Subgroups — C₅×#6872 #11925945

Order 1215.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#737	C₃	1	1	yes	maximal, characteristic
2	C₅×C₂₇⋊C₃	C₃	1	2	yes	maximal, complemented
3	C₃×C₅×C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	#6872	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₅×3₋¹⁺²	—	3	2	no	—
6	C₅×3₋¹⁺²	C₉	1	2	yes	—
7	C₅×H(3,𝔽₃)	C₉	1	1	yes	characteristic
8	C₃×C₅×C₉	—	3	1	no	—
9	C₃×C₅×C₉	C₃²	1	1	yes	characteristic
10	C₅×C₂₇	—	3	1	no	—
11	C₅×C₂₇	—	3	2	no	—
12	#737	C₃×C₅	1	1	yes	characteristic
13	C₂₇⋊C₃	C₃×C₅	1	2	yes	complemented
14	C₃×C₂₇	C₃×C₅	1	1	yes	characteristic, complemented
15	C₃²×C₅	—	3	1	no	—
16	C₃²×C₅	C₃×C₉	1	1	yes	characteristic
17	C₅×C₉	—	3	2	no	—
18	C₅×C₉	H(3,𝔽₃)	1	1	yes	characteristic
19	C₅×C₉	3₋¹⁺²	1	2	yes	—
20	3₋¹⁺²	—	3	2	no	—
21	3₋¹⁺²	C₅×C₉	1	2	yes	—
22	H(3,𝔽₃)	C₅×C₉	1	1	yes	characteristic
23	C₃×C₉	—	3	1	no	—
24	C₃×C₉	C₃²×C₅	1	1	yes	characteristic
25	C₂₇	—	3	1	no	—
26	C₂₇	—	3	2	no	—
27	C₃×C₅	—	3	1	no	—
28	C₃×C₅	—	9	1	no	—
29	C₃×C₅	C₃²⋊C₉	1	1	yes	characteristic
30	C₃²	—	3	1	no	—
31	C₃²	C₃×C₅×C₉	1	1	yes	characteristic
32	C₉	—	3	2	no	—
33	C₉	C₅×H(3,𝔽₃)	1	1	yes	characteristic
34	C₉	C₅×3₋¹⁺²	1	2	yes	—
35	C₅	#6872	1	1	yes	characteristic, direct product factor, Sylow
36	C₃	—	3	1	no	—
37	C₃	—	9	1	no	—
38	C₃	C₅×C₃²⋊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.