Subgroups — C₂×C₅×C₃⋊(D₃₁⋊C₅) #22604871

Order 9300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₃⋊(D₃₁⋊C₅)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×D₃₁⋊C₅	—	3	1	no	maximal, Hall
4	C₃×C₅×ΓL(1,𝔽₃₂)	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×D₉₃	C₅	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃⋊(D₃₁⋊C₅)	C₅	1	5	yes	maximal, direct product factor
7	C₂×C₅×ΓL(1,𝔽₃₂)	D₃	1	1	yes	characteristic, complemented
8	C₅×D₃₁⋊C₅	—	3	2	no	—
9	C₂×C₃×C₅×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
10	C₅×D₉₃	C₂×C₅	1	2	yes	complemented
11	C₂×C₃×ΓL(1,𝔽₃₂)	C₂×C₅	1	5	yes	complemented
12	C₃⋊(D₃₁⋊C₅)	C₂×C₅	1	10	yes	direct product factor
13	C₅×ΓL(1,𝔽₃₂)	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×D₃₁	—	3	1	no	—
15	C₂×D₃₁⋊C₅	—	3	5	no	—
16	C₃×C₅×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented
17	C₃×ΓL(1,𝔽₃₂)	C₂²×C₅	1	5	yes	complemented
18	C₂×D₉₃	C₅²	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×C₃₁	C₅×D₃	1	1	yes	characteristic, complemented
20	C₅×D₃₁	—	3	2	no	—
21	C₂×ΓL(1,𝔽₃₂)	C₅×D₃	1	5	yes	complemented
22	D₃₁⋊C₅	—	3	10	no	—
23	C₂×C₅²×D₃	—	31	1	no	maximal, Hall
24	C₂×C₃×C₃₁	C₂×C₅²	1	1	yes	characteristic, complemented
25	D₉₃	C₂×C₅²	1	2	yes	complemented
26	C₅×C₃₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented
27	ΓL(1,𝔽₃₂)	C₂×C₅×D₃	1	5	yes	complemented
28	C₂×C₃×C₅²	—	31	1	no	—
29	C₅²×D₃	—	31	2	no	—
30	C₂×D₃₁	—	3	1	no	Hall
31	C₂²×C₅²	—	93	1	no	Hall
32	C₃×C₃₁	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
33	C₃×C₅²	—	31	1	no	Hall
34	C₂×C₃₁	C₅²×D₃	1	1	yes	characteristic, complemented
35	D₃₁	—	3	2	no	—
36	C₂×C₅×D₃	—	31	5	no	—
37	C₂×C₅×D₃	—	31	1	no	—
38	C₂×C₅²	—	31	1	no	—
39	C₂×C₅²	—	93	2	no	—
40	C₃₁	C₂×C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃×C₅	—	31	5	no	—
42	C₂×C₃×C₅	D₃₁⋊C₅	1	1	yes	characteristic, complemented
43	C₅×D₃	—	31	10	no	—
44	C₅×D₃	—	31	2	no	—
45	C₅²	—	31	1	no	Sylow
46	C₂²×C₅	—	93	5	no	—
47	C₂²×C₅	—	93	1	no	—
48	C₃×C₅	—	31	5	no	—
49	C₃×C₅	C₂×D₃₁⋊C₅	1	1	yes	characteristic, complemented
50	C₂×D₃	—	31	1	no	Hall
51	C₂×C₅	—	31	5	no	—
52	C₂×C₅	—	93	10	no	—
53	C₂×C₅	—	93	2	no	—
54	C₂×C₅	C₃⋊(D₃₁⋊C₅)	1	1	yes	characteristic, direct product factor
55	C₂×C₃	C₅×D₃₁⋊C₅	1	1	yes	characteristic, complemented
56	D₃	—	31	2	no	—
57	C₅	—	31	5	no	—
58	C₅	C₂×C₃⋊(D₃₁⋊C₅)	1	1	yes	characteristic, direct product factor
59	C₂²	—	93	1	no	Sylow
60	C₃	C₂×C₅×D₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	93	2	no	—
62	C₂	C₅×C₃⋊(D₃₁⋊C₅)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	C₃⋊(D₃₁⋊C₅)
commutator, hypocenter	C₃×C₃₁	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₃₁	C₂×C₅
LCS	G ▷ C₃×C₃₁
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×ΓL(1,𝔽₃₂)	C₂	semidirect
2. C₅×C₃⋊(D₃₁⋊C₅)	C₂	direct (N × H)
4. C₃×C₅×ΓL(1,𝔽₃₂)	C₂²	semidirect
5. C₂×C₅×D₉₃	C₅	semidirect
6. C₂×C₃⋊(D₃₁⋊C₅)	C₅	direct (N × H)
7. C₂×C₅×ΓL(1,𝔽₃₂)	D₃	semidirect
9. C₂×C₃×C₅×C₃₁	C₂×C₅	semidirect
10. C₅×D₉₃	C₂×C₅	semidirect
11. C₂×C₃×ΓL(1,𝔽₃₂)	C₂×C₅	semidirect
12. C₃⋊(D₃₁⋊C₅)	C₂×C₅	direct (N × H)
13. C₅×ΓL(1,𝔽₃₂)	C₂×D₃	semidirect
16. C₃×C₅×C₃₁	C₂²×C₅	semidirect
17. C₃×ΓL(1,𝔽₃₂)	C₂²×C₅	semidirect
18. C₂×D₉₃	C₅²	semidirect
19. C₂×C₅×C₃₁	C₅×D₃	semidirect
21. C₂×ΓL(1,𝔽₃₂)	C₅×D₃	semidirect
24. C₂×C₃×C₃₁	C₂×C₅²	semidirect
25. D₉₃	C₂×C₅²	semidirect
26. C₅×C₃₁	C₂×C₅×D₃	semidirect
27. ΓL(1,𝔽₃₂)	C₂×C₅×D₃	semidirect
32. C₃×C₃₁	C₂²×C₅²	semidirect
34. C₂×C₃₁	C₅²×D₃	semidirect
40. C₃₁	C₂×C₅²×D₃	semidirect
42. C₂×C₃×C₅	D₃₁⋊C₅	semidirect
49. C₃×C₅	C₂×D₃₁⋊C₅	semidirect
54. C₂×C₅	C₃⋊(D₃₁⋊C₅)	direct (N × H)
55. C₂×C₃	C₅×D₃₁⋊C₅	semidirect
58. C₅	C₂×C₃⋊(D₃₁⋊C₅)	direct (N × H)
60. C₃	C₂×C₅×D₃₁⋊C₅	semidirect
62. C₂	C₅×C₃⋊(D₃₁⋊C₅)	direct (N × H)

Subgroups — C2×C5×C3⋊(D31⋊C5) #22604871

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×C₃⋊(D₃₁⋊C₅) #22604871