Subgroups — C₂×#6662 #91319

Order 480.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₀	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₁₀	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#6662	C₂	1	4	yes	maximal, direct product factor
5	C₂×Dic₂₀	—	3	1	no	maximal, Hall
6	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂×Dic₁₅	—	2	1	no	—
8	Dic₃₀	—	2	1	no	—
9	Dic₃₀	C₂²	1	2	yes	—
10	C₂×C₃×Dic₅	—	2	1	no	—
11	C₃×Dic₁₀	—	2	1	no	—
12	C₃×Dic₁₀	C₂²	1	2	yes	—
13	C₅×C₃⋊C₈	C₂²	1	2	yes	—
14	C₂×#216	—	5	1	no	maximal, Hall
15	C₂×Dic₁₀	—	3	1	no	—
16	C₂×Dic₁₀	D₃	1	1	yes	characteristic
17	C₂×C₅×C₈	—	3	1	no	—
18	Dic₂₀	—	3	4	no	—
19	C₂²×C₃×C₅	D₄	1	1	yes	characteristic
20	C₃×C₄×C₅	D₄	1	1	yes	characteristic
21	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
22	Dic₁₅	—	2	2	no	—
23	C₃×Dic₅	—	2	2	no	—
24	C₂×C₃×Q₈	—	5	1	no	—
25	C₂×Dic₆	—	5	1	no	—
26	#216	—	5	4	no	—
27	C₂×C₃⋊C₈	D₅	1	1	yes	characteristic
28	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
29	C₂×Dic₅	—	2	1	no	—
30	C₂×Dic₅	—	6	1	no	—
31	Dic₁₀	—	2	1	no	—
32	Dic₁₀	—	3	2	no	—
33	Dic₁₀	—	6	1	no	—
34	Dic₁₀	C₂×D₃	1	2	yes	—
35	C₅×C₈	—	3	2	no	—
36	C₂×Q₁₆	—	15	1	no	Sylow
37	C₂×C₃×C₅	Q₁₆	1	2	yes	complemented
38	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
39	C₃×Q₈	—	5	2	no	—
40	C₃×Q₈	—	10	1	no	—
41	C₂×C₃×C₄	—	10	1	no	—
42	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
43	C₂×Dic₃	—	10	1	no	—
44	Dic₆	—	5	2	no	—
45	Dic₆	—	10	1	no	—
46	C₃⋊C₈	C₂×D₅	1	2	yes	—
47	C₂²×C₅	#67	1	1	yes	characteristic
48	C₄×C₅	#67	1	1	yes	characteristic
49	C₄×C₅	C₂²×D₃	1	1	yes	characteristic
50	Dic₅	—	2	2	no	—
51	Dic₅	—	6	2	no	—
52	C₂×Q₈	—	5	1	no	—
53	C₂×Q₈	—	15	1	no	—
54	Q₁₆	—	15	4	no	—
55	C₂×C₈	—	3	1	no	—
56	C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
57	C₂²×C₃	D₂₀	1	1	yes	characteristic
58	C₃×C₄	—	10	2	no	—
59	C₃×C₄	D₂₀	1	1	yes	characteristic
60	C₃×C₄	C₂²×D₅	1	1	yes	characteristic
61	Dic₃	—	10	2	no	—
62	C₂×C₅	#216	1	2	yes	complemented
63	C₂×C₅	C₂×#67	1	1	yes	characteristic
64	Q₈	—	5	2	no	—
65	Q₈	—	10	1	no	—
66	Q₈	—	15	2	no	—
67	Q₈	—	30	1	no	—
68	C₂×C₄	—	10	1	no	—
69	C₂×C₄	—	30	1	no	—
70	C₂×C₄	D₃×D₅	1	1	yes	characteristic
71	C₈	—	3	2	no	—
72	C₂×C₃	Dic₂₀	1	2	yes	complemented
73	C₂×C₃	C₂×D₂₀	1	1	yes	characteristic
74	C₅	C₂×#216	1	1	yes	characteristic, complemented, Sylow
75	C₂²	#1202	1	1	yes	characteristic
76	C₄	—	10	2	no	—
77	C₄	—	30	2	no	—
78	C₄	#1202	1	1	yes	characteristic
79	C₄	C₂×D₃×D₅	1	1	yes	characteristic
80	C₃	C₂×Dic₂₀	1	1	yes	characteristic, complemented, Sylow
81	C₂	#6662	1	2	yes	direct product factor
82	C₂	C₂×#1202	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#1202
commutator, cosocle	C₃×C₄×C₅	C₂³
Frattini	C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₄×C₅	C₂²
socle, prime radical	C₂²×C₃×C₅	D₄
hypercenter	C₂×C₄	D₃×D₅
hypocenter	C₃×C₅	C₂×Q₁₆
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
4. #6662	C₂	direct (N × H)
37. C₂×C₃×C₅	Q₁₆	semidirect
56. C₃×C₅	C₂×Q₁₆	semidirect
62. C₂×C₅	#216	semidirect
72. C₂×C₃	Dic₂₀	semidirect
74. C₅	C₂×#216	semidirect
80. C₃	C₂×Dic₂₀	semidirect
81. C₂	#6662	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×Dic₃₀	2
C₂×C₃×Dic₁₀	2
C₂×C₅×C₃⋊C₈	2
#6662	2
C₂×Dic₂₀	3
C₂×#216	5

Subgroups — C2×#6662 #91319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6662 #91319