Subgroups — #14561846

Order 2432.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊C₆₄	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₉	C₄	1	1	yes	characteristic
4	C₁₉×C₃₂	C₄	1	1	yes	characteristic
5	C₁₉×C₃₂	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₉	C₈	1	1	yes	characteristic
7	C₁₆×C₁₉	C₈	1	1	yes	characteristic
8	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₉	C₁₆	1	1	yes	characteristic
10	C₈×C₁₉	C₁₆	1	1	yes	characteristic
11	C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
12	M₁₂₈	—	19	1	no	maximal, Sylow
13	C₂²×C₁₉	C₃₂	1	1	yes	characteristic
14	C₄×C₁₉	C₃₂	1	1	yes	characteristic
15	C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
16	C₂×C₃₂	D₁₉	1	1	yes	characteristic
17	C₆₄	—	19	2	no	—
18	C₂×C₁₉	—	2	1	no	—
19	C₂×C₁₉	C₂×C₃₂	1	1	yes	characteristic
20	C₂×C₁₆	Dic₁₉	1	1	yes	characteristic
21	C₃₂	Dic₁₉	1	1	yes	characteristic
22	C₃₂	C₂×D₁₉	1	1	yes	characteristic
23	C₁₉	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₈	C₁₉⋊C₈	1	1	yes	characteristic
25	C₁₆	C₁₉⋊C₈	1	1	yes	characteristic
26	C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
27	C₂×C₄	C₁₉⋊C₁₆	1	1	yes	characteristic
28	C₈	C₁₉⋊C₁₆	1	1	yes	characteristic
29	C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
30	C₂²	C₁₉⋊C₃₂	1	1	yes	characteristic
31	C₄	C₁₉⋊C₃₂	1	1	yes	characteristic
32	C₄	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₂×C₁₉⋊C₃₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. C₁₉⋊C₆₄	C₂	semidirect
23. C₁₉	M₁₂₈	semidirect

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