Subgroups — C₅×D₇×D₁₆₇ #37552640

Order 23380.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₇×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×D₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₁₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇×D₁₆₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×D₁₆₇	—	7	1	no	maximal, Hall
7	D₁₁₆₉	C₂×C₅	1	1	yes	characteristic, complemented
8	C₇×D₁₆₇	C₂×C₅	1	1	yes	characteristic, complemented
9	D₇×C₁₆₇	C₂×C₅	1	1	yes	characteristic, complemented
10	C₂×C₅×C₁₆₇	—	7	1	no	—
11	C₅×D₁₆₇	—	7	1	no	—
12	C₅×D₁₆₇	D₇	1	1	yes	characteristic, direct product factor
13	C₇×C₁₆₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₁₆₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₆₇	—	7	1	no	Hall
16	C₂×C₁₆₇	—	7	1	no	—
17	D₁₆₇	—	7	1	no	—
18	D₁₆₇	C₅×D₇	1	1	yes	characteristic, direct product factor
19	C₁₆₇	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₅×D₇	—	167	1	no	maximal, Hall
21	C₂×C₅×C₇	—	167	1	no	—
22	C₅×D₇	—	167	1	no	—
23	C₅×D₇	D₁₆₇	1	1	yes	characteristic, direct product factor
24	C₅×C₇	C₂×D₁₆₇	1	1	yes	characteristic, complemented, Hall
25	C₂×D₇	—	167	1	no	Hall
26	C₂²×C₅	—	1169	1	no	Hall
27	C₂×C₇	—	167	1	no	—
28	D₇	—	167	1	no	—
29	D₇	C₅×D₁₆₇	1	1	yes	characteristic, direct product factor
30	C₂×C₅	—	7	1	no	—
31	C₂×C₅	—	1169	1	no	—
32	C₂×C₅	—	167	1	no	—
33	C₇	C₂×C₅×D₁₆₇	1	1	yes	characteristic, complemented, Sylow
34	C₅	D₇×D₁₆₇	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²	—	1169	1	no	Sylow
36	C₂	—	7	1	no	—
37	C₂	—	1169	1	no	—
38	C₂	—	167	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₇×D₁₆₇
commutator, cosocle, hypocenter	C₇×C₁₆₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₆₇	C₂²
LCS	G ▷ C₇×C₁₆₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₁₆₉	C₂	semidirect
2. C₅×D₇×C₁₆₇	C₂	semidirect
3. C₅×C₇×D₁₆₇	C₂	semidirect
4. C₅×C₇×C₁₆₇	C₂²	semidirect
5. D₇×D₁₆₇	C₅	direct (N × H)
7. D₁₁₆₉	C₂×C₅	semidirect
8. C₇×D₁₆₇	C₂×C₅	semidirect
9. D₇×C₁₆₇	C₂×C₅	semidirect
12. C₅×D₁₆₇	D₇	direct (N × H)
13. C₇×C₁₆₇	C₂²×C₅	semidirect
14. C₅×C₁₆₇	C₂×D₇	semidirect
18. D₁₆₇	C₅×D₇	direct (N × H)
19. C₁₆₇	C₂×C₅×D₇	semidirect
23. C₅×D₇	D₁₆₇	direct (N × H)
24. C₅×C₇	C₂×D₁₆₇	semidirect
29. D₇	C₅×D₁₆₇	direct (N × H)
33. C₇	C₂×C₅×D₁₆₇	semidirect
34. C₅	D₇×D₁₆₇	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×D₁₁₆₉	2
C₅×D₇×C₁₆₇	2
C₅×C₇×D₁₆₇	2
D₇×D₁₆₇	5
C₂×C₅×D₁₆₇	7
C₂×C₅×D₇	167

Subgroups — C5×D7×D167 #37552640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₇×D₁₆₇ #37552640