Subgroups — C₁₃×C₂²⋊(C₅²⋊C₉) #26043470

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)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×C₁₃	—	3	2	no	—
8	C₂×C₅²×C₁₃	—	3	1	no	—
9	C₁₃×C₂²⋊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	C₃×C₁₃	1	1	yes	characteristic
13	C₂²×C₅×C₁₃	—	3	2	no	—
14	C₅²⋊C₉	—	4	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	C₉×C₁₃	—	100	1	no	Hall
20	C₂²×C₅²	C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₃	—	3	1	no	—
22	C₃×C₅²	A₄×C₁₃	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	—	25	1	no	Hall
29	C₂×C₃×C₅	—	3	6	no	—
30	C₂×C₁₃	—	3	1	no	—
31	C₅²	C₁₃×C₂²⋊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, direct product factor, Sylow
35	C₂²×C₃	C₁₃×C₅²⋊C₃	1	1	yes	characteristic
36	C₂×C₅	—	3	6	no	—
37	C₉	—	100	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	C₁₃×C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic
42	C₂	—	3	1	no	—

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

Complements

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

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

Subgroups — C13×C22⋊(C52⋊C9) #26043470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₂²⋊(C₅²⋊C₉) #26043470