Subgroups — #65414

Order 320.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#681	C₂	1	2	yes	maximal
3	#3951	C₂	1	4	yes	maximal, complemented
4	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
5	C₅×M₁₆	C₄	1	4	yes	—
6	C₂×C₅×C₈	C₂²	1	2	yes	—
7	#681	—	2	2	no	—
8	#681	C₂²	1	4	yes	—
9	C₂×#168	—	2	2	no	—
10	#430	—	5	1	no	maximal, Sylow
11	C₂³×C₅	Q₈	1	1	yes	characteristic
12	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
13	C₂×C₄×C₅	D₄	1	2	yes	—
14	C₂×C₄×C₅	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
16	C₅×C₈	C₂×C₄	1	4	yes	—
17	#168	—	2	4	no	—
18	C₂×M₁₆	—	5	2	no	—
19	C₂×M₁₆	D₅	1	1	yes	characteristic
20	#108	—	5	4	no	—
21	C₂²×C₅	—	4	1	no	—
22	C₂²×C₅	C₄⋊C₄	1	2	yes	—
23	C₂²×C₅	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₅	C₄⋊C₄	1	2	yes	—
25	C₄×C₅	C₂²×C₄	1	1	yes	characteristic
26	C₄×C₅	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₄	C₂×D₅	1	1	yes	characteristic
28	M₁₆	—	5	4	no	—
29	M₁₆	—	10	2	no	—
30	M₁₆	Dic₅	1	4	yes	—
31	C₂×C₈	—	10	2	no	—
32	C₂×C₈	C₂×D₅	1	2	yes	—
33	C₂×C₅	—	2	2	no	—
34	C₂×C₅	—	2	1	no	—
35	C₂×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂³	Dic₁₀	1	1	yes	characteristic
37	C₂×C₄	Dic₁₀	1	1	yes	characteristic
38	C₂×C₄	D₂₀	1	2	yes	—
39	C₂×C₄	C₂×Dic₅	1	2	yes	—
40	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
41	C₈	—	10	4	no	—
42	C₈	C₂×Dic₅	1	4	yes	—
43	C₅	#430	1	1	yes	characteristic, complemented, Sylow
44	C₂²	—	4	1	no	—
45	C₂²	C₄⋊Dic₅	1	2	yes	—
46	C₂²	C₂×Dic₁₀	1	1	yes	characteristic
47	C₄	C₄⋊Dic₅	1	2	yes	—
48	C₄	C₂×D₂₀	1	1	yes	characteristic
49	C₄	C₂²×Dic₅	1	1	yes	characteristic
50	C₂	—	2	2	no	—
51	C₂	—	2	1	no	—
52	C₂	C₂×C₄⋊Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₂₀
commutator	C₄×C₅	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₂×C₅×M₁₆	C₂
socle	C₂×C₅	C₂×C₄⋊C₄
prime radical	C₂³×C₅	Q₈
cosocle	C₂×C₄×C₅	C₂³
hypercenter	C₂×M₁₆	D₅
hypocenter	C₅	#430
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. #3951	C₂	semidirect
43. C₅	#430	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×M₁₆	2
C₂×#681	2
#3951	2
#430	5