Subgroups — C₁₉×#17771 #18023730

Order 4864.

990 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3508	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2990	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1557	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1555	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1553	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1552	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1547	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1540	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×#331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#559	—	2	2	no	—
11	C₁₉×#550	—	2	2	no	—
12	C₁₉×#546	—	2	2	no	—
13	C₁₉×#546	—	2	2	no	—
14	C₁₉×#540	C₄	1	4	yes	—
15	C₁₉×#535	C₄	1	2	yes	—
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#532	C₂²	1	2	yes	—
18	C₁₉×#532	C₂²	1	2	yes	—
19	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
20	C₁₉×#518	C₄	1	2	yes	—
21	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#446	—	2	2	no	—
23	C₁₉×#435	—	2	2	no	—
24	C₁₉×#435	—	2	2	no	—
25	C₈×D₄×C₁₉	—	2	2	no	—
26	C₁₉×#432	C₂²	1	2	yes	—
27	C₁₉×#432	C₂²	1	2	yes	complemented
28	C₁₉×#431	C₂²	1	2	yes	complemented
29	C₁₉×#423	C₂²	1	2	yes	complemented
30	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
31	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
32	C₁₉×#332	C₂²	1	2	yes	complemented
33	C₁₉×#332	C₂²	1	2	yes	complemented
34	C₁₉×#332	C₂²	1	2	yes	complemented
35	C₁₉×#332	C₂²	1	2	yes	complemented
36	C₁₉×#331	C₂²	1	1	yes	characteristic
37	C₁₉×#331	C₂²	1	2	yes	—
38	C₁₉×#331	C₂²	1	1	yes	characteristic
39	C₁₉×#331	C₂²	1	2	yes	—
40	C₁₉×#331	C₂²	1	1	yes	characteristic
41	C₁₉×#331	C₂²	1	1	yes	characteristic
42	C₂×#41×C₁₉	—	2	2	no	—
43	C₂×#41×C₁₉	—	2	2	no	—
44	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₉	—	2	2	no	—
46	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂²×C₈×C₁₉	—	2	2	no	—
49	C₂²×C₈×C₁₉	—	2	2	no	—
50	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
51	C₁₉×#127	—	2	2	no	—
52	C₁₉×#127	—	2	2	no	—
53	C₁₉×#127	C₂×C₄	1	2	yes	—
54	C₁₉×#127	C₂³	1	1	yes	characteristic
55	C₁₉×#127	C₂³	1	1	yes	characteristic
56	C₁₉×#125	C₂×C₄	1	2	yes	—
57	C₁₉×#124	—	2	2	no	—
58	C₁₉×#124	—	2	2	no	—
59	C₁₉×#124	—	2	2	no	—
60	C₁₉×#123	—	2	4	no	—
61	C₁₉×#123	—	2	4	no	—
62	C₁₉×C₂²⋊Q₈	—	2	2	no	—
63	C₁₉×#121	—	2	2	no	—
64	C₁₉×#121	—	2	2	no	—
65	C₁₉×#121	—	2	4	no	—
66	C₁₉×#121	—	2	4	no	—
67	C₁₉×#121	C₂×C₄	1	4	yes	—
68	C₁₉×#121	C₂×C₄	1	4	yes	—
69	C₁₉×#120	—	2	4	no	—
70	C₄×Q₈×C₁₉	—	2	2	no	—
71	C₄×Q₈×C₁₉	D₄	1	2	yes	—
72	C₄×D₄×C₁₉	—	2	4	no	—
73	C₄×D₄×C₁₉	—	2	2	no	—
74	C₄×D₄×C₁₉	—	2	2	no	—
75	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
76	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
77	C₄×D₄×C₁₉	D₄	1	2	yes	—
78	C₄×D₄×C₁₉	D₄	1	2	yes	—
79	C₄×D₄×C₁₉	D₄	1	2	yes	—
80	C₁₉×#117	C₂×C₄	1	2	yes	—
81	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
82	C₁₉×#117	C₂×C₄	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
87	C₁₉×C₄⋊C₈	—	2	2	no	—
88	C₁₉×C₄⋊C₈	—	2	2	no	—
89	C₁₉×C₄⋊C₈	—	2	2	no	—
90	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
91	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
92	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
93	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
94	C₁₉×C₂²⋊C₈	—	2	2	no	—
95	C₁₉×C₂²⋊C₈	—	2	2	no	—
96	C₁₉×C₂²⋊C₈	—	2	2	no	—
97	C₁₉×#97	—	2	2	no	—
98	C₁₉×#97	—	2	2	no	—
99	C₄×C₈×C₁₉	—	2	2	no	—
100	C₂⁴×C₁₉	—	2	2	no	—
101	#41×C₁₉	—	4	2	no	—
102	#41×C₁₉	—	8	2	no	—
103	#41×C₁₉	—	8	2	no	—
104	#41×C₁₉	—	8	2	no	—
105	#41×C₁₉	—	8	2	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×D₄×C₁₉	—	2	4	no	—
109	C₂×D₄×C₁₉	—	2	4	no	—
110	C₂×D₄×C₁₉	—	2	2	no	—
111	C₂×D₄×C₁₉	—	2	4	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	4	4	no	—
115	C₂×D₄×C₁₉	—	8	2	no	—
116	C₂×D₄×C₁₉	—	8	2	no	—
117	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
118	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
120	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
128	M₁₆×C₁₉	—	8	2	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₂×C₈×C₁₉	—	8	2	no	—
134	C₂×C₈×C₁₉	—	8	2	no	—
135	C₄⋊C₄×C₁₉	—	2	4	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
138	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
139	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
140	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
141	C₂²⋊C₄×C₁₉	—	2	2	no	—
142	C₂²⋊C₄×C₁₉	—	2	4	no	—
143	C₂²⋊C₄×C₁₉	—	2	4	no	—
144	C₂²⋊C₄×C₁₉	—	2	4	no	—
145	C₂²⋊C₄×C₁₉	—	2	4	no	—
146	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
147	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
149	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
150	C₄²×C₁₉	—	2	2	no	—
151	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
152	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₁₉	C₂×D₄	1	2	yes	—
154	C₄²×C₁₉	C₂×D₄	1	2	yes	—
155	C₄²×C₁₉	C₂×D₄	1	2	yes	—
156	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
157	#17771	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	—	4	4	no	—
161	C₂³×C₁₉	—	8	4	no	—
162	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	Q₈×C₁₉	—	4	1	no	—
165	Q₈×C₁₉	—	4	2	no	—
166	Q₈×C₁₉	—	4	2	no	—
167	D₄×C₁₉	—	2	4	no	—
168	D₄×C₁₉	—	4	1	no	—
169	D₄×C₁₉	—	4	2	no	—
170	D₄×C₁₉	—	4	2	no	—
171	D₄×C₁₉	—	4	4	no	—
172	D₄×C₁₉	—	4	2	no	—
173	D₄×C₁₉	—	4	2	no	—
174	D₄×C₁₉	—	4	2	no	—
175	D₄×C₁₉	—	4	2	no	—
176	D₄×C₁₉	—	8	4	no	—
177	D₄×C₁₉	—	8	4	no	—
178	D₄×C₁₉	—	8	4	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	8	4	no	—
189	C₂×C₄×C₁₉	—	8	4	no	—
190	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
197	C₈×C₁₉	—	4	2	no	—
198	C₈×C₁₉	—	4	2	no	—
199	C₈×C₁₉	—	4	2	no	—
200	C₈×C₁₉	—	4	2	no	—
201	#3508	C₂×C₁₉	1	1	yes	characteristic
202	#2990	C₂×C₁₉	1	2	yes	complemented
203	#1557	C₂×C₁₉	1	2	yes	complemented
204	#1555	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#1553	C₂×C₁₉	1	2	yes	complemented
206	#1552	C₂×C₁₉	1	2	yes	complemented
207	#1547	C₂×C₁₉	1	2	yes	complemented
208	#1540	C₂×C₁₉	1	2	yes	complemented
209	C₂×#331	C₂×C₁₉	1	1	yes	characteristic, complemented
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	4	2	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	4	4	no	—
217	C₂²×C₁₉	—	4	4	no	—
218	C₂²×C₁₉	—	16	4	no	—
219	C₂²×C₁₉	#413	1	2	yes	—
220	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	2	2	no	—
224	C₄×C₁₉	—	2	2	no	—
225	C₄×C₁₉	—	2	2	no	—
226	C₄×C₁₉	—	2	2	no	—
227	C₄×C₁₉	—	4	4	no	—
228	C₄×C₁₉	#576	1	2	yes	—
229	C₄×C₁₉	#577	1	2	yes	—
230	#559	—	2	2	no	—
231	#550	—	2	2	no	—
232	#546	—	2	2	no	—
233	#546	—	2	2	no	—
234	#540	C₄×C₁₉	1	4	yes	—
235	#535	C₄×C₁₉	1	2	yes	—
236	#533	C₂²×C₁₉	1	1	yes	characteristic
237	#532	C₂²×C₁₉	1	2	yes	—
238	#532	C₂²×C₁₉	1	2	yes	—
239	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
240	#518	C₄×C₁₉	1	2	yes	—
241	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
242	#446	—	2	2	no	—
243	#435	—	2	2	no	—
244	#435	—	2	2	no	—
245	C₈×D₄	—	2	2	no	—
246	#432	C₂²×C₁₉	1	2	yes	—
247	#432	C₂²×C₁₉	1	2	yes	complemented
248	#431	C₂²×C₁₉	1	2	yes	complemented
249	#423	C₂²×C₁₉	1	2	yes	complemented
250	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
251	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
252	#332	C₂²×C₁₉	1	2	yes	complemented
253	#332	C₂²×C₁₉	1	2	yes	complemented
254	#332	C₂²×C₁₉	1	2	yes	complemented
255	#332	C₂²×C₁₉	1	2	yes	complemented
256	#331	C₂²×C₁₉	1	1	yes	characteristic
257	#331	C₂²×C₁₉	1	2	yes	—
258	#331	C₂²×C₁₉	1	1	yes	characteristic
259	#331	C₂²×C₁₉	1	2	yes	—
260	#331	C₂²×C₁₉	1	1	yes	characteristic
261	#331	C₂²×C₁₉	1	1	yes	characteristic
262	C₂×C₁₉	—	2	2	no	—
263	C₂×C₁₉	—	4	2	no	—
264	C₂×C₁₉	—	8	2	no	—
265	C₂×C₁₉	—	8	2	no	—
266	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
267	C₂×C₁₉	#2897	1	2	yes	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
271	C₂²×D₄	—	2	2	no	—
272	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
277	#127	—	2	2	no	—
278	#127	—	2	2	no	—
279	#127	C₂×C₄×C₁₉	1	2	yes	—
280	#127	C₂³×C₁₉	1	1	yes	characteristic
281	#127	C₂³×C₁₉	1	1	yes	characteristic
282	#125	C₂×C₄×C₁₉	1	2	yes	—
283	#124	—	2	2	no	—
284	#124	—	2	2	no	—
285	#124	—	2	2	no	—
286	#123	—	2	4	no	—
287	#123	—	2	4	no	—
288	C₂²⋊Q₈	—	2	2	no	—
289	#121	—	2	2	no	—
290	#121	—	2	2	no	—
291	#121	—	2	4	no	—
292	#121	—	2	4	no	—
293	#121	C₂×C₄×C₁₉	1	4	yes	—
294	#121	C₂×C₄×C₁₉	1	4	yes	—
295	#120	—	2	4	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×Q₈	D₄×C₁₉	1	2	yes	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
302	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
303	C₄×D₄	D₄×C₁₉	1	2	yes	—
304	C₄×D₄	D₄×C₁₉	1	2	yes	—
305	C₄×D₄	D₄×C₁₉	1	2	yes	—
306	#117	C₂×C₄×C₁₉	1	2	yes	—
307	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
308	#117	C₂×C₄×C₁₉	1	2	yes	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	—	2	2	no	—
315	C₄⋊C₈	—	2	2	no	—
316	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
317	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
318	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
319	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
320	C₂²⋊C₈	—	2	2	no	—
321	C₂²⋊C₈	—	2	2	no	—
322	C₂²⋊C₈	—	2	2	no	—
323	#97	—	2	2	no	—
324	#97	—	2	2	no	—
325	C₄×C₈	—	2	2	no	—
326	C₁₉	#17771	1	1	yes	characteristic, direct product factor, Sylow
327	C₂⁴	—	2	2	no	—
328	#41	—	4	2	no	—
329	#41	—	8	2	no	—
330	#41	—	8	2	no	—
331	#41	—	8	2	no	—
332	#41	—	8	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	4	4	no	—
342	C₂×D₄	—	8	2	no	—
343	C₂×D₄	—	8	2	no	—
344	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
345	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
346	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
347	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
355	M₁₆	—	8	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	8	2	no	—
361	C₂×C₈	—	8	2	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
365	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
366	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
367	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
374	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
375	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
376	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
377	C₄²	—	2	2	no	—
378	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
379	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
380	C₄²	C₂×D₄×C₁₉	1	2	yes	—
381	C₄²	C₂×D₄×C₁₉	1	2	yes	—
382	C₄²	C₂×D₄×C₁₉	1	2	yes	—
383	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	8	4	no	—
388	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
389	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
390	Q₈	—	4	1	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	D₄	—	2	4	no	—
394	D₄	—	4	1	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	4	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	8	4	no	—
403	D₄	—	8	4	no	—
404	D₄	—	8	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	8	4	no	—
415	C₂×C₄	—	8	4	no	—
416	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
417	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
418	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
419	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
420	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
421	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
422	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
423	C₈	—	4	2	no	—
424	C₈	—	4	2	no	—
425	C₈	—	4	2	no	—
426	C₈	—	4	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	16	4	no	—
436	C₂²	C₁₉×#413	1	2	yes	—
437	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	4	4	no	—
445	C₄	C₁₉×#576	1	2	yes	—
446	C₄	C₁₉×#577	1	2	yes	—
447	C₂	—	2	2	no	—
448	C₂	—	4	2	no	—
449	C₂	—	8	2	no	—
450	C₂	—	8	2	no	—
451	C₂	C₂×C₁₉×#413	1	1	yes	characteristic
452	C₂	C₁₉×#2897	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×#3508	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×#2990	C₂	semidirect
3. C₁₉×#1557	C₂	semidirect
4. C₁₉×#1555	C₂	semidirect
5. C₁₉×#1553	C₂	semidirect
6. C₁₉×#1552	C₂	semidirect
7. C₁₉×#1547	C₂	semidirect
8. C₁₉×#1540	C₂	semidirect
9. C₂×C₁₉×#331	C₂	semidirect
27. C₁₉×#432	C₂²	semidirect
28. C₁₉×#431	C₂²	semidirect
29. C₁₉×#423	C₂²	semidirect
31. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
32. C₁₉×#332	C₂²	semidirect
33. C₁₉×#332	C₂²	semidirect
34. C₁₉×#332	C₂²	semidirect
35. C₁₉×#332	C₂²	semidirect
157. #17771	C₁₉	direct (N × H)
202. #2990	C₂×C₁₉	semidirect
203. #1557	C₂×C₁₉	semidirect
204. #1555	C₂×C₁₉	semidirect
205. #1553	C₂×C₁₉	semidirect
206. #1552	C₂×C₁₉	semidirect
207. #1547	C₂×C₁₉	semidirect
208. #1540	C₂×C₁₉	semidirect
209. C₂×#331	C₂×C₁₉	semidirect
247. #432	C₂²×C₁₉	semidirect
248. #431	C₂²×C₁₉	semidirect
249. #423	C₂²×C₁₉	semidirect
251. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
252. #332	C₂²×C₁₉	semidirect
253. #332	C₂²×C₁₉	semidirect
254. #332	C₂²×C₁₉	semidirect
255. #332	C₂²×C₁₉	semidirect
326. C₁₉	#17771	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×#3508	2
C₁₉×#2990	2
C₁₉×#1557	2
C₁₉×#1555	2
C₁₉×#1553	2
C₁₉×#1552	2
C₁₉×#1547	2
C₁₉×#1540	2
C₂×C₁₉×#331	2
#17771	19

Subgroups — C19×#17771 #18023730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17771 #18023730