Subgroups — #41000125

Order 26816.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20269395	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₄₁₉	C₂	1	1	yes	maximal, characteristic
4	#20269395	—	2	1	no	—
5	#20269395	C₄	1	2	yes	—
6	C₂×C₄₁₉⋊C₈	—	2	1	no	—
7	C₂×C₄₁₉⋊C₈	—	2	1	no	—
8	C₂×C₄₁₉⋊C₈	—	2	1	no	—
9	C₂×C₄₁₉⋊C₈	C₄	1	2	yes	—
10	C₂²×C₄×C₄₁₉	C₂²	1	1	yes	characteristic
11	M₁₆×C₄₁₉	—	2	1	no	—
12	M₁₆×C₄₁₉	C₄	1	2	yes	—
13	C₂×C₈×C₄₁₉	—	2	1	no	—
14	C₄₁₉⋊C₈	—	2	2	no	—
15	C₄₁₉⋊C₈	—	2	2	no	—
16	C₂³×C₄₁₉	Q₈	1	1	yes	characteristic
17	C₂×C₄×C₄₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₄₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₄₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₄₁₉	D₄	1	1	yes	characteristic
21	C₂×C₄×C₄₁₉	D₄	1	1	yes	characteristic
22	C₂×C₄×C₄₁₉	D₄	1	1	yes	characteristic
23	C₈×C₄₁₉	—	2	2	no	—
24	C₂²×C₄₁₉	—	2	2	no	—
25	C₂²×C₄₁₉	C₄⋊C₄	1	1	yes	characteristic
26	C₂²×C₄₁₉	C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₄₁₉	C₄⋊C₄	1	1	yes	characteristic
28	C₄×C₄₁₉	C₄²	1	1	yes	characteristic
29	C₄×C₄₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₄×C₄₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₄₁₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄₁₉	—	2	1	no	—
33	C₂×C₄₁₉	—	2	1	no	—
34	C₂×C₄₁₉	#95	1	1	yes	characteristic
35	C₂×C₄₁₉	#108	1	2	yes	—
36	C₄₁₉	#341	1	1	yes	characteristic, complemented, Sylow
37	#341	—	419	1	no	maximal, Sylow
38	C₂×M₁₆	—	419	1	no	—
39	C₂×M₁₆	D₄₁₉	1	1	yes	characteristic
40	C₂²×C₈	—	419	1	no	—
41	C₂²×C₄	C₂×D₄₁₉	1	1	yes	characteristic
42	M₁₆	—	2	1	no	—
43	M₁₆	—	838	1	no	—
44	M₁₆	—	419	2	no	—
45	M₁₆	Dic₄₁₉	1	2	yes	—
46	C₂×C₈	—	2	1	no	—
47	C₂×C₈	—	838	1	no	—
48	C₂×C₈	—	838	1	no	—
49	C₂×C₈	—	838	1	no	—
50	C₂×C₈	—	419	2	no	—
51	C₂³	Dic₈₃₈	1	1	yes	characteristic
52	C₂×C₄	C₄×D₄₁₉	1	1	yes	characteristic
53	C₂×C₄	C₄×D₄₁₉	1	1	yes	characteristic
54	C₂×C₄	C₂×Dic₄₁₉	1	1	yes	characteristic
55	C₂×C₄	C₂²⋊D₄₁₉	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₄₁₉	1	1	yes	characteristic
57	C₂×C₄	D₁₆₇₆	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₈	—	838	2	no	—
60	C₈	—	838	2	no	—
61	C₂²	—	2	2	no	—
62	C₂²	Dic₄₁₉⋊C₄	1	1	yes	characteristic
63	C₂²	Dic₄₁₉⋊C₄	1	1	yes	characteristic
64	C₂²	C₄⋊Dic₄₁₉	1	1	yes	characteristic
65	C₄	C₄×Dic₄₁₉	1	1	yes	characteristic
66	C₄	(C₂×D₄₁₉)⋊C₄	1	1	yes	characteristic
67	C₄	(C₂×D₄₁₉)⋊C₄	1	1	yes	characteristic
68	C₄	C₂²⋊Dic₄₁₉	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	—	2	1	no	—
71	C₂	C₄₁₉⋊#95	1	1	yes	characteristic
72	C₂	#27211653	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₄₁₉
commutator	C₄×C₄₁₉	C₄²
Frattini	C₂²×C₄	C₂×D₄₁₉
Fitting	C₂×M₁₆×C₄₁₉	C₂
socle	C₂²×C₄₁₉	C₄⋊C₄
prime radical	C₂³×C₄₁₉	Q₈
cosocle	C₂²×C₄×C₄₁₉	C₂²
hypercenter	C₂×M₁₆	D₄₁₉
hypocenter	C₄₁₉	#341
LCS	G ▷ C₄×C₄₁₉ ▷ C₂×C₄₁₉ ▷ C₄₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
36. C₄₁₉	#341	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20269395	2
C₂²×C₄₁₉⋊C₈	2
C₂×M₁₆×C₄₁₉	2
#341	419