Subgroups — C₂⁵×#10596842 #34035063

Order 18688.

15454 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×#10596842	C₂	1	62	yes	maximal, direct product factor
2	C₂⁵×#64408	C₂	1	1	yes	maximal, characteristic
3	C₂³×#10596842	C₂²	1	620	yes	direct product factor
4	C₂⁴×#64408	C₄	1	31	yes	—
5	C₂⁴×#64408	C₂²	1	31	yes	—
6	C₂⁵×D₇₃	C₄	1	1	yes	characteristic
7	C₂²×#10596842	C₂³	1	1240	yes	direct product factor
8	C₂³×#64408	C₂×C₄	1	465	yes	—
9	C₂³×#64408	C₂³	1	155	yes	—
10	C₂⁴×D₇₃	C₈	1	31	yes	complemented
11	C₂⁴×D₇₃	C₂×C₄	1	31	yes	—
12	C₂⁵×C₇₃	C₈	1	1	yes	characteristic, complemented
13	C₂×#10596842	C₂⁴	1	496	yes	direct product factor
14	C₂²×#64408	C₂²×C₄	1	1085	yes	—
15	C₂²×#64408	C₂⁴	1	155	yes	—
16	C₂³×D₇₃	C₂×C₈	1	465	yes	complemented
17	C₂³×D₇₃	C₂²×C₄	1	155	yes	—
18	C₂⁴×C₇₃	C₂×C₈	1	31	yes	complemented
19	C₂³×C₇₃	C₂²×C₈	1	155	yes	complemented
20	C₂²×D₇₃	C₂²×C₈	1	1085	yes	complemented
21	C₂²×D₇₃	C₂³×C₄	1	155	yes	—
22	C₂×#64408	C₂³×C₄	1	465	yes	—
23	C₂×#64408	C₂⁵	1	31	yes	—
24	#10596842	C₂⁵	1	32	yes	direct product factor
25	C₂²×C₇₃	C₂³×C₈	1	155	yes	complemented
26	C₂×D₇₃	C₂³×C₈	1	465	yes	complemented
27	C₂×D₇₃	C₂⁴×C₄	1	31	yes	—
28	#64408	C₂⁴×C₄	1	31	yes	—
29	#64408	C₂⁶	1	1	yes	characteristic
30	C₂⁵×C₈	—	73	1	no	maximal, Sylow
31	C₂×C₇₃	C₂⁴×C₈	1	31	yes	complemented
32	D₇₃	C₂⁴×C₈	1	31	yes	complemented
33	D₇₃	C₂⁵×C₄	1	1	yes	characteristic
34	C₂⁵×C₄	—	73	1	no	—
35	C₂⁴×C₈	—	73	62	no	—
36	C₇₃	C₂⁵×C₈	1	1	yes	characteristic, complemented, Sylow
37	C₂⁶	—	73	1	no	—
38	C₂⁴×C₄	—	73	31	no	—
39	C₂⁴×C₄	—	73	31	no	—
40	C₂³×C₈	—	73	620	no	—
41	C₂⁵	—	73	31	no	—
42	C₂⁵	—	73	31	no	—
43	C₂⁵	#10596842	1	1	yes	characteristic, direct product factor
44	C₂³×C₄	—	73	465	no	—
45	C₂³×C₄	—	73	155	no	—
46	C₂²×C₈	—	73	1240	no	—
47	C₂⁴	—	73	465	no	—
48	C₂⁴	—	73	155	no	—
49	C₂⁴	C₂×#10596842	1	31	yes	direct product factor
50	C₂²×C₄	—	73	1085	no	—
51	C₂²×C₄	—	73	155	no	—
52	C₂×C₈	—	73	496	no	—
53	C₂³	—	73	155	no	—
54	C₂³	—	73	1085	no	—
55	C₂³	C₂²×#10596842	1	155	yes	direct product factor
56	C₂×C₄	—	73	31	no	—
57	C₂×C₄	—	73	465	no	—
58	C₈	—	73	32	no	—
59	C₂²	—	73	31	no	—
60	C₂²	—	73	465	no	—
61	C₂²	C₂³×#10596842	1	155	yes	direct product factor
62	C₄	—	73	1	no	—
63	C₄	—	73	31	no	—
64	C₂	—	73	1	no	—
65	C₂	—	73	31	no	—
66	C₂	C₂⁴×#10596842	1	31	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁵	#10596842
commutator, hypocenter	C₇₃	C₂⁵×C₈
Frattini	C₁	G
Fitting, socle	C₂⁵×C₇₃	C₈
prime radical	C₂⁵×D₇₃	C₄
cosocle	#64408	C₂⁶
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂⁴×#10596842	C₂	direct (N × H)
3. C₂³×#10596842	C₂²	direct (N × H)
7. C₂²×#10596842	C₂³	direct (N × H)
10. C₂⁴×D₇₃	C₈	semidirect
12. C₂⁵×C₇₃	C₈	semidirect
13. C₂×#10596842	C₂⁴	direct (N × H)
16. C₂³×D₇₃	C₂×C₈	semidirect
18. C₂⁴×C₇₃	C₂×C₈	semidirect
19. C₂³×C₇₃	C₂²×C₈	semidirect
20. C₂²×D₇₃	C₂²×C₈	semidirect
24. #10596842	C₂⁵	direct (N × H)
25. C₂²×C₇₃	C₂³×C₈	semidirect
26. C₂×D₇₃	C₂³×C₈	semidirect
31. C₂×C₇₃	C₂⁴×C₈	semidirect
32. D₇₃	C₂⁴×C₈	semidirect
36. C₇₃	C₂⁵×C₈	semidirect
43. C₂⁵	#10596842	direct (N × H)
49. C₂⁴	C₂×#10596842	direct (N × H)
55. C₂³	C₂²×#10596842	direct (N × H)
61. C₂²	C₂³×#10596842	direct (N × H)
66. C₂	C₂⁴×#10596842	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×#10596842	2
C₂⁵×#64408	2
C₂⁵×C₈	73

Subgroups — C25×#10596842 #34035063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×#10596842 #34035063