Subgroups — C₂×#3993 #65719

Order 320.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal
2	C₂×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	#3993	C₂	1	4	yes	maximal, direct product factor
4	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
5	C₂×C₄×D₅	C₂²	1	1	yes	characteristic
6	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
7	C₄⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
8	C₂×C₅×C₈	C₄	1	1	yes	characteristic, complemented
9	C₂×#168	C₄	1	1	yes	characteristic, complemented
10	C₈×D₅	C₄	1	2	yes	complemented
11	C₈×D₅	C₂²	1	2	yes	—
12	C₂×#106	—	5	1	no	maximal, Sylow
13	C₂²×D₅	D₄	1	1	yes	characteristic
14	C₂×AGL(1,𝔽₅)	—	2	4	no	—
15	C₂×AGL(1,𝔽₅)	—	4	4	no	—
16	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₅	Q₈	1	1	yes	characteristic
18	C₄×D₅	C₂×C₄	1	1	yes	characteristic
19	C₄×D₅	D₄	1	1	yes	characteristic
20	C₄×D₅	Q₈	1	1	yes	characteristic
21	C₄×D₅	C₂³	1	1	yes	characteristic
22	C₅×C₈	C₂×C₄	1	2	yes	complemented
23	#168	C₂×C₄	1	2	yes	complemented
24	C₂²×C₈	—	5	1	no	—
25	C₂×C₄⋊C₄	—	5	2	no	—
26	#106	—	5	4	no	—
27	C₂²×C₅	C₄⋊C₄	1	1	yes	characteristic
28	C₂×D₅	C₄⋊C₄	1	1	yes	characteristic
29	C₂×D₅	SD₁₆	1	4	yes	—
30	C₂×D₅	C₂×D₄	1	1	yes	characteristic
31	AGL(1,𝔽₅)	—	4	4	no	—
32	C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
33	C₄×C₅	C₂²×C₄	1	1	yes	characteristic
34	Dic₅	C₄⋊C₄	1	1	yes	characteristic
35	Dic₅	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₄	—	5	1	no	—
37	C₂²×C₄	—	10	2	no	—
38	C₂×C₈	—	5	1	no	—
39	C₂×C₈	—	5	2	no	—
40	C₂×C₈	—	5	2	no	—
41	C₂×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
42	C₄⋊C₄	—	5	4	no	—
43	C₄⋊C₄	—	10	2	no	—
44	C₂×C₅	#106	1	2	yes	complemented
45	C₂×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
46	D₅	#106	1	2	yes	complemented
47	D₅	C₂×SD₁₆	1	2	yes	—
48	C₂³	—	5	1	no	—
49	C₂×C₄	—	5	1	no	—
50	C₂×C₄	—	5	1	no	—
51	C₂×C₄	—	5	1	no	—
52	C₂×C₄	—	5	1	no	—
53	C₂×C₄	—	5	1	no	—
54	C₂×C₄	—	10	4	no	—
55	C₂×C₄	—	20	4	no	—
56	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
57	C₈	—	5	2	no	—
58	C₈	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
59	C₅	C₂×#106	1	1	yes	characteristic, complemented, Sylow
60	C₂²	—	5	1	no	—
61	C₂²	—	5	1	no	—
62	C₂²	—	5	4	no	—
63	C₂²	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
64	C₄	—	5	1	no	—
65	C₄	—	5	1	no	—
66	C₄	—	20	4	no	—
67	C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
68	C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
69	C₂	—	5	2	no	—
70	C₂	—	5	2	no	—
71	C₂	#3993	1	2	yes	direct product factor
72	C₂	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂²×C₄
Frattini	C₄	C₂²×AGL(1,𝔽₅)
Fitting	C₂×C₅×C₈	C₄
socle	C₂²×C₅	C₄⋊C₄
prime radical	C₂²×D₅	D₄
cosocle	C₄×D₅	C₂³
hypercenter	C₂×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₂×#106
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. #3993	C₂	direct (N × H)
8. C₂×C₅×C₈	C₄	semidirect
9. C₂×#168	C₄	semidirect
10. C₈×D₅	C₄	semidirect
22. C₅×C₈	C₂×C₄	semidirect
23. #168	C₂×C₄	semidirect
41. C₂×C₈	AGL(1,𝔽₅)	semidirect
44. C₂×C₅	#106	semidirect
46. D₅	#106	semidirect
58. C₈	C₂×AGL(1,𝔽₅)	semidirect
59. C₅	C₂×#106	semidirect
71. C₂	#3993	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×C₄⋊AGL(1,𝔽₅)	2
C₂×C₈×D₅	2
#3993	2
C₂×#106	5

Subgroups — C2×#3993 #65719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3993 #65719