Subgroups — C₂²×C₄×C₂₅×C₂₉ #72190040

Order 11600.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂₅×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₂₅×C₂₉	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₄×C₅×C₂₉	C₅	1	1	yes	maximal, characteristic
4	C₂²×C₂₅×C₂₉	C₄	1	4	yes	direct product factor
5	C₂²×C₂₅×C₂₉	C₂²	1	3	yes	—
6	C₄×C₂₅×C₂₉	C₂²	1	4	yes	direct product factor
7	C₂×C₂₅×C₂₉	C₂×C₄	1	6	yes	direct product factor
8	C₂×C₂₅×C₂₉	C₂³	1	1	yes	characteristic
9	C₂³×C₅×C₂₉	C₂×C₅	1	1	yes	characteristic
10	C₂×C₄×C₅×C₂₉	C₂×C₅	1	6	yes	—
11	C₂₅×C₂₉	C₂²×C₄	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₅×C₂₉	C₄×C₅	1	4	yes	—
13	C₂²×C₅×C₂₉	C₂²×C₅	1	3	yes	—
14	C₄×C₅×C₂₉	C₂²×C₅	1	4	yes	—
15	C₂²×C₄×C₂₉	C₂₅	1	1	yes	characteristic, direct product factor, Hall
16	C₂²×C₄×C₂₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₅×C₂₉	C₂×C₄×C₅	1	6	yes	—
18	C₂×C₅×C₂₉	C₂³×C₅	1	1	yes	characteristic
19	C₂³×C₂₉	C₂×C₂₅	1	1	yes	characteristic
20	C₂×C₄×C₂₉	C₂×C₂₅	1	6	yes	direct product factor
21	C₂³×C₂₅	C₂×C₂₉	1	1	yes	characteristic
22	C₂×C₄×C₂₅	C₂×C₂₉	1	6	yes	direct product factor
23	C₅×C₂₉	C₂²×C₄×C₅	1	1	yes	characteristic
24	C₂²×C₂₉	C₄×C₂₅	1	4	yes	direct product factor
25	C₂²×C₂₉	C₂²×C₂₅	1	3	yes	—
26	C₄×C₂₉	C₂²×C₂₅	1	4	yes	direct product factor
27	C₂²×C₂₅	C₄×C₂₉	1	4	yes	direct product factor
28	C₂²×C₂₅	C₂²×C₂₉	1	3	yes	—
29	C₄×C₂₅	C₂²×C₂₉	1	4	yes	direct product factor
30	C₂²×C₄×C₅	C₅×C₂₉	1	1	yes	characteristic
31	C₂×C₂₉	C₂×C₄×C₂₅	1	6	yes	direct product factor
32	C₂×C₂₉	C₂³×C₂₅	1	1	yes	characteristic
33	C₂×C₂₅	C₂×C₄×C₂₉	1	6	yes	direct product factor
34	C₂×C₂₅	C₂³×C₂₉	1	1	yes	characteristic
35	C₂³×C₅	C₂×C₅×C₂₉	1	1	yes	characteristic
36	C₂×C₄×C₅	C₂×C₅×C₂₉	1	6	yes	—
37	C₂₉	C₂²×C₄×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
38	C₂₅	C₂²×C₄×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²×C₅	C₄×C₅×C₂₉	1	4	yes	—
40	C₂²×C₅	C₂²×C₅×C₂₉	1	3	yes	—
41	C₄×C₅	C₂²×C₅×C₂₉	1	4	yes	—
42	C₂²×C₄	C₂₅×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₅	C₂×C₄×C₅×C₂₉	1	6	yes	—
44	C₂×C₅	C₂³×C₅×C₂₉	1	1	yes	characteristic
45	C₂³	C₂×C₂₅×C₂₉	1	1	yes	characteristic
46	C₂×C₄	C₂×C₂₅×C₂₉	1	6	yes	direct product factor
47	C₅	C₂²×C₄×C₅×C₂₉	1	1	yes	characteristic
48	C₂²	C₄×C₂₅×C₂₉	1	4	yes	direct product factor
49	C₂²	C₂²×C₂₅×C₂₉	1	3	yes	—
50	C₄	C₂²×C₂₅×C₂₉	1	4	yes	direct product factor
51	C₂	C₂×C₄×C₂₅×C₂₉	1	6	yes	direct product factor
52	C₂	C₂³×C₂₅×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂³×C₅×C₂₉
socle, prime radical	C₂³×C₅×C₂₉	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₂₅×C₂₉	C₂	direct (N × H)
4. C₂²×C₂₅×C₂₉	C₄	direct (N × H)
6. C₄×C₂₅×C₂₉	C₂²	direct (N × H)
7. C₂×C₂₅×C₂₉	C₂×C₄	direct (N × H)
11. C₂₅×C₂₉	C₂²×C₄	direct (N × H)
15. C₂²×C₄×C₂₉	C₂₅	direct (N × H)
16. C₂²×C₄×C₂₅	C₂₉	direct (N × H)
20. C₂×C₄×C₂₉	C₂×C₂₅	direct (N × H)
22. C₂×C₄×C₂₅	C₂×C₂₉	direct (N × H)
24. C₂²×C₂₉	C₄×C₂₅	direct (N × H)
26. C₄×C₂₉	C₂²×C₂₅	direct (N × H)
27. C₂²×C₂₅	C₄×C₂₉	direct (N × H)
29. C₄×C₂₅	C₂²×C₂₉	direct (N × H)
31. C₂×C₂₉	C₂×C₄×C₂₅	direct (N × H)
33. C₂×C₂₅	C₂×C₄×C₂₉	direct (N × H)
37. C₂₉	C₂²×C₄×C₂₅	direct (N × H)
38. C₂₅	C₂²×C₄×C₂₉	direct (N × H)
42. C₂²×C₄	C₂₅×C₂₉	direct (N × H)
46. C₂×C₄	C₂×C₂₅×C₂₉	direct (N × H)
48. C₂²	C₄×C₂₅×C₂₉	direct (N × H)
50. C₄	C₂²×C₂₅×C₂₉	direct (N × H)
51. C₂	C₂×C₄×C₂₅×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
C₂³×C₂₅×C₂₉	2
C₂×C₄×C₂₅×C₂₉	2
C₂²×C₄×C₅×C₂₉	5
C₂²×C₄×C₂₅	29

Subgroups — C22×C4×C25×C29 #72190040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×C₂₅×C₂₉ #72190040