Subgroups — C₁₃×#1161 #13089899

Order 1456.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₂₈	C₂	1	3	yes	maximal, complemented
3	C₄×C₁₃×D₇	C₂	1	3	yes	maximal, complemented
4	C₂×C₁₃×D₇	C₂²	1	3	yes	—
5	C₄×C₇×C₁₃	C₂²	1	3	yes	—
6	C₁₃×Dic₇	C₂²	1	1	yes	characteristic
7	C₁₃×#41	—	7	1	no	maximal, Hall
8	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
9	C₁₃×D₇	—	2	3	no	—
10	#1161	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	Q₈×C₁₃	D₇	1	1	yes	characteristic, complemented
12	D₄×C₁₃	—	7	3	no	—
13	C₂×C₄×C₁₃	—	7	3	no	—
14	C₇×C₁₃	#41	1	1	yes	characteristic, complemented, Hall
15	C₇×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
16	D₂₈	C₂×C₁₃	1	3	yes	complemented
17	C₄×D₇	C₂×C₁₃	1	3	yes	complemented
18	C₂²×C₁₃	—	7	3	no	—
19	C₄×C₁₃	—	7	1	no	—
20	C₄×C₁₃	C₂×D₇	1	3	yes	—
21	C₂×D₇	C₂²×C₁₃	1	3	yes	—
22	C₄×C₇	C₂²×C₁₃	1	3	yes	—
23	Dic₇	C₂²×C₁₃	1	1	yes	characteristic
24	C₂×C₁₃	—	14	3	no	—
25	C₂×C₁₃	C₂²×D₇	1	1	yes	characteristic
26	#41	—	7	1	no	Sylow
27	C₂×C₇	C₂³×C₁₃	1	1	yes	characteristic
28	D₇	—	2	3	no	—
29	C₁₃	#1161	1	1	yes	characteristic, direct product factor, Sylow
30	Q₈	C₁₃×D₇	1	1	yes	characteristic, complemented
31	D₄	—	7	3	no	—
32	C₂×C₄	—	7	3	no	—
33	C₇	C₁₃×#41	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	7	3	no	—
35	C₄	—	7	1	no	—
36	C₄	C₂×C₁₃×D₇	1	3	yes	—
37	C₂	—	14	3	no	—
38	C₂	C₂²×C₁₃×D₇	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.