Subgroups — C₃×C₅×#401 #11751376

Order 960.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#95	C₂	1	7	yes	maximal
2	C₅×#401	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂²×C₃×C₄×C₅	C₂²	1	7	yes	—
4	C₃×#401	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×#95	C₂×C₃	1	7	yes	—
6	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
7	C₂×C₃×C₄×C₅	—	2	21	no	—
8	C₃×#95	C₂×C₅	1	7	yes	—
9	C₂²×C₄×C₅	C₂²×C₃	1	7	yes	—
10	#401	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
11	C₂²×C₃×C₅	#41	1	7	yes	—
12	C₃×C₄×C₅	—	4	7	no	—
13	C₂²×C₃×C₄	C₂²×C₅	1	7	yes	—
14	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
15	C₂×C₄×C₅	—	2	21	no	—
16	#95	C₂×C₃×C₅	1	7	yes	—
17	C₂×C₃×C₅	#126	1	7	yes	—
18	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
19	C₂×C₃×C₄	—	2	21	no	—
20	C₂²×C₅	C₃×#41	1	7	yes	—
21	C₄×C₅	—	4	7	no	—
22	C₂²×C₄	C₂²×C₃×C₅	1	7	yes	—
23	C₃×C₅	#401	1	1	yes	characteristic, direct product factor, Hall
24	C₂²×C₃	C₅×#41	1	7	yes	—
25	C₃×C₄	—	4	7	no	—
26	C₂×C₅	C₃×#126	1	7	yes	—
27	C₂³	C₂³×C₃×C₅	1	1	yes	characteristic
28	C₂×C₄	—	2	21	no	—
29	C₂×C₃	C₅×#126	1	7	yes	—
30	C₅	C₃×#401	1	1	yes	characteristic, direct product factor, Sylow
31	C₂²	C₃×C₅×#41	1	7	yes	—
32	C₄	—	4	7	no	—
33	C₃	C₅×#401	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₃×C₅×#126	1	7	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂³
commutator, Frattini, cosocle	C₂³	C₂³×C₃×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×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.