Subgroups — D₁₂×C₂₅ #10597041

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	2	yes	maximal, complemented
2	C₃×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂₅	—	3	1	no	maximal, Hall
4	C₂×C₃×C₂₅	C₂²	1	1	yes	characteristic
5	D₃×C₂₅	—	2	2	no	—
6	C₅×D₁₂	C₅	1	1	yes	maximal, characteristic
7	C₂²×C₂₅	—	3	2	no	—
8	C₄×C₂₅	D₃	1	1	yes	characteristic, complemented
9	C₃×C₂₅	D₄	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×D₃	C₂×C₅	1	2	yes	—
11	C₃×C₄×C₅	C₂×C₅	1	1	yes	characteristic
12	C₂×C₂₅	—	6	2	no	—
13	C₂×C₂₅	C₂×D₃	1	1	yes	characteristic
14	C₅×D₄	—	3	1	no	—
15	C₂×C₃×C₅	C₂²×C₅	1	1	yes	characteristic
16	C₅×D₃	—	2	2	no	—
17	C₂₅	D₁₂	1	1	yes	characteristic, direct product factor, Sylow
18	D₁₂	C₂₅	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₅	—	3	2	no	—
20	C₄×C₅	C₅×D₃	1	1	yes	characteristic
21	C₃×C₅	C₅×D₄	1	1	yes	characteristic
22	C₂×D₃	C₂×C₂₅	1	2	yes	complemented
23	C₃×C₄	C₂×C₂₅	1	1	yes	characteristic, complemented
24	C₂×C₅	—	6	2	no	—
25	C₂×C₅	C₂×C₅×D₃	1	1	yes	characteristic
26	D₄	—	3	1	no	Sylow
27	C₂×C₃	C₂²×C₂₅	1	1	yes	characteristic
28	D₃	—	2	2	no	—
29	C₅	C₅×D₁₂	1	1	yes	characteristic
30	C₂²	—	3	2	no	—
31	C₄	D₃×C₂₅	1	1	yes	characteristic, complemented
32	C₃	D₄×C₂₅	1	1	yes	characteristic, complemented, Sylow
33	C₂	—	6	2	no	—
34	C₂	C₂×D₃×C₂₅	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.