Subgroups — (C₅⋊D₅)⋊(C₁₁⋊D₁₁) #27130995

Order 12100.

336 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₅⋊(C₁₁⋊D₁₁)	C₂	1	2	yes	maximal, complemented
3	C₅²×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₅×C₁₁⋊D₁₁	—	5	2	no	maximal
5	C₅⋊(C₁₁⋊D₁₁)	D₅	1	2	yes	complemented
6	D₅×C₁₁²	—	5	2	no	—
7	D₅×C₁₁²	—	10	2	no	—
8	C₅×C₁₁⋊D₁₁	—	5	2	no	—
9	(C₅⋊D₅)⋊D₁₁	—	11	12	no	maximal
10	C₅×C₁₁²	—	2	2	no	—
11	C₅×C₁₁²	C₂×D₅	1	2	yes	complemented
12	C₁₁×C₅⋊D₅	D₁₁	1	12	yes	complemented
13	C₅×D₅₅	—	11	24	no	—
14	C₂×C₁₁⋊D₁₁	—	25	1	no	Hall
15	C₅²×C₁₁	C₂×D₁₁	1	12	yes	complemented
16	C₂×C₁₁²	—	25	1	no	—
17	C₁₁⋊D₁₁	—	5	2	no	—
18	D₅×D₁₁	—	55	24	no	—
19	C₁₁²	D₅²	1	1	yes	characteristic, complemented, Sylow
20	D₅₅	—	11	24	no	—
21	C₅×D₁₁	—	55	24	no	—
22	D₅×C₁₁	—	5	24	no	—
23	D₅×C₁₁	—	10	24	no	—
24	D₅²	—	121	1	no	Hall
25	C₅×C₁₁	—	2	24	no	—
26	C₅×C₁₁	D₅×D₁₁	1	24	yes	complemented
27	C₅⋊D₅	C₁₁⋊D₁₁	1	1	yes	characteristic, complemented
28	C₅×D₅	—	121	2	no	—
29	C₂×D₁₁	—	275	12	no	—
30	C₅²	C₂×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₁₁	—	25	12	no	—
32	D₁₁	—	55	24	no	—
33	C₂×D₅	—	605	2	no	—
34	C₁₁	(C₅⋊D₅)⋊D₁₁	1	12	yes	complemented
35	C₂×C₅	—	605	2	no	—
36	D₅	—	5	2	no	—
37	D₅	—	10	2	no	—
38	D₅	—	121	2	no	—
39	C₅	—	2	2	no	—
40	C₅	D₅×C₁₁⋊D₁₁	1	2	yes	complemented
41	C₂²	—	3025	1	no	Sylow
42	C₂	—	25	1	no	—
43	C₂	—	605	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₁₁²	C₂²
LCS	G ▷ C₅²×C₁₁²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₁²×C₅⋊D₅	C₂	semidirect
2. C₅×C₅⋊(C₁₁⋊D₁₁)	C₂	semidirect
3. C₅²×C₁₁²	C₂²	semidirect
5. C₅⋊(C₁₁⋊D₁₁)	D₅	semidirect
11. C₅×C₁₁²	C₂×D₅	semidirect
12. C₁₁×C₅⋊D₅	D₁₁	semidirect
15. C₅²×C₁₁	C₂×D₁₁	semidirect
19. C₁₁²	D₅²	semidirect
26. C₅×C₁₁	D₅×D₁₁	semidirect
27. C₅⋊D₅	C₁₁⋊D₁₁	semidirect
30. C₅²	C₂×C₁₁⋊D₁₁	semidirect
34. C₁₁	(C₅⋊D₅)⋊D₁₁	semidirect
40. C₅	D₅×C₁₁⋊D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₁²×C₅⋊D₅	2
C₅×C₅⋊(C₁₁⋊D₁₁)	2
D₅×C₁₁⋊D₁₁	5
(C₅⋊D₅)⋊D₁₁	11

Subgroups — (C5⋊D5)⋊(C11⋊D11) #27130995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₅⋊D₅)⋊(C₁₁⋊D₁₁) #27130995