Subgroups — D₅×D₁₃₅₁ #41028362

Order 27020.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₇₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₅×C₁₉₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₃₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₁₉₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₃₅₁	—	5	1	no	maximal, Hall
6	D₅×D₁₉₃	—	7	1	no	maximal, Hall
7	C₂×C₇×C₁₉₃	—	5	1	no	—
8	D₁₃₅₁	—	5	1	no	—
9	D₁₃₅₁	D₅	1	1	yes	characteristic, direct product factor
10	D₉₆₅	—	7	1	no	—
11	C₅×D₁₉₃	—	7	1	no	—
12	D₅×C₁₉₃	D₇	1	1	yes	characteristic, complemented
13	C₇×C₁₉₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₁₉₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₉₃	—	35	1	no	Hall
16	C₂×C₁₉₃	—	5	1	no	—
17	D₁₉₃	—	7	1	no	—
18	D₁₉₃	—	35	1	no	—
19	C₁₉₃	D₅×D₇	1	1	yes	characteristic, complemented, Sylow
20	D₅×D₇	—	193	1	no	maximal, Hall
21	D₃₅	—	193	1	no	—
22	C₅×D₇	—	193	1	no	—
23	C₇×D₅	D₁₉₃	1	1	yes	characteristic, complemented
24	C₅×C₇	C₂×D₁₉₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₇	—	965	1	no	Hall
26	C₂×D₅	—	1351	1	no	Hall
27	C₂×C₇	—	5	1	no	—
28	D₇	—	193	1	no	—
29	D₇	—	965	1	no	—
30	C₂×C₅	—	1351	1	no	—
31	D₅	—	1351	1	no	—
32	D₅	D₁₃₅₁	1	1	yes	characteristic, direct product factor
33	C₇	D₅×D₁₉₃	1	1	yes	characteristic, complemented, Sylow
34	C₅	C₂×D₁₃₅₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	6755	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	1351	1	no	—
38	C₂	—	6755	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇×C₁₉₃	C₂²
LCS	G ▷ C₅×C₇×C₁₉₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₆₇₅₅	C₂	semidirect
2. C₇×D₅×C₁₉₃	C₂	semidirect
3. C₅×D₁₃₅₁	C₂	semidirect
4. C₅×C₇×C₁₉₃	C₂²	semidirect
9. D₁₃₅₁	D₅	direct (N × H)
12. D₅×C₁₉₃	D₇	semidirect
13. C₇×C₁₉₃	C₂×D₅	semidirect
14. C₅×C₁₉₃	C₂×D₇	semidirect
19. C₁₉₃	D₅×D₇	semidirect
23. C₇×D₅	D₁₉₃	semidirect
24. C₅×C₇	C₂×D₁₉₃	semidirect
32. D₅	D₁₃₅₁	direct (N × H)
33. C₇	D₅×D₁₉₃	semidirect
34. C₅	C₂×D₁₃₅₁	semidirect

Maximal subgroups

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

subgroup	index
D₆₇₅₅	2
C₇×D₅×C₁₉₃	2
C₅×D₁₃₅₁	2
C₂×D₁₃₅₁	5
D₅×D₁₉₃	7
D₅×D₇	193

Subgroups — D5×D1351 #41028362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₁₃₅₁ #41028362