Subgroups — #18073569

Order 4864.

376 conjugacy classes of subgroups.

The subgroup lattice has 270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14562300	C₂	1	1	yes	maximal, characteristic
2	#14562230	C₂	1	1	yes	maximal, characteristic
3	#14561924	C₂	1	1	yes	maximal, characteristic
4	C₈×#64520	C₂	1	1	yes	maximal, characteristic
5	#14561524	C₂	1	1	yes	maximal, characteristic
6	#14561524	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926597	C₂²	1	1	yes	characteristic
10	C₄×#64520	C₂²	1	1	yes	characteristic
11	C₄×#64520	C₂²	1	1	yes	characteristic
12	#11926290	C₄	1	2	yes	—
13	#11926290	C₄	1	2	yes	—
14	#11926286	C₄	1	4	yes	—
15	#11926266	—	2	1	no	—
16	#11926266	—	2	1	no	—
17	#11926265	—	2	1	no	—
18	C₈×C₁₉⋊C₈	—	2	1	no	—
19	C₁₉×#533	C₂²	1	1	yes	characteristic
20	C₁₉×#446	—	2	1	no	—
21	C₁₉×#446	—	2	1	no	—
22	C₈×Q₈×C₁₉	—	2	1	no	—
23	C₈×Q₈×C₁₉	—	2	1	no	—
24	C₁₉×#424	C₄	1	2	yes	—
25	C₁₉×#423	C₂²	1	1	yes	characteristic
26	C₁₉×#405	C₄	1	2	yes	—
27	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
32	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
33	C₁₉×#125	C₂×C₄	1	2	yes	—
34	C₁₉×C₂²⋊Q₈	—	2	1	no	—
35	C₁₉×C₂²⋊Q₈	—	2	1	no	—
36	C₄×Q₈×C₁₉	—	2	1	no	—
37	C₄×Q₈×C₁₉	—	2	1	no	—
38	C₁₉×#117	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×#64520	—	2	1	no	—
41	C₂×#64520	—	2	1	no	—
42	C₁₉×C₄⋊C₈	—	2	2	no	—
43	C₁₉×C₄⋊C₈	—	2	2	no	—
44	C₁₉×C₄⋊C₈	—	2	1	no	—
45	C₁₉×C₄⋊C₈	—	2	1	no	—
46	C₁₉×#97	—	2	2	no	—
47	C₄×C₈×C₁₉	—	2	2	no	—
48	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
49	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
50	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
51	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
52	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
53	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
54	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
55	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
56	#10597260	C₂×C₄	1	2	yes	—
57	#10597260	C₂×C₄	1	2	yes	—
58	C₄×C₁₉⋊C₈	—	2	1	no	—
59	C₄×C₁₉⋊C₈	—	2	1	no	—
60	C₄×C₁₉⋊C₈	—	2	1	no	—
61	C₄×C₁₉⋊C₈	—	2	1	no	—
62	C₂×Q₈×C₁₉	—	2	1	no	—
63	C₂×Q₈×C₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
67	M₁₆×C₁₉	—	4	2	no	—
68	C₂×C₈×C₁₉	—	2	2	no	—
69	C₂×C₈×C₁₉	—	2	2	no	—
70	C₂×C₈×C₁₉	—	4	1	no	—
71	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₄⋊C₄×C₁₉	C₄²	1	2	yes	—
80	C₄⋊C₄×C₁₉	C₄²	1	2	yes	—
81	C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₄²×C₁₉	—	2	2	no	—
83	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
84	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
87	#64520	—	2	4	no	—
88	#64520	—	4	2	no	—
89	C₂×C₁₉⋊C₈	—	2	2	no	—
90	C₂×C₁₉⋊C₈	—	2	2	no	—
91	C₂×C₁₉⋊C₈	—	2	2	no	—
92	C₂×C₁₉⋊C₈	—	2	2	no	—
93	#8246	—	19	1	no	maximal, Sylow
94	C₂³×C₁₉	#117	1	1	yes	characteristic
95	Q₈×C₁₉	—	4	2	no	—
96	Q₈×C₁₉	—	4	2	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	2	2	no	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	2	2	no	—
102	C₂×C₄×C₁₉	—	2	2	no	—
103	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
104	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
106	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
107	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
108	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
109	C₈×C₁₉	—	2	1	no	—
110	C₈×C₁₉	—	2	1	no	—
111	C₈×C₁₉	—	2	1	no	—
112	C₈×C₁₉	—	4	2	no	—
113	C₈×C₁₉	#101	1	2	yes	—
114	C₁₉⋊C₈	—	2	4	no	—
115	C₁₉⋊C₈	—	4	2	no	—
116	C₁₉⋊C₈	—	4	2	no	—
117	C₁₉⋊C₈	—	4	2	no	—
118	#2960	D₁₉	1	1	yes	characteristic
119	#1544	—	19	1	no	—
120	#1526	—	19	1	no	—
121	#1451	—	19	1	no	—
122	C₈×M₁₆	—	19	1	no	—
123	#1299	—	19	1	no	—
124	#1299	—	19	1	no	—
125	C₂²×C₁₉	—	2	1	no	—
126	C₂²×C₁₉	—	2	1	no	—
127	C₂²×C₁₉	—	2	1	no	—
128	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	4	2	no	—
133	C₄×C₁₉	—	4	2	no	—
134	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
135	C₄×C₁₉	#413	1	1	yes	characteristic
136	C₄×C₁₉	#443	1	2	yes	—
137	C₄×C₁₉	#444	1	2	yes	—
138	#533	C₂×D₁₉	1	1	yes	characteristic
139	#446	—	2	1	no	—
140	#446	—	2	1	no	—
141	C₈×Q₈	—	2	1	no	—
142	C₈×Q₈	—	2	1	no	—
143	#431	—	19	1	no	—
144	#431	—	19	1	no	—
145	#424	Dic₁₉	1	2	yes	—
146	#423	C₂×D₁₉	1	1	yes	characteristic
147	#405	Dic₁₉	1	2	yes	—
148	C₄×M₁₆	—	19	1	no	—
149	C₄×M₁₆	—	19	1	no	—
150	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
151	#332	—	19	2	no	—
152	#332	—	19	2	no	—
153	#330	—	19	4	no	—
154	#322	—	38	1	no	—
155	#322	—	38	1	no	—
156	#322	—	38	1	no	—
157	C₈²	—	38	1	no	—
158	C₂×C₁₉	—	4	1	no	—
159	C₂×C₁₉	C₄×#101	1	1	yes	characteristic
160	C₂×C₁₉	#1764	1	1	yes	characteristic
161	C₂×C₁₉	#1765	1	1	yes	characteristic
162	C₂×M₁₆	—	38	1	no	—
163	C₂×M₁₆	—	38	1	no	—
164	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
165	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
166	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
167	C₄⋊Q₈	C₄×D₁₉	1	1	yes	characteristic
168	C₄⋊Q₈	C₄×D₁₉	1	1	yes	characteristic
169	#125	C₄×D₁₉	1	2	yes	—
170	C₂²⋊Q₈	—	2	1	no	—
171	C₂²⋊Q₈	—	2	1	no	—
172	C₄×Q₈	—	2	1	no	—
173	C₄×Q₈	—	2	1	no	—
174	#117	C₂×Dic₁₉	1	2	yes	—
175	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
176	C₄⋊C₈	—	2	2	no	—
177	C₄⋊C₈	—	2	2	no	—
178	C₄⋊C₈	—	2	1	no	—
179	C₄⋊C₈	—	2	1	no	—
180	C₄⋊C₈	—	19	2	no	—
181	C₄⋊C₈	—	19	2	no	—
182	C₂²⋊C₈	—	38	1	no	—
183	C₂²⋊C₈	—	38	1	no	—
184	#97	—	2	2	no	—
185	#97	—	19	2	no	—
186	#97	—	19	2	no	—
187	C₄×C₈	—	2	2	no	—
188	C₄×C₈	—	38	1	no	—
189	C₄×C₈	—	38	1	no	—
190	C₄×C₈	—	38	1	no	—
191	C₄×C₈	—	38	1	no	—
192	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
193	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
194	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
195	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
196	C₁₉	#8246	1	1	yes	characteristic, complemented, Sylow
197	C₂×Q₈	—	2	1	no	—
198	C₂×Q₈	—	2	1	no	—
199	C₂²×C₄	#64541	1	1	yes	characteristic
200	C₂²×C₄	#64541	1	1	yes	characteristic
201	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
202	M₁₆	—	4	2	no	—
203	M₁₆	—	38	4	no	—
204	M₁₆	—	76	2	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	2	2	no	—
207	C₂×C₈	—	4	1	no	—
208	C₂×C₈	—	38	2	no	—
209	C₂×C₈	—	38	2	no	—
210	C₂×C₈	—	38	2	no	—
211	C₂×C₈	—	38	2	no	—
212	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
213	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
214	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
215	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
216	C₄⋊C₄	—	2	2	no	—
217	C₄⋊C₄	—	2	2	no	—
218	C₄⋊C₄	—	2	1	no	—
219	C₄⋊C₄	—	2	1	no	—
220	C₄⋊C₄	C₄×Dic₁₉	1	2	yes	—
221	C₄⋊C₄	C₄×Dic₁₉	1	2	yes	—
222	C₂²⋊C₄	—	2	2	no	—
223	C₄²	—	2	2	no	—
224	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
225	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
226	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
227	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
228	C₂³	#10597372	1	1	yes	characteristic
229	Q₈	—	4	2	no	—
230	Q₈	—	4	2	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	2	1	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
238	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
239	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
240	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
241	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
242	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
243	C₈	—	2	1	no	—
244	C₈	—	2	1	no	—
245	C₈	—	2	1	no	—
246	C₈	—	4	2	no	—
247	C₈	—	38	4	no	—
248	C₈	—	76	2	no	—
249	C₈	—	76	2	no	—
250	C₈	—	76	2	no	—
251	C₈	#10597293	1	2	yes	—
252	C₂²	—	2	1	no	—
253	C₂²	—	2	1	no	—
254	C₂²	—	2	1	no	—
255	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
256	C₄	—	2	1	no	—
257	C₄	—	2	1	no	—
258	C₄	—	2	1	no	—
259	C₄	—	4	2	no	—
260	C₄	—	4	2	no	—
261	C₄	C₂×#10597293	1	1	yes	characteristic
262	C₄	#11926528	1	1	yes	characteristic
263	C₄	#11926659	1	2	yes	—
264	C₄	#11926664	1	2	yes	—
265	C₂	—	4	1	no	—
266	C₂	C₄×#10597293	1	1	yes	characteristic
267	C₂	#14563470	1	1	yes	characteristic
268	C₂	#14563477	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2960	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2960	D₁₉
hypocenter	C₁₉	#8246
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
196. C₁₉	#8246	semidirect

Maximal subgroups

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

subgroup	index
#14562300	2
#14562230	2
#14561924	2
C₈×#64520	2
#14561524	2
C₁₉×#2960	2
#8246	19