Subgroups — C₂²×C₅²×C₃₁⋊C₃ #22604934

Order 9300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₃₁⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₅²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₃₁⋊C₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₅×C₃₁⋊C₃	C₅	1	6	yes	maximal, direct product factor
5	C₂×C₅²×C₃₁	C₂×C₃	1	3	yes	complemented
6	C₂×C₅×C₃₁⋊C₃	C₂×C₅	1	18	yes	direct product factor
7	C₅²×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₅×C₃₁	C₃×C₅	1	6	yes	complemented
9	C₅×C₃₁⋊C₃	C₂²×C₅	1	6	yes	direct product factor
10	C₂²×C₃₁⋊C₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₃₁	C₂×C₃×C₅	1	18	yes	complemented
12	C₂²×C₃×C₅²	—	31	1	no	maximal, Hall
13	C₂×C₃₁⋊C₃	C₂×C₅²	1	3	yes	direct product factor
14	C₅×C₃₁	C₂²×C₃×C₅	1	6	yes	complemented
15	C₂×C₃×C₅²	—	31	3	no	—
16	C₂²×C₃₁	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₅²	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
18	C₃₁⋊C₃	C₂²×C₅²	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₅²	—	31	1	no	Hall
20	C₂×C₃₁	C₂×C₃×C₅²	1	3	yes	complemented
21	C₂²×C₃×C₅	—	31	6	no	—
22	C₂×C₅²	C₂×C₃₁⋊C₃	1	3	yes	direct product factor
23	C₃₁	C₂²×C₃×C₅²	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃×C₅	—	31	18	no	—
25	C₅²	C₂²×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²×C₅	C₅×C₃₁⋊C₃	1	6	yes	direct product factor
27	C₃×C₅	—	31	6	no	—
28	C₂²×C₃	—	31	1	no	Hall
29	C₂×C₅	C₂×C₅×C₃₁⋊C₃	1	18	yes	direct product factor
30	C₂×C₃	—	31	3	no	—
31	C₅	C₂²×C₅×C₃₁⋊C₃	1	6	yes	direct product factor
32	C₂²	C₅²×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	—	31	1	no	Sylow
34	C₂	C₂×C₅²×C₃₁⋊C₃	1	3	yes	direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²×C₃₁⋊C₃	C₂	direct (N × H)
2. C₂²×C₅²×C₃₁	C₃	semidirect
3. C₅²×C₃₁⋊C₃	C₂²	direct (N × H)
4. C₂²×C₅×C₃₁⋊C₃	C₅	direct (N × H)
5. C₂×C₅²×C₃₁	C₂×C₃	semidirect
6. C₂×C₅×C₃₁⋊C₃	C₂×C₅	direct (N × H)
7. C₅²×C₃₁	C₂²×C₃	semidirect
8. C₂²×C₅×C₃₁	C₃×C₅	semidirect
9. C₅×C₃₁⋊C₃	C₂²×C₅	direct (N × H)
10. C₂²×C₃₁⋊C₃	C₅²	direct (N × H)
11. C₂×C₅×C₃₁	C₂×C₃×C₅	semidirect
13. C₂×C₃₁⋊C₃	C₂×C₅²	direct (N × H)
14. C₅×C₃₁	C₂²×C₃×C₅	semidirect
16. C₂²×C₃₁	C₃×C₅²	semidirect
17. C₂²×C₅²	C₃₁⋊C₃	direct (N × H)
18. C₃₁⋊C₃	C₂²×C₅²	direct (N × H)
20. C₂×C₃₁	C₂×C₃×C₅²	semidirect
22. C₂×C₅²	C₂×C₃₁⋊C₃	direct (N × H)
23. C₃₁	C₂²×C₃×C₅²	semidirect
25. C₅²	C₂²×C₃₁⋊C₃	direct (N × H)
26. C₂²×C₅	C₅×C₃₁⋊C₃	direct (N × H)
29. C₂×C₅	C₂×C₅×C₃₁⋊C₃	direct (N × H)
31. C₅	C₂²×C₅×C₃₁⋊C₃	direct (N × H)
32. C₂²	C₅²×C₃₁⋊C₃	direct (N × H)
34. C₂	C₂×C₅²×C₃₁⋊C₃	direct (N × H)

Subgroups — C22×C52×C31⋊C3 #22604934

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₅²×C₃₁⋊C₃ #22604934