Subgroups — C₃×D₃×C₂₅ #90641

Order 450.

27 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₃×C₂₅	—	3	1	no	maximal
3	D₃×C₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×C₅×D₃	C₅	1	1	yes	maximal, characteristic
5	C₃×C₂₅	—	2	1	no	—
6	C₃×C₂₅	D₃	1	1	yes	characteristic, direct product factor
7	C₃×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₂₅	—	3	1	no	Hall
9	C₃²×C₅	C₂×C₅	1	1	yes	characteristic
10	C₂×C₃×C₅	—	3	1	no	—
11	C₅×D₃	C₃×C₅	1	1	yes	characteristic
12	C₂₅	C₃×D₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×D₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₅	—	2	1	no	—
15	C₃×C₅	C₅×D₃	1	1	yes	characteristic
16	C₃×C₅	C₂×C₃×C₅	1	1	yes	characteristic
17	C₂×C₅	—	3	1	no	—
18	C₃²	C₂×C₂₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	3	1	no	—
20	D₃	C₃×C₂₅	1	1	yes	characteristic, direct product factor
21	C₅	C₃×C₅×D₃	1	1	yes	characteristic
22	C₃	—	2	1	no	—
23	C₃	D₃×C₂₅	1	1	yes	characteristic, direct product factor
24	C₃	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented
25	C₂	—	3	1	no	Sylow

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.