Subgroups — #10597026

Order 600.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₇₅	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₂₅	C₂	1	1	yes	maximal, characteristic
3	Dic₃×C₂₅	C₂	1	1	yes	maximal, characteristic
4	Dic₅₀	—	3	1	no	maximal, Hall
5	C₂×C₃×C₂₅	C₂²	1	1	yes	characteristic
6	#1204	—	5	1	no	maximal
7	C₄×C₂₅	—	3	1	no	—
8	Dic₂₅	—	3	1	no	—
9	Dic₂₅	D₃	1	1	yes	characteristic
10	C₃×C₂₅	Q₈	1	1	yes	characteristic, complemented, Hall
11	Dic₁₅	—	5	1	no	—
12	C₃×Dic₅	—	5	1	no	—
13	C₅×Dic₃	D₅	1	1	yes	characteristic
14	C₂×C₂₅	C₂×D₃	1	1	yes	characteristic
15	Dic₁₀	—	15	1	no	—
16	C₂×C₃×C₅	C₂×D₅	1	1	yes	characteristic
17	C₂₅	Dic₆	1	1	yes	characteristic, complemented, Sylow
18	Dic₆	—	25	1	no	Hall
19	C₄×C₅	—	3	1	no	—
20	Dic₅	—	5	1	no	—
21	Dic₅	—	15	1	no	—
22	C₃×C₅	Dic₁₀	1	1	yes	characteristic
23	C₃×C₄	—	25	1	no	—
24	Dic₃	—	25	1	no	—
25	Dic₃	D₂₅	1	1	yes	characteristic
26	C₂×C₅	D₃×D₅	1	1	yes	characteristic
27	Q₈	—	75	1	no	Sylow
28	C₂×C₃	C₂×D₂₅	1	1	yes	characteristic
29	C₅	#1204	1	1	yes	characteristic
30	C₄	—	3	1	no	—
31	C₄	—	25	1	no	—
32	C₄	—	75	1	no	—
33	C₃	Dic₅₀	1	1	yes	characteristic, complemented, Sylow
34	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.