Subgroups — C₂²⋊(C₁₃⋊(C₅²⋊C₉)) #26043471

Order 11700.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅²×C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₁₃⋊(C₅²⋊C₉)	—	4	1	no	maximal, Hall
3	C₂×C₃×C₅²×C₁₃	—	3	1	no	—
4	C₂²×C₅²×C₁₃	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅²×C₁₃	A₄	1	1	yes	characteristic
6	C₂²⋊(C₅²⋊C₉)	—	13	1	no	maximal, Hall
7	C₂²×C₃×C₅×C₁₃	—	3	2	no	—
8	C₂×C₅²×C₁₃	—	3	1	no	—
9	C₂²⋊(C₁₃⋊C₉)	—	25	1	no	maximal, Hall
10	C₂×C₃×C₅×C₁₃	—	3	6	no	—
11	C₅²×C₁₃	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₃×C₅²	C₁₃⋊C₃	1	1	yes	characteristic
13	C₂²×C₅×C₁₃	—	3	2	no	—
14	C₅²⋊C₉	—	52	1	no	Hall
15	C₃×C₅×C₁₃	—	3	2	no	—
16	C₂²×C₃×C₁₃	C₅²⋊C₃	1	1	yes	characteristic
17	C₂×C₃×C₅²	—	3	1	no	—
18	C₂×C₅×C₁₃	—	3	6	no	—
19	C₁₃⋊C₉	—	100	1	no	Hall
20	C₂²×C₅²	C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₃	—	3	1	no	—
22	C₃×C₅²	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
23	C₅×C₁₃	—	3	2	no	—
24	C₂²×C₃×C₅	—	3	2	no	—
25	C₂²×C₁₃	C₅²⋊C₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅²	—	3	1	no	—
27	C₃×C₁₃	C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic
28	C₂²⋊C₉	—	325	1	no	Hall
29	C₂×C₃×C₅	—	3	6	no	—
30	C₂×C₁₃	—	3	1	no	—
31	C₅²	C₂²⋊(C₁₃⋊C₉)	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₅	—	3	2	no	—
33	C₃×C₅	—	3	2	no	—
34	C₁₃	C₂²⋊(C₅²⋊C₉)	1	1	yes	characteristic, complemented, Sylow
35	C₂²×C₃	C₁₃⋊(C₅²⋊C₃)	1	1	yes	characteristic
36	C₂×C₅	—	3	6	no	—
37	C₉	—	1300	1	no	Sylow
38	C₂×C₃	—	3	1	no	—
39	C₅	—	3	2	no	—
40	C₂²	C₁₃⋊(C₅²⋊C₉)	1	1	yes	characteristic, complemented, Sylow
41	C₃	C₂²⋊(C₁₃⋊(C₅²⋊C₃))	1	1	yes	characteristic
42	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₂²⋊(C₁₃⋊(C₅²⋊C₃))
commutator, hypocenter	C₂²×C₅²×C₁₃	C₉
Fitting, socle, prime radical, cosocle	C₂²×C₃×C₅²×C₁₃	C₃
LCS	G ▷ C₂²×C₅²×C₁₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
4. C₂²×C₅²×C₁₃	C₉	semidirect
11. C₅²×C₁₃	C₂²⋊C₉	semidirect
20. C₂²×C₅²	C₁₃⋊C₉	semidirect
25. C₂²×C₁₃	C₅²⋊C₉	semidirect
31. C₅²	C₂²⋊(C₁₃⋊C₉)	semidirect
34. C₁₃	C₂²⋊(C₅²⋊C₉)	semidirect
40. C₂²	C₁₃⋊(C₅²⋊C₉)	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅²×C₁₃	3
C₁₃⋊(C₅²⋊C₉)	4
C₂²⋊(C₅²⋊C₉)	13
C₂²⋊(C₁₃⋊C₉)	25

Subgroups — C22⋊(C13⋊(C52⋊C9)) #26043471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊(C₁₃⋊(C₅²⋊C₉)) #26043471