Subgroups — C₄×#95×C₄₁ #19105212

Order 5248.

752 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₄₁	C₂	1	3	yes	maximal
2	C₂×#95×C₄₁	C₂	1	4	yes	maximal
3	C₂³×C₄×C₄₁	C₂²	1	6	yes	—
4	C₂³×C₄×C₄₁	C₂²	1	1	yes	characteristic
5	C₂×C₄²×C₄₁	—	2	12	no	—
6	C₂×C₄²×C₄₁	C₄	1	12	yes	complemented
7	#95×C₄₁	C₄	1	16	yes	direct product factor
8	C₂⁴×C₄₁	C₂³	1	1	yes	characteristic
9	C₂²×C₄×C₄₁	—	2	12	no	—
10	C₂²×C₄×C₄₁	—	2	12	no	—
11	C₂²×C₄×C₄₁	C₂×C₄	1	24	yes	—
12	C₂²×C₄×C₄₁	C₂×C₄	1	12	yes	—
13	C₂²×C₄×C₄₁	C₂×C₄	1	6	yes	—
14	C₂²×C₄×C₄₁	D₄	1	6	yes	—
15	C₂²×C₄×C₄₁	Q₈	1	2	yes	—
16	C₄²×C₄₁	—	2	24	no	—
17	C₂³×C₄₁	C₂²×C₄	1	3	yes	—
18	C₂³×C₄₁	C₂²×C₄	1	4	yes	—
19	C₂³×C₄₁	C₂×D₄	1	3	yes	—
20	C₂³×C₄₁	C₂×Q₈	1	1	yes	characteristic
21	C₂³×C₄₁	#41	1	4	yes	—
22	C₂×C₄×C₄₁	—	2	12	no	—
23	C₂×C₄×C₄₁	—	2	12	no	—
24	C₂×C₄×C₄₁	—	2	48	no	—
25	C₂×C₄×C₄₁	C₄²	1	4	yes	—
26	C₂×C₄×C₄₁	C₄²	1	24	yes	complemented
27	C₂×C₄×C₄₁	C₂²⋊C₄	1	12	yes	—
28	C₂×C₄×C₄₁	C₄⋊C₄	1	12	yes	—
29	C₂²×C₄₁	C₂×C₄²	1	1	yes	characteristic
30	C₂²×C₄₁	C₂×C₄²	1	6	yes	—
31	C₂²×C₄₁	C₂×C₂²⋊C₄	1	3	yes	—
32	C₂²×C₄₁	C₂×C₄⋊C₄	1	3	yes	—
33	C₂²×C₄₁	#117	1	6	yes	—
34	C₂²×C₄₁	C₄×D₄	1	12	yes	—
35	C₂²×C₄₁	C₄×Q₈	1	4	yes	—
36	C₄×C₄₁	—	2	24	no	—
37	C₄×C₄₁	#95	1	8	yes	direct product factor
38	C₄×#95	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂×C₄₁	C₄³	1	1	yes	characteristic
40	C₂×C₄₁	C₂×#95	1	1	yes	characteristic
41	C₂×C₄₁	#376	1	1	yes	characteristic
42	C₂×C₄₁	C₄×C₂²⋊C₄	1	6	yes	—
43	C₂×C₄₁	C₄×C₄⋊C₄	1	6	yes	—
44	C₂²×C₄²	C₂×C₄₁	1	3	yes	—
45	C₂×#95	C₂×C₄₁	1	4	yes	—
46	C₄₁	C₄×#95	1	1	yes	characteristic, direct product factor, Sylow
47	C₂³×C₄	C₂²×C₄₁	1	6	yes	—
48	C₂³×C₄	C₂²×C₄₁	1	1	yes	characteristic
49	C₂×C₄²	—	2	12	no	—
50	C₂×C₄²	C₄×C₄₁	1	12	yes	complemented
51	#95	C₄×C₄₁	1	16	yes	direct product factor
52	C₂⁴	C₂³×C₄₁	1	1	yes	characteristic
53	C₂²×C₄	—	2	12	no	—
54	C₂²×C₄	—	2	12	no	—
55	C₂²×C₄	C₂×C₄×C₄₁	1	24	yes	—
56	C₂²×C₄	C₂×C₄×C₄₁	1	12	yes	—
57	C₂²×C₄	C₂×C₄×C₄₁	1	6	yes	—
58	C₂²×C₄	D₄×C₄₁	1	6	yes	—
59	C₂²×C₄	Q₈×C₄₁	1	2	yes	—
60	C₄²	—	2	24	no	—
61	C₂³	C₂²×C₄×C₄₁	1	3	yes	—
62	C₂³	C₂²×C₄×C₄₁	1	4	yes	—
63	C₂³	C₂×D₄×C₄₁	1	3	yes	—
64	C₂³	C₂×Q₈×C₄₁	1	1	yes	characteristic
65	C₂³	#41×C₄₁	1	4	yes	—
66	C₂×C₄	—	2	12	no	—
67	C₂×C₄	—	2	12	no	—
68	C₂×C₄	—	2	48	no	—
69	C₂×C₄	C₄²×C₄₁	1	4	yes	—
70	C₂×C₄	C₄²×C₄₁	1	24	yes	complemented
71	C₂×C₄	C₂²⋊C₄×C₄₁	1	12	yes	—
72	C₂×C₄	C₄⋊C₄×C₄₁	1	12	yes	—
73	C₂²	C₂×C₄²×C₄₁	1	1	yes	characteristic
74	C₂²	C₂×C₄²×C₄₁	1	6	yes	—
75	C₂²	C₂×C₂²⋊C₄×C₄₁	1	3	yes	—
76	C₂²	C₂×C₄⋊C₄×C₄₁	1	3	yes	—
77	C₂²	#117×C₄₁	1	6	yes	—
78	C₂²	C₄×D₄×C₄₁	1	12	yes	—
79	C₂²	C₄×Q₈×C₄₁	1	4	yes	—
80	C₄	—	2	24	no	—
81	C₄	#95×C₄₁	1	8	yes	direct product factor
82	C₂	C₄³×C₄₁	1	1	yes	characteristic
83	C₂	C₂×#95×C₄₁	1	1	yes	characteristic
84	C₂	C₄₁×#376	1	1	yes	characteristic
85	C₂	C₄×C₂²⋊C₄×C₄₁	1	6	yes	—
86	C₂	C₄×C₄⋊C₄×C₄₁	1	6	yes	—

	subgroup	G/H
center	C₂³×C₄×C₄₁	C₂²
commutator	C₂	C₄³×C₄₁
Frattini, cosocle	C₂⁴	C₂³×C₄₁
socle, prime radical	C₂⁴×C₄₁	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₂×C₄²×C₄₁	C₄	semidirect
7. #95×C₄₁	C₄	direct (N × H)
26. C₂×C₄×C₄₁	C₄²	semidirect
37. C₄×C₄₁	#95	direct (N × H)
38. C₄×#95	C₄₁	direct (N × H)
46. C₄₁	C₄×#95	direct (N × H)
50. C₂×C₄²	C₄×C₄₁	semidirect
51. #95	C₄×C₄₁	direct (N × H)
70. C₂×C₄	C₄²×C₄₁	semidirect
81. C₄	#95×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
C₂²×C₄²×C₄₁	2
C₂×#95×C₄₁	2
C₄×#95	41

Subgroups — C4×#95×C41 #19105212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#95×C₄₁ #19105212