Subgroups — C₄₁×#1420 #19105200

Order 5248.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₃₂×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₄₁×M₆₄	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#368	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₄₁	—	2	1	no	—
5	Q₃₂×C₄₁	—	2	1	no	—
6	Q₃₂×C₄₁	C₄	1	2	yes	—
7	C₂×C₁₆×C₄₁	C₂²	1	1	yes	characteristic
8	#108×C₄₁	—	2	1	no	—
9	C₃₂×C₄₁	—	2	1	no	—
10	C₂×Q₈×C₄₁	—	4	1	no	—
11	Q₁₆×C₄₁	—	2	2	no	—
12	Q₁₆×C₄₁	—	4	1	no	—
13	M₁₆×C₄₁	—	4	1	no	—
14	C₂×C₈×C₄₁	D₄	1	1	yes	characteristic
15	C₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₄₁	D₄	1	1	yes	characteristic
17	Q₈×C₄₁	—	4	2	no	—
18	Q₈×C₄₁	—	8	1	no	—
19	C₂×C₄×C₄₁	—	8	1	no	—
20	C₂×C₄×C₄₁	D₈	1	1	yes	characteristic
21	C₈×C₄₁	—	8	1	no	—
22	C₈×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₄₁	SD₁₆	1	1	yes	characteristic
24	C₂²×C₄₁	SD₃₂	1	1	yes	characteristic
25	C₄×C₄₁	—	8	2	no	—
26	C₄×C₄₁	#102	1	1	yes	characteristic
27	C₄×C₄₁	D₁₆	1	1	yes	characteristic
28	#1420	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂×C₄₁	—	2	1	no	—
30	C₂×C₄₁	#357	1	1	yes	characteristic
31	C₂×Q₃₂	C₂×C₄₁	1	1	yes	characteristic
32	M₆₄	C₂×C₄₁	1	1	yes	characteristic
33	#368	C₂×C₄₁	1	1	yes	characteristic
34	C₄₁	#1420	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×Q₁₆	—	2	1	no	—
36	Q₃₂	—	2	1	no	—
37	Q₃₂	C₄×C₄₁	1	2	yes	—
38	C₂×C₁₆	C₂²×C₄₁	1	1	yes	characteristic
39	#108	—	2	1	no	—
40	C₃₂	—	2	1	no	—
41	C₂×Q₈	—	4	1	no	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	4	1	no	—
44	M₁₆	—	4	1	no	—
45	C₂×C₈	D₄×C₄₁	1	1	yes	characteristic
46	C₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
47	C₁₆	D₄×C₄₁	1	1	yes	characteristic
48	Q₈	—	4	2	no	—
49	Q₈	—	8	1	no	—
50	C₂×C₄	—	8	1	no	—
51	C₂×C₄	D₈×C₄₁	1	1	yes	characteristic
52	C₈	—	8	1	no	—
53	C₈	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
54	C₈	SD₁₆×C₄₁	1	1	yes	characteristic
55	C₂²	SD₃₂×C₄₁	1	1	yes	characteristic
56	C₄	—	8	2	no	—
57	C₄	#102×C₄₁	1	1	yes	characteristic
58	C₄	D₁₆×C₄₁	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	C₄₁×#357	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₁	#357
commutator	C₁₆	C₂×C₄×C₄₁
Frattini, cosocle	C₂×C₁₆	C₂²×C₄₁
prime radical	C₂²×C₄₁	SD₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₁ ◁ C₂×C₄×C₄₁ ◁ C₂×C₈×C₄₁ ◁ C₂×C₁₆×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
28. #1420	C₄₁	direct (N × H)
34. C₄₁	#1420	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₃₂×C₄₁	2
C₄₁×M₆₄	2
C₄₁×#368	2
#1420	41

Subgroups — C41×#1420 #19105200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#1420 #19105200