Subgroups — C₂×C₅×C₇⋊D₂₁₇ #44477199

Order 30380.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₅	C₇⋊D₂₁₇
commutator, cosocle, hypocenter	C₇²×C₃₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₃₁	C₂
LCS	G ▷ C₇²×C₃₁
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₇⋊D₂₁₇	C₂	direct (N × H)
2. C₂×C₅×C₇²×C₃₁	C₂	semidirect
3. C₅×C₇²×C₃₁	C₂²	semidirect
4. C₂×C₇⋊D₂₁₇	C₅	direct (N × H)
6. C₇⋊D₂₁₇	C₂×C₅	direct (N × H)
7. C₂×C₇²×C₃₁	C₂×C₅	semidirect
9. C₂×C₅×C₇×C₃₁	D₇	semidirect
10. C₇²×C₃₁	C₂²×C₅	semidirect
11. C₅×C₇×C₃₁	C₂×D₇	semidirect
15. C₂×C₅×C₇²	D₃₁	semidirect
17. C₂×C₇×C₃₁	C₅×D₇	semidirect
19. C₂×C₅×C₃₁	C₇⋊D₇	semidirect
21. C₅×C₇²	C₂×D₃₁	semidirect
22. C₇×C₃₁	C₂×C₅×D₇	semidirect
24. C₅×C₃₁	C₂×C₇⋊D₇	semidirect
27. C₂×C₇²	C₅×D₃₁	semidirect
29. C₂×C₅×C₇	D₂₁₇	semidirect
31. C₂×C₃₁	C₅×C₇⋊D₇	semidirect
33. C₇²	C₂×C₅×D₃₁	semidirect
34. C₅×C₇	C₂×D₂₁₇	semidirect
35. C₃₁	C₂×C₅×C₇⋊D₇	semidirect
38. C₂×C₇	C₅×D₂₁₇	semidirect
41. C₂×C₅	C₇⋊D₂₁₇	direct (N × H)
42. C₇	C₂×C₅×D₂₁₇	semidirect
43. C₅	C₂×C₇⋊D₂₁₇	direct (N × H)
46. C₂	C₅×C₇⋊D₂₁₇	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×C₇⋊D₂₁₇	2
C₂×C₅×C₇²×C₃₁	2
C₂×C₇⋊D₂₁₇	5
C₂×C₅×D₂₁₇	7
C₂×C₅×C₇⋊D₇	31

Subgroups — C2×C5×C7⋊D217 #44477199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₇⋊D₂₁₇ #44477199