Subgroups — #17987372

Order 4617.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095322	C₃	1	1	yes	maximal, characteristic, complemented
2	#13095320	C₃	1	1	yes	maximal, characteristic
3	C₉×#4294	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#733	C₃	1	1	yes	maximal, characteristic, complemented
5	C₁₉×3₋¹⁺²	—	3	1	no	—
6	C₃×C₉×C₁₉	C₃²	1	1	yes	characteristic
7	C₃²⋊(C₁₉⋊C₃)	—	3	1	no	—
8	#10587025	—	3	1	no	—
9	C₃×#4294	—	3	1	no	—
10	#6878	—	19	1	no	maximal, Sylow
11	C₃²×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
12	C₃×C₁₉⋊C₃	—	9	1	no	—
13	C₉×C₁₉	—	3	1	no	—
14	C₉×C₁₉	—	9	1	no	—
15	#4294	—	3	3	no	—
16	#4294	—	9	1	no	—
17	#733	—	19	1	no	—
18	#733	C₁₉⋊C₃	1	1	yes	characteristic, complemented
19	#732	—	19	1	no	—
20	C₉²	—	19	1	no	—
21	C₃×C₁₉	—	3	1	no	—
22	C₃×C₁₉	#732	1	1	yes	characteristic
23	C₁₉⋊C₃	—	27	1	no	—
24	3₋¹⁺²	—	3	1	no	—
25	3₋¹⁺²	—	57	1	no	—
26	H(3,𝔽₃)	—	57	1	no	—
27	C₃×C₉	—	57	1	no	—
28	C₃×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
29	C₁₉	#6878	1	1	yes	characteristic, complemented, Sylow
30	C₃²	—	171	1	no	—
31	C₃²	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
32	C₉	—	3	1	no	—
33	C₉	—	9	1	no	—
34	C₉	—	57	3	no	—
35	C₉	—	171	1	no	—
36	C₃	—	513	1	no	—
37	C₃	—	3	1	no	—
38	C₃	#13095319	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.