Subgroups — C₂×C₃×#261 #64636

Order 312.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×#261	C₂	1	2	yes	maximal, direct product factor
3	C₂×#261	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₁₃	C₄	1	1	yes	characteristic, complemented
5	C₃×D₁₃	C₄	1	1	yes	characteristic, complemented
6	C₃×D₁₃	C₂²	1	1	yes	characteristic
7	C₂×D₁₃	C₂×C₃	1	1	yes	characteristic
8	#261	C₂×C₃	1	2	yes	direct product factor
9	C₃×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
11	D₁₃	C₃×C₄	1	1	yes	characteristic, complemented
12	D₁₃	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₃×C₄	—	13	1	no	maximal, Hall
14	C₁₃	C₂×C₃×C₄	1	1	yes	characteristic, complemented, Sylow
15	C₂²×C₃	—	13	1	no	—
16	C₃×C₄	—	13	2	no	—
17	C₂×C₄	—	13	1	no	Sylow
18	C₂×C₃	—	13	1	no	—
19	C₂×C₃	—	13	1	no	—
20	C₂×C₃	#261	1	1	yes	characteristic, direct product factor
21	C₂²	—	13	1	no	—
22	C₄	—	13	2	no	—
23	C₃	C₂×#261	1	1	yes	characteristic, direct product factor, Sylow
24	C₂	—	13	1	no	—
25	C₂	—	13	1	no	—
26	C₂	C₃×#261	1	1	yes	characteristic, direct product factor

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.