Subgroups — C₂×#6656 #91308

Order 480.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
4	#6656	C₂	1	4	yes	maximal, direct product factor
5	C₂×#687	—	3	1	no	maximal, Hall
6	C₂²×C₅×D₃	—	2	1	no	—
7	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₅×D₁₂	—	2	1	no	—
9	C₅×D₁₂	C₂²	1	2	yes	—
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×#215	—	5	1	no	maximal, Hall
15	C₂×C₅×D₄	—	3	1	no	—
16	C₂×Dic₁₀	D₃	1	1	yes	characteristic, complemented
17	#687	—	3	4	no	—
18	C₂×#168	—	3	1	no	—
19	C₂²×C₃×C₅	D₄	1	1	yes	characteristic
20	C₂×C₅×D₃	—	2	2	no	—
21	C₂×C₅×D₃	—	4	2	no	—
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×D₁₂	D₅	1	1	yes	characteristic
27	#215	—	5	4	no	—
28	C₂×C₃⋊C₈	—	5	1	no	—
29	C₂³×C₅	—	6	1	no	—
30	C₅×D₄	—	3	2	no	—
31	C₅×D₄	—	6	1	no	—
32	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
33	C₂×Dic₅	—	2	1	no	—
34	Dic₁₀	—	2	1	no	—
35	Dic₁₀	C₂×D₃	1	2	yes	complemented
36	#168	—	3	2	no	—
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	C₅×D₃	—	4	2	no	—
41	C₂²×D₃	—	2	1	no	—
42	C₃×Q₈	—	5	2	no	—
43	C₃×Q₈	—	10	1	no	—
44	C₂×C₃×C₄	—	10	1	no	—
45	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
46	D₁₂	—	2	1	no	—
47	D₁₂	C₂×D₅	1	2	yes	—
48	C₃⋊C₈	—	5	2	no	—
49	C₂²×C₅	—	6	2	no	—
50	C₂²×C₅	—	12	2	no	—
51	C₂²×C₅	#67	1	1	yes	characteristic
52	C₄×C₅	#67	1	1	yes	characteristic
53	C₄×C₅	C₂²×D₃	1	1	yes	characteristic
54	Dic₅	—	2	2	no	—
55	C₂×Q₈	—	5	1	no	—
56	C₂×D₄	—	3	1	no	—
57	SD₁₆	—	15	4	no	—
58	C₂×C₈	—	15	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	—	2	2	no	—
62	C₂×D₃	—	4	2	no	—
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	—	12	2	no	—
67	C₂×C₅	#215	1	2	yes	complemented
68	C₂×C₅	C₂×#67	1	1	yes	characteristic
69	C₂³	—	6	1	no	—
70	Q₈	—	5	2	no	—
71	Q₈	—	10	1	no	—
72	D₄	—	3	2	no	—
73	D₄	—	6	1	no	—
74	C₂×C₄	—	10	1	no	—
75	C₂×C₄	D₃×D₅	1	1	yes	characteristic
76	C₈	—	15	2	no	—
77	C₂×C₃	#687	1	2	yes	complemented
78	C₂×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
79	D₃	—	4	2	no	—
80	C₅	C₂×#215	1	1	yes	characteristic, complemented, Sylow
81	C₂²	—	6	2	no	—
82	C₂²	—	12	2	no	—
83	C₂²	#1201	1	1	yes	characteristic
84	C₄	—	10	2	no	—
85	C₄	#1201	1	1	yes	characteristic
86	C₄	C₂×D₃×D₅	1	1	yes	characteristic
87	C₃	C₂×#687	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	12	2	no	—
89	C₂	#6656	1	2	yes	direct product factor
90	C₂	C₂×#1201	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#1201
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×C₅×D₁₂	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×C₃×Dic₁₀	C₂	semidirect
3. C₂×C₃⋊#168	C₂	semidirect
4. #6656	C₂	direct (N × H)
12. C₃×Dic₁₀	C₂²	semidirect
13. C₃⋊#168	C₂²	semidirect
16. C₂×Dic₁₀	D₃	semidirect
35. Dic₁₀	C₂×D₃	semidirect
38. C₂×C₃×C₅	SD₁₆	semidirect
59. C₃×C₅	C₂×SD₁₆	semidirect
67. C₂×C₅	#215	semidirect
77. C₂×C₃	#687	semidirect
80. C₅	C₂×#215	semidirect
87. C₃	C₂×#687	semidirect
89. C₂	#6656	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×C₅×D₁₂	2
C₂×C₃×Dic₁₀	2
C₂×C₃⋊#168	2
#6656	2
C₂×#687	3
C₂×#215	5

Subgroups — C2×#6656 #91308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6656 #91308