Subgroups — C₃×(C₁₉⋊C₃)⋊C₂₇ #17987593

Order 4617.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₉⋊C₃)⋊C₂₇	C₃	1	9	yes	maximal, direct product factor
2	C₃×#10587020	C₃	1	3	yes	maximal, complemented
3	C₃×C₉×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₁₉⋊C₃	C₉	1	1	yes	characteristic
5	C₃×C₉×C₁₉	C₉	1	1	yes	characteristic
6	C₃×#4294	C₉	1	1	yes	characteristic
7	C₃×#4294	C₃²	1	1	yes	characteristic
8	C₉×C₁₉⋊C₃	C₉	1	6	yes	—
9	C₉×C₁₉⋊C₃	C₃²	1	3	yes	—
10	#10587020	C₃²	1	9	yes	complemented
11	C₃²×C₂₇	—	19	1	no	maximal, Sylow
12	C₃²×C₁₉	C₃×C₉	1	1	yes	characteristic
13	C₃×C₁₉⋊C₃	C₂₇	1	9	yes	complemented
14	C₃×C₁₉⋊C₃	C₃×C₉	1	3	yes	—
15	C₉×C₁₉	C₃×C₉	1	3	yes	—
16	#4294	C₃×C₉	1	2	yes	—
17	#4294	C₃×C₉	1	3	yes	—
18	#4294	C₃³	1	1	yes	characteristic
19	C₃²×C₉	—	19	1	no	—
20	C₃×C₂₇	—	19	3	no	—
21	C₃×C₂₇	—	19	9	no	—
22	C₃×C₁₉	C₃×C₂₇	1	3	yes	complemented
23	C₃×C₁₉	C₃²×C₉	1	1	yes	characteristic
24	C₁₉⋊C₃	C₃×C₂₇	1	9	yes	complemented
25	C₃³	—	19	1	no	—
26	C₃×C₉	—	19	1	no	—
27	C₃×C₉	—	19	1	no	—
28	C₃×C₉	—	19	6	no	—
29	C₃×C₉	—	19	3	no	—
30	C₃×C₉	#4296	1	1	yes	characteristic
31	C₂₇	—	19	9	no	—
32	C₁₉	C₃²×C₂₇	1	1	yes	characteristic, complemented, Sylow
33	C₃²	—	19	9	no	—
34	C₃²	—	19	3	no	—
35	C₃²	C₃×#4296	1	1	yes	characteristic
36	C₉	—	19	1	no	—
37	C₉	—	19	3	no	—
38	C₉	—	19	2	no	—
39	C₉	C₃×#4296	1	3	yes	—
40	C₃	—	19	9	no	—
41	C₃	(C₁₉⋊C₃)⋊C₂₇	1	3	yes	direct product factor
42	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.