Subgroups — C₃×C₁₁×D₃₉₅ #39907623

Order 26070.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₃₉₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁×D₇₉	—	5	1	no	maximal, Hall
4	C₅×C₁₁×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₇₉	D₅	1	1	yes	characteristic, complemented, Hall
6	C₃×D₃₉₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×D₇₉	—	5	1	no	Hall
8	C₃×C₅×C₇₉	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₇₉	C₃×D₅	1	1	yes	characteristic, complemented, Hall
10	D₃₉₅	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
11	C₃×D₇₉	—	5	1	no	Hall
12	C₅×C₇₉	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₃×D₅×C₁₁	—	79	1	no	maximal, Hall
14	C₃×C₇₉	D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×C₁₁	D₇₉	1	1	yes	characteristic, complemented, Hall
16	D₇₉	—	5	1	no	Hall
17	D₅×C₁₁	—	79	1	no	Hall
18	C₇₉	C₃×D₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃×C₁₁	—	395	1	no	Hall
20	C₅×C₁₁	C₃×D₇₉	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	D₃₉₅	1	1	yes	characteristic, direct product factor, Hall
22	C₃×D₅	—	79	1	no	Hall
23	C₂×C₁₁	—	395	1	no	Hall
24	C₃×C₅	C₁₁×D₇₉	1	1	yes	characteristic, complemented, Hall
25	C₁₁	C₃×D₃₉₅	1	1	yes	characteristic, direct product factor, Sylow
26	D₅	—	79	1	no	Hall
27	C₂×C₃	—	395	1	no	Hall
28	C₅	C₃×C₁₁×D₇₉	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₁₁×D₃₉₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	395	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₁	D₃₉₅
commutator, cosocle, hypocenter	C₅×C₇₉	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₇₉	C₂
LCS	G ▷ C₅×C₇₉
UCS	C₁ ◁ C₃×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₇₉	C₂	semidirect
2. C₁₁×D₃₉₅	C₃	direct (N × H)
4. C₅×C₁₁×C₇₉	C₂×C₃	semidirect
5. C₃×C₁₁×C₇₉	D₅	semidirect
6. C₃×D₃₉₅	C₁₁	direct (N × H)
8. C₃×C₅×C₇₉	C₂×C₁₁	semidirect
9. C₁₁×C₇₉	C₃×D₅	semidirect
10. D₃₉₅	C₃×C₁₁	direct (N × H)
12. C₅×C₇₉	C₂×C₃×C₁₁	semidirect
14. C₃×C₇₉	D₅×C₁₁	semidirect
15. C₃×C₅×C₁₁	D₇₉	semidirect
18. C₇₉	C₃×D₅×C₁₁	semidirect
20. C₅×C₁₁	C₃×D₇₉	semidirect
21. C₃×C₁₁	D₃₉₅	direct (N × H)
24. C₃×C₅	C₁₁×D₇₉	semidirect
25. C₁₁	C₃×D₃₉₅	direct (N × H)
28. C₅	C₃×C₁₁×D₇₉	semidirect
29. C₃	C₁₁×D₃₉₅	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×C₁₁×C₇₉	2
C₁₁×D₃₉₅	3
C₃×C₁₁×D₇₉	5
C₃×D₃₉₅	11
C₃×D₅×C₁₁	79

Subgroups — C3×C11×D395 #39907623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×D₃₉₅ #39907623