Subgroups — C₂×C₅×C₇⋊D₉₁ #27164976

Order 12740.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇⋊D₉₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇⋊D₉₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×D₉₁	—	7	8	no	maximal
6	C₂×C₇²×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented
7	C₇⋊D₉₁	C₂×C₅	1	2	yes	direct product factor
8	C₂×C₅×C₇⋊D₇	—	13	1	no	maximal, Hall
9	C₂×C₅×C₇×C₁₃	D₇	1	8	yes	complemented
10	C₅×D₉₁	—	7	16	no	—
11	C₇²×C₁₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₇²	D₁₃	1	1	yes	characteristic, complemented
13	C₅×C₇⋊D₇	—	13	2	no	—
14	C₅×C₇×C₁₃	C₂×D₇	1	8	yes	complemented
15	C₂×D₉₁	—	7	8	no	—
16	C₂×C₅×D₁₃	—	49	1	no	Hall
17	C₅×C₇²	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇⋊D₇	—	13	1	no	Hall
19	C₂×C₇×C₁₃	C₅×D₇	1	8	yes	complemented
20	D₉₁	—	7	16	no	—
21	C₂×C₅×D₇	—	91	8	no	—
22	C₂×C₅×C₁₃	C₇⋊D₇	1	1	yes	characteristic, complemented
23	C₅×D₁₃	—	49	2	no	—
24	C₂×C₇²	C₅×D₁₃	1	1	yes	characteristic, complemented
25	C₇⋊D₇	—	13	2	no	—
26	C₇×C₁₃	C₂×C₅×D₇	1	8	yes	complemented
27	C₂×C₅×C₇	D₉₁	1	8	yes	complemented
28	C₅×D₇	—	91	16	no	—
29	C₅×C₁₃	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
30	C₂×D₁₃	—	49	1	no	Hall
31	C₇²	C₂×C₅×D₁₃	1	1	yes	characteristic, complemented, Sylow
32	C₅×C₇	C₂×D₉₁	1	8	yes	complemented
33	C₂×D₇	—	91	8	no	—
34	C₂×C₁₃	C₅×C₇⋊D₇	1	1	yes	characteristic, complemented
35	D₁₃	—	49	2	no	—
36	C₂²×C₅	—	637	1	no	Hall
37	C₂×C₇	C₅×D₉₁	1	8	yes	complemented
38	D₇	—	91	16	no	—
39	C₁₃	C₂×C₅×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₅	—	637	2	no	—
41	C₂×C₅	C₇⋊D₉₁	1	1	yes	characteristic, direct product factor
42	C₇	C₂×C₅×D₉₁	1	8	yes	complemented
43	C₅	C₂×C₇⋊D₉₁	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²	—	637	1	no	Sylow
45	C₂	—	637	2	no	—
46	C₂	C₅×C₇⋊D₉₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	C₇⋊D₉₁
commutator, cosocle, hypocenter	C₇²×C₁₃	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₁₃	C₂
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₇⋊D₉₁	C₂	direct (N × H)
2. C₂×C₅×C₇²×C₁₃	C₂	semidirect
3. C₅×C₇²×C₁₃	C₂²	semidirect
4. C₂×C₇⋊D₉₁	C₅	direct (N × H)
6. C₂×C₇²×C₁₃	C₂×C₅	semidirect
7. C₇⋊D₉₁	C₂×C₅	direct (N × H)
9. C₂×C₅×C₇×C₁₃	D₇	semidirect
11. C₇²×C₁₃	C₂²×C₅	semidirect
12. C₂×C₅×C₇²	D₁₃	semidirect
14. C₅×C₇×C₁₃	C₂×D₇	semidirect
17. C₅×C₇²	C₂×D₁₃	semidirect
19. C₂×C₇×C₁₃	C₅×D₇	semidirect
22. C₂×C₅×C₁₃	C₇⋊D₇	semidirect
24. C₂×C₇²	C₅×D₁₃	semidirect
26. C₇×C₁₃	C₂×C₅×D₇	semidirect
27. C₂×C₅×C₇	D₉₁	semidirect
29. C₅×C₁₃	C₂×C₇⋊D₇	semidirect
31. C₇²	C₂×C₅×D₁₃	semidirect
32. C₅×C₇	C₂×D₉₁	semidirect
34. C₂×C₁₃	C₅×C₇⋊D₇	semidirect
37. C₂×C₇	C₅×D₉₁	semidirect
39. C₁₃	C₂×C₅×C₇⋊D₇	semidirect
41. C₂×C₅	C₇⋊D₉₁	direct (N × H)
42. C₇	C₂×C₅×D₉₁	semidirect
43. C₅	C₂×C₇⋊D₉₁	direct (N × H)
46. C₂	C₅×C₇⋊D₉₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇⋊D₉₁	2
C₂×C₅×C₇²×C₁₃	2
C₂×C₇⋊D₉₁	5
C₂×C₅×D₉₁	7
C₂×C₅×C₇⋊D₇	13

Subgroups — C2×C5×C7⋊D91 #27164976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₇⋊D₉₁ #27164976