Subgroups — C₂⁵×#1057 #16809641

Order 3328.

15454 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×#1057	C₂	1	62	yes	maximal, direct product factor
2	C₂⁵×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂⁶×C₁₃	C₄	1	1	yes	characteristic
4	C₂⁴×Dic₁₃	C₄	1	31	yes	—
5	C₂⁴×Dic₁₃	C₂²	1	31	yes	—
6	C₂³×#1057	C₂²	1	620	yes	direct product factor
7	C₂⁵×C₁₃	C₈	1	32	yes	complemented
8	C₂⁵×C₁₃	C₂×C₄	1	31	yes	—
9	C₂³×Dic₁₃	C₂×C₄	1	465	yes	—
10	C₂³×Dic₁₃	C₂³	1	155	yes	—
11	C₂²×#1057	C₂³	1	1240	yes	direct product factor
12	C₂⁵×C₈	—	13	1	no	maximal, Sylow
13	C₂⁴×C₁₃	C₂×C₈	1	496	yes	complemented
14	C₂⁴×C₁₃	C₂²×C₄	1	155	yes	—
15	C₂²×Dic₁₃	C₂²×C₄	1	1085	yes	—
16	C₂²×Dic₁₃	C₂⁴	1	155	yes	—
17	C₂×#1057	C₂⁴	1	496	yes	direct product factor
18	C₂⁵×C₄	—	13	1	no	—
19	C₂⁴×C₈	—	13	62	no	—
20	C₂³×C₁₃	C₂²×C₈	1	1240	yes	complemented
21	C₂³×C₁₃	C₂³×C₄	1	155	yes	—
22	C₂×Dic₁₃	C₂³×C₄	1	465	yes	—
23	C₂×Dic₁₃	C₂⁵	1	31	yes	—
24	#1057	C₂⁵	1	32	yes	direct product factor
25	C₂⁶	#261	1	1	yes	characteristic
26	C₂⁴×C₄	—	13	31	no	—
27	C₂⁴×C₄	—	13	31	no	—
28	C₂³×C₈	—	13	620	no	—
29	C₂²×C₁₃	C₂³×C₈	1	620	yes	complemented
30	C₂²×C₁₃	C₂⁴×C₄	1	31	yes	—
31	Dic₁₃	C₂⁴×C₄	1	31	yes	—
32	Dic₁₃	C₂⁶	1	1	yes	characteristic
33	C₂⁵	#1057	1	32	yes	direct product factor
34	C₂⁵	C₂×#261	1	31	yes	—
35	C₂³×C₄	—	13	155	no	—
36	C₂³×C₄	—	13	465	no	—
37	C₂²×C₈	—	13	1240	no	—
38	C₂×C₁₃	C₂⁴×C₈	1	62	yes	complemented
39	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
40	C₂⁴	C₂×#1057	1	496	yes	direct product factor
41	C₂⁴	C₂²×#261	1	155	yes	—
42	C₂²×C₄	—	13	155	no	—
43	C₂²×C₄	—	13	1085	no	—
44	C₂×C₈	—	13	496	no	—
45	C₁₃	C₂⁵×C₈	1	1	yes	characteristic, complemented, Sylow
46	C₂³	C₂²×#1057	1	1240	yes	direct product factor
47	C₂³	C₂³×#261	1	155	yes	—
48	C₂×C₄	—	13	31	no	—
49	C₂×C₄	—	13	465	no	—
50	C₈	—	13	32	no	—
51	C₂²	C₂³×#1057	1	620	yes	direct product factor
52	C₂²	C₂⁴×#261	1	31	yes	—
53	C₄	—	13	31	no	—
54	C₄	—	13	1	no	—
55	C₂	C₂⁴×#1057	1	62	yes	direct product factor
56	C₂	C₂⁵×#261	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁶	#261
commutator, hypocenter	C₁₃	C₂⁵×C₈
Frattini	C₂	C₂⁵×#261
Fitting, socle, prime radical	C₂⁶×C₁₃	C₄
cosocle	Dic₁₃	C₂⁶
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
1. C₂⁴×#1057	C₂	direct (N × H)
6. C₂³×#1057	C₂²	direct (N × H)
7. C₂⁵×C₁₃	C₈	semidirect
11. C₂²×#1057	C₂³	direct (N × H)
13. C₂⁴×C₁₃	C₂×C₈	semidirect
17. C₂×#1057	C₂⁴	direct (N × H)
20. C₂³×C₁₃	C₂²×C₈	semidirect
24. #1057	C₂⁵	direct (N × H)
29. C₂²×C₁₃	C₂³×C₈	semidirect
33. C₂⁵	#1057	direct (N × H)
38. C₂×C₁₃	C₂⁴×C₈	semidirect
40. C₂⁴	C₂×#1057	direct (N × H)
45. C₁₃	C₂⁵×C₈	semidirect
46. C₂³	C₂²×#1057	direct (N × H)
51. C₂²	C₂³×#1057	direct (N × H)
55. C₂	C₂⁴×#1057	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×#1057	2
C₂⁵×Dic₁₃	2
C₂⁵×C₈	13

Subgroups — C25×#1057 #16809641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×#1057 #16809641