Subgroups — C₁₉×#32937 #18038896

Order 4864.

1502 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	C₂³×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#470	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2848	C₂	1	2	yes	maximal
5	C₁₉×#1894	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1892	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1809	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1807	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
11	C₂²×M₁₆×C₁₉	—	2	8	no	—
12	C₂²×M₁₆×C₁₉	—	2	4	no	—
13	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
15	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
19	C₁₉×#470	—	2	8	no	—
20	C₁₉×#467	—	2	4	no	—
21	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
23	C₂×C₁₉×#103	C₂²	1	4	yes	complemented
24	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
25	C₁₉×#385	—	2	4	no	—
26	C₁₉×#385	—	2	2	no	—
27	C₁₉×#380	C₂²	1	2	yes	—
28	C₁₉×#380	C₂²	1	4	yes	—
29	C₁₉×#379	—	2	2	no	—
30	C₁₉×#340	C₂²	1	4	yes	complemented
31	C₁₉×#340	C₂²	1	2	yes	complemented
32	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₉	—	2	4	no	—
35	C₂³×C₄×C₁₉	—	2	2	no	—
36	C₂³×C₄×C₁₉	—	2	4	no	—
37	C₂³×C₄×C₁₉	—	2	2	no	—
38	C₂³×C₄×C₁₉	D₄	1	2	yes	—
39	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
42	C₂×Q₁₆×C₁₉	—	2	2	no	—
43	C₂×Q₁₆×C₁₉	—	2	4	no	—
44	C₂×M₁₆×C₁₉	—	2	32	no	—
45	C₂×M₁₆×C₁₉	—	2	4	no	—
46	C₂×M₁₆×C₁₉	—	2	4	no	—
47	C₂×M₁₆×C₁₉	—	2	4	no	—
48	C₂×M₁₆×C₁₉	—	2	4	no	—
49	C₂×M₁₆×C₁₉	—	2	4	no	—
50	C₂×M₁₆×C₁₉	D₄	1	8	yes	—
51	C₂²×C₈×C₁₉	—	2	2	no	—
52	C₂²×C₈×C₁₉	—	2	4	no	—
53	C₂²×C₈×C₁₉	—	2	4	no	—
54	C₂²×C₈×C₁₉	D₄	1	4	yes	—
55	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×C₂²⋊Q₈	—	2	4	no	—
59	C₁₉×C₂²⋊Q₈	—	2	8	no	—
60	C₁₉×C₂²⋊Q₈	—	2	4	no	—
61	C₁₉×C₂²⋊Q₈	—	2	8	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₁₉×#107	—	2	2	no	—
71	C₁₉×#106	—	2	4	no	—
72	C₁₉×#103	—	2	4	no	—
73	C₁₉×#103	—	2	8	no	—
74	C₁₉×#95	—	2	2	no	—
75	C₁₉×#95	—	2	4	no	—
76	C₂⁴×C₁₉	—	2	4	no	—
77	C₂⁴×C₁₉	—	2	2	no	—
78	C₂⁴×C₁₉	—	2	4	no	—
79	C₂⁴×C₁₉	—	4	2	no	—
80	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
81	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂×Q₈×C₁₉	—	2	2	no	—
83	C₂×Q₈×C₁₉	—	2	4	no	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×Q₈×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	2	8	no	—
87	C₂²×C₄×C₁₉	—	2	8	no	—
88	C₂²×C₄×C₁₉	—	2	16	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	4	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₁₉	#41	1	4	yes	—
108	C₂²×C₄×C₁₉	#41	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
110	Q₁₆×C₁₉	—	4	4	no	—
111	M₁₆×C₁₉	—	2	16	no	—
112	M₁₆×C₁₉	—	2	16	no	—
113	C₂×C₈×C₁₉	—	2	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	8	no	—
118	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
119	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
121	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
122	C₄⋊C₄×C₁₉	—	2	4	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	4	4	no	—
127	C₄⋊C₄×C₁₉	—	4	8	no	—
128	C₂²⋊C₄×C₁₉	—	4	8	no	—
129	C₂²⋊C₄×C₁₉	—	4	8	no	—
130	C₂²⋊C₄×C₁₉	—	4	4	no	—
131	C₂²⋊C₄×C₁₉	—	4	4	no	—
132	#32937	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₁₉	—	2	2	no	—
134	C₂³×C₁₉	—	2	2	no	—
135	C₂³×C₁₉	—	2	8	no	—
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	2	2	no	—
138	C₂³×C₁₉	—	2	4	no	—
139	C₂³×C₁₉	—	2	4	no	—
140	C₂³×C₁₉	—	4	16	no	—
141	C₂³×C₁₉	—	4	4	no	—
142	C₂³×C₁₉	—	4	4	no	—
143	C₂³×C₁₉	#121	1	4	yes	—
144	C₂³×C₁₉	#121	1	2	yes	—
145	C₂³×C₁₉	#137	1	4	yes	—
146	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₁₉	—	4	2	no	—
148	Q₈×C₁₉	—	4	2	no	—
149	Q₈×C₁₉	—	4	4	no	—
150	C₂×C₄×C₁₉	—	2	8	no	—
151	C₂×C₄×C₁₉	—	2	16	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	4	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	4	no	—
166	C₂×C₄×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	#121	1	2	yes	—
170	C₂×C₄×C₁₉	#121	1	4	yes	—
171	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
173	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
175	C₈×C₁₉	—	2	4	no	—
176	C₈×C₁₉	—	2	2	no	—
177	C₈×C₁₉	#120	1	4	yes	—
178	C₂³×M₁₆	C₂×C₁₉	1	1	yes	characteristic
179	C₂×#470	C₂×C₁₉	1	2	yes	complemented
180	C₂×#467	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#2848	C₂×C₁₉	1	2	yes	—
182	#1894	C₂×C₁₉	1	4	yes	complemented
183	#1892	C₂×C₁₉	1	2	yes	complemented
184	#1809	C₂×C₁₉	1	2	yes	complemented
185	#1807	C₂×C₁₉	1	1	yes	characteristic, complemented
186	C₂²×C₁₉	—	2	2	no	—
187	C₂²×C₁₉	—	2	2	no	—
188	C₂²×C₁₉	—	2	8	no	—
189	C₂²×C₁₉	—	2	4	no	—
190	C₂²×C₁₉	—	2	8	no	—
191	C₂²×C₁₉	—	4	16	no	—
192	C₂²×C₁₉	—	4	2	no	—
193	C₂²×C₁₉	—	4	2	no	—
194	C₂²×C₁₉	—	4	4	no	—
195	C₂²×C₁₉	#470	1	4	yes	complemented
196	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
197	C₂²×C₁₉	C₂×#121	1	2	yes	—
198	C₂²×C₁₉	C₂×#137	1	2	yes	—
199	C₂²×C₁₉	#575	1	2	yes	—
200	C₄×C₁₉	—	2	2	no	—
201	C₄×C₁₉	—	2	4	no	—
202	C₄×C₁₉	—	8	2	no	—
203	C₄×C₁₉	—	8	2	no	—
204	C₄×C₁₉	—	8	4	no	—
205	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
206	C₄×C₁₉	#525	1	1	yes	characteristic
207	C₄×C₁₉	#525	1	2	yes	—
208	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
209	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
210	C₂²×M₁₆	—	2	8	no	—
211	C₂²×M₁₆	—	2	4	no	—
212	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
213	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
214	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
215	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
216	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
217	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
218	#470	—	2	8	no	—
219	#467	—	2	4	no	—
220	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
221	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
222	C₂×#103	C₂²×C₁₉	1	4	yes	complemented
223	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
224	#385	—	2	4	no	—
225	#385	—	2	2	no	—
226	#380	C₂²×C₁₉	1	2	yes	—
227	#380	C₂²×C₁₉	1	4	yes	—
228	#379	—	2	2	no	—
229	#340	C₂²×C₁₉	1	2	yes	complemented
230	#340	C₂²×C₁₉	1	4	yes	complemented
231	C₂×C₁₉	—	2	4	no	—
232	C₂×C₁₉	—	4	4	no	—
233	C₂×C₁₉	#2847	1	1	yes	characteristic
234	C₂×C₁₉	C₂×#470	1	1	yes	characteristic
235	C₂×C₁₉	#3054	1	1	yes	characteristic
236	C₂×C₁₉	#3056	1	4	yes	—
237	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
238	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
239	C₂³×C₄	—	2	4	no	—
240	C₂³×C₄	—	2	2	no	—
241	C₂³×C₄	—	2	4	no	—
242	C₂³×C₄	—	2	2	no	—
243	C₂³×C₄	D₄×C₁₉	1	2	yes	—
244	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
245	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
246	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
247	C₂×Q₁₆	—	2	2	no	—
248	C₂×Q₁₆	—	2	4	no	—
249	C₂×M₁₆	—	2	32	no	—
250	C₂×M₁₆	—	2	4	no	—
251	C₂×M₁₆	—	2	4	no	—
252	C₂×M₁₆	—	2	4	no	—
253	C₂×M₁₆	—	2	4	no	—
254	C₂×M₁₆	—	2	4	no	—
255	C₂×M₁₆	D₄×C₁₉	1	8	yes	—
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	—	2	4	no	—
258	C₂²×C₈	—	2	4	no	—
259	C₂²×C₈	D₄×C₁₉	1	4	yes	—
260	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
261	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
263	C₂²⋊Q₈	—	2	4	no	—
264	C₂²⋊Q₈	—	2	8	no	—
265	C₂²⋊Q₈	—	2	4	no	—
266	C₂²⋊Q₈	—	2	8	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	4	no	—
269	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	4	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	4	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	#107	—	2	2	no	—
276	#106	—	2	4	no	—
277	#103	—	2	4	no	—
278	#103	—	2	8	no	—
279	#95	—	2	2	no	—
280	#95	—	2	4	no	—
281	C₁₉	#32937	1	1	yes	characteristic, direct product factor, Sylow
282	C₂⁴	—	2	4	no	—
283	C₂⁴	—	2	2	no	—
284	C₂⁴	—	2	4	no	—
285	C₂⁴	—	4	2	no	—
286	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
287	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	—	2	16	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
313	C₂²×C₄	#41×C₁₉	1	4	yes	—
314	C₂²×C₄	#41×C₁₉	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
316	Q₁₆	—	4	4	no	—
317	M₁₆	—	2	16	no	—
318	M₁₆	—	2	16	no	—
319	C₂×C₈	—	2	8	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	8	no	—
324	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
325	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
326	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
327	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	4	no	—
333	C₄⋊C₄	—	4	8	no	—
334	C₂²⋊C₄	—	4	8	no	—
335	C₂²⋊C₄	—	4	8	no	—
336	C₂²⋊C₄	—	4	4	no	—
337	C₂²⋊C₄	—	4	4	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	8	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	4	16	no	—
346	C₂³	—	4	4	no	—
347	C₂³	—	4	4	no	—
348	C₂³	C₁₉×#121	1	4	yes	—
349	C₂³	C₁₉×#121	1	2	yes	—
350	C₂³	C₁₉×#137	1	4	yes	—
351	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
352	Q₈	—	4	2	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	4	4	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	16	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	C₁₉×#121	1	2	yes	—
375	C₂×C₄	C₁₉×#121	1	4	yes	—
376	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
378	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
379	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
380	C₈	—	2	4	no	—
381	C₈	—	2	2	no	—
382	C₈	C₁₉×#120	1	4	yes	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	8	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	8	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	4	16	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	4	no	—
392	C₂²	C₁₉×#470	1	4	yes	complemented
393	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
394	C₂²	C₂×C₁₉×#121	1	2	yes	—
395	C₂²	C₂×C₁₉×#137	1	2	yes	—
396	C₂²	C₁₉×#575	1	2	yes	—
397	C₄	—	2	2	no	—
398	C₄	—	2	4	no	—
399	C₄	—	8	2	no	—
400	C₄	—	8	4	no	—
401	C₄	—	8	2	no	—
402	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
403	C₄	C₁₉×#525	1	1	yes	characteristic
404	C₄	C₁₉×#525	1	2	yes	—
405	C₂	—	2	4	no	—
406	C₂	—	4	4	no	—
407	C₂	C₁₉×#2847	1	1	yes	characteristic
408	C₂	C₂×C₁₉×#470	1	1	yes	characteristic
409	C₂	C₁₉×#3054	1	1	yes	characteristic
410	C₂	C₁₉×#3056	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#470	C₂	semidirect
3. C₂×C₁₉×#467	C₂	semidirect
5. C₁₉×#1894	C₂	semidirect
6. C₁₉×#1892	C₂	semidirect
7. C₁₉×#1809	C₂	semidirect
8. C₁₉×#1807	C₂	semidirect
10. C₂²×Q₁₆×C₁₉	C₂²	semidirect
21. C₂×C₁₉×#107	C₂²	semidirect
22. C₂×C₁₉×#106	C₂²	semidirect
23. C₂×C₁₉×#103	C₂²	semidirect
24. C₂×C₁₉×#103	C₂²	semidirect
30. C₁₉×#340	C₂²	semidirect
31. C₁₉×#340	C₂²	semidirect
132. #32937	C₁₉	direct (N × H)
179. C₂×#470	C₂×C₁₉	semidirect
180. C₂×#467	C₂×C₁₉	semidirect
182. #1894	C₂×C₁₉	semidirect
183. #1892	C₂×C₁₉	semidirect
184. #1809	C₂×C₁₉	semidirect
185. #1807	C₂×C₁₉	semidirect
195. C₂²×C₁₉	#470	semidirect
209. C₂²×Q₁₆	C₂²×C₁₉	semidirect
220. C₂×#107	C₂²×C₁₉	semidirect
221. C₂×#106	C₂²×C₁₉	semidirect
222. C₂×#103	C₂²×C₁₉	semidirect
223. C₂×#103	C₂²×C₁₉	semidirect
229. #340	C₂²×C₁₉	semidirect
230. #340	C₂²×C₁₉	semidirect
281. C₁₉	#32937	direct (N × H)
392. C₂²	C₁₉×#470	semidirect

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₁₉	2
C₂×C₁₉×#470	2
C₂×C₁₉×#467	2
C₁₉×#2848	2
C₁₉×#1894	2
C₁₉×#1892	2
C₁₉×#1809	2
C₁₉×#1807	2
#32937	19

Subgroups — C19×#32937 #18038896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32937 #18038896