Subgroups — C₂×C₇×C₃₁×D₃₅ #44477202

Order 30380.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₁×D₃₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×D₇×C₃₁	—	5	1	no	maximal, Hall
5	C₂×C₇×D₅×C₃₁	—	7	1	no	maximal
6	C₂×C₃₁×D₃₅	C₇	1	1	yes	maximal, characteristic, direct product factor
7	C₇×D₇×C₃₁	—	5	2	no	—
8	C₂×C₇²×C₃₁	D₅	1	1	yes	characteristic, complemented
9	C₃₁×D₃₅	C₂×C₇	1	2	yes	direct product factor
10	C₇×D₅×C₃₁	—	7	2	no	—
11	C₂×C₅×C₇×C₃₁	—	2	3	no	—
12	C₂×C₅×C₇×C₃₁	D₇	1	1	yes	characteristic, complemented
13	C₂×C₅×C₇×C₃₁	C₂×C₇	1	1	yes	characteristic, complemented
14	C₇²×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	C₅×C₇×C₃₁	—	2	3	no	—
16	C₅×C₇×C₃₁	C₂×D₇	1	1	yes	characteristic, complemented
17	C₅×C₇×C₃₁	C₂²×C₇	1	1	yes	characteristic, complemented
18	C₂×C₇×D₃₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂²×C₇×C₃₁	—	35	1	no	—
20	C₂×D₇×C₃₁	—	5	1	no	—
21	C₂×D₅×C₃₁	—	7	1	no	Hall
22	C₂×C₅×C₇²	C₂×C₃₁	1	1	yes	characteristic, complemented
23	C₇×D₃₅	C₂×C₃₁	1	2	yes	direct product factor
24	C₂×C₇×C₃₁	—	2	3	no	—
25	C₂×C₇×C₃₁	—	35	2	no	—
26	C₂×C₇×C₃₁	C₇×D₅	1	1	yes	characteristic, complemented
27	C₂×C₇×C₃₁	D₃₅	1	1	yes	characteristic, direct product factor
28	D₇×C₃₁	—	5	2	no	—
29	C₂×C₅×C₃₁	C₇×D₇	1	1	yes	characteristic, complemented
30	D₅×C₃₁	—	7	2	no	—
31	C₅×C₇²	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
32	C₇×C₃₁	—	2	3	no	—
33	C₇×C₃₁	C₂×C₇×D₅	1	1	yes	characteristic, complemented
34	C₇×C₃₁	C₂×D₃₅	1	1	yes	characteristic, direct product factor
35	C₂×C₇×D₇	—	5	1	no	Hall
36	C₅×C₃₁	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
37	C₂×D₃₅	C₇×C₃₁	1	1	yes	characteristic, direct product factor
38	C₂×C₇×D₅	—	7	1	no	—
39	C₂²×C₃₁	—	35	1	no	Hall
40	C₂×C₇²	D₅×C₃₁	1	1	yes	characteristic, complemented
41	C₇×D₇	—	5	2	no	—
42	C₂×C₅×C₇	—	2	3	no	—
43	C₂×C₅×C₇	D₇×C₃₁	1	1	yes	characteristic, complemented
44	C₂×C₅×C₇	C₂×C₇×C₃₁	1	1	yes	characteristic, complemented
45	D₃₅	C₂×C₇×C₃₁	1	2	yes	direct product factor
46	C₇×D₅	—	7	2	no	—
47	C₂×C₃₁	—	35	2	no	—
48	C₂×C₃₁	C₇×D₃₅	1	1	yes	characteristic, direct product factor
49	C₇²	C₂×D₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
50	C₅×C₇	—	2	3	no	—
51	C₅×C₇	C₂×D₇×C₃₁	1	1	yes	characteristic, complemented
52	C₅×C₇	C₂²×C₇×C₃₁	1	1	yes	characteristic, complemented
53	C₃₁	C₂×C₇×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²×C₇	—	35	1	no	—
55	C₂×D₇	—	5	1	no	—
56	C₂×D₅	—	7	1	no	Hall
57	C₂×C₇	—	2	3	no	—
58	C₂×C₇	—	35	2	no	—
59	C₂×C₇	C₇×D₅×C₃₁	1	1	yes	characteristic, complemented
60	C₂×C₇	C₃₁×D₃₅	1	1	yes	characteristic, direct product factor
61	D₇	—	5	2	no	—
62	C₂×C₅	C₇×D₇×C₃₁	1	1	yes	characteristic, complemented
63	D₅	—	7	2	no	—
64	C₇	—	2	3	no	—
65	C₇	C₂×C₃₁×D₃₅	1	1	yes	characteristic, direct product factor
66	C₇	C₂×C₇×D₅×C₃₁	1	1	yes	characteristic, complemented
67	C₅	C₂×C₇×D₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
68	C₂²	—	35	1	no	Sylow
69	C₂	—	35	2	no	—
70	C₂	C₇×C₃₁×D₃₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₃₁	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂²×C₇×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₃₁	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₇×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₃₁×D₃₅	C₂	direct (N × H)
2. C₂×C₅×C₇²×C₃₁	C₂	semidirect
3. C₅×C₇²×C₃₁	C₂²	semidirect
6. C₂×C₃₁×D₃₅	C₇	direct (N × H)
8. C₂×C₇²×C₃₁	D₅	semidirect
9. C₃₁×D₃₅	C₂×C₇	direct (N × H)
12. C₂×C₅×C₇×C₃₁	D₇	semidirect
13. C₂×C₅×C₇×C₃₁	C₂×C₇	semidirect
14. C₇²×C₃₁	C₂×D₅	semidirect
16. C₅×C₇×C₃₁	C₂×D₇	semidirect
17. C₅×C₇×C₃₁	C₂²×C₇	semidirect
18. C₂×C₇×D₃₅	C₃₁	direct (N × H)
22. C₂×C₅×C₇²	C₂×C₃₁	semidirect
23. C₇×D₃₅	C₂×C₃₁	direct (N × H)
26. C₂×C₇×C₃₁	C₇×D₅	semidirect
27. C₂×C₇×C₃₁	D₃₅	direct (N × H)
29. C₂×C₅×C₃₁	C₇×D₇	semidirect
31. C₅×C₇²	C₂²×C₃₁	semidirect
33. C₇×C₃₁	C₂×C₇×D₅	semidirect
34. C₇×C₃₁	C₂×D₃₅	direct (N × H)
36. C₅×C₃₁	C₂×C₇×D₇	semidirect
37. C₂×D₃₅	C₇×C₃₁	direct (N × H)
40. C₂×C₇²	D₅×C₃₁	semidirect
43. C₂×C₅×C₇	D₇×C₃₁	semidirect
44. C₂×C₅×C₇	C₂×C₇×C₃₁	semidirect
45. D₃₅	C₂×C₇×C₃₁	direct (N × H)
48. C₂×C₃₁	C₇×D₃₅	direct (N × H)
49. C₇²	C₂×D₅×C₃₁	semidirect
51. C₅×C₇	C₂×D₇×C₃₁	semidirect
52. C₅×C₇	C₂²×C₇×C₃₁	semidirect
53. C₃₁	C₂×C₇×D₃₅	direct (N × H)
59. C₂×C₇	C₇×D₅×C₃₁	semidirect
60. C₂×C₇	C₃₁×D₃₅	direct (N × H)
62. C₂×C₅	C₇×D₇×C₃₁	semidirect
65. C₇	C₂×C₃₁×D₃₅	direct (N × H)
66. C₇	C₂×C₇×D₅×C₃₁	semidirect
67. C₅	C₂×C₇×D₇×C₃₁	semidirect
70. C₂	C₇×C₃₁×D₃₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₃₁×D₃₅	2
C₂×C₅×C₇²×C₃₁	2
C₂×C₇×D₇×C₃₁	5
C₂×C₇×D₅×C₃₁	7
C₂×C₃₁×D₃₅	7
C₂×C₇×D₃₅	31

Subgroups — C2×C7×C31×D35 #44477202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₃₁×D₃₅ #44477202