Subgroups — C₅×D₃₁×C₇⋊D₇ #44477166

Order 30380.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇²×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₃₁×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇⋊D₂₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃₁×C₇⋊D₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₇×D₃₁	—	7	8	no	maximal
7	C₇⋊D₂₁₇	C₂×C₅	1	1	yes	characteristic, complemented
8	C₃₁×C₇⋊D₇	C₂×C₅	1	1	yes	characteristic, complemented
9	C₇²×D₃₁	C₂×C₅	1	1	yes	characteristic, complemented
10	C₅×D₂₁₇	—	7	8	no	—
11	C₅×D₇×C₃₁	—	7	8	no	—
12	C₅×C₇×D₃₁	D₇	1	8	yes	complemented
13	C₇²×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₇×C₃₁	C₂×D₇	1	8	yes	complemented
15	C₂×C₅×C₇⋊D₇	—	31	1	no	maximal, Hall
16	D₇×D₃₁	—	7	8	no	—
17	C₂×C₅×D₃₁	—	49	1	no	Hall
18	C₂×C₅×C₇²	—	31	1	no	—
19	C₅×C₇⋊D₇	—	31	1	no	—
20	C₅×C₇⋊D₇	D₃₁	1	1	yes	characteristic, direct product factor
21	D₂₁₇	—	7	8	no	—
22	C₇×D₃₁	C₅×D₇	1	8	yes	complemented
23	D₇×C₃₁	—	7	8	no	—
24	C₂×C₅×C₃₁	—	49	1	no	—
25	C₅×D₃₁	—	49	1	no	—
26	C₅×D₃₁	C₇⋊D₇	1	1	yes	characteristic, direct product factor
27	C₅×C₇²	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
28	C₇×C₃₁	C₂×C₅×D₇	1	8	yes	complemented
29	C₂×C₇⋊D₇	—	31	1	no	Hall
30	C₅×C₃₁	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅×D₇	—	217	8	no	—
32	C₂×D₃₁	—	49	1	no	Hall
33	C₂×C₇²	—	31	1	no	—
34	C₇⋊D₇	—	31	1	no	—
35	C₇⋊D₇	C₅×D₃₁	1	1	yes	characteristic, direct product factor
36	C₂×C₅×C₇	—	31	8	no	—
37	C₅×D₇	—	7	8	no	—
38	C₅×D₇	—	217	8	no	—
39	C₂×C₃₁	—	49	1	no	—
40	D₃₁	—	49	1	no	—
41	D₃₁	C₅×C₇⋊D₇	1	1	yes	characteristic, direct product factor
42	C₇²	C₂×C₅×D₃₁	1	1	yes	characteristic, complemented, Sylow
43	C₅×C₇	D₇×D₃₁	1	8	yes	complemented
44	C₃₁	C₂×C₅×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₇	—	217	8	no	—
46	C₂²×C₅	—	1519	1	no	Hall
47	C₂×C₇	—	31	8	no	—
48	D₇	—	7	8	no	—
49	D₇	—	217	8	no	—
50	C₂×C₅	—	31	1	no	—
51	C₂×C₅	—	49	1	no	—
52	C₂×C₅	—	1519	1	no	—
53	C₇	C₅×D₇×D₃₁	1	8	yes	complemented
54	C₅	D₃₁×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
55	C₂²	—	1519	1	no	Sylow
56	C₂	—	31	1	no	—
57	C₂	—	49	1	no	—
58	C₂	—	1519	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₃₁×C₇⋊D₇
commutator, cosocle, hypocenter	C₇²×C₃₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₃₁	C₂²
LCS	G ▷ C₇²×C₃₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₇²×D₃₁	C₂	semidirect
2. C₅×C₃₁×C₇⋊D₇	C₂	semidirect
3. C₅×C₇⋊D₂₁₇	C₂	semidirect
4. C₅×C₇²×C₃₁	C₂²	semidirect
5. D₃₁×C₇⋊D₇	C₅	direct (N × H)
7. C₇⋊D₂₁₇	C₂×C₅	semidirect
8. C₃₁×C₇⋊D₇	C₂×C₅	semidirect
9. C₇²×D₃₁	C₂×C₅	semidirect
12. C₅×C₇×D₃₁	D₇	semidirect
13. C₇²×C₃₁	C₂²×C₅	semidirect
14. C₅×C₇×C₃₁	C₂×D₇	semidirect
20. C₅×C₇⋊D₇	D₃₁	direct (N × H)
22. C₇×D₃₁	C₅×D₇	semidirect
26. C₅×D₃₁	C₇⋊D₇	direct (N × H)
27. C₅×C₇²	C₂×D₃₁	semidirect
28. C₇×C₃₁	C₂×C₅×D₇	semidirect
30. C₅×C₃₁	C₂×C₇⋊D₇	semidirect
35. C₇⋊D₇	C₅×D₃₁	direct (N × H)
41. D₃₁	C₅×C₇⋊D₇	direct (N × H)
42. C₇²	C₂×C₅×D₃₁	semidirect
43. C₅×C₇	D₇×D₃₁	semidirect
44. C₃₁	C₂×C₅×C₇⋊D₇	semidirect
53. C₇	C₅×D₇×D₃₁	semidirect
54. C₅	D₃₁×C₇⋊D₇	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×D₃₁	2
C₅×C₃₁×C₇⋊D₇	2
C₅×C₇⋊D₂₁₇	2
D₃₁×C₇⋊D₇	5
C₅×D₇×D₃₁	7
C₂×C₅×C₇⋊D₇	31

Subgroups — C5×D31×C7⋊D7 #44477166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃₁×C₇⋊D₇ #44477166