Subgroups — #11926322

Order 1216.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#97	C₂	1	1	yes	maximal, characteristic
2	#10597269	C₂	1	2	yes	maximal
3	C₂×C₈×C₁₉	C₄	1	1	yes	characteristic
4	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
5	C₄²×C₁₉	C₄	1	1	yes	characteristic
6	C₁₉⋊C₁₆	C₄	1	4	yes	complemented
7	C₂×C₄×C₁₉	—	2	1	no	—
8	C₂×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₉	—	2	1	no	—
10	C₈×C₁₉	C₂×C₄	1	2	yes	—
11	C₂²×C₁₉	M₁₆	1	1	yes	characteristic
12	C₄×C₁₉	—	4	1	no	—
13	C₄×C₁₉	C₄²	1	1	yes	characteristic
14	C₄×C₁₉	M₁₆	1	1	yes	characteristic
15	#347	—	19	1	no	maximal, Sylow
16	C₂×C₁₉	—	2	1	no	—
17	C₂×C₁₉	#97	1	1	yes	characteristic
18	M₃₂	—	19	2	no	—
19	#97	D₁₉	1	1	yes	characteristic
20	C₁₉	#347	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₈	Dic₁₉	1	1	yes	characteristic
22	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
23	C₄²	Dic₁₉	1	1	yes	characteristic
24	C₁₆	—	19	4	no	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	C₂×Dic₁₉	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₈	C₄×D₁₉	1	2	yes	—
29	C₂²	#64520	1	1	yes	characteristic
30	C₄	—	4	1	no	—
31	C₄	#64520	1	1	yes	characteristic
32	C₄	C₄×Dic₁₉	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#10597260	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. C₁₉⋊C₁₆	C₄	semidirect
20. C₁₉	#347	semidirect

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