Subgroups — C₃⋊(C₁₇₉⋊AGL(1,𝔽₅)) #24924403

Order 10740.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₁₇₉	C₂	1	1	yes	maximal, characteristic
2	C₁₇₉⋊AGL(1,𝔽₅)	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₇₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₅₃₇	—	5	1	no	maximal, Hall
5	D₅×C₁₇₉	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₇₉	—	5	1	no	—
7	C₅×C₁₇₉	Dic₃	1	1	yes	characteristic, complemented, Hall
8	Dic₁₇₉	—	15	1	no	Hall
9	C₃×C₁₇₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₇₉	—	5	1	no	—
11	C₁₇₉	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
12	ΓL(1,𝔽₁₆)	—	179	1	no	maximal, Hall
13	C₃×D₅	D₁₇₉	1	1	yes	characteristic
14	AGL(1,𝔽₅)	—	537	1	no	Hall
15	C₃×C₅	Dic₁₇₉	1	1	yes	characteristic, complemented, Hall
16	Dic₃	—	895	1	no	Hall
17	D₅	D₅₃₇	1	1	yes	characteristic
18	C₂×C₃	—	5	1	no	—
19	C₅	Dic₅₃₇	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	2685	1	no	Sylow
21	C₃	C₁₇₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₁₇₉	C₄
prime radical, cosocle	C₃×D₅×C₁₇₉	C₂
LCS	G ▷ C₃×C₅×C₁₇₉
UCS	C₁

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