Subgroups — C₅×D₂₃₁ #14556331

Order 2310.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₇₇	—	3	1	no	maximal, Hall
3	D₂₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₁₁	D₃	1	1	yes	characteristic, complemented, Hall
5	C₅×D₃₃	—	7	1	no	maximal, Hall
6	C₃×C₇×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×D₂₁	—	11	1	no	maximal, Hall
8	C₃×C₅×C₁₁	D₇	1	1	yes	characteristic, complemented, Hall
9	D₇₇	—	3	1	no	Hall
10	C₅×D₁₁	—	21	1	no	Hall
11	C₃×C₅×C₇	D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₁	C₅×D₃	1	1	yes	characteristic, complemented, Hall
13	C₅×D₇	—	33	1	no	Hall
14	D₃₃	—	7	1	no	Hall
15	C₅×C₁₁	D₂₁	1	1	yes	characteristic, complemented, Hall
16	D₂₁	—	11	1	no	Hall
17	C₅×C₇	D₃₃	1	1	yes	characteristic, complemented, Hall
18	C₃×C₁₁	C₅×D₇	1	1	yes	characteristic, complemented, Hall
19	C₅×D₃	—	77	1	no	Hall
20	D₁₁	—	21	1	no	Hall
21	C₃×C₇	C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
22	C₃×C₅	D₇₇	1	1	yes	characteristic, complemented, Hall
23	D₇	—	33	1	no	Hall
24	C₁₁	C₅×D₂₁	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅	—	231	1	no	Hall
26	C₇	C₅×D₃₃	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	77	1	no	Hall
28	C₅	D₂₃₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×D₇₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	231	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₂₃₁
commutator, cosocle, hypocenter	C₃×C₇×C₁₁	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₁	C₂
LCS	G ▷ C₃×C₇×C₁₁
UCS	C₁ ◁ C₅

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.