Subgroups — (C₂²⋊(C₁₃⋊C₃))⋊(C₅²⋊C₃) #26043687

Order 11700.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊(C₁₃⋊(C₅²⋊C₃))	C₃	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₂²⋊(C₅²⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₂²⋊(C₁₃⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃⋊(C₅²⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
5	C₁₃⋊C₃×C₅²⋊C₃	—	4	1	no	maximal, Hall
6	C₂×C₁₃⋊(C₅²⋊C₃)	—	3	1	no	—
7	C₂²×C₅²×C₁₃	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₁₃⋊(C₅²⋊C₃)	—	4	1	no	—
9	C₁₃⋊(C₅²⋊C₃)	A₄	1	1	yes	characteristic, complemented
10	C₁₃×C₅²⋊C₃	—	4	1	no	—
11	C₅²×C₁₃⋊C₃	—	4	1	no	—
12	A₄×C₅²⋊C₃	—	13	1	no	maximal, Hall
13	C₅×C₂²⋊(C₁₃⋊C₃)	—	3	2	no	—
14	C₂×C₅²×C₁₃	—	3	1	no	—
15	A₄×C₁₃⋊C₃	—	25	1	no	maximal, Hall
16	C₅²×C₁₃	C₃×A₄	1	1	yes	characteristic, complemented, Hall
17	C₂²⋊(C₅²⋊C₃)	—	13	1	no	—
18	C₂²⋊(C₅²⋊C₃)	C₁₃⋊C₃	1	1	yes	characteristic, complemented
19	C₅²×A₄	—	13	1	no	—
20	C₂²×C₅²⋊C₃	—	13	1	no	—
21	C₂²×C₅×C₁₃	—	3	2	no	—
22	C₃×C₅²⋊C₃	—	52	1	no	Hall
23	C₅×C₁₃⋊C₃	—	12	2	no	—
24	C₂²⋊(C₁₃⋊C₃)	—	25	1	no	—
25	C₂²⋊(C₁₃⋊C₃)	C₅²⋊C₃	1	1	yes	characteristic, complemented
26	A₄×C₁₃	—	25	1	no	—
27	C₂²×C₁₃⋊C₃	—	25	1	no	—
28	C₂×C₅²⋊C₃	—	39	1	no	—
29	C₂×C₅×C₁₃	—	9	2	no	—
30	C₃×C₁₃⋊C₃	—	100	1	no	Hall
31	C₂²×C₅²	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
32	C₂×C₁₃⋊C₃	—	75	1	no	—
33	C₃×C₅²	—	52	1	no	—
34	C₅²⋊C₃	—	4	1	no	—
35	C₅²⋊C₃	—	13	1	no	—
36	C₅²⋊C₃	—	52	1	no	—
37	C₅×C₁₃	—	3	2	no	—
38	C₅×A₄	—	39	2	no	—
39	C₂²×C₁₃	C₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
40	C₂×C₅²	—	3	1	no	—
41	C₃×C₁₃	—	100	1	no	—
42	C₁₃⋊C₃	—	4	1	no	—
43	C₁₃⋊C₃	—	25	1	no	—
44	C₁₃⋊C₃	—	100	1	no	—
45	C₃×A₄	—	325	1	no	Hall
46	C₂×C₁₃	—	3	1	no	—
47	C₅²	A₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₅	—	3	2	no	—
49	C₃×C₅	—	156	2	no	—
50	C₁₃	A₄×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₃	—	325	1	no	—
52	A₄	—	13	1	no	—
53	A₄	—	25	1	no	—
54	A₄	—	325	1	no	—
55	C₂×C₅	—	9	2	no	—
56	C₃²	—	1300	1	no	Sylow
57	C₂×C₃	—	975	1	no	—
58	C₅	—	3	2	no	—
59	C₂²	C₁₃⋊C₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
60	C₃	—	1300	1	no	—
61	C₃	—	52	1	no	—
62	C₃	—	325	1	no	—
63	C₃	—	100	1	no	—
64	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₅²×C₁₃	C₃²
LCS	G ▷ C₂²×C₅²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂²⋊(C₁₃⋊(C₅²⋊C₃))	C₃	semidirect
2. C₁₃×C₂²⋊(C₅²⋊C₃)	C₃	semidirect
3. C₅²×C₂²⋊(C₁₃⋊C₃)	C₃	semidirect
4. C₂²×C₁₃⋊(C₅²⋊C₃)	C₃	semidirect
7. C₂²×C₅²×C₁₃	C₃²	semidirect
9. C₁₃⋊(C₅²⋊C₃)	A₄	semidirect
16. C₅²×C₁₃	C₃×A₄	semidirect
18. C₂²⋊(C₅²⋊C₃)	C₁₃⋊C₃	semidirect
25. C₂²⋊(C₁₃⋊C₃)	C₅²⋊C₃	semidirect
31. C₂²×C₅²	C₃×C₁₃⋊C₃	semidirect
39. C₂²×C₁₃	C₃×C₅²⋊C₃	semidirect
47. C₅²	A₄×C₁₃⋊C₃	semidirect
50. C₁₃	A₄×C₅²⋊C₃	semidirect
59. C₂²	C₁₃⋊C₃×C₅²⋊C₃	semidirect

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
C₁₃×C₂²⋊(C₅²⋊C₃)	3
C₅²×C₂²⋊(C₁₃⋊C₃)	3
C₂²×C₁₃⋊(C₅²⋊C₃)	3
C₁₃⋊C₃×C₅²⋊C₃	4
A₄×C₅²⋊C₃	13
A₄×C₁₃⋊C₃	25

Subgroups — (C22⋊(C13⋊C3))⋊(C52⋊C3) #26043687

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂²⋊(C₁₃⋊C₃))⋊(C₅²⋊C₃) #26043687