Subgroups — C₃×C₅×#564 #11756653

Order 960.

344 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#125	C₂	1	15	yes	maximal
2	C₅×#564	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₄⋊C₄	C₂²	1	30	yes	—
4	C₃×C₄²×C₅	C₂²	1	5	yes	—
5	C₃×#564	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×#125	C₂×C₃	1	15	yes	—
7	C₂×C₃×C₄×C₅	C₂³	1	15	yes	—
8	C₃×#125	C₂×C₅	1	15	yes	—
9	C₅×C₄⋊C₄	C₂²×C₃	1	30	yes	—
10	C₄²×C₅	C₂²×C₃	1	5	yes	—
11	#564	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
13	C₃×C₄×C₅	—	2	15	no	—
14	C₃×C₄⋊C₄	C₂²×C₅	1	30	yes	—
15	C₃×C₄²	C₂²×C₅	1	5	yes	—
16	C₂×C₄×C₅	C₂³×C₃	1	15	yes	—
17	#125	C₂×C₃×C₅	1	15	yes	—
18	C₂×C₃×C₅	2₋¹⁺⁴	1	3	yes	—
19	C₂×C₃×C₄	C₂³×C₅	1	15	yes	—
20	C₂²×C₅	C₂⁴×C₃	1	1	yes	characteristic
21	C₄×C₅	—	2	15	no	—
22	C₄⋊C₄	C₂²×C₃×C₅	1	30	yes	—
23	C₄²	C₂²×C₃×C₅	1	5	yes	—
24	C₃×C₅	#564	1	1	yes	characteristic, direct product factor, Hall
25	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
26	C₃×C₄	—	2	15	no	—
27	C₂×C₅	C₃×2₋¹⁺⁴	1	3	yes	—
28	C₂×C₄	C₂³×C₃×C₅	1	15	yes	—
29	C₂×C₃	C₅×2₋¹⁺⁴	1	3	yes	—
30	C₅	C₃×#564	1	1	yes	characteristic, direct product factor, Sylow
31	C₂²	C₂⁴×C₃×C₅	1	1	yes	characteristic
32	C₄	—	2	15	no	—
33	C₃	C₅×#564	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₃×C₅×2₋¹⁺⁴	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ G

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.