Subgroups — C₅×C₁₁×D₂₇₉ #44501656

Order 30690.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₁×D₉₃	—	3	1	no	maximal
3	C₁₁×D₂₇₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₁×C₃₁	D₃	1	1	yes	characteristic
5	C₅×C₁₁×D₃₁	—	9	1	no	Hall
6	C₉×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×D₂₇₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₁×D₉₃	—	3	1	no	—
9	C₅×C₁₁×C₃₁	D₉	1	1	yes	characteristic, complemented, Hall
10	C₅×C₉×C₃₁	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₁×C₃₁	C₅×D₃	1	1	yes	characteristic
12	C₅×C₁₁×D₉	—	31	1	no	maximal, Hall
13	C₅×D₉₃	—	3	1	no	—
14	C₁₁×D₃₁	—	9	1	no	Hall
15	D₂₇₉	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
16	C₅×C₉×C₁₁	D₃₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×C₃₁	D₃×C₁₁	1	1	yes	characteristic
18	C₁₁×C₃₁	C₅×D₉	1	1	yes	characteristic, complemented, Hall
19	C₅×D₃×C₁₁	—	93	1	no	—
20	C₅×D₃₁	—	9	1	no	Hall
21	C₉×C₃₁	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
22	C₁₁×D₉	—	31	1	no	Hall
23	D₉₃	—	3	1	no	—
24	C₃×C₅×C₁₁	D₉₃	1	1	yes	characteristic
25	C₅×C₃₁	C₁₁×D₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅×C₁₁	—	279	1	no	Hall
27	C₉×C₁₁	C₅×D₃₁	1	1	yes	characteristic, complemented, Hall
28	C₃×C₃₁	C₅×D₃×C₁₁	1	1	yes	characteristic
29	C₅×D₉	—	31	1	no	Hall
30	D₃×C₁₁	—	93	1	no	—
31	D₃₁	—	9	1	no	Hall
32	C₅×C₁₁	D₂₇₉	1	1	yes	characteristic, direct product factor, Hall
33	C₅×C₉	C₁₁×D₃₁	1	1	yes	characteristic, complemented, Hall
34	C₃×C₁₁	C₅×D₉₃	1	1	yes	characteristic
35	C₃₁	C₅×C₁₁×D₉	1	1	yes	characteristic, complemented, Sylow
36	C₅×D₃	—	93	1	no	—
37	C₂×C₁₁	—	279	1	no	Hall
38	D₉	—	31	1	no	Hall
39	C₃×C₅	C₁₁×D₉₃	1	1	yes	characteristic
40	C₁₁	C₅×D₂₇₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	—	279	1	no	Hall
42	C₉	C₅×C₁₁×D₃₁	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	93	1	no	—
44	C₅	C₁₁×D₂₇₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×C₁₁×D₉₃	1	1	yes	characteristic
46	C₂	—	279	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₁	D₂₇₉
commutator, cosocle, hypocenter	C₉×C₃₁	C₂×C₅×C₁₁
Frattini	C₃	C₅×C₁₁×D₉₃
Fitting	C₅×C₉×C₁₁×C₃₁	C₂
socle	C₃×C₅×C₁₁×C₃₁	D₃
LCS	G ▷ C₉×C₃₁
UCS	C₁ ◁ C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₁×C₃₁	C₂	semidirect
3. C₁₁×D₂₇₉	C₅	direct (N × H)
6. C₉×C₁₁×C₃₁	C₂×C₅	semidirect
7. C₅×D₂₇₉	C₁₁	direct (N × H)
9. C₅×C₁₁×C₃₁	D₉	semidirect
10. C₅×C₉×C₃₁	C₂×C₁₁	semidirect
15. D₂₇₉	C₅×C₁₁	direct (N × H)
16. C₅×C₉×C₁₁	D₃₁	semidirect
18. C₁₁×C₃₁	C₅×D₉	semidirect
21. C₉×C₃₁	C₂×C₅×C₁₁	semidirect
25. C₅×C₃₁	C₁₁×D₉	semidirect
27. C₉×C₁₁	C₅×D₃₁	semidirect
32. C₅×C₁₁	D₂₇₉	direct (N × H)
33. C₅×C₉	C₁₁×D₃₁	semidirect
35. C₃₁	C₅×C₁₁×D₉	semidirect
40. C₁₁	C₅×D₂₇₉	direct (N × H)
42. C₉	C₅×C₁₁×D₃₁	semidirect
44. C₅	C₁₁×D₂₇₉	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×C₉×C₁₁×C₃₁	2
C₅×C₁₁×D₉₃	3
C₁₁×D₂₇₉	5
C₅×D₂₇₉	11
C₅×C₁₁×D₉	31

Subgroups — C5×C11×D279 #44501656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×D₂₇₉ #44501656