Subgroups — C₁₃×(C₃₁⋊C₃)⋊D₁₃ #44537653

Order 31434.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₄₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	(C₃₁⋊C₃)⋊D₁₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor
5	C₁₃×D₃₁⋊C₃	—	13	1	no	maximal
6	C₁₃×C₃₁⋊C₃	—	2	6	no	—
7	C₁₃×C₃₁⋊C₃	D₁₃	1	1	yes	characteristic, complemented
8	C₁₃×C₃₁⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
9	C₃×C₁₃×D₁₃	—	31	1	no	maximal, Hall
10	D₄₀₃	C₃×C₁₃	1	1	yes	characteristic, complemented
11	C₁₃×D₃₁	—	13	1	no	—
12	C₃×C₁₃²	—	31	1	no	Hall
13	C₁₃×C₃₁	—	2	6	no	—
14	C₁₃×C₃₁	C₃×D₁₃	1	1	yes	characteristic, complemented
15	C₁₃×C₃₁	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
16	C₁₃×D₁₃	—	31	1	no	Hall
17	D₃₁⋊C₃	—	13	1	no	Hall
18	C₁₃²	D₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₃₁⋊C₃	C₁₃×D₁₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₁₃	—	403	1	no	—
21	C₃×D₁₃	—	31	1	no	—
22	D₃₁	—	13	1	no	Hall
23	C₃×C₁₃	—	31	1	no	—
24	C₃×C₁₃	—	31	1	no	—
25	C₃×C₁₃	—	62	6	no	—
26	C₃₁	C₃×C₁₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₃	—	403	1	no	—
28	D₁₃	—	31	1	no	—
29	C₁₃	—	2	6	no	—
30	C₁₃	C₁₃×D₃₁⋊C₃	1	1	yes	characteristic, complemented
31	C₁₃	(C₃₁⋊C₃)⋊D₁₃	1	1	yes	characteristic, direct product factor
32	C₂×C₃	—	403	1	no	Hall
33	C₃	—	31	1	no	Sylow
34	C₂	—	403	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	(C₃₁⋊C₃)⋊D₁₃
commutator, cosocle, hypocenter	C₁₃×C₃₁	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃²×C₃₁	C₂×C₃
LCS	G ▷ C₁₃×C₃₁
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃²×C₃₁⋊C₃	C₂	semidirect
2. C₁₃×D₄₀₃	C₃	semidirect
3. C₁₃²×C₃₁	C₂×C₃	semidirect
4. (C₃₁⋊C₃)⋊D₁₃	C₁₃	direct (N × H)
7. C₁₃×C₃₁⋊C₃	D₁₃	semidirect
8. C₁₃×C₃₁⋊C₃	C₂×C₁₃	semidirect
10. D₄₀₃	C₃×C₁₃	semidirect
14. C₁₃×C₃₁	C₃×D₁₃	semidirect
15. C₁₃×C₃₁	C₂×C₃×C₁₃	semidirect
18. C₁₃²	D₃₁⋊C₃	semidirect
19. C₃₁⋊C₃	C₁₃×D₁₃	semidirect
26. C₃₁	C₃×C₁₃×D₁₃	semidirect
30. C₁₃	C₁₃×D₃₁⋊C₃	semidirect
31. C₁₃	(C₃₁⋊C₃)⋊D₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃²×C₃₁⋊C₃	2
C₁₃×D₄₀₃	3
(C₃₁⋊C₃)⋊D₁₃	13
C₁₃×D₃₁⋊C₃	13
C₃×C₁₃×D₁₃	31

Subgroups — C13×(C31⋊C3)⋊D13 #44537653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×(C₃₁⋊C₃)⋊D₁₃ #44537653