Subgroups — #408×C₄₁₉ #40999901

Order 26816.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×C₄₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×C₄₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₈×C₄₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊C₈×C₄₁₉	C₂	1	4	yes	maximal, complemented
5	#41×C₄₁₉	—	2	2	no	—
6	#41×C₄₁₉	—	2	2	no	—
7	C₂×Q₈×C₄₁₉	C₄	1	1	yes	characteristic
8	C₂×D₄×C₄₁₉	C₄	1	2	yes	—
9	C₂×D₄×C₄₁₉	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₄₁₉	C₂²	1	2	yes	—
11	C₂²×C₄×C₄₁₉	C₂²	1	1	yes	characteristic
12	M₁₆×C₄₁₉	—	2	2	no	—
13	C₂×C₈×C₄₁₉	—	2	2	no	—
14	C₂×C₈×C₄₁₉	C₂²	1	2	yes	—
15	C₂×C₈×C₄₁₉	C₂²	1	2	yes	—
16	C₂³×C₄₁₉	C₂×C₄	1	2	yes	—
17	C₂³×C₄₁₉	C₂×C₄	1	1	yes	characteristic
18	Q₈×C₄₁₉	—	2	2	no	—
19	D₄×C₄₁₉	—	2	4	no	—
20	D₄×C₄₁₉	—	2	2	no	—
21	C₂×C₄×C₄₁₉	—	2	2	no	—
22	C₂×C₄×C₄₁₉	—	2	2	no	—
23	C₂×C₄×C₄₁₉	C₂×C₄	1	2	yes	—
24	C₂×C₄×C₄₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×C₄₁₉	D₄	1	2	yes	—
26	C₂×C₄×C₄₁₉	D₄	1	2	yes	—
27	C₂×C₄×C₄₁₉	C₂³	1	1	yes	characteristic
28	C₈×C₄₁₉	—	2	2	no	—
29	C₈×C₄₁₉	—	2	2	no	—
30	C₂²×C₄₁₉	—	2	2	no	—
31	C₂²×C₄₁₉	—	2	2	no	—
32	C₂²×C₄₁₉	—	2	4	no	—
33	C₂²×C₄₁₉	C₂²⋊C₄	1	2	yes	—
34	C₂²×C₄₁₉	C₂²×C₄	1	1	yes	characteristic
35	C₄×C₄₁₉	—	2	2	no	—
36	C₄×C₄₁₉	C₂²⋊C₄	1	2	yes	—
37	C₄×C₄₁₉	C₂×D₄	1	1	yes	characteristic
38	C₄×C₄₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄₁₉	—	2	2	no	—
40	C₂×C₄₁₉	—	4	2	no	—
41	C₂×C₄₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₄₁₉	#131	1	2	yes	—
43	C₄₁₉	#408	1	1	yes	characteristic, direct product factor, Sylow
44	#408	C₄₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂×#41	C₂×C₄₁₉	1	1	yes	characteristic
46	C₂×M₁₆	C₂×C₄₁₉	1	1	yes	characteristic, complemented
47	C₂²×C₈	C₂×C₄₁₉	1	1	yes	characteristic, complemented
48	C₂²⋊C₈	C₂×C₄₁₉	1	4	yes	complemented
49	#41	—	2	2	no	—
50	#41	—	2	2	no	—
51	C₂×Q₈	C₄×C₄₁₉	1	1	yes	characteristic
52	C₂×D₄	C₄×C₄₁₉	1	2	yes	—
53	C₂×D₄	C₄×C₄₁₉	1	1	yes	characteristic
54	C₂²×C₄	C₂²×C₄₁₉	1	2	yes	—
55	C₂²×C₄	C₂²×C₄₁₉	1	1	yes	characteristic
56	M₁₆	—	2	2	no	—
57	C₂×C₈	—	2	2	no	—
58	C₂×C₈	C₂²×C₄₁₉	1	2	yes	—
59	C₂×C₈	C₂²×C₄₁₉	1	2	yes	—
60	C₂³	C₂×C₄×C₄₁₉	1	2	yes	—
61	C₂³	C₂×C₄×C₄₁₉	1	1	yes	characteristic
62	Q₈	—	2	2	no	—
63	D₄	—	2	4	no	—
64	D₄	—	2	2	no	—
65	C₂×C₄	—	2	2	no	—
66	C₂×C₄	—	2	2	no	—
67	C₂×C₄	C₂×C₄×C₄₁₉	1	2	yes	—
68	C₂×C₄	C₂×C₄×C₄₁₉	1	1	yes	characteristic
69	C₂×C₄	D₄×C₄₁₉	1	2	yes	—
70	C₂×C₄	D₄×C₄₁₉	1	2	yes	—
71	C₂×C₄	C₂³×C₄₁₉	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₈	—	2	2	no	—
74	C₂²	—	2	2	no	—
75	C₂²	—	2	2	no	—
76	C₂²	—	2	4	no	—
77	C₂²	C₂²⋊C₄×C₄₁₉	1	2	yes	—
78	C₂²	C₂²×C₄×C₄₁₉	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	C₂²⋊C₄×C₄₁₉	1	2	yes	—
81	C₄	C₂×D₄×C₄₁₉	1	1	yes	characteristic
82	C₄	C₂×D₄×C₄₁₉	1	1	yes	characteristic
83	C₂	—	2	2	no	—
84	C₂	—	4	2	no	—
85	C₂	C₂×C₂²⋊C₄×C₄₁₉	1	1	yes	characteristic
86	C₂	#131×C₄₁₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₁₉	C₂³
commutator	C₂²	C₂²×C₄×C₄₁₉
Frattini, cosocle	C₂×C₄	C₂³×C₄₁₉
socle	C₂²×C₄₁₉	C₂²×C₄
prime radical	C₂×#41×C₄₁₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×M₁₆×C₄₁₉	C₂	semidirect
3. C₂²×C₈×C₄₁₉	C₂	semidirect
4. C₂²⋊C₈×C₄₁₉	C₂	semidirect
43. C₄₁₉	#408	direct (N × H)
44. #408	C₄₁₉	direct (N × H)
46. C₂×M₁₆	C₂×C₄₁₉	semidirect
47. C₂²×C₈	C₂×C₄₁₉	semidirect
48. C₂²⋊C₈	C₂×C₄₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×C₄₁₉	2
C₂×M₁₆×C₄₁₉	2
C₂²×C₈×C₄₁₉	2
C₂²⋊C₈×C₄₁₉	2
#408	419

Subgroups — #408×C419 #40999901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #408×C₄₁₉ #40999901