Subgroups — C₂×#6660 #91317

Order 480.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₆₀	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	#6660	C₂	1	4	yes	maximal, direct product factor
5	C₂×#688	—	3	1	no	maximal, Hall
6	C₂²×D₁₅	—	2	1	no	—
7	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	D₆₀	—	2	1	no	—
9	D₆₀	C₂²	1	2	yes	—
10	C₂×C₅×Dic₃	—	2	1	no	—
11	C₅×Dic₆	—	2	1	no	—
12	C₅×Dic₆	C₂²	1	2	yes	complemented
13	C₃×#168	C₂²	1	2	yes	complemented
14	C₂×#204	—	5	1	no	maximal, Hall
15	C₂×C₅×Q₈	—	3	1	no	—
16	C₂×D₂₀	—	3	1	no	—
17	#688	—	3	4	no	—
18	C₂×#168	D₃	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₅	D₄	1	1	yes	characteristic
20	C₂×D₁₅	—	2	2	no	—
21	C₂×D₁₅	—	4	2	no	—
22	C₃×C₄×C₅	D₄	1	1	yes	characteristic
23	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
24	C₅×Dic₃	—	2	2	no	—
25	C₂×D₁₂	—	5	1	no	—
26	C₂×Dic₆	D₅	1	1	yes	characteristic, complemented
27	C₂×C₃×C₈	—	5	1	no	—
28	#204	—	5	4	no	—
29	C₂²×D₅	—	6	1	no	—
30	C₅×Q₈	—	3	2	no	—
31	C₅×Q₈	—	6	1	no	—
32	C₂×C₄×C₅	—	6	1	no	—
33	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
34	D₂₀	—	3	2	no	—
35	D₂₀	—	6	1	no	—
36	#168	C₂×D₃	1	2	yes	complemented
37	C₂×SD₁₆	—	15	1	no	Sylow
38	C₂×C₃×C₅	SD₁₆	1	2	yes	complemented
39	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
40	D₁₅	—	4	2	no	—
41	C₂²×D₃	—	10	1	no	—
42	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
43	C₂×Dic₃	—	2	1	no	—
44	D₁₂	—	5	2	no	—
45	D₁₂	—	10	1	no	—
46	Dic₆	—	2	1	no	—
47	Dic₆	C₂×D₅	1	2	yes	complemented
48	C₃×C₈	—	5	2	no	—
49	C₂²×C₅	D₁₂	1	1	yes	characteristic
50	C₂×D₅	—	6	2	no	—
51	C₂×D₅	—	12	2	no	—
52	C₄×C₅	—	6	2	no	—
53	C₄×C₅	D₁₂	1	1	yes	characteristic
54	C₄×C₅	C₂²×D₃	1	1	yes	characteristic
55	C₂×Q₈	—	3	1	no	—
56	C₂×D₄	—	15	1	no	—
57	SD₁₆	—	15	4	no	—
58	C₂×C₈	—	5	1	no	—
59	C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₃	C₂²⋊D₅	1	1	yes	characteristic
61	C₂×D₃	—	10	2	no	—
62	C₂×D₃	—	20	2	no	—
63	C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
64	C₃×C₄	C₂²×D₅	1	1	yes	characteristic
65	Dic₃	—	2	2	no	—
66	C₂×C₅	#204	1	2	yes	complemented
67	C₂×C₅	C₂×D₁₂	1	1	yes	characteristic
68	D₅	—	12	2	no	—
69	C₂³	—	30	1	no	—
70	Q₈	—	3	2	no	—
71	Q₈	—	6	1	no	—
72	D₄	—	15	2	no	—
73	D₄	—	30	1	no	—
74	C₂×C₄	—	6	1	no	—
75	C₂×C₄	D₃×D₅	1	1	yes	characteristic
76	C₈	—	5	2	no	—
77	C₂×C₃	#688	1	2	yes	complemented
78	C₂×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
79	D₃	—	20	2	no	—
80	C₅	C₂×#204	1	1	yes	characteristic, complemented, Sylow
81	C₂²	—	30	2	no	—
82	C₂²	—	60	2	no	—
83	C₂²	#1203	1	1	yes	characteristic
84	C₄	—	6	2	no	—
85	C₄	#1203	1	1	yes	characteristic
86	C₄	C₂×D₃×D₅	1	1	yes	characteristic
87	C₃	C₂×#688	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	60	2	no	—
89	C₂	#6660	1	2	yes	direct product factor
90	C₂	C₂×#1203	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#1203
commutator, cosocle	C₃×C₄×C₅	C₂³
Frattini	C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₄×C₅	C₂²
socle	C₂²×C₃×C₅	D₄
prime radical	C₂×D₆₀	C₂
hypercenter	C₂×C₄	D₃×D₅
hypocenter	C₃×C₅	C₂×SD₁₆
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×Dic₆	C₂	semidirect
3. C₂×C₃×#168	C₂	semidirect
4. #6660	C₂	direct (N × H)
12. C₅×Dic₆	C₂²	semidirect
13. C₃×#168	C₂²	semidirect
18. C₂×#168	D₃	semidirect
26. C₂×Dic₆	D₅	semidirect
36. #168	C₂×D₃	semidirect
38. C₂×C₃×C₅	SD₁₆	semidirect
47. Dic₆	C₂×D₅	semidirect
59. C₃×C₅	C₂×SD₁₆	semidirect
66. C₂×C₅	#204	semidirect
77. C₂×C₃	#688	semidirect
80. C₅	C₂×#204	semidirect
87. C₃	C₂×#688	semidirect
89. C₂	#6660	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×D₆₀	2
C₂×C₅×Dic₆	2
C₂×C₃×#168	2
#6660	2
C₂×#688	3
C₂×#204	5

Subgroups — C2×#6660 #91317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6660 #91317