Subgroups — C₃×C₇×C₂₅×Dic₇ #28412913

Order 14700.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇²×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₇×C₂₅×Dic₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇²×C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅×C₇×Dic₇	C₅	1	1	yes	maximal, characteristic
5	C₂×C₇²×C₂₅	C₂×C₃	1	1	yes	characteristic
6	C₃×C₂₅×Dic₇	C₇	1	1	yes	maximal, characteristic, direct product factor
7	C₃×C₄×C₇×C₂₅	—	7	1	no	maximal
8	C₂×C₃×C₅×C₇²	C₂×C₅	1	1	yes	characteristic
9	C₇²×C₂₅	C₃×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₇×C₂₅	—	2	3	no	—
11	C₂×C₃×C₇×C₂₅	D₇	1	1	yes	characteristic
12	C₂×C₃×C₇×C₂₅	C₂×C₇	1	1	yes	characteristic
13	C₅×C₇×Dic₇	C₃×C₅	1	1	yes	characteristic
14	C₃×C₅×C₇²	C₄×C₅	1	1	yes	characteristic
15	C₄×C₇×C₂₅	—	7	1	no	—
16	C₂₅×Dic₇	C₃×C₇	1	1	yes	characteristic, direct product factor
17	C₃×C₇×Dic₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₇×C₂₅	—	2	3	no	—
19	C₃×C₇×C₂₅	Dic₇	1	1	yes	characteristic, direct product factor
20	C₃×C₇×C₂₅	C₄×C₇	1	1	yes	characteristic, complemented
21	C₂×C₅×C₇²	C₂×C₃×C₅	1	1	yes	characteristic
22	C₃×C₄×C₅×C₇	—	7	1	no	—
23	C₃×C₅×Dic₇	C₅×C₇	1	1	yes	characteristic
24	C₂×C₇×C₂₅	—	2	3	no	—
25	C₂×C₇×C₂₅	C₃×D₇	1	1	yes	characteristic
26	C₂×C₇×C₂₅	C₂×C₃×C₇	1	1	yes	characteristic
27	C₃×C₄×C₂₅	—	7	1	no	Hall
28	C₂×C₃×C₇²	C₂×C₂₅	1	1	yes	characteristic
29	C₅×C₇²	C₃×C₄×C₅	1	1	yes	characteristic
30	C₂×C₃×C₅×C₇	—	2	3	no	—
31	C₂×C₃×C₅×C₇	C₅×D₇	1	1	yes	characteristic
32	C₂×C₃×C₅×C₇	C₂×C₅×C₇	1	1	yes	characteristic
33	C₇×Dic₇	C₃×C₂₅	1	1	yes	characteristic, direct product factor, Hall
34	C₇×C₂₅	—	2	3	no	—
35	C₇×C₂₅	C₃×Dic₇	1	1	yes	characteristic, direct product factor
36	C₇×C₂₅	C₃×C₄×C₇	1	1	yes	characteristic, complemented
37	C₂×C₃×C₂₅	C₇×D₇	1	1	yes	characteristic
38	C₃×C₇²	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
39	C₄×C₅×C₇	—	7	1	no	—
40	C₅×Dic₇	C₃×C₅×C₇	1	1	yes	characteristic
41	C₃×C₅×C₇	—	2	3	no	—
42	C₃×C₅×C₇	C₅×Dic₇	1	1	yes	characteristic
43	C₃×C₅×C₇	C₄×C₅×C₇	1	1	yes	characteristic
44	C₄×C₂₅	—	7	1	no	Hall
45	C₂×C₇²	C₂×C₃×C₂₅	1	1	yes	characteristic
46	C₃×C₄×C₇	—	7	1	no	—
47	C₃×Dic₇	C₇×C₂₅	1	1	yes	characteristic, direct product factor
48	C₃×C₂₅	C₇×Dic₇	1	1	yes	characteristic, direct product factor, Hall
49	C₂×C₅×C₇	—	2	3	no	—
50	C₂×C₅×C₇	C₃×C₅×D₇	1	1	yes	characteristic
51	C₂×C₅×C₇	C₂×C₃×C₅×C₇	1	1	yes	characteristic
52	C₃×C₄×C₅	—	7	1	no	—
53	C₂×C₂₅	C₃×C₇×D₇	1	1	yes	characteristic
54	C₇²	C₃×C₄×C₂₅	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃×C₇	—	2	3	no	—
56	C₂×C₃×C₇	D₇×C₂₅	1	1	yes	characteristic
57	C₂×C₃×C₇	C₂×C₇×C₂₅	1	1	yes	characteristic
58	C₅×C₇	—	2	3	no	—
59	C₅×C₇	C₃×C₅×Dic₇	1	1	yes	characteristic
60	C₅×C₇	C₃×C₄×C₅×C₇	1	1	yes	characteristic
61	C₂×C₃×C₅	C₅×C₇×D₇	1	1	yes	characteristic
62	C₄×C₇	—	7	1	no	—
63	Dic₇	C₃×C₇×C₂₅	1	1	yes	characteristic, direct product factor
64	C₂₅	C₃×C₇×Dic₇	1	1	yes	characteristic, direct product factor, Sylow
65	C₃×C₇	—	2	3	no	—
66	C₃×C₇	C₂₅×Dic₇	1	1	yes	characteristic, direct product factor
67	C₃×C₇	C₄×C₇×C₂₅	1	1	yes	characteristic, complemented
68	C₄×C₅	—	7	1	no	—
69	C₃×C₅	C₅×C₇×Dic₇	1	1	yes	characteristic
70	C₂×C₇	—	2	3	no	—
71	C₂×C₇	C₃×D₇×C₂₅	1	1	yes	characteristic
72	C₂×C₇	C₂×C₃×C₇×C₂₅	1	1	yes	characteristic
73	C₃×C₄	—	7	1	no	Hall
74	C₂×C₅	C₃×C₅×C₇×D₇	1	1	yes	characteristic
75	C₇	—	2	3	no	—
76	C₇	C₃×C₄×C₇×C₂₅	1	1	yes	characteristic, complemented
77	C₇	C₃×C₂₅×Dic₇	1	1	yes	characteristic, direct product factor
78	C₂×C₃	C₇×D₇×C₂₅	1	1	yes	characteristic
79	C₅	C₃×C₅×C₇×Dic₇	1	1	yes	characteristic
80	C₄	—	7	1	no	Sylow
81	C₃	C₇×C₂₅×Dic₇	1	1	yes	characteristic, direct product factor, Sylow
82	C₂	C₃×C₇×D₇×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₂₅	D₇
commutator, hypocenter	C₇	C₃×C₄×C₇×C₂₅
Frattini	C₂×C₅	C₃×C₅×C₇×D₇
Fitting	C₂×C₃×C₇²×C₂₅	C₂
socle, prime radical	C₂×C₃×C₅×C₇²	C₂×C₅
cosocle	C₂×C₅×C₇	C₂×C₃×C₅×C₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₇×C₂₅

Complements

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

N	H ≅ G/N	type
2. C₇×C₂₅×Dic₇	C₃	direct (N × H)
3. C₃×C₇²×C₂₅	C₄	semidirect
6. C₃×C₂₅×Dic₇	C₇	direct (N × H)
9. C₇²×C₂₅	C₃×C₄	semidirect
16. C₂₅×Dic₇	C₃×C₇	direct (N × H)
17. C₃×C₇×Dic₇	C₂₅	direct (N × H)
19. C₃×C₇×C₂₅	Dic₇	direct (N × H)
20. C₃×C₇×C₂₅	C₄×C₇	semidirect
33. C₇×Dic₇	C₃×C₂₅	direct (N × H)
35. C₇×C₂₅	C₃×Dic₇	direct (N × H)
36. C₇×C₂₅	C₃×C₄×C₇	semidirect
38. C₃×C₇²	C₄×C₂₅	semidirect
47. C₃×Dic₇	C₇×C₂₅	direct (N × H)
48. C₃×C₂₅	C₇×Dic₇	direct (N × H)
54. C₇²	C₃×C₄×C₂₅	semidirect
63. Dic₇	C₃×C₇×C₂₅	direct (N × H)
64. C₂₅	C₃×C₇×Dic₇	direct (N × H)
66. C₃×C₇	C₂₅×Dic₇	direct (N × H)
67. C₃×C₇	C₄×C₇×C₂₅	semidirect
76. C₇	C₃×C₄×C₇×C₂₅	semidirect
77. C₇	C₃×C₂₅×Dic₇	direct (N × H)
81. C₃	C₇×C₂₅×Dic₇	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×C₃×C₇²×C₂₅	2
C₇×C₂₅×Dic₇	3
C₃×C₅×C₇×Dic₇	5
C₃×C₂₅×Dic₇	7
C₃×C₄×C₇×C₂₅	7

Subgroups — C3×C7×C25×Dic7 #28412913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₂₅×Dic₇ #28412913