Subgroups — AGL(1,𝔽₅)×C₂₃²⋊C₃ #44540713

Order 31740.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₂₃²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	AGL(1,𝔽₅)×C₂₃²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₂₃²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄×C₂₃²⋊C₃	—	5	1	no	maximal, Hall
5	D₅×C₂₃²	C₂×C₃	1	1	yes	characteristic
6	C₂×C₂₃²⋊C₃	—	5	1	no	—
7	C₅×C₂₃²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₄×C₂₃²	—	5	1	no	Hall
9	C₂₃²⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₂₃²	—	5	1	no	—
11	C₂₃²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
12	AGL(1,𝔽₅)×C₂₃	—	3	8	no	—
13	D₅×C₂₃	—	3	8	no	—
14	C₅×C₂₃	—	3	8	no	—
15	C₄×C₂₃	—	15	8	no	—
16	C₃×AGL(1,𝔽₅)	—	529	1	no	maximal, Hall
17	C₂×C₂₃	—	15	8	no	—
18	C₃×D₅	—	529	1	no	—
19	C₂₃	—	3	8	no	—
20	AGL(1,𝔽₅)	C₂₃²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₅	—	529	1	no	Hall
22	C₃×C₄	—	2645	1	no	Hall
23	D₅	C₂×C₂₃²⋊C₃	1	1	yes	characteristic
24	C₂×C₃	—	2645	1	no	—
25	C₅	C₄×C₂₃²⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₄	—	5	1	no	Sylow
27	C₃	—	529	1	no	Sylow
28	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₂₃²	C₃×C₄
prime radical	D₅×C₂₃²⋊C₃	C₂
cosocle	D₅×C₂₃²	C₂×C₃
LCS	G ▷ C₅×C₂₃²
UCS	C₁

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

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