Subgroups — C₂×C₃×C₁₁×C₇₁⋊C₅ #37552853

Order 23430.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₇₁⋊C₅	C₂	direct (N × H)
2. C₂×C₁₁×C₇₁⋊C₅	C₃	direct (N × H)
3. C₂×C₃×C₁₁×C₇₁	C₅	semidirect
4. C₁₁×C₇₁⋊C₅	C₂×C₃	direct (N × H)
5. C₃×C₁₁×C₇₁	C₂×C₅	semidirect
6. C₂×C₃×C₇₁⋊C₅	C₁₁	direct (N × H)
7. C₂×C₁₁×C₇₁	C₃×C₅	semidirect
8. C₃×C₇₁⋊C₅	C₂×C₁₁	direct (N × H)
9. C₁₁×C₇₁	C₂×C₃×C₅	semidirect
10. C₂×C₇₁⋊C₅	C₃×C₁₁	direct (N × H)
11. C₂×C₃×C₇₁	C₅×C₁₁	semidirect
12. C₇₁⋊C₅	C₂×C₃×C₁₁	direct (N × H)
14. C₃×C₇₁	C₂×C₅×C₁₁	semidirect
16. C₂×C₇₁	C₃×C₅×C₁₁	semidirect
18. C₇₁	C₂×C₃×C₅×C₁₁	semidirect
19. C₂×C₃×C₁₁	C₇₁⋊C₅	direct (N × H)
21. C₃×C₁₁	C₂×C₇₁⋊C₅	direct (N × H)
23. C₂×C₁₁	C₃×C₇₁⋊C₅	direct (N × H)
25. C₁₁	C₂×C₃×C₇₁⋊C₅	direct (N × H)
27. C₂×C₃	C₁₁×C₇₁⋊C₅	direct (N × H)
29. C₃	C₂×C₁₁×C₇₁⋊C₅	direct (N × H)
30. C₂	C₃×C₁₁×C₇₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₁×C₇₁⋊C₅	2
C₂×C₁₁×C₇₁⋊C₅	3
C₂×C₃×C₁₁×C₇₁	5
C₂×C₃×C₇₁⋊C₅	11
C₂×C₃×C₅×C₁₁	71

Subgroups — C2×C3×C11×C71⋊C5 #37552853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₁×C₇₁⋊C₅ #37552853