Subgroups — C₁₉×#17690 #18023649

Order 4864.

898 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3512	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2970	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1535	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1534	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1532	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1530	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1529	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1524	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×#330	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#553	—	2	2	no	—
11	C₁₉×#553	—	2	2	no	—
12	C₁₉×#553	—	2	2	no	—
13	C₁₉×#552	—	2	2	no	—
14	C₁₉×#541	C₄	1	2	yes	—
15	C₁₉×#540	C₄	1	2	yes	—
16	C₁₉×#537	C₄	1	2	yes	—
17	C₁₉×#532	C₂²	1	1	yes	characteristic
18	C₁₉×#529	C₂²	1	2	yes	—
19	C₁₉×#529	C₂²	1	2	yes	—
20	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
21	C₁₉×#520	C₄	1	2	yes	—
22	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#446	—	2	2	no	—
24	C₁₉×#435	—	2	2	no	—
25	C₁₉×#435	—	2	2	no	—
26	C₈×D₄×C₁₉	—	2	2	no	—
27	C₁₉×#432	C₂²	1	2	yes	—
28	C₁₉×#432	C₂²	1	2	yes	—
29	C₁₉×#432	C₂²	1	2	yes	—
30	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
31	C₂×C₁₉×#97	C₂²	1	2	yes	—
32	C₂×C₁₉×#97	C₂²	1	2	yes	—
33	C₁₉×#330	C₂²	1	1	yes	characteristic
34	C₁₉×#330	C₂²	1	2	yes	—
35	C₁₉×#330	C₂²	1	1	yes	characteristic
36	C₁₉×#330	C₂²	1	2	yes	—
37	C₁₉×#330	C₂²	1	1	yes	characteristic
38	C₁₉×#330	C₂²	1	1	yes	characteristic
39	C₁₉×#329	C₂²	1	2	yes	—
40	C₁₉×#329	C₂²	1	2	yes	—
41	C₁₉×#329	C₂²	1	2	yes	—
42	C₁₉×#329	C₂²	1	2	yes	—
43	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
44	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₂×M₁₆×C₁₉	—	2	2	no	—
46	C₂²×C₈×C₁₉	—	2	2	no	—
47	C₂²×C₈×C₁₉	—	2	2	no	—
48	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
49	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
50	C₁₉×#126	—	2	2	no	—
51	C₁₉×#126	—	2	2	no	—
52	C₁₉×#126	—	2	2	no	—
53	C₁₉×#126	—	2	2	no	—
54	C₁₉×#125	—	2	2	no	—
55	C₁₉×#125	—	2	2	no	—
56	C₁₉×#125	—	2	2	no	—
57	C₁₉×#125	C₂×C₄	1	2	yes	—
58	C₁₉×#125	C₂³	1	1	yes	characteristic
59	C₁₉×#125	C₂³	1	1	yes	characteristic
60	C₁₉×#124	C₂³	1	2	yes	—
61	C₁₉×#123	—	2	2	no	—
62	C₁₉×#123	—	2	2	no	—
63	C₁₉×#123	—	2	2	no	—
64	C₁₉×#123	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
67	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
68	C₁₉×#121	—	2	2	no	—
69	C₁₉×#121	—	2	2	no	—
70	C₁₉×#121	—	2	2	no	—
71	C₁₉×#121	—	2	2	no	—
72	C₁₉×#121	—	2	2	no	—
73	C₁₉×#121	—	2	2	no	—
74	C₁₉×#121	C₂×C₄	1	2	yes	—
75	C₁₉×#121	C₂×C₄	1	2	yes	—
76	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
77	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
78	C₄×Q₈×C₁₉	D₄	1	2	yes	—
79	C₄×D₄×C₁₉	—	2	2	no	—
80	C₄×D₄×C₁₉	—	2	2	no	—
81	C₄×D₄×C₁₉	—	2	2	no	—
82	C₄×D₄×C₁₉	—	2	2	no	—
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
85	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
86	C₄×D₄×C₁₉	D₄	1	2	yes	—
87	C₄×D₄×C₁₉	D₄	1	2	yes	—
88	C₄×D₄×C₁₉	D₄	1	2	yes	—
89	C₁₉×#117	—	2	2	no	—
90	C₁₉×#117	—	2	2	no	—
91	C₁₉×#117	—	2	2	no	—
92	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
93	C₁₉×#117	C₂×C₄	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
99	C₁₉×C₄⋊C₈	—	2	2	no	—
100	C₁₉×C₄⋊C₈	—	2	2	no	—
101	C₁₉×C₄⋊C₈	—	2	2	no	—
102	C₁₉×C₂²⋊C₈	—	2	2	no	—
103	C₁₉×C₂²⋊C₈	—	2	2	no	—
104	C₁₉×C₂²⋊C₈	—	2	2	no	—
105	C₁₉×#97	—	2	2	no	—
106	C₁₉×#97	—	2	2	no	—
107	C₁₉×#97	C₂³	1	2	yes	—
108	C₁₉×#97	C₂³	1	2	yes	—
109	C₁₉×#97	C₂³	1	2	yes	—
110	C₁₉×#97	C₂³	1	2	yes	—
111	C₄×C₈×C₁₉	—	2	2	no	—
112	#41×C₁₉	—	4	2	no	—
113	#41×C₁₉	—	4	4	no	—
114	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
121	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
122	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
132	M₁₆×C₁₉	—	4	4	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	4	4	no	—
138	C₂×C₈×C₁₉	—	4	4	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
150	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
151	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
152	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
153	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
154	C₂²⋊C₄×C₁₉	—	2	2	no	—
155	C₂²⋊C₄×C₁₉	—	2	2	no	—
156	C₂²⋊C₄×C₁₉	—	2	2	no	—
157	C₂²⋊C₄×C₁₉	—	2	2	no	—
158	C₂²⋊C₄×C₁₉	—	2	2	no	—
159	C₂²⋊C₄×C₁₉	—	2	2	no	—
160	C₂²⋊C₄×C₁₉	—	2	2	no	—
161	C₂²⋊C₄×C₁₉	—	2	2	no	—
162	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
163	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
164	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
165	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
166	C₄²×C₁₉	—	2	2	no	—
167	C₄²×C₁₉	—	2	2	no	—
168	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
169	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₁₉	C₂×D₄	1	2	yes	—
171	C₄²×C₁₉	C₂×D₄	1	2	yes	—
172	C₄²×C₁₉	C₂×D₄	1	2	yes	—
173	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
174	#17690	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂³×C₁₉	—	2	2	no	—
176	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	Q₈×C₁₉	—	4	1	no	—
179	Q₈×C₁₉	—	4	2	no	—
180	D₄×C₁₉	—	2	4	no	—
181	D₄×C₁₉	—	4	1	no	—
182	D₄×C₁₉	—	4	2	no	—
183	D₄×C₁₉	—	4	4	no	—
184	D₄×C₁₉	—	8	2	no	—
185	D₄×C₁₉	—	8	2	no	—
186	D₄×C₁₉	—	8	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	4	no	—
196	C₂×C₄×C₁₉	—	8	2	no	—
197	C₂×C₄×C₁₉	—	8	2	no	—
198	C₂×C₄×C₁₉	—	8	2	no	—
199	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
200	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
201	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
202	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
203	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
206	C₈×C₁₉	—	2	4	no	—
207	C₈×C₁₉	—	4	2	no	—
208	C₈×C₁₉	—	4	2	no	—
209	C₈×C₁₉	—	4	2	no	—
210	#3512	C₂×C₁₉	1	1	yes	characteristic
211	#2970	C₂×C₁₉	1	2	yes	complemented
212	#1535	C₂×C₁₉	1	2	yes	complemented
213	#1534	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#1532	C₂×C₁₉	1	2	yes	complemented
215	#1530	C₂×C₁₉	1	2	yes	complemented
216	#1529	C₂×C₁₉	1	2	yes	complemented
217	#1524	C₂×C₁₉	1	2	yes	complemented
218	C₂×#330	C₂×C₁₉	1	1	yes	characteristic, complemented
219	C₂²×C₁₉	—	2	2	no	—
220	C₂²×C₁₉	—	2	2	no	—
221	C₂²×C₁₉	—	2	2	no	—
222	C₂²×C₁₉	—	2	2	no	—
223	C₂²×C₁₉	—	4	2	no	—
224	C₂²×C₁₉	—	4	2	no	—
225	C₂²×C₁₉	—	4	2	no	—
226	C₂²×C₁₉	#413	1	2	yes	—
227	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	2	1	no	—
230	C₄×C₁₉	—	2	2	no	—
231	C₄×C₁₉	—	2	2	no	—
232	C₄×C₁₉	—	2	2	no	—
233	C₄×C₁₉	—	2	2	no	—
234	C₄×C₁₉	—	2	2	no	—
235	C₄×C₁₉	—	4	2	no	—
236	C₄×C₁₉	—	4	2	no	—
237	C₄×C₁₉	—	4	2	no	—
238	#553	—	2	2	no	—
239	#553	—	2	2	no	—
240	#553	—	2	2	no	—
241	#552	—	2	2	no	—
242	#541	C₄×C₁₉	1	2	yes	—
243	#540	C₄×C₁₉	1	2	yes	—
244	#537	C₄×C₁₉	1	2	yes	—
245	#532	C₂²×C₁₉	1	1	yes	characteristic
246	#529	C₂²×C₁₉	1	2	yes	—
247	#529	C₂²×C₁₉	1	2	yes	—
248	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
249	#520	C₄×C₁₉	1	2	yes	—
250	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
251	#446	—	2	2	no	—
252	#435	—	2	2	no	—
253	#435	—	2	2	no	—
254	C₈×D₄	—	2	2	no	—
255	#432	C₂²×C₁₉	1	2	yes	—
256	#432	C₂²×C₁₉	1	2	yes	—
257	#432	C₂²×C₁₉	1	2	yes	—
258	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
259	C₂×#97	C₂²×C₁₉	1	2	yes	—
260	C₂×#97	C₂²×C₁₉	1	2	yes	—
261	#330	C₂²×C₁₉	1	1	yes	characteristic
262	#330	C₂²×C₁₉	1	2	yes	—
263	#330	C₂²×C₁₉	1	1	yes	characteristic
264	#330	C₂²×C₁₉	1	2	yes	—
265	#330	C₂²×C₁₉	1	1	yes	characteristic
266	#330	C₂²×C₁₉	1	1	yes	characteristic
267	#329	C₂²×C₁₉	1	2	yes	—
268	#329	C₂²×C₁₉	1	2	yes	—
269	#329	C₂²×C₁₉	1	2	yes	—
270	#329	C₂²×C₁₉	1	2	yes	—
271	C₂×C₁₉	—	2	2	no	—
272	C₂×C₁₉	—	4	2	no	—
273	C₂×C₁₉	—	8	2	no	—
274	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
275	C₂×C₁₉	#2901	1	2	yes	—
276	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
277	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
278	C₂×M₁₆	—	2	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
282	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
283	#126	—	2	2	no	—
284	#126	—	2	2	no	—
285	#126	—	2	2	no	—
286	#126	—	2	2	no	—
287	#125	—	2	2	no	—
288	#125	—	2	2	no	—
289	#125	—	2	2	no	—
290	#125	C₂×C₄×C₁₉	1	2	yes	—
291	#125	C₂³×C₁₉	1	1	yes	characteristic
292	#125	C₂³×C₁₉	1	1	yes	characteristic
293	#124	C₂³×C₁₉	1	2	yes	—
294	#123	—	2	2	no	—
295	#123	—	2	2	no	—
296	#123	—	2	2	no	—
297	#123	—	2	2	no	—
298	C₂²⋊Q₈	—	2	2	no	—
299	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
300	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
301	#121	—	2	2	no	—
302	#121	—	2	2	no	—
303	#121	—	2	2	no	—
304	#121	—	2	2	no	—
305	#121	—	2	2	no	—
306	#121	—	2	2	no	—
307	#121	C₂×C₄×C₁₉	1	2	yes	—
308	#121	C₂×C₄×C₁₉	1	2	yes	—
309	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
310	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
311	C₄×Q₈	D₄×C₁₉	1	2	yes	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	2	2	no	—
315	C₄×D₄	—	2	2	no	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
318	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
319	C₄×D₄	D₄×C₁₉	1	2	yes	—
320	C₄×D₄	D₄×C₁₉	1	2	yes	—
321	C₄×D₄	D₄×C₁₉	1	2	yes	—
322	#117	—	2	2	no	—
323	#117	—	2	2	no	—
324	#117	—	2	2	no	—
325	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
326	#117	C₂×C₄×C₁₉	1	2	yes	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
330	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
332	C₄⋊C₈	—	2	2	no	—
333	C₄⋊C₈	—	2	2	no	—
334	C₄⋊C₈	—	2	2	no	—
335	C₂²⋊C₈	—	2	2	no	—
336	C₂²⋊C₈	—	2	2	no	—
337	C₂²⋊C₈	—	2	2	no	—
338	#97	—	2	2	no	—
339	#97	—	2	2	no	—
340	#97	C₂³×C₁₉	1	2	yes	—
341	#97	C₂³×C₁₉	1	2	yes	—
342	#97	C₂³×C₁₉	1	2	yes	—
343	#97	C₂³×C₁₉	1	2	yes	—
344	C₄×C₈	—	2	2	no	—
345	C₁₉	#17690	1	1	yes	characteristic, direct product factor, Sylow
346	#41	—	4	2	no	—
347	#41	—	4	4	no	—
348	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
349	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
355	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
356	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
362	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
366	M₁₆	—	4	4	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	4	4	no	—
372	C₂×C₈	—	4	4	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
384	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
385	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
386	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
387	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
397	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
398	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
399	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
403	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
404	C₄²	C₂×D₄×C₁₉	1	2	yes	—
405	C₄²	C₂×D₄×C₁₉	1	2	yes	—
406	C₄²	C₂×D₄×C₁₉	1	2	yes	—
407	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
408	C₂³	—	2	2	no	—
409	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
410	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
411	Q₈	—	4	1	no	—
412	Q₈	—	4	2	no	—
413	D₄	—	2	4	no	—
414	D₄	—	4	1	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	4	no	—
417	D₄	—	8	2	no	—
418	D₄	—	8	2	no	—
419	D₄	—	8	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	8	2	no	—
430	C₂×C₄	—	8	2	no	—
431	C₂×C₄	—	8	2	no	—
432	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
433	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
434	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
435	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
436	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
437	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
438	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
439	C₈	—	2	4	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	2	no	—
442	C₈	—	4	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	C₁₉×#413	1	2	yes	—
451	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₂	—	2	2	no	—
463	C₂	—	4	2	no	—
464	C₂	—	8	2	no	—
465	C₂	C₂×C₁₉×#413	1	1	yes	characteristic
466	C₂	C₁₉×#2901	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3512	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2970	C₂	semidirect
3. C₁₉×#1535	C₂	semidirect
4. C₁₉×#1534	C₂	semidirect
5. C₁₉×#1532	C₂	semidirect
6. C₁₉×#1530	C₂	semidirect
7. C₁₉×#1529	C₂	semidirect
8. C₁₉×#1524	C₂	semidirect
9. C₂×C₁₉×#330	C₂	semidirect
174. #17690	C₁₉	direct (N × H)
211. #2970	C₂×C₁₉	semidirect
212. #1535	C₂×C₁₉	semidirect
213. #1534	C₂×C₁₉	semidirect
214. #1532	C₂×C₁₉	semidirect
215. #1530	C₂×C₁₉	semidirect
216. #1529	C₂×C₁₉	semidirect
217. #1524	C₂×C₁₉	semidirect
218. C₂×#330	C₂×C₁₉	semidirect
345. C₁₉	#17690	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×#3512	2
C₁₉×#2970	2
C₁₉×#1535	2
C₁₉×#1534	2
C₁₉×#1532	2
C₁₉×#1530	2
C₁₉×#1529	2
C₁₉×#1524	2
C₂×C₁₉×#330	2
#17690	19

Subgroups — C19×#17690 #18023649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17690 #18023649