Subgroups — C₅×C₇²×#3866 #49136406

Order 36260.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇²×D₃₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇²×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇²×#3866	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×#3866	C₇	1	8	yes	maximal, direct product factor
5	C₇²×D₃₇	C₂×C₅	1	1	yes	characteristic
6	C₅×C₇×D₃₇	C₂×C₇	1	8	yes	—
7	C₇²×C₃₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₇×C₃₇	C₄×C₇	1	8	yes	complemented
9	C₇×#3866	C₅×C₇	1	8	yes	direct product factor
10	C₄×C₅×C₇²	—	37	1	no	maximal, Hall
11	C₅×#3866	C₇²	1	1	yes	characteristic, direct product factor, Hall
12	C₇×D₃₇	C₂×C₅×C₇	1	8	yes	—
13	C₂×C₅×C₇²	—	37	1	no	—
14	C₅×D₃₇	C₂×C₇²	1	1	yes	characteristic
15	C₇×C₃₇	C₄×C₅×C₇	1	8	yes	complemented
16	C₅×C₇²	#3866	1	1	yes	characteristic, direct product factor, Hall
17	C₄×C₇²	—	37	1	no	Hall
18	C₅×C₃₇	C₄×C₇²	1	1	yes	characteristic, complemented, Hall
19	#3866	C₅×C₇²	1	1	yes	characteristic, direct product factor, Hall
20	C₄×C₅×C₇	—	37	8	no	—
21	C₂×C₇²	—	37	1	no	—
22	D₃₇	C₂×C₅×C₇²	1	1	yes	characteristic
23	C₂×C₅×C₇	—	37	8	no	—
24	C₇²	C₅×#3866	1	1	yes	characteristic, direct product factor, Sylow
25	C₃₇	C₄×C₅×C₇²	1	1	yes	characteristic, complemented, Sylow
26	C₅×C₇	C₇×#3866	1	8	yes	direct product factor
27	C₄×C₇	—	37	8	no	—
28	C₄×C₅	—	37	1	no	Hall
29	C₂×C₇	—	37	8	no	—
30	C₂×C₅	—	37	1	no	—
31	C₇	C₅×C₇×#3866	1	8	yes	direct product factor
32	C₅	C₇²×#3866	1	1	yes	characteristic, direct product factor, Sylow
33	C₄	—	37	1	no	Sylow
34	C₂	—	37	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₇²	#3866
commutator, hypocenter	C₃₇	C₄×C₅×C₇²
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₃₇	C₄
prime radical	C₅×C₇²×D₃₇	C₂
cosocle	D₃₇	C₂×C₅×C₇²
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₅×C₇²

Complements

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

N	H ≅ G/N	type
2. C₅×C₇²×C₃₇	C₄	semidirect
3. C₇²×#3866	C₅	direct (N × H)
4. C₅×C₇×#3866	C₇	direct (N × H)
7. C₇²×C₃₇	C₄×C₅	semidirect
8. C₅×C₇×C₃₇	C₄×C₇	semidirect
9. C₇×#3866	C₅×C₇	direct (N × H)
11. C₅×#3866	C₇²	direct (N × H)
15. C₇×C₃₇	C₄×C₅×C₇	semidirect
16. C₅×C₇²	#3866	direct (N × H)
18. C₅×C₃₇	C₄×C₇²	semidirect
19. #3866	C₅×C₇²	direct (N × H)
24. C₇²	C₅×#3866	direct (N × H)
25. C₃₇	C₄×C₅×C₇²	semidirect
26. C₅×C₇	C₇×#3866	direct (N × H)
31. C₇	C₅×C₇×#3866	direct (N × H)
32. C₅	C₇²×#3866	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×C₇²×D₃₇	2
C₇²×#3866	5
C₅×C₇×#3866	7
C₄×C₅×C₇²	37

Subgroups — C5×C72×#3866 #49136406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇²×#3866 #49136406