Subgroups — C₃×D₃₁×C₅²⋊C₃ #28358484

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	C₃×C₅²×D₃₁	C₃	1	1	yes	maximal, characteristic, complemented
3	D₃₁×C₅²⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃₁×C₅²⋊C₃	C₂×C₃	1	3	yes	complemented
5	C₃×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅²×D₃₁	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×D₃₁	—	3	2	no	—
8	C₅²×C₃₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃²×D₃₁	—	25	1	no	maximal, Hall
10	C₃×C₅×C₃₁	—	3	2	no	—
11	C₂×C₃×C₅²⋊C₃	—	31	1	no	maximal, Hall
12	C₅×D₃₁	—	3	2	no	—
13	C₃²×C₃₁	—	25	1	no	Hall
14	C₃×C₅²⋊C₃	D₃₁	1	1	yes	characteristic, direct product factor, Hall
15	C₃×D₃₁	—	25	3	no	—
16	C₃×D₃₁	C₅²⋊C₃	1	1	yes	characteristic, direct product factor
17	C₅×C₃₁	—	3	2	no	—
18	C₂×C₃×C₅²	—	31	1	no	—
19	C₂×C₅²⋊C₃	—	31	3	no	—
20	C₃×C₃₁	—	25	3	no	—
21	C₃×C₃₁	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
22	C₃×C₅²	C₃×D₃₁	1	1	yes	characteristic, complemented
23	C₅²⋊C₃	C₃×D₃₁	1	3	yes	direct product factor
24	D₃₁	C₃×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₅²	—	31	1	no	Hall
26	C₃₁	C₂×C₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃×C₅	—	93	2	no	—
28	C₅²	C₃²×D₃₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃²	—	775	1	no	Hall
30	C₃×C₅	—	3	2	no	—
31	C₂×C₅	—	93	2	no	—
32	C₃²	—	25	1	no	Sylow
33	C₂×C₃	—	775	3	no	—
34	C₂×C₃	—	31	1	no	—
35	C₅	—	3	2	no	—
36	C₃	—	25	3	no	—
37	C₃	D₃₁×C₅²⋊C₃	1	1	yes	characteristic, direct product factor
38	C₂	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₃₁×C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²×C₃₁	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₁	C₂×C₃
LCS	G ▷ C₅²×C₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₁×C₅²⋊C₃	C₂	semidirect
2. C₃×C₅²×D₃₁	C₃	semidirect
3. D₃₁×C₅²⋊C₃	C₃	direct (N × H)
4. C₃₁×C₅²⋊C₃	C₂×C₃	semidirect
5. C₃×C₅²×C₃₁	C₂×C₃	semidirect
6. C₅²×D₃₁	C₃²	semidirect
8. C₅²×C₃₁	C₂×C₃²	semidirect
14. C₃×C₅²⋊C₃	D₃₁	direct (N × H)
16. C₃×D₃₁	C₅²⋊C₃	direct (N × H)
21. C₃×C₃₁	C₂×C₅²⋊C₃	semidirect
22. C₃×C₅²	C₃×D₃₁	semidirect
23. C₅²⋊C₃	C₃×D₃₁	direct (N × H)
24. D₃₁	C₃×C₅²⋊C₃	direct (N × H)
26. C₃₁	C₂×C₃×C₅²⋊C₃	semidirect
28. C₅²	C₃²×D₃₁	semidirect
37. C₃	D₃₁×C₅²⋊C₃	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×C₅²×D₃₁	3
D₃₁×C₅²⋊C₃	3
C₃²×D₃₁	25
C₂×C₃×C₅²⋊C₃	31

Subgroups — C3×D31×C52⋊C3 #28358484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃₁×C₅²⋊C₃ #28358484