Subgroups — C₂×#6668 #91541

Order 480.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×Dic₅	C₂	1	1	yes	maximal, characteristic
4	#6668	C₂	1	4	yes	maximal, direct product factor
5	C₂×#683	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic
7	C₂×Dic₁₅	—	2	2	no	—
8	C₂×Dic₁₅	C₂²	1	2	yes	—
9	C₂×C₅×Dic₃	—	2	2	no	—
10	C₂×C₅×Dic₃	C₂²	1	2	yes	—
11	C₂×C₃×Dic₅	C₄	1	4	yes	complemented
12	C₂×C₃×Dic₅	C₂²	1	2	yes	—
13	C₂×C₄⋊Dic₃	—	5	1	no	maximal, Hall
14	C₂²×C₄×C₅	—	3	1	no	—
15	C₂²×Dic₅	—	3	1	no	—
16	C₂²×Dic₅	D₃	1	1	yes	characteristic
17	#683	—	3	4	no	—
18	C₂²×C₃×C₅	C₂×C₄	1	2	yes	—
19	C₂²×C₃×C₅	D₄	1	2	yes	—
20	C₂²×C₃×C₅	Q₈	1	2	yes	—
21	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
22	Dic₁₅	—	2	2	no	—
23	C₃×Dic₅	C₂×C₄	1	4	yes	complemented
24	C₅×Dic₃	—	2	2	no	—
25	C₂²×C₃×C₄	—	5	1	no	—
26	C₂²×Dic₃	—	5	1	no	—
27	C₂²×Dic₃	D₅	1	1	yes	characteristic
28	C₄⋊Dic₃	—	5	4	no	—
29	C₂³×C₅	C₂×D₃	1	1	yes	characteristic
30	C₂×C₄×C₅	—	3	2	no	—
31	C₂×C₄×C₅	—	6	2	no	—
32	C₂×Dic₅	—	3	2	no	—
33	C₂×Dic₅	—	6	2	no	—
34	C₂×Dic₅	Dic₃	1	4	yes	complemented
35	C₂×Dic₅	C₂×D₃	1	2	yes	—
36	C₂×C₄⋊C₄	—	15	1	no	Sylow
37	C₂×C₃×C₅	C₄⋊C₄	1	4	yes	complemented
38	C₂×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
40	C₂×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
41	C₂³×C₃	C₂×D₅	1	1	yes	characteristic
42	C₂×C₃×C₄	—	5	4	no	—
43	C₂×C₃×C₄	—	5	2	no	—
44	C₂×Dic₃	—	2	2	no	—
45	C₂×Dic₃	—	5	2	no	—
46	C₂×Dic₃	—	10	2	no	—
47	C₂×Dic₃	C₂×D₅	1	2	yes	—
48	C₂²×C₅	Dic₆	1	2	yes	—
49	C₂²×C₅	D₁₂	1	2	yes	—
50	C₂²×C₅	C₂×Dic₃	1	2	yes	—
51	C₂²×C₅	C₂²×D₃	1	1	yes	characteristic
52	C₄×C₅	—	6	2	no	—
53	Dic₅	—	6	2	no	—
54	Dic₅	C₂×Dic₃	1	4	yes	complemented
55	C₂²×C₄	—	3	1	no	—
56	C₂²×C₄	—	5	1	no	—
57	C₂²×C₄	—	15	1	no	—
58	C₄⋊C₄	—	15	4	no	—
59	C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₃	Dic₁₀	1	2	yes	—
61	C₂²×C₃	C₄×D₅	1	2	yes	—
62	C₂²×C₃	C₂²⋊D₅	1	2	yes	—
63	C₂²×C₃	C₂²×D₅	1	1	yes	characteristic
64	C₃×C₄	—	5	4	no	—
65	Dic₃	—	2	2	no	—
66	Dic₃	—	10	2	no	—
67	C₂×C₅	C₄⋊Dic₃	1	4	yes	complemented
68	C₂×C₅	C₂×Dic₆	1	1	yes	characteristic
69	C₂×C₅	C₂×D₁₂	1	1	yes	characteristic
70	C₂×C₅	C₂²×Dic₃	1	1	yes	characteristic
71	C₂³	D₃×D₅	1	1	yes	characteristic
72	C₂×C₄	—	3	2	no	—
73	C₂×C₄	—	5	4	no	—
74	C₂×C₄	—	5	2	no	—
75	C₂×C₄	—	6	2	no	—
76	C₂×C₄	—	15	2	no	—
77	C₂×C₄	—	30	2	no	—
78	C₂×C₃	#683	1	4	yes	complemented
79	C₂×C₃	C₂×Dic₁₀	1	1	yes	characteristic
80	C₂×C₃	C₂×C₄×D₅	1	1	yes	characteristic
81	C₂×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
82	C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
83	C₂²	D₅×Dic₃	1	2	yes	—
84	C₂²	#1203	1	2	yes	—
85	C₂²	#1204	1	2	yes	—
86	C₂²	C₂×D₃×D₅	1	1	yes	characteristic
87	C₄	—	5	4	no	—
88	C₄	—	6	2	no	—
89	C₄	—	30	2	no	—
90	C₃	C₂×#683	1	1	yes	characteristic, complemented, Sylow
91	C₂	#6668	1	4	yes	direct product factor
92	C₂	C₂×D₅×Dic₃	1	1	yes	characteristic
93	C₂	C₂×#1203	1	1	yes	characteristic
94	C₂	C₂×#1204	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. #6668	C₂	direct (N × H)
11. C₂×C₃×Dic₅	C₄	semidirect
23. C₃×Dic₅	C₂×C₄	semidirect
34. C₂×Dic₅	Dic₃	semidirect
37. C₂×C₃×C₅	C₄⋊C₄	semidirect
54. Dic₅	C₂×Dic₃	semidirect
59. C₃×C₅	C₂×C₄⋊C₄	semidirect
67. C₂×C₅	C₄⋊Dic₃	semidirect
78. C₂×C₃	#683	semidirect
82. C₅	C₂×C₄⋊Dic₃	semidirect
90. C₃	C₂×#683	semidirect
91. C₂	#6668	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×Dic₁₅	2
C₂²×C₅×Dic₃	2
C₂²×C₃×Dic₅	2
#6668	2
C₂×#683	3
C₂×C₄⋊Dic₃	5

Subgroups — C2×#6668 #91541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6668 #91541