Subgroups — C₂×#4050 #66075

Order 320.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#709	C₂	1	2	yes	maximal, complemented
2	C₂²×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	#4050	C₂	1	8	yes	maximal, direct product factor
5	C₂×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#677	C₂	1	2	yes	maximal, complemented
7	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₂²⋊D₅	—	2	2	no	—
9	#709	—	2	4	no	—
10	#709	C₂²	1	8	yes	complemented
11	C₂×D₂₀	C₂²	1	2	yes	—
12	C₂×C₄×D₅	—	2	2	no	—
13	C₂×Dic₁₀	C₂²	1	2	yes	—
14	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₈	C₂²	1	4	yes	complemented
17	Dic₂₀	C₂²	1	4	yes	complemented
18	D₄₀	C₂²	1	4	yes	complemented
19	#677	C₂²	1	8	yes	complemented
20	C₂×#135	—	5	1	no	maximal, Sylow
21	C₂³×C₅	D₄	1	1	yes	characteristic
22	C₂²×D₅	—	2	2	no	—
23	C₂×C₄×C₅	D₄	1	2	yes	—
24	C₂×C₄×C₅	D₄	1	1	yes	characteristic
25	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
26	C₂×C₄×C₅	C₂³	1	2	yes	—
27	C₂²⋊D₅	—	2	8	no	—
28	C₂×Dic₅	—	2	2	no	—
29	D₂₀	—	2	2	no	—
30	D₂₀	C₂³	1	4	yes	—
31	C₄×D₅	—	2	8	no	—
32	Dic₁₀	—	2	2	no	—
33	Dic₁₀	C₂³	1	4	yes	—
34	C₅×C₈	C₂³	1	2	yes	—
35	C₅×C₈	C₂³	1	2	yes	—
36	C₂×#41	—	5	2	no	—
37	#135	—	5	8	no	—
38	C₂×Q₁₆	—	5	1	no	—
39	C₂×SD₁₆	—	5	2	no	—
40	C₂×D₈	—	5	1	no	—
41	C₂²×C₈	D₅	1	1	yes	characteristic, complemented
42	C₂²×C₅	—	2	2	no	—
43	C₂²×C₅	C₂×D₄	1	2	yes	—
44	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
45	C₂×D₅	—	2	4	no	—
46	C₂×D₅	—	4	4	no	—
47	C₄×C₅	C₂×D₄	1	1	yes	characteristic
48	C₄×C₅	C₂×D₄	1	2	yes	—
49	C₄×C₅	C₂⁴	1	1	yes	characteristic
50	Dic₅	—	2	4	no	—
51	#41	—	5	8	no	—
52	#41	—	10	4	no	—
53	C₂×Q₈	—	5	2	no	—
54	C₂×D₄	—	5	2	no	—
55	C₂×D₄	—	10	2	no	—
56	C₂²×C₄	—	10	2	no	—
57	C₂²×C₄	C₂×D₅	1	1	yes	characteristic
58	Q₁₆	—	5	4	no	—
59	SD₁₆	—	5	8	no	—
60	D₈	—	5	4	no	—
61	C₂×C₈	C₂×D₅	1	1	yes	characteristic
62	C₂×C₈	C₂×D₅	1	1	yes	characteristic
63	C₂×C₈	C₂×D₅	1	4	yes	complemented
64	C₂×C₅	—	2	2	no	—
65	C₂×C₅	#135	1	2	yes	complemented
66	C₂×C₅	C₂²×D₄	1	1	yes	characteristic
67	D₅	—	4	4	no	—
68	C₂³	—	10	2	no	—
69	C₂³	D₂₀	1	1	yes	characteristic
70	Q₈	—	5	4	no	—
71	Q₈	—	10	2	no	—
72	D₄	—	5	4	no	—
73	D₄	—	10	8	no	—
74	D₄	—	10	2	no	—
75	C₂×C₄	—	10	2	no	—
76	C₂×C₄	—	10	8	no	—
77	C₂×C₄	D₂₀	1	2	yes	—
78	C₂×C₄	D₂₀	1	1	yes	characteristic
79	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
80	C₂×C₄	C₂²×D₅	1	2	yes	—
81	C₈	C₂²×D₅	1	2	yes	—
82	C₈	C₂²×D₅	1	2	yes	—
83	C₅	C₂×#135	1	1	yes	characteristic, complemented, Sylow
84	C₂²	—	2	2	no	—
85	C₂²	—	10	4	no	—
86	C₂²	—	20	4	no	—
87	C₂²	C₂×D₂₀	1	2	yes	—
88	C₂²	C₂×D₂₀	1	1	yes	characteristic
89	C₄	—	10	4	no	—
90	C₄	C₂×D₂₀	1	2	yes	—
91	C₄	C₂×D₂₀	1	1	yes	characteristic
92	C₄	C₂³×D₅	1	1	yes	characteristic
93	C₂	—	2	2	no	—
94	C₂	—	20	4	no	—
95	C₂	#4050	1	2	yes	direct product factor
96	C₂	C₂²×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₂₀
commutator, cosocle	C₄×C₅	C₂⁴
Frattini	C₄	C₂³×D₅
Fitting	C₂²×C₅×C₈	C₂
socle	C₂²×C₅	C₂×D₄
hypercenter	C₂²×C₈	D₅
hypocenter	C₅	C₂×#135
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#709	C₂	semidirect
2. C₂²×C₅×C₈	C₂	semidirect
3. C₂×Dic₂₀	C₂	semidirect
4. #4050	C₂	direct (N × H)
5. C₂×D₄₀	C₂	semidirect
6. C₂×#677	C₂	semidirect
10. #709	C₂²	semidirect
16. C₂×C₅×C₈	C₂²	semidirect
17. Dic₂₀	C₂²	semidirect
18. D₄₀	C₂²	semidirect
19. #677	C₂²	semidirect
41. C₂²×C₈	D₅	semidirect
63. C₂×C₈	C₂×D₅	semidirect
65. C₂×C₅	#135	semidirect
83. C₅	C₂×#135	semidirect
95. C₂	#4050	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#709	2
C₂²×C₅×C₈	2
C₂×Dic₂₀	2
#4050	2
C₂×D₄₀	2
C₂×#677	2
C₂×#135	5

Subgroups — C2×#4050 #66075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4050 #66075