Subgroups — #17987469

Order 4617.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#10587022	C₃	1	4	yes	maximal
2	#13095306	C₃	1	8	yes	maximal, complemented
3	C₉²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
5	C₃×C₉×C₁₉	C₃²	1	4	yes	—
6	C₃×#4294	C₃²	1	8	yes	—
7	#10587022	—	3	12	no	—
8	#6900	—	19	1	no	maximal, Sylow
9	C₃²×C₁₉	C₃³	1	1	yes	characteristic
10	C₃×C₁₉⋊C₃	—	3	4	no	—
11	C₉×C₁₉	3₋¹⁺²	1	12	yes	complemented
12	#4294	—	3	8	no	—
13	C₃×3₋¹⁺²	—	19	4	no	—
14	C₉⋊C₉	—	19	8	no	—
15	C₉²	C₁₉⋊C₃	1	1	yes	characteristic, complemented
16	C₃×C₁₉	C₃×3₋¹⁺²	1	4	yes	—
17	C₁₉⋊C₃	—	9	1	no	—
18	C₃³	—	19	1	no	—
19	3₋¹⁺²	—	57	12	no	—
20	C₃×C₉	—	19	8	no	—
21	C₃×C₉	C₃×C₁₉⋊C₃	1	4	yes	—
22	C₁₉	#6900	1	1	yes	characteristic, complemented, Sylow
23	C₃²	—	57	4	no	—
24	C₃²	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
25	C₉	—	57	8	no	—
26	C₉	#10587022	1	12	yes	complemented
27	C₃	—	171	1	no	—
28	C₃	C₃×#10587022	1	4	yes	—

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.