Subgroups — D₃₁×C₃⋊(C₅⋊D₅) #22604916

Order 9300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₅⋊D₁₅₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×C₃⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅²×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅⋊D₅×D₃₁	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₅×D₃₁	—	5	6	no	maximal
7	C₅⋊D₁₅₅	—	3	1	no	—
8	C₃₁×C₅⋊D₅	—	3	1	no	—
9	C₅²×D₃₁	D₃	1	1	yes	characteristic, complemented
10	D₄₆₅	—	5	6	no	—
11	D₁₅×C₃₁	—	5	6	no	—
12	C₃×C₅×D₃₁	D₅	1	6	yes	complemented
13	C₅²×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	D₅×D₃₁	—	15	6	no	—
15	C₃×C₅×C₃₁	C₂×D₅	1	6	yes	complemented
16	D₃×D₃₁	—	25	1	no	Hall
17	D₁₅₅	—	15	6	no	—
18	C₅×D₃₁	D₁₅	1	6	yes	complemented
19	D₅×C₃₁	—	15	6	no	—
20	C₂×C₃⋊(C₅⋊D₅)	—	31	1	no	maximal, Hall
21	D₉₃	—	25	1	no	—
22	C₃×D₃₁	C₅⋊D₅	1	1	yes	characteristic, complemented
23	D₃×C₃₁	—	25	1	no	—
24	C₅×C₃₁	C₂×D₁₅	1	6	yes	complemented
25	C₂×C₃×C₅²	—	31	1	no	—
26	C₃⋊(C₅⋊D₅)	—	31	1	no	—
27	C₃⋊(C₅⋊D₅)	D₃₁	1	1	yes	characteristic, direct product factor
28	C₂×D₃₁	—	75	1	no	Hall
29	C₂×C₅⋊D₅	—	93	1	no	Hall
30	C₃×C₃₁	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅²	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃₁	—	75	1	no	—
33	D₃₁	—	75	1	no	—
34	D₃₁	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, direct product factor
35	C₂×D₁₅	—	155	6	no	—
36	C₂×C₅²	—	31	1	no	—
37	C₅⋊D₅	—	3	1	no	—
38	C₅⋊D₅	—	93	1	no	—
39	C₃₁	C₂×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃×C₅	—	31	6	no	—
41	D₁₅	—	5	6	no	—
42	D₁₅	—	155	6	no	—
43	C₅²	D₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₅	—	465	6	no	—
45	C₃×C₅	D₅×D₃₁	1	6	yes	complemented
46	C₂×D₃	—	775	1	no	Hall
47	C₂×C₅	—	31	6	no	—
48	D₅	—	15	6	no	—
49	D₅	—	465	6	no	—
50	C₂×C₃	—	31	1	no	—
51	D₃	—	775	1	no	—
52	D₃	—	25	1	no	—
53	C₅	D₁₅×D₃₁	1	6	yes	complemented
54	C₂²	—	2325	1	no	Sylow
55	C₃	C₅⋊D₅×D₃₁	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	2325	1	no	—
57	C₂	—	31	1	no	—
58	C₂	—	75	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₃₁	C₂²
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⋊(C₅⋊D₁₅₅)	C₂	semidirect
2. C₃₁×C₃⋊(C₅⋊D₅)	C₂	semidirect
3. C₃×C₅²×D₃₁	C₂	semidirect
5. C₃×C₅²×C₃₁	C₂²	semidirect
9. C₅²×D₃₁	D₃	semidirect
12. C₃×C₅×D₃₁	D₅	semidirect
13. C₅²×C₃₁	C₂×D₃	semidirect
15. C₃×C₅×C₃₁	C₂×D₅	semidirect
18. C₅×D₃₁	D₁₅	semidirect
22. C₃×D₃₁	C₅⋊D₅	semidirect
24. C₅×C₃₁	C₂×D₁₅	semidirect
27. C₃⋊(C₅⋊D₅)	D₃₁	direct (N × H)
30. C₃×C₃₁	C₂×C₅⋊D₅	semidirect
31. C₃×C₅²	C₂×D₃₁	semidirect
34. D₃₁	C₃⋊(C₅⋊D₅)	direct (N × H)
39. C₃₁	C₂×C₃⋊(C₅⋊D₅)	semidirect
43. C₅²	D₃×D₃₁	semidirect
45. C₃×C₅	D₅×D₃₁	semidirect
53. C₅	D₁₅×D₃₁	semidirect
55. C₃	C₅⋊D₅×D₃₁	semidirect

Subgroups — D31×C3⋊(C5⋊D5) #22604916

Conjugacy classes of subgroups

Complements

Subgroups — D₃₁×C₃⋊(C₅⋊D₅) #22604916