Subgroups — #64721

Order 320.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×#672	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
5	C₄×Dic₅	C₄	1	1	yes	characteristic
6	C₂×#168	C₄	1	1	yes	characteristic
7	C₅×C₁₆	—	2	1	no	—
8	#672	—	2	1	no	—
9	C₄⋊C₁₆	—	5	1	no	maximal, Sylow
10	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
11	C₂×Dic₅	C₈	1	1	yes	characteristic
12	C₂×Dic₅	C₈	1	1	yes	characteristic
13	C₅×C₈	D₄	1	1	yes	characteristic
14	C₅×C₈	Q₈	1	1	yes	characteristic
15	#168	—	2	1	no	—
16	C₂×C₁₆	—	5	1	no	—
17	C₂×C₁₆	D₅	1	1	yes	characteristic
18	C₄×C₈	—	5	1	no	—
19	C₂²×C₅	C₂×C₈	1	1	yes	characteristic
20	C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
21	C₄×C₅	M₁₆	1	1	yes	characteristic
22	Dic₅	—	2	1	no	—
23	Dic₅	C₁₆	1	2	yes	complemented
24	C₂×C₈	—	5	1	no	—
25	C₂×C₈	C₂×D₅	1	1	yes	characteristic
26	C₄²	—	5	1	no	—
27	C₁₆	—	2	1	no	—
28	C₁₆	—	10	1	no	—
29	C₂×C₅	C₄⋊C₈	1	1	yes	characteristic
30	C₂×C₅	C₂×C₁₆	1	1	yes	characteristic
31	C₂×C₅	M₃₂	1	1	yes	characteristic
32	C₂×C₄	—	5	1	no	—
33	C₂×C₄	—	5	1	no	—
34	C₂×C₄	C₄×D₅	1	1	yes	characteristic
35	C₈	—	10	1	no	—
36	C₈	Dic₁₀	1	1	yes	characteristic
37	C₈	C₂²⋊D₅	1	1	yes	characteristic
38	C₅	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
39	C₂²	C₈×D₅	1	1	yes	characteristic
40	C₄	—	5	2	no	—
41	C₄	—	10	1	no	—
42	C₄	#676	1	1	yes	characteristic
43	C₄	#683	1	1	yes	characteristic
44	C₂	D₅×C₁₆	1	1	yes	characteristic
45	C₂	#3930	1	1	yes	characteristic
46	C₂	#3946	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₅
commutator	C₂×C₅	C₂×C₁₆
Fitting	C₂×C₅×C₁₆	C₂
socle, prime radical	C₂²×C₅	C₂×C₈
cosocle	C₂×C₅×C₈	C₂²
hypercenter	C₂×C₁₆	D₅
hypocenter	C₅	C₄⋊C₁₆
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
23. Dic₅	C₁₆	semidirect
38. C₅	C₄⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₁₆	2
C₈×Dic₅	2
C₂×#672	2
C₄⋊C₁₆	5