Subgroups — C₁₉×2₋¹⁺⁶ #14561452

Order 2432.

5796 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#585	C₂	1	36	yes	maximal, complemented
2	C₂×C₁₉×2₋¹⁺⁴	C₂	1	27	yes	maximal, complemented
3	C₁₉×2₋¹⁺⁴	C₂²	1	216	yes	complemented
4	C₁₉×H(5,𝔽₂)	C₂²	1	120	yes	complemented
5	C₂×#41×C₁₉	C₂²	1	270	yes	complemented
6	C₂²×Q₈×C₁₉	C₂²	1	45	yes	complemented
7	#41×C₁₉	C₂³	1	720	yes	—
8	C₂×Q₈×C₁₉	C₂³	1	270	yes	—
9	C₂×D₄×C₁₉	C₂³	1	270	yes	—
10	C₂²×C₄×C₁₉	C₂³	1	135	yes	—
11	C₂³×C₁₉	C₂⁴	1	45	yes	—
12	Q₈×C₁₉	C₂⁴	1	120	yes	—
13	D₄×C₁₉	C₂⁴	1	216	yes	—
14	C₂×C₄×C₁₉	C₂⁴	1	270	yes	—
15	2₋¹⁺⁶	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂²×C₁₉	—	4	45	no	—
17	C₂²×C₁₉	C₂⁵	1	27	yes	—
18	C₄×C₁₉	C₂⁵	1	36	yes	—
19	#585	C₂×C₁₉	1	36	yes	complemented
20	C₂×2₋¹⁺⁴	C₂×C₁₉	1	27	yes	complemented
21	C₂×C₁₉	—	2	27	no	—
22	C₂×C₁₉	C₂⁶	1	1	yes	characteristic
23	2₋¹⁺⁴	C₂²×C₁₉	1	216	yes	complemented
24	H(5,𝔽₂)	C₂²×C₁₉	1	120	yes	complemented
25	C₂×#41	C₂²×C₁₉	1	270	yes	complemented
26	C₂²×Q₈	C₂²×C₁₉	1	45	yes	complemented
27	C₁₉	2₋¹⁺⁶	1	1	yes	characteristic, direct product factor, Sylow
28	#41	C₂³×C₁₉	1	720	yes	—
29	C₂×Q₈	C₂³×C₁₉	1	270	yes	—
30	C₂×D₄	C₂³×C₁₉	1	270	yes	—
31	C₂²×C₄	C₂³×C₁₉	1	135	yes	—
32	C₂³	C₂⁴×C₁₉	1	45	yes	—
33	Q₈	C₂⁴×C₁₉	1	120	yes	—
34	D₄	C₂⁴×C₁₉	1	216	yes	—
35	C₂×C₄	C₂⁴×C₁₉	1	270	yes	—
36	C₂²	—	4	45	no	—
37	C₂²	C₂⁵×C₁₉	1	27	yes	—
38	C₄	C₂⁵×C₁₉	1	36	yes	—
39	C₂	—	2	27	no	—
40	C₂	C₂⁶×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	C₂⁶
commutator, Frattini, cosocle	C₂	C₂⁶×C₁₉
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#585	C₂	semidirect
2. C₂×C₁₉×2₋¹⁺⁴	C₂	semidirect
3. C₁₉×2₋¹⁺⁴	C₂²	semidirect
4. C₁₉×H(5,𝔽₂)	C₂²	semidirect
5. C₂×#41×C₁₉	C₂²	semidirect
6. C₂²×Q₈×C₁₉	C₂²	semidirect
15. 2₋¹⁺⁶	C₁₉	direct (N × H)
19. #585	C₂×C₁₉	semidirect
20. C₂×2₋¹⁺⁴	C₂×C₁₉	semidirect
23. 2₋¹⁺⁴	C₂²×C₁₉	semidirect
24. H(5,𝔽₂)	C₂²×C₁₉	semidirect
25. C₂×#41	C₂²×C₁₉	semidirect
26. C₂²×Q₈	C₂²×C₁₉	semidirect
27. C₁₉	2₋¹⁺⁶	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#585	2
C₂×C₁₉×2₋¹⁺⁴	2
2₋¹⁺⁶	19

Subgroups — C19×2−1+6 #14561452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×2₋¹⁺⁶ #14561452