Subgroups — C₃₁×(C₁₃⋊C₃)⋊D₁₃ #44537641

Order 31434.

48 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	C₃₁×C₁₃⋊D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃₁×D₁₃⋊C₃	—	13	1	no	maximal
5	C₃×D₁₃×C₃₁	—	13	1	no	maximal
6	C₃×C₁₃×C₃₁	—	13	1	no	—
7	C₃₁×C₁₃⋊C₃	D₁₃	1	1	yes	characteristic, complemented
8	(C₁₃⋊C₃)⋊D₁₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	D₁₃×C₃₁	—	13	1	no	—
10	D₁₃×C₃₁	—	13	1	no	—
11	D₁₃×C₃₁	—	39	4	no	—
12	C₁₃×C₁₃⋊C₃	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
13	C₁₃×C₃₁	—	3	4	no	—
14	C₁₃×C₃₁	D₁₃⋊C₃	1	1	yes	characteristic, complemented
15	C₁₃×C₃₁	C₃×D₁₃	1	1	yes	characteristic, complemented
16	C₁₃⋊D₁₃	C₃×C₃₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₃₁	—	169	1	no	Hall
18	C₁₃²	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
19	C₃×C₃₁	—	13	1	no	Hall
20	C₃×D₁₃	—	13	1	no	—
21	D₁₃⋊C₃	—	13	1	no	—
22	C₂×C₃₁	—	169	1	no	Hall
23	C₃×C₁₃	—	13	1	no	—
24	C₁₃⋊C₃	D₁₃×C₃₁	1	1	yes	characteristic, complemented
25	C₃₁	(C₁₃⋊C₃)⋊D₁₃	1	1	yes	characteristic, direct product factor, Sylow
26	D₁₃	—	13	1	no	—
27	D₁₃	—	13	1	no	—
28	D₁₃	—	39	4	no	—
29	C₁₃	—	3	4	no	—
30	C₁₃	C₃×D₁₃×C₃₁	1	1	yes	characteristic, complemented
31	C₁₃	C₃₁×D₁₃⋊C₃	1	1	yes	characteristic, complemented
32	C₂×C₃	—	169	1	no	Hall
33	C₃	—	13	1	no	Sylow
34	C₂	—	169	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃₁×C₁₃⋊C₃	C₂	semidirect
2. C₃₁×C₁₃⋊D₁₃	C₃	semidirect
3. C₁₃²×C₃₁	C₂×C₃	semidirect
7. C₃₁×C₁₃⋊C₃	D₁₃	semidirect
8. (C₁₃⋊C₃)⋊D₁₃	C₃₁	direct (N × H)
12. C₁₃×C₁₃⋊C₃	C₂×C₃₁	semidirect
14. C₁₃×C₃₁	D₁₃⋊C₃	semidirect
15. C₁₃×C₃₁	C₃×D₁₃	semidirect
16. C₁₃⋊D₁₃	C₃×C₃₁	semidirect
18. C₁₃²	C₂×C₃×C₃₁	semidirect
24. C₁₃⋊C₃	D₁₃×C₃₁	semidirect
25. C₃₁	(C₁₃⋊C₃)⋊D₁₃	direct (N × H)
30. C₁₃	C₃×D₁₃×C₃₁	semidirect
31. C₁₃	C₃₁×D₁₃⋊C₃	semidirect

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
C₃₁×C₁₃⋊D₁₃	3
C₃₁×D₁₃⋊C₃	13
C₃×D₁₃×C₃₁	13
(C₁₃⋊C₃)⋊D₁₃	31

Subgroups — C31×(C13⋊C3)⋊D13 #44537641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×(C₁₃⋊C₃)⋊D₁₃ #44537641