Subgroups — C₇×#6131 #13089889

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	C₇×D₅₂	C₂	1	3	yes	maximal, complemented
3	C₄×C₇×D₁₃	C₂	1	3	yes	maximal, complemented
4	C₂×C₇×D₁₃	C₂²	1	3	yes	—
5	C₄×C₇×C₁₃	C₂²	1	3	yes	—
6	C₇×Dic₁₃	C₂²	1	1	yes	characteristic
7	#6131	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
9	C₇×D₁₃	—	2	3	no	—
10	C₇×#41	—	13	1	no	maximal, Hall
11	Q₈×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented
12	D₅₂	C₂×C₇	1	3	yes	complemented
13	C₄×D₁₃	C₂×C₇	1	3	yes	complemented
14	C₇×C₁₃	#41	1	1	yes	characteristic, complemented, Hall
15	C₇×Q₈	D₁₃	1	1	yes	characteristic, complemented
16	C₇×D₄	—	13	3	no	—
17	C₂×C₄×C₇	—	13	3	no	—
18	C₂×D₁₃	C₂²×C₇	1	3	yes	—
19	C₄×C₁₃	C₂²×C₇	1	3	yes	—
20	Dic₁₃	C₂²×C₇	1	1	yes	characteristic
21	C₂²×C₇	—	13	3	no	—
22	C₄×C₇	—	13	1	no	—
23	C₄×C₇	C₂×D₁₃	1	3	yes	—
24	C₂×C₁₃	C₂³×C₇	1	1	yes	characteristic
25	D₁₃	—	2	3	no	—
26	#41	—	13	1	no	Sylow
27	C₂×C₇	—	26	3	no	—
28	C₂×C₇	C₂²×D₁₃	1	1	yes	characteristic
29	C₁₃	C₇×#41	1	1	yes	characteristic, complemented, Sylow
30	Q₈	C₇×D₁₃	1	1	yes	characteristic, complemented
31	D₄	—	13	3	no	—
32	C₂×C₄	—	13	3	no	—
33	C₇	#6131	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²	—	13	3	no	—
35	C₄	—	13	1	no	—
36	C₄	C₂×C₇×D₁₃	1	3	yes	—
37	C₂	—	26	3	no	—
38	C₂	C₂²×C₇×D₁₃	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.