Subgroups — C₃₁×C₃⋊#3874 #28358491

Order 13950.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₅×C₃₁	—	3	1	no	maximal
3	C₃₁×#3874	—	3	3	no	maximal
4	C₃₁×C₅²⋊C₃	D₃	1	3	yes	complemented
5	C₃×C₅²×C₃₁	D₃	1	1	yes	characteristic, complemented
6	C₅×D₅×C₃₁	—	9	1	no	Hall
7	D₁₅×C₃₁	—	3	1	no	—
8	C₅×D₃×C₃₁	—	15	1	no	—
9	C₅²×C₃₁	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
10	C₃⋊D₃×C₃₁	—	25	1	no	maximal, Hall
11	C₃×C₅×C₃₁	—	3	1	no	—
12	C₃×C₅×C₃₁	—	3	1	no	—
13	C₃⋊#3874	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₅×C₃₁	—	45	1	no	—
15	D₅×C₃₁	—	9	1	no	—
16	C₃²×C₃₁	—	25	1	no	Hall
17	C₃×C₅²⋊C₃	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
18	D₃×C₃₁	—	15	1	no	—
19	D₃×C₃₁	—	75	3	no	—
20	C₅×C₃₁	—	3	1	no	—
21	C₅×C₃₁	—	3	1	no	—
22	C₅×D₁₅	—	3	1	no	—
23	#3874	—	3	3	no	—
24	C₃×C₃₁	—	25	3	no	—
25	C₃×C₃₁	#3874	1	1	yes	characteristic, complemented
26	C₃×C₅²	D₃×C₃₁	1	1	yes	characteristic, complemented
27	C₅²⋊C₃	D₃×C₃₁	1	3	yes	complemented
28	C₂×C₃₁	—	45	1	no	Hall
29	C₅×D₅	—	9	1	no	Hall
30	C₃₁	C₃⋊#3874	1	1	yes	characteristic, direct product factor, Sylow
31	D₁₅	—	3	1	no	—
32	C₅×D₃	—	15	1	no	—
33	C₅²	C₃⋊D₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
34	C₃⋊D₃	—	25	1	no	Hall
35	C₃×C₅	—	3	1	no	—
36	C₃×C₅	—	3	1	no	—
37	C₂×C₅	—	45	1	no	—
38	D₅	—	9	1	no	—
39	C₃²	—	25	1	no	Sylow
40	D₃	—	15	1	no	—
41	D₃	—	75	3	no	—
42	C₅	—	3	1	no	—
43	C₅	—	3	1	no	—
44	C₃	—	25	3	no	—
45	C₃	C₃₁×#3874	1	1	yes	characteristic, complemented
46	C₂	—	45	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁	C₃⋊#3874
commutator, cosocle, hypocenter	C₃×C₅²⋊C₃	C₂×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₁	D₃
LCS	G ▷ C₃×C₅²⋊C₃
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₁×C₅²⋊C₃	C₂	semidirect
4. C₃₁×C₅²⋊C₃	D₃	semidirect
5. C₃×C₅²×C₃₁	D₃	semidirect
9. C₅²×C₃₁	C₃⋊D₃	semidirect
13. C₃⋊#3874	C₃₁	direct (N × H)
17. C₃×C₅²⋊C₃	C₂×C₃₁	semidirect
25. C₃×C₃₁	#3874	semidirect
26. C₃×C₅²	D₃×C₃₁	semidirect
27. C₅²⋊C₃	D₃×C₃₁	semidirect
30. C₃₁	C₃⋊#3874	direct (N × H)
33. C₅²	C₃⋊D₃×C₃₁	semidirect
45. C₃	C₃₁×#3874	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃₁×C₅²⋊C₃	2
C₅×D₁₅×C₃₁	3
C₃₁×#3874	3
C₃⋊D₃×C₃₁	25
C₃⋊#3874	31

Subgroups — C31×C3⋊#3874 #28358491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×C₃⋊#3874 #28358491