Subgroups — C₄×C₁₃×C₁₇×C₂₇ #72201160

Order 23868.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₁₇×C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₁₇×C₂₇	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₉×C₁₃×C₁₇	C₃	1	1	yes	maximal, characteristic
4	C₂×C₉×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic
5	C₃×C₄×C₁₃×C₁₇	C₉	1	1	yes	characteristic
6	C₉×C₁₃×C₁₇	C₃×C₄	1	1	yes	characteristic
7	C₄×C₁₇×C₂₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₄×C₁₃×C₂₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₁₃×C₁₇	C₂×C₉	1	1	yes	characteristic
10	C₂×C₁₇×C₂₇	C₂×C₁₃	1	1	yes	characteristic
11	C₄×C₁₃×C₁₇	C₂₇	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₁₃×C₂₇	C₂×C₁₇	1	1	yes	characteristic
13	C₃×C₁₃×C₁₇	C₄×C₉	1	1	yes	characteristic
14	C₄×C₉×C₁₇	C₃×C₁₃	1	1	yes	characteristic
15	C₄×C₉×C₁₃	C₃×C₁₇	1	1	yes	characteristic
16	C₁₇×C₂₇	C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₁₃×C₁₇	C₂×C₂₇	1	1	yes	characteristic
18	C₁₃×C₂₇	C₄×C₁₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₉×C₁₇	C₂×C₃×C₁₃	1	1	yes	characteristic
20	C₂×C₉×C₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic
21	C₁₃×C₁₇	C₄×C₂₇	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₄×C₁₇	C₉×C₁₃	1	1	yes	characteristic
23	C₃×C₄×C₁₃	C₉×C₁₇	1	1	yes	characteristic
24	C₉×C₁₇	C₃×C₄×C₁₃	1	1	yes	characteristic
25	C₉×C₁₃	C₃×C₄×C₁₇	1	1	yes	characteristic
26	C₄×C₂₇	C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃×C₁₇	C₂×C₉×C₁₃	1	1	yes	characteristic
28	C₂×C₃×C₁₃	C₂×C₉×C₁₇	1	1	yes	characteristic
29	C₄×C₁₇	C₁₃×C₂₇	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₂₇	C₂×C₁₃×C₁₇	1	1	yes	characteristic
31	C₄×C₁₃	C₁₇×C₂₇	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₁₇	C₄×C₉×C₁₃	1	1	yes	characteristic
33	C₃×C₁₃	C₄×C₉×C₁₇	1	1	yes	characteristic
34	C₄×C₉	C₃×C₁₃×C₁₇	1	1	yes	characteristic
35	C₂×C₁₇	C₂×C₁₃×C₂₇	1	1	yes	characteristic
36	C₂₇	C₄×C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₁₃	C₂×C₁₇×C₂₇	1	1	yes	characteristic
38	C₂×C₉	C₂×C₃×C₁₃×C₁₇	1	1	yes	characteristic
39	C₁₇	C₄×C₁₃×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
40	C₁₃	C₄×C₁₇×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
41	C₃×C₄	C₉×C₁₃×C₁₇	1	1	yes	characteristic
42	C₉	C₃×C₄×C₁₃×C₁₇	1	1	yes	characteristic
43	C₂×C₃	C₂×C₉×C₁₃×C₁₇	1	1	yes	characteristic
44	C₄	C₁₃×C₁₇×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₄×C₉×C₁₃×C₁₇	1	1	yes	characteristic
46	C₂	C₂×C₁₃×C₁₇×C₂₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₉	C₂×C₃×C₁₃×C₁₇
socle, prime radical	C₂×C₃×C₁₃×C₁₇	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×C₁₇×C₂₇	C₄	direct (N × H)
7. C₄×C₁₇×C₂₇	C₁₃	direct (N × H)
8. C₄×C₁₃×C₂₇	C₁₇	direct (N × H)
11. C₄×C₁₃×C₁₇	C₂₇	direct (N × H)
16. C₁₇×C₂₇	C₄×C₁₃	direct (N × H)
18. C₁₃×C₂₇	C₄×C₁₇	direct (N × H)
21. C₁₃×C₁₇	C₄×C₂₇	direct (N × H)
26. C₄×C₂₇	C₁₃×C₁₇	direct (N × H)
29. C₄×C₁₇	C₁₃×C₂₇	direct (N × H)
31. C₄×C₁₃	C₁₇×C₂₇	direct (N × H)
36. C₂₇	C₄×C₁₃×C₁₇	direct (N × H)
39. C₁₇	C₄×C₁₃×C₂₇	direct (N × H)
40. C₁₃	C₄×C₁₇×C₂₇	direct (N × H)
44. C₄	C₁₃×C₁₇×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×C₁₇×C₂₇	2
C₄×C₉×C₁₃×C₁₇	3
C₄×C₁₇×C₂₇	13
C₄×C₁₃×C₂₇	17

Subgroups — C4×C13×C17×C27 #72201160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×C₁₇×C₂₇ #72201160