Subgroups — C₂×#4380 #67220

Order 360.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic
2	#4380	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃²×C₅	C₄	1	1	yes	characteristic, complemented
4	C₃⋊D₁₅	C₄	1	1	yes	characteristic, complemented
5	C₃⋊D₁₅	C₂²	1	1	yes	characteristic
6	C₂×#157	—	5	1	no	maximal, Hall
7	C₂×D₁₅	—	6	2	no	—
8	C₃²×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
9	C₂×AGL(1,𝔽₅)	—	9	1	no	maximal, Hall
10	C₂×C₃⋊D₃	—	5	1	no	—
11	#157	—	5	2	no	—
12	C₂×C₃×C₅	—	2	2	no	—
13	D₁₅	—	6	2	no	—
14	D₁₅	—	6	2	no	—
15	C₂×D₅	—	9	1	no	—
16	AGL(1,𝔽₅)	—	9	2	no	—
17	C₂×C₃²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
18	C₃⋊D₃	—	5	1	no	—
19	C₃⋊D₃	—	5	1	no	—
20	C₃×C₅	—	2	2	no	—
21	C₂×D₃	—	30	2	no	—
22	C₂×C₅	#157	1	1	yes	characteristic, complemented
23	D₅	—	9	1	no	—
24	D₅	—	9	1	no	—
25	C₃²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₄	—	45	1	no	Sylow
27	C₂×C₃	—	2	2	no	—
28	D₃	—	30	2	no	—
29	D₃	—	30	2	no	—
30	C₅	C₂×#157	1	1	yes	characteristic, complemented, Sylow
31	C₂²	—	45	1	no	—
32	C₄	—	45	2	no	—
33	C₃	—	2	2	no	—
34	C₂	—	45	1	no	—
35	C₂	—	45	1	no	—
36	C₂	#4380	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.