Subgroups — C₄×#10597260 #14563320

Order 2432.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597260	C₂	1	4	yes	maximal
2	C₂×C₄×C₁₉⋊C₈	C₂	1	2	yes	maximal
3	C₄³×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄²×C₁₉	C₄	1	4	yes	—
5	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₁₉⋊C₈	C₂²	1	4	yes	—
8	#10597260	C₄	1	16	yes	direct product factor
9	C₄×C₁₉⋊C₈	C₄	1	8	yes	complemented
10	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
11	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
12	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
13	C₄²×C₁₉	—	2	8	no	—
14	C₄²×C₁₉	C₂×C₄	1	4	yes	—
15	C₄²×C₁₉	C₂×C₄	1	8	yes	—
16	C₂×C₁₉⋊C₈	C₂×C₄	1	8	yes	—
17	C₂×C₁₉⋊C₈	C₂×C₄	1	16	yes	—
18	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₉	—	2	8	no	—
20	C₂×C₄×C₁₉	C₄²	1	8	yes	—
21	C₂×C₄×C₁₉	C₄²	1	4	yes	—
22	C₂×C₄×C₁₉	M₁₆	1	8	yes	—
23	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
24	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
25	C₁₉⋊C₈	C₄²	1	16	yes	complemented
26	C₄×#97	—	19	1	no	maximal, Sylow
27	C₂²×C₁₉	C₂×C₄²	1	1	yes	characteristic
28	C₂²×C₁₉	C₂×C₄²	1	2	yes	—
29	C₂²×C₁₉	C₂×M₁₆	1	4	yes	—
30	C₄×C₁₉	—	2	8	no	—
31	C₄×C₁₉	#97	1	8	yes	complemented
32	C₄×C₁₉	C₂×C₄²	1	4	yes	—
33	C₂×#97	—	19	4	no	—
34	C₂×C₄×C₈	—	19	2	no	—
35	C₄³	D₁₉	1	1	yes	characteristic
36	C₂×C₁₉	C₄³	1	1	yes	characteristic
37	C₂×C₁₉	C₂×#97	1	2	yes	—
38	C₂×C₁₉	C₄×M₁₆	1	4	yes	—
39	C₂²×C₈	—	19	4	no	—
40	C₂×C₄²	Dic₁₉	1	4	yes	—
41	C₂×C₄²	C₂×D₁₉	1	2	yes	—
42	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
43	#97	—	19	16	no	—
44	C₄×C₈	—	19	8	no	—
45	C₁₉	C₄×#97	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₄	C₂×Dic₁₉	1	4	yes	—
47	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
48	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
49	C₂×C₈	—	19	8	no	—
50	C₂×C₈	—	19	16	no	—
51	C₄²	—	2	8	no	—
52	C₄²	C₄×D₁₉	1	4	yes	—
53	C₄²	C₄×D₁₉	1	8	yes	—
54	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
55	C₂×C₄	—	2	8	no	—
56	C₂×C₄	#64520	1	8	yes	—
57	C₂×C₄	C₄×Dic₁₉	1	8	yes	—
58	C₂×C₄	C₄×Dic₁₉	1	4	yes	—
59	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
60	C₂×C₄	C₂×C₄×D₁₉	1	4	yes	—
61	C₈	—	19	16	no	—
62	C₂²	C₂×#64520	1	4	yes	—
63	C₂²	C₂×C₄×Dic₁₉	1	1	yes	characteristic
64	C₂²	C₂×C₄×Dic₁₉	1	2	yes	—
65	C₄	—	2	8	no	—
66	C₄	#10597260	1	8	yes	direct product factor
67	C₄	C₄²×D₁₉	1	4	yes	—
68	C₂	C₄²×Dic₁₉	1	1	yes	characteristic
69	C₂	C₂×#10597260	1	2	yes	—
70	C₂	C₄×#64520	1	4	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂×D₁₉
commutator	C₂×C₁₉	C₄³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₄³×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂²×C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₄³	D₁₉
hypocenter	C₁₉	C₄×#97
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ C₄³

Complements

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

N	H ≅ G/N	type
8. #10597260	C₄	direct (N × H)
9. C₄×C₁₉⋊C₈	C₄	semidirect
25. C₁₉⋊C₈	C₄²	semidirect
31. C₄×C₁₉	#97	semidirect
45. C₁₉	C₄×#97	semidirect
66. C₄	#10597260	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×#10597260	2
C₂×C₄×C₁₉⋊C₈	2
C₄³×C₁₉	2
C₄×#97	19

Subgroups — C4×#10597260 #14563320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10597260 #14563320