Subgroups — C₅×C₇×C₁₆×C₂₅ #72192185

Order 14000.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₇×C₂₅	C₄	1	1	yes	characteristic
3	C₅²×C₇×C₁₆	C₅	1	1	yes	maximal, characteristic
4	C₇×C₁₆×C₂₅	C₅	1	5	yes	maximal, direct product factor
5	C₅×C₁₆×C₂₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₂₅	C₈	1	1	yes	characteristic
7	C₅²×C₇×C₈	C₂×C₅	1	1	yes	characteristic
8	C₇×C₈×C₂₅	C₂×C₅	1	5	yes	—
9	C₅×C₈×C₂₅	C₂×C₇	1	1	yes	characteristic
10	C₅×C₇×C₂₅	C₁₆	1	1	yes	characteristic, direct product factor, Hall
11	C₄×C₅²×C₇	C₄×C₅	1	1	yes	characteristic
12	C₄×C₇×C₂₅	C₄×C₅	1	5	yes	—
13	C₅×C₇×C₁₆	C₂₅	1	5	yes	direct product factor
14	C₅×C₇×C₁₆	C₅²	1	1	yes	characteristic
15	C₄×C₅×C₂₅	C₄×C₇	1	1	yes	characteristic
16	C₅²×C₁₆	C₅×C₇	1	1	yes	characteristic
17	C₁₆×C₂₅	C₅×C₇	1	5	yes	direct product factor
18	C₂×C₅²×C₇	C₅×C₈	1	1	yes	characteristic
19	C₂×C₇×C₂₅	C₅×C₈	1	5	yes	—
20	C₅×C₇×C₈	C₂×C₂₅	1	5	yes	—
21	C₅×C₇×C₈	C₂×C₅²	1	1	yes	characteristic
22	C₂×C₅×C₂₅	C₇×C₈	1	1	yes	characteristic
23	C₅²×C₈	C₂×C₅×C₇	1	1	yes	characteristic
24	C₈×C₂₅	C₂×C₅×C₇	1	5	yes	—
25	C₅²×C₇	C₅×C₁₆	1	1	yes	characteristic
26	C₇×C₂₅	C₅×C₁₆	1	5	yes	direct product factor
27	C₄×C₅×C₇	C₄×C₂₅	1	5	yes	—
28	C₄×C₅×C₇	C₄×C₅²	1	1	yes	characteristic
29	C₅×C₂₅	C₇×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
30	C₇×C₁₆	C₅×C₂₅	1	1	yes	characteristic, direct product factor, Hall
31	C₄×C₅²	C₄×C₅×C₇	1	1	yes	characteristic
32	C₄×C₂₅	C₄×C₅×C₇	1	5	yes	—
33	C₅×C₁₆	C₇×C₂₅	1	5	yes	direct product factor
34	C₅×C₁₆	C₅²×C₇	1	1	yes	characteristic
35	C₂×C₅×C₇	C₈×C₂₅	1	5	yes	—
36	C₂×C₅×C₇	C₅²×C₈	1	1	yes	characteristic
37	C₇×C₈	C₂×C₅×C₂₅	1	1	yes	characteristic
38	C₂×C₅²	C₅×C₇×C₈	1	1	yes	characteristic
39	C₂×C₂₅	C₅×C₇×C₈	1	5	yes	—
40	C₅×C₈	C₂×C₇×C₂₅	1	5	yes	—
41	C₅×C₈	C₂×C₅²×C₇	1	1	yes	characteristic
42	C₅×C₇	C₁₆×C₂₅	1	5	yes	direct product factor
43	C₅×C₇	C₅²×C₁₆	1	1	yes	characteristic
44	C₄×C₇	C₄×C₅×C₂₅	1	1	yes	characteristic
45	C₅²	C₅×C₇×C₁₆	1	1	yes	characteristic
46	C₂₅	C₅×C₇×C₁₆	1	5	yes	direct product factor
47	C₄×C₅	C₄×C₇×C₂₅	1	5	yes	—
48	C₄×C₅	C₄×C₅²×C₇	1	1	yes	characteristic
49	C₁₆	C₅×C₇×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₇	C₅×C₈×C₂₅	1	1	yes	characteristic
51	C₂×C₅	C₇×C₈×C₂₅	1	5	yes	—
52	C₂×C₅	C₅²×C₇×C₈	1	1	yes	characteristic
53	C₈	C₂×C₅×C₇×C₂₅	1	1	yes	characteristic
54	C₇	C₅×C₁₆×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
55	C₅	C₇×C₁₆×C₂₅	1	5	yes	direct product factor
56	C₅	C₅²×C₇×C₁₆	1	1	yes	characteristic
57	C₄	C₄×C₅×C₇×C₂₅	1	1	yes	characteristic
58	C₂	C₅×C₇×C₈×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅×C₈	C₂×C₅²×C₇
socle, prime radical	C₂×C₅²×C₇	C₅×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₇×C₁₆×C₂₅	C₅	direct (N × H)
5. C₅×C₁₆×C₂₅	C₇	direct (N × H)
10. C₅×C₇×C₂₅	C₁₆	direct (N × H)
13. C₅×C₇×C₁₆	C₂₅	direct (N × H)
17. C₁₆×C₂₅	C₅×C₇	direct (N × H)
26. C₇×C₂₅	C₅×C₁₆	direct (N × H)
29. C₅×C₂₅	C₇×C₁₆	direct (N × H)
30. C₇×C₁₆	C₅×C₂₅	direct (N × H)
33. C₅×C₁₆	C₇×C₂₅	direct (N × H)
42. C₅×C₇	C₁₆×C₂₅	direct (N × H)
46. C₂₅	C₅×C₇×C₁₆	direct (N × H)
49. C₁₆	C₅×C₇×C₂₅	direct (N × H)
54. C₇	C₅×C₁₆×C₂₅	direct (N × H)
55. C₅	C₇×C₁₆×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
C₅×C₇×C₈×C₂₅	2
C₅²×C₇×C₁₆	5
C₇×C₁₆×C₂₅	5
C₅×C₁₆×C₂₅	7

Subgroups — C5×C7×C16×C25 #72192185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×C₁₆×C₂₅ #72192185