Subgroups — #17987463

Order 4617.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#10587022	C₃	1	1	yes	maximal, characteristic
2	#13095306	C₃	1	2	yes	maximal, complemented
3	#13095305	C₃	1	6	yes	maximal, complemented
4	#13095303	C₃	1	3	yes	maximal
5	C₉²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
7	C₃×C₉×C₁₉	C₃²	1	3	yes	—
8	C₃×C₉×C₁₉	C₃²	1	1	yes	characteristic
9	C₃×#4294	C₃²	1	6	yes	—
10	C₃×#4294	C₃²	1	2	yes	—
11	#10587022	—	3	3	no	—
12	#6899	—	19	1	no	maximal, Sylow
13	C₃²×C₁₉	C₃³	1	1	yes	characteristic
14	C₃×C₁₉⋊C₃	—	3	1	no	—
15	C₃×C₁₉⋊C₃	—	3	3	no	—
16	C₉×C₁₉	—	3	3	no	—
17	C₉×C₁₉	3₋¹⁺²	1	3	yes	—
18	#4294	—	3	2	no	—
19	#4294	—	3	6	no	—
20	C₃×3₋¹⁺²	—	19	1	no	—
21	C₉⋊C₉	—	19	6	no	—
22	C₉⋊C₉	—	19	2	no	—
23	C₃²⋊C₉	—	19	3	no	—
24	C₉²	C₁₉⋊C₃	1	1	yes	characteristic, complemented
25	C₃×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
26	C₃×C₁₉	#737	1	3	yes	—
27	C₁₉⋊C₃	—	9	1	no	—
28	C₃³	—	19	1	no	—
29	3₋¹⁺²	—	57	3	no	—
30	C₃×C₉	—	19	6	no	—
31	C₃×C₉	—	19	2	no	—
32	C₃×C₉	C₃×C₁₉⋊C₃	1	3	yes	—
33	C₃×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
34	C₁₉	#6899	1	1	yes	characteristic, complemented, Sylow
35	C₃²	—	57	1	no	—
36	C₃²	—	57	3	no	—
37	C₃²	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
38	C₉	—	3	3	no	—
39	C₉	—	57	2	no	—
40	C₉	—	57	6	no	—
41	C₉	#10587022	1	3	yes	—
42	C₃	—	171	1	no	—
43	C₃	C₃×#10587022	1	1	yes	characteristic
44	C₃	#13095332	1	3	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.