Subgroups — C₂×C₈×#261 #11719087

Order 832.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#261	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₈×#261	C₂	1	4	yes	maximal, direct product factor
5	C₂²×#261	C₄	1	2	yes	—
6	C₂×C₄×D₁₃	C₂²	1	1	yes	characteristic
7	C₂×#1057	C₄	1	2	yes	complemented
8	C₄×#261	C₄	1	2	yes	—
9	C₄×#261	C₂²	1	2	yes	—
10	D₁₃⋊C₈	C₄	1	2	yes	complemented
11	D₁₃⋊C₈	C₂²	1	2	yes	—
12	C₂×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
13	C₂×#1055	C₄	1	1	yes	characteristic, complemented
14	C₈×D₁₃	C₄	1	2	yes	complemented
15	C₈×D₁₃	C₂²	1	2	yes	—
16	C₂²×D₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×#261	C₈	1	8	yes	direct product factor
18	C₂×#261	C₂×C₄	1	4	yes	—
19	C₂×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₃	C₂×C₄	1	1	yes	characteristic
21	C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
22	C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
24	C₄×D₁₃	C₂³	1	1	yes	characteristic
25	#1057	C₂×C₄	1	4	yes	complemented
26	C₈×C₁₃	C₂×C₄	1	2	yes	complemented
27	#1055	C₂×C₄	1	2	yes	complemented
28	C₂×C₄×C₈	—	13	1	no	maximal, Sylow
29	C₂²×C₁₃	C₄²	1	1	yes	characteristic
30	C₂×D₁₃	C₄²	1	1	yes	characteristic
31	C₂×D₁₃	C₂×C₈	1	4	yes	—
32	C₂×D₁₃	C₂²×C₄	1	1	yes	characteristic
33	#261	C₂×C₈	1	8	yes	direct product factor
34	C₄×C₁₃	C₄²	1	1	yes	characteristic
35	C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	Dic₁₃	C₄²	1	1	yes	characteristic
37	Dic₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₂²×C₈	—	13	1	no	—
39	C₂²×C₈	—	13	1	no	—
40	C₂×C₄²	—	13	1	no	—
41	C₄×C₈	—	13	4	no	—
42	C₂×C₁₃	C₄×C₈	1	2	yes	complemented
43	C₂×C₁₃	C₂×C₄²	1	1	yes	characteristic
44	D₁₃	C₄×C₈	1	2	yes	complemented
45	D₁₃	C₂²×C₈	1	2	yes	—
46	C₂²×C₄	—	13	2	no	—
47	C₂²×C₄	—	13	1	no	—
48	C₂×C₈	—	13	2	no	—
49	C₂×C₈	—	13	2	no	—
50	C₂×C₈	—	13	2	no	—
51	C₂×C₈	—	13	1	no	—
52	C₂×C₈	—	13	2	no	—
53	C₂×C₈	—	13	2	no	—
54	C₂×C₈	#261	1	1	yes	characteristic, direct product factor
55	C₄²	—	13	2	no	—
56	C₄²	—	13	2	no	—
57	C₁₃	C₂×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
58	C₂³	—	13	1	no	—
59	C₂×C₄	—	13	4	no	—
60	C₂×C₄	—	13	8	no	—
61	C₂×C₄	—	13	1	no	—
62	C₂×C₄	—	13	1	no	—
63	C₂×C₄	—	13	1	no	—
64	C₂×C₄	—	13	1	no	—
65	C₂×C₄	—	13	1	no	—
66	C₂×C₄	C₂×#261	1	1	yes	characteristic
67	C₈	—	13	4	no	—
68	C₈	—	13	2	no	—
69	C₈	C₂×#261	1	2	yes	direct product factor
70	C₂²	—	13	4	no	—
71	C₂²	—	13	1	no	—
72	C₂²	—	13	1	no	—
73	C₂²	C₄×#261	1	1	yes	characteristic
74	C₄	—	13	8	no	—
75	C₄	—	13	1	no	—
76	C₄	—	13	1	no	—
77	C₄	C₄×#261	1	1	yes	characteristic
78	C₄	C₂²×#261	1	1	yes	characteristic
79	C₂	—	13	2	no	—
80	C₂	—	13	2	no	—
81	C₂	C₈×#261	1	2	yes	direct product factor
82	C₂	C₂×C₄×#261	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈	#261
commutator, hypocenter	C₁₃	C₂×C₄×C₈
Frattini	C₄	C₂²×#261
Fitting	C₂×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₄²
prime radical	C₂²×D₁₃	C₂×C₄
cosocle	C₄×D₁₃	C₂³
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
4. C₈×#261	C₂	direct (N × H)
7. C₂×#1057	C₄	semidirect
10. D₁₃⋊C₈	C₄	semidirect
12. C₂×C₈×C₁₃	C₄	semidirect
13. C₂×#1055	C₄	semidirect
14. C₈×D₁₃	C₄	semidirect
17. C₂×#261	C₈	direct (N × H)
25. #1057	C₂×C₄	semidirect
26. C₈×C₁₃	C₂×C₄	semidirect
27. #1055	C₂×C₄	semidirect
33. #261	C₂×C₈	direct (N × H)
42. C₂×C₁₃	C₄×C₈	semidirect
44. D₁₃	C₄×C₈	semidirect
54. C₂×C₈	#261	direct (N × H)
57. C₁₃	C₂×C₄×C₈	semidirect
69. C₈	C₂×#261	direct (N × H)
81. C₂	C₈×#261	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×C₄×#261	2
C₂×D₁₃⋊C₈	2
C₂×C₈×D₁₃	2
C₈×#261	2
C₂×C₄×C₈	13

Subgroups — C2×C8×#261 #11719087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×#261 #11719087