Subgroups — #13129998

Order 1664.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718221	C₂	1	2	yes	maximal
2	D₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic
3	#88102	—	2	2	no	—
4	C₁₆×D₁₃	C₂²	1	1	yes	characteristic
5	C₁₃×C₃₂	C₄	1	1	yes	characteristic, complemented
6	#88034	C₄	1	1	yes	characteristic, complemented
7	C₄⋊#261	—	4	2	no	—
8	C₈×D₁₃	D₄	1	1	yes	characteristic
9	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
10	#6090	Q₈	1	1	yes	characteristic
11	#1424	—	13	1	no	maximal, Sylow
12	C₂×#261	—	8	2	no	—
13	C₄×D₁₃	D₈	1	1	yes	characteristic
14	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
15	#1055	Q₁₆	1	1	yes	characteristic
16	C₂×C₃₂	—	13	1	no	—
17	#366	—	13	2	no	—
18	C₂×D₁₃	D₁₆	1	1	yes	characteristic
19	#261	—	16	2	no	—
20	C₄×C₁₃	#107	1	1	yes	characteristic
21	Dic₁₃	Q₃₂	1	1	yes	characteristic
22	C₂×C₁₆	—	13	1	no	—
23	#107	—	26	2	no	—
24	C₃₂	—	13	1	no	—
25	C₃₂	#261	1	1	yes	characteristic, complemented
26	C₂×C₁₃	#366	1	1	yes	characteristic
27	D₁₃	SD₆₄	1	2	yes	—
28	C₂×C₈	—	13	1	no	—
29	C₄⋊C₄	—	52	2	no	—
30	C₁₆	—	13	1	no	—
31	C₁₆	C₂×#261	1	1	yes	characteristic
32	C₁₃	#1424	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₄	—	13	1	no	—
34	C₂×C₄	—	104	2	no	—
35	C₈	—	13	1	no	—
36	C₈	C₄⋊#261	1	1	yes	characteristic
37	C₂²	—	13	1	no	—
38	C₄	—	13	1	no	—
39	C₄	—	208	2	no	—
40	C₄	#88102	1	1	yes	characteristic
41	C₂	—	13	2	no	—
42	C₂	#11718221	1	1	yes	characteristic

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.