Subgroups — C₃×C₃₁×#3874 #28358477

Order 13950.

52 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	C₃×C₅×D₅×C₃₁	—	3	1	no	maximal
3	C₃₁×#3874	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃₁×C₅²⋊C₃	—	2	1	no	—
5	C₃₁×C₅²⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×C₅²×C₃₁	D₃	1	1	yes	characteristic, complemented
7	C₅×D₅×C₃₁	—	3	1	no	Hall
8	C₂×C₃×C₅×C₃₁	—	15	1	no	—
9	C₃×D₅×C₃₁	—	3	1	no	—
10	C₅²×C₃₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	C₃×D₃×C₃₁	—	25	1	no	maximal, Hall
12	C₃×C₅×C₃₁	—	3	1	no	—
13	C₃×C₅×C₃₁	—	3	1	no	—
14	C₃×#3874	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₅×C₃₁	—	15	1	no	—
16	D₅×C₃₁	—	3	1	no	—
17	C₃²×C₃₁	—	25	1	no	Hall
18	C₃×C₅²⋊C₃	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₃₁	—	15	1	no	—
20	D₃×C₃₁	—	25	1	no	—
21	C₅×C₃₁	—	3	1	no	—
22	C₅×C₃₁	—	3	1	no	—
23	C₃×C₅×D₅	—	3	1	no	—
24	#3874	C₃×C₃₁	1	1	yes	characteristic, direct product factor
25	C₃×C₃₁	—	25	1	no	—
26	C₃×C₃₁	—	50	1	no	—
27	C₃×C₃₁	#3874	1	1	yes	characteristic, direct product factor
28	C₃×C₅²	D₃×C₃₁	1	1	yes	characteristic, complemented
29	C₅²⋊C₃	—	2	1	no	—
30	C₅²⋊C₃	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented
31	C₂×C₃₁	—	15	1	no	Hall
32	C₅×D₅	—	3	1	no	Hall
33	C₃₁	C₃×#3874	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₃×C₅	—	15	1	no	—
35	C₃×D₅	—	3	1	no	—
36	C₅²	C₃×D₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
37	C₃×D₃	—	25	1	no	Hall
38	C₃×C₅	—	3	1	no	—
39	C₃×C₅	—	3	1	no	—
40	C₂×C₅	—	15	1	no	—
41	D₅	—	3	1	no	—
42	C₃²	—	25	1	no	Sylow
43	C₂×C₃	—	15	1	no	—
44	D₃	—	25	1	no	—
45	C₅	—	3	1	no	—
46	C₅	—	3	1	no	—
47	C₃	—	25	1	no	—
48	C₃	—	50	1	no	—
49	C₃	C₃₁×#3874	1	1	yes	characteristic, direct product factor
50	C₂	—	15	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₁×C₅²⋊C₃	C₂	semidirect
3. C₃₁×#3874	C₃	direct (N × H)
5. C₃₁×C₅²⋊C₃	C₂×C₃	semidirect
6. C₃×C₅²×C₃₁	D₃	semidirect
10. C₅²×C₃₁	C₃×D₃	semidirect
14. C₃×#3874	C₃₁	direct (N × H)
18. C₃×C₅²⋊C₃	C₂×C₃₁	semidirect
24. #3874	C₃×C₃₁	direct (N × H)
27. C₃×C₃₁	#3874	direct (N × H)
28. C₃×C₅²	D₃×C₃₁	semidirect
30. C₅²⋊C₃	C₂×C₃×C₃₁	semidirect
33. C₃₁	C₃×#3874	direct (N × H)
36. C₅²	C₃×D₃×C₃₁	semidirect
49. C₃	C₃₁×#3874	direct (N × H)

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
C₃×C₅×D₅×C₃₁	3
C₃₁×#3874	3
C₃×D₃×C₃₁	25
C₃×#3874	31

Subgroups — C3×C31×#3874 #28358477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃₁×#3874 #28358477