Subgroups — C₁₉×#26280 #18032239

Order 4864.

682 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2567	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2099	C₂	1	2	yes	maximal
4	C₁₉×#2084	C₂	1	2	yes	maximal
5	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1987	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1984	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1948	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1920	C₂	1	2	yes	maximal
10	C₁₉×#1920	C₂	1	2	yes	maximal
11	C₄×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#106	C₂²	1	2	yes	—
16	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#395	—	2	2	no	—
21	C₁₉×#391	—	2	1	no	—
22	C₁₉×#389	—	2	1	no	—
23	C₁₉×#389	—	2	2	no	—
24	C₁₉×#389	C₂²	1	2	yes	—
25	C₁₉×#389	C₂²	1	2	yes	—
26	C₁₉×#384	—	2	1	no	—
27	C₁₉×#384	C₂²	1	1	yes	characteristic
28	C₁₉×#384	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×#340	C₂²	1	2	yes	—
33	C₁₉×#340	C₂²	1	1	yes	characteristic
34	C₁₉×#340	C₂²	1	2	yes	—
35	C₁₉×#340	C₂²	1	2	yes	—
36	C₁₉×#340	C₂²	1	2	yes	—
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	1	yes	characteristic
39	C₁₉×#336	C₂²	1	2	yes	—
40	C₁₉×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₁₉×C₄⋊Q₈	—	2	2	no	—
47	C₁₉×C₄⋊Q₈	—	2	2	no	—
48	C₄×Q₈×C₁₉	—	2	2	no	—
49	C₄×Q₈×C₁₉	—	2	2	no	—
50	C₄×Q₈×C₁₉	—	4	4	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	—	2	2	no	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
71	C₁₉×#106	—	2	2	no	—
72	C₁₉×#106	—	2	4	no	—
73	C₁₉×#106	Q₈	1	4	yes	complemented
74	C₁₉×C₄⋊C₈	—	2	2	no	—
75	C₄×C₈×C₁₉	—	2	2	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	1	no	—
78	C₁₉×#95	—	2	1	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₁₉×#95	—	2	2	no	—
81	C₂×Q₈×C₁₉	—	2	2	no	—
82	C₂×Q₈×C₁₉	—	2	2	no	—
83	C₂×Q₈×C₁₉	—	4	2	no	—
84	C₂×Q₈×C₁₉	—	8	1	no	—
85	C₂×Q₈×C₁₉	—	8	1	no	—
86	C₂×Q₈×C₁₉	SD₁₆	1	4	yes	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₁₉	—	2	1	no	—
99	C₂×C₈×C₁₉	—	2	1	no	—
100	C₂×C₈×C₁₉	—	2	1	no	—
101	C₂×C₈×C₁₉	—	2	2	no	—
102	C₂×C₈×C₁₉	—	2	2	no	—
103	C₂×C₈×C₁₉	—	2	1	no	—
104	C₂×C₈×C₁₉	—	2	1	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
107	C₄⋊C₄×C₁₉	—	2	4	no	—
108	C₄⋊C₄×C₁₉	—	2	2	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₄⋊C₄×C₁₉	—	4	2	no	—
119	C₄⋊C₄×C₁₉	—	4	4	no	—
120	C₄⋊C₄×C₁₉	—	4	2	no	—
121	C₄⋊C₄×C₁₉	—	8	1	no	—
122	C₄⋊C₄×C₁₉	—	8	2	no	—
123	C₄⋊C₄×C₁₉	—	8	2	no	—
124	C₄⋊C₄×C₁₉	—	8	2	no	—
125	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
126	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
127	C₄⋊C₄×C₁₉	#41	1	2	yes	—
128	C₄²×C₁₉	—	2	2	no	—
129	C₄²×C₁₉	—	2	2	no	—
130	C₄²×C₁₉	—	4	4	no	—
131	C₄²×C₁₉	—	4	2	no	—
132	C₄²×C₁₉	—	4	2	no	—
133	C₄²×C₁₉	#41	1	2	yes	—
134	C₄²×C₁₉	#41	1	2	yes	—
135	#26280	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₁₉	—	2	8	no	—
138	Q₈×C₁₉	—	8	4	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	#123	1	2	yes	—
165	C₂×C₄×C₁₉	#123	1	2	yes	—
166	C₂×C₄×C₁₉	C₂×SD₁₆	1	4	yes	—
167	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
168	C₂×C₄×C₁₉	#137	1	2	yes	—
169	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
174	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
175	C₈×C₁₉	—	2	2	no	—
176	C₈×C₁₉	—	4	1	no	—
177	C₈×C₁₉	—	4	2	no	—
178	#2567	C₂×C₁₉	1	1	yes	characteristic
179	Q₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
180	#2099	C₂×C₁₉	1	2	yes	—
181	#2084	C₂×C₁₉	1	2	yes	—
182	#1990	C₂×C₁₉	1	1	yes	characteristic
183	#1987	C₂×C₁₉	1	1	yes	characteristic
184	#1984	C₂×C₁₉	1	1	yes	characteristic
185	#1948	C₂×C₁₉	1	1	yes	characteristic
186	#1920	C₂×C₁₉	1	2	yes	—
187	#1920	C₂×C₁₉	1	2	yes	—
188	C₄×#106	C₂×C₁₉	1	1	yes	characteristic
189	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
190	C₂²×C₁₉	#548	1	1	yes	characteristic
191	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
192	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
193	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
194	C₂²×C₁₉	#576	1	1	yes	characteristic
195	C₂²×C₁₉	#577	1	1	yes	characteristic
196	C₄×C₁₉	—	2	4	no	—
197	C₄×C₁₉	—	2	2	no	—
198	C₄×C₁₉	—	4	2	no	—
199	C₄×C₁₉	—	4	2	no	—
200	C₄×C₁₉	—	4	2	no	—
201	C₄×C₁₉	—	4	2	no	—
202	C₄×C₁₉	—	8	2	no	—
203	C₄×C₁₉	—	8	2	no	—
204	C₄×C₁₉	—	8	1	no	—
205	C₄×C₁₉	#483	1	4	yes	—
206	C₄×C₁₉	#533	1	1	yes	characteristic
207	C₄×C₁₉	#541	1	1	yes	characteristic
208	C₄×C₁₉	#556	1	1	yes	characteristic
209	C₄×C₁₉	#557	1	1	yes	characteristic
210	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×C₄×Q₈	—	2	1	no	—
212	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
213	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
214	C₂×#106	C₂²×C₁₉	1	2	yes	—
215	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
218	#395	—	2	2	no	—
219	#391	—	2	1	no	—
220	#389	—	2	1	no	—
221	#389	—	2	2	no	—
222	#389	C₂²×C₁₉	1	2	yes	—
223	#389	C₂²×C₁₉	1	2	yes	—
224	#384	—	2	1	no	—
225	#384	C₂²×C₁₉	1	2	yes	—
226	#384	C₂²×C₁₉	1	1	yes	characteristic
227	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
228	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
229	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
230	#340	C₂²×C₁₉	1	2	yes	—
231	#340	C₂²×C₁₉	1	2	yes	—
232	#340	C₂²×C₁₉	1	1	yes	characteristic
233	#340	C₂²×C₁₉	1	2	yes	—
234	#340	C₂²×C₁₉	1	2	yes	—
235	#340	C₂²×C₁₉	1	2	yes	—
236	#340	C₂²×C₁₉	1	1	yes	characteristic
237	#336	C₂²×C₁₉	1	2	yes	—
238	#336	C₂²×C₁₉	1	2	yes	—
239	C₂×C₁₉	#2446	1	1	yes	characteristic
240	C₂×C₁₉	C₂×#483	1	1	yes	characteristic
241	C₂×C₁₉	#3096	1	1	yes	characteristic
242	C₂×C₁₉	#3362	1	1	yes	characteristic
243	C₂×C₁₉	#3372	1	1	yes	characteristic
244	C₂×C₁₉	Q₈×SD₁₆	1	1	yes	characteristic
245	C₂×C₁₉	#3385	1	1	yes	characteristic
246	C₂²×Q₈	—	2	1	no	—
247	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
250	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
251	C₄⋊Q₈	—	2	2	no	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	—	4	4	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
264	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
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	1	yes	characteristic
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
275	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
276	#106	—	2	2	no	—
277	#106	—	2	4	no	—
278	#106	Q₈×C₁₉	1	4	yes	complemented
279	C₄⋊C₈	—	2	2	no	—
280	C₄×C₈	—	2	2	no	—
281	#95	—	2	2	no	—
282	#95	—	2	1	no	—
283	#95	—	2	1	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	C₁₉	#26280	1	1	yes	characteristic, direct product factor, Sylow
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	—	8	1	no	—
291	C₂×Q₈	—	8	1	no	—
292	C₂×Q₈	SD₁₆×C₁₉	1	4	yes	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
300	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
303	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	8	1	no	—
328	C₄⋊C₄	—	8	2	no	—
329	C₄⋊C₄	—	8	2	no	—
330	C₄⋊C₄	—	8	2	no	—
331	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
332	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
333	C₄⋊C₄	#41×C₁₉	1	2	yes	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	4	4	no	—
337	C₄²	—	4	2	no	—
338	C₄²	—	4	2	no	—
339	C₄²	#41×C₁₉	1	2	yes	—
340	C₄²	#41×C₁₉	1	2	yes	—
341	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
342	Q₈	—	2	8	no	—
343	Q₈	—	8	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	C₁₉×#123	1	2	yes	—
370	C₂×C₄	C₁₉×#123	1	2	yes	—
371	C₂×C₄	C₂×SD₁₆×C₁₉	1	4	yes	—
372	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
373	C₂×C₄	C₁₉×#137	1	2	yes	—
374	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
375	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
376	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
377	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
378	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
379	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
380	C₈	—	2	2	no	—
381	C₈	—	4	1	no	—
382	C₈	—	4	2	no	—
383	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
384	C₂²	C₁₉×#548	1	1	yes	characteristic
385	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
386	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
387	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
388	C₂²	C₁₉×#576	1	1	yes	characteristic
389	C₂²	C₁₉×#577	1	1	yes	characteristic
390	C₄	—	2	4	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	1	no	—
399	C₄	C₁₉×#483	1	4	yes	—
400	C₄	C₁₉×#533	1	1	yes	characteristic
401	C₄	C₁₉×#541	1	1	yes	characteristic
402	C₄	C₁₉×#556	1	1	yes	characteristic
403	C₄	C₁₉×#557	1	1	yes	characteristic
404	C₂	C₁₉×#2446	1	1	yes	characteristic
405	C₂	C₂×C₁₉×#483	1	1	yes	characteristic
406	C₂	C₁₉×#3096	1	1	yes	characteristic
407	C₂	C₁₉×#3362	1	1	yes	characteristic
408	C₂	C₁₉×#3372	1	1	yes	characteristic
409	C₂	Q₈×SD₁₆×C₁₉	1	1	yes	characteristic
410	C₂	C₁₉×#3385	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 ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
73. C₁₉×#106	Q₈	semidirect
135. #26280	C₁₉	direct (N × H)
278. #106	Q₈×C₁₉	semidirect
286. C₁₉	#26280	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×#2567	2
Q₈×C₄⋊C₄×C₁₉	2
C₁₉×#2099	2
C₁₉×#2084	2
C₁₉×#1990	2
C₁₉×#1987	2
C₁₉×#1984	2
C₁₉×#1948	2
C₁₉×#1920	2
C₄×C₁₉×#106	2
#26280	19

Subgroups — C19×#26280 #18032239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26280 #18032239