Subgroups — C₁₉×#32914 #18038873

Order 4864.

1546 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#518	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#461	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#450	C₂	1	2	yes	maximal
4	C₁₉×#2621	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1877	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1873	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1804	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1798	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×SD₁₆×C₁₉	C₂²	1	4	yes	—
11	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
13	C₁₉×#518	—	2	8	no	—
14	C₂×C₄×D₄×C₁₉	—	2	2	no	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
17	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
20	C₁₉×#461	—	2	8	no	—
21	C₁₉×#450	—	2	8	no	—
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
23	C₂×C₁₉×#103	C₂²	1	4	yes	complemented
24	C₂×C₁₉×#102	C₂²	1	4	yes	—
25	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₁₉×#398	—	2	2	no	—
27	C₁₉×#397	—	2	2	no	—
28	C₁₉×#391	C₂²	1	2	yes	complemented
29	C₁₉×#382	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#340	C₂²	1	4	yes	complemented
31	C₁₉×#336	C₂²	1	2	yes	complemented
32	C₂⁵×C₁₉	—	2	1	no	—
33	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
34	C₂²×D₄×C₁₉	—	2	4	no	—
35	C₂²×D₄×C₁₉	—	2	4	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	2	no	—
38	C₂²×D₄×C₁₉	D₄	1	4	yes	—
39	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₉	—	2	2	no	—
41	C₂³×C₄×C₁₉	—	2	2	no	—
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×SD₁₆×C₁₉	—	2	8	no	—
44	C₂×SD₁₆×C₁₉	—	2	8	no	—
45	C₂×SD₁₆×C₁₉	—	2	8	no	—
46	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
47	C₁₉×C₄⋊Q₈	—	2	4	no	—
48	C₁₉×C₂²⋊Q₈	—	2	4	no	—
49	C₁₉×C₂²⋊Q₈	—	2	4	no	—
50	C₄×D₄×C₁₉	—	2	16	no	—
51	C₄×D₄×C₁₉	—	2	4	no	—
52	C₄×D₄×C₁₉	—	2	4	no	—
53	C₄×D₄×C₁₉	—	2	4	no	—
54	C₄×D₄×C₁₉	D₄	1	8	yes	—
55	C₁₉×#117	—	2	4	no	—
56	C₁₉×#117	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
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×C₂²⋊C₄×C₁₉	—	2	16	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
71	C₁₉×C₄⋊C₈	—	2	4	no	—
72	C₁₉×#103	—	2	8	no	—
73	C₁₉×#102	—	2	8	no	—
74	C₁₉×C₂²⋊C₈	—	2	4	no	—
75	C₁₉×#95	—	2	2	no	—
76	C₁₉×#95	—	2	4	no	—
77	C₂⁴×C₁₉	—	2	4	no	—
78	C₂⁴×C₁₉	—	2	4	no	—
79	C₂⁴×C₁₉	—	2	2	no	—
80	C₂⁴×C₁₉	—	2	4	no	—
81	C₂⁴×C₁₉	—	8	4	no	—
82	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂×Q₈×C₁₉	—	2	2	no	—
84	C₂×Q₈×C₁₉	—	2	4	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	—	2	4	no	—
87	C₂×D₄×C₁₉	—	2	4	no	—
88	C₂×D₄×C₁₉	—	2	4	no	—
89	C₂×D₄×C₁₉	—	2	16	no	—
90	C₂×D₄×C₁₉	—	2	16	no	—
91	C₂×D₄×C₁₉	—	2	4	no	—
92	C₂×D₄×C₁₉	—	2	2	no	—
93	C₂×D₄×C₁₉	—	2	2	no	—
94	C₂×D₄×C₁₉	—	2	2	no	—
95	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
96	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
97	C₂×D₄×C₁₉	#41	1	4	yes	—
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	8	no	—
102	C₂²×C₄×C₁₉	—	2	8	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	8	4	no	—
106	C₂²×C₄×C₁₉	—	8	4	no	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₉	#41	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
113	SD₁₆×C₁₉	—	4	16	no	—
114	C₂×C₈×C₁₉	—	2	4	no	—
115	C₂×C₈×C₁₉	—	2	4	no	—
116	C₂×C₈×C₁₉	—	2	4	no	—
117	C₄⋊C₄×C₁₉	—	2	4	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	4	4	no	—
122	C₄⋊C₄×C₁₉	—	4	4	no	—
123	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
124	C₂²⋊C₄×C₁₉	—	2	4	no	—
125	C₂²⋊C₄×C₁₉	—	2	8	no	—
126	C₂²⋊C₄×C₁₉	—	2	4	no	—
127	C₂²⋊C₄×C₁₉	—	2	8	no	—
128	C₂²⋊C₄×C₁₉	—	4	4	no	—
129	C₄²×C₁₉	—	2	4	no	—
130	C₄²×C₁₉	—	2	2	no	—
131	C₄²×C₁₉	C₂×D₄	1	4	yes	—
132	#32914	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₁₉	—	2	16	no	—
134	C₂³×C₁₉	—	2	1	no	—
135	C₂³×C₁₉	—	2	4	no	—
136	C₂³×C₁₉	—	2	4	no	—
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	2	4	no	—
139	C₂³×C₁₉	—	2	4	no	—
140	C₂³×C₁₉	—	4	4	no	—
141	C₂³×C₁₉	—	4	4	no	—
142	C₂³×C₁₉	—	8	8	no	—
143	C₂³×C₁₉	—	8	8	no	—
144	C₂³×C₁₉	—	8	8	no	—
145	C₂³×C₁₉	#121	1	2	yes	—
146	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₁₉	—	4	4	no	—
148	Q₈×C₁₉	—	4	4	no	—
149	D₄×C₁₉	—	2	16	no	—
150	D₄×C₁₉	—	2	4	no	—
151	D₄×C₁₉	—	2	4	no	—
152	D₄×C₁₉	—	2	4	no	—
153	D₄×C₁₉	#121	1	8	yes	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	8	8	no	—
169	C₂×C₄×C₁₉	—	8	8	no	—
170	C₂×C₄×C₁₉	#120	1	4	yes	—
171	C₂×C₄×C₁₉	#121	1	2	yes	—
172	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
174	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
175	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
176	C₈×C₁₉	—	4	4	no	—
177	C₂×#518	C₂×C₁₉	1	1	yes	characteristic
178	C₂×#461	C₂×C₁₉	1	2	yes	complemented
179	C₂×#450	C₂×C₁₉	1	2	yes	—
180	#2621	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#1877	C₂×C₁₉	1	4	yes	complemented
182	#1873	C₂×C₁₉	1	2	yes	complemented
183	#1804	C₂×C₁₉	1	2	yes	complemented
184	#1798	C₂×C₁₉	1	1	yes	characteristic, complemented
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	2	8	no	—
187	C₂²×C₁₉	—	2	4	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	—	4	8	no	—
190	C₂²×C₁₉	—	4	4	no	—
191	C₂²×C₁₉	—	4	4	no	—
192	C₂²×C₁₉	—	4	2	no	—
193	C₂²×C₁₉	—	4	8	no	—
194	C₂²×C₁₉	—	8	16	no	—
195	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
196	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
197	C₂²×C₁₉	#525	1	1	yes	characteristic
198	C₂²×C₁₉	#577	1	4	yes	—
199	C₄×C₁₉	—	2	2	no	—
200	C₄×C₁₉	—	2	4	no	—
201	C₄×C₁₉	—	4	2	no	—
202	C₄×C₁₉	—	4	4	no	—
203	C₄×C₁₉	—	8	2	no	—
204	C₄×C₁₉	—	8	2	no	—
205	C₄×C₁₉	C₂×#121	1	2	yes	—
206	C₄×C₁₉	#525	1	2	yes	—
207	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
208	C₂²×SD₁₆	C₂²×C₁₉	1	4	yes	—
209	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
210	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
211	#518	—	2	8	no	—
212	C₂×C₄×D₄	—	2	2	no	—
213	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
214	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
215	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
216	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
217	C₂²×C₂²⋊C₄	—	2	2	no	—
218	#461	—	2	8	no	—
219	#450	—	2	8	no	—
220	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
221	C₂×#103	C₂²×C₁₉	1	4	yes	complemented
222	C₂×#102	C₂²×C₁₉	1	4	yes	—
223	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
224	#398	—	2	2	no	—
225	#397	—	2	2	no	—
226	#391	C₂²×C₁₉	1	2	yes	complemented
227	#382	C₂²×C₁₉	1	1	yes	characteristic, complemented
228	#340	C₂²×C₁₉	1	4	yes	complemented
229	#336	C₂²×C₁₉	1	2	yes	complemented
230	C₂×C₁₉	—	4	2	no	—
231	C₂×C₁₉	—	4	8	no	—
232	C₂×C₁₉	#2847	1	1	yes	characteristic
233	C₂×C₁₉	#3009	1	2	yes	—
234	C₂×C₁₉	#3042	1	2	yes	—
235	C₂×C₁₉	#3123	1	2	yes	—
236	C₂⁵	—	2	1	no	—
237	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
238	C₂²×D₄	—	2	4	no	—
239	C₂²×D₄	—	2	4	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	D₄×C₁₉	1	4	yes	—
243	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
244	C₂³×C₄	—	2	2	no	—
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
247	C₂×SD₁₆	—	2	8	no	—
248	C₂×SD₁₆	—	2	8	no	—
249	C₂×SD₁₆	—	2	8	no	—
250	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
251	C₄⋊Q₈	—	2	4	no	—
252	C₂²⋊Q₈	—	2	4	no	—
253	C₂²⋊Q₈	—	2	4	no	—
254	C₄×D₄	—	2	16	no	—
255	C₄×D₄	—	2	4	no	—
256	C₄×D₄	—	2	4	no	—
257	C₄×D₄	—	2	4	no	—
258	C₄×D₄	D₄×C₁₉	1	8	yes	—
259	#117	—	2	4	no	—
260	#117	—	2	4	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
266	C₂×C₂²⋊C₄	—	2	16	no	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
275	C₄⋊C₈	—	2	4	no	—
276	#103	—	2	8	no	—
277	#102	—	2	8	no	—
278	C₂²⋊C₈	—	2	4	no	—
279	#95	—	2	2	no	—
280	#95	—	2	4	no	—
281	C₁₉	#32914	1	1	yes	characteristic, direct product factor, Sylow
282	C₂⁴	—	2	4	no	—
283	C₂⁴	—	2	4	no	—
284	C₂⁴	—	2	2	no	—
285	C₂⁴	—	2	4	no	—
286	C₂⁴	—	8	4	no	—
287	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	16	no	—
295	C₂×D₄	—	2	16	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
301	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
302	C₂×D₄	#41×C₁₉	1	4	yes	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	8	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	8	4	no	—
311	C₂²×C₄	—	8	4	no	—
312	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
316	C₂²×C₄	#41×C₁₉	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
318	SD₁₆	—	4	16	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	4	4	no	—
327	C₄⋊C₄	—	4	4	no	—
328	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₂²⋊C₄	—	2	8	no	—
333	C₂²⋊C₄	—	4	4	no	—
334	C₄²	—	2	4	no	—
335	C₄²	—	2	2	no	—
336	C₄²	C₂×D₄×C₁₉	1	4	yes	—
337	C₂³	—	2	16	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	4	4	no	—
345	C₂³	—	4	4	no	—
346	C₂³	—	8	8	no	—
347	C₂³	—	8	8	no	—
348	C₂³	—	8	8	no	—
349	C₂³	C₁₉×#121	1	2	yes	—
350	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
351	Q₈	—	4	4	no	—
352	Q₈	—	4	4	no	—
353	D₄	—	2	16	no	—
354	D₄	—	2	4	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	4	no	—
357	D₄	C₁₉×#121	1	8	yes	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	8	8	no	—
373	C₂×C₄	—	8	8	no	—
374	C₂×C₄	C₁₉×#120	1	4	yes	—
375	C₂×C₄	C₁₉×#121	1	2	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	2	yes	—
379	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
380	C₈	—	4	4	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	8	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	8	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	8	no	—
390	C₂²	—	8	16	no	—
391	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
392	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
393	C₂²	C₁₉×#525	1	1	yes	characteristic
394	C₂²	C₁₉×#577	1	4	yes	—
395	C₄	—	2	4	no	—
396	C₄	—	2	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	4	no	—
399	C₄	—	8	2	no	—
400	C₄	—	8	2	no	—
401	C₄	C₂×C₁₉×#121	1	2	yes	—
402	C₄	C₁₉×#525	1	2	yes	—
403	C₂	—	4	2	no	—
404	C₂	—	4	8	no	—
405	C₂	C₁₉×#2847	1	1	yes	characteristic
406	C₂	C₁₉×#3009	1	2	yes	—
407	C₂	C₁₉×#3042	1	2	yes	—
408	C₂	C₁₉×#3123	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#461	C₂	semidirect
4. C₁₉×#2621	C₂	semidirect
5. C₁₉×#1877	C₂	semidirect
6. C₁₉×#1873	C₂	semidirect
7. C₁₉×#1804	C₂	semidirect
8. C₁₉×#1798	C₂	semidirect
11. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
23. C₂×C₁₉×#103	C₂²	semidirect
28. C₁₉×#391	C₂²	semidirect
29. C₁₉×#382	C₂²	semidirect
30. C₁₉×#340	C₂²	semidirect
31. C₁₉×#336	C₂²	semidirect
132. #32914	C₁₉	direct (N × H)
178. C₂×#461	C₂×C₁₉	semidirect
180. #2621	C₂×C₁₉	semidirect
181. #1877	C₂×C₁₉	semidirect
182. #1873	C₂×C₁₉	semidirect
183. #1804	C₂×C₁₉	semidirect
184. #1798	C₂×C₁₉	semidirect
209. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
220. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
221. C₂×#103	C₂²×C₁₉	semidirect
226. #391	C₂²×C₁₉	semidirect
227. #382	C₂²×C₁₉	semidirect
228. #340	C₂²×C₁₉	semidirect
229. #336	C₂²×C₁₉	semidirect
281. C₁₉	#32914	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#518	2
C₂×C₁₉×#461	2
C₂×C₁₉×#450	2
C₁₉×#2621	2
C₁₉×#1877	2
C₁₉×#1873	2
C₁₉×#1804	2
C₁₉×#1798	2
#32914	19

Subgroups — C19×#32914 #18038873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32914 #18038873