Subgroups — (C₁₃₁⋊C₅)⋊#157 #37556083

Order 23580.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₁₃₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₃₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₃₁⋊#157	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	D₃×C₁₃₁⋊C₅	—	6	2	no	—
5	Dic₁₃₁⋊C₅	—	9	1	no	maximal, Hall
6	C₃⋊D₃×C₁₃₁	C₂×C₅	1	1	yes	characteristic
7	C₃×C₁₃₁⋊C₅	—	2	2	no	—
8	C₂×C₁₃₁⋊C₅	—	9	1	no	—
9	C₃²×C₁₃₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
10	D₃×C₁₃₁	—	6	2	no	—
11	C₁₃₁⋊C₅	#157	1	1	yes	characteristic, complemented, Hall
12	Dic₁₃₁	—	9	1	no	Hall
13	C₃×C₁₃₁	—	2	2	no	—
14	C₂×C₁₃₁	—	9	1	no	—
15	C₅×#157	—	131	1	no	maximal, Hall
16	C₁₃₁	C₅×#157	1	1	yes	characteristic, complemented, Sylow
17	C₅×C₃⋊D₃	—	131	1	no	—
18	C₃²×C₅	—	131	1	no	Hall
19	#157	—	655	1	no	Hall
20	C₅×D₃	—	786	2	no	—
21	C₄×C₅	—	1179	1	no	Hall
22	C₃⋊D₃	D₁₃₁⋊C₅	1	1	yes	characteristic
23	C₃×C₅	—	262	2	no	—
24	C₂×C₅	—	1179	1	no	—
25	C₃²	Dic₁₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
26	D₃	—	6	2	no	—
27	C₅	—	131	1	no	Sylow
28	C₄	—	5895	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₃₁	C₄×C₅
prime radical	C₃⋊D₃×C₁₃₁⋊C₅	C₂
cosocle	C₃⋊D₃×C₁₃₁	C₂×C₅
LCS	G ▷ C₃²×C₁₃₁
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.