Subgroups — C₁₉×#23841 #18029800

Order 4864.

714 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2085	C₂	1	2	yes	maximal
4	C₁₉×#2084	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2083	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2059	C₂	1	2	yes	maximal
7	C₁₉×#2058	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#2057	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1776	C₂	1	2	yes	maximal
10	C₁₉×#1776	C₂	1	2	yes	maximal
11	C₁₉×#1745	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
15	C₂×C₁₉×#107	C₂²	1	2	yes	—
16	C₂×C₁₉×#107	C₂²	1	2	yes	—
17	C₂×C₁₉×#106	C₂²	1	2	yes	—
18	C₂×C₁₉×#106	C₂²	1	2	yes	—
19	C₂×C₁₉×#97	C₂²	1	2	yes	—
20	C₁₉×#391	—	2	1	no	—
21	C₁₉×#389	—	2	1	no	—
22	C₁₉×#389	C₂²	1	1	yes	characteristic
23	C₁₉×#389	C₂²	1	1	yes	characteristic
24	C₁₉×#389	C₂²	1	2	yes	—
25	C₁₉×#387	—	2	1	no	—
26	C₁₉×#387	—	2	1	no	—
27	C₁₉×#384	C₂²	1	1	yes	characteristic
28	C₁₉×#382	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
35	C₄³×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#340	C₂²	1	2	yes	—
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#336	C₂²	1	1	yes	characteristic
41	C₁₉×#336	C₂²	1	1	yes	characteristic
42	C₁₉×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
46	C₁₉×C₄⋊Q₈	—	2	4	no	—
47	C₁₉×#125	—	2	2	no	—
48	C₁₉×#125	—	2	2	no	—
49	C₄×Q₈×C₁₉	—	4	4	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×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	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₉	—	2	1	no	—
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	2	no	—
67	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×#107	—	2	4	no	—
75	C₁₉×#107	—	2	4	no	—
76	C₁₉×#106	—	2	4	no	—
77	C₁₉×#106	—	2	4	no	—
78	C₁₉×#97	Q₈	1	8	yes	complemented
79	C₁₉×#95	—	2	1	no	—
80	C₁₉×#95	—	2	1	no	—
81	C₁₉×#95	—	2	1	no	—
82	C₁₉×#95	—	2	1	no	—
83	C₁₉×#95	—	2	2	no	—
84	C₁₉×#95	—	2	1	no	—
85	C₁₉×#95	—	2	1	no	—
86	C₁₉×#95	—	2	2	no	—
87	C₂×Q₈×C₁₉	—	2	4	no	—
88	C₂×Q₈×C₁₉	—	4	2	no	—
89	C₂×Q₈×C₁₉	—	4	2	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
103	C₂×C₈×C₁₉	—	2	2	no	—
104	C₂×C₈×C₁₉	—	2	2	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	C₂×Q₈	1	4	yes	—
108	C₂×C₈×C₁₉	C₂×Q₈	1	4	yes	—
109	C₄⋊C₄×C₁₉	—	2	4	no	—
110	C₄⋊C₄×C₁₉	—	2	4	no	—
111	C₄⋊C₄×C₁₉	—	2	4	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	4	2	no	—
120	C₄⋊C₄×C₁₉	—	4	4	no	—
121	C₄⋊C₄×C₁₉	—	4	2	no	—
122	C₄⋊C₄×C₁₉	—	4	2	no	—
123	C₄⋊C₄×C₁₉	—	4	2	no	—
124	C₄⋊C₄×C₁₉	#41	1	2	yes	—
125	C₄⋊C₄×C₁₉	#41	1	2	yes	—
126	C₄⋊C₄×C₁₉	#41	1	4	yes	—
127	C₄²×C₁₉	—	2	2	no	—
128	C₄²×C₁₉	—	2	2	no	—
129	C₄²×C₁₉	—	2	1	no	—
130	C₄²×C₁₉	—	2	1	no	—
131	C₄²×C₁₉	—	2	2	no	—
132	C₄²×C₁₉	—	4	1	no	—
133	C₄²×C₁₉	—	4	1	no	—
134	C₄²×C₁₉	—	4	2	no	—
135	C₄²×C₁₉	—	4	2	no	—
136	C₄²×C₁₉	—	4	4	no	—
137	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
138	#23841	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₁₉	—	4	8	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
174	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
175	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
176	C₂×C₄×C₁₉	#137	1	2	yes	—
177	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
178	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
179	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
181	C₈×C₁₉	—	2	4	no	—
182	C₈×C₁₉	—	2	4	no	—
183	C₄×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
184	C₄×#125	C₂×C₁₉	1	1	yes	characteristic
185	#2085	C₂×C₁₉	1	2	yes	—
186	#2084	C₂×C₁₉	1	1	yes	characteristic
187	#2083	C₂×C₁₉	1	1	yes	characteristic
188	#2059	C₂×C₁₉	1	2	yes	—
189	#2058	C₂×C₁₉	1	1	yes	characteristic
190	#2057	C₂×C₁₉	1	1	yes	characteristic
191	#1776	C₂×C₁₉	1	2	yes	—
192	#1776	C₂×C₁₉	1	2	yes	—
193	#1745	C₂×C₁₉	1	1	yes	characteristic
194	C₂²×C₁₉	#525	1	1	yes	characteristic
195	C₂²×C₁₉	#525	1	1	yes	characteristic
196	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
197	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
199	C₂²×C₁₉	#575	1	1	yes	characteristic
200	C₂²×C₁₉	#575	1	1	yes	characteristic
201	C₄×C₁₉	—	2	2	no	—
202	C₄×C₁₉	—	2	2	no	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	2	2	no	—
205	C₄×C₁₉	—	4	4	no	—
206	C₄×C₁₉	—	4	1	no	—
207	C₄×C₁₉	—	4	2	no	—
208	C₄×C₁₉	—	4	1	no	—
209	C₄×C₁₉	—	4	2	no	—
210	C₄×C₁₉	—	8	1	no	—
211	C₄×C₁₉	—	8	2	no	—
212	C₄×C₁₉	—	8	1	no	—
213	C₄×C₁₉	#533	1	2	yes	—
214	C₄×C₁₉	#533	1	2	yes	—
215	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
216	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×C₄×Q₈	—	2	1	no	—
218	C₂×#107	C₂²×C₁₉	1	2	yes	—
219	C₂×#107	C₂²×C₁₉	1	2	yes	—
220	C₂×#106	C₂²×C₁₉	1	2	yes	—
221	C₂×#106	C₂²×C₁₉	1	2	yes	—
222	C₂×#97	C₂²×C₁₉	1	2	yes	—
223	#391	—	2	1	no	—
224	#389	—	2	1	no	—
225	#389	C₂²×C₁₉	1	1	yes	characteristic
226	#389	C₂²×C₁₉	1	1	yes	characteristic
227	#389	C₂²×C₁₉	1	2	yes	—
228	#387	—	2	1	no	—
229	#387	—	2	1	no	—
230	#384	C₂²×C₁₉	1	1	yes	characteristic
231	#382	C₂²×C₁₉	1	1	yes	characteristic
232	C₄×C₄⋊C₄	—	2	1	no	—
233	C₄×C₄⋊C₄	—	2	1	no	—
234	C₄×C₄⋊C₄	—	2	1	no	—
235	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
236	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
237	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
238	C₄³	C₂²×C₁₉	1	1	yes	characteristic
239	#340	C₂²×C₁₉	1	2	yes	—
240	#340	C₂²×C₁₉	1	2	yes	—
241	#340	C₂²×C₁₉	1	2	yes	—
242	#340	C₂²×C₁₉	1	2	yes	—
243	#336	C₂²×C₁₉	1	1	yes	characteristic
244	#336	C₂²×C₁₉	1	1	yes	characteristic
245	#336	C₂²×C₁₉	1	2	yes	—
246	C₂×C₁₉	#2399	1	1	yes	characteristic
247	C₂×C₁₉	#3114	1	1	yes	characteristic
248	C₂×C₁₉	#3115	1	1	yes	characteristic
249	C₂×C₁₉	#3116	1	1	yes	characteristic
250	C₂×C₁₉	#3117	1	1	yes	characteristic
251	C₂×C₁₉	#3165	1	1	yes	characteristic
252	C₂×C₁₉	#3166	1	1	yes	characteristic
253	C₂²×Q₈	—	2	1	no	—
254	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
255	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
256	C₄⋊Q₈	—	2	4	no	—
257	#125	—	2	2	no	—
258	#125	—	2	2	no	—
259	C₄×Q₈	—	4	4	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
278	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
279	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
280	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
284	#107	—	2	4	no	—
285	#107	—	2	4	no	—
286	#106	—	2	4	no	—
287	#106	—	2	4	no	—
288	#97	Q₈×C₁₉	1	8	yes	complemented
289	#95	—	2	1	no	—
290	#95	—	2	1	no	—
291	#95	—	2	1	no	—
292	#95	—	2	1	no	—
293	#95	—	2	2	no	—
294	#95	—	2	1	no	—
295	#95	—	2	1	no	—
296	#95	—	2	2	no	—
297	C₁₉	#23841	1	1	yes	characteristic, direct product factor, Sylow
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×Q₈	—	4	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
313	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	C₂×Q₈×C₁₉	1	4	yes	—
319	C₂×C₈	C₂×Q₈×C₁₉	1	4	yes	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	#41×C₁₉	1	2	yes	—
336	C₄⋊C₄	#41×C₁₉	1	4	yes	—
337	C₄⋊C₄	#41×C₁₉	1	2	yes	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	4	1	no	—
344	C₄²	—	4	1	no	—
345	C₄²	—	4	2	no	—
346	C₄²	—	4	2	no	—
347	C₄²	—	4	4	no	—
348	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
349	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
350	Q₈	—	4	8	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
384	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
385	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
386	C₂×C₄	C₁₉×#137	1	2	yes	—
387	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
388	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
389	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
390	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
391	C₈	—	2	4	no	—
392	C₈	—	2	4	no	—
393	C₂²	C₁₉×#525	1	1	yes	characteristic
394	C₂²	C₁₉×#525	1	1	yes	characteristic
395	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
396	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
397	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
398	C₂²	C₁₉×#575	1	1	yes	characteristic
399	C₂²	C₁₉×#575	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	4	4	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	2	no	—
409	C₄	—	8	1	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	1	no	—
412	C₄	C₁₉×#533	1	2	yes	—
413	C₄	C₁₉×#533	1	2	yes	—
414	C₂	C₁₉×#2399	1	1	yes	characteristic
415	C₂	C₁₉×#3114	1	1	yes	characteristic
416	C₂	C₁₉×#3115	1	1	yes	characteristic
417	C₂	C₁₉×#3116	1	1	yes	characteristic
418	C₂	C₁₉×#3117	1	1	yes	characteristic
419	C₂	C₁₉×#3165	1	1	yes	characteristic
420	C₂	C₁₉×#3166	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
78. C₁₉×#97	Q₈	semidirect
138. #23841	C₁₉	direct (N × H)
288. #97	Q₈×C₁₉	semidirect
297. C₁₉	#23841	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₉×C₄⋊Q₈	2
C₄×C₁₉×#125	2
C₁₉×#2085	2
C₁₉×#2084	2
C₁₉×#2083	2
C₁₉×#2059	2
C₁₉×#2058	2
C₁₉×#2057	2
C₁₉×#1776	2
C₁₉×#1745	2
#23841	19

Subgroups — C19×#23841 #18029800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23841 #18029800