Subgroups — C₂×#4133 #66259

Order 320.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#713	C₂	1	1	yes	maximal, characteristic
2	#4133	C₂	1	8	yes	maximal, direct product factor
3	C₂×#700	C₂	1	3	yes	maximal, complemented
4	C₂×D₅⋊C₈	C₂	1	3	yes	maximal, complemented
5	C₂×C₅×Q₈	C₄	1	1	yes	characteristic
6	#713	C₄	1	4	yes	—
7	#713	C₂²	1	4	yes	—
8	C₂×D₂₀	C₄	1	3	yes	—
9	C₂×C₄×D₅	C₂²	1	3	yes	—
10	C₂×#170	C₂²	1	1	yes	characteristic
11	C₂×#170	C₂²	1	3	yes	—
12	#700	C₂²	1	12	yes	complemented
13	D₅⋊C₈	C₂²	1	12	yes	complemented
14	C₂×#131	—	5	1	no	maximal, Sylow
15	C₂²×D₅	C₂×C₄	1	3	yes	—
16	C₅×Q₈	C₂×C₄	1	4	yes	—
17	C₂×C₄×C₅	C₂×C₄	1	3	yes	—
18	C₂×Dic₅	C₂³	1	1	yes	characteristic
19	D₂₀	C₂×C₄	1	12	yes	—
20	C₄×D₅	C₂×C₄	1	6	yes	—
21	C₄×D₅	C₂³	1	6	yes	—
22	#170	C₂³	1	2	yes	—
23	#170	C₂³	1	6	yes	—
24	C₂×#41	—	5	1	no	—
25	#131	—	5	8	no	—
26	C₂×M₁₆	—	5	3	no	—
27	C₂²×C₈	—	5	3	no	—
28	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
29	C₂×D₅	—	2	6	no	—
30	C₂×D₅	C₂²×C₄	1	6	yes	—
31	C₄×C₅	C₂²×C₄	1	6	yes	—
32	Dic₅	C₂²×C₄	1	1	yes	characteristic
33	Dic₅	C₂⁴	1	1	yes	characteristic
34	#41	—	5	4	no	—
35	#41	—	5	4	no	—
36	C₂×Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic
37	C₂×D₄	—	5	3	no	—
38	C₂²×C₄	—	5	3	no	—
39	M₁₆	—	5	12	no	—
40	C₂×C₈	—	5	1	no	—
41	C₂×C₈	—	5	3	no	—
42	C₂×C₈	—	5	12	no	—
43	C₂×C₅	#131	1	2	yes	complemented
44	C₂×C₅	C₂³×C₄	1	1	yes	characteristic
45	D₅	—	2	6	no	—
46	C₂³	—	5	3	no	—
47	Q₈	C₂×AGL(1,𝔽₅)	1	4	yes	—
48	D₄	—	5	12	no	—
49	C₂×C₄	—	5	1	no	—
50	C₂×C₄	—	5	6	no	—
51	C₂×C₄	—	5	6	no	—
52	C₂×C₄	C₂×AGL(1,𝔽₅)	1	3	yes	—
53	C₈	—	5	2	no	—
54	C₈	—	5	6	no	—
55	C₅	C₂×#131	1	1	yes	characteristic, complemented, Sylow
56	C₂²	—	5	6	no	—
57	C₂²	—	10	6	no	—
58	C₂²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
59	C₄	—	5	1	no	—
60	C₄	—	5	1	no	—
61	C₄	C₂²×AGL(1,𝔽₅)	1	6	yes	—
62	C₂	—	10	6	no	—
63	C₂	#4133	1	2	yes	direct product factor
64	C₂	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂³×C₄
Frattini	C₂	C₂³×AGL(1,𝔽₅)
Fitting	C₂×C₅×Q₈	C₄
socle	C₂²×C₅	C₂²×C₄
prime radical	C₂×#713	C₂
cosocle	Dic₅	C₂⁴
hypercenter	C₂×Q₈	AGL(1,𝔽₅)
hypocenter	C₅	C₂×#131
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #4133	C₂	direct (N × H)
3. C₂×#700	C₂	semidirect
4. C₂×D₅⋊C₈	C₂	semidirect
12. #700	C₂²	semidirect
13. D₅⋊C₈	C₂²	semidirect
43. C₂×C₅	#131	semidirect
55. C₅	C₂×#131	semidirect
63. C₂	#4133	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
#4133	2
C₂×#700	2
C₂×D₅⋊C₈	2
C₂×#131	5

Subgroups — C2×#4133 #66259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4133 #66259