Subgroups — #17987568

Order 4617.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095342	C₃	1	2	yes	maximal, complemented
2	C₃×#10587020	C₃	1	1	yes	maximal, characteristic, complemented
3	#13095331	C₃	1	1	yes	maximal, characteristic
4	C₁₉×H(3,𝔽₃)	C₉	1	1	yes	characteristic
5	#10587025	—	3	2	no	—
6	#10587025	C₉	1	2	yes	—
7	C₃×#4294	—	3	1	no	—
8	C₃×#4294	C₃²	1	1	yes	characteristic
9	#10587020	—	3	1	no	—
10	#10587020	—	3	2	no	—
11	#6873	—	19	1	no	maximal, Sylow
12	C₃²×C₁₉	—	3	1	no	—
13	C₃²×C₁₉	C₃×C₉	1	1	yes	characteristic
14	#4294	—	3	2	no	—
15	#4294	H(3,𝔽₃)	1	1	yes	characteristic
16	#4294	3₋¹⁺²	1	2	yes	—
17	#737	—	19	1	no	—
18	C₂₇⋊C₃	—	19	2	no	—
19	C₃×C₂₇	—	19	1	no	—
20	C₃×C₁₉	—	3	1	no	—
21	C₃×C₁₉	—	9	1	no	—
22	C₃×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
23	3₋¹⁺²	—	19	2	no	—
24	3₋¹⁺²	—	57	2	no	—
25	H(3,𝔽₃)	#4296	1	1	yes	characteristic
26	C₃×C₉	—	19	1	no	—
27	C₃×C₉	—	57	1	no	—
28	C₂₇	—	57	1	no	—
29	C₂₇	—	57	2	no	—
30	C₁₉	#6873	1	1	yes	characteristic, complemented, Sylow
31	C₃²	—	3	1	no	—
32	C₃²	C₃×#4296	1	1	yes	characteristic
33	C₉	—	19	1	no	—
34	C₉	—	19	2	no	—
35	C₉	—	57	2	no	—
36	C₃	—	3	1	no	—
37	C₃	—	9	1	no	—
38	C₃	C₃²⋊#4296	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.