Subgroups — C₃×C₅×#104 #91131

Order 480.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#104	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
6	C₃×C₅×D₄	—	2	1	no	—
7	C₃×C₅×D₄	C₄	1	1	yes	characteristic, complemented
8	C₂×C₃×C₄×C₅	—	2	1	no	—
9	C₂×C₃×C₄×C₅	—	2	1	no	—
10	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₃×C₅×C₈	—	2	1	no	—
12	C₃×#104	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅×#41	C₂×C₃	1	1	yes	characteristic
14	C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
15	C₄²×C₅	C₂×C₃	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₅	—	2	1	no	—
17	C₂²×C₃×C₅	D₄	1	1	yes	characteristic
18	C₃×C₄×C₅	—	2	2	no	—
19	C₃×C₄×C₅	—	2	1	no	—
20	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
21	C₃×C₄×C₅	D₄	1	1	yes	characteristic
22	C₃×#41	C₂×C₅	1	1	yes	characteristic
23	C₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
24	C₃×C₄²	C₂×C₅	1	1	yes	characteristic, complemented
25	C₅×Q₈	C₃×C₄	1	1	yes	characteristic, complemented
26	C₅×D₄	—	2	1	no	—
27	C₅×D₄	C₃×C₄	1	1	yes	characteristic, complemented
28	C₂×C₄×C₅	—	2	1	no	—
29	C₂×C₄×C₅	—	2	1	no	—
30	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
31	C₅×C₈	—	2	1	no	—
32	#104	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₃×C₅	—	2	1	no	—
34	C₂×C₃×C₅	—	4	1	no	—
35	C₂×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
36	C₃×Q₈	C₄×C₅	1	1	yes	characteristic, complemented
37	C₃×D₄	—	2	1	no	—
38	C₃×D₄	C₄×C₅	1	1	yes	characteristic, complemented
39	C₂×C₃×C₄	—	2	1	no	—
40	C₂×C₃×C₄	—	2	1	no	—
41	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
42	C₃×C₈	—	2	1	no	—
43	C₂²×C₅	—	2	1	no	—
44	C₂²×C₅	C₃×D₄	1	1	yes	characteristic
45	C₄×C₅	—	2	2	no	—
46	C₄×C₅	—	2	1	no	—
47	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
48	C₄×C₅	C₃×D₄	1	1	yes	characteristic
49	#41	C₂×C₃×C₅	1	1	yes	characteristic
50	M₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
51	C₄²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
52	C₃×C₅	#104	1	1	yes	characteristic, direct product factor, Hall
53	C₂²×C₃	—	2	1	no	—
54	C₂²×C₃	C₅×D₄	1	1	yes	characteristic
55	C₃×C₄	—	2	2	no	—
56	C₃×C₄	—	2	1	no	—
57	C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
58	C₃×C₄	C₅×D₄	1	1	yes	characteristic
59	C₂×C₅	—	2	1	no	—
60	C₂×C₅	—	4	1	no	—
61	C₂×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
62	Q₈	C₃×C₄×C₅	1	1	yes	characteristic, complemented
63	D₄	—	2	1	no	—
64	D₄	C₃×C₄×C₅	1	1	yes	characteristic, complemented
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
68	C₈	—	2	1	no	—
69	C₂×C₃	—	2	1	no	—
70	C₂×C₃	—	4	1	no	—
71	C₂×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
72	C₅	C₃×#104	1	1	yes	characteristic, direct product factor, Sylow
73	C₂²	—	2	1	no	—
74	C₂²	C₃×C₅×D₄	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	2	1	no	—
77	C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
78	C₄	C₃×C₅×D₄	1	1	yes	characteristic
79	C₃	C₅×#104	1	1	yes	characteristic, direct product factor, Sylow
80	C₂	—	2	1	no	—
81	C₂	—	4	1	no	—
82	C₂	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄×C₅	D₄
commutator	C₄	C₂×C₃×C₄×C₅
Frattini, cosocle	C₂×C₄	C₂²×C₃×C₅
socle	C₂×C₃×C₅	C₂²⋊C₄
prime radical	C₃×C₅×#41	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₅ ◁ C₂×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×M₁₆	C₂	semidirect
3. C₃×C₄²×C₅	C₂	semidirect
4. C₅×#104	C₃	direct (N × H)
5. C₃×C₅×Q₈	C₄	semidirect
7. C₃×C₅×D₄	C₄	semidirect
12. C₃×#104	C₅	direct (N × H)
14. C₅×M₁₆	C₂×C₃	semidirect
15. C₄²×C₅	C₂×C₃	semidirect
23. C₃×M₁₆	C₂×C₅	semidirect
24. C₃×C₄²	C₂×C₅	semidirect
25. C₅×Q₈	C₃×C₄	semidirect
27. C₅×D₄	C₃×C₄	semidirect
32. #104	C₃×C₅	direct (N × H)
36. C₃×Q₈	C₄×C₅	semidirect
38. C₃×D₄	C₄×C₅	semidirect
50. M₁₆	C₂×C₃×C₅	semidirect
51. C₄²	C₂×C₃×C₅	semidirect
52. C₃×C₅	#104	direct (N × H)
62. Q₈	C₃×C₄×C₅	semidirect
64. D₄	C₃×C₄×C₅	semidirect
72. C₅	C₃×#104	direct (N × H)
79. C₃	C₅×#104	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#41	2
C₃×C₅×M₁₆	2
C₃×C₄²×C₅	2
C₅×#104	3
C₃×#104	5

Subgroups — C3×C5×#104 #91131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#104 #91131