Subgroups — C₅×#494 #65657

Order 320.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₁₆	C₂	1	4	yes	maximal
2	C₅×C₄⋊Q₈	C₂	1	2	yes	maximal
3	C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×Q₈	C₂²	1	4	yes	—
5	C₅×Q₁₆	—	2	8	no	—
6	C₂×C₅×C₈	C₂²	1	2	yes	—
7	C₅×C₄⋊C₄	—	2	4	no	—
8	C₄²×C₅	C₂²	1	1	yes	characteristic
9	#494	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₅×Q₈	—	2	8	no	—
11	C₂×C₄×C₅	—	2	4	no	—
12	C₂×C₄×C₅	D₄	1	2	yes	—
13	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
14	C₅×C₈	D₄	1	4	yes	—
15	C₂×Q₁₆	C₂×C₅	1	4	yes	—
16	C₄⋊Q₈	C₂×C₅	1	2	yes	—
17	C₄×C₈	C₂×C₅	1	1	yes	characteristic
18	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
19	C₄×C₅	—	4	4	no	—
20	C₄×C₅	Q₁₆	1	4	yes	complemented
21	C₄×C₅	C₂×D₄	1	2	yes	—
22	C₂×Q₈	C₂²×C₅	1	4	yes	—
23	Q₁₆	—	2	8	no	—
24	C₂×C₈	C₂²×C₅	1	2	yes	—
25	C₄⋊C₄	—	2	4	no	—
26	C₄²	C₂²×C₅	1	1	yes	characteristic
27	C₂×C₅	#127	1	1	yes	characteristic
28	C₂×C₅	C₂×Q₁₆	1	2	yes	—
29	Q₈	—	2	8	no	—
30	C₂×C₄	—	2	4	no	—
31	C₂×C₄	C₅×D₄	1	2	yes	—
32	C₂×C₄	C₂³×C₅	1	1	yes	characteristic
33	C₈	C₅×D₄	1	4	yes	—
34	C₅	#494	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²	C₂×C₅×D₄	1	1	yes	characteristic
36	C₄	—	4	4	no	—
37	C₄	C₅×Q₁₆	1	4	yes	complemented
38	C₄	C₂×C₅×D₄	1	2	yes	—
39	C₂	C₅×#127	1	1	yes	characteristic
40	C₂	C₂×C₅×Q₁₆	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ G

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

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