Subgroups — C₂×C₇×D₆₃₉ #31822025

Order 17892.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₆₃₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₉×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₂₁₃	—	3	1	no	maximal
4	C₇×C₉×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₂₁₃	—	3	2	no	—
6	C₂×C₃×C₇×C₇₁	D₃	1	1	yes	characteristic
7	C₂×D₆₃₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×D₇₁	—	9	1	no	Hall
9	C₃×C₇×C₇₁	C₂×D₃	1	1	yes	characteristic
10	C₂×C₉×C₇₁	C₂×C₇	1	1	yes	characteristic, complemented
11	D₆₃₉	C₂×C₇	1	2	yes	direct product factor
12	C₂×C₇×C₇₁	D₉	1	1	yes	characteristic, complemented
13	C₇×D₇₁	—	9	2	no	—
14	C₂×D₂₁₃	—	3	1	no	—
15	C₉×C₇₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₇₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₇₁	D₃×C₇	1	1	yes	characteristic
18	D₂₁₃	—	3	2	no	—
19	C₂×D₇₁	—	9	1	no	Hall
20	C₂×C₇×D₉	—	71	1	no	maximal, Hall
21	C₃×C₇₁	C₂×D₃×C₇	1	1	yes	characteristic
22	C₂×C₇₁	C₇×D₉	1	1	yes	characteristic, complemented
23	D₇₁	—	9	2	no	—
24	C₂×C₇×C₉	D₇₁	1	1	yes	characteristic, complemented
25	C₇×D₉	—	71	2	no	—
26	C₂×D₃×C₇	—	213	1	no	—
27	C₇₁	C₂×C₇×D₉	1	1	yes	characteristic, complemented, Sylow
28	C₇×C₉	C₂×D₇₁	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₇	D₂₁₃	1	1	yes	characteristic
30	D₃×C₇	—	213	2	no	—
31	C₂×D₉	—	71	1	no	Hall
32	C₂²×C₇	—	639	1	no	Hall
33	C₃×C₇	C₂×D₂₁₃	1	1	yes	characteristic
34	C₂×C₉	C₇×D₇₁	1	1	yes	characteristic, complemented
35	D₉	—	71	2	no	—
36	C₂×C₇	—	639	2	no	—
37	C₂×C₇	D₆₃₉	1	1	yes	characteristic, direct product factor
38	C₂×D₃	—	213	1	no	—
39	C₉	C₂×C₇×D₇₁	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×D₆₃₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	C₇×D₂₁₃	1	1	yes	characteristic
42	D₃	—	213	2	no	—
43	C₂²	—	639	1	no	Sylow
44	C₃	C₂×C₇×D₂₁₃	1	1	yes	characteristic
45	C₂	—	639	2	no	—
46	C₂	C₇×D₆₃₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₆₃₉
commutator, cosocle, hypocenter	C₉×C₇₁	C₂²×C₇
Frattini	C₃	C₂×C₇×D₂₁₃
Fitting	C₂×C₇×C₉×C₇₁	C₂
socle	C₂×C₃×C₇×C₇₁	D₃
LCS	G ▷ C₉×C₇₁
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₆₃₉	C₂	direct (N × H)
2. C₂×C₇×C₉×C₇₁	C₂	semidirect
4. C₇×C₉×C₇₁	C₂²	semidirect
7. C₂×D₆₃₉	C₇	direct (N × H)
10. C₂×C₉×C₇₁	C₂×C₇	semidirect
11. D₆₃₉	C₂×C₇	direct (N × H)
12. C₂×C₇×C₇₁	D₉	semidirect
15. C₉×C₇₁	C₂²×C₇	semidirect
16. C₇×C₇₁	C₂×D₉	semidirect
22. C₂×C₇₁	C₇×D₉	semidirect
24. C₂×C₇×C₉	D₇₁	semidirect
27. C₇₁	C₂×C₇×D₉	semidirect
28. C₇×C₉	C₂×D₇₁	semidirect
34. C₂×C₉	C₇×D₇₁	semidirect
37. C₂×C₇	D₆₃₉	direct (N × H)
39. C₉	C₂×C₇×D₇₁	semidirect
40. C₇	C₂×D₆₃₉	direct (N × H)
46. C₂	C₇×D₆₃₉	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×D₆₃₉	2
C₂×C₇×C₉×C₇₁	2
C₂×C₇×D₂₁₃	3
C₂×D₆₃₉	7
C₂×C₇×D₉	71

Subgroups — C2×C7×D639 #31822025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₆₃₉ #31822025