Subgroups — C₅×#157×C₁₃₁ #37556097

Order 23580.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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.