Subgroups — C₅×D₁₁×C₁₀₃⋊C₃ #46800939

Order 33990.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₁₀₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₁×C₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	D₁₁×C₁₀₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₁×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₁×C₁₀₃⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₂×C₅×C₁₀₃⋊C₃	—	11	1	no	maximal, Hall
7	D₁₁×C₁₀₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₁₀₃⋊C₃	D₁₁	1	1	yes	characteristic, direct product factor, Hall
9	C₁₁×C₁₀₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₁₀₃	—	11	1	no	Hall
11	C₂×C₁₀₃⋊C₃	—	11	1	no	Hall
12	C₅×C₁₀₃	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
13	C₃×C₅×D₁₁	—	103	1	no	maximal, Hall
14	C₁₀₃⋊C₃	C₅×D₁₁	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₁₀₃	—	11	1	no	Hall
16	C₃×C₅×C₁₁	—	103	1	no	Hall
17	C₅×D₁₁	C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
18	C₁₀₃	C₃×C₅×D₁₁	1	1	yes	characteristic, complemented, Sylow
19	C₃×D₁₁	—	103	1	no	Hall
20	C₅×C₁₁	C₂×C₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	—	103	1	no	Hall
22	C₂×C₃×C₅	—	1133	1	no	Hall
23	D₁₁	C₅×C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₅	—	103	1	no	Hall
25	C₁₁	C₂×C₅×C₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	11	1	no	Hall
27	C₂×C₃	—	1133	1	no	Hall
28	C₅	D₁₁×C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	103	1	no	Sylow
30	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₁₁×C₁₀₃⋊C₃
commutator, cosocle, hypocenter	C₁₁×C₁₀₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₀₃	C₂×C₃
LCS	G ▷ C₁₁×C₁₀₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₁₀₃⋊C₃	C₂	semidirect
2. C₅×D₁₁×C₁₀₃	C₃	semidirect
3. D₁₁×C₁₀₃⋊C₃	C₅	direct (N × H)
4. C₅×C₁₁×C₁₀₃	C₂×C₃	semidirect
5. C₁₁×C₁₀₃⋊C₃	C₂×C₅	semidirect
7. D₁₁×C₁₀₃	C₃×C₅	semidirect
8. C₅×C₁₀₃⋊C₃	D₁₁	direct (N × H)
9. C₁₁×C₁₀₃	C₂×C₃×C₅	semidirect
12. C₅×C₁₀₃	C₃×D₁₁	semidirect
14. C₁₀₃⋊C₃	C₅×D₁₁	direct (N × H)
17. C₅×D₁₁	C₁₀₃⋊C₃	direct (N × H)
18. C₁₀₃	C₃×C₅×D₁₁	semidirect
20. C₅×C₁₁	C₂×C₁₀₃⋊C₃	semidirect
23. D₁₁	C₅×C₁₀₃⋊C₃	direct (N × H)
25. C₁₁	C₂×C₅×C₁₀₃⋊C₃	semidirect
28. C₅	D₁₁×C₁₀₃⋊C₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₁₁×C₁₀₃⋊C₃	2
C₅×D₁₁×C₁₀₃	3
D₁₁×C₁₀₃⋊C₃	5
C₂×C₅×C₁₀₃⋊C₃	11
C₃×C₅×D₁₁	103

Subgroups — C5×D11×C103⋊C3 #46800939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₁₁×C₁₀₃⋊C₃ #46800939