Subgroups — C₂⁵×C₁₆×C₄₁ #72198577

Order 20992.

20356 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₁₆×C₄₁	C₂	1	62	yes	maximal, direct product factor
3	C₂⁵×C₄×C₄₁	C₄	1	1	yes	characteristic
4	C₂⁴×C₈×C₄₁	C₄	1	31	yes	—
5	C₂⁴×C₈×C₄₁	C₂²	1	31	yes	—
6	C₂³×C₁₆×C₄₁	C₂²	1	620	yes	direct product factor
7	C₂⁶×C₄₁	C₈	1	1	yes	characteristic
8	C₂⁴×C₄×C₄₁	C₈	1	31	yes	—
9	C₂⁴×C₄×C₄₁	C₂×C₄	1	31	yes	—
10	C₂³×C₈×C₄₁	C₂×C₄	1	465	yes	—
11	C₂³×C₈×C₄₁	C₂³	1	155	yes	—
12	C₂²×C₁₆×C₄₁	C₂³	1	1240	yes	direct product factor
13	C₂⁵×C₄₁	C₁₆	1	32	yes	direct product factor
14	C₂⁵×C₄₁	C₂×C₈	1	31	yes	—
15	C₂³×C₄×C₄₁	C₂×C₈	1	465	yes	—
16	C₂³×C₄×C₄₁	C₂²×C₄	1	155	yes	—
17	C₂²×C₈×C₄₁	C₂²×C₄	1	1085	yes	—
18	C₂²×C₈×C₄₁	C₂⁴	1	155	yes	—
19	C₂×C₁₆×C₄₁	C₂⁴	1	496	yes	direct product factor
20	C₂⁴×C₄₁	C₂×C₁₆	1	496	yes	direct product factor
21	C₂⁴×C₄₁	C₂²×C₈	1	155	yes	—
22	C₂²×C₄×C₄₁	C₂²×C₈	1	1085	yes	—
23	C₂²×C₄×C₄₁	C₂³×C₄	1	155	yes	—
24	C₂×C₈×C₄₁	C₂³×C₄	1	465	yes	—
25	C₂×C₈×C₄₁	C₂⁵	1	31	yes	—
26	C₁₆×C₄₁	C₂⁵	1	32	yes	direct product factor
27	C₂⁵×C₁₆	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂³×C₄₁	C₂²×C₁₆	1	1240	yes	direct product factor
29	C₂³×C₄₁	C₂³×C₈	1	155	yes	—
30	C₂×C₄×C₄₁	C₂³×C₈	1	465	yes	—
31	C₂×C₄×C₄₁	C₂⁴×C₄	1	31	yes	—
32	C₈×C₄₁	C₂⁴×C₄	1	31	yes	—
33	C₈×C₄₁	C₂⁶	1	1	yes	characteristic
34	C₂⁵×C₈	C₂×C₄₁	1	1	yes	characteristic
35	C₂⁴×C₁₆	C₂×C₄₁	1	62	yes	direct product factor
36	C₂²×C₄₁	C₂³×C₁₆	1	620	yes	direct product factor
37	C₂²×C₄₁	C₂⁴×C₈	1	31	yes	—
38	C₄×C₄₁	C₂⁴×C₈	1	31	yes	—
39	C₄×C₄₁	C₂⁵×C₄	1	1	yes	characteristic
40	C₂⁵×C₄	C₄×C₄₁	1	1	yes	characteristic
41	C₂⁴×C₈	C₄×C₄₁	1	31	yes	—
42	C₂⁴×C₈	C₂²×C₄₁	1	31	yes	—
43	C₂³×C₁₆	C₂²×C₄₁	1	620	yes	direct product factor
44	C₂×C₄₁	C₂⁴×C₁₆	1	62	yes	direct product factor
45	C₂×C₄₁	C₂⁵×C₈	1	1	yes	characteristic
46	C₂⁶	C₈×C₄₁	1	1	yes	characteristic
47	C₂⁴×C₄	C₈×C₄₁	1	31	yes	—
48	C₂⁴×C₄	C₂×C₄×C₄₁	1	31	yes	—
49	C₂³×C₈	C₂×C₄×C₄₁	1	465	yes	—
50	C₂³×C₈	C₂³×C₄₁	1	155	yes	—
51	C₂²×C₁₆	C₂³×C₄₁	1	1240	yes	direct product factor
52	C₄₁	C₂⁵×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
53	C₂⁵	C₁₆×C₄₁	1	32	yes	direct product factor
54	C₂⁵	C₂×C₈×C₄₁	1	31	yes	—
55	C₂³×C₄	C₂×C₈×C₄₁	1	465	yes	—
56	C₂³×C₄	C₂²×C₄×C₄₁	1	155	yes	—
57	C₂²×C₈	C₂²×C₄×C₄₁	1	1085	yes	—
58	C₂²×C₈	C₂⁴×C₄₁	1	155	yes	—
59	C₂×C₁₆	C₂⁴×C₄₁	1	496	yes	direct product factor
60	C₂⁴	C₂×C₁₆×C₄₁	1	496	yes	direct product factor
61	C₂⁴	C₂²×C₈×C₄₁	1	155	yes	—
62	C₂²×C₄	C₂²×C₈×C₄₁	1	1085	yes	—
63	C₂²×C₄	C₂³×C₄×C₄₁	1	155	yes	—
64	C₂×C₈	C₂³×C₄×C₄₁	1	465	yes	—
65	C₂×C₈	C₂⁵×C₄₁	1	31	yes	—
66	C₁₆	C₂⁵×C₄₁	1	32	yes	direct product factor
67	C₂³	C₂²×C₁₆×C₄₁	1	1240	yes	direct product factor
68	C₂³	C₂³×C₈×C₄₁	1	155	yes	—
69	C₂×C₄	C₂³×C₈×C₄₁	1	465	yes	—
70	C₂×C₄	C₂⁴×C₄×C₄₁	1	31	yes	—
71	C₈	C₂⁴×C₄×C₄₁	1	31	yes	—
72	C₈	C₂⁶×C₄₁	1	1	yes	characteristic
73	C₂²	C₂³×C₁₆×C₄₁	1	620	yes	direct product factor
74	C₂²	C₂⁴×C₈×C₄₁	1	31	yes	—
75	C₄	C₂⁴×C₈×C₄₁	1	31	yes	—
76	C₄	C₂⁵×C₄×C₄₁	1	1	yes	characteristic
77	C₂	C₂⁴×C₁₆×C₄₁	1	62	yes	direct product factor
78	C₂	C₂⁵×C₈×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂⁶×C₄₁
socle, prime radical	C₂⁶×C₄₁	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₁₆×C₄₁	C₂	direct (N × H)
6. C₂³×C₁₆×C₄₁	C₂²	direct (N × H)
12. C₂²×C₁₆×C₄₁	C₂³	direct (N × H)
13. C₂⁵×C₄₁	C₁₆	direct (N × H)
19. C₂×C₁₆×C₄₁	C₂⁴	direct (N × H)
20. C₂⁴×C₄₁	C₂×C₁₆	direct (N × H)
26. C₁₆×C₄₁	C₂⁵	direct (N × H)
27. C₂⁵×C₁₆	C₄₁	direct (N × H)
28. C₂³×C₄₁	C₂²×C₁₆	direct (N × H)
35. C₂⁴×C₁₆	C₂×C₄₁	direct (N × H)
36. C₂²×C₄₁	C₂³×C₁₆	direct (N × H)
43. C₂³×C₁₆	C₂²×C₄₁	direct (N × H)
44. C₂×C₄₁	C₂⁴×C₁₆	direct (N × H)
51. C₂²×C₁₆	C₂³×C₄₁	direct (N × H)
52. C₄₁	C₂⁵×C₁₆	direct (N × H)
53. C₂⁵	C₁₆×C₄₁	direct (N × H)
59. C₂×C₁₆	C₂⁴×C₄₁	direct (N × H)
60. C₂⁴	C₂×C₁₆×C₄₁	direct (N × H)
66. C₁₆	C₂⁵×C₄₁	direct (N × H)
67. C₂³	C₂²×C₁₆×C₄₁	direct (N × H)
73. C₂²	C₂³×C₁₆×C₄₁	direct (N × H)
77. C₂	C₂⁴×C₁₆×C₄₁	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×C₈×C₄₁	2
C₂⁴×C₁₆×C₄₁	2
C₂⁵×C₁₆	41

Subgroups — C25×C16×C41 #72198577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₁₆×C₄₁ #72198577