Subgroups — D₂₅×D₂₆₁ #39907792

Order 26100.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₅₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₅×D₂₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₂₉×D₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₅×D₈₇	—	3	1	no	maximal
5	C₉×C₂₅×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₅×D₂₆₁	—	5	1	no	maximal
7	D₂₁₇₅	—	3	1	no	—
8	C₂₅×D₈₇	—	3	1	no	—
9	C₃×C₂₉×D₂₅	D₃	1	1	yes	characteristic
10	D₂₅×D₂₉	—	9	1	no	Hall
11	D₁₃₀₅	—	5	1	no	—
12	C₅×D₂₆₁	D₅	1	1	yes	characteristic
13	C₉×D₅×C₂₉	—	5	1	no	—
14	C₃×C₂₅×C₂₉	C₂×D₃	1	1	yes	characteristic
15	D₅×D₈₇	—	15	1	no	—
16	D₇₂₅	—	9	1	no	—
17	C₂₅×D₂₉	—	9	1	no	—
18	C₂₉×D₂₅	D₉	1	1	yes	characteristic, complemented
19	C₅×C₉×C₂₉	C₂×D₅	1	1	yes	characteristic
20	C₂×D₂₆₁	—	25	1	no	Hall
21	D₉×D₂₅	—	29	1	no	maximal, Hall
22	D₄₃₅	—	15	1	no	—
23	C₅×D₈₇	—	3	1	no	—
24	C₃×D₅×C₂₉	—	5	1	no	—
25	C₂₅×C₂₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
26	D₅×D₂₉	—	45	1	no	—
27	C₂×C₉×C₂₉	—	25	1	no	—
28	D₂₆₁	—	25	1	no	—
29	D₂₆₁	D₂₅	1	1	yes	characteristic, direct product factor
30	D₂₂₅	—	29	1	no	—
31	C₉×D₂₅	D₂₉	1	1	yes	characteristic, complemented
32	D₉×C₂₅	—	29	1	no	—
33	C₃×C₅×C₂₉	D₃×D₅	1	1	yes	characteristic
34	C₂×D₈₇	—	75	1	no	—
35	D₃×D₂₅	—	87	1	no	—
36	D₁₄₅	—	45	1	no	—
37	C₅×D₂₉	—	9	1	no	—
38	D₅×C₂₉	—	5	1	no	—
39	C₉×C₂₉	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
40	C₉×C₂₅	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
41	D₅×D₉	—	145	1	no	—
42	C₂×C₃×C₂₉	—	25	1	no	—
43	D₈₇	—	3	1	no	—
44	D₈₇	—	75	1	no	—
45	D₇₅	—	87	1	no	—
46	C₃×D₂₅	D₈₇	1	1	yes	characteristic
47	D₃×C₂₅	—	87	1	no	—
48	C₅×C₂₉	D₅×D₉	1	1	yes	characteristic
49	C₂×D₂₉	—	225	1	no	Hall
50	C₂×D₂₅	—	261	1	no	Hall
51	D₄₅	—	145	1	no	—
52	C₉×D₅	—	5	1	no	—
53	C₅×D₉	—	29	1	no	—
54	C₃×C₂₉	D₃×D₂₅	1	1	yes	characteristic
55	C₃×C₂₅	C₂×D₈₇	1	1	yes	characteristic
56	D₃×D₅	—	435	1	no	—
57	C₂×C₂₉	—	25	1	no	—
58	D₂₉	—	9	1	no	—
59	D₂₉	—	225	1	no	—
60	C₂×C₂₅	—	261	1	no	—
61	D₂₅	—	261	1	no	—
62	D₂₅	D₂₆₁	1	1	yes	characteristic, direct product factor
63	C₅×C₉	D₅×D₂₉	1	1	yes	characteristic
64	C₂×D₉	—	725	1	no	Hall
65	D₁₅	—	435	1	no	—
66	C₃×D₅	—	5	1	no	—
67	C₅×D₃	—	87	1	no	—
68	C₂₉	D₉×D₂₅	1	1	yes	characteristic, complemented, Sylow
69	C₂₅	C₂×D₂₆₁	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₅	—	1305	1	no	—
71	C₂×C₉	—	25	1	no	—
72	D₉	—	29	1	no	—
73	D₉	—	725	1	no	—
74	C₃×C₅	D₅×D₈₇	1	1	yes	characteristic
75	C₂×D₃	—	2175	1	no	—
76	C₂×C₅	—	261	1	no	—
77	D₅	—	5	1	no	—
78	D₅	—	1305	1	no	—
79	C₉	D₂₅×D₂₉	1	1	yes	characteristic, complemented, Sylow
80	C₂×C₃	—	25	1	no	—
81	D₃	—	87	1	no	—
82	D₃	—	2175	1	no	—
83	C₅	D₅×D₂₆₁	1	1	yes	characteristic
84	C₂²	—	6525	1	no	Sylow
85	C₃	D₂₅×D₈₇	1	1	yes	characteristic
86	C₂	—	261	1	no	—
87	C₂	—	25	1	no	—
88	C₂	—	6525	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₂₅×C₂₉	C₂²
Frattini	C₃×C₅	D₅×D₈₇
socle	C₃×C₅×C₂₉	D₃×D₅
LCS	G ▷ C₉×C₂₅×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₆₅₂₅	C₂	semidirect
2. C₂₅×D₂₆₁	C₂	semidirect
3. C₉×C₂₉×D₂₅	C₂	semidirect
5. C₉×C₂₅×C₂₉	C₂²	semidirect
18. C₂₉×D₂₅	D₉	semidirect
25. C₂₅×C₂₉	C₂×D₉	semidirect
29. D₂₆₁	D₂₅	direct (N × H)
31. C₉×D₂₅	D₂₉	semidirect
39. C₉×C₂₉	C₂×D₂₅	semidirect
40. C₉×C₂₅	C₂×D₂₉	semidirect
62. D₂₅	D₂₆₁	direct (N × H)
68. C₂₉	D₉×D₂₅	semidirect
69. C₂₅	C₂×D₂₆₁	semidirect
79. C₉	D₂₅×D₂₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₆₅₂₅	2
C₂₅×D₂₆₁	2
C₉×C₂₉×D₂₅	2
D₂₅×D₈₇	3
D₅×D₂₆₁	5
D₉×D₂₅	29

Subgroups — D25×D261 #39907792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₅×D₂₆₁ #39907792