Subgroups — #18088149

Order 4864.

918 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926299	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926298	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926298	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926298	C₂	1	1	yes	maximal, characteristic
6	C₄×C₁₉⋊#95	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₈×Dic₁₉	—	2	2	no	—
13	C₂×C₈×Dic₁₉	—	2	2	no	—
14	C₂×C₈×Dic₁₉	C₄	1	4	yes	complemented
15	C₂×C₁₉⋊#95	C₄	1	2	yes	—
16	C₂×C₁₉⋊#95	C₄	1	2	yes	—
17	#11926299	—	2	2	no	—
18	#11926298	—	2	2	no	—
19	#11926298	—	2	2	no	—
20	#11926298	C₄	1	4	yes	complemented
21	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#336	—	2	2	no	—
25	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
26	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂³×Dic₁₉	C₂×C₄	1	2	yes	—
28	C₂³×Dic₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×Dic₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
42	C₂²×C₈×C₁₉	D₄	1	2	yes	—
43	C₂²×C₈×C₁₉	D₄	1	2	yes	—
44	C₂×C₄²×C₁₉	—	2	1	no	—
45	C₂×C₄²×C₁₉	—	2	1	no	—
46	C₂×C₄²×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄×Dic₁₉	—	2	1	no	—
51	C₂×C₄×Dic₁₉	—	2	1	no	—
52	C₂×C₄×Dic₁₉	—	2	1	no	—
53	C₂×C₄×Dic₁₉	—	2	1	no	—
54	C₂×C₄×Dic₁₉	—	2	1	no	—
55	C₂×C₄×Dic₁₉	—	2	1	no	—
56	C₂×C₄×Dic₁₉	—	2	1	no	—
57	C₂×C₄×Dic₁₉	—	2	1	no	—
58	C₂×C₄×Dic₁₉	—	2	1	no	—
59	C₂×C₄×Dic₁₉	—	2	1	no	—
60	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
61	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
62	C₂²×C₁₉⋊C₈	—	2	1	no	—
63	C₂²×C₁₉⋊C₈	—	2	1	no	—
64	C₂²×C₁₉⋊C₈	—	2	1	no	—
65	C₂²×C₁₉⋊C₈	—	2	1	no	—
66	C₂²×C₁₉⋊C₈	—	2	1	no	—
67	C₂²×C₁₉⋊C₈	—	2	1	no	—
68	C₂²×C₁₉⋊C₈	—	2	1	no	—
69	C₂²×C₁₉⋊C₈	—	2	1	no	—
70	C₂²×C₁₉⋊C₈	—	2	1	no	—
71	C₂²×C₁₉⋊C₈	—	2	1	no	—
72	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
73	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
74	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
75	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
76	C₁₉⋊#95	—	2	4	no	—
77	C₁₉⋊#95	C₈	1	8	yes	complemented
78	C₈×Dic₁₉	—	2	8	no	—
79	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	C₂×C₈	1	4	yes	—
87	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
101	C₂²×Dic₁₉	—	2	1	no	—
102	C₂²×Dic₁₉	—	2	1	no	—
103	C₂²×Dic₁₉	—	2	1	no	—
104	C₂²×Dic₁₉	—	2	1	no	—
105	C₂²×Dic₁₉	—	2	2	no	—
106	C₂²×Dic₁₉	—	2	2	no	—
107	C₂²×Dic₁₉	—	2	2	no	—
108	C₂²×Dic₁₉	—	2	2	no	—
109	C₂²×Dic₁₉	—	2	2	no	—
110	C₂²×Dic₁₉	—	2	2	no	—
111	C₂²×Dic₁₉	—	2	2	no	—
112	C₂²×Dic₁₉	—	2	2	no	—
113	C₂²×Dic₁₉	C₄²	1	2	yes	—
114	C₂²×Dic₁₉	C₄²	1	2	yes	—
115	C₂²×Dic₁₉	C₂×C₈	1	4	yes	—
116	C₂²×Dic₁₉	C₂×C₈	1	4	yes	—
117	C₂²×Dic₁₉	M₁₆	1	4	yes	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	—	4	1	no	—
128	C₂×C₈×C₁₉	—	4	1	no	—
129	C₂×C₈×C₁₉	—	4	1	no	—
130	C₂×C₈×C₁₉	—	4	1	no	—
131	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
132	C₄²×C₁₉	—	4	1	no	—
133	C₄²×C₁₉	—	4	1	no	—
134	C₄²×C₁₉	—	4	1	no	—
135	C₄²×C₁₉	—	4	1	no	—
136	C₄×Dic₁₉	—	2	2	no	—
137	C₄×Dic₁₉	—	2	2	no	—
138	C₄×Dic₁₉	—	2	2	no	—
139	C₄×Dic₁₉	—	2	2	no	—
140	C₄×Dic₁₉	—	4	1	no	—
141	C₄×Dic₁₉	—	4	1	no	—
142	C₄×Dic₁₉	—	4	1	no	—
143	C₄×Dic₁₉	—	4	1	no	—
144	C₂×C₁₉⋊C₈	—	2	2	no	—
145	C₂×C₁₉⋊C₈	—	2	2	no	—
146	C₂×C₁₉⋊C₈	—	2	2	no	—
147	C₂×C₁₉⋊C₈	—	2	2	no	—
148	C₂×C₁₉⋊C₈	—	2	2	no	—
149	C₂×C₁₉⋊C₈	—	2	2	no	—
150	C₂×C₁₉⋊C₈	—	2	2	no	—
151	C₂×C₁₉⋊C₈	—	2	2	no	—
152	C₂×C₁₉⋊C₈	—	2	2	no	—
153	C₂×C₁₉⋊C₈	—	4	1	no	—
154	C₂×C₁₉⋊C₈	—	4	1	no	—
155	C₂×C₁₉⋊C₈	—	4	1	no	—
156	C₂×C₁₉⋊C₈	—	4	1	no	—
157	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
158	#10797	—	19	1	no	maximal, Sylow
159	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
160	C₂³×C₁₉	#117	1	1	yes	characteristic
161	C₂³×C₁₉	#117	1	1	yes	characteristic
162	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
163	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
164	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
165	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
166	C₂³×C₁₉	C₂²×C₈	1	2	yes	—
167	C₂³×C₁₉	C₂×M₁₆	1	2	yes	—
168	C₂³×C₁₉	#131	1	2	yes	—
169	C₂³×C₁₉	#131	1	2	yes	—
170	C₂×C₄×C₁₉	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
200	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
201	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
205	C₂×Dic₁₉	—	2	2	no	—
206	C₂×Dic₁₉	—	2	2	no	—
207	C₂×Dic₁₉	—	2	2	no	—
208	C₂×Dic₁₉	—	2	2	no	—
209	C₂×Dic₁₉	—	2	4	no	—
210	C₂×Dic₁₉	—	2	4	no	—
211	C₂×Dic₁₉	—	2	4	no	—
212	C₂×Dic₁₉	—	2	4	no	—
213	C₂×Dic₁₉	—	2	4	no	—
214	C₂×Dic₁₉	—	2	4	no	—
215	C₂×Dic₁₉	—	2	4	no	—
216	C₂×Dic₁₉	—	4	2	no	—
217	C₂×Dic₁₉	—	4	2	no	—
218	C₂×Dic₁₉	—	4	2	no	—
219	C₂×Dic₁₉	—	4	2	no	—
220	C₂×Dic₁₉	C₄×C₈	1	4	yes	—
221	C₂×Dic₁₉	#97	1	4	yes	—
222	C₈×C₁₉	—	2	4	no	—
223	C₈×C₁₉	—	4	2	no	—
224	C₁₉⋊C₈	—	2	4	no	—
225	C₁₉⋊C₈	—	4	2	no	—
226	C₂²×C₄×C₈	—	19	1	no	—
227	C₂×#336	—	19	1	no	—
228	C₂×#336	—	19	1	no	—
229	C₂×#336	—	19	1	no	—
230	C₂×#336	—	19	1	no	—
231	C₂×#336	D₁₉	1	1	yes	characteristic
232	C₄×#95	—	19	1	no	—
233	C₂²×C₁₉	#376	1	1	yes	characteristic
234	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
235	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
236	C₂²×C₁₉	#387	1	1	yes	characteristic
237	C₂²×C₁₉	#387	1	1	yes	characteristic
238	C₂²×C₁₉	#388	1	1	yes	characteristic
239	C₂²×C₁₉	#388	1	1	yes	characteristic
240	C₂²×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
241	C₂²×C₁₉	C₂×#97	1	1	yes	characteristic
242	C₂²×C₁₉	#405	1	1	yes	characteristic
243	C₂²×C₁₉	#405	1	1	yes	characteristic
244	C₂²×C₁₉	#431	1	2	yes	—
245	C₂²×C₁₉	#431	1	2	yes	—
246	C₂²×C₁₉	#433	1	2	yes	—
247	C₂²×C₁₉	#433	1	2	yes	—
248	C₂²×C₁₉	C₈×D₄	1	2	yes	—
249	C₂²×C₁₉	C₈×D₄	1	2	yes	—
250	C₂²×C₁₉	C₈×D₄	1	2	yes	—
251	C₂²×C₁₉	#435	1	2	yes	—
252	C₂²×C₁₉	#435	1	2	yes	—
253	C₂²×C₁₉	#436	1	2	yes	—
254	C₂²×C₁₉	C₈×Q₈	1	2	yes	—
255	C₂²×C₁₉	#446	1	2	yes	—
256	C₄×C₁₉	—	4	4	no	—
257	C₄×C₁₉	#380	1	1	yes	characteristic
258	C₄×C₁₉	#381	1	1	yes	characteristic
259	C₄×C₁₉	#382	1	1	yes	characteristic
260	C₄×C₁₉	#383	1	1	yes	characteristic
261	C₄×C₁₉	#387	1	1	yes	characteristic
262	C₄×C₁₉	#387	1	1	yes	characteristic
263	C₄×C₁₉	#388	1	1	yes	characteristic
264	C₄×C₁₉	#388	1	1	yes	characteristic
265	Dic₁₉	—	2	4	no	—
266	Dic₁₉	—	2	4	no	—
267	Dic₁₉	—	4	4	no	—
268	C₂³×C₈	—	19	1	no	—
269	C₂³×C₈	—	19	1	no	—
270	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
271	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
272	C₂²×C₄²	—	19	1	no	—
273	C₂²×C₄²	—	19	1	no	—
274	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
275	C₂×C₄×C₈	—	19	4	no	—
276	C₂×C₄×C₈	—	38	2	no	—
277	C₂×C₄×C₈	—	38	2	no	—
278	C₂×#95	—	19	2	no	—
279	C₂×#95	—	19	2	no	—
280	#336	—	2	2	no	—
281	#336	—	19	4	no	—
282	#336	—	38	2	no	—
283	#336	—	38	2	no	—
284	#336	—	38	2	no	—
285	C₂×C₁₉	#1434	1	1	yes	characteristic
286	C₂×C₁₉	#1744	1	1	yes	characteristic
287	C₂×C₁₉	#1746	1	1	yes	characteristic
288	C₂×C₁₉	C₈×C₂²⋊C₄	1	1	yes	characteristic
289	C₂×C₁₉	#1752	1	1	yes	characteristic
290	C₂×C₁₉	C₈×C₄⋊C₄	1	1	yes	characteristic
291	C₂×C₁₉	#1770	1	1	yes	characteristic
292	C₂×C₁₉	#1916	1	2	yes	—
293	C₂×C₁₉	#1916	1	2	yes	—
294	C₂×C₁₉	#1923	1	2	yes	—
295	C₂×C₁₉	#1923	1	2	yes	—
296	C₂³×C₄	—	19	1	no	—
297	C₂³×C₄	—	19	1	no	—
298	C₂³×C₄	—	19	2	no	—
299	C₂³×C₄	C₄×D₁₉	1	2	yes	—
300	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
301	C₂²×C₈	—	2	1	no	—
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	—	2	1	no	—
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	—	2	1	no	—
311	C₂²×C₈	—	19	2	no	—
312	C₂²×C₈	—	19	2	no	—
313	C₂²×C₈	—	19	2	no	—
314	C₂²×C₈	—	19	2	no	—
315	C₂²×C₈	—	38	1	no	—
316	C₂²×C₈	—	38	1	no	—
317	C₂²×C₈	—	38	1	no	—
318	C₂²×C₈	—	38	1	no	—
319	C₂²×C₈	—	38	1	no	—
320	C₂²×C₈	—	38	1	no	—
321	C₂²×C₈	—	38	1	no	—
322	C₂²×C₈	—	38	1	no	—
323	C₂²×C₈	—	38	1	no	—
324	C₂²×C₈	—	38	1	no	—
325	C₂²×C₈	C₄×D₁₉	1	2	yes	—
326	C₂²×C₈	C₄×D₁₉	1	2	yes	—
327	C₂²×C₈	D₇₆	1	2	yes	—
328	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	—	19	2	no	—
336	C₂×C₄²	—	19	2	no	—
337	C₂×C₄²	—	38	1	no	—
338	C₂×C₄²	—	38	1	no	—
339	C₂×C₄²	—	38	1	no	—
340	C₂×C₄²	—	38	1	no	—
341	C₂×C₄²	—	38	1	no	—
342	C₂×C₄²	—	38	1	no	—
343	C₂×C₄²	—	38	1	no	—
344	C₂×C₄²	—	38	1	no	—
345	C₂×C₄²	—	38	1	no	—
346	C₂×C₄²	—	38	1	no	—
347	C₄×C₈	—	38	8	no	—
348	#95	—	19	8	no	—
349	#95	—	38	4	no	—
350	C₁₉	#10797	1	1	yes	characteristic, complemented, Sylow
351	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	19	2	no	—
359	C₂²×C₄	—	19	2	no	—
360	C₂²×C₄	—	19	4	no	—
361	C₂²×C₄	—	19	4	no	—
362	C₂²×C₄	—	19	4	no	—
363	C₂²×C₄	—	38	1	no	—
364	C₂²×C₄	—	38	1	no	—
365	C₂²×C₄	—	38	2	no	—
366	C₂²×C₄	—	38	2	no	—
367	C₂²×C₄	—	38	1	no	—
368	C₂²×C₄	—	38	1	no	—
369	C₂²×C₄	—	38	2	no	—
370	C₂²×C₄	—	38	2	no	—
371	C₂²×C₄	—	38	2	no	—
372	C₂²×C₄	—	38	2	no	—
373	C₂²×C₄	—	38	2	no	—
374	C₂²×C₄	—	38	2	no	—
375	C₂²×C₄	C₈×D₁₉	1	4	yes	—
376	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
379	C₂²×C₄	#64541	1	1	yes	characteristic
380	C₂²×C₄	#64541	1	1	yes	characteristic
381	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
382	C₂²×C₄	#64543	1	1	yes	characteristic
383	C₂²×C₄	#64543	1	1	yes	characteristic
384	C₂²×C₄	#64543	1	1	yes	characteristic
385	C₂²×C₄	#64543	1	1	yes	characteristic
386	C₂²×C₄	#64543	1	1	yes	characteristic
387	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
388	C₂²×C₄	#64545	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	4	1	no	—
400	C₂×C₈	—	4	1	no	—
401	C₂×C₈	—	4	1	no	—
402	C₂×C₈	—	4	1	no	—
403	C₂×C₈	—	19	4	no	—
404	C₂×C₈	—	38	2	no	—
405	C₂×C₈	—	38	2	no	—
406	C₂×C₈	—	38	2	no	—
407	C₂×C₈	—	38	2	no	—
408	C₂×C₈	—	38	2	no	—
409	C₂×C₈	—	38	2	no	—
410	C₂×C₈	—	38	2	no	—
411	C₂×C₈	—	38	2	no	—
412	C₂×C₈	—	38	2	no	—
413	C₂×C₈	—	76	1	no	—
414	C₂×C₈	—	76	1	no	—
415	C₂×C₈	—	76	1	no	—
416	C₂×C₈	—	76	1	no	—
417	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
418	C₄²	—	4	1	no	—
419	C₄²	—	4	1	no	—
420	C₄²	—	4	1	no	—
421	C₄²	—	4	1	no	—
422	C₄²	—	38	2	no	—
423	C₄²	—	38	2	no	—
424	C₄²	—	38	2	no	—
425	C₄²	—	38	2	no	—
426	C₄²	—	76	1	no	—
427	C₄²	—	76	1	no	—
428	C₄²	—	76	1	no	—
429	C₄²	—	76	1	no	—
430	C₂³	C₄²×D₁₉	1	1	yes	characteristic
431	C₂³	C₄×D₇₆	1	1	yes	characteristic
432	C₂³	#10597323	1	1	yes	characteristic
433	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
434	C₂³	#10597333	1	1	yes	characteristic
435	C₂³	#10597338	1	1	yes	characteristic
436	C₂³	C₂×C₈×D₁₉	1	2	yes	—
437	C₂³	#10597347	1	2	yes	—
438	C₂³	M₁₆×D₁₉	1	2	yes	—
439	C₂³	#10597353	1	2	yes	—
440	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	19	4	no	—
449	C₂×C₄	—	19	4	no	—
450	C₂×C₄	—	38	4	no	—
451	C₂×C₄	—	38	4	no	—
452	C₂×C₄	—	38	4	no	—
453	C₂×C₄	—	38	4	no	—
454	C₂×C₄	—	38	2	no	—
455	C₂×C₄	—	38	2	no	—
456	C₂×C₄	—	38	2	no	—
457	C₂×C₄	—	38	2	no	—
458	C₂×C₄	—	38	4	no	—
459	C₂×C₄	—	38	4	no	—
460	C₂×C₄	—	38	4	no	—
461	C₂×C₄	—	76	2	no	—
462	C₂×C₄	—	76	2	no	—
463	C₂×C₄	—	76	2	no	—
464	C₂×C₄	—	76	2	no	—
465	C₂×C₄	#10597318	1	1	yes	characteristic
466	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
467	C₂×C₄	#10597323	1	1	yes	characteristic
468	C₂×C₄	#10597323	1	1	yes	characteristic
469	C₂×C₄	#10597323	1	1	yes	characteristic
470	C₂×C₄	#10597325	1	1	yes	characteristic
471	C₂×C₄	#10597325	1	1	yes	characteristic
472	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
473	C₂×C₄	#10597331	1	1	yes	characteristic
474	C₂×C₄	#10597331	1	1	yes	characteristic
475	C₂×C₄	#10597332	1	1	yes	characteristic
476	C₂×C₄	#10597332	1	1	yes	characteristic
477	C₂×C₄	#10597333	1	1	yes	characteristic
478	C₂×C₄	#10597335	1	1	yes	characteristic
479	C₂×C₄	#10597335	1	1	yes	characteristic
480	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
481	C₂×C₄	#10597338	1	1	yes	characteristic
482	C₂×C₄	#10597338	1	1	yes	characteristic
483	C₂×C₄	#10597341	1	1	yes	characteristic
484	C₂×C₄	#10597343	1	1	yes	characteristic
485	C₂×C₄	#10597344	1	1	yes	characteristic
486	C₂×C₄	#10597344	1	1	yes	characteristic
487	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
488	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
489	C₂×C₄	#10597381	1	1	yes	characteristic
490	C₂×C₄	#10597381	1	1	yes	characteristic
491	C₂×C₄	#10597384	1	1	yes	characteristic
492	C₂×C₄	#10597392	1	1	yes	characteristic
493	C₈	—	2	4	no	—
494	C₈	—	4	2	no	—
495	C₈	—	38	4	no	—
496	C₈	—	76	2	no	—
497	C₂²	#11926389	1	1	yes	characteristic
498	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
499	C₂²	#11926395	1	1	yes	characteristic
500	C₂²	#11926425	1	1	yes	characteristic
501	C₂²	#11926429	1	1	yes	characteristic
502	C₂²	#11926432	1	1	yes	characteristic
503	C₂²	#11926436	1	1	yes	characteristic
504	C₂²	C₄×C₈×D₁₉	1	1	yes	characteristic
505	C₂²	#97×D₁₉	1	1	yes	characteristic
506	C₂²	#11926498	1	1	yes	characteristic
507	C₂²	#11926501	1	1	yes	characteristic
508	C₂²	#11926594	1	2	yes	—
509	C₂²	#11926596	1	2	yes	—
510	C₂²	#11926602	1	2	yes	—
511	C₂²	#11926604	1	2	yes	—
512	C₂²	(C₂²⋊D₁₉)⋊C₈	1	2	yes	—
513	C₂²	C₈×C₂²⋊D₁₉	1	2	yes	—
514	C₂²	C₈×D₇₆	1	2	yes	—
515	C₂²	#11926613	1	2	yes	—
516	C₂²	#11926617	1	2	yes	—
517	C₂²	#11926619	1	2	yes	—
518	C₂²	#11926668	1	2	yes	—
519	C₂²	#11926673	1	2	yes	—
520	C₄	—	4	4	no	—
521	C₄	—	38	4	no	—
522	C₄	—	38	4	no	—
523	C₄	—	76	4	no	—
524	C₄	#11926401	1	1	yes	characteristic
525	C₄	#11926405	1	1	yes	characteristic
526	C₄	#11926408	1	1	yes	characteristic
527	C₄	#11926411	1	1	yes	characteristic
528	C₄	#11926425	1	1	yes	characteristic
529	C₄	#11926429	1	1	yes	characteristic
530	C₄	#11926432	1	1	yes	characteristic
531	C₄	#11926436	1	1	yes	characteristic
532	C₂	#14561859	1	1	yes	characteristic
533	C₂	#14563379	1	1	yes	characteristic
534	C₂	#14563385	1	1	yes	characteristic
535	C₂	C₈×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
536	C₂	#14563412	1	1	yes	characteristic
537	C₂	#14563496	1	1	yes	characteristic
538	C₂	#14563501	1	1	yes	characteristic
539	C₂	#14564189	1	2	yes	—
540	C₂	#14564193	1	2	yes	—
541	C₂	#14564238	1	2	yes	—
542	C₂	#14564242	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂×C₄×C₈
Fitting	C₂×C₁₉×#336	C₂
socle, prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#336	D₁₉
hypocenter	C₁₉	#10797
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
14. C₂×C₈×Dic₁₉	C₄	semidirect
20. #11926298	C₄	semidirect
77. C₁₉⋊#95	C₈	semidirect
350. C₁₉	#10797	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×Dic₁₉	2
C₂×#11926299	2
C₂×#11926298	2
C₄×C₁₉⋊#95	2
C₂×C₁₉×#336	2
#10797	19