Subgroups — C₁₉×#18443 #18024402

Order 4864.

832 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3563	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3239	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3230	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2642	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1617	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1615	C₂	1	4	yes	maximal
7	C₁₉×#1506	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1500	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1470	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#564	—	2	1	no	—
11	C₁₉×#563	—	2	1	no	—
12	C₁₉×#557	—	2	1	no	—
13	C₁₉×#554	—	2	1	no	—
14	C₁₉×#552	—	2	1	no	—
15	C₁₉×#552	—	2	1	no	—
16	C₁₉×#552	—	2	2	no	—
17	C₁₉×#544	—	2	1	no	—
18	C₁₉×#544	C₂²	1	2	yes	—
19	C₁₉×#541	—	2	1	no	—
20	C₁₉×#541	—	2	2	no	—
21	C₁₉×#539	C₂²	1	2	yes	—
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×#125	C₂²	1	1	yes	characteristic
26	C₁₉×#501	—	2	1	no	—
27	C₁₉×#500	—	2	1	no	—
28	C₁₉×#489	—	2	1	no	—
29	C₁₉×#487	—	2	1	no	—
30	C₁₉×#484	C₂²	1	4	yes	—
31	C₁₉×#484	C₂²	1	2	yes	—
32	C₁₉×#481	C₂²	1	2	yes	—
33	C₁₉×#477	—	2	2	no	—
34	C₁₉×#475	—	2	1	no	—
35	C₁₉×#474	—	2	1	no	—
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#431	C₂²	1	1	yes	characteristic
38	C₁₉×#400	—	2	2	no	—
39	C₁₉×#400	C₂²	1	4	yes	—
40	C₁₉×#391	—	2	1	no	—
41	C₁₉×#391	—	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×#324	C₂²	1	4	yes	—
47	C₂²×Q₈×C₁₉	—	2	1	no	—
48	C₁₉×C₄⋊Q₈	—	2	1	no	—
49	C₁₉×C₄⋊Q₈	—	2	2	no	—
50	C₁₉×C₄⋊Q₈	—	2	2	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	1	no	—
54	C₁₉×C₄⋊Q₈	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
57	C₁₉×#126	—	2	2	no	—
58	C₁₉×#126	—	2	2	no	—
59	C₁₉×#126	—	2	2	no	—
60	C₁₉×#126	—	2	2	no	—
61	C₁₉×#126	—	2	1	no	—
62	C₁₉×#125	—	2	2	no	—
63	C₁₉×#125	—	2	2	no	—
64	C₁₉×#125	—	2	2	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₁₉×#125	—	2	1	no	—
67	C₁₉×#125	—	2	2	no	—
68	C₁₉×#125	—	2	2	no	—
69	C₁₉×#125	—	2	2	no	—
70	C₁₉×#125	—	2	2	no	—
71	C₁₉×#125	—	2	1	no	—
72	C₁₉×#125	—	2	1	no	—
73	C₁₉×#125	—	2	1	no	—
74	C₁₉×#125	—	2	1	no	—
75	C₁₉×#125	—	2	1	no	—
76	C₁₉×#125	D₄	1	1	yes	characteristic
77	C₁₉×#124	D₄	1	1	yes	characteristic
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×#123	—	2	1	no	—
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	—	2	1	no	—
82	C₁₉×C₂²⋊Q₈	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
89	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
90	C₁₉×#121	C₂³	1	1	yes	characteristic
91	C₄×Q₈×C₁₉	—	2	1	no	—
92	C₄×Q₈×C₁₉	—	2	2	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
96	C₄×Q₈×C₁₉	D₄	1	2	yes	—
97	C₄×D₄×C₁₉	—	2	1	no	—
98	C₄×D₄×C₁₉	—	2	2	no	—
99	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
100	C₁₉×#117	—	2	2	no	—
101	C₁₉×#117	—	2	1	no	—
102	C₁₉×#117	—	2	1	no	—
103	C₁₉×#117	—	2	2	no	—
104	C₁₉×#117	—	2	1	no	—
105	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
112	C₂×C₄²×C₁₉	—	2	1	no	—
113	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₁₉×#107	—	2	2	no	—
115	C₁₉×#107	—	2	4	no	—
116	C₁₉×#106	—	2	2	no	—
117	C₁₉×C₄⋊C₈	—	2	1	no	—
118	C₁₉×C₄⋊C₈	—	2	1	no	—
119	C₁₉×#103	—	2	2	no	—
120	C₁₉×#103	—	2	4	no	—
121	C₁₉×#102	—	2	2	no	—
122	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
123	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
124	C₁₉×#97	—	2	1	no	—
125	C₄×C₈×C₁₉	—	2	1	no	—
126	C₁₉×#95	—	2	1	no	—
127	C₁₉×#95	—	2	4	no	—
128	C₁₉×#95	—	2	4	no	—
129	C₁₉×#95	C₂³	1	2	yes	—
130	C₂×Q₈×C₁₉	—	2	2	no	—
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	—	4	4	no	—
133	C₂×Q₈×C₁₉	—	4	1	no	—
134	C₂×Q₈×C₁₉	—	4	1	no	—
135	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
136	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
148	C₂×C₈×C₁₉	—	2	2	no	—
149	C₂×C₈×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	4	1	no	—
178	C₄⋊C₄×C₁₉	—	4	1	no	—
179	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
182	C₂²⋊C₄×C₁₉	—	2	2	no	—
183	C₂²⋊C₄×C₁₉	—	2	2	no	—
184	C₂²⋊C₄×C₁₉	—	2	2	no	—
185	C₂²⋊C₄×C₁₉	—	2	2	no	—
186	C₂²⋊C₄×C₁₉	—	2	1	no	—
187	C₂²⋊C₄×C₁₉	—	2	1	no	—
188	C₂²⋊C₄×C₁₉	—	2	1	no	—
189	C₂²⋊C₄×C₁₉	—	2	1	no	—
190	C₂²⋊C₄×C₁₉	—	2	1	no	—
191	C₄²×C₁₉	—	2	2	no	—
192	C₄²×C₁₉	—	2	2	no	—
193	C₄²×C₁₉	—	2	2	no	—
194	C₄²×C₁₉	—	2	2	no	—
195	C₄²×C₁₉	—	2	1	no	—
196	C₄²×C₁₉	—	4	2	no	—
197	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
201	#18443	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂³×C₁₉	—	2	1	no	—
203	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₁₉	—	4	1	no	—
205	Q₈×C₁₉	—	4	2	no	—
206	Q₈×C₁₉	—	4	2	no	—
207	Q₈×C₁₉	—	8	2	no	—
208	Q₈×C₁₉	—	8	2	no	—
209	Q₈×C₁₉	—	8	2	no	—
210	D₄×C₁₉	—	4	1	no	—
211	D₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	4	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	2	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	4	4	no	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	8	2	no	—
231	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
237	C₈×C₁₉	—	4	2	no	—
238	C₈×C₁₉	—	4	2	no	—
239	#3563	C₂×C₁₉	1	1	yes	characteristic
240	#3239	C₂×C₁₉	1	1	yes	characteristic
241	#3230	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#2642	C₂×C₁₉	1	1	yes	characteristic, complemented
243	#1617	C₂×C₁₉	1	4	yes	complemented
244	#1615	C₂×C₁₉	1	4	yes	—
245	#1506	C₂×C₁₉	1	1	yes	characteristic, complemented
246	#1500	C₂×C₁₉	1	1	yes	characteristic
247	#1470	C₂×C₁₉	1	1	yes	characteristic, complemented
248	C₂²×C₁₉	—	2	1	no	—
249	C₂²×C₁₉	—	2	1	no	—
250	C₂²×C₁₉	—	4	1	no	—
251	C₂²×C₁₉	—	4	1	no	—
252	C₂²×C₁₉	—	4	1	no	—
253	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
254	C₂²×C₁₉	#578	1	2	yes	—
255	C₄×C₁₉	—	2	1	no	—
256	C₄×C₁₉	—	2	1	no	—
257	C₄×C₁₉	—	2	1	no	—
258	C₄×C₁₉	—	2	1	no	—
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	4	2	no	—
261	C₄×C₁₉	—	4	1	no	—
262	C₄×C₁₉	—	4	1	no	—
263	C₄×C₁₉	—	4	2	no	—
264	C₄×C₁₉	—	4	2	no	—
265	C₄×C₁₉	—	4	2	no	—
266	C₄×C₁₉	—	4	1	no	—
267	C₄×C₁₉	—	8	2	no	—
268	C₄×C₁₉	—	8	2	no	—
269	C₄×C₁₉	#454	1	2	yes	—
270	#564	—	2	1	no	—
271	#563	—	2	1	no	—
272	#557	—	2	1	no	—
273	#554	—	2	1	no	—
274	#552	—	2	1	no	—
275	#552	—	2	1	no	—
276	#552	—	2	2	no	—
277	#544	—	2	1	no	—
278	#544	C₂²×C₁₉	1	2	yes	—
279	#541	—	2	1	no	—
280	#541	—	2	2	no	—
281	#539	C₂²×C₁₉	1	2	yes	—
282	#533	C₂²×C₁₉	1	1	yes	characteristic
283	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
284	#529	C₂²×C₁₉	1	1	yes	characteristic
285	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
286	#501	—	2	1	no	—
287	#500	—	2	1	no	—
288	#489	—	2	1	no	—
289	#487	—	2	1	no	—
290	#484	C₂²×C₁₉	1	4	yes	—
291	#484	C₂²×C₁₉	1	2	yes	—
292	#481	C₂²×C₁₉	1	2	yes	—
293	#477	—	2	2	no	—
294	#475	—	2	1	no	—
295	#474	—	2	1	no	—
296	#432	C₂²×C₁₉	1	1	yes	characteristic
297	#431	C₂²×C₁₉	1	1	yes	characteristic
298	#400	—	2	2	no	—
299	#400	C₂²×C₁₉	1	4	yes	—
300	#391	—	2	1	no	—
301	#391	—	2	1	no	—
302	#376	C₂²×C₁₉	1	1	yes	characteristic
303	#328	C₂²×C₁₉	1	4	yes	—
304	#328	C₂²×C₁₉	1	2	yes	—
305	#327	C₂²×C₁₉	1	2	yes	—
306	#324	C₂²×C₁₉	1	4	yes	—
307	C₂×C₁₉	—	2	2	no	—
308	C₂×C₁₉	—	8	1	no	—
309	C₂×C₁₉	#3011	1	1	yes	characteristic
310	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
311	C₂×C₁₉	#3028	1	1	yes	characteristic
312	C₂²×Q₈	—	2	1	no	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	—	2	2	no	—
315	C₄⋊Q₈	—	2	2	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	—	2	1	no	—
318	C₄⋊Q₈	—	2	1	no	—
319	C₄⋊Q₈	—	2	1	no	—
320	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
321	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
322	#126	—	2	2	no	—
323	#126	—	2	2	no	—
324	#126	—	2	2	no	—
325	#126	—	2	2	no	—
326	#126	—	2	1	no	—
327	#125	—	2	2	no	—
328	#125	—	2	2	no	—
329	#125	—	2	2	no	—
330	#125	—	2	2	no	—
331	#125	—	2	1	no	—
332	#125	—	2	2	no	—
333	#125	—	2	2	no	—
334	#125	—	2	2	no	—
335	#125	—	2	2	no	—
336	#125	—	2	1	no	—
337	#125	—	2	1	no	—
338	#125	—	2	1	no	—
339	#125	—	2	1	no	—
340	#125	—	2	1	no	—
341	#125	D₄×C₁₉	1	1	yes	characteristic
342	#124	D₄×C₁₉	1	1	yes	characteristic
343	#123	—	2	2	no	—
344	#123	—	2	1	no	—
345	#123	—	2	2	no	—
346	C₂²⋊Q₈	—	2	1	no	—
347	C₂²⋊Q₈	—	2	1	no	—
348	C₂²⋊Q₈	—	2	2	no	—
349	C₂²⋊Q₈	—	2	2	no	—
350	C₂²⋊Q₈	—	2	2	no	—
351	C₂²⋊Q₈	—	2	1	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
354	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
355	#121	C₂³×C₁₉	1	1	yes	characteristic
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	—	2	2	no	—
358	C₄×Q₈	—	2	1	no	—
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
361	C₄×Q₈	D₄×C₁₉	1	2	yes	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	2	no	—
364	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
365	#117	—	2	2	no	—
366	#117	—	2	1	no	—
367	#117	—	2	1	no	—
368	#117	—	2	2	no	—
369	#117	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
373	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
374	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
379	#107	—	2	2	no	—
380	#107	—	2	4	no	—
381	#106	—	2	2	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	#103	—	2	2	no	—
385	#103	—	2	4	no	—
386	#102	—	2	2	no	—
387	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
388	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
389	#97	—	2	1	no	—
390	C₄×C₈	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	—	2	4	no	—
393	#95	—	2	4	no	—
394	#95	C₂³×C₁₉	1	2	yes	—
395	C₁₉	#18443	1	1	yes	characteristic, direct product factor, Sylow
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	4	4	no	—
399	C₂×Q₈	—	4	1	no	—
400	C₂×Q₈	—	4	1	no	—
401	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
402	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
410	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
413	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	4	1	no	—
444	C₄⋊C₄	—	4	1	no	—
445	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	1	no	—
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	4	2	no	—
463	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
467	C₂³	—	2	1	no	—
468	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
469	Q₈	—	4	1	no	—
470	Q₈	—	4	2	no	—
471	Q₈	—	4	2	no	—
472	Q₈	—	8	2	no	—
473	Q₈	—	8	2	no	—
474	Q₈	—	8	2	no	—
475	D₄	—	4	1	no	—
476	D₄	—	4	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	8	2	no	—
496	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
497	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
498	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
499	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
500	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
502	C₈	—	4	2	no	—
503	C₈	—	4	2	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	1	no	—
509	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
510	C₂²	C₁₉×#578	1	2	yes	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	1	no	—
523	C₄	—	8	2	no	—
524	C₄	—	8	2	no	—
525	C₄	C₁₉×#454	1	2	yes	—
526	C₂	—	2	2	no	—
527	C₂	—	8	1	no	—
528	C₂	C₁₉×#3011	1	1	yes	characteristic
529	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
530	C₂	C₁₉×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#121	C₂³
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
3. C₁₉×#3230	C₂	semidirect
4. C₁₉×#2642	C₂	semidirect
5. C₁₉×#1617	C₂	semidirect
7. C₁₉×#1506	C₂	semidirect
9. C₁₉×#1470	C₂	semidirect
201. #18443	C₁₉	direct (N × H)
241. #3230	C₂×C₁₉	semidirect
242. #2642	C₂×C₁₉	semidirect
243. #1617	C₂×C₁₉	semidirect
245. #1506	C₂×C₁₉	semidirect
247. #1470	C₂×C₁₉	semidirect
395. C₁₉	#18443	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×#3563	2
C₁₉×#3239	2
C₁₉×#3230	2
C₁₉×#2642	2
C₁₉×#1617	2
C₁₉×#1615	2
C₁₉×#1506	2
C₁₉×#1500	2
C₁₉×#1470	2
#18443	19

Subgroups — C19×#18443 #18024402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18443 #18024402