Subgroups — C₂²×C₉×C₁₃₁⋊C₅ #37556044

Order 23580.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₃₁⋊C₅	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₃₁⋊C₅	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₃₁⋊C₅	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₉×C₁₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃×C₁₃₁⋊C₅	C₂×C₃	1	3	yes	—
6	C₂²×C₁₃₁⋊C₅	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₉×C₁₃₁	C₂×C₅	1	3	yes	complemented
8	C₃×C₁₃₁⋊C₅	C₂²×C₃	1	1	yes	characteristic
9	C₂²×C₃×C₁₃₁	C₃×C₅	1	1	yes	characteristic
10	C₂×C₁₃₁⋊C₅	C₂×C₉	1	3	yes	direct product factor
11	C₉×C₁₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₁₃₁	C₂×C₃×C₅	1	3	yes	—
13	C₁₃₁⋊C₅	C₂²×C₉	1	1	yes	characteristic, direct product factor, Hall
14	C₂²×C₁₃₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₃₁	C₂²×C₃×C₅	1	1	yes	characteristic
16	C₂×C₁₃₁	C₂×C₅×C₉	1	3	yes	complemented
17	C₂²×C₅×C₉	—	131	1	no	maximal, Hall
18	C₁₃₁	C₂²×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅×C₉	—	131	3	no	—
20	C₂²×C₃×C₅	—	131	1	no	—
21	C₅×C₉	—	131	1	no	Hall
22	C₂²×C₉	C₁₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₅	—	131	3	no	—
24	C₂²×C₅	—	131	1	no	Hall
25	C₂×C₉	C₂×C₁₃₁⋊C₅	1	3	yes	direct product factor
26	C₃×C₅	—	131	1	no	—
27	C₂²×C₃	C₃×C₁₃₁⋊C₅	1	1	yes	characteristic
28	C₂×C₅	—	131	3	no	—
29	C₉	C₂²×C₁₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	C₂×C₃×C₁₃₁⋊C₅	1	3	yes	—
31	C₅	—	131	1	no	Sylow
32	C₂²	C₉×C₁₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₂²×C₃×C₁₃₁⋊C₅	1	1	yes	characteristic
34	C₂	C₂×C₉×C₁₃₁⋊C₅	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₉	C₁₃₁⋊C₅
commutator, hypocenter	C₁₃₁	C₂²×C₅×C₉
Frattini	C₃	C₂²×C₃×C₁₃₁⋊C₅
Fitting	C₂²×C₉×C₁₃₁	C₅
socle	C₂²×C₃×C₁₃₁	C₃×C₅
prime radical	C₂²×C₃×C₁₃₁⋊C₅	C₃
cosocle	C₃×C₁₃₁	C₂²×C₃×C₅
LCS	G ▷ C₁₃₁
UCS	C₁ ◁ C₂²×C₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×C₁₃₁⋊C₅	C₂	direct (N × H)
3. C₉×C₁₃₁⋊C₅	C₂²	direct (N × H)
4. C₂²×C₉×C₁₃₁	C₅	semidirect
6. C₂²×C₁₃₁⋊C₅	C₉	direct (N × H)
7. C₂×C₉×C₁₃₁	C₂×C₅	semidirect
10. C₂×C₁₃₁⋊C₅	C₂×C₉	direct (N × H)
11. C₉×C₁₃₁	C₂²×C₅	semidirect
13. C₁₃₁⋊C₅	C₂²×C₉	direct (N × H)
14. C₂²×C₁₃₁	C₅×C₉	semidirect
16. C₂×C₁₃₁	C₂×C₅×C₉	semidirect
18. C₁₃₁	C₂²×C₅×C₉	semidirect
22. C₂²×C₉	C₁₃₁⋊C₅	direct (N × H)
25. C₂×C₉	C₂×C₁₃₁⋊C₅	direct (N × H)
29. C₉	C₂²×C₁₃₁⋊C₅	direct (N × H)
32. C₂²	C₉×C₁₃₁⋊C₅	direct (N × H)
34. C₂	C₂×C₉×C₁₃₁⋊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
C₂×C₉×C₁₃₁⋊C₅	2
C₂²×C₃×C₁₃₁⋊C₅	3
C₂²×C₉×C₁₃₁	5
C₂²×C₅×C₉	131

Subgroups — C22×C9×C131⋊C5 #37556044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₉×C₁₃₁⋊C₅ #37556044