Subgroups — D₃×Dic₂₅ #10597030

Order 600.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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