Subgroups — C₃₁⋊C₃×#1035 #22604751

Order 9300.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₅×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#1035	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₅×C₃₁⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	AGL(1,𝔽₅)×C₃₁⋊C₃	—	5	1	no	maximal
5	C₃₁×D₂₅	C₂×C₃	1	1	yes	characteristic
6	D₅×C₃₁⋊C₃	—	5	1	no	—
7	C₂₅×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	AGL(1,𝔽₅)×C₃₁	—	5	1	no	—
9	C₅×C₃₁⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic
10	C₄×C₃₁⋊C₃	—	25	1	no	Hall
11	D₅×C₃₁	—	5	1	no	—
12	C₃×#1035	—	31	1	no	maximal, Hall
13	C₂×C₃₁⋊C₃	—	25	1	no	—
14	C₅×C₃₁	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
15	C₃×D₂₅	—	31	1	no	—
16	C₄×C₃₁	—	25	1	no	Hall
17	#1035	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
18	C₃₁⋊C₃	#1035	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₂₅	—	31	1	no	Hall
20	C₂×C₃₁	—	25	1	no	—
21	C₃×AGL(1,𝔽₅)	—	155	1	no	—
22	D₂₅	C₂×C₃₁⋊C₃	1	1	yes	characteristic
23	C₃₁	C₃×#1035	1	1	yes	characteristic, complemented, Sylow
24	C₃×D₅	—	155	1	no	—
25	C₂₅	C₄×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	5	1	no	—
27	C₃×C₅	—	31	1	no	—
28	C₃×C₄	—	775	1	no	Hall
29	D₅	—	5	1	no	—
30	C₂×C₃	—	775	1	no	—
31	C₅	AGL(1,𝔽₅)×C₃₁⋊C₃	1	1	yes	characteristic
32	C₄	—	25	1	no	Sylow
33	C₃	—	31	1	no	Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₂₅×C₃₁	C₃×C₄
Frattini	C₅	AGL(1,𝔽₅)×C₃₁⋊C₃
socle	C₅×C₃₁	C₃×AGL(1,𝔽₅)
LCS	G ▷ C₂₅×C₃₁
UCS	C₁

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