Subgroups — #18072964

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563381	C₂	1	1	yes	maximal, characteristic
2	C₄²×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₁₉⋊#1273	C₂	1	4	yes	maximal
4	C₄×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₁₉⋊C₈	C₄	1	4	yes	—
6	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
8	#11926299	C₄	1	4	yes	—
9	C₂×C₁₉×#97	C₄	1	2	yes	—
10	C₂×C₁₉×#97	C₄	1	2	yes	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
12	C₄³×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
14	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
20	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
21	C₁₉×#97	—	2	4	no	—
22	C₁₉×#97	C₈	1	8	yes	complemented
23	C₄×C₈×C₁₉	—	2	4	no	—
24	C₄×C₁₉⋊C₈	—	2	4	no	—
25	C₄×C₁₉⋊C₈	—	2	4	no	—
26	C₄×C₁₉⋊C₈	—	2	8	no	—
27	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
28	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
29	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₉	—	2	4	no	—
33	C₂×C₈×C₁₉	—	2	4	no	—
34	C₂×C₈×C₁₉	C₂×C₈	1	8	yes	—
35	C₄²×C₁₉	—	2	4	no	—
36	C₄²×C₁₉	—	2	4	no	—
37	C₄²×C₁₉	C₂×C₈	1	4	yes	—
38	C₄²×C₁₉	M₁₆	1	4	yes	—
39	C₄²×C₁₉	#41	1	4	yes	—
40	C₂×C₁₉⋊C₈	—	2	4	no	—
41	C₂×C₁₉⋊C₈	—	2	4	no	—
42	C₂×C₁₉⋊C₈	—	2	4	no	—
43	C₂×C₁₉⋊C₈	—	2	8	no	—
44	C₂×C₁₉⋊C₈	M₁₆	1	8	yes	—
45	#8132	—	19	1	no	maximal, Sylow
46	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	C₄×C₈	1	4	yes	—
52	C₂×C₄×C₁₉	#97	1	4	yes	—
53	C₂×C₄×C₁₉	#117	1	2	yes	—
54	C₂×C₄×C₁₉	#117	1	2	yes	—
55	C₂×C₄×C₁₉	#117	1	2	yes	—
56	C₂×C₄×C₁₉	C₂²×C₈	1	2	yes	—
57	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
58	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
59	C₂×C₄×C₁₉	#131	1	4	yes	—
60	C₈×C₁₉	—	2	8	no	—
61	C₁₉⋊C₈	—	2	8	no	—
62	C₁₉⋊C₈	—	4	4	no	—
63	#1744	—	19	1	no	—
64	C₄×#97	D₁₉	1	1	yes	characteristic
65	C₄²×C₈	—	19	1	no	—
66	#1273	—	19	4	no	—
67	C₂²×C₁₉	#376	1	1	yes	characteristic
68	C₂²×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
69	C₂²×C₁₉	C₂×#97	1	1	yes	characteristic
70	C₂²×C₁₉	C₄×M₁₆	1	2	yes	—
71	C₂²×C₁₉	#405	1	2	yes	—
72	C₄×C₁₉	—	2	4	no	—
73	C₄×C₁₉	—	2	4	no	—
74	C₄×C₁₉	#431	1	4	yes	—
75	C₄×C₁₉	#432	1	4	yes	—
76	C₄×C₁₉	#433	1	4	yes	—
77	C₂×#97	Dic₁₉	1	2	yes	—
78	C₂×#97	Dic₁₉	1	2	yes	—
79	C₂×C₄×C₈	—	19	4	no	—
80	C₂×C₄×C₈	—	19	2	no	—
81	C₂×C₄×C₈	—	19	2	no	—
82	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
83	C₄³	C₂×D₁₉	1	1	yes	characteristic
84	#336	—	19	4	no	—
85	C₂×C₁₉	C₈×M₁₆	1	2	yes	—
86	C₂×C₁₉	#1451	1	2	yes	—
87	C₂×C₁₉	#1744	1	1	yes	characteristic
88	C₂×C₁₉	#1745	1	1	yes	characteristic
89	C₂×C₁₉	#1746	1	1	yes	characteristic
90	C₂²×C₈	—	19	4	no	—
91	C₂²×C₈	—	19	4	no	—
92	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
93	C₂×C₄²	C₄×D₁₉	1	2	yes	—
94	C₂×C₄²	C₄×D₁₉	1	2	yes	—
95	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
96	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
97	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
98	#97	—	2	4	no	—
99	#97	C₁₉⋊C₈	1	8	yes	complemented
100	C₄×C₈	—	2	4	no	—
101	C₄×C₈	—	38	8	no	—
102	C₄×C₈	—	38	4	no	—
103	C₄×C₈	—	38	4	no	—
104	C₁₉	#8132	1	1	yes	characteristic, complemented, Sylow
105	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
106	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
107	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
108	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
109	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
110	C₂×C₈	—	2	4	no	—
111	C₂×C₈	—	2	4	no	—
112	C₂×C₈	—	19	8	no	—
113	C₂×C₈	—	38	4	no	—
114	C₂×C₈	—	38	4	no	—
115	C₂×C₈	—	38	4	no	—
116	C₂×C₈	—	38	8	no	—
117	C₂×C₈	C₂×C₁₉⋊C₈	1	8	yes	—
118	C₄²	—	2	4	no	—
119	C₄²	—	2	4	no	—
120	C₄²	C₂×C₁₉⋊C₈	1	4	yes	—
121	C₄²	#64520	1	4	yes	—
122	C₄²	#64541	1	4	yes	—
123	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	C₄×C₁₉⋊C₈	1	4	yes	—
129	C₂×C₄	#10597260	1	4	yes	—
130	C₂×C₄	#10597318	1	2	yes	—
131	C₂×C₄	#10597318	1	2	yes	—
132	C₂×C₄	M₁₆×D₁₉	1	4	yes	—
133	C₂×C₄	#10597353	1	4	yes	—
134	C₂×C₄	C₂²×C₁₉⋊C₈	1	2	yes	—
135	C₂×C₄	C₂×#64520	1	2	yes	—
136	C₂×C₄	#10597372	1	2	yes	—
137	C₈	—	2	8	no	—
138	C₈	—	38	8	no	—
139	C₈	—	76	4	no	—
140	C₂²	#11926390	1	1	yes	characteristic
141	C₂²	C₂×C₄×C₁₉⋊C₈	1	1	yes	characteristic
142	C₂²	C₂×#10597260	1	1	yes	characteristic
143	C₂²	M₁₆×Dic₁₉	1	2	yes	—
144	C₂²	#11926502	1	2	yes	—
145	C₄	—	2	4	no	—
146	C₄	—	2	4	no	—
147	C₄	#11926597	1	4	yes	—
148	C₄	#11926599	1	4	yes	—
149	C₄	#11926606	1	4	yes	—
150	C₂	M₁₆×C₁₉⋊C₈	1	2	yes	—
151	C₂	#14561922	1	2	yes	—
152	C₂	#14563381	1	1	yes	characteristic
153	C₂	#14563383	1	1	yes	characteristic
154	C₂	#14563388	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂×C₄×C₈
Fitting	C₄×C₁₉×#97	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#97	D₁₉
hypocenter	C₁₉	#8132
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ C₄×#97

Complements

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

N	H ≅ G/N	type
22. C₁₉×#97	C₈	semidirect
99. #97	C₁₉⋊C₈	semidirect
104. C₁₉	#8132	semidirect

Maximal subgroups

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

subgroup	index
#14563381	2
C₄²×C₁₉⋊C₈	2
C₁₉⋊#1273	2
C₄×C₁₉×#97	2
#8132	19