Subgroups — C₄×#681 #65211

Order 320.

142 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×#681	C₂	1	2	yes	maximal
3	#3935	C₂	1	2	yes	maximal, complemented
4	C₄×#168	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄×C₅	C₄	1	2	yes	—
6	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₄²×C₅	C₄	1	2	yes	—
8	C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₄²×C₅	C₂²	1	1	yes	characteristic
10	#681	C₄	1	8	yes	direct product factor
11	C₂×#168	C₂²	1	4	yes	—
12	C₄×M₁₆	—	5	1	no	maximal, Sylow
13	C₂³×C₅	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₅	—	2	4	no	—
15	C₂×C₄×C₅	C₂×C₄	1	4	yes	—
16	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
20	#168	C₂×C₄	1	8	yes	complemented
21	C₂×M₁₆	—	5	2	no	—
22	C₂×C₄²	D₅	1	1	yes	characteristic
23	#97	—	5	2	no	—
24	C₄×C₈	—	5	2	no	—
25	C₂²×C₅	—	2	2	no	—
26	C₂²×C₅	C₄²	1	2	yes	—
27	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₅	—	2	2	no	—
29	C₄×C₅	C₄²	1	2	yes	—
30	C₄×C₅	M₁₆	1	4	yes	complemented
31	C₄×C₅	C₂²×C₄	1	2	yes	—
32	C₂²×C₄	Dic₅	1	2	yes	—
33	C₂²×C₄	C₂×D₅	1	1	yes	characteristic
34	M₁₆	—	5	8	no	—
35	C₂×C₈	—	5	4	no	—
36	C₄²	Dic₅	1	2	yes	—
37	C₄²	C₂×D₅	1	1	yes	characteristic
38	C₄²	C₂×D₅	1	1	yes	characteristic
39	C₂×C₅	—	2	2	no	—
40	C₂×C₅	C₂×C₄²	1	1	yes	characteristic
41	C₂×C₅	C₂×M₁₆	1	2	yes	—
42	C₂³	C₂×Dic₅	1	1	yes	characteristic
43	C₂×C₄	—	2	4	no	—
44	C₂×C₄	C₄×D₅	1	4	yes	—
45	C₂×C₄	C₂×Dic₅	1	2	yes	—
46	C₂×C₄	C₂×Dic₅	1	2	yes	—
47	C₂×C₄	C₂×Dic₅	1	1	yes	characteristic
48	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
49	C₈	—	5	8	no	—
50	C₅	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
51	C₂²	—	2	2	no	—
52	C₂²	C₄×Dic₅	1	2	yes	—
53	C₂²	C₂²×Dic₅	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	#681	1	4	yes	direct product factor
56	C₄	C₄×Dic₅	1	2	yes	—
57	C₄	C₂×C₄×D₅	1	2	yes	—
58	C₂	—	2	2	no	—
59	C₂	C₂×#681	1	2	yes	—
60	C₂	C₂×C₄×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₅
commutator	C₂×C₅	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₂×C₄²×C₅	C₂
socle	C₂²×C₅	C₂²×C₄
prime radical	C₂³×C₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂³
hypercenter	C₂×C₄²	D₅
hypocenter	C₅	C₄×M₁₆
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. #3935	C₂	semidirect
4. C₄×#168	C₂	semidirect
10. #681	C₄	direct (N × H)
20. #168	C₂×C₄	semidirect
30. C₄×C₅	M₁₆	semidirect
50. C₅	C₄×M₁₆	semidirect
55. C₄	#681	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×#681	2
#3935	2
C₄×#168	2
C₄×M₁₆	5

Subgroups — C4×#681 #65211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#681 #65211