Subgroups — C₂×C₅×#157 #67218

Order 360.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₅×#157	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃²×C₅	C₄	1	1	yes	characteristic, complemented
4	C₅×C₃⋊D₃	C₄	1	1	yes	characteristic, complemented
5	C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic
6	C₂×#157	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×D₃	—	6	2	no	—
8	C₃²×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₄×C₅	—	9	1	no	maximal, Hall
10	C₂×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic
11	#157	C₂×C₅	1	2	yes	direct product factor
12	C₂×C₃×C₅	—	2	2	no	—
13	C₅×D₃	—	6	2	no	—
14	C₅×D₃	—	6	2	no	—
15	C₂²×C₅	—	9	1	no	—
16	C₄×C₅	—	9	2	no	—
17	C₂×C₃²	C₄×C₅	1	1	yes	characteristic, complemented
18	C₃⋊D₃	C₄×C₅	1	1	yes	characteristic, complemented
19	C₃⋊D₃	C₂²×C₅	1	1	yes	characteristic
20	C₃×C₅	—	2	2	no	—
21	C₂×D₃	—	6	2	no	—
22	C₂×C₅	—	9	1	no	—
23	C₂×C₅	—	9	1	no	—
24	C₂×C₅	#157	1	1	yes	characteristic, direct product factor
25	C₃²	C₂×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₄	—	9	1	no	Sylow
27	C₂×C₃	—	2	2	no	—
28	D₃	—	6	2	no	—
29	D₃	—	6	2	no	—
30	C₅	C₂×#157	1	1	yes	characteristic, direct product factor, Sylow
31	C₂²	—	9	1	no	—
32	C₄	—	9	2	no	—
33	C₃	—	2	2	no	—
34	C₂	—	9	1	no	—
35	C₂	—	9	1	no	—
36	C₂	C₅×#157	1	1	yes	characteristic, direct product factor

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.