Subgroups — C₂×C₃²×D₃₁⋊C₅ #19150124

Order 5580.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×D₃₁⋊C₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₃₁⋊C₅	C₃	1	4	yes	maximal, direct product factor
4	C₃²×ΓL(1,𝔽₃₂)	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×D₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂×C₃×ΓL(1,𝔽₃₂)	C₂×C₃	1	4	yes	complemented
7	C₃×D₃₁⋊C₅	C₂×C₃	1	8	yes	direct product factor
8	C₂×D₃₁⋊C₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃²×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃²×D₃₁	C₂×C₅	1	2	yes	complemented
11	C₃×ΓL(1,𝔽₃₂)	C₂²×C₃	1	4	yes	complemented
12	C₂×C₃×D₃₁	C₃×C₅	1	4	yes	complemented
13	C₂×ΓL(1,𝔽₃₂)	C₂×C₃²	1	1	yes	characteristic, complemented
14	D₃₁⋊C₅	C₂×C₃²	1	2	yes	direct product factor
15	C₃²×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₃₁	C₂×C₃×C₅	1	4	yes	complemented
17	C₃×D₃₁	C₂×C₃×C₅	1	8	yes	complemented
18	C₂²×C₃²×C₅	—	31	1	no	maximal, Hall
19	ΓL(1,𝔽₃₂)	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃₁	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
21	C₃×C₃₁	C₂²×C₃×C₅	1	4	yes	complemented
22	C₂×C₃²×C₅	—	31	2	no	—
23	C₂×C₃²×C₅	—	31	1	no	—
24	C₂×C₃₁	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
25	D₃₁	C₂×C₃²×C₅	1	2	yes	complemented
26	C₂²×C₃×C₅	—	31	4	no	—
27	C₃²×C₅	—	31	1	no	Hall
28	C₂²×C₃²	—	31	1	no	Hall
29	C₃₁	C₂²×C₃²×C₅	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃×C₅	—	31	8	no	—
31	C₂×C₃×C₅	—	31	4	no	—
32	C₂²×C₅	—	31	1	no	Hall
33	C₂×C₃²	—	31	2	no	—
34	C₂×C₃²	D₃₁⋊C₅	1	1	yes	characteristic, direct product factor
35	C₃×C₅	—	31	4	no	—
36	C₂²×C₃	—	31	4	no	—
37	C₂×C₅	—	31	2	no	—
38	C₂×C₅	—	31	1	no	—
39	C₃²	C₂×D₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃	—	31	8	no	—
41	C₂×C₃	C₃×D₃₁⋊C₅	1	4	yes	direct product factor
42	C₅	—	31	1	no	Sylow
43	C₂²	—	31	1	no	Sylow
44	C₃	C₂×C₃×D₃₁⋊C₅	1	4	yes	direct product factor
45	C₂	—	31	2	no	—
46	C₂	C₃²×D₃₁⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₃₁⋊C₅
commutator, hypocenter	C₃₁	C₂²×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₃₁	C₂×C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×ΓL(1,𝔽₃₂)	C₂	semidirect
2. C₃²×D₃₁⋊C₅	C₂	direct (N × H)
3. C₂×C₃×D₃₁⋊C₅	C₃	direct (N × H)
4. C₃²×ΓL(1,𝔽₃₂)	C₂²	semidirect
5. C₂×C₃²×D₃₁	C₅	semidirect
6. C₂×C₃×ΓL(1,𝔽₃₂)	C₂×C₃	semidirect
7. C₃×D₃₁⋊C₅	C₂×C₃	direct (N × H)
8. C₂×D₃₁⋊C₅	C₃²	direct (N × H)
9. C₂×C₃²×C₃₁	C₂×C₅	semidirect
10. C₃²×D₃₁	C₂×C₅	semidirect
11. C₃×ΓL(1,𝔽₃₂)	C₂²×C₃	semidirect
12. C₂×C₃×D₃₁	C₃×C₅	semidirect
13. C₂×ΓL(1,𝔽₃₂)	C₂×C₃²	semidirect
14. D₃₁⋊C₅	C₂×C₃²	direct (N × H)
15. C₃²×C₃₁	C₂²×C₅	semidirect
16. C₂×C₃×C₃₁	C₂×C₃×C₅	semidirect
17. C₃×D₃₁	C₂×C₃×C₅	semidirect
19. ΓL(1,𝔽₃₂)	C₂²×C₃²	semidirect
20. C₂×D₃₁	C₃²×C₅	semidirect
21. C₃×C₃₁	C₂²×C₃×C₅	semidirect
24. C₂×C₃₁	C₂×C₃²×C₅	semidirect
25. D₃₁	C₂×C₃²×C₅	semidirect
29. C₃₁	C₂²×C₃²×C₅	semidirect
34. C₂×C₃²	D₃₁⋊C₅	direct (N × H)
39. C₃²	C₂×D₃₁⋊C₅	direct (N × H)
41. C₂×C₃	C₃×D₃₁⋊C₅	direct (N × H)
44. C₃	C₂×C₃×D₃₁⋊C₅	direct (N × H)
46. C₂	C₃²×D₃₁⋊C₅	direct (N × H)

Subgroups — C2×C32×D31⋊C5 #19150124

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃²×D₃₁⋊C₅ #19150124