Subgroups — C₃×#6122 #10597721

Order 624.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×#1057	C₂	1	2	yes	maximal, complemented
3	#6122	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×C₁₃	C₄	1	1	yes	characteristic
5	C₃×Dic₁₃	C₄	1	1	yes	characteristic
6	C₃×Dic₁₃	C₂²	1	1	yes	characteristic
7	C₂×Dic₁₃	C₂×C₃	1	1	yes	characteristic
8	#1057	C₂×C₃	1	2	yes	complemented
9	C₂×C₃×C₁₃	—	2	1	no	—
10	C₂×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₁₃	C₃×C₄	1	1	yes	characteristic
12	Dic₁₃	C₃×C₄	1	1	yes	characteristic
13	Dic₁₃	C₂²×C₃	1	1	yes	characteristic
14	C₃×M₁₆	—	13	1	no	maximal, Hall
15	C₃×C₁₃	M₁₆	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃	—	2	1	no	—
17	C₂×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
18	C₂×C₃×C₄	—	13	1	no	—
19	C₃×C₈	—	13	2	no	—
20	M₁₆	—	13	1	no	Sylow
21	C₁₃	C₃×M₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₃	#261	1	1	yes	characteristic
23	C₃×C₄	—	13	1	no	—
24	C₃×C₄	—	13	1	no	—
25	C₂×C₄	—	13	1	no	—
26	C₈	—	13	2	no	—
27	C₂×C₃	—	2	1	no	—
28	C₂×C₃	C₂×#261	1	1	yes	characteristic
29	C₂²	C₃×#261	1	1	yes	characteristic
30	C₄	—	13	1	no	—
31	C₄	—	13	1	no	—
32	C₃	#6122	1	1	yes	characteristic, direct product factor, Sylow
33	C₂	—	2	1	no	—
34	C₂	C₂×C₃×#261	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.