Subgroups — C₁₉×#8424 #18014383

Order 4864.

734 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3503	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1987	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1806	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1550	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1549	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1503	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1477	C₂	1	1	yes	maximal, characteristic
8	Q₈²×C₁₉	—	2	1	no	—
9	C₁₉×#557	C₄	1	2	yes	complemented
10	C₁₉×#554	—	2	1	no	—
11	C₁₉×#554	—	2	2	no	—
12	D₄×Q₈×C₁₉	—	2	2	no	—
13	D₄×Q₈×C₁₉	C₄	1	2	yes	complemented
14	C₁₉×#544	—	2	2	no	—
15	C₁₉×#544	—	2	1	no	—
16	C₁₉×#533	—	2	1	no	—
17	C₁₉×#533	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
19	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₉×#520	—	2	1	no	—
21	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#431	C₂²	1	1	yes	characteristic
23	C₁₉×#423	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#104	—	2	1	no	—
26	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#340	—	2	2	no	—
28	C₁₉×#339	—	2	1	no	—
29	C₁₉×#333	—	2	1	no	—
30	C₁₉×#332	—	2	2	no	—
31	C₁₉×#332	—	2	1	no	—
32	C₁₉×#328	—	2	2	no	—
33	C₁₉×Q₈⋊C₈	—	2	1	no	—
34	C₁₉×D₄⋊C₈	—	2	1	no	—
35	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
36	C₂²×Q₈×C₁₉	—	2	2	no	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂×M₁₆×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₁₉×C₄⋊Q₈	—	2	2	no	—
41	C₁₉×C₄⋊Q₈	—	2	2	no	—
42	C₁₉×C₄⋊Q₈	—	2	4	no	—
43	C₁₉×C₄⋊Q₈	—	2	2	no	—
44	C₁₉×C₄⋊Q₈	—	2	2	no	—
45	C₁₉×C₄⋊Q₈	—	2	1	no	—
46	C₁₉×C₄⋊Q₈	—	2	1	no	—
47	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
48	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
49	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
50	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
51	C₁₉×#125	—	2	2	no	—
52	C₁₉×#125	—	2	4	no	—
53	C₁₉×#125	—	2	2	no	—
54	C₁₉×#125	—	2	1	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	1	no	—
59	C₁₉×C₂²⋊Q₈	—	2	2	no	—
60	C₁₉×C₂²⋊Q₈	—	2	4	no	—
61	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
62	C₄×Q₈×C₁₉	—	2	2	no	—
63	C₄×Q₈×C₁₉	—	2	2	no	—
64	C₄×Q₈×C₁₉	—	2	2	no	—
65	C₄×Q₈×C₁₉	—	2	1	no	—
66	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
67	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
68	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
69	C₄×D₄×C₁₉	—	2	4	no	—
70	C₄×D₄×C₁₉	—	2	2	no	—
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
74	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
75	C₁₉×#117	—	2	2	no	—
76	C₁₉×#117	—	2	1	no	—
77	C₁₉×#117	—	2	1	no	—
78	C₁₉×#117	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
84	C₂×C₄²×C₁₉	—	2	1	no	—
85	C₂×C₄²×C₁₉	—	2	1	no	—
86	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
87	C₁₉×C₄⋊C₈	—	2	1	no	—
88	C₁₉×C₄⋊C₈	—	2	1	no	—
89	C₁₉×C₄⋊C₈	—	2	1	no	—
90	C₁₉×C₄⋊C₈	—	2	1	no	—
91	C₁₉×C₄⋊C₈	—	2	1	no	—
92	C₁₉×#104	—	4	2	no	—
93	C₁₉×C₂²⋊C₈	—	2	1	no	—
94	C₄×C₈×C₁₉	—	2	1	no	—
95	C₁₉×#95	—	2	1	no	—
96	#41×C₁₉	—	2	1	no	—
97	#41×C₁₉	—	2	1	no	—
98	#41×C₁₉	SD₁₆	1	2	yes	—
99	#41×C₁₉	Q₁₆	1	2	yes	—
100	C₂×Q₈×C₁₉	—	2	4	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	1	no	—
103	C₂×Q₈×C₁₉	—	2	2	no	—
104	C₂×Q₈×C₁₉	—	8	2	no	—
105	C₂×Q₈×C₁₉	—	8	4	no	—
106	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	4	1	no	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	M₁₆×C₁₉	—	4	1	no	—
120	M₁₆×C₁₉	—	4	1	no	—
121	C₂×C₈×C₁₉	—	4	2	no	—
122	C₂×C₈×C₁₉	—	4	1	no	—
123	C₂×C₈×C₁₉	—	4	1	no	—
124	C₂×C₈×C₁₉	—	4	1	no	—
125	C₄⋊C₄×C₁₉	—	2	4	no	—
126	C₄⋊C₄×C₁₉	—	2	4	no	—
127	C₄⋊C₄×C₁₉	—	2	4	no	—
128	C₄⋊C₄×C₁₉	—	2	4	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	4	1	no	—
141	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
142	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
143	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
144	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
145	C₂²⋊C₄×C₁₉	—	2	4	no	—
146	C₂²⋊C₄×C₁₉	—	2	2	no	—
147	C₂²⋊C₄×C₁₉	—	2	1	no	—
148	C₂²⋊C₄×C₁₉	—	2	1	no	—
149	C₂²⋊C₄×C₁₉	—	2	1	no	—
150	C₄²×C₁₉	—	2	4	no	—
151	C₄²×C₁₉	—	2	1	no	—
152	C₄²×C₁₉	—	2	2	no	—
153	C₄²×C₁₉	—	2	1	no	—
154	C₄²×C₁₉	—	2	1	no	—
155	C₄²×C₁₉	—	4	1	no	—
156	C₄²×C₁₉	—	4	1	no	—
157	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
161	#8424	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂³×C₁₉	—	2	1	no	—
163	C₂³×C₁₉	#120	1	1	yes	characteristic
164	Q₈×C₁₉	—	2	1	no	—
165	Q₈×C₁₉	—	4	2	no	—
166	Q₈×C₁₉	—	4	4	no	—
167	Q₈×C₁₉	—	4	1	no	—
168	Q₈×C₁₉	—	4	1	no	—
169	Q₈×C₁₉	—	8	2	no	—
170	Q₈×C₁₉	—	8	4	no	—
171	Q₈×C₁₉	#103	1	2	yes	—
172	D₄×C₁₉	—	2	2	no	—
173	D₄×C₁₉	—	2	2	no	—
174	D₄×C₁₉	—	2	1	no	—
175	D₄×C₁₉	#103	1	2	yes	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	8	2	no	—
192	C₂×C₄×C₁₉	—	8	4	no	—
193	C₂×C₄×C₁₉	—	8	1	no	—
194	C₂×C₄×C₁₉	—	8	1	no	—
195	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
200	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
205	C₈×C₁₉	—	8	1	no	—
206	C₈×C₁₉	—	8	1	no	—
207	C₈×C₁₉	—	8	1	no	—
208	#3503	C₂×C₁₉	1	1	yes	characteristic
209	#1987	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#1806	C₂×C₁₉	1	1	yes	characteristic
211	#1550	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#1549	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#1503	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#1477	C₂×C₁₉	1	1	yes	characteristic
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	2	no	—
218	C₂²×C₁₉	—	4	1	no	—
219	C₂²×C₁₉	—	4	1	no	—
220	C₂²×C₁₉	#379	1	1	yes	characteristic
221	C₂²×C₁₉	#448	1	1	yes	characteristic
222	C₂²×C₁₉	#451	1	1	yes	characteristic
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	2	1	no	—
225	C₄×C₁₉	—	2	1	no	—
226	C₄×C₁₉	—	2	2	no	—
227	C₄×C₁₉	—	4	1	no	—
228	C₄×C₁₉	—	4	2	no	—
229	C₄×C₁₉	—	4	1	no	—
230	C₄×C₁₉	—	4	4	no	—
231	C₄×C₁₉	—	4	2	no	—
232	C₄×C₁₉	—	8	2	no	—
233	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
234	C₄×C₁₉	#419	1	1	yes	characteristic
235	C₄×C₁₉	#448	1	1	yes	characteristic
236	C₄×C₁₉	#451	1	1	yes	characteristic
237	C₄×C₁₉	#454	1	1	yes	characteristic
238	C₄×C₁₉	#456	1	1	yes	characteristic
239	Q₈²	—	2	1	no	—
240	#557	C₄×C₁₉	1	2	yes	complemented
241	#554	—	2	1	no	—
242	#554	—	2	2	no	—
243	D₄×Q₈	—	2	2	no	—
244	D₄×Q₈	C₄×C₁₉	1	2	yes	complemented
245	#544	—	2	2	no	—
246	#544	—	2	1	no	—
247	#533	—	2	1	no	—
248	#533	C₂²×C₁₉	1	1	yes	characteristic
249	C₂×C₄⋊Q₈	—	2	1	no	—
250	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
251	#520	—	2	1	no	—
252	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
253	#431	C₂²×C₁₉	1	1	yes	characteristic
254	#423	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
256	C₂×#104	—	2	1	no	—
257	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
258	#340	—	2	2	no	—
259	#339	—	2	1	no	—
260	#333	—	2	1	no	—
261	#332	—	2	2	no	—
262	#332	—	2	1	no	—
263	#328	—	2	2	no	—
264	Q₈⋊C₈	—	2	1	no	—
265	D₄⋊C₈	—	2	1	no	—
266	C₂×C₁₉	—	2	1	no	—
267	C₂×C₁₉	—	2	1	no	—
268	C₂×C₁₉	—	4	2	no	—
269	C₂×C₁₉	#1787	1	1	yes	characteristic
270	C₂×C₁₉	#1793	1	1	yes	characteristic
271	C₂×C₁₉	#1795	1	1	yes	characteristic
272	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
273	C₂²×Q₈	—	2	2	no	—
274	C₂²×Q₈	—	2	1	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂²×C₈	—	2	1	no	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₄⋊Q₈	—	2	4	no	—
280	C₄⋊Q₈	—	2	2	no	—
281	C₄⋊Q₈	—	2	2	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
285	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
286	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
287	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
288	#125	—	2	2	no	—
289	#125	—	2	4	no	—
290	#125	—	2	2	no	—
291	#125	—	2	1	no	—
292	C₂²⋊Q₈	—	2	2	no	—
293	C₂²⋊Q₈	—	2	4	no	—
294	C₂²⋊Q₈	—	2	4	no	—
295	C₂²⋊Q₈	—	2	1	no	—
296	C₂²⋊Q₈	—	2	2	no	—
297	C₂²⋊Q₈	—	2	4	no	—
298	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×Q₈	—	2	1	no	—
303	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
304	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
305	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	—	2	1	no	—
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
311	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
312	#117	—	2	2	no	—
313	#117	—	2	1	no	—
314	#117	—	2	1	no	—
315	#117	D₄×C₁₉	1	1	yes	characteristic
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
324	C₄⋊C₈	—	2	1	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	—	2	1	no	—
328	C₄⋊C₈	—	2	1	no	—
329	#104	—	4	2	no	—
330	C₂²⋊C₈	—	2	1	no	—
331	C₄×C₈	—	2	1	no	—
332	#95	—	2	1	no	—
333	C₁₉	#8424	1	1	yes	characteristic, direct product factor, Sylow
334	#41	—	2	1	no	—
335	#41	—	2	1	no	—
336	#41	SD₁₆×C₁₉	1	2	yes	—
337	#41	Q₁₆×C₁₉	1	2	yes	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	8	2	no	—
343	C₂×Q₈	—	8	4	no	—
344	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
345	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
357	M₁₆	—	4	1	no	—
358	M₁₆	—	4	1	no	—
359	C₂×C₈	—	4	2	no	—
360	C₂×C₈	—	4	1	no	—
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	—	4	1	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
380	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
381	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
382	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₂²⋊C₄	—	2	1	no	—
388	C₄²	—	2	4	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	4	1	no	—
394	C₄²	—	4	1	no	—
395	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
396	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
399	C₂³	—	2	1	no	—
400	C₂³	C₁₉×#120	1	1	yes	characteristic
401	Q₈	—	2	1	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	4	4	no	—
404	Q₈	—	4	1	no	—
405	Q₈	—	4	1	no	—
406	Q₈	—	8	2	no	—
407	Q₈	—	8	4	no	—
408	Q₈	C₁₉×#103	1	2	yes	—
409	D₄	—	2	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	2	1	no	—
412	D₄	C₁₉×#103	1	2	yes	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	—	8	4	no	—
430	C₂×C₄	—	8	1	no	—
431	C₂×C₄	—	8	1	no	—
432	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
433	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
434	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
435	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
436	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
437	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
438	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
439	C₂×C₄	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
440	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
441	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
442	C₈	—	8	1	no	—
443	C₈	—	8	1	no	—
444	C₈	—	8	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	C₁₉×#379	1	1	yes	characteristic
451	C₂²	C₁₉×#448	1	1	yes	characteristic
452	C₂²	C₁₉×#451	1	1	yes	characteristic
453	C₄	—	2	2	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	4	no	—
461	C₄	—	4	2	no	—
462	C₄	—	8	2	no	—
463	C₄	C₂×C₁₉×#103	1	1	yes	characteristic
464	C₄	C₁₉×#419	1	1	yes	characteristic
465	C₄	C₁₉×#448	1	1	yes	characteristic
466	C₄	C₁₉×#451	1	1	yes	characteristic
467	C₄	C₁₉×#454	1	1	yes	characteristic
468	C₄	C₁₉×#456	1	1	yes	characteristic
469	C₂	—	2	1	no	—
470	C₂	—	2	1	no	—
471	C₂	—	4	2	no	—
472	C₂	C₁₉×#1787	1	1	yes	characteristic
473	C₂	C₁₉×#1793	1	1	yes	characteristic
474	C₂	C₁₉×#1795	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	D₄
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×#1987	C₂	semidirect
4. C₁₉×#1550	C₂	semidirect
5. C₁₉×#1549	C₂	semidirect
6. C₁₉×#1503	C₂	semidirect
9. C₁₉×#557	C₄	semidirect
13. D₄×Q₈×C₁₉	C₄	semidirect
161. #8424	C₁₉	direct (N × H)
209. #1987	C₂×C₁₉	semidirect
211. #1550	C₂×C₁₉	semidirect
212. #1549	C₂×C₁₉	semidirect
213. #1503	C₂×C₁₉	semidirect
240. #557	C₄×C₁₉	semidirect
244. D₄×Q₈	C₄×C₁₉	semidirect
333. C₁₉	#8424	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×#3503	2
C₁₉×#1987	2
C₁₉×#1806	2
C₁₉×#1550	2
C₁₉×#1549	2
C₁₉×#1503	2
C₁₉×#1477	2
#8424	19

Subgroups — C19×#8424 #18014383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8424 #18014383