Subgroups — C₅×#340 #64807

Order 320.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₂²×C₄×C₅	—	2	2	no	—
4	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
5	C₂×C₅×C₈	—	2	2	no	—
6	C₂×C₅×C₈	C₄	1	2	yes	complemented
7	C₅×C₄⋊C₄	—	2	2	no	—
8	C₅×C₄⋊C₄	C₄	1	4	yes	complemented
9	#340	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₅	D₄	1	1	yes	characteristic
11	C₂×C₄×C₅	—	2	4	no	—
12	C₂×C₄×C₅	—	4	2	no	—
13	C₂×C₄×C₅	—	4	2	no	—
14	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₅	D₄	1	2	yes	—
17	C₂×C₄×C₅	Q₈	1	1	yes	characteristic
18	C₅×C₈	—	2	2	no	—
19	C₂²×C₈	C₂×C₅	1	1	yes	characteristic
20	C₂×C₄⋊C₄	C₂×C₅	1	2	yes	—
21	C₂²×C₅	C₂²⋊C₄	1	2	yes	—
22	C₂²×C₅	C₄⋊C₄	1	1	yes	characteristic
23	C₂²×C₅	D₈	1	1	yes	characteristic
24	C₂²×C₅	SD₁₆	1	2	yes	—
25	C₂²×C₅	Q₁₆	1	1	yes	characteristic
26	C₄×C₅	—	4	4	no	—
27	C₄×C₅	C₄²	1	1	yes	characteristic
28	C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
29	C₄×C₅	C₄⋊C₄	1	2	yes	—
30	C₂²×C₄	—	2	2	no	—
31	C₂²×C₄	C₂²×C₅	1	1	yes	characteristic
32	C₂×C₈	—	2	2	no	—
33	C₂×C₈	C₄×C₅	1	2	yes	complemented
34	C₄⋊C₄	—	2	2	no	—
35	C₄⋊C₄	C₄×C₅	1	4	yes	complemented
36	C₂×C₅	#95	1	1	yes	characteristic
37	C₂×C₅	#102	1	2	yes	—
38	C₂×C₅	#103	1	2	yes	—
39	C₂×C₅	#106	1	1	yes	characteristic
40	C₂×C₅	#107	1	1	yes	characteristic
41	C₂³	C₅×D₄	1	1	yes	characteristic
42	C₂×C₄	—	2	4	no	—
43	C₂×C₄	—	4	2	no	—
44	C₂×C₄	—	4	2	no	—
45	C₂×C₄	C₂×C₄×C₅	1	1	yes	characteristic
46	C₂×C₄	C₂×C₄×C₅	1	2	yes	—
47	C₂×C₄	C₅×D₄	1	2	yes	—
48	C₂×C₄	C₅×Q₈	1	1	yes	characteristic
49	C₈	—	2	2	no	—
50	C₅	#340	1	1	yes	characteristic, direct product factor, Sylow
51	C₂²	C₅×C₂²⋊C₄	1	2	yes	—
52	C₂²	C₅×C₄⋊C₄	1	1	yes	characteristic
53	C₂²	C₅×D₈	1	1	yes	characteristic
54	C₂²	C₅×SD₁₆	1	2	yes	—
55	C₂²	C₅×Q₁₆	1	1	yes	characteristic
56	C₄	—	4	4	no	—
57	C₄	C₄²×C₅	1	1	yes	characteristic
58	C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
59	C₄	C₅×C₄⋊C₄	1	2	yes	—
60	C₂	C₅×#95	1	1	yes	characteristic
61	C₂	C₅×#102	1	2	yes	—
62	C₂	C₅×#103	1	2	yes	—
63	C₂	C₅×#106	1	1	yes	characteristic
64	C₂	C₅×#107	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	D₄
commutator	C₄	C₄²×C₅
Frattini, cosocle	C₂²×C₄	C₂²×C₅
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₂×C₅×C₈	C₄	semidirect
8. C₅×C₄⋊C₄	C₄	semidirect
9. #340	C₅	direct (N × H)
33. C₂×C₈	C₄×C₅	semidirect
35. C₄⋊C₄	C₄×C₅	semidirect
50. C₅	#340	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×C₅×C₈	2
C₂×C₅×C₄⋊C₄	2
#340	5

Subgroups — C5×#340 #64807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#340 #64807