Subgroups — C₁₉×#10232 #18016191

Order 4864.

644 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#461	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2538	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₁₉	—	2	1	no	—
9	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
11	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#475	—	2	2	no	—
14	C₁₉×#475	—	2	2	no	—
15	C₁₉×#461	—	2	2	no	—
16	C₁₉×#461	—	2	2	no	—
17	C₂×C₁₉×#106	—	2	1	no	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#103	—	2	1	no	—
21	C₂×C₁₉×#103	—	2	1	no	—
22	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#396	—	2	2	no	—
24	C₁₉×#390	—	2	1	no	—
25	C₁₉×#389	—	2	1	no	—
26	C₁₉×#384	C₂²	1	1	yes	characteristic
27	C₁₉×#380	—	2	1	no	—
28	C₁₉×#340	—	2	2	no	—
29	C₁₉×Q₈⋊C₈	—	2	2	no	—
30	C₁₉×D₄⋊C₈	—	2	2	no	—
31	C₂²×Q₈×C₁₉	—	2	1	no	—
32	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	—	2	1	no	—
35	C₂×SD₁₆×C₁₉	—	2	4	no	—
36	C₂×SD₁₆×C₁₉	—	4	2	no	—
37	C₂×SD₁₆×C₁₉	—	4	2	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₁₉×C₄⋊Q₈	—	2	1	no	—
42	C₁₉×C₄⋊Q₈	—	2	1	no	—
43	C₁₉×C₄⋊Q₈	—	2	1	no	—
44	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
45	C₁₉×C₂²⋊Q₈	—	4	2	no	—
46	C₁₉×C₂²⋊Q₈	—	4	2	no	—
47	C₄×Q₈×C₁₉	—	2	1	no	—
48	C₄×Q₈×C₁₉	—	2	1	no	—
49	C₄×Q₈×C₁₉	—	2	1	no	—
50	C₄×Q₈×C₁₉	—	2	1	no	—
51	C₄×D₄×C₁₉	—	2	1	no	—
52	C₄×D₄×C₁₉	—	2	1	no	—
53	C₄×D₄×C₁₉	—	2	1	no	—
54	C₄×D₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×#106	—	2	4	no	—
70	C₁₉×C₄⋊C₈	—	2	1	no	—
71	C₁₉×C₄⋊C₈	—	2	1	no	—
72	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
73	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
74	C₁₉×#103	—	2	4	no	—
75	C₁₉×#103	—	2	4	no	—
76	C₄×C₈×C₁₉	—	2	1	no	—
77	C₄×C₈×C₁₉	—	2	1	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₂⁴×C₁₉	—	2	1	no	—
80	C₂×Q₈×C₁₉	—	2	1	no	—
81	C₂×Q₈×C₁₉	—	2	1	no	—
82	C₂×Q₈×C₁₉	—	2	2	no	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×Q₈×C₁₉	—	4	1	no	—
87	C₂×Q₈×C₁₉	—	4	1	no	—
88	C₂×Q₈×C₁₉	—	4	1	no	—
89	C₂×Q₈×C₁₉	—	4	1	no	—
90	C₂×Q₈×C₁₉	—	4	1	no	—
91	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	complemented
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	—	2	1	no	—
96	C₂×D₄×C₁₉	—	2	1	no	—
97	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	—	4	1	no	—
106	C₂²×C₄×C₁₉	—	4	1	no	—
107	C₂²×C₄×C₁₉	—	4	1	no	—
108	C₂²×C₄×C₁₉	—	4	1	no	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	SD₁₆×C₁₉	—	4	8	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	4	1	no	—
117	C₂×C₈×C₁₉	—	4	1	no	—
118	C₂×C₈×C₁₉	—	4	1	no	—
119	C₂×C₈×C₁₉	—	4	1	no	—
120	C₂×C₈×C₁₉	—	4	1	no	—
121	C₂×C₈×C₁₉	—	4	1	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	4	2	no	—
129	C₄⋊C₄×C₁₉	—	4	4	no	—
130	C₄⋊C₄×C₁₉	—	4	1	no	—
131	C₄⋊C₄×C₁₉	—	4	1	no	—
132	C₄⋊C₄×C₁₉	—	4	1	no	—
133	C₄⋊C₄×C₁₉	—	4	1	no	—
134	C₄⋊C₄×C₁₉	—	4	1	no	—
135	C₄⋊C₄×C₁₉	—	4	1	no	—
136	C₄⋊C₄×C₁₉	—	4	1	no	—
137	C₄⋊C₄×C₁₉	—	4	1	no	—
138	C₂²⋊C₄×C₁₉	—	4	4	no	—
139	C₂²⋊C₄×C₁₉	—	4	1	no	—
140	C₂²⋊C₄×C₁₉	—	4	1	no	—
141	C₂²⋊C₄×C₁₉	—	8	2	no	—
142	C₄²×C₁₉	—	4	1	no	—
143	C₄²×C₁₉	—	4	1	no	—
144	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₁₉	#41	1	1	yes	characteristic
148	#10232	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂³×C₁₉	—	2	2	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	—	4	1	no	—
154	C₂³×C₁₉	—	4	1	no	—
155	C₂³×C₁₉	—	4	1	no	—
156	C₂³×C₁₉	#120	1	1	yes	characteristic
157	Q₈×C₁₉	—	2	2	no	—
158	Q₈×C₁₉	—	2	2	no	—
159	Q₈×C₁₉	—	4	1	no	—
160	Q₈×C₁₉	—	4	1	no	—
161	Q₈×C₁₉	—	4	2	no	—
162	Q₈×C₁₉	—	4	2	no	—
163	Q₈×C₁₉	—	8	1	no	—
164	Q₈×C₁₉	—	8	1	no	—
165	D₄×C₁₉	—	2	2	no	—
166	D₄×C₁₉	—	2	2	no	—
167	D₄×C₁₉	—	4	1	no	—
168	D₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	8	1	no	—
185	C₂×C₄×C₁₉	—	8	1	no	—
186	C₂×C₄×C₁₉	—	8	1	no	—
187	C₂×C₄×C₁₉	—	8	1	no	—
188	C₂×C₄×C₁₉	—	8	1	no	—
189	C₂×C₄×C₁₉	—	8	1	no	—
190	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
200	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
201	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
204	C₈×C₁₉	—	4	2	no	—
205	C₈×C₁₉	—	4	2	no	—
206	C₈×C₁₉	—	4	2	no	—
207	C₂×#475	C₂×C₁₉	1	1	yes	characteristic, complemented
208	C₂×#461	C₂×C₁₉	1	1	yes	characteristic
209	#2538	C₂×C₁₉	1	1	yes	characteristic
210	#1990	C₂×C₁₉	1	1	yes	characteristic, complemented
211	C₂×Q₈⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
212	C₂×D₄⋊C₈	C₂×C₁₉	1	1	yes	characteristic
213	#1296	C₂×C₁₉	1	1	yes	characteristic, complemented
214	C₂²×C₁₉	—	4	2	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	4	2	no	—
217	C₂²×C₁₉	—	8	1	no	—
218	C₂²×C₁₉	—	8	1	no	—
219	C₂²×C₁₉	—	8	1	no	—
220	C₂²×C₁₉	—	8	1	no	—
221	C₂²×C₁₉	#392	1	1	yes	characteristic
222	C₂²×C₁₉	#448	1	1	yes	characteristic
223	C₂²×C₁₉	#449	1	1	yes	characteristic
224	C₂²×C₁₉	#450	1	1	yes	characteristic
225	C₂²×C₁₉	#452	1	1	yes	characteristic
226	C₂²×C₁₉	#455	1	1	yes	characteristic
227	C₂²×C₁₉	#456	1	1	yes	characteristic
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	2	1	no	—
230	C₄×C₁₉	—	4	2	no	—
231	C₄×C₁₉	—	8	2	no	—
232	C₄×C₁₉	—	8	1	no	—
233	C₄×C₁₉	—	8	2	no	—
234	C₄×C₁₉	—	8	1	no	—
235	C₄×C₁₉	#448	1	1	yes	characteristic
236	C₄×C₁₉	#449	1	1	yes	characteristic
237	C₄×C₁₉	#450	1	1	yes	characteristic
238	C₄×C₁₉	#452	1	1	yes	characteristic
239	C₄×C₁₉	#465	1	1	yes	characteristic
240	C₄×C₁₉	#465	1	1	yes	characteristic
241	C₄×C₁₉	#468	1	1	yes	characteristic
242	C₄×C₁₉	#468	1	1	yes	characteristic
243	C₂²×SD₁₆	—	2	1	no	—
244	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
245	C₂×C₂²⋊Q₈	—	2	1	no	—
246	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
248	#475	—	2	2	no	—
249	#475	—	2	2	no	—
250	#461	—	2	2	no	—
251	#461	—	2	2	no	—
252	C₂×#106	—	2	1	no	—
253	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×#103	—	2	1	no	—
256	C₂×#103	—	2	1	no	—
257	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
258	#396	—	2	2	no	—
259	#390	—	2	1	no	—
260	#389	—	2	1	no	—
261	#384	C₂²×C₁₉	1	1	yes	characteristic
262	#380	—	2	1	no	—
263	#340	—	2	2	no	—
264	Q₈⋊C₈	—	2	2	no	—
265	D₄⋊C₈	—	2	2	no	—
266	C₂×C₁₉	—	8	2	no	—
267	C₂×C₁₉	#1642	1	1	yes	characteristic
268	C₂×C₁₉	#1643	1	1	yes	characteristic
269	C₂×C₁₉	#1650	1	1	yes	characteristic
270	C₂×C₁₉	#1651	1	1	yes	characteristic
271	C₂×C₁₉	#2000	1	1	yes	characteristic
272	C₂×C₁₉	#2000	1	1	yes	characteristic
273	C₂×C₁₉	#2007	1	1	yes	characteristic
274	C₂²×Q₈	—	2	1	no	—
275	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
276	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
277	C₂³×C₄	—	2	1	no	—
278	C₂×SD₁₆	—	2	4	no	—
279	C₂×SD₁₆	—	4	2	no	—
280	C₂×SD₁₆	—	4	2	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
288	C₂²⋊Q₈	—	4	2	no	—
289	C₂²⋊Q₈	—	4	2	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
305	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
306	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
312	#106	—	2	4	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
316	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
317	#103	—	2	4	no	—
318	#103	—	2	4	no	—
319	C₄×C₈	—	2	1	no	—
320	C₄×C₈	—	2	1	no	—
321	#95	—	2	2	no	—
322	C₁₉	#10232	1	1	yes	characteristic, direct product factor, Sylow
323	C₂⁴	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	4	1	no	—
331	C₂×Q₈	—	4	1	no	—
332	C₂×Q₈	—	4	1	no	—
333	C₂×Q₈	—	4	1	no	—
334	C₂×Q₈	—	4	1	no	—
335	C₂×Q₈	SD₁₆×C₁₉	1	2	yes	complemented
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	SD₁₆×C₁₉	1	2	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	—	4	1	no	—
350	C₂²×C₄	—	4	1	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
356	SD₁₆	—	4	8	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	4	1	no	—
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	—	4	1	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	4	1	no	—
366	C₄⋊C₄	—	2	1	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	1	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	4	1	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₂²⋊C₄	—	4	1	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	8	2	no	—
386	C₄²	—	4	1	no	—
387	C₄²	—	4	1	no	—
388	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
390	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
391	C₄²	#41×C₁₉	1	1	yes	characteristic
392	C₂³	—	2	2	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	C₁₉×#120	1	1	yes	characteristic
400	Q₈	—	2	2	no	—
401	Q₈	—	2	2	no	—
402	Q₈	—	4	1	no	—
403	Q₈	—	4	1	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	8	1	no	—
407	Q₈	—	8	1	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	2	no	—
410	D₄	—	4	1	no	—
411	D₄	—	4	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	8	1	no	—
428	C₂×C₄	—	8	1	no	—
429	C₂×C₄	—	8	1	no	—
430	C₂×C₄	—	8	1	no	—
431	C₂×C₄	—	8	1	no	—
432	C₂×C₄	—	8	1	no	—
433	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
434	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
435	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
436	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
437	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
438	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
439	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
440	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
441	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
442	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
443	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
444	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
445	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
446	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
447	C₈	—	4	2	no	—
448	C₈	—	4	2	no	—
449	C₈	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	C₁₉×#392	1	1	yes	characteristic
458	C₂²	C₁₉×#448	1	1	yes	characteristic
459	C₂²	C₁₉×#449	1	1	yes	characteristic
460	C₂²	C₁₉×#450	1	1	yes	characteristic
461	C₂²	C₁₉×#452	1	1	yes	characteristic
462	C₂²	C₁₉×#455	1	1	yes	characteristic
463	C₂²	C₁₉×#456	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	4	2	no	—
467	C₄	—	8	2	no	—
468	C₄	—	8	1	no	—
469	C₄	—	8	2	no	—
470	C₄	—	8	1	no	—
471	C₄	C₁₉×#448	1	1	yes	characteristic
472	C₄	C₁₉×#449	1	1	yes	characteristic
473	C₄	C₁₉×#450	1	1	yes	characteristic
474	C₄	C₁₉×#452	1	1	yes	characteristic
475	C₄	C₁₉×#465	1	1	yes	characteristic
476	C₄	C₁₉×#465	1	1	yes	characteristic
477	C₄	C₁₉×#468	1	1	yes	characteristic
478	C₄	C₁₉×#468	1	1	yes	characteristic
479	C₂	—	8	2	no	—
480	C₂	C₁₉×#1642	1	1	yes	characteristic
481	C₂	C₁₉×#1643	1	1	yes	characteristic
482	C₂	C₁₉×#1650	1	1	yes	characteristic
483	C₂	C₁₉×#1651	1	1	yes	characteristic
484	C₂	C₁₉×#2000	1	1	yes	characteristic
485	C₂	C₁₉×#2000	1	1	yes	characteristic
486	C₂	C₁₉×#2007	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#475	C₂	semidirect
4. C₁₉×#1990	C₂	semidirect
5. C₂×C₁₉×Q₈⋊C₈	C₂	semidirect
7. C₁₉×#1296	C₂	semidirect
91. C₂×Q₈×C₁₉	SD₁₆	semidirect
148. #10232	C₁₉	direct (N × H)
207. C₂×#475	C₂×C₁₉	semidirect
210. #1990	C₂×C₁₉	semidirect
211. C₂×Q₈⋊C₈	C₂×C₁₉	semidirect
213. #1296	C₂×C₁₉	semidirect
322. C₁₉	#10232	direct (N × H)
335. C₂×Q₈	SD₁₆×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#475	2
C₂×C₁₉×#461	2
C₁₉×#2538	2
C₁₉×#1990	2
C₂×C₁₉×Q₈⋊C₈	2
C₂×C₁₉×D₄⋊C₈	2
C₁₉×#1296	2
#10232	19

Subgroups — C19×#10232 #18016191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10232 #18016191