Subgroups — #67082

Order 360.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₄₅	C₂	1	1	yes	maximal, characteristic, complemented
4	#1201	—	3	1	no	maximal
5	C₂×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₉×D₅	—	2	1	no	—
7	C₅×D₉	—	2	1	no	—
8	#611	—	5	1	no	maximal, Hall
9	C₂×C₅×D₃	—	3	1	no	—
10	C₂×C₃×D₅	D₃	1	1	yes	characteristic
11	Dic₁₅	—	3	1	no	—
12	C₅×C₉	D₄	1	1	yes	characteristic, complemented, Hall
13	C₂²⋊D₅	—	9	1	no	Hall
14	C₂²×C₉	—	5	1	no	—
15	C₂×D₉	D₅	1	1	yes	characteristic, complemented
16	Dic₉	—	5	1	no	—
17	C₂×C₃×C₅	C₂×D₃	1	1	yes	characteristic
18	C₃×D₅	—	2	1	no	—
19	C₅×D₃	—	6	1	no	—
20	#67	—	15	1	no	—
21	C₂²×C₅	—	9	1	no	—
22	C₂×D₅	D₉	1	1	yes	characteristic, complemented
23	Dic₅	—	9	1	no	—
24	C₂×C₉	—	10	1	no	—
25	C₂×C₉	C₂×D₅	1	1	yes	characteristic
26	D₉	—	2	1	no	—
27	C₃×C₅	#67	1	1	yes	characteristic
28	C₂²×C₃	—	5	1	no	—
29	C₂×D₃	—	3	1	no	—
30	Dic₃	—	15	1	no	—
31	C₂×C₅	—	18	1	no	—
32	C₂×C₅	C₂×D₉	1	1	yes	characteristic
33	D₅	—	2	1	no	—
34	C₉	C₂²⋊D₅	1	1	yes	characteristic, complemented, Sylow
35	D₄	—	45	1	no	Sylow
36	C₂×C₃	—	10	1	no	—
37	C₂×C₃	D₃×D₅	1	1	yes	characteristic
38	D₃	—	6	1	no	—
39	C₅	#611	1	1	yes	characteristic, complemented, Sylow
40	C₂²	—	5	1	no	—
41	C₂²	—	9	1	no	—
42	C₄	—	45	1	no	—
43	C₃	#1201	1	1	yes	characteristic
44	C₂	—	10	1	no	—
45	C₂	—	18	1	no	—
46	C₂	D₅×D₉	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.