Subgroups — C₈²×C₁₉×C₂₅ #72207192

Order 30400.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×C₁₉×C₂₅	C₂	1	3	yes	maximal
2	C₄²×C₁₉×C₂₅	C₂²	1	1	yes	characteristic
3	C₂×C₈×C₁₉×C₂₅	C₄	1	6	yes	—
4	C₅×C₈²×C₁₉	C₅	1	1	yes	maximal, characteristic
5	C₂×C₄×C₁₉×C₂₅	C₂×C₄	1	3	yes	—
6	C₈×C₁₉×C₂₅	C₈	1	12	yes	direct product factor
7	C₄×C₅×C₈×C₁₉	C₂×C₅	1	3	yes	—
8	C₂²×C₁₉×C₂₅	C₄²	1	1	yes	characteristic
9	C₄×C₁₉×C₂₅	C₂×C₈	1	6	yes	—
10	C₈²×C₂₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₅×C₈×C₁₉	C₄×C₅	1	6	yes	—
12	C₄²×C₅×C₁₉	C₂²×C₅	1	1	yes	characteristic
13	C₈²×C₁₉	C₂₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₁₉×C₂₅	C₄×C₈	1	3	yes	—
15	C₄×C₈×C₂₅	C₂×C₁₉	1	3	yes	—
16	C₂×C₄×C₅×C₁₉	C₂×C₄×C₅	1	3	yes	—
17	C₅×C₈×C₁₉	C₅×C₈	1	12	yes	—
18	C₄×C₈×C₁₉	C₂×C₂₅	1	3	yes	—
19	C₁₉×C₂₅	C₈²	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₈×C₂₅	C₄×C₁₉	1	6	yes	—
21	C₄²×C₂₅	C₂²×C₁₉	1	1	yes	characteristic
22	C₂²×C₅×C₁₉	C₄²×C₅	1	1	yes	characteristic
23	C₄×C₅×C₁₉	C₂×C₅×C₈	1	6	yes	—
24	C₅×C₈²	C₅×C₁₉	1	1	yes	characteristic
25	C₂×C₈×C₁₉	C₄×C₂₅	1	6	yes	—
26	C₄²×C₁₉	C₂²×C₂₅	1	1	yes	characteristic
27	C₂×C₄×C₂₅	C₂×C₄×C₁₉	1	3	yes	—
28	C₈×C₂₅	C₈×C₁₉	1	12	yes	direct product factor
29	C₂×C₅×C₁₉	C₄×C₅×C₈	1	3	yes	—
30	C₄×C₅×C₈	C₂×C₅×C₁₉	1	3	yes	—
31	C₂×C₄×C₁₉	C₂×C₄×C₂₅	1	3	yes	—
32	C₈×C₁₉	C₈×C₂₅	1	12	yes	direct product factor
33	C₂²×C₂₅	C₄²×C₁₉	1	1	yes	characteristic
34	C₄×C₂₅	C₂×C₈×C₁₉	1	6	yes	—
35	C₅×C₁₉	C₅×C₈²	1	1	yes	characteristic
36	C₂×C₅×C₈	C₄×C₅×C₁₉	1	6	yes	—
37	C₄²×C₅	C₂²×C₅×C₁₉	1	1	yes	characteristic
38	C₂²×C₁₉	C₄²×C₂₅	1	1	yes	characteristic
39	C₄×C₁₉	C₂×C₈×C₂₅	1	6	yes	—
40	C₈²	C₁₉×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₂₅	C₄×C₈×C₁₉	1	3	yes	—
42	C₂×C₄×C₅	C₂×C₄×C₅×C₁₉	1	3	yes	—
43	C₅×C₈	C₅×C₈×C₁₉	1	12	yes	—
44	C₂×C₁₉	C₄×C₈×C₂₅	1	3	yes	—
45	C₄×C₈	C₂×C₁₉×C₂₅	1	3	yes	—
46	C₂₅	C₈²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
47	C₂²×C₅	C₄²×C₅×C₁₉	1	1	yes	characteristic
48	C₄×C₅	C₂×C₅×C₈×C₁₉	1	6	yes	—
49	C₁₉	C₈²×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₈	C₄×C₁₉×C₂₅	1	6	yes	—
51	C₄²	C₂²×C₁₉×C₂₅	1	1	yes	characteristic
52	C₂×C₅	C₄×C₅×C₈×C₁₉	1	3	yes	—
53	C₂×C₄	C₂×C₄×C₁₉×C₂₅	1	3	yes	—
54	C₈	C₈×C₁₉×C₂₅	1	12	yes	direct product factor
55	C₅	C₅×C₈²×C₁₉	1	1	yes	characteristic
56	C₂²	C₄²×C₁₉×C₂₅	1	1	yes	characteristic
57	C₄	C₂×C₈×C₁₉×C₂₅	1	6	yes	—
58	C₂	C₄×C₈×C₁₉×C₂₅	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄²×C₅	C₂²×C₅×C₁₉
socle, prime radical	C₂²×C₅×C₁₉	C₄²×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₈×C₁₉×C₂₅	C₈	direct (N × H)
10. C₈²×C₂₅	C₁₉	direct (N × H)
13. C₈²×C₁₉	C₂₅	direct (N × H)
19. C₁₉×C₂₅	C₈²	direct (N × H)
28. C₈×C₂₅	C₈×C₁₉	direct (N × H)
32. C₈×C₁₉	C₈×C₂₅	direct (N × H)
40. C₈²	C₁₉×C₂₅	direct (N × H)
46. C₂₅	C₈²×C₁₉	direct (N × H)
49. C₁₉	C₈²×C₂₅	direct (N × H)
54. C₈	C₈×C₁₉×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
C₄×C₈×C₁₉×C₂₅	2
C₅×C₈²×C₁₉	5
C₈²×C₂₅	19

Subgroups — C82×C19×C25 #72207192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈²×C₁₉×C₂₅ #72207192