Subgroups — #13114138

Order 1664.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#564	C₂	1	1	yes	maximal, characteristic, complemented
2	#11718728	C₂	1	3	yes	maximal
3	#11718135	C₂	1	3	yes	maximal, complemented
4	C₁₃×#125	—	2	6	no	—
5	C₁₃×#125	C₂²	1	3	yes	—
6	#88128	C₂²	1	1	yes	characteristic
7	#88049	—	2	6	no	—
8	#88043	C₂²	1	3	yes	—
9	C₂×D₅₂	—	2	3	no	—
10	C₁₃×C₄⋊C₄	—	2	6	no	—
11	C₁₃×C₄⋊C₄	—	2	6	no	—
12	C₁₃×C₄⋊C₄	D₄	1	6	yes	—
13	C₄²×C₁₃	—	2	2	no	—
14	C₄²×C₁₃	C₂³	1	1	yes	characteristic
15	C₂×#1055	—	2	3	no	—
16	#1658	—	13	1	no	maximal, Sylow
17	C₂²×D₁₃	—	4	1	no	—
18	C₂×C₄×C₁₃	—	2	6	no	—
19	C₂×C₄×C₁₃	C₂×D₄	1	3	yes	—
20	D₅₂	—	4	6	no	—
21	#1055	—	4	3	no	—
22	#564	D₁₃	1	1	yes	characteristic, complemented
23	#490	—	13	3	no	—
24	#330	—	13	3	no	—
25	C₂²×C₁₃	#120	1	1	yes	characteristic
26	C₂×D₁₃	—	8	3	no	—
27	C₄×C₁₃	—	2	3	no	—
28	C₄×C₁₃	—	4	6	no	—
29	#127	—	13	1	no	—
30	#125	—	2	6	no	—
31	#125	C₂×D₁₃	1	3	yes	—
32	#102	—	26	6	no	—
33	#97	—	13	3	no	—
34	C₂×C₁₃	#454	1	3	yes	—
35	D₁₃	—	16	1	no	—
36	C₂×D₄	—	26	3	no	—
37	C₂×C₈	—	26	3	no	—
38	C₄⋊C₄	—	2	6	no	—
39	C₄⋊C₄	—	2	6	no	—
40	C₄⋊C₄	C₂²⋊D₁₃	1	6	yes	—
41	C₄²	—	2	2	no	—
42	C₄²	C₂²×D₁₃	1	1	yes	characteristic
43	C₁₃	#1658	1	1	yes	characteristic, complemented, Sylow
44	C₂³	—	52	1	no	—
45	D₄	—	52	6	no	—
46	C₂×C₄	—	2	6	no	—
47	C₂×C₄	C₂×C₂²⋊D₁₃	1	3	yes	—
48	C₈	—	52	3	no	—
49	C₂²	—	104	3	no	—
50	C₂²	#88207	1	1	yes	characteristic
51	C₄	—	2	3	no	—
52	C₄	—	4	6	no	—
53	C₂	—	208	1	no	—
54	C₂	#11718906	1	3	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.