Subgroups — C₂×C₄×Dic₁₀ #65801

Order 320.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₀	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₂×#683	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₅	C₂	1	2	yes	maximal
6	C₄×Dic₁₀	C₂	1	8	yes	maximal, direct product factor
7	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂²×Dic₅	C₂²	1	2	yes	—
11	C₂²×Dic₅	C₂²	1	2	yes	—
12	C₂×Dic₁₀	C₄	1	8	yes	direct product factor
13	C₂×Dic₁₀	C₂²	1	4	yes	—
14	C₄²×C₅	C₂²	1	4	yes	—
15	C₄⋊Dic₅	C₂²	1	4	yes	—
16	#683	C₂²	1	8	yes	—
17	C₄×Dic₅	C₂²	1	8	yes	—
18	C₂×C₄×Q₈	—	5	1	no	maximal, Sylow
19	C₂³×C₅	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₅	—	2	2	no	—
21	C₂×C₄×C₅	C₂×C₄	1	4	yes	—
22	C₂×C₄×C₅	Q₈	1	4	yes	complemented
23	C₂×C₄×C₅	C₂³	1	2	yes	—
24	C₂×C₄×C₅	C₂³	1	2	yes	—
25	C₂×C₄×C₅	C₂³	1	2	yes	—
26	C₂×Dic₅	—	2	4	no	—
27	C₂×Dic₅	C₂×C₄	1	8	yes	—
28	C₂×Dic₅	C₂³	1	4	yes	—
29	C₂×Dic₅	C₂³	1	4	yes	—
30	Dic₁₀	C₂×C₄	1	16	yes	direct product factor
31	C₂²×Q₈	—	5	1	no	—
32	C₄×Q₈	—	5	8	no	—
33	C₂×C₄⋊C₄	—	5	2	no	—
34	C₂×C₄⋊C₄	—	5	1	no	—
35	C₂×C₄²	—	5	2	no	—
36	C₂×C₄²	D₅	1	1	yes	characteristic
37	C₂²×C₅	C₂²×C₄	1	2	yes	—
38	C₂²×C₅	C₂×Q₈	1	2	yes	—
39	C₂²×C₅	#41	1	2	yes	—
40	C₂²×C₅	C₂⁴	1	1	yes	characteristic
41	C₄×C₅	—	2	2	no	—
42	C₄×C₅	C₂²×C₄	1	4	yes	—
43	C₄×C₅	C₂×Q₈	1	4	yes	complemented
44	Dic₅	—	2	4	no	—
45	Dic₅	C₂²×C₄	1	8	yes	—
46	C₂×Q₈	—	5	8	no	—
47	C₂×Q₈	—	5	4	no	—
48	C₂²×C₄	—	5	2	no	—
49	C₂²×C₄	—	5	2	no	—
50	C₂²×C₄	C₂×D₅	1	1	yes	characteristic
51	C₂²×C₄	C₂×D₅	1	1	yes	characteristic
52	C₂²×C₄	C₂×D₅	1	1	yes	characteristic
53	C₄⋊C₄	—	5	8	no	—
54	C₄⋊C₄	—	5	4	no	—
55	C₄²	—	5	8	no	—
56	C₄²	C₂×D₅	1	4	yes	—
57	C₂×C₅	C₄×Q₈	1	4	yes	complemented
58	C₂×C₅	C₂³×C₄	1	1	yes	characteristic
59	C₂×C₅	C₂²×Q₈	1	1	yes	characteristic
60	C₂×C₅	C₂×#41	1	1	yes	characteristic
61	C₂³	C₂²×D₅	1	1	yes	characteristic
62	Q₈	—	5	16	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	5	8	no	—
65	C₂×C₄	—	5	4	no	—
66	C₂×C₄	—	5	4	no	—
67	C₂×C₄	—	10	4	no	—
68	C₂×C₄	Dic₁₀	1	4	yes	direct product factor
69	C₂×C₄	C₄×D₅	1	4	yes	—
70	C₂×C₄	C₂²×D₅	1	2	yes	—
71	C₂×C₄	C₂²×D₅	1	2	yes	—
72	C₂×C₄	C₂²×D₅	1	2	yes	—
73	C₅	C₂×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
74	C₂²	C₂×Dic₁₀	1	2	yes	—
75	C₂²	C₂×C₄×D₅	1	2	yes	—
76	C₂²	#709	1	2	yes	—
77	C₂²	C₂³×D₅	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	5	8	no	—
80	C₄	—	10	4	no	—
81	C₄	C₂×Dic₁₀	1	4	yes	direct product factor
82	C₄	C₂×C₄×D₅	1	4	yes	—
83	C₂	C₄×Dic₁₀	1	4	yes	direct product factor
84	C₂	C₂²×Dic₁₀	1	1	yes	characteristic
85	C₂	C₂²×C₄×D₅	1	1	yes	characteristic
86	C₂	C₂×#709	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₅
commutator	C₂×C₅	C₂³×C₄
Frattini	C₂²	C₂³×D₅
Fitting	C₂×C₄²×C₅	C₂
socle, prime radical	C₂³×C₅	C₂³
cosocle	C₂²×C₅	C₂⁴
hypercenter	C₂×C₄²	D₅
hypocenter	C₅	C₂×C₄×Q₈
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
6. C₄×Dic₁₀	C₂	direct (N × H)
12. C₂×Dic₁₀	C₄	direct (N × H)
22. C₂×C₄×C₅	Q₈	semidirect
30. Dic₁₀	C₂×C₄	direct (N × H)
43. C₄×C₅	C₂×Q₈	semidirect
57. C₂×C₅	C₄×Q₈	semidirect
68. C₂×C₄	Dic₁₀	direct (N × H)
73. C₅	C₂×C₄×Q₈	semidirect
81. C₄	C₂×Dic₁₀	direct (N × H)
83. C₂	C₄×Dic₁₀	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×Dic₁₀	2
C₂×C₄²×C₅	2
C₂×C₄⋊Dic₅	2
C₂×#683	2
C₂×C₄×Dic₅	2
C₄×Dic₁₀	2
C₂×C₄×Q₈	5

Subgroups — C2×C4×Dic10 #65801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×Dic₁₀ #65801