Subgroups — C₃×#13095342 #17987594

Order 4617.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095342	C₃	1	9	yes	maximal, direct product factor
2	C₃×#10587020	C₃	1	3	yes	maximal, complemented
3	C₃²×#4294	C₃	1	1	yes	maximal, characteristic
4	C₃³×C₁₉	C₉	1	1	yes	characteristic
5	C₃×#4294	C₉	1	6	yes	—
6	C₃×#4294	C₉	1	2	yes	—
7	C₃×#4294	C₃²	1	1	yes	characteristic
8	C₃×#4294	C₃²	1	3	yes	—
9	#10587020	C₃²	1	9	yes	complemented
10	C₃×C₂₇⋊C₃	—	19	1	no	maximal, Sylow
11	C₃²×C₁₉	—	3	3	no	—
12	C₃²×C₁₉	C₃×C₉	1	3	yes	—
13	C₃²×C₁₉	C₃×C₉	1	1	yes	characteristic
14	#4294	C₃×C₉	1	2	yes	—
15	#4294	C₃×C₉	1	6	yes	—
16	#4294	C₃³	1	1	yes	characteristic
17	C₃²×C₉	—	19	1	no	—
18	C₂₇⋊C₃	—	19	9	no	—
19	C₃×C₂₇	—	19	3	no	—
20	C₃×C₁₉	—	3	3	no	—
21	C₃×C₁₉	C₂₇⋊C₃	1	3	yes	complemented
22	C₃×C₁₉	C₃²×C₉	1	1	yes	characteristic
23	C₃³	#4296	1	1	yes	characteristic
24	C₃×C₉	—	19	6	no	—
25	C₃×C₉	—	19	3	no	—
26	C₃×C₉	—	19	2	no	—
27	C₃×C₉	—	19	1	no	—
28	C₂₇	—	19	9	no	—
29	C₁₉	C₃×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₃²	—	3	3	no	—
31	C₃²	C₃×#4296	1	3	yes	—
32	C₃²	C₃×#4296	1	1	yes	characteristic
33	C₉	—	19	1	no	—
34	C₉	—	19	2	no	—
35	C₉	—	19	6	no	—
36	C₃	—	3	3	no	—
37	C₃	#13095342	1	3	yes	direct product factor
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.