Subgroups — C₂³×#261 #88266

Order 416.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#261	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₁₃	C₄	1	1	yes	characteristic, complemented
4	C₂²×D₁₃	C₄	1	7	yes	complemented
5	C₂²×D₁₃	C₂²	1	7	yes	—
6	C₂×#261	C₂²	1	28	yes	direct product factor
7	C₂²×C₁₃	C₂×C₄	1	7	yes	complemented
8	C₂×D₁₃	C₂×C₄	1	21	yes	complemented
9	C₂×D₁₃	C₂³	1	7	yes	—
10	#261	C₂³	1	8	yes	direct product factor
11	C₂³×C₄	—	13	1	no	maximal, Sylow
12	C₂×C₁₃	C₂²×C₄	1	7	yes	complemented
13	D₁₃	C₂²×C₄	1	7	yes	complemented
14	D₁₃	C₂⁴	1	1	yes	characteristic
15	C₂⁴	—	13	1	no	—
16	C₂²×C₄	—	13	14	no	—
17	C₁₃	C₂³×C₄	1	1	yes	characteristic, complemented, Sylow
18	C₂³	—	13	7	no	—
19	C₂³	—	13	7	no	—
20	C₂³	#261	1	1	yes	characteristic, direct product factor
21	C₂×C₄	—	13	28	no	—
22	C₂²	—	13	21	no	—
23	C₂²	—	13	7	no	—
24	C₂²	C₂×#261	1	7	yes	direct product factor
25	C₄	—	13	8	no	—
26	C₂	—	13	1	no	—
27	C₂	—	13	7	no	—
28	C₂	C₂²×#261	1	7	yes	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.