Subgroups — C₁₉×#19057 #18025016

Order 4864.

908 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×#3548	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3216	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3135	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1662	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1661	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1536	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1531	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1530	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#562	C₂²	1	4	yes	—
11	C₁₉×#554	—	2	1	no	—
12	C₁₉×#554	—	2	1	no	—
13	C₁₉×#550	—	2	1	no	—
14	C₁₉×#550	—	2	1	no	—
15	C₁₉×#547	—	2	1	no	—
16	C₁₉×#547	—	2	1	no	—
17	C₁₉×#540	—	2	2	no	—
18	C₁₉×#537	—	2	2	no	—
19	C₁₉×#537	—	2	2	no	—
20	C₁₉×#533	C₂²	1	1	yes	characteristic
21	C₁₉×#533	C₂²	1	1	yes	characteristic
22	C₁₉×#532	C₂²	1	1	yes	characteristic
23	C₁₉×#532	C₂²	1	1	yes	characteristic
24	C₁₉×#501	C₂²	1	2	yes	—
25	C₁₉×#497	C₂²	1	2	yes	—
26	C₁₉×#491	—	2	1	no	—
27	C₁₉×#491	C₂²	1	2	yes	—
28	C₁₉×#490	—	2	1	no	—
29	C₁₉×#489	C₂²	1	2	yes	—
30	C₁₉×#489	C₂²	1	2	yes	—
31	C₁₉×#489	C₂²	1	2	yes	—
32	C₁₉×#485	—	2	2	no	—
33	C₁₉×#477	—	2	1	no	—
34	C₁₉×#475	—	2	1	no	—
35	C₁₉×#462	—	2	1	no	—
36	C₁₉×#460	—	2	1	no	—
37	C₁₉×#452	—	2	2	no	—
38	C₁₉×#432	C₂²	1	1	yes	characteristic
39	C₁₉×#432	C₂²	1	1	yes	characteristic
40	C₁₉×#416	—	2	2	no	—
41	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
42	C₁₉×#330	C₂²	1	4	yes	—
43	C₁₉×#329	C₂²	1	4	yes	—
44	C₁₉×#329	C₂²	1	4	yes	—
45	C₂×#41×C₁₉	—	2	2	no	—
46	C₂×#41×C₁₉	—	2	2	no	—
47	C₂×#41×C₁₉	D₄	1	2	yes	—
48	C₂×#41×C₁₉	D₄	1	2	yes	—
49	C₂×Q₁₆×C₁₉	—	2	2	no	—
50	C₂×SD₁₆×C₁₉	—	2	2	no	—
51	C₂²×C₈×C₁₉	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
53	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
54	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
55	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
58	C₁₉×#127	—	2	2	no	—
59	C₁₉×#127	D₄	1	1	yes	characteristic
60	C₁₉×#127	D₄	1	1	yes	characteristic
61	C₁₉×#125	—	2	2	no	—
62	C₁₉×#125	—	2	1	no	—
63	C₁₉×#125	C₂³	1	2	yes	—
64	C₁₉×#124	C₂³	1	2	yes	—
65	C₁₉×#124	C₂³	1	2	yes	—
66	C₁₉×#123	—	2	4	no	—
67	C₁₉×#123	—	2	4	no	—
68	C₁₉×C₂²⋊Q₈	—	2	2	no	—
69	C₁₉×C₂²⋊Q₈	—	2	2	no	—
70	C₁₉×C₂²⋊Q₈	—	2	4	no	—
71	C₁₉×C₂²⋊Q₈	—	2	4	no	—
72	C₁₉×C₂²⋊Q₈	—	2	1	no	—
73	C₁₉×C₂²⋊Q₈	—	2	1	no	—
74	C₁₉×C₂²⋊Q₈	—	2	1	no	—
75	C₁₉×C₂²⋊Q₈	—	2	1	no	—
76	C₁₉×#121	—	2	4	no	—
77	C₁₉×#121	—	2	4	no	—
78	C₁₉×#121	—	2	2	no	—
79	C₁₉×#121	—	2	2	no	—
80	C₁₉×#121	—	2	4	no	—
81	C₁₉×#121	—	2	4	no	—
82	C₁₉×#121	—	2	1	no	—
83	C₁₉×#121	—	2	1	no	—
84	C₁₉×#121	—	2	1	no	—
85	C₁₉×#121	—	2	1	no	—
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×Q₈×C₁₉	—	2	1	no	—
88	C₄×Q₈×C₁₉	—	2	1	no	—
89	C₄×Q₈×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	—	2	2	no	—
91	C₄×D₄×C₁₉	—	2	2	no	—
92	C₄×D₄×C₁₉	—	2	1	no	—
93	C₄×D₄×C₁₉	—	2	1	no	—
94	C₄×D₄×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	—	2	1	no	—
96	C₁₉×#117	—	2	1	no	—
97	C₁₉×#117	D₄	1	2	yes	—
98	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×#107	—	2	2	no	—
102	C₁₉×#106	—	2	2	no	—
103	C₁₉×C₄⋊C₈	—	2	1	no	—
104	C₁₉×C₄⋊C₈	—	2	1	no	—
105	C₁₉×#103	—	2	2	no	—
106	C₁₉×#103	—	2	2	no	—
107	C₁₉×#103	—	2	2	no	—
108	C₁₉×#103	—	2	2	no	—
109	C₁₉×#103	—	2	2	no	—
110	C₁₉×#102	—	2	2	no	—
111	C₁₉×#102	—	2	2	no	—
112	C₁₉×#102	—	2	2	no	—
113	C₁₉×C₂²⋊C₈	—	2	1	no	—
114	C₁₉×C₂²⋊C₈	—	2	1	no	—
115	C₁₉×#97	—	2	1	no	—
116	C₁₉×#97	C₂³	1	2	yes	—
117	C₁₉×#97	C₂³	1	2	yes	—
118	C₁₉×#97	C₂³	1	2	yes	—
119	#41×C₁₉	—	4	4	no	—
120	#41×C₁₉	—	8	2	no	—
121	#41×C₁₉	—	8	4	no	—
122	#41×C₁₉	—	8	4	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
128	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
129	C₂×D₄×C₁₉	—	2	4	no	—
130	C₂×D₄×C₁₉	—	2	4	no	—
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₉	—	2	4	no	—
140	C₂²×C₄×C₁₉	—	2	4	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	Q₁₆×C₁₉	—	8	2	no	—
147	SD₁₆×C₁₉	—	8	2	no	—
148	C₂×C₈×C₁₉	—	2	2	no	—
149	C₂×C₈×C₁₉	—	2	2	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	4	2	no	—
152	C₄⋊C₄×C₁₉	—	2	4	no	—
153	C₄⋊C₄×C₁₉	—	2	4	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	4	1	no	—
167	C₄⋊C₄×C₁₉	—	4	1	no	—
168	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
170	C₂²⋊C₄×C₁₉	—	2	4	no	—
171	C₂²⋊C₄×C₁₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂²⋊C₄×C₁₉	—	4	1	no	—
178	C₄²×C₁₉	—	2	2	no	—
179	C₄²×C₁₉	—	4	1	no	—
180	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
184	#19057	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂³×C₁₉	—	2	2	no	—
186	C₂³×C₁₉	—	2	2	no	—
187	C₂³×C₁₉	#120	1	1	yes	characteristic
188	Q₈×C₁₉	—	4	2	no	—
189	Q₈×C₁₉	—	4	2	no	—
190	Q₈×C₁₉	—	4	2	no	—
191	Q₈×C₁₉	—	4	1	no	—
192	Q₈×C₁₉	—	4	1	no	—
193	Q₈×C₁₉	—	4	2	no	—
194	Q₈×C₁₉	—	4	2	no	—
195	D₄×C₁₉	—	4	2	no	—
196	D₄×C₁₉	—	4	2	no	—
197	D₄×C₁₉	—	4	2	no	—
198	D₄×C₁₉	—	4	2	no	—
199	D₄×C₁₉	—	4	2	no	—
200	D₄×C₁₉	—	4	2	no	—
201	D₄×C₁₉	—	8	2	no	—
202	D₄×C₁₉	—	8	2	no	—
203	D₄×C₁₉	—	8	4	no	—
204	D₄×C₁₉	—	8	4	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	4	no	—
213	C₂×C₄×C₁₉	—	4	4	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	8	4	no	—
217	C₂×C₄×C₁₉	—	8	4	no	—
218	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
224	C₈×C₁₉	—	4	2	no	—
225	C₈×C₁₉	—	4	2	no	—
226	C₈×C₁₉	—	4	2	no	—
227	#3548	C₂×C₁₉	1	1	yes	characteristic
228	#3237	C₂×C₁₉	1	1	yes	characteristic, complemented
229	#3216	C₂×C₁₉	1	1	yes	characteristic, complemented
230	#3135	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#1662	C₂×C₁₉	1	4	yes	complemented
232	#1661	C₂×C₁₉	1	4	yes	complemented
233	#1536	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#1531	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#1530	C₂×C₁₉	1	1	yes	characteristic, complemented
236	C₂²×C₁₉	—	2	1	no	—
237	C₂²×C₁₉	—	2	1	no	—
238	C₂²×C₁₉	—	2	1	no	—
239	C₂²×C₁₉	—	4	2	no	—
240	C₂²×C₁₉	—	4	2	no	—
241	C₂²×C₁₉	—	4	2	no	—
242	C₂²×C₁₉	—	4	2	no	—
243	C₂²×C₁₉	—	4	2	no	—
244	C₂²×C₁₉	—	4	2	no	—
245	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
246	C₄×C₁₉	—	2	1	no	—
247	C₄×C₁₉	—	2	1	no	—
248	C₄×C₁₉	—	2	1	no	—
249	C₄×C₁₉	—	2	1	no	—
250	C₄×C₁₉	—	2	1	no	—
251	C₄×C₁₉	—	4	2	no	—
252	C₄×C₁₉	—	4	2	no	—
253	C₄×C₁₉	—	4	2	no	—
254	C₄×C₁₉	—	4	2	no	—
255	C₄×C₁₉	—	8	1	no	—
256	C₄×C₁₉	—	8	1	no	—
257	C₄×C₁₉	#455	1	2	yes	—
258	#562	C₂²×C₁₉	1	4	yes	—
259	#554	—	2	1	no	—
260	#554	—	2	1	no	—
261	#550	—	2	1	no	—
262	#550	—	2	1	no	—
263	#547	—	2	1	no	—
264	#547	—	2	1	no	—
265	#540	—	2	2	no	—
266	#537	—	2	2	no	—
267	#537	—	2	2	no	—
268	#533	C₂²×C₁₉	1	1	yes	characteristic
269	#533	C₂²×C₁₉	1	1	yes	characteristic
270	#532	C₂²×C₁₉	1	1	yes	characteristic
271	#532	C₂²×C₁₉	1	1	yes	characteristic
272	#501	C₂²×C₁₉	1	2	yes	—
273	#497	C₂²×C₁₉	1	2	yes	—
274	#491	—	2	1	no	—
275	#491	C₂²×C₁₉	1	2	yes	—
276	#490	—	2	1	no	—
277	#489	C₂²×C₁₉	1	2	yes	—
278	#489	C₂²×C₁₉	1	2	yes	—
279	#489	C₂²×C₁₉	1	2	yes	—
280	#485	—	2	2	no	—
281	#477	—	2	1	no	—
282	#475	—	2	1	no	—
283	#462	—	2	1	no	—
284	#460	—	2	1	no	—
285	#452	—	2	2	no	—
286	#432	C₂²×C₁₉	1	1	yes	characteristic
287	#432	C₂²×C₁₉	1	1	yes	characteristic
288	#416	—	2	2	no	—
289	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
290	#330	C₂²×C₁₉	1	4	yes	—
291	#329	C₂²×C₁₉	1	4	yes	—
292	#329	C₂²×C₁₉	1	4	yes	—
293	C₂×C₁₉	—	4	1	no	—
294	C₂×C₁₉	—	8	2	no	—
295	C₂×C₁₉	—	8	2	no	—
296	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
297	C₂×C₁₉	#3019	1	1	yes	characteristic
298	C₂×C₁₉	#3020	1	1	yes	characteristic
299	C₂×#41	—	2	2	no	—
300	C₂×#41	—	2	2	no	—
301	C₂×#41	D₄×C₁₉	1	2	yes	—
302	C₂×#41	D₄×C₁₉	1	2	yes	—
303	C₂×Q₁₆	—	2	2	no	—
304	C₂×SD₁₆	—	2	2	no	—
305	C₂²×C₈	—	2	1	no	—
306	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
307	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
308	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
309	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
310	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
311	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
312	#127	—	2	2	no	—
313	#127	D₄×C₁₉	1	1	yes	characteristic
314	#127	D₄×C₁₉	1	1	yes	characteristic
315	#125	—	2	2	no	—
316	#125	—	2	1	no	—
317	#125	C₂³×C₁₉	1	2	yes	—
318	#124	C₂³×C₁₉	1	2	yes	—
319	#124	C₂³×C₁₉	1	2	yes	—
320	#123	—	2	4	no	—
321	#123	—	2	4	no	—
322	C₂²⋊Q₈	—	2	2	no	—
323	C₂²⋊Q₈	—	2	2	no	—
324	C₂²⋊Q₈	—	2	4	no	—
325	C₂²⋊Q₈	—	2	4	no	—
326	C₂²⋊Q₈	—	2	1	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₂²⋊Q₈	—	2	1	no	—
329	C₂²⋊Q₈	—	2	1	no	—
330	#121	—	2	4	no	—
331	#121	—	2	4	no	—
332	#121	—	2	2	no	—
333	#121	—	2	2	no	—
334	#121	—	2	4	no	—
335	#121	—	2	4	no	—
336	#121	—	2	1	no	—
337	#121	—	2	1	no	—
338	#121	—	2	1	no	—
339	#121	—	2	1	no	—
340	C₄×Q₈	—	2	1	no	—
341	C₄×Q₈	—	2	1	no	—
342	C₄×Q₈	—	2	1	no	—
343	C₄×Q₈	—	2	1	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	2	2	no	—
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	—	2	1	no	—
348	C₄×D₄	—	2	1	no	—
349	C₄×D₄	—	2	1	no	—
350	#117	—	2	1	no	—
351	#117	D₄×C₁₉	1	2	yes	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
355	#107	—	2	2	no	—
356	#106	—	2	2	no	—
357	C₄⋊C₈	—	2	1	no	—
358	C₄⋊C₈	—	2	1	no	—
359	#103	—	2	2	no	—
360	#103	—	2	2	no	—
361	#103	—	2	2	no	—
362	#103	—	2	2	no	—
363	#103	—	2	2	no	—
364	#102	—	2	2	no	—
365	#102	—	2	2	no	—
366	#102	—	2	2	no	—
367	C₂²⋊C₈	—	2	1	no	—
368	C₂²⋊C₈	—	2	1	no	—
369	#97	—	2	1	no	—
370	#97	C₂³×C₁₉	1	2	yes	—
371	#97	C₂³×C₁₉	1	2	yes	—
372	#97	C₂³×C₁₉	1	2	yes	—
373	C₁₉	#19057	1	1	yes	characteristic, direct product factor, Sylow
374	#41	—	4	4	no	—
375	#41	—	8	2	no	—
376	#41	—	8	4	no	—
377	#41	—	8	4	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
383	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
393	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
401	Q₁₆	—	8	2	no	—
402	SD₁₆	—	8	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	4	2	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	4	1	no	—
422	C₄⋊C₄	—	4	1	no	—
423	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
424	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	4	1	no	—
433	C₄²	—	2	2	no	—
434	C₄²	—	4	1	no	—
435	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
436	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	C₁₉×#120	1	1	yes	characteristic
442	Q₈	—	4	2	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	1	no	—
446	Q₈	—	4	1	no	—
447	Q₈	—	4	2	no	—
448	Q₈	—	4	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	8	2	no	—
456	D₄	—	8	2	no	—
457	D₄	—	8	4	no	—
458	D₄	—	8	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	8	4	no	—
471	C₂×C₄	—	8	4	no	—
472	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
473	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
474	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
476	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
477	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
478	C₈	—	4	2	no	—
479	C₈	—	4	2	no	—
480	C₈	—	4	2	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	8	1	no	—
501	C₄	—	8	1	no	—
502	C₄	C₁₉×#455	1	2	yes	—
503	C₂	—	4	1	no	—
504	C₂	—	8	2	no	—
505	C₂	—	8	2	no	—
506	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
507	C₂	C₁₉×#3019	1	1	yes	characteristic
508	C₂	C₁₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3548	C₂
LCS	G ▷ C₄² ▷ 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×#3237	C₂	semidirect
3. C₁₉×#3216	C₂	semidirect
4. C₁₉×#3135	C₂	semidirect
5. C₁₉×#1662	C₂	semidirect
6. C₁₉×#1661	C₂	semidirect
7. C₁₉×#1536	C₂	semidirect
8. C₁₉×#1531	C₂	semidirect
9. C₁₉×#1530	C₂	semidirect
184. #19057	C₁₉	direct (N × H)
228. #3237	C₂×C₁₉	semidirect
229. #3216	C₂×C₁₉	semidirect
230. #3135	C₂×C₁₉	semidirect
231. #1662	C₂×C₁₉	semidirect
232. #1661	C₂×C₁₉	semidirect
233. #1536	C₂×C₁₉	semidirect
234. #1531	C₂×C₁₉	semidirect
235. #1530	C₂×C₁₉	semidirect
373. C₁₉	#19057	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×#3548	2
C₁₉×#3237	2
C₁₉×#3216	2
C₁₉×#3135	2
C₁₉×#1662	2
C₁₉×#1661	2
C₁₉×#1536	2
C₁₉×#1531	2
C₁₉×#1530	2
#19057	19

Subgroups — C19×#19057 #18025016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19057 #18025016