Subgroups — C₂⁵×C₄×D₇ #14267670

Order 1792.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×D₇	C₂	1	1	yes	maximal, characteristic
2	C₂⁵×C₄×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂⁵×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁴×C₄×D₇	C₂	1	124	yes	maximal, direct product factor
5	C₂⁶×C₇	C₂²	1	1	yes	characteristic
6	C₂⁵×D₇	C₄	1	64	yes	direct product factor
7	C₂⁵×D₇	C₂²	1	62	yes	—
8	C₂⁴×C₄×C₇	C₂²	1	62	yes	complemented
9	C₂⁴×Dic₇	C₂²	1	62	yes	complemented
10	C₂³×C₄×D₇	C₂²	1	2480	yes	direct product factor
11	C₂⁶×C₄	—	7	1	no	maximal, Sylow
12	C₂⁵×C₇	C₂×C₄	1	32	yes	complemented
13	C₂⁵×C₇	C₂³	1	31	yes	—
14	C₂⁴×D₇	C₂×C₄	1	1984	yes	direct product factor
15	C₂⁴×D₇	C₂³	1	620	yes	—
16	C₂³×C₄×C₇	C₂³	1	620	yes	complemented
17	C₂³×Dic₇	C₂³	1	620	yes	complemented
18	C₂²×C₄×D₇	C₂³	1	9920	yes	direct product factor
19	C₂⁷	—	7	1	no	—
20	C₂⁵×C₄	—	7	1	no	—
21	C₂⁵×C₄	—	7	124	no	—
22	C₂⁵×C₄	D₇	1	1	yes	characteristic, direct product factor
23	C₂⁴×C₇	C₂²×C₄	1	496	yes	complemented
24	C₂⁴×C₇	C₂⁴	1	155	yes	—
25	C₂³×D₇	C₂²×C₄	1	9920	yes	direct product factor
26	C₂³×D₇	C₂⁴	1	1240	yes	—
27	C₂²×C₄×C₇	C₂⁴	1	1240	yes	complemented
28	C₂²×Dic₇	C₂⁴	1	1240	yes	complemented
29	C₂×C₄×D₇	C₂⁴	1	7936	yes	direct product factor
30	C₂⁶	—	7	64	no	—
31	C₂⁶	—	7	62	no	—
32	C₂⁶	C₂×D₇	1	1	yes	characteristic
33	C₂⁴×C₄	—	7	62	no	—
34	C₂⁴×C₄	—	7	2480	no	—
35	C₂⁴×C₄	C₂×D₇	1	62	yes	direct product factor
36	C₂³×C₇	C₂³×C₄	1	1240	yes	complemented
37	C₂³×C₇	C₂⁵	1	155	yes	—
38	C₂²×D₇	C₂³×C₄	1	9920	yes	direct product factor
39	C₂²×D₇	C₂⁵	1	496	yes	—
40	C₂×C₄×C₇	C₂⁵	1	496	yes	complemented
41	C₂×Dic₇	C₂⁵	1	496	yes	complemented
42	C₄×D₇	C₂⁵	1	1024	yes	direct product factor
43	C₂⁵	—	7	1984	no	—
44	C₂⁵	—	7	620	no	—
45	C₂⁵	C₄×D₇	1	32	yes	direct product factor
46	C₂⁵	C₂²×D₇	1	31	yes	—
47	C₂³×C₄	—	7	620	no	—
48	C₂³×C₄	—	7	9920	no	—
49	C₂³×C₄	C₂²×D₇	1	620	yes	direct product factor
50	C₂²×C₇	C₂⁴×C₄	1	620	yes	complemented
51	C₂²×C₇	C₂⁶	1	31	yes	—
52	C₂×D₇	C₂⁴×C₄	1	1984	yes	direct product factor
53	C₂×D₇	C₂⁶	1	32	yes	—
54	C₄×C₇	C₂⁶	1	32	yes	complemented
55	Dic₇	C₂⁶	1	32	yes	complemented
56	C₂⁴	—	7	9920	no	—
57	C₂⁴	—	7	1240	no	—
58	C₂⁴	C₂×C₄×D₇	1	496	yes	direct product factor
59	C₂⁴	C₂³×D₇	1	155	yes	—
60	C₂²×C₄	—	7	1240	no	—
61	C₂²×C₄	—	7	7936	no	—
62	C₂²×C₄	C₂³×D₇	1	1240	yes	direct product factor
63	C₂×C₇	C₂⁵×C₄	1	62	yes	complemented
64	C₂×C₇	C₂⁷	1	1	yes	characteristic
65	D₇	C₂⁵×C₄	1	64	yes	direct product factor
66	C₂³	—	7	496	no	—
67	C₂³	—	7	9920	no	—
68	C₂³	C₂²×C₄×D₇	1	1240	yes	direct product factor
69	C₂³	C₂⁴×D₇	1	155	yes	—
70	C₂×C₄	—	7	496	no	—
71	C₂×C₄	—	7	1024	no	—
72	C₂×C₄	C₂⁴×D₇	1	496	yes	direct product factor
73	C₇	C₂⁶×C₄	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	7	1984	no	—
75	C₂²	—	7	32	no	—
76	C₂²	C₂³×C₄×D₇	1	620	yes	direct product factor
77	C₂²	C₂⁵×D₇	1	31	yes	—
78	C₄	—	7	32	no	—
79	C₄	C₂⁵×D₇	1	32	yes	direct product factor
80	C₂	—	7	64	no	—
81	C₂	C₂⁴×C₄×D₇	1	62	yes	direct product factor
82	C₂	C₂⁶×D₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁵×C₄	D₇
commutator, hypocenter	C₇	C₂⁶×C₄
Frattini	C₂	C₂⁶×D₇
Fitting	C₂⁵×C₄×C₇	C₂
socle	C₂⁶×C₇	C₂²
prime radical	C₂⁶×D₇	C₂
cosocle	C₂×C₇	C₂⁷
LCS	G ▷ C₇
UCS	C₁ ◁ C₂⁵×C₄

Complements

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

N	H ≅ G/N	type
2. C₂⁵×C₄×C₇	C₂	semidirect
3. C₂⁵×Dic₇	C₂	semidirect
4. C₂⁴×C₄×D₇	C₂	direct (N × H)
6. C₂⁵×D₇	C₄	direct (N × H)
8. C₂⁴×C₄×C₇	C₂²	semidirect
9. C₂⁴×Dic₇	C₂²	semidirect
10. C₂³×C₄×D₇	C₂²	direct (N × H)
12. C₂⁵×C₇	C₂×C₄	semidirect
14. C₂⁴×D₇	C₂×C₄	direct (N × H)
16. C₂³×C₄×C₇	C₂³	semidirect
17. C₂³×Dic₇	C₂³	semidirect
18. C₂²×C₄×D₇	C₂³	direct (N × H)
22. C₂⁵×C₄	D₇	direct (N × H)
23. C₂⁴×C₇	C₂²×C₄	semidirect
25. C₂³×D₇	C₂²×C₄	direct (N × H)
27. C₂²×C₄×C₇	C₂⁴	semidirect
28. C₂²×Dic₇	C₂⁴	semidirect
29. C₂×C₄×D₇	C₂⁴	direct (N × H)
35. C₂⁴×C₄	C₂×D₇	direct (N × H)
36. C₂³×C₇	C₂³×C₄	semidirect
38. C₂²×D₇	C₂³×C₄	direct (N × H)
40. C₂×C₄×C₇	C₂⁵	semidirect
41. C₂×Dic₇	C₂⁵	semidirect
42. C₄×D₇	C₂⁵	direct (N × H)
45. C₂⁵	C₄×D₇	direct (N × H)
49. C₂³×C₄	C₂²×D₇	direct (N × H)
50. C₂²×C₇	C₂⁴×C₄	semidirect
52. C₂×D₇	C₂⁴×C₄	direct (N × H)
54. C₄×C₇	C₂⁶	semidirect
55. Dic₇	C₂⁶	semidirect
58. C₂⁴	C₂×C₄×D₇	direct (N × H)
62. C₂²×C₄	C₂³×D₇	direct (N × H)
63. C₂×C₇	C₂⁵×C₄	semidirect
65. D₇	C₂⁵×C₄	direct (N × H)
68. C₂³	C₂²×C₄×D₇	direct (N × H)
72. C₂×C₄	C₂⁴×D₇	direct (N × H)
73. C₇	C₂⁶×C₄	semidirect
76. C₂²	C₂³×C₄×D₇	direct (N × H)
79. C₄	C₂⁵×D₇	direct (N × H)
81. C₂	C₂⁴×C₄×D₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁶×D₇	2
C₂⁵×C₄×C₇	2
C₂⁵×Dic₇	2
C₂⁴×C₄×D₇	2
C₂⁶×C₄	7

Subgroups — C25×C4×D7 #14267670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₄×D₇ #14267670