Subgroups — C₃×C₂²⋊(C₁₃⋊(C₅²⋊C₃)) #26043860

Order 11700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊(C₁₃⋊(C₅²⋊C₃))	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₅²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃⋊(C₅²⋊C₃)	—	4	1	no	maximal, Hall
4	C₂×C₃×C₅²×C₁₃	—	3	1	no	—
5	C₂²×C₅²×C₁₃	C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅²×C₁₃	A₄	1	1	yes	characteristic, complemented
7	C₁₃⋊(C₅²⋊C₃)	—	4	3	no	—
8	C₃×C₂²⋊(C₅²⋊C₃)	—	13	1	no	maximal, Hall
9	C₂²×C₃×C₅×C₁₃	—	3	2	no	—
10	C₂×C₅²×C₁₃	—	3	1	no	—
11	C₃×C₂²⋊(C₁₃⋊C₃)	—	25	1	no	maximal, Hall
12	C₂×C₃×C₅×C₁₃	—	3	6	no	—
13	C₅²×C₁₃	C₃×A₄	1	1	yes	characteristic, complemented, Hall
14	C₂²×C₃×C₅²	C₁₃⋊C₃	1	1	yes	characteristic, complemented
15	C₂²⋊(C₅²⋊C₃)	—	13	3	no	—
16	C₂²×C₅×C₁₃	—	3	2	no	—
17	C₃×C₅²⋊C₃	—	52	1	no	Hall
18	C₃×C₅×C₁₃	—	3	2	no	—
19	C₂²×C₃×C₁₃	C₅²⋊C₃	1	1	yes	characteristic, complemented
20	C₂²⋊(C₁₃⋊C₃)	—	25	3	no	—
21	C₂×C₃×C₅²	—	3	1	no	—
22	C₂×C₅×C₁₃	—	3	6	no	—
23	C₃×C₁₃⋊C₃	—	100	1	no	Hall
24	C₂²×C₅²	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₁₃	—	3	1	no	—
26	C₃×C₅²	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented
27	C₅²⋊C₃	—	52	3	no	—
28	C₅×C₁₃	—	3	2	no	—
29	C₂²×C₃×C₅	—	3	2	no	—
30	C₂²×C₁₃	C₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅²	—	3	1	no	—
32	C₃×C₁₃	C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented
33	C₁₃⋊C₃	—	100	3	no	—
34	C₃×A₄	—	325	1	no	Hall
35	C₂×C₃×C₅	—	3	6	no	—
36	C₂×C₁₃	—	3	1	no	—
37	C₅²	C₃×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₅	—	3	2	no	—
39	C₃×C₅	—	3	2	no	—
40	C₁₃	C₃×C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₃	C₁₃⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented
42	A₄	—	325	3	no	—
43	C₂×C₅	—	3	6	no	—
44	C₃²	—	1300	1	no	Sylow
45	C₂×C₃	—	3	1	no	—
46	C₅	—	3	2	no	—
47	C₂²	C₃×C₁₃⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented, Sylow
48	C₃	—	1300	3	no	—
49	C₃	C₂²⋊(C₁₃⋊(C₅²⋊C₃))	1	1	yes	characteristic, direct product factor
50	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₂²⋊(C₁₃⋊(C₅²⋊C₃))
commutator, cosocle, hypocenter	C₂²×C₅²×C₁₃	C₃²
Frattini	C₁	G
Fitting, socle	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
1. C₂²⋊(C₁₃⋊(C₅²⋊C₃))	C₃	direct (N × H)
2. C₂²×C₃×C₅²×C₁₃	C₃	semidirect
5. C₂²×C₅²×C₁₃	C₃²	semidirect
6. C₃×C₅²×C₁₃	A₄	semidirect
13. C₅²×C₁₃	C₃×A₄	semidirect
14. C₂²×C₃×C₅²	C₁₃⋊C₃	semidirect
19. C₂²×C₃×C₁₃	C₅²⋊C₃	semidirect
24. C₂²×C₅²	C₃×C₁₃⋊C₃	semidirect
26. C₃×C₅²	C₂²⋊(C₁₃⋊C₃)	semidirect
30. C₂²×C₁₃	C₃×C₅²⋊C₃	semidirect
32. C₃×C₁₃	C₂²⋊(C₅²⋊C₃)	semidirect
37. C₅²	C₃×C₂²⋊(C₁₃⋊C₃)	semidirect
40. C₁₃	C₃×C₂²⋊(C₅²⋊C₃)	semidirect
41. C₂²×C₃	C₁₃⋊(C₅²⋊C₃)	semidirect
47. C₂²	C₃×C₁₃⋊(C₅²⋊C₃)	semidirect
49. C₃	C₂²⋊(C₁₃⋊(C₅²⋊C₃))	direct (N × H)

Maximal subgroups

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

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

Subgroups — C3×C22⋊(C13⋊(C52⋊C3)) #26043860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂²⋊(C₁₃⋊(C₅²⋊C₃)) #26043860