Subgroups — C₂×Q₈×Dic₅ #66145

Order 320.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₅	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊Dic₅	C₂	1	3	yes	maximal
4	C₂×C₄×Dic₅	C₂	1	3	yes	maximal
5	C₂×C₅×Q₈	C₄	1	8	yes	complemented
6	C₂×C₅×Q₈	C₂²	1	4	yes	—
7	C₂²×C₄×C₅	C₂²	1	3	yes	—
8	C₂²×Dic₅	C₂²	1	3	yes	—
9	C₂²×Dic₅	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₅	C₂²	1	12	yes	—
11	C₄×Dic₅	C₂²	1	12	yes	—
12	C₂×C₄×Q₈	—	5	1	no	maximal, Sylow
13	C₂³×C₅	C₂³	1	1	yes	characteristic
14	C₅×Q₈	C₂×C₄	1	16	yes	complemented
15	C₂×C₄×C₅	C₂×C₄	1	12	yes	—
16	C₂×C₄×C₅	C₂³	1	6	yes	—
17	C₂×Dic₅	—	2	6	no	—
18	C₂×Dic₅	Q₈	1	4	yes	direct product factor
19	C₂×Dic₅	C₂³	1	6	yes	—
20	C₂×Dic₅	C₂³	1	2	yes	—
21	C₂²×Q₈	D₅	1	1	yes	characteristic
22	C₄×Q₈	—	5	8	no	—
23	C₂×C₄⋊C₄	—	5	3	no	—
24	C₂×C₄²	—	5	3	no	—
25	C₂²×C₅	C₂²×C₄	1	2	yes	—
26	C₂²×C₅	C₂×Q₈	1	2	yes	—
27	C₂²×C₅	#41	1	2	yes	—
28	C₂²×C₅	C₂⁴	1	1	yes	characteristic
29	C₄×C₅	C₂²×C₄	1	12	yes	—
30	Dic₅	—	2	6	no	—
31	Dic₅	C₂×Q₈	1	4	yes	direct product factor
32	C₂×Q₈	Dic₅	1	8	yes	direct product factor
33	C₂×Q₈	C₂×D₅	1	4	yes	—
34	C₂²×C₄	—	5	1	no	—
35	C₂²×C₄	—	5	3	no	—
36	C₂²×C₄	C₂×D₅	1	3	yes	—
37	C₄⋊C₄	—	5	12	no	—
38	C₄²	—	5	12	no	—
39	C₂×C₅	C₄×Q₈	1	4	yes	complemented
40	C₂×C₅	C₂³×C₄	1	1	yes	characteristic
41	C₂×C₅	C₂²×Q₈	1	1	yes	characteristic
42	C₂×C₅	C₂×#41	1	1	yes	characteristic
43	C₂³	C₂²×D₅	1	1	yes	characteristic
44	Q₈	C₂×Dic₅	1	16	yes	direct product factor
45	C₂×C₄	—	5	4	no	—
46	C₂×C₄	—	5	2	no	—
47	C₂×C₄	—	5	6	no	—
48	C₂×C₄	—	10	6	no	—
49	C₂×C₄	C₂×Dic₅	1	12	yes	—
50	C₂×C₄	C₂²×D₅	1	6	yes	—
51	C₅	C₂×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
52	C₂²	Q₈×D₅	1	2	yes	—
53	C₂²	#713	1	2	yes	—
54	C₂²	C₂²×Dic₅	1	2	yes	—
55	C₂²	C₂³×D₅	1	1	yes	characteristic
56	C₄	—	5	4	no	—
57	C₄	—	10	6	no	—
58	C₄	C₂²×Dic₅	1	12	yes	—
59	C₂	Q₈×Dic₅	1	4	yes	direct product factor
60	C₂	C₂×Q₈×D₅	1	1	yes	characteristic
61	C₂	C₂×#713	1	1	yes	characteristic
62	C₂	C₂³×Dic₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. Q₈×Dic₅	C₂	direct (N × H)
5. C₂×C₅×Q₈	C₄	semidirect
14. C₅×Q₈	C₂×C₄	semidirect
18. C₂×Dic₅	Q₈	direct (N × H)
31. Dic₅	C₂×Q₈	direct (N × H)
32. C₂×Q₈	Dic₅	direct (N × H)
39. C₂×C₅	C₄×Q₈	semidirect
44. Q₈	C₂×Dic₅	direct (N × H)
51. C₅	C₂×C₄×Q₈	semidirect
59. C₂	Q₈×Dic₅	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×C₅×Q₈	2
Q₈×Dic₅	2
C₂×C₄⋊Dic₅	2
C₂×C₄×Dic₅	2
C₂×C₄×Q₈	5

Subgroups — C2×Q8×Dic5 #66145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×Dic₅ #66145