Subgroups — D₅×#127 #66048

Order 320.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×D₅	C₂	1	6	yes	maximal, complemented
2	C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	#4086	C₂	1	6	yes	maximal, complemented
4	#4020	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄²×D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₅	C₂²	1	4	yes	—
7	C₂×C₅×D₄	C₂²	1	6	yes	complemented
8	C₂×C₂²⋊D₅	C₂²	1	12	yes	complemented
9	D₄×D₅	—	2	24	no	—
10	C₂×D₂₀	C₂²	1	6	yes	complemented
11	C₂×C₄×D₅	C₂²	1	3	yes	—
12	C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
13	C₄×Dic₅	C₂²	1	3	yes	complemented
14	C₂×#127	—	5	1	no	maximal, Sylow
15	C₂³×C₅	C₂³	1	4	yes	—
16	C₂²×D₅	—	2	24	no	—
17	C₂²×D₅	C₂³	1	4	yes	—
18	C₂²×D₅	C₂³	1	1	yes	characteristic
19	C₅×D₄	—	2	12	no	—
20	C₂×C₄×C₅	C₂³	1	3	yes	—
21	C₂²⋊D₅	—	2	24	no	—
22	C₂×Dic₅	C₂³	1	3	yes	—
23	D₂₀	—	2	12	no	—
24	C₄×D₅	D₄	1	12	yes	complemented
25	C₂²×D₄	—	5	6	no	—
26	#127	—	5	6	no	—
27	#127	—	5	1	no	—
28	#127	D₅	1	1	yes	characteristic, direct product factor
29	C₂×C₄²	—	5	1	no	—
30	C₂²×C₅	—	2	12	no	—
31	C₂²×C₅	C₂⁴	1	1	yes	characteristic
32	C₂×D₅	—	2	12	no	—
33	C₂×D₅	—	4	16	no	—
34	C₂×D₅	C₂×D₄	1	6	yes	—
35	C₄×C₅	C₂×D₄	1	6	yes	complemented
36	Dic₅	C₂×D₄	1	6	yes	complemented
37	C₂⁴	—	5	4	no	—
38	C₂×D₄	—	5	12	no	—
39	C₂×D₄	—	5	6	no	—
40	C₂×D₄	—	10	24	no	—
41	C₂×D₄	C₂×D₅	1	6	yes	complemented
42	C₂²×C₄	—	5	3	no	—
43	C₄²	—	5	3	no	—
44	C₄²	C₂×D₅	1	1	yes	characteristic, complemented
45	C₂×C₅	—	4	4	no	—
46	C₂×C₅	C₂²×D₄	1	3	yes	—
47	D₅	—	4	4	no	—
48	D₅	#127	1	4	yes	direct product factor
49	C₂³	—	5	1	no	—
50	C₂³	—	5	4	no	—
51	C₂³	—	10	24	no	—
52	C₂³	C₂²×D₅	1	4	yes	—
53	D₄	—	2	12	no	—
54	D₄	—	10	24	no	—
55	D₄	—	10	12	no	—
56	C₂×C₄	—	5	3	no	—
57	C₂×C₄	—	5	12	no	—
58	C₂×C₄	C₂²×D₅	1	3	yes	—
59	C₅	C₂×#127	1	1	yes	characteristic, complemented, Sylow
60	C₂²	—	2	12	no	—
61	C₂²	—	5	6	no	—
62	C₂²	—	10	12	no	—
63	C₂²	—	20	16	no	—
64	C₂²	C₂³×D₅	1	1	yes	characteristic
65	C₄	—	5	6	no	—
66	C₄	D₄×D₅	1	6	yes	complemented
67	C₂	—	4	4	no	—
68	C₂	—	5	4	no	—
69	C₂	—	20	4	no	—
70	C₂	C₂×D₄×D₅	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁴
Fitting	C₅×#127	C₂
hypercenter	#127	D₅
hypocenter	C₅	C₂×#127
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×D₅	C₂	semidirect
2. C₅×#127	C₂	semidirect
3. #4086	C₂	semidirect
4. #4020	C₂	semidirect
5. C₄²×D₅	C₂	semidirect
7. C₂×C₅×D₄	C₂²	semidirect
8. C₂×C₂²⋊D₅	C₂²	semidirect
10. C₂×D₂₀	C₂²	semidirect
12. C₄²×C₅	C₂²	semidirect
13. C₄×Dic₅	C₂²	semidirect
24. C₄×D₅	D₄	semidirect
28. #127	D₅	direct (N × H)
35. C₄×C₅	C₂×D₄	semidirect
36. Dic₅	C₂×D₄	semidirect
41. C₂×D₄	C₂×D₅	semidirect
44. C₄²	C₂×D₅	semidirect
48. D₅	#127	direct (N × H)
59. C₅	C₂×#127	semidirect
66. C₄	D₄×D₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×D₅	2
C₅×#127	2
#4086	2
#4020	2
C₄²×D₅	2
C₂×#127	5

Subgroups — D5×#127 #66048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#127 #66048