Subgroups — #11718849

Order 832.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#88200	C₂	1	2	yes	maximal
3	C₂×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
4	#88075	C₂	1	2	yes	maximal, complemented
5	#88058	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₁₃	C₂²	1	2	yes	—
7	C₂×C₄×D₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×Q₁₆	—	2	2	no	—
9	C₂×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	#6103	—	2	2	no	—
11	C₄⋊Dic₁₃	C₂²	1	2	yes	—
12	#6101	—	2	2	no	—
13	C₂×#1055	C₂²	1	1	yes	characteristic
14	C₈×D₁₃	—	2	2	no	—
15	C₂²×D₁₃	D₄	1	1	yes	characteristic
16	Q₈×C₁₃	—	2	2	no	—
17	Q₈×C₁₃	—	2	2	no	—
18	C₂×C₄×C₁₃	—	2	2	no	—
19	C₂×C₄×C₁₃	C₂³	1	1	yes	characteristic
20	C₂×Dic₁₃	—	2	2	no	—
21	C₂×Dic₁₃	D₄	1	1	yes	characteristic
22	C₄×D₁₃	—	2	1	no	—
23	C₄×D₁₃	—	2	1	no	—
24	C₈×C₁₃	D₄	1	2	yes	—
25	#1055	—	2	1	no	—
26	#467	—	13	1	no	maximal, Sylow
27	C₂²×C₁₃	C₂×D₄	1	1	yes	characteristic
28	C₂×D₁₃	—	2	1	no	—
29	C₂×D₁₃	—	2	1	no	—
30	C₂×D₁₃	Q₁₆	1	2	yes	complemented
31	C₄×C₁₃	—	4	2	no	—
32	C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₁₃	#41	1	1	yes	characteristic
34	Dic₁₃	—	2	1	no	—
35	Dic₁₃	—	4	2	no	—
36	C₂×Q₁₆	D₁₃	1	1	yes	characteristic, complemented
37	C₂²×C₈	—	13	1	no	—
38	C₂²⋊Q₈	—	13	2	no	—
39	#107	—	13	1	no	—
40	#103	—	13	2	no	—
41	C₂×C₁₃	#121	1	1	yes	characteristic
42	C₂×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
43	C₂×C₁₃	#135	1	1	yes	characteristic
44	D₁₃	—	2	2	no	—
45	C₂×Q₈	C₂×D₁₃	1	2	yes	—
46	C₂²×C₄	—	13	1	no	—
47	Q₁₆	—	2	2	no	—
48	C₂×C₈	—	13	1	no	—
49	C₂×C₈	—	26	2	no	—
50	C₂×C₈	C₂×D₁₃	1	1	yes	characteristic
51	C₄⋊C₄	—	13	2	no	—
52	C₄⋊C₄	—	26	2	no	—
53	C₂²⋊C₄	—	26	2	no	—
54	C₁₃	#467	1	1	yes	characteristic, complemented, Sylow
55	C₂³	—	13	1	no	—
56	Q₈	—	2	2	no	—
57	Q₈	—	2	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	13	1	no	—
60	C₂×C₄	—	26	1	no	—
61	C₂×C₄	—	26	1	no	—
62	C₂×C₄	—	26	2	no	—
63	C₂×C₄	C₂²×D₁₃	1	1	yes	characteristic
64	C₈	—	26	1	no	—
65	C₈	C₂²⋊D₁₃	1	2	yes	—
66	C₂²	—	13	2	no	—
67	C₂²	—	26	1	no	—
68	C₂²	—	26	1	no	—
69	C₂²	D₄×D₁₃	1	1	yes	characteristic
70	C₄	—	4	2	no	—
71	C₄	—	26	1	no	—
72	C₄	—	52	2	no	—
73	C₄	#6129	1	1	yes	characteristic
74	C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
75	C₂	—	26	2	no	—
76	C₂	Q₁₆×D₁₃	1	1	yes	characteristic
77	C₂	#88173	1	1	yes	characteristic
78	C₂	#88192	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₃
commutator, cosocle	C₂×C₄×C₁₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×Q₁₆	C₂
socle	C₂²×C₁₃	C₂×D₄
prime radical	C₂²×D₁₃	D₄
hypercenter	C₂×Q₁₆	D₁₃
hypocenter	C₁₃	#467
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×Q₁₆	C₂	semidirect
4. #88075	C₂	semidirect
5. #88058	C₂	semidirect
30. C₂×D₁₃	Q₁₆	semidirect
36. C₂×Q₁₆	D₁₃	semidirect
54. C₁₃	#467	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×Q₁₆	2
#88200	2
C₂×C₈×D₁₃	2
#88075	2
#88058	2
#467	13