Subgroups — C₂×A₄×C₂₅ #10597059

Order 600.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×C₂₅	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂³×C₂₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₃×C₂₅	—	4	1	no	maximal
4	C₂×C₅×A₄	C₅	1	1	yes	maximal, characteristic
5	C₂²×C₂₅	—	3	1	no	—
6	C₂²×C₂₅	—	3	1	no	—
7	C₂²×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×C₂₅	—	4	1	no	Hall
9	C₅×A₄	C₂×C₅	1	1	yes	characteristic
10	C₂×C₂₅	—	3	1	no	—
11	C₂×C₂₅	—	3	1	no	—
12	C₂×C₂₅	A₄	1	1	yes	characteristic, direct product factor
13	C₂³×C₅	C₃×C₅	1	1	yes	characteristic
14	C₂×C₃×C₅	—	4	1	no	—
15	C₂₅	C₂×A₄	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×A₄	C₂₅	1	1	yes	characteristic, direct product factor, Hall
17	C₂²×C₅	—	3	1	no	—
18	C₂²×C₅	—	3	1	no	—
19	C₂²×C₅	C₂×C₃×C₅	1	1	yes	characteristic
20	C₃×C₅	—	4	1	no	—
21	A₄	C₂×C₂₅	1	1	yes	characteristic, direct product factor
22	C₂×C₅	—	3	1	no	—
23	C₂×C₅	—	3	1	no	—
24	C₂×C₅	C₅×A₄	1	1	yes	characteristic
25	C₂³	C₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃	—	4	1	no	—
27	C₅	C₂×C₅×A₄	1	1	yes	characteristic
28	C₂²	—	3	1	no	—
29	C₂²	—	3	1	no	—
30	C₂²	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented
31	C₃	—	4	1	no	Sylow
32	C₂	—	3	1	no	—
33	C₂	—	3	1	no	—
34	C₂	A₄×C₂₅	1	1	yes	characteristic, direct product factor

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.