Subgroups — C₃⋊(C₃⋊(C₃₁⋊AGL(1,𝔽₅))) #19150151

Order 5580.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₅×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃₁⋊AGL(1,𝔽₅))	—	3	4	no	maximal
3	C₃²×C₅×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊Dic₉₃	—	5	1	no	maximal, Hall
5	C₃×D₅×C₃₁	D₃	1	4	yes	—
6	C₃₁⋊AGL(1,𝔽₅)	—	9	1	no	Hall
7	C₂×C₃²×C₃₁	—	5	1	no	—
8	C₃×C₅×C₃₁	Dic₃	1	4	yes	complemented
9	Dic₉₃	—	15	4	no	—
10	D₅×C₃₁	C₃⋊D₃	1	1	yes	characteristic
11	C₃²×C₃₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₃₁	—	5	4	no	—
13	C₃⋊ΓL(1,𝔽₁₆)	—	31	1	no	maximal, Hall
14	C₅×C₃₁	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
15	Dic₃₁	—	45	1	no	Hall
16	C₃×C₃₁	ΓL(1,𝔽₁₆)	1	4	yes	complemented
17	C₃²×D₅	D₃₁	1	1	yes	characteristic
18	C₂×C₃₁	—	5	1	no	—
19	ΓL(1,𝔽₁₆)	—	93	4	no	—
20	C₃²×C₅	Dic₃₁	1	1	yes	characteristic, complemented, Hall
21	C₃⋊Dic₃	—	155	1	no	Hall
22	C₃₁	C₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
23	C₃×D₅	D₉₃	1	4	yes	—
24	AGL(1,𝔽₅)	—	279	1	no	Hall
25	C₂×C₃²	—	5	1	no	—
26	C₃×C₅	Dic₉₃	1	4	yes	complemented
27	Dic₃	—	465	4	no	—
28	D₅	C₃⋊D₉₃	1	1	yes	characteristic
29	C₃²	C₃₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	—	5	4	no	—
31	C₅	C₃⋊Dic₉₃	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	1395	1	no	Sylow
33	C₃	C₃⋊(C₃₁⋊AGL(1,𝔽₅))	1	4	yes	complemented
34	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₃₁	C₄
LCS	G ▷ C₃²×C₅×C₃₁
UCS	C₁

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