Subgroups — C₁₉×#18717 #18024676

Order 4864.

984 conjugacy classes of subgroups.

The subgroup lattice has 486 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×#3230	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3227	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3152	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1632	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1631	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1543	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1485	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1484	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#137	—	2	2	no	—
11	C₁₉×#562	—	2	2	no	—
12	C₁₉×#554	—	2	1	no	—
13	C₁₉×#554	C₂²	1	2	yes	—
14	C₁₉×#550	—	2	1	no	—
15	C₁₉×#550	C₂²	1	2	yes	—
16	C₁₉×#547	—	2	1	no	—
17	C₁₉×#547	—	2	1	no	—
18	C₁₉×#540	—	2	2	no	—
19	C₁₉×#537	—	2	2	no	—
20	C₁₉×#537	—	2	2	no	—
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	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₉×#500	—	2	1	no	—
26	C₁₉×#498	—	2	1	no	—
27	C₁₉×#497	—	2	2	no	—
28	C₁₉×#494	C₂²	1	2	yes	—
29	C₁₉×#492	C₂²	1	2	yes	—
30	C₁₉×#487	—	2	1	no	—
31	C₁₉×#486	—	2	1	no	—
32	C₁₉×#484	—	2	2	no	—
33	C₁₉×#481	—	2	2	no	—
34	C₁₉×#477	C₂²	1	4	yes	—
35	C₁₉×#476	C₂²	1	4	yes	—
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₁₉×#431	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#333	C₂²	1	2	yes	—
40	C₁₉×#331	C₂²	1	2	yes	—
41	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	—
42	C₁₉×D₄⋊C₈	C₂²	1	4	yes	—
43	C₂×#41×C₁₉	—	2	2	no	—
44	C₂×#41×C₁₉	—	2	2	no	—
45	C₂×#41×C₁₉	—	2	1	no	—
46	C₂×#41×C₁₉	D₄	1	2	yes	—
47	C₂²×Q₈×C₁₉	—	2	1	no	—
48	C₁₉×#137	—	4	8	no	—
49	C₂×Q₁₆×C₁₉	—	2	4	no	—
50	C₂×SD₁₆×C₁₉	—	2	4	no	—
51	C₂×M₁₆×C₁₉	—	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×C₄⋊Q₈	D₄	1	1	yes	characteristic
58	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₉×#127	—	2	2	no	—
61	C₁₉×#127	D₄	1	1	yes	characteristic
62	C₁₉×#127	C₂³	1	1	yes	characteristic
63	C₁₉×#125	—	2	2	no	—
64	C₁₉×#125	—	2	1	no	—
65	C₁₉×#124	—	2	1	no	—
66	C₁₉×#124	D₄	1	2	yes	—
67	C₁₉×#123	—	2	4	no	—
68	C₁₉×#123	—	2	4	no	—
69	C₁₉×C₂²⋊Q₈	—	2	2	no	—
70	C₁₉×C₂²⋊Q₈	—	2	4	no	—
71	C₁₉×C₂²⋊Q₈	—	2	2	no	—
72	C₁₉×C₂²⋊Q₈	—	2	4	no	—
73	C₁₉×C₂²⋊Q₈	—	2	1	no	—
74	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
75	C₁₉×#121	—	2	4	no	—
76	C₁₉×#121	—	2	4	no	—
77	C₁₉×#121	—	2	2	no	—
78	C₁₉×#121	—	2	4	no	—
79	C₁₉×#121	—	2	4	no	—
80	C₁₉×#121	—	2	1	no	—
81	C₁₉×#121	—	2	1	no	—
82	C₁₉×#121	—	2	1	no	—
83	C₁₉×#121	—	2	2	no	—
84	C₁₉×#121	D₄	1	2	yes	—
85	C₄×Q₈×C₁₉	—	2	1	no	—
86	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
87	C₄×D₄×C₁₉	—	2	2	no	—
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₄×D₄×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	—	2	1	no	—
91	C₄×D₄×C₁₉	—	2	1	no	—
92	C₄×D₄×C₁₉	C₂³	1	2	yes	—
93	C₁₉×#117	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₁₉×#107	—	2	4	no	—
100	C₁₉×#106	—	2	4	no	—
101	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
102	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
103	C₁₉×#103	—	2	4	no	—
104	C₁₉×#102	—	2	4	no	—
105	C₁₉×C₂²⋊C₈	—	2	1	no	—
106	C₁₉×C₂²⋊C₈	—	2	1	no	—
107	C₁₉×#97	—	2	1	no	—
108	C₄×C₈×C₁₉	—	2	1	no	—
109	C₄×C₈×C₁₉	—	2	1	no	—
110	C₄×C₈×C₁₉	C₂³	1	2	yes	—
111	#41×C₁₉	—	4	4	no	—
112	#41×C₁₉	—	8	2	no	—
113	#41×C₁₉	—	8	4	no	—
114	#41×C₁₉	—	8	4	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	2	2	no	—
118	C₂×Q₈×C₁₉	—	4	4	no	—
119	C₂×Q₈×C₁₉	—	4	1	no	—
120	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
122	C₂×D₄×C₁₉	—	2	4	no	—
123	C₂×D₄×C₁₉	—	2	4	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	1	no	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	2	1	no	—
129	C₂×D₄×C₁₉	—	2	1	no	—
130	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
131	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₉	—	2	4	no	—
133	C₂²×C₄×C₁₉	—	2	4	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	4	1	no	—
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	Q₁₆×C₁₉	—	4	8	no	—
141	SD₁₆×C₁₉	—	4	8	no	—
142	M₁₆×C₁₉	—	2	4	no	—
143	C₂×C₈×C₁₉	—	2	2	no	—
144	C₂×C₈×C₁₉	—	2	2	no	—
145	C₂×C₈×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	4	no	—
147	C₄⋊C₄×C₁₉	—	2	4	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	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	—	4	1	no	—
159	C₄⋊C₄×C₁₉	—	4	1	no	—
160	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
161	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
162	C₂²⋊C₄×C₁₉	—	2	4	no	—
163	C₂²⋊C₄×C₁₉	—	2	4	no	—
164	C₂²⋊C₄×C₁₉	—	2	2	no	—
165	C₂²⋊C₄×C₁₉	—	2	2	no	—
166	C₂²⋊C₄×C₁₉	—	2	2	no	—
167	C₂²⋊C₄×C₁₉	—	2	2	no	—
168	C₂²⋊C₄×C₁₉	—	2	2	no	—
169	C₄²×C₁₉	—	2	2	no	—
170	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
174	#18717	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂³×C₁₉	—	2	2	no	—
176	C₂³×C₁₉	—	2	2	no	—
177	C₂³×C₁₉	#120	1	1	yes	characteristic
178	Q₈×C₁₉	—	2	4	no	—
179	Q₈×C₁₉	—	4	2	no	—
180	Q₈×C₁₉	—	4	4	no	—
181	Q₈×C₁₉	—	4	2	no	—
182	Q₈×C₁₉	—	8	1	no	—
183	Q₈×C₁₉	—	8	2	no	—
184	D₄×C₁₉	—	2	4	no	—
185	D₄×C₁₉	—	4	2	no	—
186	D₄×C₁₉	—	4	2	no	—
187	D₄×C₁₉	—	4	2	no	—
188	D₄×C₁₉	—	4	2	no	—
189	D₄×C₁₉	—	8	1	no	—
190	D₄×C₁₉	—	8	2	no	—
191	D₄×C₁₉	—	8	2	no	—
192	D₄×C₁₉	—	8	4	no	—
193	D₄×C₁₉	—	8	4	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	4	4	no	—
202	C₂×C₄×C₁₉	—	4	4	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	8	4	no	—
205	C₂×C₄×C₁₉	—	8	4	no	—
206	C₂×C₄×C₁₉	—	8	2	no	—
207	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
209	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
213	C₈×C₁₉	—	2	4	no	—
214	C₈×C₁₉	—	4	2	no	—
215	C₈×C₁₉	—	4	2	no	—
216	#3548	C₂×C₁₉	1	1	yes	characteristic
217	#3230	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#3227	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#3152	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#1632	C₂×C₁₉	1	4	yes	complemented
221	#1631	C₂×C₁₉	1	4	yes	complemented
222	#1543	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#1485	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#1484	C₂×C₁₉	1	1	yes	characteristic, complemented
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	—	2	1	no	—
228	C₂²×C₁₉	—	4	2	no	—
229	C₂²×C₁₉	—	4	2	no	—
230	C₂²×C₁₉	—	4	2	no	—
231	C₂²×C₁₉	—	4	2	no	—
232	C₂²×C₁₉	—	4	2	no	—
233	C₂²×C₁₉	—	4	2	no	—
234	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
235	C₄×C₁₉	—	2	1	no	—
236	C₄×C₁₉	—	2	1	no	—
237	C₄×C₁₉	—	2	1	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	4	2	no	—
240	C₄×C₁₉	—	4	2	no	—
241	C₄×C₁₉	—	4	2	no	—
242	C₄×C₁₉	—	8	2	no	—
243	C₄×C₁₉	#453	1	2	yes	—
244	C₄×C₁₉	#577	1	2	yes	—
245	C₄×C₁₉	#578	1	2	yes	—
246	C₂×#137	—	2	2	no	—
247	#562	—	2	2	no	—
248	#554	—	2	1	no	—
249	#554	C₂²×C₁₉	1	2	yes	—
250	#550	—	2	1	no	—
251	#550	C₂²×C₁₉	1	2	yes	—
252	#547	—	2	1	no	—
253	#547	—	2	1	no	—
254	#540	—	2	2	no	—
255	#537	—	2	2	no	—
256	#537	—	2	2	no	—
257	#533	C₂²×C₁₉	1	1	yes	characteristic
258	#532	C₂²×C₁₉	1	1	yes	characteristic
259	#532	C₂²×C₁₉	1	1	yes	characteristic
260	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
261	#500	—	2	1	no	—
262	#498	—	2	1	no	—
263	#497	—	2	2	no	—
264	#494	C₂²×C₁₉	1	2	yes	—
265	#492	C₂²×C₁₉	1	2	yes	—
266	#487	—	2	1	no	—
267	#486	—	2	1	no	—
268	#484	—	2	2	no	—
269	#481	—	2	2	no	—
270	#477	C₂²×C₁₉	1	4	yes	—
271	#476	C₂²×C₁₉	1	4	yes	—
272	#431	C₂²×C₁₉	1	1	yes	characteristic
273	#431	C₂²×C₁₉	1	1	yes	characteristic
274	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
275	#333	C₂²×C₁₉	1	2	yes	—
276	#331	C₂²×C₁₉	1	2	yes	—
277	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	—
278	D₄⋊C₈	C₂²×C₁₉	1	4	yes	—
279	C₂×C₁₉	—	4	1	no	—
280	C₂×C₁₉	—	8	2	no	—
281	C₂×C₁₉	—	8	2	no	—
282	C₂×C₁₉	#3009	1	1	yes	characteristic
283	C₂×C₁₉	#3011	1	1	yes	characteristic
284	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
285	C₂×#41	—	2	2	no	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	2	1	no	—
288	C₂×#41	D₄×C₁₉	1	2	yes	—
289	C₂²×Q₈	—	2	1	no	—
290	#137	—	4	8	no	—
291	C₂×Q₁₆	—	2	4	no	—
292	C₂×SD₁₆	—	2	4	no	—
293	C₂×M₁₆	—	2	1	no	—
294	C₄⋊Q₈	—	2	1	no	—
295	C₄⋊Q₈	—	2	1	no	—
296	C₄⋊Q₈	—	2	1	no	—
297	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
298	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
299	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
300	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
301	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
302	#127	—	2	2	no	—
303	#127	D₄×C₁₉	1	1	yes	characteristic
304	#127	C₂³×C₁₉	1	1	yes	characteristic
305	#125	—	2	2	no	—
306	#125	—	2	1	no	—
307	#124	—	2	1	no	—
308	#124	D₄×C₁₉	1	2	yes	—
309	#123	—	2	4	no	—
310	#123	—	2	4	no	—
311	C₂²⋊Q₈	—	2	2	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	C₂²⋊Q₈	—	2	2	no	—
314	C₂²⋊Q₈	—	2	4	no	—
315	C₂²⋊Q₈	—	2	1	no	—
316	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
317	#121	—	2	4	no	—
318	#121	—	2	4	no	—
319	#121	—	2	2	no	—
320	#121	—	2	4	no	—
321	#121	—	2	4	no	—
322	#121	—	2	1	no	—
323	#121	—	2	1	no	—
324	#121	—	2	1	no	—
325	#121	—	2	2	no	—
326	#121	D₄×C₁₉	1	2	yes	—
327	C₄×Q₈	—	2	1	no	—
328	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
329	C₄×D₄	—	2	2	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	1	no	—
332	C₄×D₄	—	2	1	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	C₂³×C₁₉	1	2	yes	—
335	#117	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
341	#107	—	2	4	no	—
342	#106	—	2	4	no	—
343	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
344	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
345	#103	—	2	4	no	—
346	#102	—	2	4	no	—
347	C₂²⋊C₈	—	2	1	no	—
348	C₂²⋊C₈	—	2	1	no	—
349	#97	—	2	1	no	—
350	C₄×C₈	—	2	1	no	—
351	C₄×C₈	—	2	1	no	—
352	C₄×C₈	C₂³×C₁₉	1	2	yes	—
353	C₁₉	#18717	1	1	yes	characteristic, direct product factor, Sylow
354	#41	—	4	4	no	—
355	#41	—	8	2	no	—
356	#41	—	8	4	no	—
357	#41	—	8	4	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	4	4	no	—
362	C₂×Q₈	—	4	1	no	—
363	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
364	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
374	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
383	Q₁₆	—	4	8	no	—
384	SD₁₆	—	4	8	no	—
385	M₁₆	—	2	4	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	4	1	no	—
402	C₄⋊C₄	—	4	1	no	—
403	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
404	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
415	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
416	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	C₁₉×#120	1	1	yes	characteristic
420	Q₈	—	2	4	no	—
421	Q₈	—	4	2	no	—
422	Q₈	—	4	4	no	—
423	Q₈	—	4	2	no	—
424	Q₈	—	8	1	no	—
425	Q₈	—	8	2	no	—
426	D₄	—	2	4	no	—
427	D₄	—	4	2	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	2	no	—
430	D₄	—	4	2	no	—
431	D₄	—	8	1	no	—
432	D₄	—	8	2	no	—
433	D₄	—	8	2	no	—
434	D₄	—	8	4	no	—
435	D₄	—	8	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	8	4	no	—
447	C₂×C₄	—	8	4	no	—
448	C₂×C₄	—	8	2	no	—
449	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
450	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
451	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
454	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
455	C₈	—	2	4	no	—
456	C₈	—	4	2	no	—
457	C₈	—	4	2	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	8	2	no	—
476	C₄	C₁₉×#453	1	2	yes	—
477	C₄	C₁₉×#577	1	2	yes	—
478	C₄	C₁₉×#578	1	2	yes	—
479	C₂	—	4	1	no	—
480	C₂	—	8	2	no	—
481	C₂	—	8	2	no	—
482	C₂	C₁₉×#3009	1	1	yes	characteristic
483	C₂	C₁₉×#3011	1	1	yes	characteristic
484	C₂	C₂×C₁₉×#453	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×#3230	C₂	semidirect
3. C₁₉×#3227	C₂	semidirect
4. C₁₉×#3152	C₂	semidirect
5. C₁₉×#1632	C₂	semidirect
6. C₁₉×#1631	C₂	semidirect
7. C₁₉×#1543	C₂	semidirect
8. C₁₉×#1485	C₂	semidirect
9. C₁₉×#1484	C₂	semidirect
174. #18717	C₁₉	direct (N × H)
217. #3230	C₂×C₁₉	semidirect
218. #3227	C₂×C₁₉	semidirect
219. #3152	C₂×C₁₉	semidirect
220. #1632	C₂×C₁₉	semidirect
221. #1631	C₂×C₁₉	semidirect
222. #1543	C₂×C₁₉	semidirect
223. #1485	C₂×C₁₉	semidirect
224. #1484	C₂×C₁₉	semidirect
353. C₁₉	#18717	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×#3230	2
C₁₉×#3227	2
C₁₉×#3152	2
C₁₉×#1632	2
C₁₉×#1631	2
C₁₉×#1543	2
C₁₉×#1485	2
C₁₉×#1484	2
#18717	19

Subgroups — C19×#18717 #18024676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18717 #18024676