Subgroups — C₅×C₂²⋊C₉×C₁₃₁ #37556056

Order 23580.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₁₃₁	C₃	1	1	yes	maximal, characteristic
2	C₅×C₉×C₁₃₁	—	4	1	no	maximal, Hall
3	C₂²⋊C₉×C₁₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₅×C₁₃₁	—	3	1	no	—
5	C₂²×C₅×C₁₃₁	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₁₃₁	A₄	1	1	yes	characteristic
7	C₂²×C₃×C₁₃₁	C₃×C₅	1	1	yes	characteristic
8	C₂×C₅×C₁₃₁	—	3	1	no	—
9	C₉×C₁₃₁	—	4	1	no	Hall
10	C₂×C₃×C₁₃₁	—	3	1	no	—
11	C₅×C₁₃₁	C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₁₃₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₃₁	C₅×A₄	1	1	yes	characteristic
14	C₂×C₁₃₁	—	3	1	no	—
15	C₅×C₂²⋊C₉	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₁₃₁	C₅×C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₂²×C₃×C₅	C₃×C₁₃₁	1	1	yes	characteristic
18	C₅×C₉	—	4	1	no	Hall
19	C₂²⋊C₉	C₅×C₁₃₁	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃×C₅	—	3	1	no	—
21	C₂²×C₅	C₉×C₁₃₁	1	1	yes	characteristic, complemented, Hall
22	C₃×C₅	A₄×C₁₃₁	1	1	yes	characteristic
23	C₂²×C₃	C₃×C₅×C₁₃₁	1	1	yes	characteristic
24	C₂×C₅	—	3	1	no	—
25	C₉	—	4	1	no	Sylow
26	C₂×C₃	—	3	1	no	—
27	C₅	C₂²⋊C₉×C₁₃₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	C₅×C₉×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₅×A₄×C₁₃₁	1	1	yes	characteristic
30	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₃₁	A₄
commutator, hypocenter	C₂²	C₅×C₉×C₁₃₁
Frattini	C₃	C₅×A₄×C₁₃₁
Fitting, socle, prime radical	C₂²×C₃×C₅×C₁₃₁	C₃
cosocle	C₂²×C₃	C₃×C₅×C₁₃₁
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₅×C₁₃₁

Complements

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

N	H ≅ G/N	type
3. C₂²⋊C₉×C₁₃₁	C₅	direct (N × H)
5. C₂²×C₅×C₁₃₁	C₉	semidirect
11. C₅×C₁₃₁	C₂²⋊C₉	direct (N × H)
12. C₂²×C₁₃₁	C₅×C₉	semidirect
15. C₅×C₂²⋊C₉	C₁₃₁	direct (N × H)
16. C₁₃₁	C₅×C₂²⋊C₉	direct (N × H)
19. C₂²⋊C₉	C₅×C₁₃₁	direct (N × H)
21. C₂²×C₅	C₉×C₁₃₁	semidirect
27. C₅	C₂²⋊C₉×C₁₃₁	direct (N × H)
28. C₂²	C₅×C₉×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×C₁₃₁	3
C₅×C₉×C₁₃₁	4
C₂²⋊C₉×C₁₃₁	5
C₅×C₂²⋊C₉	131

Subgroups — C5×C22⋊C9×C131 #37556056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂²⋊C₉×C₁₃₁ #37556056