Subgroups — #21462835⋊C₂ #30626804

Order 15620.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21462847	C₂	1	1	yes	maximal, characteristic, complemented
2	#21462841	C₂	1	1	yes	maximal, characteristic, complemented
3	#21462835	C₂	1	1	yes	maximal, characteristic, complemented
4	#16840848	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₁×D₇₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	D₇₈₁	C₂×C₅	1	1	yes	characteristic, complemented
7	C₁₁×D₇₁	C₂×C₅	1	1	yes	characteristic, complemented
8	D₁₁×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented
9	C₂×D₇₁⋊C₅	—	11	1	no	maximal, Hall
10	C₁₁×C₇₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₇₁⋊C₅	—	11	1	no	—
12	D₇₁⋊C₅	—	11	1	no	—
13	D₇₁⋊C₅	—	11	1	no	—
14	C₇₁⋊C₅	—	11	1	no	Hall
15	C₂×D₇₁	—	55	1	no	Hall
16	C₂×AGL(1,𝔽₁₁)	—	71	1	no	maximal, Hall
17	C₂×C₇₁	—	11	1	no	—
18	D₇₁	—	55	1	no	—
19	D₇₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
20	C₂×C₁₁⋊C₅	—	71	1	no	—
21	AGL(1,𝔽₁₁)	—	71	1	no	—
22	AGL(1,𝔽₁₁)	—	71	1	no	—
23	C₇₁	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
24	C₁₁⋊C₅	—	71	1	no	Hall
25	C₂×D₁₁	—	355	1	no	Hall
26	C₂×C₁₁	—	355	1	no	—
27	D₁₁	—	355	1	no	—
28	D₁₁	D₇₁⋊C₅	1	1	yes	characteristic, complemented
29	C₂²×C₅	—	781	1	no	Hall
30	C₁₁	C₂×D₇₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	781	1	no	—
32	C₂×C₅	—	781	1	no	—
33	C₂×C₅	—	781	1	no	—
34	C₅	—	781	1	no	Sylow
35	C₂²	—	3905	1	no	Sylow
36	C₂	—	55	1	no	—
37	C₂	—	3905	1	no	—
38	C₂	—	355	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₇₁	C₂²×C₅
LCS	G ▷ C₁₁×C₇₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #21462847	C₂	semidirect
2. #21462841	C₂	semidirect
3. #21462835	C₂	semidirect
4. #16840848	C₂²	semidirect
5. D₁₁×D₇₁	C₅	semidirect
6. D₇₈₁	C₂×C₅	semidirect
7. C₁₁×D₇₁	C₂×C₅	semidirect
8. D₁₁×C₇₁	C₂×C₅	semidirect
10. C₁₁×C₇₁	C₂²×C₅	semidirect
19. D₇₁	AGL(1,𝔽₁₁)	semidirect
23. C₇₁	C₂×AGL(1,𝔽₁₁)	semidirect
28. D₁₁	D₇₁⋊C₅	semidirect
30. C₁₁	C₂×D₇₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
#21462847	2
#21462841	2
#21462835	2
D₁₁×D₇₁	5
C₂×D₇₁⋊C₅	11
C₂×AGL(1,𝔽₁₁)	71

Subgroups — #21462835⋊C2 #30626804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #21462835⋊C₂ #30626804