Subgroups — C₅×C₁₁×D₃₂₇ #49112573

Order 35970.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₁×D₁₀₉	—	3	1	no	maximal, Hall
3	C₁₁×D₃₂₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₁×C₁₀₉	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₁₀₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×D₃₂₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×D₁₀₉	—	3	1	no	Hall
8	C₃×C₅×C₁₀₉	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₁₀₉	C₅×D₃	1	1	yes	characteristic, complemented, Hall
10	C₅×D₁₀₉	—	3	1	no	Hall
11	D₃₂₇	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₁₀₉	D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₅×D₃×C₁₁	—	109	1	no	maximal, Hall
14	C₃×C₁₀₉	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
15	D₁₀₉	—	3	1	no	Hall
16	C₃×C₅×C₁₁	D₁₀₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₁₁	—	327	1	no	Hall
18	C₁₀₉	C₅×D₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
19	D₃×C₁₁	—	109	1	no	Hall
20	C₅×C₁₁	D₃₂₇	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₁₁	C₅×D₁₀₉	1	1	yes	characteristic, complemented, Hall
22	C₅×D₃	—	109	1	no	Hall
23	C₂×C₁₁	—	327	1	no	Hall
24	C₃×C₅	C₁₁×D₁₀₉	1	1	yes	characteristic, complemented, Hall
25	C₁₁	C₅×D₃₂₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₅	—	327	1	no	Hall
27	D₃	—	109	1	no	Hall
28	C₅	C₁₁×D₃₂₇	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×C₁₁×D₁₀₉	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	327	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₁	D₃₂₇
commutator, cosocle, hypocenter	C₃×C₁₀₉	C₂×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₀₉	C₂
LCS	G ▷ C₃×C₁₀₉
UCS	C₁ ◁ C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₁₀₉	C₂	semidirect
3. C₁₁×D₃₂₇	C₅	direct (N × H)
4. C₅×C₁₁×C₁₀₉	D₃	semidirect
5. C₃×C₁₁×C₁₀₉	C₂×C₅	semidirect
6. C₅×D₃₂₇	C₁₁	direct (N × H)
8. C₃×C₅×C₁₀₉	C₂×C₁₁	semidirect
9. C₁₁×C₁₀₉	C₅×D₃	semidirect
11. D₃₂₇	C₅×C₁₁	direct (N × H)
12. C₅×C₁₀₉	D₃×C₁₁	semidirect
14. C₃×C₁₀₉	C₂×C₅×C₁₁	semidirect
16. C₃×C₅×C₁₁	D₁₀₉	semidirect
18. C₁₀₉	C₅×D₃×C₁₁	semidirect
20. C₅×C₁₁	D₃₂₇	direct (N × H)
21. C₃×C₁₁	C₅×D₁₀₉	semidirect
24. C₃×C₅	C₁₁×D₁₀₉	semidirect
25. C₁₁	C₅×D₃₂₇	direct (N × H)
28. C₅	C₁₁×D₃₂₇	direct (N × H)
29. C₃	C₅×C₁₁×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₁×C₁₀₉	2
C₅×C₁₁×D₁₀₉	3
C₁₁×D₃₂₇	5
C₅×D₃₂₇	11
C₅×D₃×C₁₁	109

Subgroups — C5×C11×D327 #49112573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×D₃₂₇ #49112573