Subgroups — C₇×C₈×C₁₃×C₂₇ #72197319

Order 19656.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₁₃×C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₈×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₂×C₇×C₁₃×C₂₇	C₄	1	1	yes	characteristic
4	C₈×C₁₃×C₂₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₃×C₂₇	C₈	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₇×C₈×C₁₃	C₉	1	1	yes	characteristic
7	C₄×C₇×C₉×C₁₃	C₂×C₃	1	1	yes	characteristic
8	C₂×C₇×C₉×C₁₃	C₃×C₄	1	1	yes	characteristic
9	C₇×C₈×C₂₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₄×C₁₃×C₂₇	C₂×C₇	1	1	yes	characteristic
11	C₃×C₄×C₇×C₁₃	C₂×C₉	1	1	yes	characteristic
12	C₈×C₉×C₁₃	C₃×C₇	1	1	yes	characteristic
13	C₇×C₉×C₁₃	C₃×C₈	1	1	yes	characteristic
14	C₄×C₇×C₂₇	C₂×C₁₃	1	1	yes	characteristic
15	C₇×C₈×C₁₃	C₂₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₃×C₂₇	C₄×C₇	1	1	yes	characteristic
17	C₂×C₃×C₇×C₁₃	C₄×C₉	1	1	yes	characteristic
18	C₇×C₈×C₉	C₃×C₁₃	1	1	yes	characteristic
19	C₄×C₉×C₁₃	C₂×C₃×C₇	1	1	yes	characteristic
20	C₂×C₇×C₂₇	C₄×C₁₃	1	1	yes	characteristic
21	C₄×C₇×C₁₃	C₂×C₂₇	1	1	yes	characteristic
22	C₁₃×C₂₇	C₇×C₈	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₈×C₁₃	C₇×C₉	1	1	yes	characteristic
24	C₃×C₇×C₁₃	C₈×C₉	1	1	yes	characteristic
25	C₄×C₇×C₉	C₂×C₃×C₁₃	1	1	yes	characteristic
26	C₂×C₉×C₁₃	C₃×C₄×C₇	1	1	yes	characteristic
27	C₈×C₂₇	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
28	C₇×C₂₇	C₈×C₁₃	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₇×C₁₃	C₄×C₂₇	1	1	yes	characteristic
30	C₃×C₇×C₈	C₉×C₁₃	1	1	yes	characteristic
31	C₃×C₄×C₁₃	C₂×C₇×C₉	1	1	yes	characteristic
32	C₂×C₇×C₉	C₃×C₄×C₁₃	1	1	yes	characteristic
33	C₉×C₁₃	C₃×C₇×C₈	1	1	yes	characteristic
34	C₄×C₂₇	C₂×C₇×C₁₃	1	1	yes	characteristic
35	C₈×C₁₃	C₇×C₂₇	1	1	yes	characteristic, direct product factor, Hall
36	C₇×C₁₃	C₈×C₂₇	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₄×C₇	C₂×C₉×C₁₃	1	1	yes	characteristic
38	C₂×C₃×C₁₃	C₄×C₇×C₉	1	1	yes	characteristic
39	C₈×C₉	C₃×C₇×C₁₃	1	1	yes	characteristic
40	C₇×C₉	C₃×C₈×C₁₃	1	1	yes	characteristic
41	C₇×C₈	C₁₃×C₂₇	1	1	yes	characteristic, direct product factor, Hall
42	C₂×C₂₇	C₄×C₇×C₁₃	1	1	yes	characteristic
43	C₄×C₁₃	C₂×C₇×C₂₇	1	1	yes	characteristic
44	C₂×C₃×C₇	C₄×C₉×C₁₃	1	1	yes	characteristic
45	C₃×C₁₃	C₇×C₈×C₉	1	1	yes	characteristic
46	C₄×C₉	C₂×C₃×C₇×C₁₃	1	1	yes	characteristic
47	C₄×C₇	C₂×C₁₃×C₂₇	1	1	yes	characteristic
48	C₂₇	C₇×C₈×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×C₁₃	C₄×C₇×C₂₇	1	1	yes	characteristic
50	C₃×C₈	C₇×C₉×C₁₃	1	1	yes	characteristic
51	C₃×C₇	C₈×C₉×C₁₃	1	1	yes	characteristic
52	C₂×C₉	C₃×C₄×C₇×C₁₃	1	1	yes	characteristic
53	C₂×C₇	C₄×C₁₃×C₂₇	1	1	yes	characteristic
54	C₁₃	C₇×C₈×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
55	C₃×C₄	C₂×C₇×C₉×C₁₃	1	1	yes	characteristic
56	C₉	C₃×C₇×C₈×C₁₃	1	1	yes	characteristic
57	C₈	C₇×C₁₃×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
58	C₇	C₈×C₁₃×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
59	C₂×C₃	C₄×C₇×C₉×C₁₃	1	1	yes	characteristic
60	C₄	C₂×C₇×C₁₃×C₂₇	1	1	yes	characteristic
61	C₃	C₇×C₈×C₉×C₁₃	1	1	yes	characteristic
62	C₂	C₄×C₇×C₁₃×C₂₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₉	C₂×C₃×C₇×C₁₃
socle, prime radical	C₂×C₃×C₇×C₁₃	C₄×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₈×C₁₃×C₂₇	C₇	direct (N × H)
5. C₇×C₁₃×C₂₇	C₈	direct (N × H)
9. C₇×C₈×C₂₇	C₁₃	direct (N × H)
15. C₇×C₈×C₁₃	C₂₇	direct (N × H)
22. C₁₃×C₂₇	C₇×C₈	direct (N × H)
27. C₈×C₂₇	C₇×C₁₃	direct (N × H)
28. C₇×C₂₇	C₈×C₁₃	direct (N × H)
35. C₈×C₁₃	C₇×C₂₇	direct (N × H)
36. C₇×C₁₃	C₈×C₂₇	direct (N × H)
41. C₇×C₈	C₁₃×C₂₇	direct (N × H)
48. C₂₇	C₇×C₈×C₁₃	direct (N × H)
54. C₁₃	C₇×C₈×C₂₇	direct (N × H)
57. C₈	C₇×C₁₃×C₂₇	direct (N × H)
58. C₇	C₈×C₁₃×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
C₄×C₇×C₁₃×C₂₇	2
C₇×C₈×C₉×C₁₃	3
C₈×C₁₃×C₂₇	7
C₇×C₈×C₂₇	13

Subgroups — C7×C8×C13×C27 #72197319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₈×C₁₃×C₂₇ #72197319