Subgroups — #10597029

Order 600.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₀₀	—	3	1	no	maximal, Hall
5	C₂×C₃×C₂₅	C₂²	1	1	yes	characteristic
6	D₇₅	—	2	1	no	—
7	C₃×D₂₅	—	2	1	no	—
8	#1202	—	5	1	no	maximal
9	C₂×D₂₅	—	3	1	no	—
10	C₂×D₂₅	D₃	1	1	yes	characteristic, complemented
11	C₄×C₂₅	—	3	1	no	—
12	C₃×C₂₅	D₄	1	1	yes	characteristic, complemented, Hall
13	C₂×D₁₅	—	5	1	no	—
14	C₂×C₃×D₅	—	5	1	no	—
15	C₅×Dic₃	D₅	1	1	yes	characteristic
16	C₂×C₂₅	C₂×D₃	1	1	yes	characteristic
17	D₂₅	—	2	1	no	—
18	D₂₅	—	6	1	no	—
19	D₂₀	—	15	1	no	—
20	C₂×C₃×C₅	C₂×D₅	1	1	yes	characteristic
21	D₁₅	—	10	1	no	—
22	C₃×D₅	—	10	1	no	—
23	C₂₅	#67	1	1	yes	characteristic, complemented, Sylow
24	#67	—	25	1	no	Hall
25	C₂×D₅	—	5	1	no	—
26	C₂×D₅	—	15	1	no	—
27	C₄×C₅	—	3	1	no	—
28	C₃×C₅	D₂₀	1	1	yes	characteristic
29	C₂²×C₃	—	25	1	no	—
30	C₂×D₃	—	25	1	no	—
31	Dic₃	D₂₅	1	1	yes	characteristic, complemented
32	C₂×C₅	D₃×D₅	1	1	yes	characteristic
33	D₅	—	10	1	no	—
34	D₅	—	30	1	no	—
35	D₄	—	75	1	no	Sylow
36	C₂×C₃	—	50	1	no	—
37	C₂×C₃	C₂×D₂₅	1	1	yes	characteristic
38	D₃	—	50	1	no	—
39	C₅	#1202	1	1	yes	characteristic
40	C₂²	—	25	1	no	—
41	C₂²	—	75	1	no	—
42	C₄	—	3	1	no	—
43	C₃	D₁₀₀	1	1	yes	characteristic, complemented, Sylow
44	C₂	—	50	1	no	—
45	C₂	—	150	1	no	—
46	C₂	D₃×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.