Subgroups — C₃×C₅×#95 #91122

Order 480.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₅	C₂	1	3	yes	maximal
2	C₅×#95	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic
4	C₂×C₃×C₄×C₅	—	2	6	no	—
5	C₂×C₃×C₄×C₅	C₄	1	6	yes	complemented
6	C₃×#95	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₄×C₅	C₂×C₃	1	3	yes	—
8	C₂²×C₃×C₅	C₂×C₄	1	3	yes	—
9	C₂²×C₃×C₅	D₄	1	3	yes	—
10	C₂²×C₃×C₅	Q₈	1	1	yes	characteristic
11	C₃×C₄×C₅	—	2	6	no	—
12	C₂²×C₃×C₄	C₂×C₅	1	3	yes	—
13	C₂³×C₅	C₂²×C₃	1	1	yes	characteristic
14	C₂×C₄×C₅	—	2	6	no	—
15	C₂×C₄×C₅	C₃×C₄	1	6	yes	complemented
16	#95	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₃×C₅	C₄²	1	1	yes	characteristic
18	C₂×C₃×C₅	C₂²⋊C₄	1	3	yes	—
19	C₂×C₃×C₅	C₄⋊C₄	1	3	yes	—
20	C₂³×C₃	C₂²×C₅	1	1	yes	characteristic
21	C₂×C₃×C₄	—	2	6	no	—
22	C₂×C₃×C₄	C₄×C₅	1	6	yes	complemented
23	C₂²×C₅	C₂×C₃×C₄	1	3	yes	—
24	C₂²×C₅	C₃×D₄	1	3	yes	—
25	C₂²×C₅	C₃×Q₈	1	1	yes	characteristic
26	C₄×C₅	—	2	6	no	—
27	C₂²×C₄	C₂×C₃×C₅	1	3	yes	—
28	C₃×C₅	#95	1	1	yes	characteristic, direct product factor, Hall
29	C₂²×C₃	C₂×C₄×C₅	1	3	yes	—
30	C₂²×C₃	C₅×D₄	1	3	yes	—
31	C₂²×C₃	C₅×Q₈	1	1	yes	characteristic
32	C₃×C₄	—	2	6	no	—
33	C₂×C₅	C₃×C₄²	1	1	yes	characteristic
34	C₂×C₅	C₃×C₂²⋊C₄	1	3	yes	—
35	C₂×C₅	C₃×C₄⋊C₄	1	3	yes	—
36	C₂³	C₂²×C₃×C₅	1	1	yes	characteristic
37	C₂×C₄	—	2	6	no	—
38	C₂×C₄	C₃×C₄×C₅	1	6	yes	complemented
39	C₂×C₃	C₄²×C₅	1	1	yes	characteristic
40	C₂×C₃	C₅×C₂²⋊C₄	1	3	yes	—
41	C₂×C₃	C₅×C₄⋊C₄	1	3	yes	—
42	C₅	C₃×#95	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	C₂×C₃×C₄×C₅	1	3	yes	—
44	C₂²	C₃×C₅×D₄	1	3	yes	—
45	C₂²	C₃×C₅×Q₈	1	1	yes	characteristic
46	C₄	—	2	6	no	—
47	C₃	C₅×#95	1	1	yes	characteristic, direct product factor, Sylow
48	C₂	C₃×C₄²×C₅	1	1	yes	characteristic
49	C₂	C₃×C₅×C₂²⋊C₄	1	3	yes	—
50	C₂	C₃×C₅×C₄⋊C₄	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂²
commutator	C₂	C₃×C₄²×C₅
Frattini, cosocle	C₂³	C₂²×C₃×C₅
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅×#95	C₃	direct (N × H)
5. C₂×C₃×C₄×C₅	C₄	semidirect
6. C₃×#95	C₅	direct (N × H)
15. C₂×C₄×C₅	C₃×C₄	semidirect
16. #95	C₃×C₅	direct (N × H)
22. C₂×C₃×C₄	C₄×C₅	semidirect
28. C₃×C₅	#95	direct (N × H)
38. C₂×C₄	C₃×C₄×C₅	semidirect
42. C₅	C₃×#95	direct (N × H)
47. C₃	C₅×#95	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₄×C₅	2
C₅×#95	3
C₃×#95	5

Subgroups — C3×C5×#95 #91122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#95 #91122