Subgroups — C₅×#6866 #11925939

Order 1215.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₅	C₃	1	1	yes	maximal, characteristic
2	C₅×C₃²⋊C₉	C₃	1	3	yes	maximal, complemented
3	#6866	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₃³×C₅	—	3	9	no	—
5	C₃³×C₅	—	3	1	no	—
6	C₃³×C₅	—	3	2	no	—
7	C₃³×C₅	C₉	1	3	yes	complemented
8	C₃³×C₅	C₃²	1	1	yes	characteristic
9	C₃×C₅×C₉	—	3	3	no	—
10	C₃⁴	C₃×C₅	1	1	yes	characteristic
11	C₃²⋊C₉	C₃×C₅	1	3	yes	complemented
12	C₃²×C₅	—	3	9	no	—
13	C₃²×C₅	—	3	18	no	—
14	C₃²×C₅	—	3	3	no	—
15	C₃²×C₅	—	3	9	no	—
16	C₃²×C₅	—	3	3	no	—
17	C₃²×C₅	C₃×C₉	1	1	yes	characteristic
18	C₃²×C₅	H(3,𝔽₃)	1	1	yes	characteristic
19	C₃²×C₅	3₋¹⁺²	1	2	yes	—
20	C₅×C₉	—	9	3	no	—
21	C₃³	—	3	9	no	—
22	C₃³	—	3	1	no	—
23	C₃³	—	3	2	no	—
24	C₃³	C₅×C₉	1	3	yes	complemented
25	C₃³	C₃²×C₅	1	1	yes	characteristic
26	C₃×C₉	—	3	3	no	—
27	C₃×C₅	—	3	9	no	—
28	C₃×C₅	—	3	1	no	—
29	C₃×C₅	—	3	2	no	—
30	C₃×C₅	C₃²⋊C₉	1	1	yes	characteristic
31	C₃×C₅	AΣL(1,𝔽₂₇)	1	3	yes	—
32	C₃²	—	3	9	no	—
33	C₃²	—	3	18	no	—
34	C₃²	—	3	3	no	—
35	C₃²	—	3	3	no	—
36	C₃²	—	3	9	no	—
37	C₃²	C₃×C₅×C₉	1	1	yes	characteristic
38	C₃²	C₅×H(3,𝔽₃)	1	1	yes	characteristic
39	C₃²	C₅×3₋¹⁺²	1	2	yes	—
40	C₉	—	9	3	no	—
41	C₅	#6866	1	1	yes	characteristic, direct product factor, Sylow
42	C₃	—	3	1	no	—
43	C₃	—	3	2	no	—
44	C₃	—	3	9	no	—
45	C₃	C₅×C₃²⋊C₉	1	1	yes	characteristic
46	C₃	C₅×AΣL(1,𝔽₂₇)	1	3	yes	—

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.