Subgroups — D₃×C₃₁×C₅⋊D₅ #22604917

Order 9300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×C₃⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₃×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃₁×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×C₅⋊D₅	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₅×C₃₁	—	5	6	no	maximal
7	C₂×C₅²×C₃₁	—	3	1	no	—
8	C₃₁×C₅⋊D₅	—	3	1	no	—
9	C₃₁×C₅⋊D₅	D₃	1	1	yes	characteristic, direct product factor
10	D₁₅×C₃₁	—	5	6	no	—
11	C₅×D₃×C₃₁	D₅	1	6	yes	complemented
12	C₃×D₅×C₃₁	—	5	6	no	—
13	C₅²×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×D₅×C₃₁	—	15	6	no	—
15	C₃×C₅×C₃₁	C₂×D₅	1	6	yes	complemented
16	C₂×D₃×C₃₁	—	25	1	no	Hall
17	C₂×C₅×C₃₁	—	3	6	no	—
18	D₅×C₃₁	—	5	6	no	—
19	D₅×C₃₁	—	15	6	no	—
20	D₃×C₅⋊D₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₃×C₃₁	—	25	1	no	—
22	D₃×C₃₁	—	25	1	no	—
23	D₃×C₃₁	C₅⋊D₅	1	1	yes	characteristic, direct product factor
24	C₅×C₃₁	D₃×D₅	1	6	yes	complemented
25	C₃⋊(C₅⋊D₅)	C₂×C₃₁	1	1	yes	characteristic, complemented
26	C₅²×D₃	C₂×C₃₁	1	1	yes	characteristic, complemented
27	C₃×C₅⋊D₅	C₂×C₃₁	1	1	yes	characteristic, complemented
28	C₂²×C₃₁	—	75	1	no	Hall
29	C₂×C₅⋊D₅	—	3	1	no	Hall
30	C₃×C₃₁	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅²	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃₁	—	3	1	no	—
33	C₂×C₃₁	—	25	1	no	—
34	C₂×C₃₁	—	75	1	no	—
35	D₃×D₅	—	5	6	no	—
36	C₂×C₅²	—	3	1	no	—
37	C₅⋊D₅	—	3	1	no	—
38	C₅⋊D₅	D₃×C₃₁	1	1	yes	characteristic, direct product factor
39	C₃₁	D₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
40	D₁₅	—	5	6	no	—
41	C₃×D₅	—	5	6	no	—
42	C₅×D₃	D₅×C₃₁	1	6	yes	complemented
43	C₅²	C₂×D₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₅	—	15	6	no	—
45	C₃×C₅	C₂×D₅×C₃₁	1	6	yes	complemented
46	C₂×D₃	—	25	1	no	Hall
47	C₂×C₅	—	3	6	no	—
48	D₅	—	5	6	no	—
49	D₅	—	15	6	no	—
50	C₂×C₃	—	25	1	no	—
51	D₃	—	25	1	no	—
52	D₃	C₃₁×C₅⋊D₅	1	1	yes	characteristic, direct product factor
53	C₅	D₃×D₅×C₃₁	1	6	yes	complemented
54	C₂²	—	75	1	no	Sylow
55	C₃	C₂×C₃₁×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	3	1	no	—
57	C₂	—	25	1	no	—
58	C₂	—	75	1	no	—

	subgroup	G/H
center, hypercenter	C₃₁	D₃×C₅⋊D₅
commutator, hypocenter	C₃×C₅²	C₂²×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₁	C₂²
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃₁×C₃⋊(C₅⋊D₅)	C₂	semidirect
2. C₅²×D₃×C₃₁	C₂	semidirect
3. C₃×C₃₁×C₅⋊D₅	C₂	semidirect
5. C₃×C₅²×C₃₁	C₂²	semidirect
9. C₃₁×C₅⋊D₅	D₃	direct (N × H)
11. C₅×D₃×C₃₁	D₅	semidirect
13. C₅²×C₃₁	C₂×D₃	semidirect
15. C₃×C₅×C₃₁	C₂×D₅	semidirect
20. D₃×C₅⋊D₅	C₃₁	direct (N × H)
23. D₃×C₃₁	C₅⋊D₅	direct (N × H)
24. C₅×C₃₁	D₃×D₅	semidirect
25. C₃⋊(C₅⋊D₅)	C₂×C₃₁	semidirect
26. C₅²×D₃	C₂×C₃₁	semidirect
27. C₃×C₅⋊D₅	C₂×C₃₁	semidirect
30. C₃×C₃₁	C₂×C₅⋊D₅	semidirect
31. C₃×C₅²	C₂²×C₃₁	semidirect
38. C₅⋊D₅	D₃×C₃₁	direct (N × H)
39. C₃₁	D₃×C₅⋊D₅	direct (N × H)
42. C₅×D₃	D₅×C₃₁	semidirect
43. C₅²	C₂×D₃×C₃₁	semidirect
45. C₃×C₅	C₂×D₅×C₃₁	semidirect
52. D₃	C₃₁×C₅⋊D₅	direct (N × H)
53. C₅	D₃×D₅×C₃₁	semidirect
55. C₃	C₂×C₃₁×C₅⋊D₅	semidirect

Subgroups — D3×C31×C5⋊D5 #22604917

Conjugacy classes of subgroups

Complements

Subgroups — D₃×C₃₁×C₅⋊D₅ #22604917