Subgroups — D₇×D₁₃₁₃ #49145292

Order 36764.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₇×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₁₃₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₃×C₁₀₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₃₁₃	—	7	1	no	maximal, Hall
6	D₇×D₁₀₁	—	13	1	no	maximal, Hall
7	C₂×C₁₃×C₁₀₁	—	7	1	no	—
8	D₁₃₁₃	—	7	1	no	—
9	D₁₃₁₃	D₇	1	1	yes	characteristic, direct product factor
10	D₇₀₇	—	13	1	no	—
11	C₇×D₁₀₁	—	13	1	no	—
12	D₇×C₁₀₁	D₁₃	1	1	yes	characteristic, complemented
13	C₁₃×C₁₀₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
14	C₇×C₁₀₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₀₁	—	91	1	no	Hall
16	D₇×D₁₃	—	101	1	no	maximal, Hall
17	C₂×C₁₀₁	—	7	1	no	—
18	D₁₀₁	—	13	1	no	—
19	D₁₀₁	—	91	1	no	—
20	D₉₁	—	101	1	no	—
21	C₇×D₁₃	—	101	1	no	—
22	C₁₃×D₇	D₁₀₁	1	1	yes	characteristic, complemented
23	C₁₀₁	D₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
24	C₇×C₁₃	C₂×D₁₀₁	1	1	yes	characteristic, complemented, Hall
25	C₂×D₁₃	—	707	1	no	Hall
26	C₂×D₇	—	1313	1	no	Hall
27	C₂×C₁₃	—	7	1	no	—
28	D₁₃	—	101	1	no	—
29	D₁₃	—	707	1	no	—
30	C₂×C₇	—	1313	1	no	—
31	D₇	—	1313	1	no	—
32	D₇	D₁₃₁₃	1	1	yes	characteristic, direct product factor
33	C₁₃	D₇×D₁₀₁	1	1	yes	characteristic, complemented, Sylow
34	C₇	C₂×D₁₃₁₃	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	9191	1	no	Sylow
36	C₂	—	7	1	no	—
37	C₂	—	1313	1	no	—
38	C₂	—	9191	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₃×C₁₀₁	C₂²
LCS	G ▷ C₇×C₁₃×C₁₀₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₉₁₉₁	C₂	semidirect
2. C₁₃×D₇×C₁₀₁	C₂	semidirect
3. C₇×D₁₃₁₃	C₂	semidirect
4. C₇×C₁₃×C₁₀₁	C₂²	semidirect
9. D₁₃₁₃	D₇	direct (N × H)
12. D₇×C₁₀₁	D₁₃	semidirect
13. C₁₃×C₁₀₁	C₂×D₇	semidirect
14. C₇×C₁₀₁	C₂×D₁₃	semidirect
22. C₁₃×D₇	D₁₀₁	semidirect
23. C₁₀₁	D₇×D₁₃	semidirect
24. C₇×C₁₃	C₂×D₁₀₁	semidirect
32. D₇	D₁₃₁₃	direct (N × H)
33. C₁₃	D₇×D₁₀₁	semidirect
34. C₇	C₂×D₁₃₁₃	semidirect

Maximal subgroups

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

subgroup	index
D₉₁₉₁	2
C₁₃×D₇×C₁₀₁	2
C₇×D₁₃₁₃	2
C₂×D₁₃₁₃	7
D₇×D₁₀₁	13
D₇×D₁₃	101

Subgroups — D7×D1313 #49145292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×D₁₃₁₃ #49145292