Subgroups — C₅²×D₃×C₃₁⋊C₃ #28358486

Order 13950.

144 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×D₃×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅²×C₃₁⋊C₃	—	3	1	no	maximal
4	C₅×D₃×C₃₁⋊C₃	C₅	1	6	yes	maximal, direct product factor
5	C₅²×C₃₁⋊C₃	—	2	1	no	—
6	C₅²×C₃₁⋊C₃	D₃	1	1	yes	characteristic, direct product factor
7	C₃×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₅²×C₃₁	—	3	1	no	Hall
9	C₃×C₅×C₃₁⋊C₃	C₂×C₅	1	6	yes	complemented
10	C₅×D₃×C₃₁	C₃×C₅	1	6	yes	complemented
11	C₂×C₅×C₃₁⋊C₃	—	3	6	no	—
12	C₅²×C₃₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	D₃×C₃₁⋊C₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₅×C₃₁	C₂×C₃×C₅	1	6	yes	complemented
15	C₅×C₃₁⋊C₃	—	2	6	no	—
16	C₅×C₃₁⋊C₃	C₅×D₃	1	6	yes	direct product factor
17	C₃×C₅²×D₃	—	31	1	no	maximal, Hall
18	C₂×C₅×C₃₁	—	3	6	no	—
19	C₃×C₃₁⋊C₃	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₅²	—	31	1	no	Hall
21	D₃×C₃₁	C₃×C₅²	1	1	yes	characteristic, complemented
22	C₂×C₃₁⋊C₃	—	3	1	no	—
23	C₅×C₃₁	C₃×C₅×D₃	1	6	yes	complemented
24	C₂×C₃×C₅²	—	93	1	no	—
25	C₅²×D₃	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
26	C₃×C₃₁	C₂×C₃×C₅²	1	1	yes	characteristic, complemented
27	C₃₁⋊C₃	—	2	1	no	—
28	C₃₁⋊C₃	C₅²×D₃	1	1	yes	characteristic, direct product factor
29	C₃×C₅×D₃	—	31	6	no	—
30	C₃×C₅²	—	31	1	no	—
31	C₃×C₅²	—	62	1	no	—
32	C₃×C₅²	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented
33	C₂×C₃₁	—	3	1	no	Hall
34	C₂×C₅²	—	3	1	no	Hall
35	C₃²×C₅	—	31	6	no	—
36	C₃₁	C₃×C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃×C₅	—	93	6	no	—
38	C₅×D₃	C₅×C₃₁⋊C₃	1	6	yes	direct product factor
39	C₅²	D₃×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×D₃	—	31	1	no	Hall
41	C₃×C₅	—	31	6	no	—
42	C₃×C₅	—	62	6	no	—
43	C₃×C₅	C₂×C₅×C₃₁⋊C₃	1	6	yes	complemented
44	C₂×C₅	—	3	6	no	—
45	C₃²	—	31	1	no	Sylow
46	C₂×C₃	—	93	1	no	—
47	D₃	C₅²×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
48	C₅	C₅×D₃×C₃₁⋊C₃	1	6	yes	direct product factor
49	C₃	—	31	1	no	—
50	C₃	—	62	1	no	—
51	C₃	C₂×C₅²×C₃₁⋊C₃	1	1	yes	characteristic, complemented
52	C₂	—	3	1	no	Sylow

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

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×D₃×C₃₁	C₃	semidirect
4. C₅×D₃×C₃₁⋊C₃	C₅	direct (N × H)
6. C₅²×C₃₁⋊C₃	D₃	direct (N × H)
7. C₃×C₅²×C₃₁	C₂×C₃	semidirect
9. C₃×C₅×C₃₁⋊C₃	C₂×C₅	semidirect
10. C₅×D₃×C₃₁	C₃×C₅	semidirect
12. C₅²×C₃₁	C₃×D₃	semidirect
13. D₃×C₃₁⋊C₃	C₅²	direct (N × H)
14. C₃×C₅×C₃₁	C₂×C₃×C₅	semidirect
16. C₅×C₃₁⋊C₃	C₅×D₃	direct (N × H)
19. C₃×C₃₁⋊C₃	C₂×C₅²	semidirect
21. D₃×C₃₁	C₃×C₅²	semidirect
23. C₅×C₃₁	C₃×C₅×D₃	semidirect
25. C₅²×D₃	C₃₁⋊C₃	direct (N × H)
26. C₃×C₃₁	C₂×C₃×C₅²	semidirect
28. C₃₁⋊C₃	C₅²×D₃	direct (N × H)
32. C₃×C₅²	C₂×C₃₁⋊C₃	semidirect
36. C₃₁	C₃×C₅²×D₃	semidirect
38. C₅×D₃	C₅×C₃₁⋊C₃	direct (N × H)
39. C₅²	D₃×C₃₁⋊C₃	direct (N × H)
43. C₃×C₅	C₂×C₅×C₃₁⋊C₃	semidirect
47. D₃	C₅²×C₃₁⋊C₃	direct (N × H)
48. C₅	C₅×D₃×C₃₁⋊C₃	direct (N × H)
51. C₃	C₂×C₅²×C₃₁⋊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×D₃×C₃₁	3
C₂×C₅²×C₃₁⋊C₃	3
C₅×D₃×C₃₁⋊C₃	5
C₃×C₅²×D₃	31

Subgroups — C52×D3×C31⋊C3 #28358486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×D₃×C₃₁⋊C₃ #28358486