Subgroups — C₁₉×#13089712 #42119949

Order 27588.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×C₁₁²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₉×Dic₁₁	—	3	1	no	maximal, Hall
3	C₁₉×C₁₁²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁²×C₁₉	D₃	1	1	yes	characteristic
5	C₁₁²×C₁₉	Dic₃	1	1	yes	characteristic, complemented, Hall
6	#13089712	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₄×C₁₁×C₁₉	—	33	1	no	—
8	C₁₉×Dic₁₁	—	3	1	no	—
9	C₂×C₁₁²⋊C₃	C₂×C₁₉	1	1	yes	characteristic
10	C₁₁×Dic₁₁	—	3	1	no	Hall
11	C₂×C₁₁×C₁₉	—	3	1	no	—
12	C₂×C₁₁×C₁₉	—	3	1	no	—
13	C₂×C₁₁×C₁₉	—	6	1	no	—
14	C₁₁²⋊C₃	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₁²	D₃×C₁₉	1	1	yes	characteristic
16	Dic₃×C₁₉	—	121	1	no	maximal, Hall
17	C₁₁×C₁₉	—	3	1	no	—
18	C₁₁×C₁₉	—	3	1	no	—
19	C₁₁×C₁₉	—	6	1	no	—
20	C₁₁²	Dic₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₁₉	—	121	1	no	—
22	C₄×C₁₉	—	33	1	no	Hall
23	C₃×C₁₉	—	121	1	no	Hall
24	C₄×C₁₁	—	33	1	no	—
25	Dic₁₁	—	3	1	no	—
26	C₂×C₁₉	#10624391	1	1	yes	characteristic
27	C₂×C₁₁	—	3	1	no	—
28	C₂×C₁₁	—	3	1	no	—
29	C₂×C₁₁	—	6	1	no	—
30	C₁₉	#13089712	1	1	yes	characteristic, direct product factor, Sylow
31	Dic₃	—	121	1	no	Hall
32	C₁₁	—	3	1	no	—
33	C₁₁	—	3	1	no	—
34	C₁₁	—	6	1	no	—
35	C₂×C₃	—	121	1	no	—
36	C₄	—	33	1	no	Sylow
37	C₃	—	121	1	no	Sylow
38	C₂	C₁₉×#10624391	1	1	yes	characteristic

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.