Subgroups — D₃₀₀ #10597046

Order 600.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇₅	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₀₀	—	3	1	no	maximal, Hall
4	C₂×C₃×C₂₅	C₂²	1	1	yes	characteristic
5	D₇₅	—	2	2	no	—
6	D₆₀	—	5	1	no	maximal
7	C₂×D₂₅	—	3	2	no	—
8	C₄×C₂₅	D₃	1	1	yes	characteristic, complemented
9	C₃×C₂₅	D₄	1	1	yes	characteristic, complemented, Hall
10	C₂×D₁₅	—	5	2	no	—
11	C₃×C₄×C₅	D₅	1	1	yes	characteristic
12	C₂×C₂₅	C₂×D₃	1	1	yes	characteristic
13	D₂₅	—	6	2	no	—
14	D₂₀	—	15	1	no	—
15	C₂×C₃×C₅	C₂×D₅	1	1	yes	characteristic
16	D₁₅	—	10	2	no	—
17	C₂₅	D₁₂	1	1	yes	characteristic, complemented, Sylow
18	D₁₂	—	25	1	no	Hall
19	C₂×D₅	—	15	2	no	—
20	C₄×C₅	D₁₅	1	1	yes	characteristic
21	C₃×C₅	D₂₀	1	1	yes	characteristic
22	C₂×D₃	—	25	2	no	—
23	C₃×C₄	D₂₅	1	1	yes	characteristic, complemented
24	C₂×C₅	C₂×D₁₅	1	1	yes	characteristic
25	D₅	—	30	2	no	—
26	D₄	—	75	1	no	Sylow
27	C₂×C₃	C₂×D₂₅	1	1	yes	characteristic
28	D₃	—	50	2	no	—
29	C₅	D₆₀	1	1	yes	characteristic
30	C₂²	—	75	2	no	—
31	C₄	D₇₅	1	1	yes	characteristic, complemented
32	C₃	D₁₀₀	1	1	yes	characteristic, complemented, Sylow
33	C₂	—	150	2	no	—
34	C₂	C₂×D₇₅	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.