Subgroups — C₃×C₅×#99 #91126

Order 480.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
3	C₅×#99	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂³×C₃×C₅	C₄	1	1	yes	characteristic, complemented
5	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic
6	C₃×C₅×D₄	—	2	2	no	—
7	C₂×C₃×C₄×C₅	—	2	2	no	—
8	C₂×C₃×C₄×C₅	C₄	1	1	yes	characteristic, complemented
9	C₃×#99	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₅×D₄	C₂×C₃	1	1	yes	characteristic
11	C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
12	C₂²×C₃×C₅	—	2	1	no	—
13	C₂²×C₃×C₅	—	4	1	no	—
14	C₂²×C₃×C₅	—	4	1	no	—
15	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₃×C₅	D₄	1	2	yes	—
17	C₃×C₄×C₅	—	2	1	no	—
18	C₃×C₄×C₅	—	4	2	no	—
19	C₂×C₃×D₄	C₂×C₅	1	1	yes	characteristic
20	C₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
21	C₂³×C₅	C₃×C₄	1	1	yes	characteristic, complemented
22	C₂³×C₅	C₂²×C₃	1	1	yes	characteristic
23	C₅×D₄	—	2	2	no	—
24	C₂×C₄×C₅	—	2	2	no	—
25	C₂×C₄×C₅	C₃×C₄	1	1	yes	characteristic, complemented
26	#99	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃×C₅	—	2	2	no	—
28	C₂×C₃×C₅	—	2	1	no	—
29	C₂×C₃×C₅	—	4	1	no	—
30	C₂×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
31	C₂³×C₃	C₄×C₅	1	1	yes	characteristic, complemented
32	C₂³×C₃	C₂²×C₅	1	1	yes	characteristic
33	C₃×D₄	—	2	2	no	—
34	C₂×C₃×C₄	—	2	2	no	—
35	C₂×C₃×C₄	C₄×C₅	1	1	yes	characteristic, complemented
36	C₂²×C₅	—	2	1	no	—
37	C₂²×C₅	—	4	1	no	—
38	C₂²×C₅	—	4	1	no	—
39	C₂²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
40	C₂²×C₅	C₃×D₄	1	2	yes	—
41	C₄×C₅	—	2	1	no	—
42	C₄×C₅	—	4	2	no	—
43	C₂×D₄	C₂×C₃×C₅	1	1	yes	characteristic
44	C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
45	C₃×C₅	#99	1	1	yes	characteristic, direct product factor, Hall
46	C₂²×C₃	—	2	1	no	—
47	C₂²×C₃	—	4	1	no	—
48	C₂²×C₃	—	4	1	no	—
49	C₂²×C₃	C₂×C₄×C₅	1	1	yes	characteristic
50	C₂²×C₃	C₅×D₄	1	2	yes	—
51	C₃×C₄	—	2	1	no	—
52	C₃×C₄	—	4	2	no	—
53	C₂×C₅	—	2	2	no	—
54	C₂×C₅	—	2	1	no	—
55	C₂×C₅	—	4	1	no	—
56	C₂×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
57	C₂³	C₃×C₄×C₅	1	1	yes	characteristic, complemented
58	C₂³	C₂²×C₃×C₅	1	1	yes	characteristic
59	D₄	—	2	2	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	C₃×C₄×C₅	1	1	yes	characteristic, complemented
62	C₂×C₃	—	2	2	no	—
63	C₂×C₃	—	2	1	no	—
64	C₂×C₃	—	4	1	no	—
65	C₂×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
66	C₅	C₃×#99	1	1	yes	characteristic, direct product factor, Sylow
67	C₂²	—	2	1	no	—
68	C₂²	—	4	1	no	—
69	C₂²	—	4	1	no	—
70	C₂²	C₂×C₃×C₄×C₅	1	1	yes	characteristic
71	C₂²	C₃×C₅×D₄	1	2	yes	—
72	C₄	—	2	1	no	—
73	C₄	—	4	2	no	—
74	C₃	C₅×#99	1	1	yes	characteristic, direct product factor, Sylow
75	C₂	—	2	2	no	—
76	C₂	—	2	1	no	—
77	C₂	—	4	1	no	—
78	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	C₂³	C₂²×C₃×C₅
prime radical	C₂×C₃×C₅×D₄	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×C₂²⋊C₄	C₂	semidirect
3. C₅×#99	C₃	direct (N × H)
4. C₂³×C₃×C₅	C₄	semidirect
8. C₂×C₃×C₄×C₅	C₄	semidirect
9. C₃×#99	C₅	direct (N × H)
11. C₅×C₂²⋊C₄	C₂×C₃	semidirect
20. C₃×C₂²⋊C₄	C₂×C₅	semidirect
21. C₂³×C₅	C₃×C₄	semidirect
25. C₂×C₄×C₅	C₃×C₄	semidirect
26. #99	C₃×C₅	direct (N × H)
31. C₂³×C₃	C₄×C₅	semidirect
35. C₂×C₃×C₄	C₄×C₅	semidirect
44. C₂²⋊C₄	C₂×C₃×C₅	semidirect
45. C₃×C₅	#99	direct (N × H)
57. C₂³	C₃×C₄×C₅	semidirect
61. C₂×C₄	C₃×C₄×C₅	semidirect
66. C₅	C₃×#99	direct (N × H)
74. C₃	C₅×#99	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×D₄	2
C₃×C₅×C₂²⋊C₄	2
C₅×#99	3
C₃×#99	5

Subgroups — C3×C5×#99 #91126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#99 #91126