Subgroups — C₃×C₅×#101 #91128

Order 480.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×M₁₆	C₂	1	2	yes	maximal
3	C₅×#101	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×Q₈	—	2	2	no	—
5	C₂×C₃×C₄×C₅	C₄	1	2	yes	—
6	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₃×C₅×C₈	—	2	2	no	—
8	C₃×#101	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
10	C₅×M₁₆	C₂×C₃	1	2	yes	—
11	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
12	C₃×C₄×C₅	—	2	2	no	—
13	C₃×C₄×C₅	D₄	1	2	yes	—
14	C₂×C₃×Q₈	C₂×C₅	1	1	yes	characteristic
15	C₃×M₁₆	C₂×C₅	1	2	yes	—
16	C₅×Q₈	—	2	2	no	—
17	C₂×C₄×C₅	C₃×C₄	1	2	yes	—
18	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
19	C₅×C₈	—	2	2	no	—
20	#101	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₃×C₅	—	2	1	no	—
22	C₂×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
23	C₃×Q₈	—	2	2	no	—
24	C₂×C₃×C₄	C₄×C₅	1	2	yes	—
25	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
26	C₃×C₈	—	2	2	no	—
27	C₂²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
28	C₄×C₅	—	2	2	no	—
29	C₄×C₅	C₃×D₄	1	2	yes	—
30	C₂×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
31	M₁₆	C₂×C₃×C₅	1	2	yes	—
32	C₃×C₅	#101	1	1	yes	characteristic, direct product factor, Hall
33	C₂²×C₃	C₂×C₄×C₅	1	1	yes	characteristic
34	C₃×C₄	—	2	2	no	—
35	C₃×C₄	C₅×D₄	1	2	yes	—
36	C₂×C₅	—	2	1	no	—
37	C₂×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
38	Q₈	—	2	2	no	—
39	C₂×C₄	C₃×C₄×C₅	1	2	yes	—
40	C₂×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₂×C₃	—	2	1	no	—
43	C₂×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
44	C₅	C₃×#101	1	1	yes	characteristic, direct product factor, Sylow
45	C₂²	C₂×C₃×C₄×C₅	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₃×C₅×D₄	1	2	yes	—
48	C₃	C₅×#101	1	1	yes	characteristic, direct product factor, Sylow
49	C₂	—	2	1	no	—
50	C₂	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₅	C₂²⋊C₄
commutator	C₂²	C₂×C₃×C₄×C₅
Frattini, cosocle	C₂×C₄	C₂²×C₃×C₅
prime radical	C₂²×C₃×C₅	C₂×C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#101	C₃	direct (N × H)
8. C₃×#101	C₅	direct (N × H)
20. #101	C₃×C₅	direct (N × H)
32. C₃×C₅	#101	direct (N × H)
44. C₅	C₃×#101	direct (N × H)
48. C₃	C₅×#101	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×Q₈	2
C₃×C₅×M₁₆	2
C₅×#101	3
C₃×#101	5

Subgroups — C3×C5×#101 #91128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#101 #91128