Subgroups — C₇⋊(C₇⋊(C₁₁⋊AGL(1,𝔽₅))) #24924768

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	C₇⋊Dic₇₇	—	5	1	no	maximal, Hall
4	C₇⋊(C₁₁⋊AGL(1,𝔽₅))	—	7	8	no	maximal
5	C₂×C₇²×C₁₁	—	5	1	no	—
6	C₇⋊(C₇⋊AGL(1,𝔽₅))	—	11	1	no	maximal, Hall
7	C₇×D₅×C₁₁	D₇	1	8	yes	—
8	C₇²×C₁₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
9	C₇²×D₅	D₁₁	1	1	yes	characteristic
10	C₅×C₇×C₁₁	Dic₇	1	8	yes	complemented
11	Dic₇₇	—	35	8	no	—
12	C₅×C₇²	Dic₁₁	1	1	yes	characteristic, complemented, Hall
13	C₁₁⋊AGL(1,𝔽₅)	—	49	1	no	Hall
14	C₇⋊Dic₇	—	55	1	no	Hall
15	C₂×C₇×C₁₁	—	5	8	no	—
16	C₇⋊AGL(1,𝔽₅)	—	77	8	no	—
17	D₅×C₁₁	C₇⋊D₇	1	1	yes	characteristic
18	C₂×C₇²	—	5	1	no	—
19	C₇×C₁₁	C₇⋊AGL(1,𝔽₅)	1	8	yes	complemented
20	C₇×D₅	D₇₇	1	8	yes	—
21	C₅×C₁₁	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Hall
22	C₇²	C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
23	Dic₁₁	—	245	1	no	Hall
24	C₅×C₇	Dic₇₇	1	8	yes	complemented
25	Dic₇	—	385	8	no	—
26	C₂×C₁₁	—	5	1	no	—
27	AGL(1,𝔽₅)	—	539	1	no	Hall
28	C₂×C₇	—	5	8	no	—
29	C₁₁	C₇⋊(C₇⋊AGL(1,𝔽₅))	1	1	yes	characteristic, complemented, Sylow
30	D₅	C₇⋊D₇₇	1	1	yes	characteristic
31	C₇	C₇⋊(C₁₁⋊AGL(1,𝔽₅))	1	8	yes	complemented
32	C₅	C₇⋊Dic₇₇	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	2695	1	no	Sylow
34	C₂	—	5	1	no	—

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

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