Subgroups — #16778224

Order 3328.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129651	C₂	1	2	yes	maximal, complemented
2	D₁₃×C₆₄	C₂	1	1	yes	maximal, characteristic
3	D₁₃×C₃₂	C₄	1	1	yes	characteristic
4	C₁₃×C₆₄	C₄	1	1	yes	characteristic
5	#11718035	C₂²	1	1	yes	characteristic
6	C₁₆×D₁₃	C₈	1	1	yes	characteristic
7	C₁₃×C₃₂	C₂×C₄	1	1	yes	characteristic
8	#88034	C₈	1	1	yes	characteristic
9	M₂₅₆	—	13	1	no	maximal, Sylow
10	C₈×D₁₃	C₁₆	1	1	yes	characteristic
11	C₁₃×C₁₆	C₂×C₈	1	1	yes	characteristic
12	#6090	C₁₆	1	1	yes	characteristic
13	C₂×C₆₄	—	13	1	no	—
14	C₁₂₈	—	13	2	no	—
15	C₄×D₁₃	C₃₂	1	1	yes	characteristic
16	C₈×C₁₃	C₂×C₁₆	1	1	yes	characteristic
17	#1055	C₃₂	1	1	yes	characteristic
18	C₂×C₃₂	—	13	1	no	—
19	C₆₄	—	13	1	no	—
20	C₆₄	#261	1	1	yes	characteristic
21	C₂×D₁₃	C₆₄	1	1	yes	characteristic
22	C₄×C₁₃	C₂×C₃₂	1	1	yes	characteristic
23	Dic₁₃	C₆₄	1	1	yes	characteristic
24	C₂×C₁₆	—	13	1	no	—
25	C₃₂	—	13	1	no	—
26	C₃₂	C₂×#261	1	1	yes	characteristic
27	C₂×C₁₃	C₂×C₆₄	1	1	yes	characteristic
28	D₁₃	—	2	1	no	—
29	C₂×C₈	—	13	1	no	—
30	C₁₆	—	13	1	no	—
31	C₁₆	D₁₃⋊C₈	1	1	yes	characteristic
32	C₁₃	M₂₅₆	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₄	—	13	1	no	—
34	C₈	—	13	1	no	—
35	C₈	D₁₃⋊C₁₆	1	1	yes	characteristic
36	C₂²	—	13	1	no	—
37	C₄	—	13	1	no	—
38	C₄	D₁₃⋊C₃₂	1	1	yes	characteristic
39	C₂	—	26	1	no	—
40	C₂	D₁₃⋊C₆₄	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #13129651	C₂	semidirect
32. C₁₃	M₂₅₆	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.