Subgroups — C₅×D₅×C₂₇ #13062467

Order 1350.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₉×D₅	C₃	1	1	yes	maximal, characteristic
3	C₂×C₅×C₂₇	—	5	1	no	maximal
4	D₅×C₂₇	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅²×C₉	C₂×C₃	1	1	yes	characteristic
6	C₃×C₅×D₅	C₉	1	1	yes	characteristic
7	C₅×C₂₇	—	2	2	no	—
8	C₅×C₂₇	D₅	1	1	yes	characteristic, direct product factor
9	C₅×C₂₇	C₂×C₅	1	1	yes	characteristic, complemented
10	C₂×C₅×C₉	—	5	1	no	—
11	C₉×D₅	C₃×C₅	1	1	yes	characteristic
12	C₃×C₅²	C₂×C₉	1	1	yes	characteristic
13	C₂×C₂₇	—	5	1	no	Hall
14	C₅×D₅	C₂₇	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₉	—	2	2	no	—
16	C₅×C₉	C₃×D₅	1	1	yes	characteristic
17	C₅×C₉	C₂×C₃×C₅	1	1	yes	characteristic
18	C₂×C₃×C₅	—	5	1	no	—
19	C₃×D₅	C₅×C₉	1	1	yes	characteristic
20	C₂₇	C₅×D₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₅²	C₂×C₂₇	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₉	—	5	1	no	—
23	C₃×C₅	—	2	2	no	—
24	C₃×C₅	C₉×D₅	1	1	yes	characteristic
25	C₃×C₅	C₂×C₅×C₉	1	1	yes	characteristic
26	C₂×C₅	—	5	1	no	—
27	D₅	C₅×C₂₇	1	1	yes	characteristic, direct product factor
28	C₉	C₃×C₅×D₅	1	1	yes	characteristic
29	C₂×C₃	—	5	1	no	—
30	C₅	—	2	2	no	—
31	C₅	D₅×C₂₇	1	1	yes	characteristic, direct product factor
32	C₅	C₂×C₅×C₂₇	1	1	yes	characteristic, complemented
33	C₃	C₅×C₉×D₅	1	1	yes	characteristic
34	C₂	—	5	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.