Subgroups — A₅×C₃₁⋊C₃ #19150188

Order 5580.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×A₅	C₃	1	1	yes	maximal, characteristic, complemented
2	A₄×C₃₁⋊C₃	—	5	1	no	maximal, Hall
3	D₅×C₃₁⋊C₃	—	6	1	no	maximal
4	D₃×C₃₁⋊C₃	—	10	1	no	maximal
5	C₅×C₃₁⋊C₃	—	6	1	no	—
6	C₂²⋊(C₃₁⋊C₃)	—	5	2	no	—
7	A₄×C₃₁	—	5	1	no	—
8	C₂²×C₃₁⋊C₃	—	5	1	no	—
9	D₅×C₃₁	—	6	1	no	—
10	C₃×C₃₁⋊C₃	—	10	1	no	Hall
11	D₃×C₃₁	—	10	1	no	—
12	C₂×C₃₁⋊C₃	—	15	1	no	—
13	C₃×A₅	—	31	1	no	maximal, Hall
14	C₅×C₃₁	—	6	1	no	Hall
15	C₂²×C₃₁	—	5	1	no	Hall
16	C₃×C₃₁	—	10	1	no	—
17	C₃₁⋊C₃	—	20	1	no	—
18	C₃₁⋊C₃	A₅	1	1	yes	maximal normal, characteristic, direct product factor
19	C₂×C₃₁	—	15	1	no	—
20	A₅	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
21	C₃×A₄	—	155	1	no	Hall
22	C₃₁	C₃×A₅	1	1	yes	characteristic, complemented, Sylow
23	C₃×D₅	—	186	1	no	—
24	C₃×D₃	—	310	1	no	—
25	C₃×C₅	—	186	1	no	—
26	C₂²×C₃	—	155	1	no	—
27	A₄	—	5	1	no	—
28	A₄	—	155	2	no	—
29	D₅	—	6	1	no	—
30	C₃²	—	310	1	no	Sylow
31	C₂×C₃	—	465	1	no	—
32	D₃	—	10	1	no	—
33	C₅	—	6	1	no	Sylow
34	C₂²	—	5	1	no	Sylow
35	C₃	—	10	1	no	—
36	C₃	—	31	1	no	—
37	C₃	—	620	1	no	—
38	C₂	—	15	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	C₃₁×A₅	C₃
Fitting	C₃₁	C₃×A₅
LCS	G ▷ C₃₁×A₅
UCS	C₁

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