Subgroups — C₃⋊(D₃₁⋊(C₅²⋊C₃)) #28358498

Order 13950.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²⋊(C₃₁⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×D₉₃	C₃	1	1	yes	maximal, characteristic, complemented
3	D₃₁⋊(C₅²⋊C₃)	—	3	1	no	maximal
4	C₅²⋊(C₃₁⋊C₃)	—	2	1	no	—
5	C₅²⋊(C₃₁⋊C₃)	D₃	1	1	yes	characteristic, complemented
6	C₃×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅²×D₃₁	—	3	1	no	Hall
8	C₅×D₉₃	—	3	2	no	—
9	C₅²×C₃₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃⋊(D₃₁⋊C₃)	—	25	1	no	maximal, Hall
11	C₃×C₅×C₃₁	—	3	2	no	—
12	D₃×C₅²⋊C₃	—	31	1	no	maximal, Hall
13	C₅×D₃₁	—	9	2	no	—
14	C₃×C₃₁⋊C₃	—	25	1	no	Hall
15	C₃×C₅²⋊C₃	—	31	1	no	Hall
16	D₉₃	C₅²⋊C₃	1	1	yes	characteristic, complemented
17	D₃₁⋊C₃	—	75	1	no	—
18	C₅×C₃₁	—	3	2	no	—
19	C₅²×D₃	—	31	1	no	—
20	C₂×C₅²⋊C₃	—	93	1	no	—
21	C₃×C₃₁	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
22	C₃₁⋊C₃	—	25	1	no	—
23	C₃₁⋊C₃	—	50	1	no	—
24	C₃×C₅²	D₃₁⋊C₃	1	1	yes	characteristic, complemented
25	C₅²⋊C₃	—	31	1	no	—
26	C₅²⋊C₃	—	62	1	no	—
27	D₃₁	—	3	1	no	Hall
28	C₂×C₅²	—	93	1	no	Hall
29	C₃₁	D₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₅×D₃	—	93	2	no	—
31	C₅²	C₃⋊(D₃₁⋊C₃)	1	1	yes	characteristic, complemented, Sylow
32	C₃×D₃	—	775	1	no	Hall
33	C₃×C₅	—	3	2	no	—
34	C₂×C₅	—	279	2	no	—
35	C₃²	—	775	1	no	Sylow
36	C₂×C₃	—	2325	1	no	—
37	D₃	—	31	1	no	—
38	C₅	—	3	2	no	—
39	C₃	—	775	1	no	—
40	C₃	—	1550	1	no	—
41	C₃	D₃₁⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented
42	C₂	—	93	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²⋊(C₃₁⋊C₃)	C₂	semidirect
2. C₅²×D₉₃	C₃	semidirect
5. C₅²⋊(C₃₁⋊C₃)	D₃	semidirect
6. C₃×C₅²×C₃₁	C₂×C₃	semidirect
9. C₅²×C₃₁	C₃×D₃	semidirect
16. D₉₃	C₅²⋊C₃	semidirect
21. C₃×C₃₁	C₂×C₅²⋊C₃	semidirect
24. C₃×C₅²	D₃₁⋊C₃	semidirect
29. C₃₁	D₃×C₅²⋊C₃	semidirect
31. C₅²	C₃⋊(D₃₁⋊C₃)	semidirect
41. C₃	D₃₁⋊(C₅²⋊C₃)	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅²⋊(C₃₁⋊C₃)	2
C₅²×D₉₃	3
D₃₁⋊(C₅²⋊C₃)	3
C₃⋊(D₃₁⋊C₃)	25
D₃×C₅²⋊C₃	31

Subgroups — C3⋊(D31⋊(C52⋊C3)) #28358498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(D₃₁⋊(C₅²⋊C₃)) #28358498