Subgroups — #17987567

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	#13095333	C₃	1	1	yes	maximal, characteristic
4	C₁₉×3₋¹⁺²	C₉	1	1	yes	characteristic
5	C₃²⋊(C₁₉⋊C₃)	C₉	1	1	yes	characteristic
6	#10587025	C₉	1	1	yes	characteristic
7	C₃×#4294	C₃²	1	1	yes	characteristic
8	#10587023	—	3	1	no	—
9	#10587022	—	3	1	no	—
10	C₉×C₁₉⋊C₃	—	3	1	no	—
11	#10587020	—	3	1	no	—
12	#10587020	—	3	2	no	—
13	#6872	—	19	1	no	maximal, Sylow
14	C₃²×C₁₉	C₃×C₉	1	1	yes	characteristic
15	C₃×C₁₉⋊C₃	—	3	1	no	—
16	C₉×C₁₉	—	3	1	no	—
17	#4294	—	3	1	no	—
18	#4294	H(3,𝔽₃)	1	1	yes	characteristic
19	#4294	3₋¹⁺²	1	1	yes	characteristic
20	#4294	3₋¹⁺²	1	1	yes	characteristic
21	#737	—	19	1	no	—
22	C₂₇⋊C₃	—	19	2	no	—
23	C₃×C₂₇	—	19	1	no	—
24	C₃×C₁₉	—	3	1	no	—
25	C₃×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
26	C₁₉⋊C₃	—	9	1	no	—
27	3₋¹⁺²	—	19	1	no	—
28	3₋¹⁺²	—	57	1	no	—
29	3₋¹⁺²	—	57	1	no	—
30	3₋¹⁺²	#4296	1	1	yes	characteristic
31	H(3,𝔽₃)	—	19	1	no	—
32	C₃×C₉	—	19	1	no	—
33	C₃×C₉	—	57	1	no	—
34	C₂₇	—	57	1	no	—
35	C₂₇	—	57	2	no	—
36	C₁₉	#6872	1	1	yes	characteristic, complemented, Sylow
37	C₃²	—	57	1	no	—
38	C₃²	C₃×#4296	1	1	yes	characteristic
39	C₉	—	3	1	no	—
40	C₉	—	19	1	no	—
41	C₉	—	19	1	no	—
42	C₉	—	19	1	no	—
43	C₉	—	57	1	no	—
44	C₃	—	3	1	no	—
45	C₃	—	171	1	no	—
46	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.