Subgroups — C₁₇×C₂₅×C₁₉⋊C₃ #37564478

Order 24225.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₁₉×C₂₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₇×C₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic
3	C₅×C₁₇×C₁₉	C₃×C₅	1	1	yes	characteristic
4	C₂₅×C₁₉⋊C₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₇×C₂₅	—	19	1	no	maximal, Hall
6	C₁₇×C₁₉⋊C₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
7	C₁₉×C₂₅	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
8	C₁₇×C₂₅	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
9	C₁₇×C₁₉	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
10	C₅×C₁₉⋊C₃	C₅×C₁₇	1	1	yes	characteristic
11	C₃×C₅×C₁₇	—	19	1	no	—
12	C₅×C₁₉	C₃×C₅×C₁₇	1	1	yes	characteristic
13	C₅×C₁₇	C₅×C₁₉⋊C₃	1	1	yes	characteristic
14	C₃×C₂₅	—	19	1	no	Hall
15	C₁₉⋊C₃	C₁₇×C₂₅	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₇	—	19	1	no	Hall
17	C₂₅	C₁₇×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₁₉	C₃×C₁₇×C₂₅	1	1	yes	characteristic, complemented, Sylow
19	C₁₇	C₂₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₃×C₅	—	19	1	no	—
21	C₅	C₅×C₁₇×C₁₉⋊C₃	1	1	yes	characteristic
22	C₃	—	19	1	no	Sylow

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.