Subgroups — C₂×C₅×2₋¹⁺⁴ #66295

Order 320.

794 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×2₋¹⁺⁴	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₅×#41	C₂	1	10	yes	maximal, complemented
3	C₂²×C₅×Q₈	C₂	1	5	yes	maximal, complemented
4	C₅×#41	C₂²	1	80	yes	complemented
5	C₂×C₅×Q₈	C₂²	1	10	yes	—
6	C₂×C₅×Q₈	C₂²	1	40	yes	complemented
7	C₂×C₅×D₄	C₂²	1	10	yes	—
8	C₂²×C₄×C₅	C₂²	1	15	yes	—
9	C₂×2₋¹⁺⁴	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₅	C₂³	1	5	yes	—
11	C₅×Q₈	C₂³	1	40	yes	—
12	C₅×D₄	C₂³	1	40	yes	—
13	C₂×C₄×C₅	C₂³	1	60	yes	—
14	C₂×C₄×C₅	C₂³	1	10	yes	—
15	2₋¹⁺⁴	C₂×C₅	1	16	yes	direct product factor
16	C₂×#41	C₂×C₅	1	10	yes	complemented
17	C₂²×Q₈	C₂×C₅	1	5	yes	complemented
18	C₂²×C₅	—	2	10	no	—
19	C₂²×C₅	C₂⁴	1	10	yes	—
20	C₂²×C₅	C₂⁴	1	1	yes	characteristic
21	C₄×C₅	C₂⁴	1	20	yes	—
22	#41	C₂²×C₅	1	80	yes	complemented
23	C₂×Q₈	C₂²×C₅	1	10	yes	—
24	C₂×Q₈	C₂²×C₅	1	40	yes	complemented
25	C₂×D₄	C₂²×C₅	1	10	yes	—
26	C₂²×C₄	C₂²×C₅	1	15	yes	—
27	C₂×C₅	—	2	10	no	—
28	C₂×C₅	2₋¹⁺⁴	1	2	yes	direct product factor
29	C₂×C₅	C₂⁵	1	1	yes	characteristic
30	C₂³	C₂³×C₅	1	5	yes	—
31	Q₈	C₂³×C₅	1	40	yes	—
32	D₄	C₂³×C₅	1	40	yes	—
33	C₂×C₄	C₂³×C₅	1	10	yes	—
34	C₂×C₄	C₂³×C₅	1	60	yes	—
35	C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²	—	2	10	no	—
37	C₂²	C₂⁴×C₅	1	10	yes	—
38	C₂²	C₂⁴×C₅	1	1	yes	characteristic
39	C₄	C₂⁴×C₅	1	20	yes	—
40	C₂	—	2	10	no	—
41	C₂	C₅×2₋¹⁺⁴	1	2	yes	direct product factor
42	C₂	C₂⁵×C₅	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂⁴
commutator, Frattini, cosocle	C₂	C₂⁵×C₅
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×2₋¹⁺⁴	C₂	direct (N × H)
2. C₂×C₅×#41	C₂	semidirect
3. C₂²×C₅×Q₈	C₂	semidirect
4. C₅×#41	C₂²	semidirect
6. C₂×C₅×Q₈	C₂²	semidirect
9. C₂×2₋¹⁺⁴	C₅	direct (N × H)
15. 2₋¹⁺⁴	C₂×C₅	direct (N × H)
16. C₂×#41	C₂×C₅	semidirect
17. C₂²×Q₈	C₂×C₅	semidirect
22. #41	C₂²×C₅	semidirect
24. C₂×Q₈	C₂²×C₅	semidirect
28. C₂×C₅	2₋¹⁺⁴	direct (N × H)
35. C₅	C₂×2₋¹⁺⁴	direct (N × H)
41. C₂	C₅×2₋¹⁺⁴	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×2₋¹⁺⁴	2
C₂×C₅×#41	2
C₂²×C₅×Q₈	2
C₂×2₋¹⁺⁴	5

Subgroups — C2×C5×2−1+4 #66295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×2₋¹⁺⁴ #66295