Subgroups — C₅×C₄₉×C₁₂₅ #72207402

Order 30625.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₅×C₄₉	C₅	1	1	yes	maximal, characteristic
2	C₄₉×C₁₂₅	C₅	1	5	yes	maximal, direct product factor
3	C₅×C₇×C₁₂₅	C₇	1	1	yes	maximal, characteristic
4	C₅²×C₄₉	C₂₅	1	1	yes	characteristic
5	C₂₅×C₄₉	C₂₅	1	4	yes	—
6	C₂₅×C₄₉	C₅²	1	1	yes	characteristic
7	C₅×C₇×C₂₅	C₅×C₇	1	1	yes	characteristic
8	C₇×C₁₂₅	C₅×C₇	1	5	yes	—
9	C₅×C₁₂₅	C₄₉	1	1	yes	characteristic, direct product factor, Sylow
10	C₅×C₄₉	C₁₂₅	1	5	yes	direct product factor
11	C₅×C₄₉	C₅×C₂₅	1	1	yes	characteristic
12	C₅²×C₇	C₇×C₂₅	1	1	yes	characteristic
13	C₇×C₂₅	C₇×C₂₅	1	4	yes	—
14	C₇×C₂₅	C₅²×C₇	1	1	yes	characteristic
15	C₅×C₂₅	C₅×C₄₉	1	1	yes	characteristic
16	C₁₂₅	C₅×C₄₉	1	5	yes	direct product factor
17	C₄₉	C₅×C₁₂₅	1	1	yes	characteristic, direct product factor, Sylow
18	C₅×C₇	C₇×C₁₂₅	1	5	yes	—
19	C₅×C₇	C₅×C₇×C₂₅	1	1	yes	characteristic
20	C₅²	C₂₅×C₄₉	1	1	yes	characteristic
21	C₂₅	C₂₅×C₄₉	1	4	yes	—
22	C₂₅	C₅²×C₄₉	1	1	yes	characteristic
23	C₇	C₅×C₇×C₁₂₅	1	1	yes	characteristic
24	C₅	C₄₉×C₁₂₅	1	5	yes	direct product factor
25	C₅	C₅×C₂₅×C₄₉	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.