Subgroups — C₅²×C₂²⋊(C₁₃⋊C₉) #26043469

Order 11700.

128 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	C₅²×C₁₃⋊C₉	—	4	1	no	maximal, Hall
3	C₅×C₂²⋊(C₁₃⋊C₉)	C₅	1	6	yes	maximal, direct product factor
4	C₂×C₃×C₅²×C₁₃	—	3	1	no	—
5	C₂²×C₅²×C₁₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅²×C₁₃	A₄	1	1	yes	characteristic
7	C₅²×C₂²⋊C₉	—	13	1	no	maximal, Hall
8	C₂²×C₃×C₅×C₁₃	C₃×C₅	1	6	yes	—
9	C₂×C₅²×C₁₃	—	3	1	no	—
10	C₅×C₁₃⋊C₉	—	4	6	no	—
11	C₂²⋊(C₁₃⋊C₉)	C₅²	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃×C₅×C₁₃	—	3	6	no	—
13	C₅²×C₁₃	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
14	C₂²×C₃×C₅²	C₁₃⋊C₃	1	1	yes	characteristic
15	C₂²×C₅×C₁₃	C₅×C₉	1	6	yes	complemented
16	C₅²×C₉	—	52	1	no	Hall
17	C₃×C₅×C₁₃	C₅×A₄	1	6	yes	—
18	C₅×C₂²⋊C₉	—	13	6	no	—
19	C₂²×C₃×C₁₃	C₃×C₅²	1	1	yes	characteristic
20	C₂×C₃×C₅²	—	3	1	no	—
21	C₂×C₅×C₁₃	—	3	6	no	—
22	C₁₃⋊C₉	—	4	1	no	Hall
23	C₂²×C₅²	C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₁₃	—	3	1	no	—
25	C₃×C₅²	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
26	C₅×C₁₃	C₅×C₂²⋊C₉	1	6	yes	complemented
27	C₂²×C₃×C₅	C₅×C₁₃⋊C₃	1	6	yes	—
28	C₂²×C₁₃	C₅²×C₉	1	1	yes	characteristic, complemented, Hall
29	C₂×C₅²	—	3	1	no	—
30	C₅×C₉	—	52	6	no	—
31	C₃×C₁₃	C₅²×A₄	1	1	yes	characteristic
32	C₂²⋊C₉	—	13	1	no	Hall
33	C₂×C₃×C₅	—	3	6	no	—
34	C₂×C₁₃	—	3	1	no	—
35	C₅²	C₂²⋊(C₁₃⋊C₉)	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²×C₅	C₅×C₁₃⋊C₉	1	6	yes	complemented
37	C₃×C₅	C₅×C₂²⋊(C₁₃⋊C₃)	1	6	yes	—
38	C₁₃	C₅²×C₂²⋊C₉	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	C₅²×C₁₃⋊C₃	1	1	yes	characteristic
40	C₂×C₅	—	3	6	no	—
41	C₉	—	52	1	no	Sylow
42	C₂×C₃	—	3	1	no	—
43	C₅	C₅×C₂²⋊(C₁₃⋊C₉)	1	6	yes	direct product factor
44	C₂²	C₅²×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₅²×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
46	C₂	—	3	1	no	—

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

Complements

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

N	H ≅ G/N	type
3. C₅×C₂²⋊(C₁₃⋊C₉)	C₅	direct (N × H)
5. C₂²×C₅²×C₁₃	C₉	semidirect
11. C₂²⋊(C₁₃⋊C₉)	C₅²	direct (N × H)
13. C₅²×C₁₃	C₂²⋊C₉	semidirect
15. C₂²×C₅×C₁₃	C₅×C₉	semidirect
23. C₂²×C₅²	C₁₃⋊C₉	semidirect
26. C₅×C₁₃	C₅×C₂²⋊C₉	semidirect
28. C₂²×C₁₃	C₅²×C₉	semidirect
35. C₅²	C₂²⋊(C₁₃⋊C₉)	direct (N × H)
36. C₂²×C₅	C₅×C₁₃⋊C₉	semidirect
38. C₁₃	C₅²×C₂²⋊C₉	semidirect
43. C₅	C₅×C₂²⋊(C₁₃⋊C₉)	direct (N × H)
44. C₂²	C₅²×C₁₃⋊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
C₅²×C₁₃⋊C₉	4
C₅×C₂²⋊(C₁₃⋊C₉)	5
C₅²×C₂²⋊C₉	13

Subgroups — C52×C22⋊(C13⋊C9) #26043469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₂²⋊(C₁₃⋊C₉) #26043469