Subgroups — C₁₉×#18353 #18024312

Order 4864.

946 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3501	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3195	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2638	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1611	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1608	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1605	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1602	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1511	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1465	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#554	—	2	4	no	—
11	C₁₉×#554	—	2	2	no	—
12	D₄×Q₈×C₁₉	—	2	2	no	—
13	C₁₉×#544	C₂²	1	2	yes	—
14	C₁₉×#543	—	2	1	no	—
15	C₁₉×#543	C₂²	1	2	yes	—
16	C₁₉×#533	—	2	1	no	—
17	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₉×#518	—	2	1	no	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#483	—	2	2	no	—
23	C₁₉×#483	C₂²	1	4	yes	—
24	C₁₉×#470	—	2	4	no	—
25	C₁₉×#451	—	2	2	no	—
26	C₁₉×#451	C₂²	1	4	yes	—
27	C₁₉×#407	C₂²	1	2	yes	—
28	C₁₉×#398	C₂²	1	1	yes	characteristic
29	C₁₉×#397	—	2	1	no	—
30	C₁₉×#397	C₂²	1	1	yes	characteristic
31	C₁₉×#395	C₂²	1	1	yes	characteristic
32	C₁₉×#394	—	2	1	no	—
33	C₁₉×#393	C₂²	1	1	yes	characteristic
34	C₁₉×#387	—	2	1	no	—
35	C₁₉×#385	—	2	1	no	—
36	C₁₉×#381	C₂²	1	1	yes	characteristic
37	C₁₉×#328	C₂²	1	4	yes	—
38	C₁₉×#328	C₂²	1	4	yes	—
39	C₁₉×#324	C₂²	1	2	yes	—
40	C₁₉×#323	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
43	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₁₉	—	2	4	no	—
48	C₂×M₁₆×C₁₉	—	2	2	no	—
49	C₁₉×C₄⋊Q₈	—	2	1	no	—
50	C₁₉×C₄⋊Q₈	—	2	1	no	—
51	C₁₉×C₄⋊Q₈	—	2	4	no	—
52	C₁₉×#125	—	2	2	no	—
53	C₁₉×#125	—	2	4	no	—
54	C₁₉×C₂²⋊Q₈	—	2	2	no	—
55	C₁₉×C₂²⋊Q₈	—	2	2	no	—
56	C₁₉×C₂²⋊Q₈	—	2	4	no	—
57	C₁₉×C₂²⋊Q₈	—	2	4	no	—
58	C₁₉×C₂²⋊Q₈	—	2	4	no	—
59	C₁₉×C₂²⋊Q₈	—	2	2	no	—
60	C₁₉×C₂²⋊Q₈	—	2	2	no	—
61	C₁₉×C₂²⋊Q₈	—	2	2	no	—
62	C₁₉×C₂²⋊Q₈	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	4	no	—
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
67	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
68	C₄×Q₈×C₁₉	—	2	2	no	—
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₄×D₄×C₁₉	—	2	4	no	—
71	C₄×D₄×C₁₉	—	2	4	no	—
72	C₄×D₄×C₁₉	—	2	2	no	—
73	C₄×D₄×C₁₉	—	2	2	no	—
74	C₁₉×#117	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
93	C₁₉×#106	—	2	4	no	—
94	C₁₉×#103	—	2	4	no	—
95	C₁₉×#103	—	2	4	no	—
96	C₁₉×C₂²⋊C₈	—	2	2	no	—
97	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
98	C₁₉×#95	—	2	1	no	—
99	C₁₉×#95	—	2	1	no	—
100	C₁₉×#95	—	2	1	no	—
101	C₁₉×#95	—	2	1	no	—
102	C₁₉×#95	—	2	1	no	—
103	C₁₉×#95	C₂³	1	1	yes	characteristic
104	C₁₉×#95	C₂³	1	1	yes	characteristic
105	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	2	2	no	—
110	C₂×Q₈×C₁₉	—	2	2	no	—
111	C₂×Q₈×C₁₉	—	8	1	no	—
112	C₂×Q₈×C₁₉	—	8	2	no	—
113	C₂×Q₈×C₁₉	—	8	2	no	—
114	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	8	1	no	—
129	C₂²×C₄×C₁₉	—	8	1	no	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
137	Q₁₆×C₁₉	—	8	4	no	—
138	M₁₆×C₁₉	—	8	2	no	—
139	C₂×C₈×C₁₉	—	2	4	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	4	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	4	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	4	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	4	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	4	1	no	—
152	C₄⋊C₄×C₁₉	—	4	1	no	—
153	C₄⋊C₄×C₁₉	—	4	2	no	—
154	C₄⋊C₄×C₁₉	—	8	1	no	—
155	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
156	C₂²⋊C₄×C₁₉	—	2	4	no	—
157	C₂²⋊C₄×C₁₉	—	2	4	no	—
158	C₂²⋊C₄×C₁₉	—	2	2	no	—
159	C₂²⋊C₄×C₁₉	—	2	4	no	—
160	C₂²⋊C₄×C₁₉	—	2	2	no	—
161	C₂²⋊C₄×C₁₉	—	4	2	no	—
162	C₂²⋊C₄×C₁₉	—	4	2	no	—
163	C₂²⋊C₄×C₁₉	—	8	1	no	—
164	C₂²⋊C₄×C₁₉	—	8	1	no	—
165	C₄²×C₁₉	—	2	4	no	—
166	C₄²×C₁₉	—	2	1	no	—
167	C₄²×C₁₉	—	2	1	no	—
168	#18353	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂³×C₁₉	—	2	1	no	—
170	C₂³×C₁₉	—	2	1	no	—
171	C₂³×C₁₉	—	2	1	no	—
172	C₂³×C₁₉	—	2	1	no	—
173	C₂³×C₁₉	—	4	1	no	—
174	C₂³×C₁₉	—	4	1	no	—
175	C₂³×C₁₉	—	4	1	no	—
176	C₂³×C₁₉	—	4	1	no	—
177	C₂³×C₁₉	#120	1	2	yes	—
178	C₂³×C₁₉	#137	1	2	yes	—
179	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₁₉	—	4	4	no	—
181	Q₈×C₁₉	—	4	4	no	—
182	Q₈×C₁₉	—	4	4	no	—
183	Q₈×C₁₉	—	8	2	no	—
184	Q₈×C₁₉	—	8	2	no	—
185	D₄×C₁₉	—	2	8	no	—
186	C₂×C₄×C₁₉	—	2	1	no	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	8	1	no	—
212	C₂×C₄×C₁₉	—	8	2	no	—
213	C₂×C₄×C₁₉	—	8	2	no	—
214	C₂×C₄×C₁₉	—	8	2	no	—
215	C₂×C₄×C₁₉	—	8	2	no	—
216	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
217	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
218	C₂×C₄×C₁₉	#137	1	2	yes	—
219	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
220	C₈×C₁₉	—	4	4	no	—
221	#3501	C₂×C₁₉	1	1	yes	characteristic
222	#3195	C₂×C₁₉	1	2	yes	complemented
223	#2638	C₂×C₁₉	1	1	yes	characteristic
224	#1611	C₂×C₁₉	1	2	yes	complemented
225	#1608	C₂×C₁₉	1	2	yes	complemented
226	#1605	C₂×C₁₉	1	2	yes	complemented
227	#1602	C₂×C₁₉	1	2	yes	complemented
228	#1511	C₂×C₁₉	1	2	yes	complemented
229	#1465	C₂×C₁₉	1	1	yes	characteristic
230	C₂²×C₁₉	—	2	1	no	—
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	2	no	—
233	C₂²×C₁₉	—	2	2	no	—
234	C₂²×C₁₉	—	2	2	no	—
235	C₂²×C₁₉	—	2	2	no	—
236	C₂²×C₁₉	—	4	2	no	—
237	C₂²×C₁₉	—	4	1	no	—
238	C₂²×C₁₉	—	4	1	no	—
239	C₂²×C₁₉	—	8	1	no	—
240	C₂²×C₁₉	—	8	1	no	—
241	C₂²×C₁₉	—	8	1	no	—
242	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
243	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
244	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
245	C₄×C₁₉	—	2	2	no	—
246	C₄×C₁₉	—	2	2	no	—
247	C₄×C₁₉	—	2	1	no	—
248	C₄×C₁₉	—	2	1	no	—
249	C₄×C₁₉	—	4	1	no	—
250	C₄×C₁₉	—	4	4	no	—
251	C₄×C₁₉	—	4	1	no	—
252	C₄×C₁₉	—	4	4	no	—
253	C₄×C₁₉	—	8	1	no	—
254	C₄×C₁₉	—	8	1	no	—
255	C₄×C₁₉	—	8	1	no	—
256	C₄×C₁₉	—	8	1	no	—
257	#554	—	2	4	no	—
258	#554	—	2	2	no	—
259	D₄×Q₈	—	2	2	no	—
260	#544	C₂²×C₁₉	1	2	yes	—
261	#543	—	2	1	no	—
262	#543	C₂²×C₁₉	1	2	yes	—
263	#533	—	2	1	no	—
264	C₂×C₂²⋊Q₈	—	2	1	no	—
265	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
266	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
267	#518	—	2	1	no	—
268	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
269	#483	—	2	2	no	—
270	#483	C₂²×C₁₉	1	4	yes	—
271	#470	—	2	4	no	—
272	#451	—	2	2	no	—
273	#451	C₂²×C₁₉	1	4	yes	—
274	#407	C₂²×C₁₉	1	2	yes	—
275	#398	C₂²×C₁₉	1	1	yes	characteristic
276	#397	—	2	1	no	—
277	#397	C₂²×C₁₉	1	1	yes	characteristic
278	#395	C₂²×C₁₉	1	1	yes	characteristic
279	#394	—	2	1	no	—
280	#393	C₂²×C₁₉	1	1	yes	characteristic
281	#387	—	2	1	no	—
282	#385	—	2	1	no	—
283	#381	C₂²×C₁₉	1	1	yes	characteristic
284	#328	C₂²×C₁₉	1	4	yes	—
285	#328	C₂²×C₁₉	1	4	yes	—
286	#324	C₂²×C₁₉	1	2	yes	—
287	#323	C₂²×C₁₉	1	2	yes	—
288	C₂×C₁₉	—	2	1	no	—
289	C₂×C₁₉	—	2	1	no	—
290	C₂×C₁₉	—	4	2	no	—
291	C₂×C₁₉	—	4	2	no	—
292	C₂×C₁₉	#3004	1	1	yes	characteristic
293	C₂×C₁₉	#3022	1	1	yes	characteristic
294	C₂×C₁₉	#3026	1	1	yes	characteristic
295	C₂²×Q₈	—	2	1	no	—
296	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
297	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
298	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
299	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
300	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
301	C₂×Q₁₆	—	2	4	no	—
302	C₂×M₁₆	—	2	2	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	—	2	4	no	—
306	#125	—	2	2	no	—
307	#125	—	2	4	no	—
308	C₂²⋊Q₈	—	2	2	no	—
309	C₂²⋊Q₈	—	2	2	no	—
310	C₂²⋊Q₈	—	2	4	no	—
311	C₂²⋊Q₈	—	2	4	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	C₂²⋊Q₈	—	2	2	no	—
314	C₂²⋊Q₈	—	2	2	no	—
315	C₂²⋊Q₈	—	2	2	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	—	2	4	no	—
318	C₂²⋊Q₈	—	2	2	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
321	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
322	C₄×Q₈	—	2	2	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×D₄	—	2	4	no	—
325	C₄×D₄	—	2	4	no	—
326	C₄×D₄	—	2	2	no	—
327	C₄×D₄	—	2	2	no	—
328	#117	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
346	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
347	#106	—	2	4	no	—
348	#103	—	2	4	no	—
349	#103	—	2	4	no	—
350	C₂²⋊C₈	—	2	2	no	—
351	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
352	#95	—	2	1	no	—
353	#95	—	2	1	no	—
354	#95	—	2	1	no	—
355	#95	—	2	1	no	—
356	#95	—	2	1	no	—
357	#95	C₂³×C₁₉	1	1	yes	characteristic
358	#95	C₂³×C₁₉	1	1	yes	characteristic
359	C₁₉	#18353	1	1	yes	characteristic, direct product factor, Sylow
360	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	8	1	no	—
367	C₂×Q₈	—	8	2	no	—
368	C₂×Q₈	—	8	2	no	—
369	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	8	1	no	—
384	C₂²×C₄	—	8	1	no	—
385	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
391	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
392	Q₁₆	—	8	4	no	—
393	M₁₆	—	8	2	no	—
394	C₂×C₈	—	2	4	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	4	1	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	8	1	no	—
410	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₂²⋊C₄	—	8	1	no	—
419	C₂²⋊C₄	—	8	1	no	—
420	C₄²	—	2	4	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	1	no	—
426	C₂³	—	2	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	—	4	1	no	—
431	C₂³	C₁₉×#120	1	2	yes	—
432	C₂³	C₁₉×#137	1	2	yes	—
433	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
434	Q₈	—	4	4	no	—
435	Q₈	—	4	4	no	—
436	Q₈	—	4	4	no	—
437	Q₈	—	8	2	no	—
438	Q₈	—	8	2	no	—
439	D₄	—	2	8	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	8	1	no	—
466	C₂×C₄	—	8	2	no	—
467	C₂×C₄	—	8	2	no	—
468	C₂×C₄	—	8	2	no	—
469	C₂×C₄	—	8	2	no	—
470	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
471	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
472	C₂×C₄	C₁₉×#137	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
474	C₈	—	4	4	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	8	1	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
488	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
489	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	4	no	—
498	C₄	—	8	1	no	—
499	C₄	—	8	1	no	—
500	C₄	—	8	1	no	—
501	C₄	—	8	1	no	—
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	4	2	no	—
505	C₂	—	4	2	no	—
506	C₂	C₁₉×#3004	1	1	yes	characteristic
507	C₂	C₁₉×#3022	1	1	yes	characteristic
508	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3195	C₂	semidirect
4. C₁₉×#1611	C₂	semidirect
5. C₁₉×#1608	C₂	semidirect
6. C₁₉×#1605	C₂	semidirect
7. C₁₉×#1602	C₂	semidirect
8. C₁₉×#1511	C₂	semidirect
168. #18353	C₁₉	direct (N × H)
222. #3195	C₂×C₁₉	semidirect
224. #1611	C₂×C₁₉	semidirect
225. #1608	C₂×C₁₉	semidirect
226. #1605	C₂×C₁₉	semidirect
227. #1602	C₂×C₁₉	semidirect
228. #1511	C₂×C₁₉	semidirect
359. C₁₉	#18353	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3501	2
C₁₉×#3195	2
C₁₉×#2638	2
C₁₉×#1611	2
C₁₉×#1608	2
C₁₉×#1605	2
C₁₉×#1602	2
C₁₉×#1511	2
C₁₉×#1465	2
#18353	19

Subgroups — C19×#18353 #18024312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18353 #18024312