Subgroups — C₂⁶×Dic₇₉ #35202144

Order 20224.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×Dic₇₉	C₂	1	126	yes	maximal, direct product factor
2	C₂⁷×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₂⁴×Dic₇₉	C₂²	1	2604	yes	direct product factor
4	C₂⁶×C₇₉	C₄	1	64	yes	complemented
5	C₂⁶×C₇₉	C₂²	1	63	yes	—
6	C₂³×Dic₇₉	C₂³	1	11160	yes	direct product factor
7	C₂⁵×C₇₉	C₂×C₄	1	2016	yes	complemented
8	C₂⁵×C₇₉	C₂³	1	651	yes	—
9	C₂²×Dic₇₉	C₂⁴	1	10416	yes	direct product factor
10	C₂⁴×C₇₉	C₂²×C₄	1	10416	yes	complemented
11	C₂⁴×C₇₉	C₂⁴	1	1395	yes	—
12	C₂³×C₇₉	C₂³×C₄	1	11160	yes	complemented
13	C₂³×C₇₉	C₂⁵	1	651	yes	—
14	C₂×Dic₇₉	C₂⁵	1	2016	yes	direct product factor
15	C₂²×C₇₉	C₂⁴×C₄	1	2604	yes	complemented
16	C₂²×C₇₉	C₂⁶	1	63	yes	—
17	Dic₇₉	C₂⁶	1	64	yes	direct product factor
18	C₂⁶×C₄	—	79	1	no	maximal, Sylow
19	C₂×C₇₉	C₂⁵×C₄	1	126	yes	complemented
20	C₂×C₇₉	C₂⁷	1	1	yes	characteristic
21	C₂⁷	D₇₉	1	1	yes	characteristic
22	C₂⁵×C₄	—	79	126	no	—
23	C₇₉	C₂⁶×C₄	1	1	yes	characteristic, complemented, Sylow
24	C₂⁶	Dic₇₉	1	64	yes	direct product factor
25	C₂⁶	C₂×D₇₉	1	63	yes	—
26	C₂⁴×C₄	—	79	2604	no	—
27	C₂⁵	C₂×Dic₇₉	1	2016	yes	direct product factor
28	C₂⁵	C₂²×D₇₉	1	651	yes	—
29	C₂³×C₄	—	79	11160	no	—
30	C₂⁴	C₂²×Dic₇₉	1	10416	yes	direct product factor
31	C₂⁴	C₂³×D₇₉	1	1395	yes	—
32	C₂²×C₄	—	79	10416	no	—
33	C₂³	C₂³×Dic₇₉	1	11160	yes	direct product factor
34	C₂³	C₂⁴×D₇₉	1	651	yes	—
35	C₂×C₄	—	79	2016	no	—
36	C₂²	C₂⁴×Dic₇₉	1	2604	yes	direct product factor
37	C₂²	C₂⁵×D₇₉	1	63	yes	—
38	C₄	—	79	64	no	—
39	C₂	C₂⁵×Dic₇₉	1	126	yes	direct product factor
40	C₂	C₂⁶×D₇₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂⁵×Dic₇₉	C₂	direct (N × H)
3. C₂⁴×Dic₇₉	C₂²	direct (N × H)
4. C₂⁶×C₇₉	C₄	semidirect
6. C₂³×Dic₇₉	C₂³	direct (N × H)
7. C₂⁵×C₇₉	C₂×C₄	semidirect
9. C₂²×Dic₇₉	C₂⁴	direct (N × H)
10. C₂⁴×C₇₉	C₂²×C₄	semidirect
12. C₂³×C₇₉	C₂³×C₄	semidirect
14. C₂×Dic₇₉	C₂⁵	direct (N × H)
15. C₂²×C₇₉	C₂⁴×C₄	semidirect
17. Dic₇₉	C₂⁶	direct (N × H)
19. C₂×C₇₉	C₂⁵×C₄	semidirect
23. C₇₉	C₂⁶×C₄	semidirect
24. C₂⁶	Dic₇₉	direct (N × H)
27. C₂⁵	C₂×Dic₇₉	direct (N × H)
30. C₂⁴	C₂²×Dic₇₉	direct (N × H)
33. C₂³	C₂³×Dic₇₉	direct (N × H)
36. C₂²	C₂⁴×Dic₇₉	direct (N × H)
39. C₂	C₂⁵×Dic₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×Dic₇₉	2
C₂⁷×C₇₉	2
C₂⁶×C₄	79

Subgroups — C26×Dic79 #35202144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×Dic₇₉ #35202144