Subgroups — D₅×#157 #67200

Order 360.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	#4379	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#157	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃⋊D₁₅	C₄	1	1	yes	characteristic, complemented
5	C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic
6	C₃²×D₅	C₄	1	1	yes	characteristic, complemented
7	C₂×#157	—	5	1	no	maximal, Hall
8	D₃×D₅	—	6	2	no	—
9	C₃²×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	C₄×D₅	—	9	1	no	maximal, Hall
11	C₂×C₃⋊D₃	—	5	1	no	—
12	#157	—	5	1	no	—
13	#157	D₅	1	1	yes	characteristic, direct product factor
14	D₁₅	—	6	2	no	—
15	C₃×D₅	—	2	2	no	—
16	C₅×D₃	—	6	2	no	—
17	C₂×D₅	—	9	1	no	—
18	C₄×C₅	—	9	1	no	—
19	Dic₅	—	9	1	no	—
20	C₂×C₃²	—	5	1	no	—
21	C₃⋊D₃	—	5	1	no	—
22	C₃⋊D₃	C₂×D₅	1	1	yes	characteristic
23	C₃×C₅	—	2	2	no	—
24	C₂×D₃	—	30	2	no	—
25	C₂×C₅	—	9	1	no	—
26	D₅	—	9	1	no	—
27	D₅	#157	1	1	yes	characteristic, direct product factor
28	C₃²	C₄×D₅	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₄	—	45	1	no	Sylow
30	C₂×C₃	—	10	2	no	—
31	D₃	—	6	2	no	—
32	D₃	—	30	2	no	—
33	C₅	C₂×#157	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	45	1	no	—
35	C₄	—	9	1	no	—
36	C₄	—	45	1	no	—
37	C₃	—	2	2	no	—
38	C₂	—	5	1	no	—
39	C₂	—	9	1	no	—
40	C₂	—	45	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅	C₂×C₄
prime radical	D₅×C₃⋊D₃	C₂
cosocle	C₅×C₃⋊D₃	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁

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.