Subgroups — C₂⁵×D₃₁₆ #35202147

Order 20224.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×D₇₉	C₂	1	2	yes	maximal, complemented
2	C₂⁴×D₃₁₆	C₂	1	124	yes	maximal, direct product factor
3	C₂⁵×C₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁵×D₇₉	—	2	64	no	—
5	C₂⁵×D₇₉	C₂²	1	124	yes	complemented
6	C₂³×D₃₁₆	C₂²	1	2480	yes	direct product factor
7	C₂⁶×C₇₉	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₇₉	C₂²	1	62	yes	complemented
9	C₂⁴×D₇₉	—	2	1984	no	—
10	C₂⁴×D₇₉	C₂³	1	1240	yes	complemented
11	C₂²×D₃₁₆	C₂³	1	9920	yes	direct product factor
12	C₂⁵×C₇₉	D₄	1	32	yes	complemented
13	C₂⁵×C₇₉	C₂³	1	31	yes	—
14	C₂³×C₄×C₇₉	C₂³	1	620	yes	complemented
15	C₂³×D₇₉	—	2	9920	no	—
16	C₂³×D₇₉	C₂⁴	1	2480	yes	complemented
17	C₂×D₃₁₆	C₂⁴	1	7936	yes	direct product factor
18	C₂⁴×C₇₉	C₂×D₄	1	496	yes	complemented
19	C₂⁴×C₇₉	C₂⁴	1	155	yes	—
20	C₂²×C₄×C₇₉	C₂⁴	1	1240	yes	complemented
21	C₂³×C₇₉	C₂²×D₄	1	1240	yes	complemented
22	C₂³×C₇₉	C₂⁵	1	155	yes	—
23	C₂²×D₇₉	—	2	9920	no	—
24	C₂²×D₇₉	C₂⁵	1	992	yes	complemented
25	C₂×C₄×C₇₉	C₂⁵	1	496	yes	complemented
26	D₃₁₆	C₂⁵	1	1024	yes	direct product factor
27	C₂²×C₇₉	C₂³×D₄	1	620	yes	complemented
28	C₂²×C₇₉	C₂⁶	1	31	yes	—
29	C₂×D₇₉	—	2	1984	no	—
30	C₂×D₇₉	C₂⁶	1	64	yes	complemented
31	C₄×C₇₉	C₂⁶	1	32	yes	complemented
32	C₂⁵×D₄	—	79	1	no	maximal, Sylow
33	C₂×C₇₉	C₂⁴×D₄	1	62	yes	complemented
34	C₂×C₇₉	C₂⁷	1	1	yes	characteristic
35	D₇₉	—	2	64	no	—
36	C₂⁷	—	79	2	no	—
37	C₂⁴×D₄	—	79	124	no	—
38	C₂⁵×C₄	D₇₉	1	1	yes	characteristic, complemented
39	C₇₉	C₂⁵×D₄	1	1	yes	characteristic, complemented, Sylow
40	C₂⁶	—	79	124	no	—
41	C₂⁶	—	158	64	no	—
42	C₂⁶	C₂×D₇₉	1	1	yes	characteristic
43	C₂³×D₄	—	79	2480	no	—
44	C₂⁴×C₄	C₂×D₇₉	1	62	yes	complemented
45	C₂⁵	—	79	1240	no	—
46	C₂⁵	—	158	1984	no	—
47	C₂⁵	D₃₁₆	1	32	yes	direct product factor
48	C₂⁵	C₂²×D₇₉	1	31	yes	—
49	C₂²×D₄	—	79	9920	no	—
50	C₂³×C₄	C₂²×D₇₉	1	620	yes	complemented
51	C₂⁴	—	79	2480	no	—
52	C₂⁴	—	158	9920	no	—
53	C₂⁴	C₂×D₃₁₆	1	496	yes	direct product factor
54	C₂⁴	C₂³×D₇₉	1	155	yes	—
55	C₂×D₄	—	79	7936	no	—
56	C₂²×C₄	C₂³×D₇₉	1	1240	yes	complemented
57	C₂³	—	79	992	no	—
58	C₂³	—	158	9920	no	—
59	C₂³	C₂²×D₃₁₆	1	1240	yes	direct product factor
60	C₂³	C₂⁴×D₇₉	1	155	yes	—
61	D₄	—	79	1024	no	—
62	C₂×C₄	C₂⁴×D₇₉	1	496	yes	complemented
63	C₂²	—	79	64	no	—
64	C₂²	—	158	1984	no	—
65	C₂²	C₂³×D₃₁₆	1	620	yes	direct product factor
66	C₂²	C₂⁵×D₇₉	1	31	yes	—
67	C₄	C₂⁵×D₇₉	1	32	yes	complemented
68	C₂	—	158	64	no	—
69	C₂	C₂⁴×D₃₁₆	1	62	yes	direct product factor
70	C₂	C₂⁶×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁶	C₂×D₇₉
commutator, cosocle	C₂×C₇₉	C₂⁷
Frattini	C₂	C₂⁶×D₇₉
Fitting	C₂⁵×C₄×C₇₉	C₂
socle	C₂⁶×C₇₉	C₂²
hypercenter	C₂⁵×C₄	D₇₉
hypocenter	C₇₉	C₂⁵×D₄
LCS	G ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁶ ◁ C₂⁵×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁶×D₇₉	C₂	semidirect
2. C₂⁴×D₃₁₆	C₂	direct (N × H)
3. C₂⁵×C₄×C₇₉	C₂	semidirect
5. C₂⁵×D₇₉	C₂²	semidirect
6. C₂³×D₃₁₆	C₂²	direct (N × H)
8. C₂⁴×C₄×C₇₉	C₂²	semidirect
10. C₂⁴×D₇₉	C₂³	semidirect
11. C₂²×D₃₁₆	C₂³	direct (N × H)
12. C₂⁵×C₇₉	D₄	semidirect
14. C₂³×C₄×C₇₉	C₂³	semidirect
16. C₂³×D₇₉	C₂⁴	semidirect
17. C₂×D₃₁₆	C₂⁴	direct (N × H)
18. C₂⁴×C₇₉	C₂×D₄	semidirect
20. C₂²×C₄×C₇₉	C₂⁴	semidirect
21. C₂³×C₇₉	C₂²×D₄	semidirect
24. C₂²×D₇₉	C₂⁵	semidirect
25. C₂×C₄×C₇₉	C₂⁵	semidirect
26. D₃₁₆	C₂⁵	direct (N × H)
27. C₂²×C₇₉	C₂³×D₄	semidirect
30. C₂×D₇₉	C₂⁶	semidirect
31. C₄×C₇₉	C₂⁶	semidirect
33. C₂×C₇₉	C₂⁴×D₄	semidirect
38. C₂⁵×C₄	D₇₉	semidirect
39. C₇₉	C₂⁵×D₄	semidirect
44. C₂⁴×C₄	C₂×D₇₉	semidirect
47. C₂⁵	D₃₁₆	direct (N × H)
50. C₂³×C₄	C₂²×D₇₉	semidirect
53. C₂⁴	C₂×D₃₁₆	direct (N × H)
56. C₂²×C₄	C₂³×D₇₉	semidirect
59. C₂³	C₂²×D₃₁₆	direct (N × H)
62. C₂×C₄	C₂⁴×D₇₉	semidirect
65. C₂²	C₂³×D₃₁₆	direct (N × H)
67. C₄	C₂⁵×D₇₉	semidirect
69. C₂	C₂⁴×D₃₁₆	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×D₇₉	2
C₂⁴×D₃₁₆	2
C₂⁵×C₄×C₇₉	2
C₂⁵×D₄	79

Subgroups — C25×D316 #35202147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×D₃₁₆ #35202147