Subgroups — (C₁₉⋊C₃)⋊C₂₄₃ #28356836

Order 13851.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987549	C₃	1	3	yes	maximal, complemented
2	C₁₉⋊C₃×C₈₁	C₃	1	1	yes	maximal, characteristic
3	C₂₇×C₁₉⋊C₃	C₉	1	1	yes	characteristic
4	#13095301	C₉	1	1	yes	characteristic
5	#13095301	C₃²	1	1	yes	characteristic
6	C₁₉×C₈₁	C₉	1	1	yes	characteristic
7	C₃×C₂₄₃	—	19	1	no	maximal, Sylow
8	C₉×C₁₉⋊C₃	C₂₇	1	1	yes	characteristic
9	C₁₉×C₂₇	C₃×C₉	1	1	yes	characteristic
10	#10587018	C₂₇	1	2	yes	—
11	C₃×C₈₁	—	19	1	no	—
12	C₂₄₃	—	19	3	no	—
13	C₃×C₁₉⋊C₃	C₈₁	1	1	yes	characteristic
14	C₉×C₁₉	C₃×C₂₇	1	1	yes	characteristic
15	#4294	C₈₁	1	2	yes	—
16	C₃×C₂₇	—	19	1	no	—
17	C₈₁	—	19	1	no	—
18	C₈₁	—	19	1	no	—
19	C₈₁	#4296	1	1	yes	characteristic
20	C₃×C₁₉	C₃×C₈₁	1	1	yes	characteristic
21	C₁₉⋊C₃	C₂₄₃	1	3	yes	complemented
22	C₃×C₉	—	19	1	no	—
23	C₂₇	—	19	2	no	—
24	C₂₇	C₃×#4296	1	1	yes	characteristic
25	C₁₉	C₃×C₂₄₃	1	1	yes	characteristic, complemented, Sylow
26	C₃²	—	19	1	no	—
27	C₉	—	19	2	no	—
28	C₉	(C₁₉⋊C₃)⋊C₂₇	1	1	yes	characteristic
29	C₃	—	19	3	no	—
30	C₃	(C₁₉⋊C₃)⋊C₈₁	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.