Subgroups — C₂×#4016 #65803

Order 320.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₅	C₂	1	2	yes	maximal
3	C₂×#683	C₂	1	4	yes	maximal
4	#4016	C₂	1	8	yes	maximal, direct product factor
5	C₂²×C₄×C₅	C₂²	1	2	yes	—
6	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂²×Dic₅	C₂²	1	4	yes	—
8	C₄²×C₅	C₂²	1	4	yes	—
9	C₄⋊Dic₅	C₂²	1	8	yes	—
10	#683	C₂²	1	16	yes	—
11	C₂×#125	—	5	1	no	maximal, Sylow
12	C₂³×C₅	C₂³	1	1	yes	characteristic
13	C₂×C₄×C₅	—	2	4	no	—
14	C₂×C₄×C₅	Q₈	1	4	yes	—
15	C₂×C₄×C₅	C₂³	1	4	yes	—
16	C₂×C₄×C₅	C₂³	1	2	yes	—
17	C₂×Dic₅	—	2	8	no	—
18	C₂×Dic₅	C₂³	1	8	yes	—
19	#125	—	5	8	no	—
20	C₂×C₄⋊C₄	—	5	4	no	—
21	C₂×C₄⋊C₄	—	5	2	no	—
22	C₂×C₄²	D₅	1	1	yes	characteristic
23	C₂²×C₅	C₂×Q₈	1	2	yes	—
24	C₂²×C₅	#41	1	4	yes	—
25	C₂²×C₅	C₂⁴	1	1	yes	characteristic
26	C₄×C₅	—	2	4	no	—
27	C₄×C₅	C₂×Q₈	1	4	yes	—
28	Dic₅	—	2	8	no	—
29	C₂²×C₄	—	5	4	no	—
30	C₂²×C₄	C₂×D₅	1	2	yes	—
31	C₂²×C₄	C₂×D₅	1	1	yes	characteristic
32	C₄⋊C₄	—	5	16	no	—
33	C₄⋊C₄	—	5	8	no	—
34	C₄²	C₂×D₅	1	4	yes	—
35	C₂×C₅	#125	1	4	yes	complemented
36	C₂×C₅	C₂²×Q₈	1	1	yes	characteristic
37	C₂×C₅	C₂×#41	1	2	yes	—
38	C₂³	C₂²×D₅	1	1	yes	characteristic
39	C₂×C₄	—	2	4	no	—
40	C₂×C₄	—	5	8	no	—
41	C₂×C₄	—	10	8	no	—
42	C₂×C₄	Dic₁₀	1	4	yes	—
43	C₂×C₄	C₂²×D₅	1	4	yes	—
44	C₂×C₄	C₂²×D₅	1	2	yes	—
45	C₅	C₂×#125	1	1	yes	characteristic, complemented, Sylow
46	C₂²	C₂×Dic₁₀	1	2	yes	—
47	C₂²	#709	1	4	yes	—
48	C₂²	C₂³×D₅	1	1	yes	characteristic
49	C₄	—	2	4	no	—
50	C₄	—	10	8	no	—
51	C₄	C₂×Dic₁₀	1	4	yes	—
52	C₂	#4016	1	4	yes	direct product factor
53	C₂	C₂²×Dic₁₀	1	1	yes	characteristic
54	C₂	C₂×#709	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂⁴
Frattini	C₂²	C₂³×D₅
Fitting	C₂×C₄²×C₅	C₂
socle, prime radical	C₂³×C₅	C₂³
hypercenter	C₂×C₄²	D₅
hypocenter	C₅	C₂×#125
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
4. #4016	C₂	direct (N × H)
35. C₂×C₅	#125	semidirect
45. C₅	C₂×#125	semidirect
52. C₂	#4016	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×C₄²×C₅	2
C₂×C₄⋊Dic₅	2
C₂×#683	2
#4016	2
C₂×#125	5

Subgroups — C2×#4016 #65803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4016 #65803