Subgroups — C₇²×C₁₁×AGL(1,𝔽₅) #24924763

Order 10780.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₅×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇²×C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₇²×C₁₁	—	5	1	no	maximal, Hall
4	C₇×C₁₁×AGL(1,𝔽₅)	C₇	1	8	yes	maximal, direct product factor
5	C₂×C₇²×C₁₁	—	5	1	no	—
6	C₇²×AGL(1,𝔽₅)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×D₅×C₁₁	C₂×C₇	1	8	yes	—
8	C₇²×C₁₁	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
9	C₇²×D₅	C₂×C₁₁	1	1	yes	characteristic
10	C₅×C₇×C₁₁	C₄×C₇	1	8	yes	complemented
11	C₄×C₇×C₁₁	—	5	8	no	—
12	C₅×C₇²	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₁₁×AGL(1,𝔽₅)	C₇²	1	1	yes	characteristic, direct product factor, Hall
14	C₄×C₇²	—	5	1	no	Hall
15	C₂×C₇×C₁₁	—	5	8	no	—
16	C₇×AGL(1,𝔽₅)	C₇×C₁₁	1	8	yes	direct product factor
17	D₅×C₁₁	C₂×C₇²	1	1	yes	characteristic
18	C₂×C₇²	—	5	1	no	—
19	C₇×C₁₁	C₇×AGL(1,𝔽₅)	1	8	yes	direct product factor
20	C₇×D₅	C₂×C₇×C₁₁	1	8	yes	—
21	C₅×C₁₁	C₄×C₇²	1	1	yes	characteristic, complemented, Hall
22	C₇²	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
23	C₄×C₁₁	—	5	1	no	Hall
24	C₅×C₇	C₄×C₇×C₁₁	1	8	yes	complemented
25	C₄×C₇	—	5	8	no	—
26	C₂×C₁₁	—	5	1	no	—
27	AGL(1,𝔽₅)	C₇²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₇	—	5	8	no	—
29	C₁₁	C₇²×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
30	D₅	C₂×C₇²×C₁₁	1	1	yes	characteristic
31	C₇	C₇×C₁₁×AGL(1,𝔽₅)	1	8	yes	direct product factor
32	C₅	C₄×C₇²×C₁₁	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	5	1	no	Sylow
34	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₇²×C₁₁	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₄×C₇²×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₁	C₄
prime radical	C₇²×D₅×C₁₁	C₂
cosocle	D₅	C₂×C₇²×C₁₁
LCS	G ▷ C₅
UCS	C₁ ◁ C₇²×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₅×C₇²×C₁₁	C₄	semidirect
4. C₇×C₁₁×AGL(1,𝔽₅)	C₇	direct (N × H)
6. C₇²×AGL(1,𝔽₅)	C₁₁	direct (N × H)
8. C₇²×C₁₁	AGL(1,𝔽₅)	direct (N × H)
10. C₅×C₇×C₁₁	C₄×C₇	semidirect
12. C₅×C₇²	C₄×C₁₁	semidirect
13. C₁₁×AGL(1,𝔽₅)	C₇²	direct (N × H)
16. C₇×AGL(1,𝔽₅)	C₇×C₁₁	direct (N × H)
19. C₇×C₁₁	C₇×AGL(1,𝔽₅)	direct (N × H)
21. C₅×C₁₁	C₄×C₇²	semidirect
22. C₇²	C₁₁×AGL(1,𝔽₅)	direct (N × H)
24. C₅×C₇	C₄×C₇×C₁₁	semidirect
27. AGL(1,𝔽₅)	C₇²×C₁₁	direct (N × H)
29. C₁₁	C₇²×AGL(1,𝔽₅)	direct (N × H)
31. C₇	C₇×C₁₁×AGL(1,𝔽₅)	direct (N × H)
32. C₅	C₄×C₇²×C₁₁	semidirect

Subgroups — C72×C11×AGL(1,𝔽5) #24924763

Conjugacy classes of subgroups

Complements

Subgroups — C₇²×C₁₁×AGL(1,𝔽₅) #24924763