Subgroups — C₁₃×#11717941 #24922397

Order 10647.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃²	C₃	1	1	yes	maximal, characteristic
2	C₁₃×C₁₃⋊C₉	—	7	1	no	maximal, Hall
3	C₇×C₁₃²	C₉	1	1	yes	characteristic, complemented, Hall
4	#11717941	C₁₃	1	1	yes	maximal, characteristic, direct product factor
5	C₁₃×C₇⋊C₉	—	13	1	no	maximal
6	C₃×C₁₃²	ΓL(1,𝔽₈)	1	1	yes	characteristic
7	C₃×C₇×C₁₃	—	3	4	no	—
8	C₃×C₇×C₁₃	C₁₃⋊C₃	1	1	yes	characteristic
9	C₃×C₇×C₁₃	C₃×C₁₃	1	1	yes	characteristic
10	C₁₃²	C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
11	C₉×C₁₃	—	91	1	no	—
12	C₁₃⋊C₉	—	7	1	no	—
13	C₇×C₁₃	—	3	4	no	—
14	C₇×C₁₃	C₁₃⋊C₉	1	1	yes	characteristic, complemented
15	C₇×C₁₃	C₉×C₁₃	1	1	yes	characteristic, complemented
16	C₇⋊C₉	—	13	1	no	Hall
17	C₃×C₁₃	—	3	4	no	—
18	C₃×C₁₃	C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
19	C₃×C₁₃	#63270	1	1	yes	characteristic
20	C₃×C₇	C₁₃×C₁₃⋊C₃	1	1	yes	characteristic
21	C₁₃	—	3	4	no	—
22	C₁₃	C₁₃×C₇⋊C₉	1	1	yes	characteristic, complemented
23	C₁₃	#11717941	1	1	yes	characteristic, direct product factor
24	C₉	—	91	1	no	Sylow
25	C₇	C₁₃×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
26	C₃	C₁₃×#63270	1	1	yes	characteristic

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