Subgroups — C₂×#4065 #66099

Order 320.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#713	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#688	C₂	1	2	yes	maximal, complemented
4	#4065	C₂	1	8	yes	maximal, direct product factor
5	C₂×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×Q₈	C₂²	1	2	yes	—
8	#713	—	2	4	no	—
9	#713	C₂²	1	8	yes	complemented
10	C₂×D₂₀	—	2	2	no	—
11	C₂×D₂₀	C₂²	1	2	yes	—
12	C₂×C₄×D₅	—	2	2	no	—
13	C₂×C₄×D₅	C₂²	1	1	yes	characteristic
14	C₅×Q₁₆	C₂²	1	4	yes	complemented
15	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
16	#688	C₂²	1	8	yes	complemented
17	C₂×#168	C₂²	1	1	yes	characteristic
18	D₄₀	C₂²	1	4	yes	complemented
19	C₈×D₅	C₂²	1	4	yes	complemented
20	C₂×#135	—	5	1	no	maximal, Sylow
21	C₂²×D₅	—	2	2	no	—
22	C₂²×D₅	D₄	1	1	yes	characteristic
23	C₅×Q₈	—	2	2	no	—
24	C₅×Q₈	C₂³	1	4	yes	—
25	C₂×C₄×C₅	—	2	2	no	—
26	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
27	C₂×Dic₅	D₄	1	1	yes	characteristic
28	D₂₀	—	2	8	no	—
29	D₂₀	—	2	2	no	—
30	D₂₀	C₂³	1	4	yes	—
31	C₄×D₅	—	2	8	no	—
32	C₄×D₅	D₄	1	2	yes	—
33	C₄×D₅	C₂³	1	2	yes	—
34	C₅×C₈	C₂³	1	2	yes	—
35	#168	C₂³	1	2	yes	—
36	C₂×#41	—	5	2	no	—
37	#135	—	5	8	no	—
38	C₂×Q₁₆	D₅	1	1	yes	characteristic, complemented
39	C₂×SD₁₆	—	5	2	no	—
40	C₂×D₈	—	5	1	no	—
41	C₂²×C₈	—	5	1	no	—
42	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
43	C₂×D₅	—	2	2	no	—
44	C₂×D₅	—	2	4	no	—
45	C₂×D₅	—	4	4	no	—
46	C₂×D₅	C₂×D₄	1	2	yes	—
47	C₄×C₅	—	2	4	no	—
48	C₄×C₅	C₂×D₄	1	1	yes	characteristic
49	C₄×C₅	C₂⁴	1	1	yes	characteristic
50	Dic₅	C₂×D₄	1	2	yes	—
51	#41	—	5	8	no	—
52	#41	—	10	4	no	—
53	C₂×Q₈	C₂×D₅	1	2	yes	—
54	C₂×D₄	—	5	2	no	—
55	C₂×D₄	—	10	2	no	—
56	C₂²×C₄	—	5	1	no	—
57	C₂²×C₄	—	10	2	no	—
58	Q₁₆	C₂×D₅	1	4	yes	complemented
59	SD₁₆	—	5	8	no	—
60	D₈	—	5	4	no	—
61	C₂×C₈	—	5	1	no	—
62	C₂×C₈	—	5	4	no	—
63	C₂×C₈	C₂×D₅	1	1	yes	characteristic
64	C₂×C₅	#135	1	2	yes	complemented
65	C₂×C₅	C₂²×D₄	1	1	yes	characteristic
66	D₅	—	2	2	no	—
67	D₅	—	4	4	no	—
68	C₂³	—	5	1	no	—
69	C₂³	—	10	2	no	—
70	Q₈	—	2	2	no	—
71	Q₈	C₂²×D₅	1	4	yes	—
72	D₄	—	5	4	no	—
73	D₄	—	10	8	no	—
74	D₄	—	10	2	no	—
75	C₂×C₄	—	2	2	no	—
76	C₂×C₄	—	5	1	no	—
77	C₂×C₄	—	5	2	no	—
78	C₂×C₄	—	5	2	no	—
79	C₂×C₄	—	10	8	no	—
80	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
81	C₈	—	5	2	no	—
82	C₈	C₂²×D₅	1	2	yes	—
83	C₅	C₂×#135	1	1	yes	characteristic, complemented, Sylow
84	C₂²	—	5	2	no	—
85	C₂²	—	10	2	no	—
86	C₂²	—	10	4	no	—
87	C₂²	—	20	4	no	—
88	C₂²	D₄×D₅	1	1	yes	characteristic
89	C₄	—	2	4	no	—
90	C₄	—	5	2	no	—
91	C₄	D₄×D₅	1	1	yes	characteristic
92	C₄	C₂³×D₅	1	1	yes	characteristic
93	C₂	—	10	2	no	—
94	C₂	—	20	4	no	—
95	C₂	#4065	1	2	yes	direct product factor
96	C₂	C₂×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₅
commutator, cosocle	C₄×C₅	C₂⁴
Frattini	C₄	C₂³×D₅
Fitting	C₂×C₅×Q₁₆	C₂
socle	C₂²×C₅	C₂×D₄
hypercenter	C₂×Q₁₆	D₅
hypocenter	C₅	C₂×#135
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#713	C₂	semidirect
2. C₂×C₅×Q₁₆	C₂	semidirect
3. C₂×#688	C₂	semidirect
4. #4065	C₂	direct (N × H)
5. C₂×D₄₀	C₂	semidirect
6. C₂×C₈×D₅	C₂	semidirect
9. #713	C₂²	semidirect
14. C₅×Q₁₆	C₂²	semidirect
16. #688	C₂²	semidirect
18. D₄₀	C₂²	semidirect
19. C₈×D₅	C₂²	semidirect
38. C₂×Q₁₆	D₅	semidirect
58. Q₁₆	C₂×D₅	semidirect
64. C₂×C₅	#135	semidirect
83. C₅	C₂×#135	semidirect
95. C₂	#4065	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×#713	2
C₂×C₅×Q₁₆	2
C₂×#688	2
#4065	2
C₂×D₄₀	2
C₂×C₈×D₅	2
C₂×#135	5

Subgroups — C2×#4065 #66099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4065 #66099