Subgroups — C₃×C₃₁×A₅ #19150187

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, direct product factor
2	C₃×A₄×C₃₁	—	5	1	no	maximal, Hall
3	C₃×D₅×C₃₁	—	6	1	no	maximal
4	C₃×D₃×C₃₁	—	10	1	no	maximal
5	C₃×C₅×C₃₁	—	6	1	no	—
6	C₂²×C₃×C₃₁	—	5	1	no	—
7	A₄×C₃₁	—	5	1	no	—
8	A₄×C₃₁	—	5	2	no	—
9	D₅×C₃₁	—	6	1	no	—
10	C₃²×C₃₁	—	10	1	no	Hall
11	C₂×C₃×C₃₁	—	15	1	no	—
12	D₃×C₃₁	—	10	1	no	—
13	C₃×A₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₅×C₃₁	—	6	1	no	Hall
15	C₂²×C₃₁	—	5	1	no	Hall
16	C₃×C₃₁	—	10	1	no	—
17	C₃×C₃₁	—	20	1	no	—
18	C₃×C₃₁	A₅	1	1	yes	maximal normal, characteristic, direct product factor
19	C₂×C₃₁	—	15	1	no	—
20	A₅	C₃×C₃₁	1	1	yes	characteristic, direct product factor
21	C₃×A₄	—	5	1	no	Hall
22	C₃₁	C₃×A₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×D₅	—	6	1	no	—
24	C₃×D₃	—	10	1	no	—
25	C₃×C₅	—	6	1	no	—
26	C₂²×C₃	—	5	1	no	—
27	A₄	—	5	1	no	—
28	A₄	—	5	2	no	—
29	D₅	—	6	1	no	—
30	C₃²	—	10	1	no	Sylow
31	C₂×C₃	—	15	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	—	20	1	no	—
37	C₃	C₃₁×A₅	1	1	yes	characteristic, direct product factor
38	C₂	—	15	1	no	—

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