Subgroups — C₁₃×#686 #11760134

Order 1040.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×C₁₃	—	2	1	no	—
5	C₂×D₅×C₁₃	—	2	1	no	—
6	C₄×C₅×C₁₃	C₂²	1	1	yes	characteristic
7	C₁₃×D₈	—	5	1	no	maximal, Hall
8	C₂×C₅×C₁₃	—	4	1	no	—
9	C₂×C₅×C₁₃	D₄	1	1	yes	characteristic
10	D₅×C₁₃	—	4	1	no	—
11	D₄×C₁₃	—	5	1	no	—
12	D₄×C₁₃	D₅	1	1	yes	characteristic, complemented
13	C₈×C₁₃	—	5	1	no	—
14	#686	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₅×C₁₃	D₈	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₁₃	—	2	1	no	—
17	C₂²×C₁₃	—	10	1	no	—
18	C₄×C₁₃	C₂×D₅	1	1	yes	characteristic
19	C₅×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
20	D₂₀	C₂×C₁₃	1	1	yes	characteristic, complemented
21	#168	C₂×C₁₃	1	1	yes	characteristic, complemented
22	C₂×C₁₃	—	4	1	no	—
23	C₂×C₁₃	—	20	1	no	—
24	C₂×C₁₃	C₂²⋊D₅	1	1	yes	characteristic
25	C₂²×C₅	—	2	1	no	—
26	C₂×D₅	—	2	1	no	—
27	C₄×C₅	C₂²×C₁₃	1	1	yes	characteristic
28	D₈	—	5	1	no	Sylow
29	C₁₃	#686	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₅	—	4	1	no	—
31	C₂×C₅	D₄×C₁₃	1	1	yes	characteristic
32	D₅	—	4	1	no	—
33	D₄	—	5	1	no	—
34	D₄	D₅×C₁₃	1	1	yes	characteristic, complemented
35	C₈	—	5	1	no	—
36	C₅	C₁₃×D₈	1	1	yes	characteristic, complemented, Sylow
37	C₂²	—	2	1	no	—
38	C₂²	—	10	1	no	—
39	C₄	C₂×D₅×C₁₃	1	1	yes	characteristic
40	C₂	—	4	1	no	—
41	C₂	—	20	1	no	—
42	C₂	C₁₃×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₃	C₂²⋊D₅
commutator, cosocle	C₄×C₅	C₂²×C₁₃
Frattini	C₄	C₂×D₅×C₁₃
Fitting	C₅×D₄×C₁₃	C₂
socle	C₂×C₅×C₁₃	D₄
hypercenter	D₄×C₁₃	D₅
hypocenter	C₅	C₁₃×D₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₃ ◁ C₄×C₁₃ ◁ D₄×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×D₄×C₁₃	C₂	semidirect
2. C₁₃×D₂₀	C₂	semidirect
3. C₁₃×#168	C₂	semidirect
12. D₄×C₁₃	D₅	semidirect
14. #686	C₁₃	direct (N × H)
15. C₅×C₁₃	D₈	semidirect
19. C₅×D₄	C₂×C₁₃	semidirect
20. D₂₀	C₂×C₁₃	semidirect
21. #168	C₂×C₁₃	semidirect
29. C₁₃	#686	direct (N × H)
34. D₄	D₅×C₁₃	semidirect
36. C₅	C₁₃×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₄×C₁₃	2
C₁₃×D₂₀	2
C₁₃×#168	2
C₁₃×D₈	5
#686	13

Subgroups — C13×#686 #11760134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#686 #11760134