Subgroups — C₃×C₅×#102 #91129

Order 480.

100 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	C₂×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#102	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂³×C₃×C₅	—	2	1	no	—
6	C₃×C₅×D₄	—	2	1	no	—
7	C₃×C₅×D₄	C₄	1	2	yes	complemented
8	C₂×C₃×C₄×C₅	—	2	1	no	—
9	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₃×C₅×C₈	—	2	1	no	—
11	C₃×#102	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₅×D₄	C₂×C₃	1	1	yes	characteristic
13	C₂×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
14	C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₅	—	2	2	no	—
16	C₂²×C₃×C₅	—	4	1	no	—
17	C₂²×C₃×C₅	—	4	1	no	—
18	C₂²×C₃×C₅	D₄	1	1	yes	characteristic
19	C₃×C₄×C₅	—	4	1	no	—
20	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
21	C₃×C₄×C₅	D₄	1	1	yes	characteristic
22	C₂×C₃×D₄	C₂×C₅	1	1	yes	characteristic
23	C₂×C₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
24	C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
25	C₂³×C₅	—	2	1	no	—
26	C₅×D₄	—	2	1	no	—
27	C₅×D₄	C₃×C₄	1	2	yes	complemented
28	C₂×C₄×C₅	—	2	1	no	—
29	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
30	C₅×C₈	—	2	1	no	—
31	#102	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₃×C₅	—	4	2	no	—
33	C₂×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₃×C₅	D₈	1	1	yes	characteristic
35	C₂×C₃×C₅	SD₁₆	1	1	yes	characteristic
36	C₂³×C₃	—	2	1	no	—
37	C₃×D₄	—	2	1	no	—
38	C₃×D₄	C₄×C₅	1	2	yes	complemented
39	C₂×C₃×C₄	—	2	1	no	—
40	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
41	C₃×C₈	—	2	1	no	—
42	C₂²×C₅	—	2	2	no	—
43	C₂²×C₅	—	4	1	no	—
44	C₂²×C₅	—	4	1	no	—
45	C₂²×C₅	C₃×D₄	1	1	yes	characteristic
46	C₄×C₅	—	4	1	no	—
47	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
48	C₄×C₅	C₃×D₄	1	1	yes	characteristic
49	C₂×D₄	C₂×C₃×C₅	1	1	yes	characteristic
50	C₂×C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
51	C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
52	C₃×C₅	#102	1	1	yes	characteristic, direct product factor, Hall
53	C₂²×C₃	—	2	2	no	—
54	C₂²×C₃	—	4	1	no	—
55	C₂²×C₃	—	4	1	no	—
56	C₂²×C₃	C₅×D₄	1	1	yes	characteristic
57	C₃×C₄	—	4	1	no	—
58	C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
59	C₃×C₄	C₅×D₄	1	1	yes	characteristic
60	C₂×C₅	—	4	2	no	—
61	C₂×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₅	C₃×D₈	1	1	yes	characteristic
63	C₂×C₅	C₃×SD₁₆	1	1	yes	characteristic
64	C₂³	—	2	1	no	—
65	D₄	—	2	1	no	—
66	D₄	C₃×C₄×C₅	1	2	yes	complemented
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₂×C₃	—	4	2	no	—
71	C₂×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₃	C₅×D₈	1	1	yes	characteristic
73	C₂×C₃	C₅×SD₁₆	1	1	yes	characteristic
74	C₅	C₃×#102	1	1	yes	characteristic, direct product factor, Sylow
75	C₂²	—	2	2	no	—
76	C₂²	—	4	1	no	—
77	C₂²	—	4	1	no	—
78	C₂²	C₃×C₅×D₄	1	1	yes	characteristic
79	C₄	—	4	1	no	—
80	C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
81	C₄	C₃×C₅×D₄	1	1	yes	characteristic
82	C₃	C₅×#102	1	1	yes	characteristic, direct product factor, Sylow
83	C₂	—	4	2	no	—
84	C₂	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
85	C₂	C₃×C₅×D₈	1	1	yes	characteristic
86	C₂	C₃×C₅×SD₁₆	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×C₈	C₂	semidirect
3. C₃×C₅×C₄⋊C₄	C₂	semidirect
4. C₅×#102	C₃	direct (N × H)
7. C₃×C₅×D₄	C₄	semidirect
11. C₃×#102	C₅	direct (N × H)
13. C₂×C₅×C₈	C₂×C₃	semidirect
14. C₅×C₄⋊C₄	C₂×C₃	semidirect
23. C₂×C₃×C₈	C₂×C₅	semidirect
24. C₃×C₄⋊C₄	C₂×C₅	semidirect
27. C₅×D₄	C₃×C₄	semidirect
31. #102	C₃×C₅	direct (N × H)
38. C₃×D₄	C₄×C₅	semidirect
50. C₂×C₈	C₂×C₃×C₅	semidirect
51. C₄⋊C₄	C₂×C₃×C₅	semidirect
52. C₃×C₅	#102	direct (N × H)
66. D₄	C₃×C₄×C₅	semidirect
74. C₅	C₃×#102	direct (N × H)
82. C₃	C₅×#102	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
C₂×C₃×C₅×C₈	2
C₃×C₅×C₄⋊C₄	2
C₅×#102	3
C₃×#102	5

Subgroups — C3×C5×#102 #91129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#102 #91129