Subgroups — A₄×C₂₅×C₆₁ #32912939

Order 18300.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₅×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₂₅×C₆₁	—	4	1	no	maximal, Hall
3	C₅×A₄×C₆₁	C₅	1	1	yes	maximal, characteristic
4	C₂×C₂₅×C₆₁	—	3	1	no	—
5	C₂₅×C₆₁	A₄	1	1	yes	characteristic, direct product factor, Hall
6	C₂²×C₅×C₆₁	C₃×C₅	1	1	yes	characteristic
7	C₃×C₅×C₆₁	—	4	1	no	—
8	A₄×C₆₁	C₂₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₆₁	—	3	1	no	—
10	C₅×C₆₁	C₅×A₄	1	1	yes	characteristic
11	A₄×C₂₅	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₆₁	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
13	C₃×C₆₁	—	4	1	no	Hall
14	C₂×C₆₁	—	3	1	no	—
15	C₂²×C₂₅	C₃×C₆₁	1	1	yes	characteristic, complemented, Hall
16	C₃×C₂₅	—	4	1	no	Hall
17	C₆₁	A₄×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
18	C₅×A₄	C₅×C₆₁	1	1	yes	characteristic
19	C₂×C₂₅	—	3	1	no	—
20	C₂₅	A₄×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²×C₅	C₃×C₅×C₆₁	1	1	yes	characteristic
22	C₃×C₅	—	4	1	no	—
23	A₄	C₂₅×C₆₁	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₅	—	3	1	no	—
25	C₅	C₅×A₄×C₆₁	1	1	yes	characteristic
26	C₂²	C₃×C₂₅×C₆₁	1	1	yes	characteristic, complemented, Sylow
27	C₃	—	4	1	no	Sylow
28	C₂	—	3	1	no	—

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.