Subgroups — C₄×C₁₃×C₁₉×C₂₇ #72203809

Order 26676.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₁₉×C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₁₉×C₂₇	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₁₉×C₂₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₄×C₉×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic
5	C₂×C₉×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic
6	C₃×C₄×C₁₃×C₁₉	C₉	1	1	yes	characteristic
7	C₉×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic
8	C₂×C₃×C₁₃×C₁₉	C₂×C₉	1	1	yes	characteristic
9	C₄×C₁₃×C₂₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₉×C₂₇	C₂×C₁₃	1	1	yes	characteristic
11	C₄×C₁₃×C₁₉	C₂₇	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₁₃×C₁₉	C₄×C₉	1	1	yes	characteristic
13	C₂×C₁₃×C₂₇	C₂×C₁₉	1	1	yes	characteristic
14	C₄×C₉×C₁₉	C₃×C₁₃	1	1	yes	characteristic
15	C₁₉×C₂₇	C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₃×C₁₉	C₂×C₂₇	1	1	yes	characteristic
17	C₄×C₉×C₁₃	C₃×C₁₉	1	1	yes	characteristic
18	C₁₃×C₂₇	C₄×C₁₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₉×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic
20	C₁₃×C₁₉	C₄×C₂₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₉×C₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic
22	C₃×C₄×C₁₉	C₉×C₁₃	1	1	yes	characteristic
23	C₉×C₁₉	C₃×C₄×C₁₃	1	1	yes	characteristic
24	C₃×C₄×C₁₃	C₉×C₁₉	1	1	yes	characteristic
25	C₉×C₁₃	C₃×C₄×C₁₉	1	1	yes	characteristic
26	C₂×C₃×C₁₉	C₂×C₉×C₁₃	1	1	yes	characteristic
27	C₄×C₂₇	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₃×C₁₃	C₂×C₉×C₁₉	1	1	yes	characteristic
29	C₄×C₁₉	C₁₃×C₂₇	1	1	yes	characteristic, direct product factor, Hall
30	C₃×C₁₉	C₄×C₉×C₁₃	1	1	yes	characteristic
31	C₂×C₂₇	C₂×C₁₃×C₁₉	1	1	yes	characteristic
32	C₄×C₁₃	C₁₉×C₂₇	1	1	yes	characteristic, direct product factor, Hall
33	C₃×C₁₃	C₄×C₉×C₁₉	1	1	yes	characteristic
34	C₂×C₁₉	C₂×C₁₃×C₂₇	1	1	yes	characteristic
35	C₄×C₉	C₃×C₁₃×C₁₉	1	1	yes	characteristic
36	C₂₇	C₄×C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₁₃	C₂×C₁₉×C₂₇	1	1	yes	characteristic
38	C₁₉	C₄×C₁₃×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₉	C₂×C₃×C₁₃×C₁₉	1	1	yes	characteristic
40	C₁₃	C₄×C₁₉×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
41	C₃×C₄	C₉×C₁₃×C₁₉	1	1	yes	characteristic
42	C₉	C₃×C₄×C₁₃×C₁₉	1	1	yes	characteristic
43	C₂×C₃	C₂×C₉×C₁₃×C₁₉	1	1	yes	characteristic
44	C₄	C₁₃×C₁₉×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₄×C₉×C₁₃×C₁₉	1	1	yes	characteristic
46	C₂	C₂×C₁₃×C₁₉×C₂₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₉	C₂×C₃×C₁₃×C₁₉
socle, prime radical	C₂×C₃×C₁₃×C₁₉	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. C₁₃×C₁₉×C₂₇	C₄	direct (N × H)
3. C₄×C₁₉×C₂₇	C₁₃	direct (N × H)
9. C₄×C₁₃×C₂₇	C₁₉	direct (N × H)
11. C₄×C₁₃×C₁₉	C₂₇	direct (N × H)
15. C₁₉×C₂₇	C₄×C₁₃	direct (N × H)
18. C₁₃×C₂₇	C₄×C₁₉	direct (N × H)
20. C₁₃×C₁₉	C₄×C₂₇	direct (N × H)
27. C₄×C₂₇	C₁₃×C₁₉	direct (N × H)
29. C₄×C₁₉	C₁₃×C₂₇	direct (N × H)
32. C₄×C₁₃	C₁₉×C₂₇	direct (N × H)
36. C₂₇	C₄×C₁₃×C₁₉	direct (N × H)
38. C₁₉	C₄×C₁₃×C₂₇	direct (N × H)
40. C₁₃	C₄×C₁₉×C₂₇	direct (N × H)
44. C₄	C₁₃×C₁₉×C₂₇	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×C₁₃×C₁₉×C₂₇	2
C₄×C₁₉×C₂₇	13
C₄×C₉×C₁₃×C₁₉	3
C₄×C₁₃×C₂₇	19

Subgroups — C4×C13×C19×C27 #72203809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×C₁₉×C₂₇ #72203809