Subgroups — C₂⁵×#10596833 #34032706

Order 18688.

15454 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×#10596833	C₂	1	62	yes	maximal, direct product factor
2	C₂⁵×Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂³×#10596833	C₂²	1	620	yes	direct product factor
4	C₂⁴×Dic₇₃	C₄	1	31	yes	—
5	C₂⁴×Dic₇₃	C₂²	1	31	yes	—
6	C₂⁶×C₇₃	C₄	1	1	yes	characteristic
7	C₂²×#10596833	C₂³	1	1240	yes	direct product factor
8	C₂³×Dic₇₃	C₂×C₄	1	465	yes	—
9	C₂³×Dic₇₃	C₂³	1	155	yes	—
10	C₂⁵×C₇₃	C₈	1	32	yes	complemented
11	C₂⁵×C₇₃	C₂×C₄	1	31	yes	—
12	C₂×#10596833	C₂⁴	1	496	yes	direct product factor
13	C₂²×Dic₇₃	C₂²×C₄	1	1085	yes	—
14	C₂²×Dic₇₃	C₂⁴	1	155	yes	—
15	C₂⁴×C₇₃	C₂×C₈	1	496	yes	complemented
16	C₂⁴×C₇₃	C₂²×C₄	1	155	yes	—
17	C₂³×C₇₃	C₂²×C₈	1	1240	yes	complemented
18	C₂³×C₇₃	C₂³×C₄	1	155	yes	—
19	C₂×Dic₇₃	C₂³×C₄	1	465	yes	—
20	C₂×Dic₇₃	C₂⁵	1	31	yes	—
21	#10596833	C₂⁵	1	32	yes	direct product factor
22	C₂²×C₇₃	C₂³×C₈	1	620	yes	complemented
23	C₂²×C₇₃	C₂⁴×C₄	1	31	yes	—
24	Dic₇₃	C₂⁴×C₄	1	31	yes	—
25	Dic₇₃	C₂⁶	1	1	yes	characteristic
26	C₂⁵×C₈	—	73	1	no	maximal, Sylow
27	C₂×C₇₃	C₂⁴×C₈	1	62	yes	complemented
28	C₂×C₇₃	C₂⁵×C₄	1	1	yes	characteristic
29	C₂⁵×C₄	—	73	1	no	—
30	C₂⁴×C₈	—	73	62	no	—
31	C₇₃	C₂⁵×C₈	1	1	yes	characteristic, complemented, Sylow
32	C₂⁶	#64408	1	1	yes	characteristic
33	C₂⁴×C₄	—	73	31	no	—
34	C₂⁴×C₄	—	73	31	no	—
35	C₂³×C₈	—	73	620	no	—
36	C₂⁵	#10596833	1	32	yes	direct product factor
37	C₂⁵	C₂×#64408	1	31	yes	—
38	C₂³×C₄	—	73	155	no	—
39	C₂³×C₄	—	73	465	no	—
40	C₂²×C₈	—	73	1240	no	—
41	C₂⁴	C₂×#10596833	1	496	yes	direct product factor
42	C₂⁴	C₂²×#64408	1	155	yes	—
43	C₂²×C₄	—	73	1085	no	—
44	C₂²×C₄	—	73	155	no	—
45	C₂×C₈	—	73	496	no	—
46	C₂³	C₂²×#10596833	1	1240	yes	direct product factor
47	C₂³	C₂³×#64408	1	155	yes	—
48	C₂×C₄	—	73	31	no	—
49	C₂×C₄	—	73	465	no	—
50	C₈	—	73	32	no	—
51	C₂²	C₂³×#10596833	1	620	yes	direct product factor
52	C₂²	C₂⁴×#64408	1	31	yes	—
53	C₄	—	73	1	no	—
54	C₄	—	73	31	no	—
55	C₂	C₂⁴×#10596833	1	62	yes	direct product factor
56	C₂	C₂⁵×#64408	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁶	#64408
commutator, hypocenter	C₇₃	C₂⁵×C₈
Frattini	C₂	C₂⁵×#64408
Fitting, socle, prime radical	C₂⁶×C₇₃	C₄
cosocle	Dic₇₃	C₂⁶
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
1. C₂⁴×#10596833	C₂	direct (N × H)
3. C₂³×#10596833	C₂²	direct (N × H)
7. C₂²×#10596833	C₂³	direct (N × H)
10. C₂⁵×C₇₃	C₈	semidirect
12. C₂×#10596833	C₂⁴	direct (N × H)
15. C₂⁴×C₇₃	C₂×C₈	semidirect
17. C₂³×C₇₃	C₂²×C₈	semidirect
21. #10596833	C₂⁵	direct (N × H)
22. C₂²×C₇₃	C₂³×C₈	semidirect
27. C₂×C₇₃	C₂⁴×C₈	semidirect
31. C₇₃	C₂⁵×C₈	semidirect
36. C₂⁵	#10596833	direct (N × H)
41. C₂⁴	C₂×#10596833	direct (N × H)
46. C₂³	C₂²×#10596833	direct (N × H)
51. C₂²	C₂³×#10596833	direct (N × H)
55. C₂	C₂⁴×#10596833	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×#10596833	2
C₂⁵×Dic₇₃	2
C₂⁵×C₈	73

Subgroups — C25×#10596833 #34032706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×#10596833 #34032706