Subgroups — C₄₁×#1453 #19105233

Order 5248.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#431	C₂	1	2	yes	maximal
2	C₄×M₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#322	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#322	C₂	1	2	yes	maximal, complemented
5	C₈²×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×M₁₆×C₄₁	C₄	1	2	yes	—
7	C₂×C₄²×C₄₁	C₂²	1	1	yes	characteristic
8	C₄⋊C₈×C₄₁	C₄	1	4	yes	—
9	C₂²⋊C₈×C₄₁	C₄	1	4	yes	—
10	#97×C₄₁	C₄	1	2	yes	—
11	C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₄₁	C₂²	1	2	yes	—
13	C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₄₁	C₂²	1	2	yes	—
15	C₂²×C₄×C₄₁	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
17	M₁₆×C₄₁	—	2	4	no	—
18	C₂×C₈×C₄₁	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₄₁	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₄₁	C₂×C₄	1	4	yes	—
21	C₂×C₈×C₄₁	C₂×C₄	1	2	yes	—
22	C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₄₁	C₂×C₄	1	2	yes	—
24	C₄²×C₄₁	C₂³	1	1	yes	characteristic
25	C₂³×C₄₁	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₄₁	—	2	2	no	—
27	C₂×C₄×C₄₁	—	2	4	no	—
28	C₂×C₄×C₄₁	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₄₁	C₄²	1	2	yes	—
30	C₂×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₁	C₂²×C₄	1	2	yes	—
32	C₈×C₄₁	—	2	2	no	—
33	C₈×C₄₁	—	2	4	no	—
34	C₈×C₄₁	—	2	4	no	—
35	C₈×C₄₁	M₁₆	1	4	yes	—
36	C₂²×C₄₁	—	2	1	no	—
37	C₂²×C₄₁	—	2	2	no	—
38	C₂²×C₄₁	C₂×C₄²	1	1	yes	characteristic
39	C₄×C₄₁	—	2	1	no	—
40	C₄×C₄₁	—	2	2	no	—
41	C₄×C₄₁	C₂×M₁₆	1	2	yes	—
42	C₄×C₄₁	#131	1	4	yes	—
43	#1453	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₄₁	—	4	1	no	—
45	C₂×C₄₁	C₄×M₁₆	1	1	yes	characteristic
46	C₂×C₄₁	#405	1	2	yes	—
47	#431	C₂×C₄₁	1	2	yes	—
48	C₄×M₁₆	C₂×C₄₁	1	1	yes	characteristic
49	#322	C₂×C₄₁	1	1	yes	characteristic, complemented
50	#322	C₂×C₄₁	1	2	yes	complemented
51	C₈²	C₂×C₄₁	1	1	yes	characteristic, complemented
52	C₄₁	#1453	1	1	yes	characteristic, direct product factor, Sylow
53	C₂×M₁₆	C₄×C₄₁	1	2	yes	—
54	C₂×C₄²	C₂²×C₄₁	1	1	yes	characteristic
55	C₄⋊C₈	C₄×C₄₁	1	4	yes	—
56	C₂²⋊C₈	C₄×C₄₁	1	4	yes	—
57	#97	C₄×C₄₁	1	2	yes	—
58	C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
59	C₄×C₈	C₂²×C₄₁	1	2	yes	—
60	C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
61	C₄×C₈	C₂²×C₄₁	1	2	yes	—
62	C₂²×C₄	C₂×C₄×C₄₁	1	2	yes	—
63	C₂²×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
64	M₁₆	—	2	4	no	—
65	C₂×C₈	C₂×C₄×C₄₁	1	2	yes	—
66	C₂×C₈	C₂×C₄×C₄₁	1	4	yes	—
67	C₂×C₈	C₂×C₄×C₄₁	1	4	yes	—
68	C₂×C₈	C₂×C₄×C₄₁	1	2	yes	—
69	C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
70	C₄²	C₂×C₄×C₄₁	1	2	yes	—
71	C₄²	C₂³×C₄₁	1	1	yes	characteristic
72	C₂³	C₄²×C₄₁	1	1	yes	characteristic
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	C₄²×C₄₁	1	1	yes	characteristic
76	C₂×C₄	C₄²×C₄₁	1	2	yes	—
77	C₂×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
78	C₂×C₄	C₂²×C₄×C₄₁	1	2	yes	—
79	C₈	—	2	2	no	—
80	C₈	—	2	4	no	—
81	C₈	—	2	4	no	—
82	C₈	M₁₆×C₄₁	1	4	yes	—
83	C₂²	—	2	1	no	—
84	C₂²	—	2	2	no	—
85	C₂²	C₂×C₄²×C₄₁	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	2	2	no	—
88	C₄	C₂×M₁₆×C₄₁	1	2	yes	—
89	C₄	#131×C₄₁	1	4	yes	—
90	C₂	—	4	1	no	—
91	C₂	C₄×M₁₆×C₄₁	1	1	yes	characteristic
92	C₂	C₄₁×#405	1	2	yes	—

	subgroup	G/H
center	C₄²×C₄₁	C₂³
commutator	C₂²	C₂×C₄²×C₄₁
Frattini, cosocle	C₄²	C₂³×C₄₁
socle	C₂²×C₄₁	C₂×C₄²
prime radical	C₂³×C₄₁	C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₁×#322	C₂	semidirect
4. C₄₁×#322	C₂	semidirect
5. C₈²×C₄₁	C₂	semidirect
43. #1453	C₄₁	direct (N × H)
49. #322	C₂×C₄₁	semidirect
50. #322	C₂×C₄₁	semidirect
51. C₈²	C₂×C₄₁	semidirect
52. C₄₁	#1453	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#431	2
C₄×M₁₆×C₄₁	2
C₄₁×#322	2
C₈²×C₄₁	2
#1453	41

Subgroups — C41×#1453 #19105233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#1453 #19105233