Subgroups — #10597028

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
2	C₃×Dic₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₂₅	—	3	1	no	maximal, Hall
5	C₂×C₃×C₂₅	C₂²	1	1	yes	characteristic
6	D₇₅	C₄	1	2	yes	complemented
7	#1200	—	5	1	no	maximal
8	C₂×D₂₅	—	3	1	no	—
9	C₄×C₂₅	—	3	1	no	—
10	Dic₂₅	D₃	1	1	yes	characteristic, complemented
11	C₃×C₂₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×D₁₅	—	5	1	no	—
13	C₃×Dic₅	—	5	1	no	—
14	C₅×Dic₃	D₅	1	1	yes	characteristic
15	C₂×C₂₅	C₂×D₃	1	1	yes	characteristic
16	D₂₅	—	3	2	no	—
17	C₄×D₅	—	15	1	no	—
18	C₂×C₃×C₅	C₂×D₅	1	1	yes	characteristic
19	D₁₅	—	5	2	no	—
20	C₂₅	C₄×D₃	1	1	yes	characteristic, complemented, Sylow
21	C₄×D₃	—	25	1	no	Hall
22	C₂×D₅	—	15	1	no	—
23	C₄×C₅	—	3	1	no	—
24	Dic₅	—	5	1	no	—
25	C₃×C₅	C₄×D₅	1	1	yes	characteristic
26	C₂×D₃	—	25	1	no	—
27	C₃×C₄	—	25	1	no	—
28	Dic₃	D₂₅	1	1	yes	characteristic, complemented
29	C₂×C₅	D₃×D₅	1	1	yes	characteristic
30	D₅	—	15	2	no	—
31	C₂×C₄	—	75	1	no	Sylow
32	C₂×C₃	C₂×D₂₅	1	1	yes	characteristic
33	D₃	—	25	2	no	—
34	C₅	#1200	1	1	yes	characteristic
35	C₂²	—	75	1	no	—
36	C₄	—	3	1	no	—
37	C₄	—	25	1	no	—
38	C₃	C₄×D₂₅	1	1	yes	characteristic, complemented, Sylow
39	C₂	—	75	2	no	—
40	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.