Subgroups — #20269516⋊C₂ #27211849

Order 13420.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20269528	C₂	1	1	yes	maximal, characteristic, complemented
2	#20269522	C₂	1	1	yes	maximal, characteristic, complemented
3	#20269516	C₂	1	1	yes	maximal, characteristic, complemented
4	#16809823	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₁×D₆₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	D₆₇₁	C₂×C₅	1	1	yes	characteristic, complemented
7	C₁₁×D₆₁	C₂×C₅	1	1	yes	characteristic, complemented
8	D₁₁×C₆₁	C₂×C₅	1	1	yes	characteristic, complemented
9	C₂×D₆₁⋊C₅	—	11	1	no	maximal, Hall
10	C₁₁×C₆₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₆₁⋊C₅	—	11	1	no	—
12	D₆₁⋊C₅	—	11	1	no	—
13	D₆₁⋊C₅	—	11	1	no	—
14	C₆₁⋊C₅	—	11	1	no	Hall
15	C₂×D₆₁	—	11	1	no	Hall
16	C₂×AGL(1,𝔽₁₁)	—	61	1	no	maximal, Hall
17	C₂×C₆₁	—	11	1	no	—
18	D₆₁	—	11	1	no	—
19	D₆₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
20	C₂×C₁₁⋊C₅	—	61	1	no	—
21	AGL(1,𝔽₁₁)	—	61	1	no	—
22	AGL(1,𝔽₁₁)	—	61	1	no	—
23	C₆₁	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
24	C₁₁⋊C₅	—	61	1	no	Hall
25	C₂×D₁₁	—	61	1	no	Hall
26	C₂×C₁₁	—	61	1	no	—
27	D₁₁	—	61	1	no	—
28	D₁₁	D₆₁⋊C₅	1	1	yes	characteristic, complemented
29	C₂²×C₅	—	671	1	no	Hall
30	C₁₁	C₂×D₆₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	671	1	no	—
32	C₂×C₅	—	671	1	no	—
33	C₂×C₅	—	671	1	no	—
34	C₅	—	671	1	no	Sylow
35	C₂²	—	671	1	no	Sylow
36	C₂	—	11	1	no	—
37	C₂	—	61	1	no	—
38	C₂	—	671	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₆₁	C₂²×C₅
LCS	G ▷ C₁₁×C₆₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #20269528	C₂	semidirect
2. #20269522	C₂	semidirect
3. #20269516	C₂	semidirect
4. #16809823	C₂²	semidirect
5. D₁₁×D₆₁	C₅	semidirect
6. D₆₇₁	C₂×C₅	semidirect
7. C₁₁×D₆₁	C₂×C₅	semidirect
8. D₁₁×C₆₁	C₂×C₅	semidirect
10. C₁₁×C₆₁	C₂²×C₅	semidirect
19. D₆₁	AGL(1,𝔽₁₁)	semidirect
23. C₆₁	C₂×AGL(1,𝔽₁₁)	semidirect
28. D₁₁	D₆₁⋊C₅	semidirect
30. C₁₁	C₂×D₆₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
#20269528	2
#20269522	2
#20269516	2
D₁₁×D₆₁	5
C₂×D₆₁⋊C₅	11
C₂×AGL(1,𝔽₁₁)	61

Subgroups — #20269516⋊C2 #27211849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #20269516⋊C₂ #27211849