Subgroups — C₁₃×#10624462 #23744613

Order 9477.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₉⋊C₂₇	C₃	1	3	yes	maximal
2	C₁₃×#6864	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃×C₂₇	—	3	3	no	—
4	C₃×C₁₃×C₂₇	C₉	1	2	yes	—
5	C₃×C₁₃×C₂₇	C₉	1	1	yes	characteristic
6	C₉²×C₁₃	C₃²	1	1	yes	characteristic
7	#10624462	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
9	C₃×C₉×C₁₃	3₋¹⁺²	1	3	yes	—
10	C₁₃×C₂₇	—	3	2	no	—
11	C₁₃×C₂₇	—	9	3	no	—
12	C₁₃×C₂₇	C₂₇	1	3	yes	complemented
13	C₉⋊C₂₇	C₃×C₁₃	1	3	yes	—
14	#6864	C₃×C₁₃	1	1	yes	characteristic
15	C₃²×C₁₃	C₉⋊C₉	1	1	yes	characteristic
16	C₉×C₁₃	—	3	3	no	—
17	C₉×C₁₃	C₃×C₂₇	1	1	yes	characteristic
18	C₉×C₁₃	C₂₇⋊C₃	1	2	yes	—
19	C₃×C₂₇	—	3	3	no	—
20	C₃×C₂₇	C₉×C₁₃	1	2	yes	—
21	C₃×C₂₇	C₉×C₁₃	1	1	yes	characteristic
22	C₉²	C₃²×C₁₃	1	1	yes	characteristic
23	C₃×C₁₃	C₉⋊C₂₇	1	1	yes	characteristic
24	C₃×C₁₃	#6875	1	3	yes	—
25	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
26	C₃×C₉	C₁₃×3₋¹⁺²	1	3	yes	—
27	C₂₇	—	3	2	no	—
28	C₂₇	—	9	3	no	—
29	C₂₇	C₁₃×C₂₇	1	3	yes	complemented
30	C₁₃	#10624462	1	1	yes	characteristic, direct product factor, Sylow
31	C₃²	C₁₃×C₉⋊C₉	1	1	yes	characteristic
32	C₉	—	3	3	no	—
33	C₉	C₃×C₁₃×C₂₇	1	1	yes	characteristic
34	C₉	C₁₃×C₂₇⋊C₃	1	2	yes	—
35	C₃	C₁₃×C₉⋊C₂₇	1	1	yes	characteristic
36	C₃	C₁₃×#6875	1	3	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.