Subgroups — C₃₁×#11759817 #44537664

Order 31434.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#92788	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₁₃×C₃₁	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	C₂×C₃₁×C₁₃⋊C₃	—	13	1	no	maximal
6	C₃₁×C₁₃⋊C₃	—	13	1	no	—
7	C₃₁×C₁₃⋊C₃	—	13	1	no	—
8	C₃₁×C₁₃⋊C₃	—	26	6	no	—
9	#11759817	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₃×C₃₁	—	13	1	no	—
11	D₁₃×C₃₁	C₁₃⋊C₃	1	1	yes	characteristic, complemented
12	#92788	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
13	C₁₃×C₃₁	—	2	6	no	—
14	C₁₃×C₃₁	D₁₃⋊C₃	1	1	yes	characteristic, complemented
15	C₁₃×C₃₁	C₂×C₁₃⋊C₃	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	—	169	1	no	Hall
20	C₂×C₁₃⋊C₃	—	13	1	no	—
21	D₁₃⋊C₃	—	13	1	no	—
22	C₂×C₃₁	—	13	1	no	Hall
23	C₁₃⋊C₃	—	13	1	no	—
24	C₁₃⋊C₃	—	13	1	no	—
25	C₁₃⋊C₃	—	26	6	no	—
26	C₃₁	#11759817	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₁₃	—	13	1	no	—
28	D₁₃	C₃₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented
29	C₁₃	—	2	6	no	—
30	C₁₃	C₂×C₃₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented
31	C₁₃	C₃₁×D₁₃⋊C₃	1	1	yes	characteristic, complemented
32	C₂×C₃	—	169	1	no	Hall
33	C₃	—	169	1	no	Sylow
34	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁	#11759817
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. C₃₁×#92788	C₂	semidirect
2. C₁₃×D₁₃×C₃₁	C₃	semidirect
3. C₁₃²×C₃₁	C₂×C₃	semidirect
9. #11759817	C₃₁	direct (N × H)
11. D₁₃×C₃₁	C₁₃⋊C₃	semidirect
12. #92788	C₂×C₃₁	semidirect
14. C₁₃×C₃₁	D₁₃⋊C₃	semidirect
15. C₁₃×C₃₁	C₂×C₁₃⋊C₃	semidirect
16. C₁₃×D₁₃	C₃×C₃₁	semidirect
18. C₁₃²	C₂×C₃×C₃₁	semidirect
26. C₃₁	#11759817	direct (N × H)
28. D₁₃	C₃₁×C₁₃⋊C₃	semidirect
30. C₁₃	C₂×C₃₁×C₁₃⋊C₃	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
C₃₁×#92788	2
C₁₃×D₁₃×C₃₁	3
C₃₁×D₁₃⋊C₃	13
C₂×C₃₁×C₁₃⋊C₃	13
#11759817	31

Subgroups — C31×#11759817 #44537664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#11759817 #44537664