Subgroups — C₅×C₁₁×D₂₁₃ #37552867

Order 23430.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₁×D₇₁	—	3	1	no	maximal, Hall
3	C₁₁×D₂₁₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₁×C₇₁	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×D₂₁₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×D₇₁	—	3	1	no	Hall
8	C₃×C₅×C₇₁	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₇₁	C₅×D₃	1	1	yes	characteristic, complemented, Hall
10	C₅×D₇₁	—	3	1	no	Hall
11	D₂₁₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₇₁	D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₅×D₃×C₁₁	—	71	1	no	maximal, Hall
14	C₃×C₇₁	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×C₁₁	D₇₁	1	1	yes	characteristic, complemented, Hall
16	D₇₁	—	3	1	no	Hall
17	C₂×C₅×C₁₁	—	213	1	no	Hall
18	C₇₁	C₅×D₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
19	D₃×C₁₁	—	71	1	no	Hall
20	C₅×C₁₁	D₂₁₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₁₁	C₅×D₇₁	1	1	yes	characteristic, complemented, Hall
22	C₅×D₃	—	71	1	no	Hall
23	C₂×C₁₁	—	213	1	no	Hall
24	C₃×C₅	C₁₁×D₇₁	1	1	yes	characteristic, complemented, Hall
25	C₁₁	C₅×D₂₁₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₅	—	213	1	no	Hall
27	D₃	—	71	1	no	Hall
28	C₅	C₁₁×D₂₁₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×C₁₁×D₇₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	213	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₁	D₂₁₃
commutator, cosocle, hypocenter	C₃×C₇₁	C₂×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₇₁	C₂
LCS	G ▷ C₃×C₇₁
UCS	C₁ ◁ C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₇₁	C₂	semidirect
3. C₁₁×D₂₁₃	C₅	direct (N × H)
4. C₅×C₁₁×C₇₁	D₃	semidirect
5. C₃×C₁₁×C₇₁	C₂×C₅	semidirect
6. C₅×D₂₁₃	C₁₁	direct (N × H)
8. C₃×C₅×C₇₁	C₂×C₁₁	semidirect
9. C₁₁×C₇₁	C₅×D₃	semidirect
11. D₂₁₃	C₅×C₁₁	direct (N × H)
12. C₅×C₇₁	D₃×C₁₁	semidirect
14. C₃×C₇₁	C₂×C₅×C₁₁	semidirect
15. C₃×C₅×C₁₁	D₇₁	semidirect
18. C₇₁	C₅×D₃×C₁₁	semidirect
20. C₅×C₁₁	D₂₁₃	direct (N × H)
21. C₃×C₁₁	C₅×D₇₁	semidirect
24. C₃×C₅	C₁₁×D₇₁	semidirect
25. C₁₁	C₅×D₂₁₃	direct (N × H)
28. C₅	C₁₁×D₂₁₃	direct (N × H)
29. C₃	C₅×C₁₁×D₇₁	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×C₇₁	2
C₅×C₁₁×D₇₁	3
C₁₁×D₂₁₃	5
C₅×D₂₁₃	11
C₅×D₃×C₁₁	71

Subgroups — C5×C11×D213 #37552867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×D₂₁₃ #37552867