Subgroups — C₃×C₅²×C₂₇ #72182017

Order 2025.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₉	C₃	1	1	yes	maximal, characteristic
2	C₅²×C₂₇	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₅×C₂₇	C₅	1	6	yes	maximal, direct product factor
4	C₃²×C₅²	C₉	1	1	yes	characteristic
5	C₅²×C₉	C₉	1	2	yes	—
6	C₅²×C₉	C₃²	1	1	yes	characteristic
7	C₃×C₅×C₉	C₃×C₅	1	6	yes	—
8	C₅×C₂₇	C₃×C₅	1	18	yes	direct product factor
9	C₃×C₂₇	C₅²	1	1	yes	characteristic, direct product factor, Sylow
10	C₃×C₅²	C₂₇	1	3	yes	direct product factor
11	C₃×C₅²	C₃×C₉	1	1	yes	characteristic
12	C₃²×C₅	C₅×C₉	1	6	yes	—
13	C₅×C₉	C₅×C₉	1	12	yes	—
14	C₅×C₉	C₃²×C₅	1	6	yes	—
15	C₃×C₉	C₃×C₅²	1	1	yes	characteristic
16	C₂₇	C₃×C₅²	1	3	yes	direct product factor
17	C₅²	C₃×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₅	C₅×C₂₇	1	18	yes	direct product factor
19	C₃×C₅	C₃×C₅×C₉	1	6	yes	—
20	C₃²	C₅²×C₉	1	1	yes	characteristic
21	C₉	C₅²×C₉	1	2	yes	—
22	C₉	C₃²×C₅²	1	1	yes	characteristic
23	C₅	C₃×C₅×C₂₇	1	6	yes	direct product factor
24	C₃	C₅²×C₂₇	1	3	yes	direct product factor
25	C₃	C₃×C₅²×C₉	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.