Subgroups — C₃×Dic₅₀ #10597034

Order 600.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₂₅	C₂	1	2	yes	maximal
3	Dic₅₀	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₂₅	C₂²	1	1	yes	characteristic
5	C₃×Dic₁₀	—	5	1	no	maximal
6	C₄×C₂₅	C₂×C₃	1	1	yes	characteristic
7	Dic₂₅	C₂×C₃	1	2	yes	—
8	C₃×C₂₅	Q₈	1	1	yes	characteristic, complemented, Hall
9	C₃×C₄×C₅	D₅	1	1	yes	characteristic
10	C₃×Dic₅	—	5	2	no	—
11	C₂×C₂₅	C₂²×C₃	1	1	yes	characteristic
12	Dic₁₀	—	5	1	no	—
13	C₂×C₃×C₅	C₂×D₅	1	1	yes	characteristic
14	C₂₅	C₃×Q₈	1	1	yes	characteristic, complemented, Sylow
15	C₃×Q₈	—	25	1	no	Hall
16	C₄×C₅	C₃×D₅	1	1	yes	characteristic
17	Dic₅	—	5	2	no	—
18	C₃×C₅	Dic₁₀	1	1	yes	characteristic
19	C₃×C₄	—	25	2	no	—
20	C₃×C₄	D₂₅	1	1	yes	characteristic
21	C₂×C₅	C₂×C₃×D₅	1	1	yes	characteristic
22	Q₈	—	25	1	no	Sylow
23	C₂×C₃	C₂×D₂₅	1	1	yes	characteristic
24	C₅	C₃×Dic₁₀	1	1	yes	characteristic
25	C₄	—	25	2	no	—
26	C₄	C₃×D₂₅	1	1	yes	characteristic
27	C₃	Dic₅₀	1	1	yes	characteristic, direct product factor, Sylow
28	C₂	C₂×C₃×D₂₅	1	1	yes	characteristic

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.