Subgroups — D₅×2₋¹⁺⁴ #66286

Order 320.

794 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	#4150	C₂	1	10	yes	maximal, complemented
3	D₅×#41	C₂	1	10	yes	maximal, complemented
4	#4147	C₂	1	5	yes	maximal, complemented
5	C₂×Q₈×D₅	C₂	1	5	yes	maximal, complemented
6	C₅×#41	C₂²	1	10	yes	complemented
7	C₂×C₅×Q₈	C₂²	1	5	yes	complemented
8	#713	C₂²	1	10	yes	complemented
9	Q₈×D₅	C₂²	1	10	yes	—
10	Q₈×D₅	C₂²	1	20	yes	complemented
11	#711	C₂²	1	30	yes	complemented
12	D₄×D₅	C₂²	1	10	yes	—
13	#709	C₂²	1	30	yes	complemented
14	C₂×C₄×D₅	C₂²	1	15	yes	—
15	C₂×Dic₁₀	C₂²	1	15	yes	complemented
16	C₂×2₋¹⁺⁴	—	5	1	no	maximal, Sylow
17	C₂²×D₅	C₂³	1	5	yes	—
18	C₅×Q₈	C₂³	1	10	yes	—
19	C₅×D₄	C₂³	1	10	yes	—
20	C₂×C₄×C₅	C₂³	1	15	yes	—
21	C₂²⋊D₅	C₂³	1	20	yes	—
22	C₂×Dic₅	C₂³	1	15	yes	—
23	D₂₀	C₂³	1	10	yes	—
24	C₄×D₅	C₂³	1	10	yes	—
25	C₄×D₅	C₂³	1	30	yes	—
26	Dic₁₀	C₂³	1	30	yes	—
27	2₋¹⁺⁴	—	5	10	no	—
28	2₋¹⁺⁴	—	5	5	no	—
29	2₋¹⁺⁴	D₅	1	1	yes	characteristic, direct product factor
30	C₂×#41	—	5	10	no	—
31	C₂²×Q₈	—	5	5	no	—
32	C₂²×C₅	C₂⁴	1	5	yes	—
33	C₂×D₅	—	2	10	no	—
34	C₂×D₅	C₂⁴	1	5	yes	—
35	C₂×D₅	C₂⁴	1	1	yes	characteristic
36	C₄×C₅	C₂⁴	1	10	yes	—
37	Dic₅	C₂⁴	1	10	yes	—
38	#41	—	5	10	no	—
39	#41	—	5	30	no	—
40	#41	—	5	30	no	—
41	#41	C₂×D₅	1	10	yes	complemented
42	C₂×Q₈	—	5	10	no	—
43	C₂×Q₈	—	5	20	no	—
44	C₂×Q₈	—	5	15	no	—
45	C₂×Q₈	C₂×D₅	1	5	yes	complemented
46	C₂×D₄	—	5	10	no	—
47	C₂²×C₄	—	5	15	no	—
48	C₂×C₅	—	2	5	no	—
49	C₂×C₅	C₂⁵	1	1	yes	characteristic
50	D₅	—	2	5	no	—
51	D₅	2₋¹⁺⁴	1	2	yes	direct product factor
52	C₂³	—	5	5	no	—
53	Q₈	—	5	30	no	—
54	Q₈	C₂²×D₅	1	10	yes	—
55	D₄	—	5	20	no	—
56	D₄	—	5	10	no	—
57	D₄	C₂²×D₅	1	10	yes	—
58	C₂×C₄	—	5	15	no	—
59	C₂×C₄	—	5	10	no	—
60	C₂×C₄	—	5	30	no	—
61	C₂×C₄	C₂²×D₅	1	15	yes	—
62	C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
63	C₂²	—	5	1	no	—
64	C₂²	—	5	5	no	—
65	C₂²	—	10	10	no	—
66	C₂²	C₂³×D₅	1	5	yes	—
67	C₄	—	5	10	no	—
68	C₄	C₂³×D₅	1	10	yes	—
69	C₂	—	2	5	no	—
70	C₂	—	5	2	no	—
71	C₂	—	10	5	no	—
72	C₂	C₂⁴×D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂⁴×D₅
commutator, socle, cosocle	C₂×C₅	C₂⁵
Fitting	C₅×2₋¹⁺⁴	C₂
hypercenter	2₋¹⁺⁴	D₅
hypocenter	C₅	C₂×2₋¹⁺⁴
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ 2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. C₅×2₋¹⁺⁴	C₂	semidirect
2. #4150	C₂	semidirect
3. D₅×#41	C₂	semidirect
4. #4147	C₂	semidirect
5. C₂×Q₈×D₅	C₂	semidirect
6. C₅×#41	C₂²	semidirect
7. C₂×C₅×Q₈	C₂²	semidirect
8. #713	C₂²	semidirect
10. Q₈×D₅	C₂²	semidirect
11. #711	C₂²	semidirect
13. #709	C₂²	semidirect
15. C₂×Dic₁₀	C₂²	semidirect
29. 2₋¹⁺⁴	D₅	direct (N × H)
41. #41	C₂×D₅	semidirect
45. C₂×Q₈	C₂×D₅	semidirect
51. D₅	2₋¹⁺⁴	direct (N × H)
62. C₅	C₂×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₅×2₋¹⁺⁴	2
#4150	2
D₅×#41	2
#4147	2
C₂×Q₈×D₅	2
C₂×2₋¹⁺⁴	5

Subgroups — D5×2−1+4 #66286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×2₋¹⁺⁴ #66286