Subgroups — Q₈×Dic₁₀ #65900

Order 320.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₅	C₂	1	2	yes	maximal
3	#4034	C₂	1	6	yes	maximal
4	#4015	C₂	1	3	yes	maximal
5	C₄×Dic₁₀	C₂	1	3	yes	maximal
6	C₂×C₅×Q₈	C₂²	1	1	yes	characteristic
7	C₂×Dic₁₀	C₂²	1	6	yes	—
8	C₂×Dic₁₀	C₂²	1	1	yes	characteristic
9	C₅×C₄⋊C₄	C₂²	1	3	yes	—
10	C₄²×C₅	C₂²	1	3	yes	—
11	C₄⋊Dic₅	C₂²	1	3	yes	—
12	C₄⋊Dic₅	C₂²	1	6	yes	—
13	#683	C₂²	1	6	yes	—
14	C₄×Dic₅	C₂²	1	6	yes	—
15	Q₈²	—	5	1	no	maximal, Sylow
16	C₅×Q₈	Q₈	1	4	yes	complemented
17	C₂×C₄×C₅	C₂³	1	3	yes	—
18	C₂×C₄×C₅	C₂³	1	3	yes	—
19	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
20	C₂×Dic₅	C₂³	1	6	yes	—
21	C₂×Dic₅	C₂³	1	2	yes	—
22	Dic₁₀	—	4	6	no	—
23	Dic₁₀	Q₈	1	4	yes	direct product factor
24	C₄⋊Q₈	—	5	6	no	—
25	C₄⋊Q₈	—	5	3	no	—
26	C₄×Q₈	—	5	2	no	—
27	C₄×Q₈	—	5	3	no	—
28	C₄×Q₈	D₅	1	1	yes	characteristic
29	C₂²×C₅	C₂⁴	1	1	yes	characteristic
30	C₄×C₅	—	2	3	no	—
31	C₄×C₅	C₂×Q₈	1	6	yes	—
32	C₄×C₅	C₂×Q₈	1	2	yes	—
33	Dic₅	—	2	6	no	—
34	Dic₅	C₂×Q₈	1	4	yes	—
35	C₂×Q₈	—	5	1	no	—
36	C₂×Q₈	—	5	6	no	—
37	C₂×Q₈	C₂×D₅	1	1	yes	characteristic
38	C₄⋊C₄	—	5	6	no	—
39	C₄⋊C₄	—	5	6	no	—
40	C₄⋊C₄	—	5	3	no	—
41	C₄⋊C₄	C₂×D₅	1	3	yes	—
42	C₄²	—	5	6	no	—
43	C₄²	C₂×D₅	1	3	yes	—
44	C₂×C₅	C₂²×Q₈	1	1	yes	characteristic
45	C₂×C₅	C₂²×Q₈	1	1	yes	characteristic
46	C₂×C₅	H(5,𝔽₂)	1	1	yes	characteristic
47	Q₈	—	5	4	no	—
48	Q₈	—	20	6	no	—
49	Q₈	Dic₁₀	1	4	yes	direct product factor
50	C₂×C₄	—	5	2	no	—
51	C₂×C₄	—	5	6	no	—
52	C₂×C₄	C₂²×D₅	1	3	yes	—
53	C₂×C₄	C₂²×D₅	1	3	yes	—
54	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
55	C₅	Q₈²	1	1	yes	characteristic, complemented, Sylow
56	C₂²	C₂³×D₅	1	1	yes	characteristic
57	C₄	—	2	3	no	—
58	C₄	—	5	4	no	—
59	C₄	—	10	6	no	—
60	C₄	C₂×Dic₁₀	1	6	yes	—
61	C₄	Q₈×D₅	1	2	yes	—
62	C₂	C₂²×Dic₁₀	1	1	yes	characteristic
63	C₂	C₂×Q₈×D₅	1	1	yes	characteristic
64	C₂	#4149	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₅
commutator, socle, prime radical, cosocle	C₂²×C₅	C₂⁴
Fitting	C₄×C₅×Q₈	C₂
hypercenter	C₄×Q₈	D₅
hypocenter	C₅	Q₈²
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
16. C₅×Q₈	Q₈	semidirect
23. Dic₁₀	Q₈	direct (N × H)
49. Q₈	Dic₁₀	direct (N × H)
55. C₅	Q₈²	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×Q₈	2
Q₈×Dic₅	2
#4034	2
#4015	2
C₄×Dic₁₀	2
Q₈²	5

Subgroups — Q8×Dic10 #65900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×Dic₁₀ #65900