Subgroups — C₈₁×#4296 #28356748

Order 13851.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₉⋊C₃)⋊C₈₁	C₃	1	2	yes	maximal
2	C₂₇×#4296	C₃	1	1	yes	maximal, characteristic
3	C₁₉⋊C₃×C₈₁	C₃	1	1	yes	maximal, characteristic
4	(C₁₉⋊C₃)⋊C₂₇	C₉	1	2	yes	—
5	C₉×#4296	C₉	1	1	yes	characteristic
6	#13095335	C₉	1	6	yes	complemented
7	C₂₇×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
8	#13095301	C₉	1	2	yes	complemented
9	C₁₉×C₈₁	C₉	1	1	yes	characteristic, complemented
10	C₉×C₈₁	—	19	1	no	maximal, Sylow
11	C₃×#4296	C₂₇	1	3	yes	—
12	C₉×C₁₉⋊C₃	C₃×C₉	1	1	yes	characteristic
13	#10587020	C₂₇	1	6	yes	—
14	C₁₉×C₂₇	C₃×C₉	1	1	yes	characteristic
15	#10587018	C₃×C₉	1	2	yes	—
16	C₃×C₈₁	—	19	2	no	—
17	C₃×C₈₁	—	19	1	no	—
18	C₉×C₂₇	—	19	1	no	—
19	C₃×C₁₉⋊C₃	C₃×C₂₇	1	1	yes	characteristic
20	#4296	C₈₁	1	9	yes	direct product factor
21	C₉×C₁₉	C₉²	1	1	yes	characteristic
22	#4294	C₃×C₂₇	1	2	yes	—
23	C₃×C₂₇	—	19	2	no	—
24	C₃×C₂₇	—	19	1	no	—
25	C₉²	—	19	1	no	—
26	C₈₁	—	19	6	no	—
27	C₈₁	—	19	2	no	—
28	C₈₁	#4296	1	1	yes	characteristic, direct product factor
29	C₃×C₁₉	C₉×C₂₇	1	1	yes	characteristic
30	C₁₉⋊C₃	C₃×C₈₁	1	3	yes	—
31	C₃×C₉	—	19	3	no	—
32	C₃×C₉	—	19	1	no	—
33	C₂₇	—	19	6	no	—
34	C₂₇	—	19	2	no	—
35	C₂₇	C₃×#4296	1	1	yes	characteristic
36	C₁₉	C₉×C₈₁	1	1	yes	characteristic, complemented, Sylow
37	C₃²	—	19	1	no	—
38	C₉	—	19	9	no	—
39	C₉	—	19	2	no	—
40	C₉	C₉×#4296	1	1	yes	characteristic
41	C₃	—	19	3	no	—
42	C₃	C₂₇×#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.