Subgroups — C₄×C₅×C₂₇×C₄₁ #72199609

Order 22140.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₇×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₇×C₄₁	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₂₇×C₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₂₇×C₄₁	C₂×C₅	1	1	yes	characteristic
5	C₄×C₅×C₉×C₄₁	C₃	1	1	yes	maximal, characteristic
6	C₂×C₅×C₉×C₄₁	C₂×C₃	1	1	yes	characteristic
7	C₃×C₄×C₅×C₄₁	C₉	1	1	yes	characteristic
8	C₅×C₉×C₄₁	C₃×C₄	1	1	yes	characteristic
9	C₄×C₉×C₄₁	C₃×C₅	1	1	yes	characteristic
10	C₂×C₃×C₅×C₄₁	C₂×C₉	1	1	yes	characteristic
11	C₂₇×C₄₁	C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
12	C₄×C₅×C₄₁	C₂₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₉×C₄₁	C₂×C₃×C₅	1	1	yes	characteristic
14	C₃×C₅×C₄₁	C₄×C₉	1	1	yes	characteristic
15	C₄×C₅×C₂₇	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃×C₄×C₄₁	C₅×C₉	1	1	yes	characteristic
17	C₂×C₅×C₄₁	C₂×C₂₇	1	1	yes	characteristic
18	C₉×C₄₁	C₃×C₄×C₅	1	1	yes	characteristic
19	C₂×C₅×C₂₇	C₂×C₄₁	1	1	yes	characteristic
20	C₂×C₃×C₄₁	C₂×C₅×C₉	1	1	yes	characteristic
21	C₅×C₄₁	C₄×C₂₇	1	1	yes	characteristic, direct product factor, Hall
22	C₄×C₅×C₉	C₃×C₄₁	1	1	yes	characteristic
23	C₄×C₄₁	C₅×C₂₇	1	1	yes	characteristic, direct product factor, Hall
24	C₅×C₂₇	C₄×C₄₁	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₄₁	C₄×C₅×C₉	1	1	yes	characteristic
26	C₄×C₂₇	C₅×C₄₁	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₅×C₉	C₂×C₃×C₄₁	1	1	yes	characteristic
28	C₂×C₄₁	C₂×C₅×C₂₇	1	1	yes	characteristic
29	C₃×C₄×C₅	C₉×C₄₁	1	1	yes	characteristic
30	C₂×C₂₇	C₂×C₅×C₄₁	1	1	yes	characteristic
31	C₅×C₉	C₃×C₄×C₄₁	1	1	yes	characteristic
32	C₄₁	C₄×C₅×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
33	C₄×C₉	C₃×C₅×C₄₁	1	1	yes	characteristic
34	C₂×C₃×C₅	C₂×C₉×C₄₁	1	1	yes	characteristic
35	C₂₇	C₄×C₅×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
36	C₄×C₅	C₂₇×C₄₁	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₉	C₂×C₃×C₅×C₄₁	1	1	yes	characteristic
38	C₃×C₅	C₄×C₉×C₄₁	1	1	yes	characteristic
39	C₃×C₄	C₅×C₉×C₄₁	1	1	yes	characteristic
40	C₂×C₅	C₂×C₂₇×C₄₁	1	1	yes	characteristic
41	C₉	C₃×C₄×C₅×C₄₁	1	1	yes	characteristic
42	C₂×C₃	C₂×C₅×C₉×C₄₁	1	1	yes	characteristic
43	C₅	C₄×C₂₇×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	C₅×C₂₇×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₄×C₅×C₉×C₄₁	1	1	yes	characteristic
46	C₂	C₂×C₅×C₂₇×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₉	C₂×C₃×C₅×C₄₁
socle, prime radical	C₂×C₃×C₅×C₄₁	C₂×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×C₂₇×C₄₁	C₄	direct (N × H)
3. C₄×C₂₇×C₄₁	C₅	direct (N × H)
11. C₂₇×C₄₁	C₄×C₅	direct (N × H)
12. C₄×C₅×C₄₁	C₂₇	direct (N × H)
15. C₄×C₅×C₂₇	C₄₁	direct (N × H)
21. C₅×C₄₁	C₄×C₂₇	direct (N × H)
23. C₄×C₄₁	C₅×C₂₇	direct (N × H)
24. C₅×C₂₇	C₄×C₄₁	direct (N × H)
26. C₄×C₂₇	C₅×C₄₁	direct (N × H)
32. C₄₁	C₄×C₅×C₂₇	direct (N × H)
35. C₂₇	C₄×C₅×C₄₁	direct (N × H)
36. C₄×C₅	C₂₇×C₄₁	direct (N × H)
43. C₅	C₄×C₂₇×C₄₁	direct (N × H)
44. C₄	C₅×C₂₇×C₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₂₇×C₄₁	2
C₄×C₂₇×C₄₁	5
C₄×C₅×C₉×C₄₁	3
C₄×C₅×C₂₇	41

Subgroups — C4×C5×C27×C41 #72199609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₂₇×C₄₁ #72199609