Subgroups — C₅²×D₃×D₃₁ #22604902

Order 9300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₉₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₃×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅²×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅²×D₃₁	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅×D₃×D₃₁	C₅	1	6	yes	maximal, direct product factor
7	C₂×C₅²×C₃₁	—	3	1	no	—
8	C₅²×D₃₁	—	3	1	no	—
9	C₅²×D₃₁	D₃	1	1	yes	characteristic, direct product factor
10	C₅×D₉₃	C₂×C₅	1	6	yes	complemented
11	C₅×D₃×C₃₁	C₂×C₅	1	6	yes	complemented
12	C₃×C₅×D₃₁	C₂×C₅	1	6	yes	complemented
13	C₅²×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×D₃₁	—	3	6	no	—
15	C₃×C₅×C₃₁	C₂²×C₅	1	6	yes	complemented
16	D₃×D₃₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅×C₃₁	—	3	6	no	—
18	C₅×D₃₁	—	3	6	no	—
19	C₅×D₃₁	C₅×D₃	1	6	yes	direct product factor
20	C₂×C₅²×D₃	—	31	1	no	maximal, Hall
21	D₉₃	C₂×C₅²	1	1	yes	characteristic, complemented
22	C₃×D₃₁	C₂×C₅²	1	1	yes	characteristic, complemented
23	D₃×C₃₁	C₂×C₅²	1	1	yes	characteristic, complemented
24	C₅×C₃₁	C₂×C₅×D₃	1	6	yes	complemented
25	C₂×C₃×C₅²	—	31	1	no	—
26	C₅²×D₃	—	31	1	no	—
27	C₅²×D₃	D₃₁	1	1	yes	characteristic, direct product factor
28	C₂×D₃₁	—	3	1	no	Hall
29	C₂²×C₅²	—	93	1	no	Hall
30	C₃×C₃₁	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅²	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃₁	—	3	1	no	—
33	D₃₁	—	3	1	no	—
34	D₃₁	C₅²×D₃	1	1	yes	characteristic, direct product factor
35	C₂×C₅×D₃	—	31	6	no	—
36	C₂×C₅²	—	3	1	no	—
37	C₂×C₅²	—	31	1	no	—
38	C₂×C₅²	—	93	1	no	—
39	C₃₁	C₂×C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃×C₅	—	31	6	no	—
41	C₅×D₃	—	31	6	no	—
42	C₅×D₃	C₅×D₃₁	1	6	yes	direct product factor
43	C₅²	D₃×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²×C₅	—	93	6	no	—
45	C₃×C₅	C₂×C₅×D₃₁	1	6	yes	complemented
46	C₂×D₃	—	31	1	no	Hall
47	C₂×C₅	—	3	6	no	—
48	C₂×C₅	—	31	6	no	—
49	C₂×C₅	—	93	6	no	—
50	C₂×C₃	—	31	1	no	—
51	D₃	—	31	1	no	—
52	D₃	C₅²×D₃₁	1	1	yes	characteristic, direct product factor
53	C₅	C₅×D₃×D₃₁	1	6	yes	direct product factor
54	C₂²	—	93	1	no	Sylow
55	C₃	C₂×C₅²×D₃₁	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	3	1	no	—
57	C₂	—	31	1	no	—
58	C₂	—	93	1	no	—

	subgroup	G/H
center, hypercenter	C₅²	D₃×D₃₁
commutator, hypocenter	C₃×C₃₁	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₁	C₂²
LCS	G ▷ C₃×C₃₁
UCS	C₁ ◁ C₅²

Complements

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

N	H ≅ G/N	type
1. C₅²×D₉₃	C₂	semidirect
2. C₅²×D₃×C₃₁	C₂	semidirect
3. C₃×C₅²×D₃₁	C₂	semidirect
5. C₃×C₅²×C₃₁	C₂²	semidirect
6. C₅×D₃×D₃₁	C₅	direct (N × H)
9. C₅²×D₃₁	D₃	direct (N × H)
10. C₅×D₉₃	C₂×C₅	semidirect
11. C₅×D₃×C₃₁	C₂×C₅	semidirect
12. C₃×C₅×D₃₁	C₂×C₅	semidirect
13. C₅²×C₃₁	C₂×D₃	semidirect
15. C₃×C₅×C₃₁	C₂²×C₅	semidirect
16. D₃×D₃₁	C₅²	direct (N × H)
19. C₅×D₃₁	C₅×D₃	direct (N × H)
21. D₉₃	C₂×C₅²	semidirect
22. C₃×D₃₁	C₂×C₅²	semidirect
23. D₃×C₃₁	C₂×C₅²	semidirect
24. C₅×C₃₁	C₂×C₅×D₃	semidirect
27. C₅²×D₃	D₃₁	direct (N × H)
30. C₃×C₃₁	C₂²×C₅²	semidirect
31. C₃×C₅²	C₂×D₃₁	semidirect
34. D₃₁	C₅²×D₃	direct (N × H)
39. C₃₁	C₂×C₅²×D₃	semidirect
42. C₅×D₃	C₅×D₃₁	direct (N × H)
43. C₅²	D₃×D₃₁	direct (N × H)
45. C₃×C₅	C₂×C₅×D₃₁	semidirect
52. D₃	C₅²×D₃₁	direct (N × H)
53. C₅	C₅×D₃×D₃₁	direct (N × H)
55. C₃	C₂×C₅²×D₃₁	semidirect

Subgroups — C52×D3×D31 #22604902

Conjugacy classes of subgroups

Complements

Subgroups — C₅²×D₃×D₃₁ #22604902