Subgroups — C₂×#4005 #65760

Order 320.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₀	C₂	1	1	yes	maximal, characteristic
2	C₂×#704	C₂	1	2	yes	maximal
3	#4005	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₅	C₄	1	1	yes	characteristic
5	C₂²×Dic₅	C₄	1	1	yes	characteristic
6	C₂²×Dic₅	C₂²	1	1	yes	characteristic
7	C₂×Dic₁₀	—	2	2	no	—
8	C₂×Dic₁₀	—	2	2	no	—
9	C₂×Dic₁₀	C₄	1	2	yes	—
10	C₂×Dic₁₀	C₂²	1	2	yes	—
11	#704	—	2	2	no	—
12	#704	C₂²	1	4	yes	—
13	C₂×#170	—	2	2	no	—
14	C₂×#101	—	5	1	no	maximal, Sylow
15	C₂³×C₅	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₅	—	2	1	no	—
17	C₂×C₄×C₅	—	2	1	no	—
18	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
19	C₂×Dic₅	—	2	1	no	—
20	C₂×Dic₅	—	2	1	no	—
21	C₂×Dic₅	C₂×C₄	1	2	yes	—
22	C₂×Dic₅	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₅	D₄	1	2	yes	—
24	C₂×Dic₅	D₄	1	2	yes	—
25	C₂×Dic₅	C₂³	1	1	yes	characteristic
26	Dic₁₀	—	2	4	no	—
27	Dic₁₀	—	2	4	no	—
28	#170	—	2	4	no	—
29	C₂²×Q₈	—	5	1	no	—
30	C₂×M₁₆	—	5	2	no	—
31	#101	—	5	4	no	—
32	C₂²×C₅	—	2	2	no	—
33	C₂²×C₅	C₂²⋊C₄	1	1	yes	characteristic
34	C₂²×C₅	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
36	C₄×C₅	—	2	2	no	—
37	Dic₅	—	2	2	no	—
38	Dic₅	C₂²⋊C₄	1	2	yes	—
39	Dic₅	C₂×D₄	1	2	yes	—
40	C₂×Q₈	—	5	2	no	—
41	C₂×Q₈	—	5	2	no	—
42	C₂×Q₈	—	10	2	no	—
43	C₂×Q₈	—	10	2	no	—
44	C₂²×C₄	—	5	1	no	—
45	C₂²×C₄	—	5	1	no	—
46	C₂²×C₄	AGL(1,𝔽₅)	1	1	yes	characteristic
47	M₁₆	—	5	4	no	—
48	M₁₆	—	10	2	no	—
49	C₂×C₈	—	10	2	no	—
50	C₂×C₅	—	2	1	no	—
51	C₂×C₅	—	2	1	no	—
52	C₂×C₅	#101	1	2	yes	complemented
53	C₂×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
54	C₂³	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
55	Q₈	—	10	4	no	—
56	Q₈	—	10	4	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	5	2	no	—
60	C₂×C₄	—	5	2	no	—
61	C₂×C₄	—	5	1	no	—
62	C₂×C₄	—	5	1	no	—
63	C₂×C₄	—	5	2	no	—
64	C₂×C₄	—	10	1	no	—
65	C₂×C₄	—	10	1	no	—
66	C₂×C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
67	C₈	—	10	4	no	—
68	C₅	C₂×#101	1	1	yes	characteristic, complemented, Sylow
69	C₂²	—	2	2	no	—
70	C₂²	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
71	C₂²	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
72	C₂²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
73	C₄	—	2	2	no	—
74	C₄	—	5	2	no	—
75	C₄	—	5	2	no	—
76	C₄	—	10	2	no	—
77	C₂	—	2	1	no	—
78	C₂	—	2	1	no	—
79	C₂	#4005	1	2	yes	direct product factor
80	C₂	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂²×C₄
Frattini	C₂²	C₂²×AGL(1,𝔽₅)
Fitting	C₂²×C₄×C₅	C₄
socle	C₂²×C₅	C₂²⋊C₄
prime radical	C₂³×C₅	C₂×C₄
cosocle	C₂×Dic₅	C₂³
hypercenter	C₂²×C₄	AGL(1,𝔽₅)
hypocenter	C₅	C₂×#101
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
3. #4005	C₂	direct (N × H)
52. C₂×C₅	#101	semidirect
68. C₅	C₂×#101	semidirect
79. C₂	#4005	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×Dic₁₀	2
C₂×#704	2
#4005	2
C₂×#101	5

Subgroups — C2×#4005 #65760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4005 #65760