Subgroups — C₁₉×#29495 #18035454

Order 4864.

728 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2863	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2083	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2072	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2043	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2016	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1969	C₂	1	2	yes	maximal
8	C₁₉×#1933	C₂	1	2	yes	maximal
9	C₁₉×#1878	C₂	1	2	yes	maximal
10	C₁₉×#1863	C₂	1	2	yes	maximal
11	C₁₉×#1744	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
15	C₂×C₁₉×#107	C₂²	1	2	yes	—
16	C₂×C₁₉×#103	C₂²	1	2	yes	—
17	C₂×C₁₉×#103	C₂²	1	2	yes	—
18	C₂×C₁₉×#103	C₂²	1	2	yes	—
19	C₂×C₁₉×#103	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
21	C₁₉×#391	C₂²	1	2	yes	—
22	C₁₉×#391	C₂²	1	1	yes	characteristic
23	C₁₉×#391	C₂²	1	1	yes	characteristic
24	C₁₉×#391	C₂²	1	1	yes	characteristic
25	C₁₉×#389	—	2	1	no	—
26	C₁₉×#389	—	2	1	no	—
27	C₁₉×#389	C₂²	1	1	yes	characteristic
28	C₁₉×#389	C₂²	1	1	yes	characteristic
29	C₁₉×#389	C₂²	1	1	yes	characteristic
30	C₁₉×#387	—	2	1	no	—
31	C₁₉×#387	—	2	1	no	—
32	C₁₉×#387	—	2	1	no	—
33	C₁₉×#384	C₂²	1	1	yes	characteristic
34	C₁₉×#383	—	2	1	no	—
35	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₄³×C₁₉	C₂²	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
45	C₂×Q₁₆×C₁₉	—	2	4	no	—
46	C₂×Q₁₆×C₁₉	—	2	4	no	—
47	C₂×Q₁₆×C₁₉	—	4	2	no	—
48	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
50	C₁₉×C₄⋊Q₈	—	2	4	no	—
51	C₄×Q₈×C₁₉	—	4	2	no	—
52	C₄×Q₈×C₁₉	—	4	2	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	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
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×C₄²×C₁₉	—	2	2	no	—
66	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×#107	—	4	2	no	—
74	C₁₉×#103	—	2	4	no	—
75	C₁₉×#103	—	2	4	no	—
76	C₁₉×#103	—	4	2	no	—
77	C₁₉×#103	—	4	2	no	—
78	C₄×C₈×C₁₉	—	2	4	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₁₉×#95	—	2	2	no	—
81	C₁₉×#95	—	2	1	no	—
82	C₁₉×#95	—	2	1	no	—
83	C₁₉×#95	—	2	1	no	—
84	C₁₉×#95	—	2	1	no	—
85	C₁₉×#95	—	2	1	no	—
86	C₁₉×#95	—	2	1	no	—
87	C₁₉×#95	—	2	1	no	—
88	C₁₉×#95	—	2	1	no	—
89	C₁₉×#95	—	2	1	no	—
90	C₂×Q₈×C₁₉	—	2	2	no	—
91	C₂×Q₈×C₁₉	—	2	2	no	—
92	C₂×Q₈×C₁₉	—	2	2	no	—
93	C₂×Q₈×C₁₉	—	2	2	no	—
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	1	no	—
98	C₂×Q₈×C₁₉	—	2	1	no	—
99	C₂×Q₈×C₁₉	#41	1	4	yes	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
113	Q₁₆×C₁₉	—	4	8	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	#41	1	4	yes	—
120	C₄⋊C₄×C₁₉	—	2	4	no	—
121	C₄⋊C₄×C₁₉	—	2	4	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	2	2	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	2	no	—
130	C₄⋊C₄×C₁₉	—	4	4	no	—
131	C₄⋊C₄×C₁₉	—	4	2	no	—
132	C₄⋊C₄×C₁₉	—	4	2	no	—
133	C₄⋊C₄×C₁₉	—	4	2	no	—
134	C₄²×C₁₉	—	2	2	no	—
135	C₄²×C₁₉	—	2	2	no	—
136	C₄²×C₁₉	—	2	2	no	—
137	C₄²×C₁₉	—	2	2	no	—
138	C₄²×C₁₉	—	2	1	no	—
139	C₄²×C₁₉	—	2	1	no	—
140	C₄²×C₁₉	—	4	1	no	—
141	C₄²×C₁₉	—	4	4	no	—
142	C₄²×C₁₉	Q₁₆	1	4	yes	complemented
143	#29495	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₁₉	—	2	4	no	—
146	Q₈×C₁₉	—	2	4	no	—
147	Q₈×C₁₉	—	4	2	no	—
148	Q₈×C₁₉	—	4	2	no	—
149	Q₈×C₁₉	—	4	2	no	—
150	Q₈×C₁₉	—	4	2	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	2	1	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	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	1	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	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	2	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
183	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
184	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
185	C₂×C₄×C₁₉	#135	1	2	yes	—
186	C₂×C₄×C₁₉	#137	1	2	yes	—
187	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
188	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
189	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
191	C₈×C₁₉	—	2	4	no	—
192	C₈×C₁₉	—	4	2	no	—
193	#2863	C₂×C₁₉	1	1	yes	characteristic
194	C₄×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
195	#2083	C₂×C₁₉	1	1	yes	characteristic
196	#2072	C₂×C₁₉	1	1	yes	characteristic
197	#2043	C₂×C₁₉	1	1	yes	characteristic
198	#2016	C₂×C₁₉	1	1	yes	characteristic
199	#1969	C₂×C₁₉	1	2	yes	—
200	#1933	C₂×C₁₉	1	2	yes	—
201	#1878	C₂×C₁₉	1	2	yes	—
202	#1863	C₂×C₁₉	1	2	yes	—
203	#1744	C₂×C₁₉	1	1	yes	characteristic
204	C₂²×C₁₉	#525	1	1	yes	characteristic
205	C₂²×C₁₉	#532	1	1	yes	characteristic
206	C₂²×C₁₉	#535	1	1	yes	characteristic
207	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
208	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
209	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
210	C₂²×C₁₉	#575	1	1	yes	characteristic
211	C₄×C₁₉	—	2	2	no	—
212	C₄×C₁₉	—	2	2	no	—
213	C₄×C₁₉	—	2	2	no	—
214	C₄×C₁₉	—	2	2	no	—
215	C₄×C₁₉	—	2	2	no	—
216	C₄×C₁₉	—	4	4	no	—
217	C₄×C₁₉	—	4	1	no	—
218	C₄×C₁₉	—	8	1	no	—
219	C₄×C₁₉	—	8	1	no	—
220	C₄×C₁₉	—	8	1	no	—
221	C₄×C₁₉	—	8	2	no	—
222	C₄×C₁₉	—	8	1	no	—
223	C₄×C₁₉	#551	1	2	yes	—
224	C₄×C₁₉	#553	1	2	yes	—
225	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	—
226	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
228	C₂×#107	C₂²×C₁₉	1	2	yes	—
229	C₂×#103	C₂²×C₁₉	1	2	yes	—
230	C₂×#103	C₂²×C₁₉	1	2	yes	—
231	C₂×#103	C₂²×C₁₉	1	2	yes	—
232	C₂×#103	C₂²×C₁₉	1	2	yes	—
233	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
234	#391	C₂²×C₁₉	1	2	yes	—
235	#391	C₂²×C₁₉	1	1	yes	characteristic
236	#391	C₂²×C₁₉	1	1	yes	characteristic
237	#391	C₂²×C₁₉	1	1	yes	characteristic
238	#389	—	2	1	no	—
239	#389	—	2	1	no	—
240	#389	C₂²×C₁₉	1	1	yes	characteristic
241	#389	C₂²×C₁₉	1	1	yes	characteristic
242	#389	C₂²×C₁₉	1	1	yes	characteristic
243	#387	—	2	1	no	—
244	#387	—	2	1	no	—
245	#387	—	2	1	no	—
246	#384	C₂²×C₁₉	1	1	yes	characteristic
247	#383	—	2	1	no	—
248	C₄×C₄⋊C₄	—	2	1	no	—
249	C₄×C₄⋊C₄	—	2	1	no	—
250	C₄³	C₂²×C₁₉	1	1	yes	characteristic
251	#340	C₂²×C₁₉	1	2	yes	—
252	#340	C₂²×C₁₉	1	2	yes	—
253	#336	C₂²×C₁₉	1	1	yes	characteristic
254	#336	C₂²×C₁₉	1	1	yes	characteristic
255	#336	C₂²×C₁₉	1	2	yes	—
256	C₂×C₁₉	#2603	1	1	yes	characteristic
257	C₂×C₁₉	#3104	1	1	yes	characteristic
258	C₂×C₁₉	#3108	1	1	yes	characteristic
259	C₂×C₁₉	#3170	1	1	yes	characteristic
260	C₂×C₁₉	#3181	1	1	yes	characteristic
261	C₂×C₁₉	#3209	1	1	yes	characteristic
262	C₂×C₁₉	#3212	1	1	yes	characteristic
263	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
264	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
265	C₂×Q₁₆	—	2	4	no	—
266	C₂×Q₁₆	—	2	4	no	—
267	C₂×Q₁₆	—	4	2	no	—
268	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
269	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
270	C₄⋊Q₈	—	2	4	no	—
271	C₄×Q₈	—	4	2	no	—
272	C₄×Q₈	—	4	2	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
287	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
288	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
289	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
293	#107	—	4	2	no	—
294	#103	—	2	4	no	—
295	#103	—	2	4	no	—
296	#103	—	4	2	no	—
297	#103	—	4	2	no	—
298	C₄×C₈	—	2	4	no	—
299	#95	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	—	2	1	no	—
302	#95	—	2	1	no	—
303	#95	—	2	1	no	—
304	#95	—	2	1	no	—
305	#95	—	2	1	no	—
306	#95	—	2	1	no	—
307	#95	—	2	1	no	—
308	#95	—	2	1	no	—
309	#95	—	2	1	no	—
310	C₁₉	#29495	1	1	yes	characteristic, direct product factor, Sylow
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	#41×C₁₉	1	4	yes	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
333	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
334	Q₁₆	—	4	8	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	#41×C₁₉	1	4	yes	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	4	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	4	1	no	—
362	C₄²	—	4	4	no	—
363	C₄²	Q₁₆×C₁₉	1	4	yes	complemented
364	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
365	Q₈	—	2	4	no	—
366	Q₈	—	2	4	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
403	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
404	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
405	C₂×C₄	C₁₉×#135	1	2	yes	—
406	C₂×C₄	C₁₉×#137	1	2	yes	—
407	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
408	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
409	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
410	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
411	C₈	—	2	4	no	—
412	C₈	—	4	2	no	—
413	C₂²	C₁₉×#525	1	1	yes	characteristic
414	C₂²	C₁₉×#532	1	1	yes	characteristic
415	C₂²	C₁₉×#535	1	1	yes	characteristic
416	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
417	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
418	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
419	C₂²	C₁₉×#575	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	4	no	—
427	C₄	—	8	1	no	—
428	C₄	—	8	2	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	1	no	—
431	C₄	—	8	1	no	—
432	C₄	C₁₉×#551	1	2	yes	—
433	C₄	C₁₉×#553	1	2	yes	—
434	C₂	C₁₉×#2603	1	1	yes	characteristic
435	C₂	C₁₉×#3104	1	1	yes	characteristic
436	C₂	C₁₉×#3108	1	1	yes	characteristic
437	C₂	C₁₉×#3170	1	1	yes	characteristic
438	C₂	C₁₉×#3181	1	1	yes	characteristic
439	C₂	C₁₉×#3209	1	1	yes	characteristic
440	C₂	C₁₉×#3212	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
142. C₄²×C₁₉	Q₁₆	semidirect
143. #29495	C₁₉	direct (N × H)
310. C₁₉	#29495	direct (N × H)
363. C₄²	Q₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#2863	2
C₄×C₁₉×C₄⋊Q₈	2
C₁₉×#2083	2
C₁₉×#2072	2
C₁₉×#2043	2
C₁₉×#2016	2
C₁₉×#1969	2
C₁₉×#1933	2
C₁₉×#1878	2
C₁₉×#1863	2
C₁₉×#1744	2
#29495	19

Subgroups — C19×#29495 #18035454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#29495 #18035454