Subgroups — C₂₅×C₃⋊C₁₆ #11924791

Order 1200.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₁₆×C₂₅	—	3	1	no	maximal, Hall
3	C₃×C₄×C₂₅	C₄	1	1	yes	characteristic
4	C₅×C₃⋊C₁₆	C₅	1	1	yes	maximal, characteristic
5	C₈×C₂₅	D₃	1	1	yes	characteristic
6	C₂×C₃×C₂₅	C₈	1	1	yes	characteristic
7	C₃×C₅×C₈	C₂×C₅	1	1	yes	characteristic
8	C₄×C₂₅	Dic₃	1	1	yes	characteristic
9	C₅×C₁₆	—	3	1	no	—
10	C₃×C₂₅	C₁₆	1	1	yes	characteristic, complemented, Hall
11	C₃×C₄×C₅	C₄×C₅	1	1	yes	characteristic
12	C₂×C₂₅	C₃⋊C₈	1	1	yes	characteristic
13	C₃⋊C₁₆	C₂₅	1	1	yes	characteristic, direct product factor, Hall
14	C₅×C₈	C₅×D₃	1	1	yes	characteristic
15	C₂×C₃×C₅	C₅×C₈	1	1	yes	characteristic
16	C₂₅	C₃⋊C₁₆	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₈	C₂×C₂₅	1	1	yes	characteristic
18	C₄×C₅	C₅×Dic₃	1	1	yes	characteristic
19	C₁₆	—	3	1	no	Sylow
20	C₃×C₅	C₅×C₁₆	1	1	yes	characteristic
21	C₃×C₄	C₄×C₂₅	1	1	yes	characteristic
22	C₂×C₅	C₅×C₃⋊C₈	1	1	yes	characteristic
23	C₈	D₃×C₂₅	1	1	yes	characteristic
24	C₂×C₃	C₈×C₂₅	1	1	yes	characteristic
25	C₅	C₅×C₃⋊C₁₆	1	1	yes	characteristic
26	C₄	Dic₃×C₂₅	1	1	yes	characteristic
27	C₃	C₁₆×C₂₅	1	1	yes	characteristic, complemented, Sylow
28	C₂	C₃⋊C₈×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.