Subgroups — C₂×C₇×D₂₇₉ #21462913

Order 7812.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₂₇₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₉×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₉₃	—	3	1	no	maximal
4	C₇×C₉×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₃₁	D₃	1	1	yes	characteristic
6	C₇×D₉₃	—	3	2	no	—
7	C₂×D₂₇₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×D₃₁	—	9	1	no	Hall
9	C₃×C₇×C₃₁	C₂×D₃	1	1	yes	characteristic
10	C₂×C₉×C₃₁	C₂×C₇	1	1	yes	characteristic, complemented
11	D₂₇₉	C₂×C₇	1	2	yes	direct product factor
12	C₂×C₇×C₃₁	D₉	1	1	yes	characteristic, complemented
13	C₇×D₃₁	—	9	2	no	—
14	C₂×D₉₃	—	3	1	no	—
15	C₉×C₃₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇×D₉	—	31	1	no	maximal, Hall
17	C₇×C₃₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₃₁	D₃×C₇	1	1	yes	characteristic
19	D₉₃	—	3	2	no	—
20	C₂×C₇×C₉	D₃₁	1	1	yes	characteristic, complemented
21	C₇×D₉	—	31	2	no	—
22	C₂×D₃₁	—	9	1	no	Hall
23	C₃×C₃₁	C₂×D₃×C₇	1	1	yes	characteristic
24	C₂×D₃×C₇	—	93	1	no	—
25	C₇×C₉	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃₁	C₇×D₉	1	1	yes	characteristic, complemented
27	D₃₁	—	9	2	no	—
28	C₂×C₃×C₇	D₉₃	1	1	yes	characteristic
29	D₃×C₇	—	93	2	no	—
30	C₂×D₉	—	31	1	no	Hall
31	C₃₁	C₂×C₇×D₉	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₇	—	279	1	no	Hall
33	C₃×C₇	C₂×D₉₃	1	1	yes	characteristic
34	C₂×C₉	C₇×D₃₁	1	1	yes	characteristic, complemented
35	D₉	—	31	2	no	—
36	C₂×C₇	—	279	2	no	—
37	C₂×C₇	D₂₇₉	1	1	yes	characteristic, direct product factor
38	C₂×D₃	—	93	1	no	—
39	C₉	C₂×C₇×D₃₁	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×D₂₇₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	C₇×D₉₃	1	1	yes	characteristic
42	D₃	—	93	2	no	—
43	C₂²	—	279	1	no	Sylow
44	C₃	C₂×C₇×D₉₃	1	1	yes	characteristic
45	C₂	—	279	2	no	—
46	C₂	C₇×D₂₇₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₂₇₉
commutator, hypocenter	C₉×C₃₁	C₂²×C₇
Frattini	C₃	C₂×C₇×D₉₃
Fitting	C₂×C₇×C₉×C₃₁	C₂
socle	C₂×C₃×C₇×C₃₁	D₃
LCS	G ▷ C₉×C₃₁
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₂₇₉	C₂	direct (N × H)
2. C₂×C₇×C₉×C₃₁	C₂	semidirect
4. C₇×C₉×C₃₁	C₂²	semidirect
7. C₂×D₂₇₉	C₇	direct (N × H)
10. C₂×C₉×C₃₁	C₂×C₇	semidirect
11. D₂₇₉	C₂×C₇	direct (N × H)
12. C₂×C₇×C₃₁	D₉	semidirect
15. C₉×C₃₁	C₂²×C₇	semidirect
17. C₇×C₃₁	C₂×D₉	semidirect
20. C₂×C₇×C₉	D₃₁	semidirect
25. C₇×C₉	C₂×D₃₁	semidirect
26. C₂×C₃₁	C₇×D₉	semidirect
31. C₃₁	C₂×C₇×D₉	semidirect
34. C₂×C₉	C₇×D₃₁	semidirect
37. C₂×C₇	D₂₇₉	direct (N × H)
39. C₉	C₂×C₇×D₃₁	semidirect
40. C₇	C₂×D₂₇₉	direct (N × H)
46. C₂	C₇×D₂₇₉	direct (N × H)

Subgroups — C2×C7×D279 #21462913

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₇×D₂₇₉ #21462913