Subgroups — C₃×C₅×A₅ #11744676

Order 900.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×A₅	C₃	1	1	yes	maximal, characteristic, direct product factor
2	C₃×C₅×A₄	—	5	1	no	maximal
3	C₃×A₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₃×C₅×D₅	—	6	1	no	maximal
5	C₃×C₅×D₃	—	10	1	no	maximal
6	C₃×C₅²	—	6	1	no	—
7	C₂²×C₃×C₅	—	5	1	no	—
8	C₅×A₄	—	5	1	no	—
9	C₅×A₄	—	5	2	no	—
10	A₅	C₃×C₅	1	1	yes	characteristic, direct product factor
11	C₅×D₅	—	6	1	no	—
12	C₃²×C₅	—	10	1	no	—
13	C₃×A₄	—	5	1	no	Hall
14	C₂×C₃×C₅	—	15	1	no	—
15	C₃×D₅	—	6	1	no	—
16	C₅×D₃	—	10	1	no	—
17	C₅²	—	6	1	no	Sylow
18	C₂²×C₅	—	5	1	no	—
19	C₃×D₃	—	10	1	no	—
20	C₃×C₅	—	6	1	no	—
21	C₃×C₅	—	10	1	no	—
22	C₃×C₅	—	12	2	no	—
23	C₃×C₅	—	20	1	no	—
24	C₃×C₅	A₅	1	1	yes	maximal normal, characteristic, direct product factor
25	C₂²×C₃	—	5	1	no	—
26	A₄	—	5	1	no	—
27	A₄	—	5	2	no	—
28	C₂×C₅	—	15	1	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	—
34	C₅	—	12	2	no	—
35	C₅	C₃×A₅	1	1	yes	characteristic, direct product factor
36	C₂²	—	5	1	no	Sylow
37	C₃	—	10	1	no	—
38	C₃	—	20	1	no	—
39	C₃	C₅×A₅	1	1	yes	characteristic, direct product factor
40	C₂	—	15	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.