Subgroups — C₁₉×#8343 #18014302

Order 4864.

802 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#333	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#332	C₂	1	2	yes	maximal, complemented
6	C₁₉×#533	—	2	4	no	—
7	C₁₉×#533	—	2	4	no	—
8	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#125	—	2	1	no	—
11	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
12	C₂×C₁₉×C₂²⋊Q₈	C₄	1	2	yes	—
13	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₉	C₄	1	2	yes	—
15	C₂×C₁₉×#117	—	2	1	no	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
20	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
21	C₁₉×#336	—	2	1	no	—
22	C₁₉×#336	—	2	1	no	—
23	C₁₉×#333	—	2	4	no	—
24	C₁₉×#332	—	2	4	no	—
25	C₂²×Q₈×C₁₉	—	2	1	no	—
26	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	—	2	2	no	—
31	C₂²×C₈×C₁₉	—	2	2	no	—
32	C₁₉×C₄⋊Q₈	—	2	2	no	—
33	C₁₉×C₄⋊Q₈	—	2	2	no	—
34	C₁₉×C₄⋊Q₈	D₄	1	4	yes	—
35	C₁₉×C₄⋊Q₈	D₄	1	4	yes	—
36	C₁₉×#125	—	2	8	no	—
37	C₁₉×C₂²⋊Q₈	—	2	8	no	—
38	C₁₉×C₂²⋊Q₈	—	2	4	no	—
39	C₁₉×C₂²⋊Q₈	—	2	4	no	—
40	C₄×Q₈×C₁₉	—	2	8	no	—
41	C₄×Q₈×C₁₉	—	2	4	no	—
42	C₄×Q₈×C₁₉	—	2	4	no	—
43	C₁₉×#117	—	2	8	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄²×C₁₉	—	2	2	no	—
52	C₂×C₄²×C₁₉	—	2	2	no	—
53	C₂×C₄²×C₁₉	—	2	2	no	—
54	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×C₄⋊C₈	—	2	2	no	—
59	C₁₉×C₄⋊C₈	—	2	2	no	—
60	C₁₉×C₄⋊C₈	—	2	2	no	—
61	C₁₉×C₄⋊C₈	—	2	2	no	—
62	C₁₉×C₂²⋊C₈	—	4	2	no	—
63	C₁₉×C₂²⋊C₈	—	4	2	no	—
64	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×Q₈×C₁₉	—	2	2	no	—
66	C₂×Q₈×C₁₉	—	2	4	no	—
67	C₂×Q₈×C₁₉	—	4	2	no	—
68	C₂×Q₈×C₁₉	—	4	2	no	—
69	C₂×Q₈×C₁₉	—	4	2	no	—
70	C₂×Q₈×C₁₉	—	4	1	no	—
71	C₂×Q₈×C₁₉	—	4	1	no	—
72	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	—	4	1	no	—
85	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
89	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
90	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂×C₈×C₁₉	—	4	2	no	—
94	C₂×C₈×C₁₉	—	4	2	no	—
95	C₂×C₈×C₁₉	—	4	2	no	—
96	C₂×C₈×C₁₉	—	4	2	no	—
97	C₂×C₈×C₁₉	—	4	2	no	—
98	C₂×C₈×C₁₉	—	4	2	no	—
99	C₄⋊C₄×C₁₉	—	2	8	no	—
100	C₄⋊C₄×C₁₉	—	2	8	no	—
101	C₄⋊C₄×C₁₉	—	2	2	no	—
102	C₄⋊C₄×C₁₉	—	2	4	no	—
103	C₄⋊C₄×C₁₉	—	2	4	no	—
104	C₄⋊C₄×C₁₉	—	2	4	no	—
105	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
106	C₂²⋊C₄×C₁₉	—	2	8	no	—
107	C₄²×C₁₉	—	2	8	no	—
108	C₄²×C₁₉	—	2	1	no	—
109	C₄²×C₁₉	—	2	1	no	—
110	C₄²×C₁₉	—	2	2	no	—
111	C₄²×C₁₉	—	2	2	no	—
112	C₄²×C₁₉	C₂×D₄	1	2	yes	—
113	C₄²×C₁₉	C₂×D₄	1	2	yes	—
114	#8343	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₁₉	—	2	1	no	—
116	C₂³×C₁₉	—	2	1	no	—
117	C₂³×C₁₉	—	2	1	no	—
118	C₂³×C₁₉	—	2	1	no	—
119	C₂³×C₁₉	—	2	1	no	—
120	C₂³×C₁₉	—	2	1	no	—
121	C₂³×C₁₉	#103	1	2	yes	—
122	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	Q₈×C₁₉	—	4	4	no	—
124	Q₈×C₁₉	—	4	4	no	—
125	Q₈×C₁₉	—	4	4	no	—
126	Q₈×C₁₉	—	4	4	no	—
127	C₂×C₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	4	no	—
132	C₂×C₄×C₁₉	—	2	4	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	4	no	—
136	C₂×C₄×C₁₉	—	2	4	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	2	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	#103	1	2	yes	—
150	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#120	1	2	yes	—
153	C₂×C₄×C₁₉	#120	1	2	yes	—
154	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#135	1	2	yes	—
157	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#137	1	2	yes	—
159	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
160	C₈×C₁₉	—	8	2	no	—
161	C₈×C₁₉	—	8	2	no	—
162	C₂×#533	C₂×C₁₉	1	1	yes	characteristic
163	#1797	C₂×C₁₉	1	1	yes	characteristic
164	#1797	C₂×C₁₉	1	1	yes	characteristic
165	C₂×#333	C₂×C₁₉	1	2	yes	complemented
166	C₂×#332	C₂×C₁₉	1	2	yes	complemented
167	C₂²×C₁₉	—	2	2	no	—
168	C₂²×C₁₉	—	2	2	no	—
169	C₂²×C₁₉	—	2	2	no	—
170	C₂²×C₁₉	—	4	1	no	—
171	C₂²×C₁₉	—	4	1	no	—
172	C₂²×C₁₉	—	4	1	no	—
173	C₂²×C₁₉	—	4	1	no	—
174	C₂²×C₁₉	#379	1	1	yes	characteristic
175	C₂²×C₁₉	#413	1	1	yes	characteristic
176	C₂²×C₁₉	#413	1	1	yes	characteristic
177	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
178	C₂²×C₁₉	#416	1	1	yes	characteristic
179	C₂²×C₁₉	#417	1	1	yes	characteristic
180	C₂²×C₁₉	#419	1	1	yes	characteristic
181	C₄×C₁₉	—	2	1	no	—
182	C₄×C₁₉	—	2	1	no	—
183	C₄×C₁₉	—	2	2	no	—
184	C₄×C₁₉	—	4	1	no	—
185	C₄×C₁₉	—	4	4	no	—
186	C₄×C₁₉	—	4	1	no	—
187	C₄×C₁₉	—	4	4	no	—
188	C₄×C₁₉	#448	1	2	yes	—
189	C₄×C₁₉	#449	1	2	yes	—
190	C₄×C₁₉	#451	1	2	yes	—
191	C₄×C₁₉	#452	1	2	yes	—
192	#533	—	2	4	no	—
193	#533	—	2	4	no	—
194	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
195	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
196	C₂×#125	—	2	1	no	—
197	C₂×C₂²⋊Q₈	—	2	1	no	—
198	C₂×C₂²⋊Q₈	C₄×C₁₉	1	2	yes	—
199	C₂×C₄×Q₈	—	2	1	no	—
200	C₂×C₄×Q₈	C₄×C₁₉	1	2	yes	—
201	C₂×#117	—	2	1	no	—
202	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
203	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
205	C₂×C₂²⋊C₈	—	2	1	no	—
206	C₂×C₂²⋊C₈	—	2	1	no	—
207	#336	—	2	1	no	—
208	#336	—	2	1	no	—
209	#333	—	2	4	no	—
210	#332	—	2	4	no	—
211	C₂×C₁₉	—	4	2	no	—
212	C₂×C₁₉	#1542	1	1	yes	characteristic
213	C₂×C₁₉	#1550	1	1	yes	characteristic
214	C₂×C₁₉	#1554	1	1	yes	characteristic
215	C₂×C₁₉	#1559	1	1	yes	characteristic
216	C₂×C₁₉	#1785	1	1	yes	characteristic
217	C₂×C₁₉	#1787	1	1	yes	characteristic
218	C₂×C₁₉	#1788	1	1	yes	characteristic
219	C₂²×Q₈	—	2	1	no	—
220	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
221	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
222	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
223	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
224	C₂²×C₈	—	2	2	no	—
225	C₂²×C₈	—	2	2	no	—
226	C₄⋊Q₈	—	2	2	no	—
227	C₄⋊Q₈	—	2	2	no	—
228	C₄⋊Q₈	D₄×C₁₉	1	4	yes	—
229	C₄⋊Q₈	D₄×C₁₉	1	4	yes	—
230	#125	—	2	8	no	—
231	C₂²⋊Q₈	—	2	8	no	—
232	C₂²⋊Q₈	—	2	4	no	—
233	C₂²⋊Q₈	—	2	4	no	—
234	C₄×Q₈	—	2	8	no	—
235	C₄×Q₈	—	2	4	no	—
236	C₄×Q₈	—	2	4	no	—
237	#117	—	2	8	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
249	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
250	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
252	C₄⋊C₈	—	2	2	no	—
253	C₄⋊C₈	—	2	2	no	—
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	2	2	no	—
256	C₂²⋊C₈	—	4	2	no	—
257	C₂²⋊C₈	—	4	2	no	—
258	C₁₉	#8343	1	1	yes	characteristic, direct product factor, Sylow
259	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	—	2	4	no	—
262	C₂×Q₈	—	4	2	no	—
263	C₂×Q₈	—	4	2	no	—
264	C₂×Q₈	—	4	2	no	—
265	C₂×Q₈	—	4	1	no	—
266	C₂×Q₈	—	4	1	no	—
267	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
281	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
282	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
283	C₂²×C₄	SD₁₆×C₁₉	1	2	yes	—
284	C₂²×C₄	Q₁₆×C₁₉	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
288	C₂×C₈	—	4	2	no	—
289	C₂×C₈	—	4	2	no	—
290	C₂×C₈	—	4	2	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	—	4	2	no	—
293	C₂×C₈	—	4	2	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
301	C₂²⋊C₄	—	2	8	no	—
302	C₄²	—	2	8	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	C₂×D₄×C₁₉	1	2	yes	—
308	C₄²	C₂×D₄×C₁₉	1	2	yes	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	C₁₉×#103	1	2	yes	—
316	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
317	Q₈	—	4	4	no	—
318	Q₈	—	4	4	no	—
319	Q₈	—	4	4	no	—
320	Q₈	—	4	4	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	C₁₉×#103	1	2	yes	—
344	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
345	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
346	C₂×C₄	C₁₉×#120	1	2	yes	—
347	C₂×C₄	C₁₉×#120	1	2	yes	—
348	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
349	C₂×C₄	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
350	C₂×C₄	C₁₉×#135	1	2	yes	—
351	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
352	C₂×C₄	C₁₉×#137	1	2	yes	—
353	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
354	C₈	—	8	2	no	—
355	C₈	—	8	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	C₁₉×#379	1	1	yes	characteristic
364	C₂²	C₁₉×#413	1	1	yes	characteristic
365	C₂²	C₁₉×#413	1	1	yes	characteristic
366	C₂²	C₂×C₁₉×#103	1	1	yes	characteristic
367	C₂²	C₁₉×#416	1	1	yes	characteristic
368	C₂²	C₁₉×#417	1	1	yes	characteristic
369	C₂²	C₁₉×#419	1	1	yes	characteristic
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	2	no	—
373	C₄	—	4	1	no	—
374	C₄	—	4	4	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	4	no	—
377	C₄	C₁₉×#448	1	2	yes	—
378	C₄	C₁₉×#449	1	2	yes	—
379	C₄	C₁₉×#451	1	2	yes	—
380	C₄	C₁₉×#452	1	2	yes	—
381	C₂	—	4	2	no	—
382	C₂	C₁₉×#1542	1	1	yes	characteristic
383	C₂	C₁₉×#1550	1	1	yes	characteristic
384	C₂	C₁₉×#1554	1	1	yes	characteristic
385	C₂	C₁₉×#1559	1	1	yes	characteristic
386	C₂	C₁₉×#1785	1	1	yes	characteristic
387	C₂	C₁₉×#1787	1	1	yes	characteristic
388	C₂	C₁₉×#1788	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₁₉×#333	C₂	semidirect
5. C₂×C₁₉×#332	C₂	semidirect
114. #8343	C₁₉	direct (N × H)
165. C₂×#333	C₂×C₁₉	semidirect
166. C₂×#332	C₂×C₁₉	semidirect
258. C₁₉	#8343	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×C₁₉×#533	2
C₁₉×#1797	2
C₂×C₁₉×#333	2
C₂×C₁₉×#332	2
#8343	19

Subgroups — C19×#8343 #18014302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8343 #18014302