Subgroups — C₃⋊(C₃₁⋊#1043) #22604911

Order 9300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₃₁⋊#1043	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃₁⋊AGL(1,𝔽₅))	—	5	6	no	maximal
5	C₃₁×C₅⋊D₅	D₃	1	1	yes	characteristic
6	C₃×D₅×C₃₁	—	5	6	no	—
7	C₅²×C₃₁	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₃₁⋊AGL(1,𝔽₅)	—	15	6	no	—
9	C₃×C₅×C₃₁	AGL(1,𝔽₅)	1	6	yes	complemented
10	Dic₉₃	—	25	1	no	Hall
11	D₅×C₃₁	—	5	6	no	—
12	C₃⋊#1043	—	31	1	no	maximal, Hall
13	C₂×C₃×C₃₁	—	25	1	no	—
14	C₅×C₃₁	ΓL(1,𝔽₁₆)	1	6	yes	complemented
15	C₃×C₅⋊D₅	D₃₁	1	1	yes	characteristic
16	Dic₃₁	—	75	1	no	Hall
17	#1043	—	93	1	no	Hall
18	C₃×C₃₁	#1043	1	1	yes	characteristic, complemented, Hall
19	C₃×C₅²	Dic₃₁	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃₁	—	25	1	no	—
21	ΓL(1,𝔽₁₆)	—	155	6	no	—
22	C₅⋊D₅	D₉₃	1	1	yes	characteristic
23	C₃₁	C₃⋊#1043	1	1	yes	characteristic, complemented, Sylow
24	C₃×D₅	—	5	6	no	—
25	C₅²	Dic₉₃	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	465	6	no	—
27	C₃×C₅	C₃₁⋊AGL(1,𝔽₅)	1	6	yes	complemented
28	Dic₃	—	775	1	no	Hall
29	D₅	—	5	6	no	—
30	C₂×C₃	—	25	1	no	—
31	C₅	C₃⋊(C₃₁⋊AGL(1,𝔽₅))	1	6	yes	complemented
32	C₄	—	2325	1	no	Sylow
33	C₃	C₃₁⋊#1043	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₃₁	C₄
LCS	G ▷ C₃×C₅²×C₃₁
UCS	C₁

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