Subgroups — C₂×C₃×#687 #91650

Order 480.

136 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×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#687	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#687	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×C₅	—	2	1	no	—
7	C₃×C₅×D₄	—	2	1	no	—
8	C₃×C₅×D₄	C₂²	1	2	yes	—
9	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×Dic₅	—	2	1	no	—
11	C₃×Dic₁₀	—	2	1	no	—
12	C₃×Dic₁₀	C₂²	1	2	yes	complemented
13	C₃×#168	C₂²	1	2	yes	complemented
14	C₂×C₃×SD₁₆	—	5	1	no	maximal, Hall
15	C₂×C₅×D₄	C₂×C₃	1	1	yes	characteristic
16	C₂×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
17	#687	C₂×C₃	1	4	yes	direct product factor
18	C₂×#168	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₅	—	2	2	no	—
20	C₂²×C₃×C₅	—	4	2	no	—
21	C₂²×C₃×C₅	D₄	1	1	yes	characteristic
22	C₃×C₄×C₅	D₄	1	1	yes	characteristic
23	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
24	C₃×Dic₅	—	2	2	no	—
25	C₂×C₃×Q₈	—	5	1	no	—
26	C₂×C₃×D₄	D₅	1	1	yes	characteristic
27	C₃×SD₁₆	—	5	4	no	—
28	C₂×C₃×C₈	—	5	1	no	—
29	C₂³×C₅	—	2	1	no	—
30	C₅×D₄	—	2	1	no	—
31	C₅×D₄	C₂²×C₃	1	2	yes	—
32	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
33	C₂×Dic₅	—	2	1	no	—
34	Dic₁₀	—	2	1	no	—
35	Dic₁₀	C₂²×C₃	1	2	yes	complemented
36	#168	C₂²×C₃	1	2	yes	complemented
37	C₂×SD₁₆	—	5	1	no	Sylow
38	C₂×C₃×C₅	—	4	2	no	—
39	C₂×C₃×C₅	SD₁₆	1	2	yes	complemented
40	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
41	C₂³×C₃	—	2	1	no	—
42	C₃×Q₈	—	5	2	no	—
43	C₃×Q₈	—	10	1	no	—
44	C₃×D₄	—	2	1	no	—
45	C₃×D₄	C₂×D₅	1	2	yes	—
46	C₂×C₃×C₄	—	10	1	no	—
47	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
48	C₃×C₈	—	5	2	no	—
49	C₂²×C₅	—	2	2	no	—
50	C₂²×C₅	—	4	2	no	—
51	C₂²×C₅	C₃×D₄	1	1	yes	characteristic
52	C₄×C₅	C₃×D₄	1	1	yes	characteristic
53	C₄×C₅	C₂³×C₃	1	1	yes	characteristic
54	Dic₅	—	2	2	no	—
55	C₂×Q₈	—	5	1	no	—
56	C₂×D₄	C₃×D₅	1	1	yes	characteristic
57	SD₁₆	—	5	4	no	—
58	C₂×C₈	—	5	1	no	—
59	C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₃	—	2	2	no	—
61	C₂²×C₃	—	4	2	no	—
62	C₂²×C₃	C₂²⋊D₅	1	1	yes	characteristic
63	C₃×C₄	—	10	2	no	—
64	C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
65	C₃×C₄	C₂²×D₅	1	1	yes	characteristic
66	C₂×C₅	—	4	2	no	—
67	C₂×C₅	C₃×SD₁₆	1	2	yes	complemented
68	C₂×C₅	C₂×C₃×D₄	1	1	yes	characteristic
69	C₂³	—	2	1	no	—
70	Q₈	—	5	2	no	—
71	Q₈	—	10	1	no	—
72	D₄	—	2	1	no	—
73	D₄	C₂×C₃×D₅	1	2	yes	—
74	C₂×C₄	—	10	1	no	—
75	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
76	C₈	—	5	2	no	—
77	C₂×C₃	—	4	2	no	—
78	C₂×C₃	#687	1	2	yes	direct product factor
79	C₂×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
80	C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic, complemented, Sylow
81	C₂²	—	2	2	no	—
82	C₂²	—	4	2	no	—
83	C₂²	C₃×C₂²⋊D₅	1	1	yes	characteristic
84	C₄	—	10	2	no	—
85	C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
86	C₄	C₂²×C₃×D₅	1	1	yes	characteristic
87	C₃	C₂×#687	1	1	yes	characteristic, direct product factor, Sylow
88	C₂	—	4	2	no	—
89	C₂	C₃×#687	1	2	yes	direct product factor
90	C₂	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²⋊D₅
commutator, cosocle	C₄×C₅	C₂³×C₃
Frattini	C₄	C₂²×C₃×D₅
Fitting, prime radical	C₂×C₃×C₅×D₄	C₂
socle	C₂²×C₃×C₅	D₄
hypercenter	C₂×C₃×D₄	D₅
hypocenter	C₅	C₂×C₃×SD₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×Dic₁₀	C₂	semidirect
3. C₃×#687	C₂	direct (N × H)
4. C₂×C₃×#168	C₂	semidirect
5. C₂×#687	C₃	direct (N × H)
12. C₃×Dic₁₀	C₂²	semidirect
13. C₃×#168	C₂²	semidirect
16. C₂×Dic₁₀	C₂×C₃	semidirect
17. #687	C₂×C₃	direct (N × H)
18. C₂×#168	C₂×C₃	semidirect
35. Dic₁₀	C₂²×C₃	semidirect
36. #168	C₂²×C₃	semidirect
39. C₂×C₃×C₅	SD₁₆	semidirect
59. C₃×C₅	C₂×SD₁₆	semidirect
67. C₂×C₅	C₃×SD₁₆	semidirect
78. C₂×C₃	#687	direct (N × H)
80. C₅	C₂×C₃×SD₁₆	semidirect
87. C₃	C₂×#687	direct (N × H)
89. C₂	C₃×#687	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×Dic₁₀	2
C₃×#687	2
C₂×C₃×#168	2
C₂×#687	3
C₂×C₃×SD₁₆	5

Subgroups — C2×C3×#687 #91650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#687 #91650