Subgroups — #11718539

Order 832.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#88144	C₂	1	2	yes	maximal
2	C₁₃×#107	C₂	1	1	yes	maximal, characteristic
3	#88058	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
5	#88048	C₂	1	2	yes	maximal
6	C₂×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
8	C₄⋊Dic₁₃	—	2	2	no	—
9	C₄⋊Dic₁₃	C₂²	1	2	yes	—
10	#6101	—	2	2	no	—
11	C₄×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂×#1055	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₁₃	—	2	2	no	—
14	C₂×C₄×C₁₃	C₂³	1	1	yes	characteristic
15	C₂×Dic₁₃	—	2	2	no	—
16	C₂×Dic₁₃	D₄	1	1	yes	characteristic
17	C₂×Dic₁₃	D₄	1	1	yes	characteristic
18	C₈×C₁₃	Q₈	1	2	yes	—
19	#1055	Q₈	1	2	yes	—
20	#499	—	13	1	no	maximal, Sylow
21	C₂²×C₁₃	C₂×D₄	1	1	yes	characteristic
22	C₄×C₁₃	—	4	2	no	—
23	C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
25	Dic₁₃	—	2	1	no	—
26	Dic₁₃	—	2	1	no	—
27	Dic₁₃	—	4	2	no	—
28	#125	—	13	2	no	—
29	#107	—	13	1	no	—
30	#107	D₁₃	1	1	yes	characteristic
31	#106	—	13	2	no	—
32	C₄×C₈	—	13	1	no	—
33	C₂×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
34	C₂×C₁₃	#135	1	1	yes	characteristic
35	C₂×C₁₃	#135	1	1	yes	characteristic
36	C₂×C₈	—	13	1	no	—
37	C₂×C₈	C₂×D₁₃	1	1	yes	characteristic
38	C₄⋊C₄	—	13	2	no	—
39	C₄⋊C₄	—	26	2	no	—
40	C₄⋊C₄	—	26	2	no	—
41	C₄⋊C₄	C₂×D₁₃	1	2	yes	—
42	C₄²	—	13	1	no	—
43	C₁₃	#499	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₄	—	2	2	no	—
45	C₂×C₄	—	13	1	no	—
46	C₂×C₄	—	13	1	no	—
47	C₂×C₄	—	26	2	no	—
48	C₂×C₄	C₂²×D₁₃	1	1	yes	characteristic
49	C₈	—	13	2	no	—
50	C₈	Dic₂₆	1	2	yes	—
51	C₂²	D₄×D₁₃	1	1	yes	characteristic
52	C₄	—	4	2	no	—
53	C₄	—	26	1	no	—
54	C₄	—	26	1	no	—
55	C₄	—	52	2	no	—
56	C₄	C₂×Dic₂₆	1	1	yes	characteristic
57	C₄	Q₈×D₁₃	1	1	yes	characteristic
58	C₂	#88142	1	1	yes	characteristic
59	C₂	#88166	1	1	yes	characteristic
60	C₂	#88173	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₃
commutator, cosocle	C₂×C₄×C₁₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₃
Fitting	C₁₃×#107	C₂
socle, prime radical	C₂²×C₁₃	C₂×D₄
hypercenter	#107	D₁₃
hypocenter	C₁₃	#499
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
43. C₁₃	#499	semidirect

Maximal subgroups

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

subgroup	index
#88144	2
C₁₃×#107	2
#88058	2
C₈×Dic₁₃	2
#88048	2
#499	13