Subgroups — C₁₉×#18429 #18024388

Order 4864.

932 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3561	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3218	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2640	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1606	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1602	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1506	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1500	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1469	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#563	—	2	1	no	—
11	C₁₉×#562	—	2	1	no	—
12	C₁₉×#556	—	2	1	no	—
13	C₁₉×#551	—	2	2	no	—
14	D₄×Q₈×C₁₉	—	2	1	no	—
15	C₁₉×#548	—	2	1	no	—
16	C₁₉×#546	—	2	1	no	—
17	C₁₉×#543	C₂²	1	2	yes	—
18	C₁₉×#542	—	2	1	no	—
19	C₁₉×#542	—	2	2	no	—
20	C₁₉×#538	C₂²	1	2	yes	—
21	C₁₉×#536	—	2	1	no	—
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₉×#529	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
26	C₁₉×#497	—	2	1	no	—
27	C₁₉×#494	—	2	1	no	—
28	C₁₉×#491	—	2	1	no	—
29	C₁₉×#487	—	2	1	no	—
30	C₁₉×#462	—	2	2	no	—
31	C₁₉×#462	—	2	1	no	—
32	C₁₉×#461	—	2	1	no	—
33	C₁₉×#451	C₂²	1	4	yes	—
34	C₁₉×#451	C₂²	1	2	yes	—
35	C₁₉×#448	C₂²	1	2	yes	—
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#431	C₂²	1	1	yes	characteristic
38	C₁₉×#397	—	2	2	no	—
39	C₁₉×#393	C₂²	1	4	yes	—
40	C₁₉×#391	—	2	1	no	—
41	C₁₉×#390	—	2	1	no	—
42	C₁₉×#376	C₂²	1	1	yes	characteristic
43	C₁₉×#328	C₂²	1	2	yes	—
44	C₁₉×#328	C₂²	1	4	yes	—
45	C₁₉×#327	C₂²	1	2	yes	—
46	C₁₉×#323	C₂²	1	4	yes	—
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	—	2	1	no	—
49	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
50	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂×Q₁₆×C₁₉	—	2	4	no	—
53	C₂×Q₁₆×C₁₉	—	2	2	no	—
54	C₂×SD₁₆×C₁₉	—	2	2	no	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	2	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
62	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#126	—	2	2	no	—
65	C₁₉×#126	—	2	2	no	—
66	C₁₉×#126	—	2	1	no	—
67	C₁₉×#125	—	2	1	no	—
68	C₁₉×#125	D₄	1	1	yes	characteristic
69	C₁₉×#124	—	2	1	no	—
70	C₁₉×#124	—	2	2	no	—
71	C₁₉×#124	—	2	2	no	—
72	C₁₉×#124	—	2	1	no	—
73	C₁₉×#124	—	2	1	no	—
74	C₁₉×#124	—	2	1	no	—
75	C₁₉×#124	—	2	1	no	—
76	C₁₉×#124	D₄	1	1	yes	characteristic
77	C₁₉×#123	—	2	2	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×#123	—	2	2	no	—
80	C₁₉×#123	—	2	1	no	—
81	C₁₉×#123	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	1	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	2	no	—
87	C₁₉×C₂²⋊Q₈	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	2	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
92	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#121	—	2	2	no	—
95	C₁₉×#121	—	2	2	no	—
96	C₁₉×#121	C₂³	1	1	yes	characteristic
97	C₁₉×#120	—	2	2	no	—
98	C₄×Q₈×C₁₉	—	2	1	no	—
99	C₄×Q₈×C₁₉	—	2	1	no	—
100	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
101	C₄×Q₈×C₁₉	D₄	1	2	yes	—
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	—	2	2	no	—
104	C₄×D₄×C₁₉	—	2	1	no	—
105	C₄×D₄×C₁₉	—	2	2	no	—
106	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
107	C₁₉×#117	—	2	2	no	—
108	C₁₉×#117	—	2	1	no	—
109	C₁₉×#117	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
114	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
115	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₉	—	2	1	no	—
117	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊C₈	—	2	1	no	—
119	C₁₉×C₄⋊C₈	—	2	1	no	—
120	C₁₉×#103	—	2	2	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#103	—	2	4	no	—
123	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
124	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
125	C₁₉×#97	—	2	1	no	—
126	C₄×C₈×C₁₉	—	2	1	no	—
127	C₁₉×#95	—	2	1	no	—
128	C₁₉×#95	—	2	4	no	—
129	C₁₉×#95	C₂³	1	2	yes	—
130	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
131	#41×C₁₉	—	8	2	no	—
132	C₂×Q₈×C₁₉	—	2	2	no	—
133	C₂×Q₈×C₁₉	—	2	1	no	—
134	C₂×Q₈×C₁₉	—	2	1	no	—
135	C₂×Q₈×C₁₉	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	2	2	no	—
137	C₂×Q₈×C₁₉	—	2	2	no	—
138	C₂×Q₈×C₁₉	—	4	2	no	—
139	C₂×Q₈×C₁₉	—	8	2	no	—
140	C₂×Q₈×C₁₉	—	8	2	no	—
141	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	—	4	2	no	—
149	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
160	Q₁₆×C₁₉	—	8	2	no	—
161	Q₁₆×C₁₉	—	8	4	no	—
162	SD₁₆×C₁₉	—	8	2	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	4	1	no	—
179	C₄⋊C₄×C₁₉	—	4	1	no	—
180	C₄⋊C₄×C₁₉	—	4	1	no	—
181	C₄⋊C₄×C₁₉	—	4	1	no	—
182	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
185	C₂²⋊C₄×C₁₉	—	2	2	no	—
186	C₂²⋊C₄×C₁₉	—	2	2	no	—
187	C₂²⋊C₄×C₁₉	—	2	2	no	—
188	C₂²⋊C₄×C₁₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	1	no	—
191	C₂²⋊C₄×C₁₉	—	2	2	no	—
192	C₂²⋊C₄×C₁₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	2	1	no	—
195	C₂²⋊C₄×C₁₉	—	2	1	no	—
196	C₂²⋊C₄×C₁₉	—	2	1	no	—
197	C₂²⋊C₄×C₁₉	—	2	2	no	—
198	C₂²⋊C₄×C₁₉	—	2	2	no	—
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂²⋊C₄×C₁₉	—	8	4	no	—
201	C₄²×C₁₉	—	2	2	no	—
202	C₄²×C₁₉	—	2	2	no	—
203	C₄²×C₁₉	—	2	1	no	—
204	C₄²×C₁₉	—	4	2	no	—
205	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
209	#18429	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂³×C₁₉	—	2	2	no	—
211	C₂³×C₁₉	—	2	1	no	—
212	C₂³×C₁₉	—	2	4	no	—
213	C₂³×C₁₉	—	4	2	no	—
214	C₂³×C₁₉	—	4	2	no	—
215	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
216	Q₈×C₁₉	—	4	1	no	—
217	Q₈×C₁₉	—	4	2	no	—
218	Q₈×C₁₉	—	4	2	no	—
219	Q₈×C₁₉	—	4	2	no	—
220	Q₈×C₁₉	—	4	4	no	—
221	Q₈×C₁₉	—	4	2	no	—
222	Q₈×C₁₉	—	4	2	no	—
223	Q₈×C₁₉	—	8	1	no	—
224	Q₈×C₁₉	—	8	2	no	—
225	D₄×C₁₉	—	4	1	no	—
226	D₄×C₁₉	—	4	2	no	—
227	D₄×C₁₉	—	4	2	no	—
228	D₄×C₁₉	—	8	1	no	—
229	D₄×C₁₉	—	8	2	no	—
230	D₄×C₁₉	—	8	2	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	4	4	no	—
245	C₂×C₄×C₁₉	—	4	2	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	8	2	no	—
248	C₂×C₄×C₁₉	—	8	2	no	—
249	C₂×C₄×C₁₉	—	8	2	no	—
250	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
251	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
252	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
256	C₈×C₁₉	—	4	2	no	—
257	C₈×C₁₉	—	4	2	no	—
258	#3561	C₂×C₁₉	1	1	yes	characteristic
259	#3218	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#3209	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#2640	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1606	C₂×C₁₉	1	4	yes	complemented
263	#1602	C₂×C₁₉	1	4	yes	complemented
264	#1506	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1500	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1469	C₂×C₁₉	1	1	yes	characteristic, complemented
267	C₂²×C₁₉	—	2	1	no	—
268	C₂²×C₁₉	—	2	1	no	—
269	C₂²×C₁₉	—	4	1	no	—
270	C₂²×C₁₉	—	4	2	no	—
271	C₂²×C₁₉	—	4	1	no	—
272	C₂²×C₁₉	—	4	2	no	—
273	C₂²×C₁₉	—	4	2	no	—
274	C₂²×C₁₉	—	4	1	no	—
275	C₂²×C₁₉	—	8	4	no	—
276	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
277	C₂²×C₁₉	#578	1	2	yes	—
278	C₄×C₁₉	—	2	1	no	—
279	C₄×C₁₉	—	2	1	no	—
280	C₄×C₁₉	—	2	1	no	—
281	C₄×C₁₉	—	2	1	no	—
282	C₄×C₁₉	—	2	1	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	4	1	no	—
285	C₄×C₁₉	—	4	2	no	—
286	C₄×C₁₉	—	4	2	no	—
287	C₄×C₁₉	—	4	1	no	—
288	C₄×C₁₉	—	4	2	no	—
289	C₄×C₁₉	—	8	2	no	—
290	C₄×C₁₉	—	8	2	no	—
291	C₄×C₁₉	#455	1	2	yes	—
292	#563	—	2	1	no	—
293	#562	—	2	1	no	—
294	#556	—	2	1	no	—
295	#551	—	2	2	no	—
296	D₄×Q₈	—	2	1	no	—
297	#548	—	2	1	no	—
298	#546	—	2	1	no	—
299	#543	C₂²×C₁₉	1	2	yes	—
300	#542	—	2	1	no	—
301	#542	—	2	2	no	—
302	#538	C₂²×C₁₉	1	2	yes	—
303	#536	—	2	1	no	—
304	#533	C₂²×C₁₉	1	1	yes	characteristic
305	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
306	#529	C₂²×C₁₉	1	1	yes	characteristic
307	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
308	#497	—	2	1	no	—
309	#494	—	2	1	no	—
310	#491	—	2	1	no	—
311	#487	—	2	1	no	—
312	#462	—	2	2	no	—
313	#462	—	2	1	no	—
314	#461	—	2	1	no	—
315	#451	C₂²×C₁₉	1	2	yes	—
316	#451	C₂²×C₁₉	1	4	yes	—
317	#448	C₂²×C₁₉	1	2	yes	—
318	#432	C₂²×C₁₉	1	1	yes	characteristic
319	#431	C₂²×C₁₉	1	1	yes	characteristic
320	#397	—	2	2	no	—
321	#393	C₂²×C₁₉	1	4	yes	—
322	#391	—	2	1	no	—
323	#390	—	2	1	no	—
324	#376	C₂²×C₁₉	1	1	yes	characteristic
325	#328	C₂²×C₁₉	1	2	yes	—
326	#328	C₂²×C₁₉	1	4	yes	—
327	#327	C₂²×C₁₉	1	2	yes	—
328	#323	C₂²×C₁₉	1	4	yes	—
329	C₂×C₁₉	—	2	2	no	—
330	C₂×C₁₉	—	8	1	no	—
331	C₂×C₁₉	—	8	2	no	—
332	C₂×C₁₉	#3011	1	1	yes	characteristic
333	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
334	C₂×C₁₉	#3027	1	1	yes	characteristic
335	C₂×#41	—	2	1	no	—
336	C₂²×Q₈	—	2	1	no	—
337	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
338	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
339	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
340	C₂×Q₁₆	—	2	4	no	—
341	C₂×Q₁₆	—	2	2	no	—
342	C₂×SD₁₆	—	2	2	no	—
343	C₄⋊Q₈	—	2	1	no	—
344	C₄⋊Q₈	—	2	2	no	—
345	C₄⋊Q₈	—	2	1	no	—
346	C₄⋊Q₈	—	2	1	no	—
347	C₄⋊Q₈	—	2	1	no	—
348	C₄⋊Q₈	—	2	1	no	—
349	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
350	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
351	#126	—	2	2	no	—
352	#126	—	2	2	no	—
353	#126	—	2	2	no	—
354	#126	—	2	1	no	—
355	#125	—	2	1	no	—
356	#125	D₄×C₁₉	1	1	yes	characteristic
357	#124	—	2	1	no	—
358	#124	—	2	2	no	—
359	#124	—	2	2	no	—
360	#124	—	2	1	no	—
361	#124	—	2	1	no	—
362	#124	—	2	1	no	—
363	#124	—	2	1	no	—
364	#124	D₄×C₁₉	1	1	yes	characteristic
365	#123	—	2	2	no	—
366	#123	—	2	2	no	—
367	#123	—	2	2	no	—
368	#123	—	2	1	no	—
369	#123	—	2	2	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	C₂²⋊Q₈	—	2	2	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	C₂²⋊Q₈	—	2	2	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₂²⋊Q₈	—	2	2	no	—
377	C₂²⋊Q₈	—	2	2	no	—
378	C₂²⋊Q₈	—	2	2	no	—
379	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
380	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
381	#121	—	2	1	no	—
382	#121	—	2	2	no	—
383	#121	—	2	2	no	—
384	#121	C₂³×C₁₉	1	1	yes	characteristic
385	#120	—	2	2	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
389	C₄×Q₈	D₄×C₁₉	1	2	yes	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
395	#117	—	2	2	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	—	2	2	no	—
401	C₂×C₂²⋊C₄	—	2	4	no	—
402	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
406	C₄⋊C₈	—	2	1	no	—
407	C₄⋊C₈	—	2	1	no	—
408	#103	—	2	2	no	—
409	#103	—	2	2	no	—
410	#103	—	2	4	no	—
411	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
412	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
413	#97	—	2	1	no	—
414	C₄×C₈	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	4	no	—
417	#95	C₂³×C₁₉	1	2	yes	—
418	C₁₉	#18429	1	1	yes	characteristic, direct product factor, Sylow
419	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
420	#41	—	8	2	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	2	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	4	2	no	—
428	C₂×Q₈	—	8	2	no	—
429	C₂×Q₈	—	8	2	no	—
430	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
431	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	4	2	no	—
438	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
449	Q₁₆	—	8	2	no	—
450	Q₁₆	—	8	4	no	—
451	SD₁₆	—	8	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
472	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
473	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	2	2	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	8	4	no	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	2	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	4	2	no	—
494	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₂³	—	2	2	no	—
499	C₂³	—	2	1	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
504	Q₈	—	4	1	no	—
505	Q₈	—	4	2	no	—
506	Q₈	—	4	2	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	4	4	no	—
509	Q₈	—	4	2	no	—
510	Q₈	—	4	2	no	—
511	Q₈	—	8	1	no	—
512	Q₈	—	8	2	no	—
513	D₄	—	4	1	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	8	1	no	—
517	D₄	—	8	2	no	—
518	D₄	—	8	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	4	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	8	2	no	—
536	C₂×C₄	—	8	2	no	—
537	C₂×C₄	—	8	2	no	—
538	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
539	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
540	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
541	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
544	C₈	—	4	2	no	—
545	C₈	—	4	2	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	8	4	no	—
555	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
556	C₂²	C₁₉×#578	1	2	yes	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	2	no	—
568	C₄	—	8	2	no	—
569	C₄	—	8	2	no	—
570	C₄	C₁₉×#455	1	2	yes	—
571	C₂	—	2	2	no	—
572	C₂	—	8	2	no	—
573	C₂	—	8	1	no	—
574	C₂	C₁₉×#3011	1	1	yes	characteristic
575	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
576	C₂	C₁₉×#3027	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3561	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3218	C₂	semidirect
3. C₁₉×#3209	C₂	semidirect
4. C₁₉×#2640	C₂	semidirect
5. C₁₉×#1606	C₂	semidirect
6. C₁₉×#1602	C₂	semidirect
7. C₁₉×#1506	C₂	semidirect
8. C₁₉×#1500	C₂	semidirect
9. C₁₉×#1469	C₂	semidirect
209. #18429	C₁₉	direct (N × H)
259. #3218	C₂×C₁₉	semidirect
260. #3209	C₂×C₁₉	semidirect
261. #2640	C₂×C₁₉	semidirect
262. #1606	C₂×C₁₉	semidirect
263. #1602	C₂×C₁₉	semidirect
264. #1506	C₂×C₁₉	semidirect
265. #1500	C₂×C₁₉	semidirect
266. #1469	C₂×C₁₉	semidirect
418. C₁₉	#18429	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×#3561	2
C₁₉×#3218	2
C₁₉×#3209	2
C₁₉×#2640	2
C₁₉×#1606	2
C₁₉×#1602	2
C₁₉×#1506	2
C₁₉×#1500	2
C₁₉×#1469	2
#18429	19

Subgroups — C19×#18429 #18024388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18429 #18024388