Subgroups — C₂×#4086 #66137

Order 320.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂⁴
Frattini	C₂²	C₂³×D₅
Fitting	C₂²×C₅×D₄	C₂
socle	C₂³×C₅	C₂³
hypercenter	C₂²×D₄	D₅
hypocenter	C₅	C₂×#127
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₄	C₂	semidirect
2. C₂²×C₂²⋊D₅	C₂	semidirect
3. C₂²×D₂₀	C₂	semidirect
4. #4086	C₂	direct (N × H)
5. C₂×C₄×Dic₅	C₂	semidirect
9. C₂×C₅×D₄	C₂²	semidirect
12. C₂×C₂²⋊D₅	C₂²	semidirect
15. C₂×D₂₀	C₂²	semidirect
16. C₄×Dic₅	C₂²	semidirect
26. C₂×C₄×C₅	D₄	semidirect
29. C₂×Dic₅	D₄	semidirect
34. C₂²×D₄	D₅	semidirect
46. C₄×C₅	C₂×D₄	semidirect
47. Dic₅	C₂×D₄	semidirect
55. C₂×D₄	C₂×D₅	semidirect
60. C₂×C₅	#127	semidirect
76. C₂×C₄	C₂²⋊D₅	semidirect
78. C₅	C₂×#127	semidirect
89. C₄	C₂×C₂²⋊D₅	semidirect
92. C₂	#4086	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×D₄	2
C₂²×C₂²⋊D₅	2
C₂²×D₂₀	2
#4086	2
C₂×C₄×Dic₅	2
C₂×#127	5

Subgroups — C2×#4086 #66137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4086 #66137