Subgroups — C₂×C₅×C₁₁×C₃₁⋊C₃ #23779409

Order 10230.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₁₁×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₁₁×C₃₁⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₁×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₁×C₃₁⋊C₃	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₅×C₃₁⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₁×C₃₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₃₁⋊C₃	C₂×C₁₁	1	1	yes	characteristic, direct product factor, Hall
9	C₁₁×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₅×C₁₁	—	31	1	no	maximal, Hall
11	C₂×C₅×C₃₁	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃₁⋊C₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₁₁	—	31	1	no	Hall
14	C₅×C₃₁	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₁₁	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
16	C₃₁⋊C₃	C₂×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₁₁	—	31	1	no	Hall
18	C₂×C₃₁	C₃×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
19	C₅×C₁₁	C₂×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₁₁	—	31	1	no	Hall
21	C₃₁	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃×C₅	—	31	1	no	Hall
23	C₂×C₁₁	C₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₅	—	31	1	no	Hall
25	C₁₁	C₂×C₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₅	C₁₁×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃	—	31	1	no	Hall
28	C₅	C₂×C₁₁×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	31	1	no	Sylow
30	C₂	C₅×C₁₁×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₁	C₃₁⋊C₃
commutator, cosocle, hypocenter	C₃₁	C₂×C₃×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁×C₃₁	C₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₃₁⋊C₃	C₂	direct (N × H)
2. C₂×C₅×C₁₁×C₃₁	C₃	semidirect
3. C₂×C₁₁×C₃₁⋊C₃	C₅	direct (N × H)
4. C₅×C₁₁×C₃₁	C₂×C₃	semidirect
5. C₁₁×C₃₁⋊C₃	C₂×C₅	direct (N × H)
6. C₂×C₅×C₃₁⋊C₃	C₁₁	direct (N × H)
7. C₂×C₁₁×C₃₁	C₃×C₅	semidirect
8. C₅×C₃₁⋊C₃	C₂×C₁₁	direct (N × H)
9. C₁₁×C₃₁	C₂×C₃×C₅	semidirect
11. C₂×C₅×C₃₁	C₃×C₁₁	semidirect
12. C₂×C₃₁⋊C₃	C₅×C₁₁	direct (N × H)
14. C₅×C₃₁	C₂×C₃×C₁₁	semidirect
15. C₂×C₅×C₁₁	C₃₁⋊C₃	direct (N × H)
16. C₃₁⋊C₃	C₂×C₅×C₁₁	direct (N × H)
18. C₂×C₃₁	C₃×C₅×C₁₁	semidirect
19. C₅×C₁₁	C₂×C₃₁⋊C₃	direct (N × H)
21. C₃₁	C₂×C₃×C₅×C₁₁	semidirect
23. C₂×C₁₁	C₅×C₃₁⋊C₃	direct (N × H)
25. C₁₁	C₂×C₅×C₃₁⋊C₃	direct (N × H)
26. C₂×C₅	C₁₁×C₃₁⋊C₃	direct (N × H)
28. C₅	C₂×C₁₁×C₃₁⋊C₃	direct (N × H)
30. C₂	C₅×C₁₁×C₃₁⋊C₃	direct (N × H)

Subgroups — C2×C5×C11×C31⋊C3 #23779409

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×C₁₁×C₃₁⋊C₃ #23779409