Subgroups — C₁₃×#2867 #13111925

Order 1664.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#127	C₂	1	14	yes	maximal, complemented
2	C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₄×C₁₃	C₂²	1	28	yes	—
4	C₁₃×#127	—	2	56	no	—
5	C₂×C₄²×C₁₃	C₂²	1	7	yes	—
6	C₂⁴×C₁₃	C₂³	1	8	yes	—
7	C₂×D₄×C₁₃	—	2	168	no	—
8	C₂²×C₄×C₁₃	C₂³	1	7	yes	—
9	C₄²×C₁₃	D₄	1	28	yes	complemented
10	#2867	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂³×C₁₃	—	2	56	no	—
12	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
13	D₄×C₁₃	—	4	112	no	—
14	C₂×C₄×C₁₃	C₂×D₄	1	42	yes	—
15	C₂×#127	C₂×C₁₃	1	14	yes	complemented
16	C₄³	C₂×C₁₃	1	1	yes	characteristic, complemented
17	C₂²×C₁₃	—	4	56	no	—
18	C₂²×C₁₃	C₂²×D₄	1	7	yes	—
19	C₄×C₁₃	#127	1	28	yes	complemented
20	C₂²×D₄	C₂²×C₁₃	1	28	yes	—
21	#127	—	2	56	no	—
22	C₂×C₄²	C₂²×C₁₃	1	7	yes	—
23	C₂×C₁₃	—	8	8	no	—
24	C₂×C₁₃	C₂×#127	1	7	yes	—
25	C₂⁴	C₂³×C₁₃	1	8	yes	—
26	C₂×D₄	—	2	168	no	—
27	C₂²×C₄	C₂³×C₁₃	1	7	yes	—
28	C₄²	D₄×C₁₃	1	28	yes	complemented
29	C₁₃	#2867	1	1	yes	characteristic, direct product factor, Sylow
30	C₂³	—	2	56	no	—
31	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
32	D₄	—	4	112	no	—
33	C₂×C₄	C₂×D₄×C₁₃	1	42	yes	—
34	C₂²	—	4	56	no	—
35	C₂²	C₂²×D₄×C₁₃	1	7	yes	—
36	C₄	C₁₃×#127	1	28	yes	complemented
37	C₂	—	8	8	no	—
38	C₂	C₂×C₁₃×#127	1	7	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

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.