Subgroups — C₁₃×(C₁₃⋊C₃)⋊D₃₁ #44537640

Order 31434.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₁₃	(C₁₃⋊C₃)⋊D₃₁
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. C₁₃×C₃₁×C₁₃⋊C₃	C₂	semidirect
2. C₁₃×D₄₀₃	C₃	semidirect
3. C₁₃²×C₃₁	C₂×C₃	semidirect
4. (C₁₃⋊C₃)⋊D₃₁	C₁₃	direct (N × H)
7. C₃₁×C₁₃⋊C₃	C₂×C₁₃	semidirect
9. D₄₀₃	C₃×C₁₃	semidirect
11. C₁₃×C₁₃⋊C₃	D₃₁	semidirect
13. C₁₃×C₃₁	D₁₃⋊C₃	semidirect
14. C₁₃×C₃₁	C₂×C₃×C₁₃	semidirect
17. C₁₃²	C₃×D₃₁	semidirect
23. C₁₃⋊C₃	C₁₃×D₃₁	semidirect
24. C₃₁	C₁₃×D₁₃⋊C₃	semidirect
28. C₁₃	C₃×C₁₃×D₃₁	semidirect
29. C₁₃	(C₁₃⋊C₃)⋊D₃₁	direct (N × H)

Maximal subgroups

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

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

Subgroups — C13×(C13⋊C3)⋊D31 #44537640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×(C₁₃⋊C₃)⋊D₃₁ #44537640