Subgroups — C₂×C₈×C₂₇×C₂₉ #72190868

Order 12528.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₇×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₈×C₂₇×C₂₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₈×C₉×C₂₉	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₂₇×C₂₉	C₄	1	1	yes	characteristic
5	C₄×C₂₇×C₂₉	C₄	1	1	yes	characteristic
6	C₄×C₂₇×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₉×C₂₉	C₂×C₃	1	1	yes	characteristic
8	C₈×C₉×C₂₉	C₂×C₃	1	2	yes	—
9	C₂×C₂₇×C₂₉	C₈	1	2	yes	direct product factor
10	C₂×C₂₇×C₂₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₃×C₈×C₂₉	C₉	1	1	yes	characteristic
12	C₂²×C₉×C₂₉	C₃×C₄	1	1	yes	characteristic
13	C₄×C₉×C₂₉	C₃×C₄	1	1	yes	characteristic
14	C₄×C₉×C₂₉	C₂²×C₃	1	1	yes	characteristic
15	C₂₇×C₂₉	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₄×C₂₉	C₂×C₉	1	1	yes	characteristic
17	C₃×C₈×C₂₉	C₂×C₉	1	2	yes	—
18	C₂×C₉×C₂₉	C₃×C₈	1	2	yes	—
19	C₂×C₉×C₂₉	C₂×C₃×C₄	1	1	yes	characteristic
20	C₂×C₈×C₂₉	C₂₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₈×C₂₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂²×C₃×C₂₉	C₄×C₉	1	1	yes	characteristic
23	C₃×C₄×C₂₉	C₄×C₉	1	1	yes	characteristic
24	C₃×C₄×C₂₉	C₂²×C₉	1	1	yes	characteristic
25	C₉×C₂₉	C₂×C₃×C₈	1	1	yes	characteristic
26	C₂×C₄×C₂₉	C₂×C₂₇	1	1	yes	characteristic
27	C₈×C₂₉	C₂×C₂₇	1	2	yes	direct product factor
28	C₂×C₄×C₂₇	C₂×C₂₉	1	1	yes	characteristic
29	C₈×C₂₇	C₂×C₂₉	1	2	yes	direct product factor
30	C₂×C₃×C₂₉	C₈×C₉	1	2	yes	—
31	C₂×C₃×C₂₉	C₂×C₄×C₉	1	1	yes	characteristic
32	C₂×C₈×C₉	C₃×C₂₉	1	1	yes	characteristic
33	C₂²×C₂₉	C₄×C₂₇	1	1	yes	characteristic
34	C₄×C₂₉	C₄×C₂₇	1	1	yes	characteristic
35	C₄×C₂₉	C₂²×C₂₇	1	1	yes	characteristic
36	C₂²×C₂₇	C₄×C₂₉	1	1	yes	characteristic
37	C₄×C₂₇	C₄×C₂₉	1	1	yes	characteristic
38	C₄×C₂₇	C₂²×C₂₉	1	1	yes	characteristic
39	C₃×C₂₉	C₂×C₈×C₉	1	1	yes	characteristic
40	C₂×C₄×C₉	C₂×C₃×C₂₉	1	1	yes	characteristic
41	C₈×C₉	C₂×C₃×C₂₉	1	2	yes	—
42	C₂×C₂₉	C₈×C₂₇	1	2	yes	direct product factor
43	C₂×C₂₉	C₂×C₄×C₂₇	1	1	yes	characteristic
44	C₂×C₂₇	C₈×C₂₉	1	2	yes	direct product factor
45	C₂×C₂₇	C₂×C₄×C₂₉	1	1	yes	characteristic
46	C₂×C₃×C₈	C₉×C₂₉	1	1	yes	characteristic
47	C₂²×C₉	C₃×C₄×C₂₉	1	1	yes	characteristic
48	C₄×C₉	C₃×C₄×C₂₉	1	1	yes	characteristic
49	C₄×C₉	C₂²×C₃×C₂₉	1	1	yes	characteristic
50	C₂₉	C₂×C₈×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
51	C₂₇	C₂×C₈×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
52	C₂×C₃×C₄	C₂×C₉×C₂₉	1	1	yes	characteristic
53	C₃×C₈	C₂×C₉×C₂₉	1	2	yes	—
54	C₂×C₉	C₃×C₈×C₂₉	1	2	yes	—
55	C₂×C₉	C₂×C₃×C₄×C₂₉	1	1	yes	characteristic
56	C₂×C₈	C₂₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²×C₃	C₄×C₉×C₂₉	1	1	yes	characteristic
58	C₃×C₄	C₄×C₉×C₂₉	1	1	yes	characteristic
59	C₃×C₄	C₂²×C₉×C₂₉	1	1	yes	characteristic
60	C₉	C₂×C₃×C₈×C₂₉	1	1	yes	characteristic
61	C₂×C₄	C₂×C₂₇×C₂₉	1	1	yes	characteristic
62	C₈	C₂×C₂₇×C₂₉	1	2	yes	direct product factor
63	C₂×C₃	C₈×C₉×C₂₉	1	2	yes	—
64	C₂×C₃	C₂×C₄×C₉×C₂₉	1	1	yes	characteristic
65	C₂²	C₄×C₂₇×C₂₉	1	1	yes	characteristic
66	C₄	C₄×C₂₇×C₂₉	1	1	yes	characteristic
67	C₄	C₂²×C₂₇×C₂₉	1	1	yes	characteristic
68	C₃	C₂×C₈×C₉×C₂₉	1	1	yes	characteristic
69	C₂	C₈×C₂₇×C₂₉	1	2	yes	direct product factor
70	C₂	C₂×C₄×C₂₇×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₉	C₂²×C₃×C₂₉
socle, prime radical	C₂²×C₃×C₂₉	C₄×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈×C₂₇×C₂₉	C₂	direct (N × H)
9. C₂×C₂₇×C₂₉	C₈	direct (N × H)
15. C₂₇×C₂₉	C₂×C₈	direct (N × H)
20. C₂×C₈×C₂₉	C₂₇	direct (N × H)
21. C₂×C₈×C₂₇	C₂₉	direct (N × H)
27. C₈×C₂₉	C₂×C₂₇	direct (N × H)
29. C₈×C₂₇	C₂×C₂₉	direct (N × H)
42. C₂×C₂₉	C₈×C₂₇	direct (N × H)
44. C₂×C₂₇	C₈×C₂₉	direct (N × H)
50. C₂₉	C₂×C₈×C₂₇	direct (N × H)
51. C₂₇	C₂×C₈×C₂₉	direct (N × H)
56. C₂×C₈	C₂₇×C₂₉	direct (N × H)
62. C₈	C₂×C₂₇×C₂₉	direct (N × H)
69. C₂	C₈×C₂₇×C₂₉	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×C₄×C₂₇×C₂₉	2
C₈×C₂₇×C₂₉	2
C₂×C₈×C₉×C₂₉	3
C₂×C₈×C₂₇	29

Subgroups — C2×C8×C27×C29 #72190868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×C₂₇×C₂₉ #72190868