Subgroups — C₄³×C₉×C₂₅ #72192566

Order 14400.

1161 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₉×C₂₅	C₂	1	7	yes	maximal
2	C₃×C₄³×C₂₅	C₃	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₉×C₂₅	C₂²	1	7	yes	—
4	C₄²×C₉×C₂₅	C₄	1	28	yes	direct product factor
5	C₄³×C₅×C₉	C₅	1	1	yes	maximal, characteristic
6	C₂×C₃×C₄²×C₂₅	C₂×C₃	1	7	yes	—
7	C₂³×C₉×C₂₅	C₂³	1	1	yes	characteristic
8	C₂×C₄×C₉×C₂₅	C₂×C₄	1	42	yes	—
9	C₄³×C₂₅	C₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₄²×C₅×C₉	C₂×C₅	1	7	yes	—
11	C₂²×C₃×C₄×C₂₅	C₂²×C₃	1	7	yes	—
12	C₃×C₄²×C₂₅	C₃×C₄	1	28	yes	—
13	C₃×C₄³×C₅	C₃×C₅	1	1	yes	characteristic
14	C₂²×C₉×C₂₅	C₂²×C₄	1	7	yes	—
15	C₄×C₉×C₂₅	C₄²	1	28	yes	direct product factor
16	C₂×C₄²×C₂₅	C₂×C₉	1	7	yes	—
17	C₂²×C₄×C₅×C₉	C₂²×C₅	1	7	yes	—
18	C₄²×C₅×C₉	C₄×C₅	1	28	yes	—
19	C₂³×C₃×C₂₅	C₂³×C₃	1	1	yes	characteristic
20	C₂×C₃×C₄×C₂₅	C₂×C₃×C₄	1	42	yes	—
21	C₄³×C₉	C₂₅	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₄²×C₅	C₂×C₃×C₅	1	7	yes	—
23	C₂×C₉×C₂₅	C₂×C₄²	1	7	yes	—
24	C₂²×C₄×C₂₅	C₂²×C₉	1	7	yes	—
25	C₄²×C₂₅	C₄×C₉	1	28	yes	direct product factor
26	C₂³×C₅×C₉	C₂³×C₅	1	1	yes	characteristic
27	C₂×C₄×C₅×C₉	C₂×C₄×C₅	1	42	yes	—
28	C₄³×C₅	C₅×C₉	1	1	yes	characteristic
29	C₂²×C₃×C₂₅	C₂²×C₃×C₄	1	7	yes	—
30	C₃×C₄×C₂₅	C₃×C₄²	1	28	yes	—
31	C₂×C₄²×C₉	C₂×C₂₅	1	7	yes	—
32	C₂²×C₃×C₄×C₅	C₂²×C₃×C₅	1	7	yes	—
33	C₃×C₄²×C₅	C₃×C₄×C₅	1	28	yes	—
34	C₉×C₂₅	C₄³	1	1	yes	characteristic, direct product factor, Hall
35	C₂³×C₂₅	C₂³×C₉	1	1	yes	characteristic
36	C₂×C₄×C₂₅	C₂×C₄×C₉	1	42	yes	—
37	C₃×C₄³	C₃×C₂₅	1	1	yes	characteristic
38	C₂²×C₅×C₉	C₂²×C₄×C₅	1	7	yes	—
39	C₄×C₅×C₉	C₄²×C₅	1	28	yes	—
40	C₂×C₄²×C₅	C₂×C₅×C₉	1	7	yes	—
41	C₂×C₃×C₂₅	C₂×C₃×C₄²	1	7	yes	—
42	C₂²×C₄×C₉	C₂²×C₂₅	1	7	yes	—
43	C₄²×C₉	C₄×C₂₅	1	28	yes	direct product factor
44	C₂³×C₃×C₅	C₂³×C₃×C₅	1	1	yes	characteristic
45	C₂×C₃×C₄×C₅	C₂×C₃×C₄×C₅	1	42	yes	—
46	C₂²×C₂₅	C₂²×C₄×C₉	1	7	yes	—
47	C₄×C₂₅	C₄²×C₉	1	28	yes	direct product factor
48	C₂×C₃×C₄²	C₂×C₃×C₂₅	1	7	yes	—
49	C₂×C₅×C₉	C₂×C₄²×C₅	1	7	yes	—
50	C₂²×C₄×C₅	C₂²×C₅×C₉	1	7	yes	—
51	C₄²×C₅	C₄×C₅×C₉	1	28	yes	—
52	C₃×C₂₅	C₃×C₄³	1	1	yes	characteristic
53	C₂³×C₉	C₂³×C₂₅	1	1	yes	characteristic
54	C₂×C₄×C₉	C₂×C₄×C₂₅	1	42	yes	—
55	C₄³	C₉×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
56	C₂²×C₃×C₅	C₂²×C₃×C₄×C₅	1	7	yes	—
57	C₃×C₄×C₅	C₃×C₄²×C₅	1	28	yes	—
58	C₂×C₂₅	C₂×C₄²×C₉	1	7	yes	—
59	C₂²×C₃×C₄	C₂²×C₃×C₂₅	1	7	yes	—
60	C₃×C₄²	C₃×C₄×C₂₅	1	28	yes	—
61	C₅×C₉	C₄³×C₅	1	1	yes	characteristic
62	C₂³×C₅	C₂³×C₅×C₉	1	1	yes	characteristic
63	C₂×C₄×C₅	C₂×C₄×C₅×C₉	1	42	yes	—
64	C₂²×C₉	C₂²×C₄×C₂₅	1	7	yes	—
65	C₄×C₉	C₄²×C₂₅	1	28	yes	direct product factor
66	C₂×C₄²	C₂×C₉×C₂₅	1	7	yes	—
67	C₂×C₃×C₅	C₂×C₃×C₄²×C₅	1	7	yes	—
68	C₂₅	C₄³×C₉	1	1	yes	characteristic, direct product factor, Sylow
69	C₂³×C₃	C₂³×C₃×C₂₅	1	1	yes	characteristic
70	C₂×C₃×C₄	C₂×C₃×C₄×C₂₅	1	42	yes	—
71	C₂²×C₅	C₂²×C₄×C₅×C₉	1	7	yes	—
72	C₄×C₅	C₄²×C₅×C₉	1	28	yes	—
73	C₂×C₉	C₂×C₄²×C₂₅	1	7	yes	—
74	C₂²×C₄	C₂²×C₉×C₂₅	1	7	yes	—
75	C₄²	C₄×C₉×C₂₅	1	28	yes	direct product factor
76	C₃×C₅	C₃×C₄³×C₅	1	1	yes	characteristic
77	C₂²×C₃	C₂²×C₃×C₄×C₂₅	1	7	yes	—
78	C₃×C₄	C₃×C₄²×C₂₅	1	28	yes	—
79	C₂×C₅	C₂×C₄²×C₅×C₉	1	7	yes	—
80	C₉	C₄³×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
81	C₂³	C₂³×C₉×C₂₅	1	1	yes	characteristic
82	C₂×C₄	C₂×C₄×C₉×C₂₅	1	42	yes	—
83	C₂×C₃	C₂×C₃×C₄²×C₂₅	1	7	yes	—
84	C₅	C₄³×C₅×C₉	1	1	yes	characteristic
85	C₂²	C₂²×C₄×C₉×C₂₅	1	7	yes	—
86	C₄	C₄²×C₉×C₂₅	1	28	yes	direct product factor
87	C₃	C₃×C₄³×C₂₅	1	1	yes	characteristic
88	C₂	C₂×C₄²×C₉×C₂₅	1	7	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, socle, prime radical, cosocle	C₂³×C₃×C₅	C₂³×C₃×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄²×C₉×C₂₅	C₄	direct (N × H)
9. C₄³×C₂₅	C₉	direct (N × H)
15. C₄×C₉×C₂₅	C₄²	direct (N × H)
21. C₄³×C₉	C₂₅	direct (N × H)
25. C₄²×C₂₅	C₄×C₉	direct (N × H)
34. C₉×C₂₅	C₄³	direct (N × H)
43. C₄²×C₉	C₄×C₂₅	direct (N × H)
47. C₄×C₂₅	C₄²×C₉	direct (N × H)
55. C₄³	C₉×C₂₅	direct (N × H)
65. C₄×C₉	C₄²×C₂₅	direct (N × H)
68. C₂₅	C₄³×C₉	direct (N × H)
75. C₄²	C₄×C₉×C₂₅	direct (N × H)
80. C₉	C₄³×C₂₅	direct (N × H)
86. C₄	C₄²×C₉×C₂₅	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×C₄²×C₉×C₂₅	2
C₃×C₄³×C₂₅	3
C₄³×C₅×C₉	5

Subgroups — C43×C9×C25 #72192566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×C₉×C₂₅ #72192566