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
264	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
265	#395	C₂²×C₄₁	1	16	yes	complemented
266	#394	C₂²×C₄₁	1	16	yes	complemented
267	#386	C₂²×C₄₁	1	16	yes	complemented
268	#385	C₂²×C₄₁	1	32	yes	complemented
269	#381	C₂²×C₄₁	1	8	yes	complemented
270	C₂×#95	C₂²×C₄₁	1	2	yes	—
271	C₂×#95	C₂²×C₄₁	1	4	yes	—
272	C₂×#95	C₂²×C₄₁	1	2	yes	—
273	C₄₁	C₂×#2406	1	1	yes	characteristic, direct product factor, Sylow
274	C₂⁵	C₂³×C₄₁	1	2	yes	—
275	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
276	C₂×#41	—	2	128	no	—
277	C₂×#41	—	2	64	no	—
278	C₂×#41	—	2	32	no	—
279	C₂²×Q₈	—	2	8	no	—
280	C₂²×Q₈	—	2	4	no	—
281	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
282	C₂²×D₄	—	2	8	no	—
283	C₂²×D₄	—	2	8	no	—
284	C₂²×D₄	—	2	8	no	—
285	C₂²×D₄	—	2	4	no	—
286	C₂²×D₄	D₄×C₄₁	1	16	yes	—
287	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
288	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
289	C₂³×C₄	—	2	4	no	—
290	C₂³×C₄	—	2	8	no	—
291	C₂³×C₄	—	2	8	no	—
292	C₂³×C₄	—	2	8	no	—
293	C₂³×C₄	—	2	8	no	—
294	C₂³×C₄	—	2	8	no	—
295	C₂³×C₄	—	2	4	no	—
296	C₂³×C₄	—	2	8	no	—
297	C₂³×C₄	D₄×C₄₁	1	8	yes	—
298	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
299	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
300	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
301	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
302	C₂³×C₄	C₂³×C₄₁	1	8	yes	—
303	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
305	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
307	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
308	#123	—	2	64	no	—
309	C₂×C₄⋊C₄	—	2	8	no	—
310	C₂×C₄⋊C₄	—	2	8	no	—
311	C₂×C₄⋊C₄	—	2	32	no	—
312	C₂×C₄⋊C₄	—	2	16	no	—
313	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
314	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
315	C₂×C₄⋊C₄	C₂³×C₄₁	1	16	yes	—
316	C₂×C₂²⋊C₄	—	2	8	no	—
317	C₂×C₂²⋊C₄	—	2	16	no	—
318	C₂×C₂²⋊C₄	—	2	16	no	—
319	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₄₁	1	16	yes	—
321	C₂×C₂²⋊C₄	C₂³×C₄₁	1	16	yes	—
322	#95	C₂³×C₄₁	1	8	yes	—
323	#95	C₂³×C₄₁	1	8	yes	—
324	#95	C₂³×C₄₁	1	16	yes	—
325	C₂⁴	—	2	4	no	—
326	C₂⁴	—	2	4	no	—
327	C₂⁴	—	2	4	no	—
328	C₂⁴	—	2	4	no	—
329	C₂⁴	—	2	8	no	—
330	C₂⁴	—	2	8	no	—
331	C₂⁴	C₂×D₄×C₄₁	1	8	yes	—
332	C₂⁴	C₂×D₄×C₄₁	1	8	yes	—
333	C₂⁴	C₂×D₄×C₄₁	1	4	yes	—
334	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
335	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
336	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
337	#41	—	2	256	no	—
338	C₂×Q₈	—	2	32	no	—
339	C₂×Q₈	—	2	16	no	—
340	C₂×Q₈	—	2	8	no	—
341	C₂×D₄	—	2	32	no	—
342	C₂×D₄	—	2	64	no	—
343	C₂×D₄	—	2	16	no	—
344	C₂×D₄	—	2	16	no	—
345	C₂×D₄	—	2	16	no	—
346	C₂×D₄	—	2	8	no	—
347	C₂×D₄	C₂×D₄×C₄₁	1	32	yes	—
348	C₂²×C₄	—	2	64	no	—
349	C₂²×C₄	—	2	32	no	—
350	C₂²×C₄	—	2	32	no	—
351	C₂²×C₄	—	2	8	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	16	no	—
358	C₂²×C₄	—	2	16	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	16	no	—
361	C₂²×C₄	—	2	16	no	—
362	C₂²×C₄	—	2	16	no	—
363	C₂²×C₄	—	2	8	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	2	8	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	16	no	—
368	C₂²×C₄	—	2	8	no	—
369	C₂²×C₄	—	2	8	no	—
370	C₂²×C₄	—	4	16	no	—
371	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
372	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
373	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
374	C₂²×C₄	C₂×D₄×C₄₁	1	16	yes	—
375	C₂²×C₄	#41×C₄₁	1	8	yes	complemented
376	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
377	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
378	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
379	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
380	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
382	C₄⋊C₄	—	2	16	no	—
383	C₄⋊C₄	—	2	16	no	—
384	C₄⋊C₄	—	2	32	no	—
385	C₂²⋊C₄	—	2	16	no	—
386	C₂²⋊C₄	—	2	32	no	—
387	C₂²⋊C₄	—	2	32	no	—
388	C₂³	—	2	8	no	—
389	C₂³	—	2	8	no	—
390	C₂³	—	2	32	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	16	no	—
394	C₂³	—	2	32	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	8	no	—
398	C₂³	—	2	8	no	—
399	C₂³	—	4	8	no	—
400	C₂³	—	4	8	no	—
401	C₂³	—	4	16	no	—
402	C₂³	#120×C₄₁	1	16	yes	—
403	C₂³	C₂²×D₄×C₄₁	1	8	yes	—
404	C₂³	C₂²×D₄×C₄₁	1	8	yes	—
405	C₂³	C₂²×D₄×C₄₁	1	4	yes	—
406	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
407	C₂³	C₂²×D₄×C₄₁	1	4	yes	—
408	C₂³	C₂×#41×C₄₁	1	4	yes	—
409	C₂³	2₋¹⁺⁴×C₄₁	1	4	yes	—
410	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
411	Q₈	—	2	32	no	—
412	D₄	—	2	32	no	—
413	D₄	—	2	64	no	—
414	C₂×C₄	—	2	64	no	—
415	C₂×C₄	—	2	32	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	16	no	—
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	2	32	no	—
420	C₂×C₄	—	2	16	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	4	16	no	—
433	C₂×C₄	—	4	8	no	—
434	C₂×C₄	—	4	16	no	—
435	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
436	C₂×C₄	C₂²×D₄×C₄₁	1	8	yes	—
437	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
438	C₂×C₄	C₂×#41×C₄₁	1	8	yes	complemented
439	C₂²	—	2	32	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	16	no	—
443	C₂²	—	2	8	no	—
444	C₂²	—	2	16	no	—
445	C₂²	—	4	32	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	8	no	—
449	C₂²	C₂×#120×C₄₁	1	8	yes	—
450	C₂²	C₂×#120×C₄₁	1	4	yes	—
451	C₂²	C₄₁×#525	1	4	yes	—
452	C₂²	C₄₁×#536	1	4	yes	—
453	C₂²	C₄₁×#547	1	16	yes	—
454	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
455	C₂²	C₂³×D₄×C₄₁	1	2	yes	—
456	C₂²	C₂²×#41×C₄₁	1	2	yes	—
457	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	2	yes	—
458	C₄	—	2	4	no	—
459	C₄	—	2	8	no	—
460	C₄	—	2	4	no	—
461	C₄	—	2	8	no	—
462	C₄	—	4	4	no	—
463	C₄	—	4	8	no	—
464	C₂	—	2	8	no	—
465	C₂	—	4	8	no	—
466	C₂	C₄₁×#2406	1	8	yes	direct product factor
467	C₂	C₂²×#120×C₄₁	1	1	yes	characteristic
468	C₂	C₂×C₄₁×#525	1	1	yes	characteristic
469	C₂	C₂×C₄₁×#536	1	1	yes	characteristic
470	C₂	C₂×C₄₁×#547	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂³×#41×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. C₂²×#123×C₄₁	C₂	semidirect
3. C₂³×C₄⋊C₄×C₄₁	C₂	semidirect
4. C₄₁×#2406	C₂	direct (N × H)
5. C₂×C₄₁×#395	C₂	semidirect
6. C₂×C₄₁×#394	C₂	semidirect
7. C₂×C₄₁×#386	C₂	semidirect
8. C₂×C₄₁×#385	C₂	semidirect
9. C₂×C₄₁×#381	C₂	semidirect
21. C₂×#123×C₄₁	C₂²	semidirect
26. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
30. C₄₁×#395	C₂²	semidirect
31. C₄₁×#394	C₂²	semidirect
32. C₄₁×#386	C₂²	semidirect
33. C₄₁×#385	C₂²	semidirect
34. C₄₁×#381	C₂²	semidirect
139. C₂²×C₄×C₄₁	#41	semidirect
202. C₂×C₄×C₄₁	C₂×#41	semidirect
203. C₂×#2406	C₄₁	direct (N × H)
230. C₂²×#123	C₂×C₄₁	semidirect
231. C₂³×C₄⋊C₄	C₂×C₄₁	semidirect
232. #2406	C₂×C₄₁	direct (N × H)
233. C₂×#395	C₂×C₄₁	semidirect
234. C₂×#394	C₂×C₄₁	semidirect
235. C₂×#386	C₂×C₄₁	semidirect
236. C₂×#385	C₂×C₄₁	semidirect
237. C₂×#381	C₂×C₄₁	semidirect
240. C₂×C₄₁	#2406	direct (N × H)
256. C₂×#123	C₂²×C₄₁	semidirect
261. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
265. #395	C₂²×C₄₁	semidirect
266. #394	C₂²×C₄₁	semidirect
267. #386	C₂²×C₄₁	semidirect
268. #385	C₂²×C₄₁	semidirect
269. #381	C₂²×C₄₁	semidirect
273. C₄₁	C₂×#2406	direct (N × H)
375. C₂²×C₄	#41×C₄₁	semidirect
438. C₂×C₄	C₂×#41×C₄₁	semidirect
466. C₂	C₄₁×#2406	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₄₁	2
C₂²×#123×C₄₁	2
C₂³×C₄⋊C₄×C₄₁	2
C₄₁×#2406	2
C₂×C₄₁×#395	2
C₂×C₄₁×#394	2
C₂×C₄₁×#386	2
C₂×C₄₁×#385	2
C₂×C₄₁×#381	2
C₂×#2406	41

Subgroups — C2×C41×#2406 #23810934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2406 #23810934