Subgroups — C₂₇×C₃³⋊C₁₃ #23748627

Order 9477.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₃³⋊C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₃×C₃³⋊C₁₃	C₉	1	1	yes	characteristic
3	C₃³×C₂₇	C₁₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₃³⋊C₁₃	C₂₇	1	1	yes	characteristic, direct product factor
5	C₁₃×C₂₇	—	27	1	no	maximal
6	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
7	C₃²×C₂₇	—	13	1	no	—
8	C₃²×C₂₇	—	13	2	no	—
9	C₉×C₁₃	—	27	1	no	—
10	C₃⁴	C₉×C₁₃	1	1	yes	characteristic
11	C₃²×C₉	—	13	1	no	—
12	C₃²×C₉	—	13	2	no	—
13	C₃×C₂₇	—	13	1	no	—
14	C₃×C₂₇	—	13	6	no	—
15	C₃×C₂₇	—	13	2	no	—
16	C₃×C₁₃	—	27	1	no	—
17	C₃³	—	13	2	no	—
18	C₃³	—	13	1	no	—
19	C₃³	C₁₃×C₂₇	1	1	yes	characteristic, complemented
20	C₃×C₉	—	13	1	no	—
21	C₃×C₉	—	13	6	no	—
22	C₃×C₉	—	13	2	no	—
23	C₂₇	—	13	2	no	—
24	C₂₇	C₃³⋊C₁₃	1	1	yes	characteristic, direct product factor
25	C₁₃	—	27	1	no	Sylow
26	C₃²	—	13	1	no	—
27	C₃²	—	13	2	no	—
28	C₃²	—	13	6	no	—
29	C₃²	—	13	1	no	—
30	C₉	—	13	2	no	—
31	C₉	C₃×C₃³⋊C₁₃	1	1	yes	characteristic
32	C₃	—	13	2	no	—
33	C₃	—	13	1	no	—
34	C₃	C₉×C₃³⋊C₁₃	1	1	yes	characteristic

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