Subgroups — #11926852

Order 1216.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10597316	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic
3	C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#10597275	C₂	1	1	yes	maximal, characteristic
5	#10597274	C₂	1	1	yes	maximal, characteristic
6	#10597273	C₂	1	1	yes	maximal, characteristic
7	#10597273	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	Dic₁₉⋊C₄	—	2	1	no	—
16	Dic₁₉⋊C₄	—	2	1	no	—
17	Dic₁₉⋊C₄	—	2	1	no	—
18	C₄×Dic₁₉	—	2	1	no	—
19	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×Dic₁₉	—	2	1	no	—
23	C₂×Dic₁₉	—	2	1	no	—
24	C₂×Dic₁₉	—	2	1	no	—
25	C₂×Dic₁₉	—	2	1	no	—
26	Dic₃₈	—	2	1	no	—
27	Dic₃₈	Q₈	1	2	yes	—
28	C₈×C₁₉	—	2	1	no	—
29	C₈×C₁₉	—	2	1	no	—
30	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₉	—	2	1	no	—
32	C₄×C₁₉	—	2	1	no	—
33	C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
34	C₄×C₁₉	#41	1	1	yes	characteristic
35	Dic₁₉	—	2	2	no	—
36	Dic₁₉	—	4	1	no	—
37	Dic₁₉	—	4	1	no	—
38	Dic₁₉	—	4	1	no	—
39	#479	—	19	1	no	maximal, Sylow
40	C₂×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
41	C₂×C₁₉	#135	1	1	yes	characteristic
42	C₂×C₁₉	#137	1	1	yes	characteristic
43	#125	—	19	1	no	—
44	C₄×Q₈	—	19	1	no	—
45	#107	—	19	1	no	—
46	#106	—	19	1	no	—
47	C₄⋊C₈	D₁₉	1	1	yes	characteristic
48	#103	—	19	1	no	—
49	#103	—	19	1	no	—
50	C₁₉	#479	1	1	yes	characteristic, complemented, Sylow
51	C₂×Q₈	—	19	1	no	—
52	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
53	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
54	C₄⋊C₄	—	19	1	no	—
55	C₄⋊C₄	—	19	1	no	—
56	C₄⋊C₄	—	19	1	no	—
57	C₄⋊C₄	—	38	1	no	—
58	C₄⋊C₄	—	38	1	no	—
59	C₄⋊C₄	—	38	1	no	—
60	C₄²	—	38	1	no	—
61	C₄²	C₂×D₁₉	1	1	yes	characteristic
62	Q₈	—	19	2	no	—
63	Q₈	—	38	1	no	—
64	C₂×C₄	—	38	1	no	—
65	C₂×C₄	—	38	1	no	—
66	C₂×C₄	—	38	1	no	—
67	C₂×C₄	—	38	1	no	—
68	C₂×C₄	D₇₆	1	1	yes	characteristic
69	C₂×C₄	D₇₆	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	—	2	1	no	—
73	C₂²	C₂×D₇₆	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	38	2	no	—
77	C₄	—	76	1	no	—
78	C₄	—	76	1	no	—
79	C₄	—	76	1	no	—
80	C₄	#64543	1	1	yes	characteristic
81	C₄	Q₈×D₁₉	1	1	yes	characteristic
82	C₂	#10597343	1	1	yes	characteristic
83	C₂	#10597350	1	1	yes	characteristic
84	C₂	#10597355	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₁₉×C₄⋊C₈	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₄
hypercenter	C₄⋊C₈	D₁₉
hypocenter	C₁₉	#479
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
50. C₁₉	#479	semidirect

Maximal subgroups

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

subgroup	index
#10597316	2
C₄×Dic₃₈	2
C₁₉×C₄⋊C₈	2
#10597275	2
#10597274	2
#10597273	2
#479	19