Subgroups — C₁₃×#1308 #13110366

Order 1664.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#432	C₂	1	3	yes	maximal
2	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
3	C₁₃×C₄⋊C₈	—	2	3	no	—
4	C₁₃×C₂²⋊C₈	C₄	1	6	yes	—
5	C₁₃×#97	—	2	3	no	—
6	C₂²×C₄×C₁₃	C₂×C₄	1	3	yes	—
7	C₂×C₈×C₁₃	—	2	6	no	—
8	C₄²×C₁₃	D₄	1	3	yes	—
9	C₄²×C₁₃	Q₈	1	1	yes	characteristic
10	#1308	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂³×C₁₃	C₄²	1	1	yes	characteristic
12	C₂×C₄×C₁₃	—	4	3	no	—
13	C₂×C₄×C₁₃	C₂²⋊C₄	1	3	yes	—
14	C₂×C₄×C₁₃	C₄⋊C₄	1	3	yes	—
15	C₈×C₁₃	—	4	6	no	—
16	#432	C₂×C₁₃	1	3	yes	—
17	C₂²×C₁₃	—	2	3	no	—
18	C₂²×C₁₃	#95	1	1	yes	characteristic
19	C₄×C₁₃	—	2	3	no	—
20	C₄×C₁₃	—	2	3	no	—
21	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
22	C₄⋊C₈	—	2	3	no	—
23	C₂²⋊C₈	C₄×C₁₃	1	6	yes	—
24	#97	—	2	3	no	—
25	C₂×C₁₃	—	4	1	no	—
26	C₂×C₁₃	#344	1	3	yes	—
27	C₂²×C₄	C₂×C₄×C₁₃	1	3	yes	—
28	C₂×C₈	—	2	6	no	—
29	C₄²	D₄×C₁₃	1	3	yes	—
30	C₄²	Q₈×C₁₃	1	1	yes	characteristic
31	C₁₃	#1308	1	1	yes	characteristic, direct product factor, Sylow
32	C₂³	C₄²×C₁₃	1	1	yes	characteristic
33	C₂×C₄	—	4	3	no	—
34	C₂×C₄	C₁₃×C₂²⋊C₄	1	3	yes	—
35	C₂×C₄	C₁₃×C₄⋊C₄	1	3	yes	—
36	C₈	—	4	6	no	—
37	C₂²	—	2	3	no	—
38	C₂²	C₁₃×#95	1	1	yes	characteristic
39	C₄	—	2	3	no	—
40	C₄	—	2	3	no	—
41	C₂	—	4	1	no	—
42	C₂	C₁₃×#344	1	3	yes	—

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

N	H ≅ G/N	type
10. #1308	C₁₃	direct (N × H)
31. C₁₃	#1308	direct (N × H)

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

subgroup	index
C₁₃×#432	2
#1308	13