Subgroups — #66244

Order 320.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	2₋¹⁺⁴⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	#454	—	5	1	no	maximal, Sylow
3	2₋¹⁺⁴	D₅	1	1	yes	characteristic, complemented
4	AGL(1,ℤ/8)	—	5	2	no	—
5	#124	—	5	1	no	—
6	#104	—	5	2	no	—
7	#101	—	5	1	no	—
8	C₂×D₅	—	16	1	no	maximal
9	#41	—	5	2	no	—
10	C₂×Q₈	—	5	1	no	—
11	C₂×D₄	—	5	1	no	—
12	SD₁₆	—	10	2	no	—
13	D₈	—	10	2	no	—
14	M₁₆	—	5	2	no	—
15	C₂²⋊C₄	—	10	2	no	—
16	C₄²	—	5	1	no	—
17	C₂×C₅	—	16	1	no	—
18	D₅	—	16	2	no	—
19	C₂³	—	10	1	no	—
20	Q₈	—	5	2	no	—
21	D₄	—	5	2	no	—
22	D₄	—	10	2	no	—
23	C₂×C₄	—	5	1	no	—
24	C₂×C₄	—	5	2	no	—
25	C₂×C₄	—	10	1	no	—
26	C₈	—	10	2	no	—
27	C₅	—	16	1	no	Sylow
28	C₂²	—	5	1	no	—
29	C₂²	—	20	2	no	—
30	C₂²	—	20	1	no	—
31	C₄	—	5	2	no	—
32	C₄	—	20	1	no	—
33	C₂	—	10	1	no	—
34	C₂	—	40	1	no	—
35	C₂	(C₂⁴⋊C₅)⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle, hypercenter	C₂	(C₂⁴⋊C₅)⋊C₂
commutator, cosocle, hypocenter	2₋¹⁺⁴⋊C₅	C₂
Fitting	2₋¹⁺⁴	D₅
LCS	G ▷ 2₋¹⁺⁴⋊C₅
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
1. 2₋¹⁺⁴⋊C₅	C₂	semidirect
3. 2₋¹⁺⁴	D₅	semidirect

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