Subgroups — #13123231

Order 1664.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88128	C₂	1	14	yes	maximal, complemented
2	C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₅₂	C₂²	1	28	yes	—
4	C₂×C₄²×C₁₃	C₂²	1	7	yes	—
5	#88128	—	2	56	no	—
6	C₂³×D₁₃	C₂³	1	8	yes	—
7	C₂²×C₄×C₁₃	C₂³	1	7	yes	—
8	C₂×D₅₂	—	2	168	no	—
9	C₄²×C₁₃	D₄	1	28	yes	complemented
10	#2867	—	13	1	no	maximal, Sylow
11	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
12	C₂²×D₁₃	—	2	56	no	—
13	C₂×C₄×C₁₃	C₂×D₄	1	42	yes	—
14	D₅₂	—	4	112	no	—
15	C₂×#127	—	13	14	no	—
16	C₄³	D₁₃	1	1	yes	characteristic, complemented
17	C₂²×C₁₃	C₂²×D₄	1	7	yes	—
18	C₂×D₁₃	—	4	56	no	—
19	C₄×C₁₃	#127	1	28	yes	complemented
20	C₂²×D₄	—	13	28	no	—
21	#127	—	26	56	no	—
22	C₂×C₄²	C₂×D₁₃	1	7	yes	—
23	C₂×C₁₃	C₂×#127	1	7	yes	—
24	D₁₃	—	8	8	no	—
25	C₂⁴	—	13	8	no	—
26	C₂×D₄	—	26	168	no	—
27	C₂²×C₄	C₂²×D₁₃	1	7	yes	—
28	C₄²	D₅₂	1	28	yes	complemented
29	C₁₃	#2867	1	1	yes	characteristic, complemented, Sylow
30	C₂³	—	26	56	no	—
31	C₂³	C₂³×D₁₃	1	1	yes	characteristic
32	D₄	—	52	112	no	—
33	C₂×C₄	C₂×D₅₂	1	42	yes	—
34	C₂²	—	52	56	no	—
35	C₂²	C₂²×D₅₂	1	7	yes	—
36	C₄	#88128	1	28	yes	complemented
37	C₂	—	104	8	no	—
38	C₂	C₂×#88128	1	7	yes	—

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.