Subgroups — C₃×D₁₀₀ #10597036

Order 600.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₂₅	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₀₀	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₂₅	C₂²	1	1	yes	characteristic
5	C₃×D₂₅	—	2	2	no	—
6	C₃×D₂₀	—	5	1	no	maximal
7	C₂×D₂₅	C₂×C₃	1	2	yes	complemented
8	C₄×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×C₂₅	D₄	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×D₅	—	5	2	no	—
11	C₃×C₄×C₅	D₅	1	1	yes	characteristic
12	C₂×C₂₅	C₂²×C₃	1	1	yes	characteristic
13	D₂₅	—	2	2	no	—
14	D₂₀	—	5	1	no	—
15	C₂×C₃×C₅	C₂×D₅	1	1	yes	characteristic
16	C₃×D₅	—	10	2	no	—
17	C₂₅	C₃×D₄	1	1	yes	characteristic, complemented, Sylow
18	C₃×D₄	—	25	1	no	Hall
19	C₂×D₅	—	5	2	no	—
20	C₄×C₅	C₃×D₅	1	1	yes	characteristic
21	C₃×C₅	D₂₀	1	1	yes	characteristic
22	C₂²×C₃	—	25	2	no	—
23	C₃×C₄	D₂₅	1	1	yes	characteristic, complemented
24	C₂×C₅	C₂×C₃×D₅	1	1	yes	characteristic
25	D₅	—	10	2	no	—
26	D₄	—	25	1	no	Sylow
27	C₂×C₃	—	50	2	no	—
28	C₂×C₃	C₂×D₂₅	1	1	yes	characteristic
29	C₅	C₃×D₂₀	1	1	yes	characteristic
30	C₂²	—	25	2	no	—
31	C₄	C₃×D₂₅	1	1	yes	characteristic, complemented
32	C₃	D₁₀₀	1	1	yes	characteristic, direct product factor, Sylow
33	C₂	—	50	2	no	—
34	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.