Subgroups — #17987390

Order 4617.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095322	C₃	1	2	yes	maximal, complemented
2	#13095320	C₃	1	1	yes	maximal, characteristic
3	C₁₉×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×C₁₉	—	3	1	no	—
5	C₃×C₉×C₁₉	C₃²	1	1	yes	characteristic
6	C₃²⋊(C₁₉⋊C₃)	—	3	1	no	—
7	#10587025	—	3	2	no	—
8	#6883	—	19	1	no	maximal, Sylow
9	C₃²×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
10	C₃×C₁₉⋊C₃	—	9	1	no	—
11	C₉×C₁₉	—	3	1	no	—
12	C₉×C₁₉	—	9	1	no	—
13	#4294	—	9	2	no	—
14	#733	—	19	2	no	—
15	#732	—	19	1	no	—
16	C₉⋊C₉	C₁₉⋊C₃	1	1	yes	characteristic, complemented
17	C₃×C₁₉	—	3	1	no	—
18	C₃×C₁₉	#732	1	1	yes	characteristic
19	C₁₉⋊C₃	—	27	1	no	—
20	3₋¹⁺²	—	57	2	no	—
21	H(3,𝔽₃)	—	57	1	no	—
22	C₃×C₉	—	3	1	no	—
23	C₃×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
24	C₁₉	#6883	1	1	yes	characteristic, complemented, Sylow
25	C₃²	—	171	1	no	—
26	C₃²	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
27	C₉	—	3	1	no	—
28	C₉	—	9	1	no	—
29	C₉	—	171	2	no	—
30	C₃	—	513	1	no	—
31	C₃	—	3	1	no	—
32	C₃	#13095320	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.