Subgroups — C₁₉×#23675 #18029634

Order 4864.

774 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2911	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2905	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2090	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2089	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1742	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1738	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#428	—	2	2	no	—
18	C₁₉×#428	—	2	2	no	—
19	C₁₉×#428	—	2	2	no	—
20	C₁₉×#428	—	2	1	no	—
21	C₁₉×#428	—	2	1	no	—
22	C₁₉×#428	C₂²	1	2	yes	—
23	C₁₉×#428	C₂²	1	2	yes	—
24	C₁₉×#428	C₂²	1	4	yes	—
25	C₁₉×#427	—	2	2	no	—
26	C₂×C₁₉×#107	—	2	1	no	—
27	C₂×C₁₉×#107	C₂²	1	2	yes	—
28	C₂×C₁₉×#106	—	2	1	no	—
29	C₂×C₁₉×#106	C₂²	1	2	yes	—
30	C₁₉×#424	—	2	2	no	—
31	C₁₉×#424	C₂²	1	4	yes	—
32	C₁₉×#423	—	2	2	no	—
33	C₁₉×#343	C₂²	1	4	yes	—
34	C₁₉×#343	C₂²	1	2	yes	—
35	C₁₉×#343	C₂²	1	2	yes	—
36	C₁₉×#341	C₂²	1	4	yes	—
37	C₂³×C₄×C₁₉	—	2	1	no	—
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₁₉	—	2	1	no	—
40	C₂×M₁₆×C₁₉	—	2	1	no	—
41	C₂×M₁₆×C₁₉	—	2	2	no	—
42	C₂×M₁₆×C₁₉	—	2	2	no	—
43	C₂×M₁₆×C₁₉	—	2	2	no	—
44	C₂×M₁₆×C₁₉	—	2	2	no	—
45	C₂×M₁₆×C₁₉	—	2	1	no	—
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
49	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
50	C₂×M₁₆×C₁₉	Q₈	1	4	yes	—
51	C₂×M₁₆×C₁₉	Q₈	1	4	yes	—
52	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
53	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
54	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₉	—	2	1	no	—
56	C₂²×C₈×C₁₉	—	2	1	no	—
57	C₂²×C₈×C₁₉	—	2	1	no	—
58	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
59	C₁₉×#117	—	2	1	no	—
60	C₁₉×#117	—	2	1	no	—
61	C₁₉×#117	—	2	1	no	—
62	C₁₉×#117	—	2	1	no	—
63	C₁₉×#117	—	2	1	no	—
64	C₁₉×#117	—	2	1	no	—
65	C₁₉×#117	D₄	1	2	yes	—
66	C₁₉×#117	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	—	2	1	no	—
80	C₂×C₄²×C₁₉	—	2	1	no	—
81	C₁₉×#107	—	2	4	no	—
82	C₁₉×#107	—	2	4	no	—
83	C₁₉×#107	—	2	2	no	—
84	C₁₉×#107	—	2	2	no	—
85	C₁₉×#106	—	2	4	no	—
86	C₁₉×#106	—	2	4	no	—
87	C₁₉×#106	—	2	2	no	—
88	C₁₉×#106	—	2	2	no	—
89	C₁₉×C₄⋊C₈	—	2	8	no	—
90	C₂⁴×C₁₉	#41	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	8	2	no	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
105	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	#41	1	2	yes	—
107	C₂²×C₄×C₁₉	#41	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
109	M₁₆×C₁₉	—	2	4	no	—
110	M₁₆×C₁₉	—	2	4	no	—
111	M₁₆×C₁₉	—	2	4	no	—
112	M₁₆×C₁₉	—	2	4	no	—
113	M₁₆×C₁₉	—	2	2	no	—
114	M₁₆×C₁₉	—	2	2	no	—
115	M₁₆×C₁₉	—	2	2	no	—
116	M₁₆×C₁₉	—	2	2	no	—
117	M₁₆×C₁₉	—	4	2	no	—
118	M₁₆×C₁₉	C₂×Q₈	1	4	yes	—
119	M₁₆×C₁₉	C₂×Q₈	1	4	yes	—
120	C₂×C₈×C₁₉	—	2	4	no	—
121	C₂×C₈×C₁₉	—	2	4	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	—	4	2	no	—
128	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	1	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	4	1	no	—
138	C₄⋊C₄×C₁₉	—	4	1	no	—
139	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
141	C₂²⋊C₄×C₁₉	—	2	2	no	—
142	C₂²⋊C₄×C₁₉	—	2	2	no	—
143	C₂²⋊C₄×C₁₉	—	4	1	no	—
144	C₂²⋊C₄×C₁₉	—	4	1	no	—
145	C₄²×C₁₉	—	2	2	no	—
146	C₄²×C₁₉	—	2	2	no	—
147	C₄²×C₁₉	—	4	1	no	—
148	C₄²×C₁₉	—	4	1	no	—
149	#23675	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	#121	1	1	yes	characteristic
153	C₂³×C₁₉	#121	1	1	yes	characteristic
154	C₂³×C₁₉	#125	1	2	yes	—
155	C₂³×C₁₉	#125	1	2	yes	—
156	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	8	1	no	—
163	C₂×C₄×C₁₉	—	8	1	no	—
164	C₂×C₄×C₁₉	—	8	2	no	—
165	C₂×C₄×C₁₉	—	8	2	no	—
166	C₂×C₄×C₁₉	—	8	1	no	—
167	C₂×C₄×C₁₉	—	8	1	no	—
168	C₂×C₄×C₁₉	—	8	2	no	—
169	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
172	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
173	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
174	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
175	C₂×C₄×C₁₉	#123	1	2	yes	—
176	C₂×C₄×C₁₉	#123	1	2	yes	—
177	C₂×C₄×C₁₉	#125	1	2	yes	—
178	C₂×C₄×C₁₉	#125	1	2	yes	—
179	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
180	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
181	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
187	C₈×C₁₉	—	2	4	no	—
188	C₈×C₁₉	—	2	4	no	—
189	C₈×C₁₉	—	2	4	no	—
190	C₈×C₁₉	—	4	2	no	—
191	#2911	C₂×C₁₉	1	1	yes	characteristic
192	C₂×#428	C₂×C₁₉	1	1	yes	characteristic
193	C₂×#428	C₂×C₁₉	1	1	yes	characteristic
194	#2905	C₂×C₁₉	1	1	yes	characteristic
195	#2090	C₂×C₁₉	1	4	yes	complemented
196	#2089	C₂×C₁₉	1	4	yes	complemented
197	#1742	C₂×C₁₉	1	1	yes	characteristic
198	C₂×#343	C₂×C₁₉	1	1	yes	characteristic
199	#1738	C₂×C₁₉	1	1	yes	characteristic
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	2	1	no	—
203	C₂²×C₁₉	—	2	1	no	—
204	C₂²×C₁₉	—	2	1	no	—
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	4	2	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	#398	1	2	yes	—
209	C₂²×C₁₉	#398	1	2	yes	—
210	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
211	C₂²×C₁₉	C₂×#125	1	1	yes	characteristic
212	C₂²×C₁₉	C₂×#125	1	1	yes	characteristic
213	C₄×C₁₉	—	4	2	no	—
214	C₄×C₁₉	—	4	2	no	—
215	C₄×C₁₉	—	8	1	no	—
216	C₄×C₁₉	—	8	2	no	—
217	C₄×C₁₉	—	8	1	no	—
218	C₄×C₁₉	#398	1	2	yes	—
219	C₄×C₁₉	#398	1	2	yes	—
220	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
221	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
222	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
223	C₄×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
224	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
225	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
226	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
227	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
230	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
231	#428	—	2	2	no	—
232	#428	—	2	2	no	—
233	#428	—	2	2	no	—
234	#428	—	2	1	no	—
235	#428	—	2	1	no	—
236	#428	C₂²×C₁₉	1	2	yes	—
237	#428	C₂²×C₁₉	1	4	yes	—
238	#428	C₂²×C₁₉	1	2	yes	—
239	#427	—	2	2	no	—
240	C₂×#107	—	2	1	no	—
241	C₂×#107	C₂²×C₁₉	1	2	yes	—
242	C₂×#106	—	2	1	no	—
243	C₂×#106	C₂²×C₁₉	1	2	yes	—
244	#424	—	2	2	no	—
245	#424	C₂²×C₁₉	1	4	yes	—
246	#423	—	2	2	no	—
247	#343	C₂²×C₁₉	1	2	yes	—
248	#343	C₂²×C₁₉	1	4	yes	—
249	#343	C₂²×C₁₉	1	2	yes	—
250	#341	C₂²×C₁₉	1	4	yes	—
251	C₂×C₁₉	—	2	1	no	—
252	C₂×C₁₉	—	2	1	no	—
253	C₂×C₁₉	—	2	2	no	—
254	C₂×C₁₉	—	2	2	no	—
255	C₂×C₁₉	C₂×#398	1	1	yes	characteristic
256	C₂×C₁₉	#3068	1	1	yes	characteristic
257	C₂×C₁₉	#3069	1	1	yes	characteristic
258	C₂³×C₄	—	2	1	no	—
259	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	—	2	2	no	—
265	C₂×M₁₆	—	2	2	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
270	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
271	C₂×M₁₆	Q₈×C₁₉	1	4	yes	—
272	C₂×M₁₆	Q₈×C₁₉	1	4	yes	—
273	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
274	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
275	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
280	#117	—	2	1	no	—
281	#117	—	2	1	no	—
282	#117	—	2	1	no	—
283	#117	—	2	1	no	—
284	#117	—	2	1	no	—
285	#117	—	2	1	no	—
286	#117	D₄×C₁₉	1	2	yes	—
287	#117	C₂³×C₁₉	1	2	yes	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
294	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	—	2	1	no	—
302	#107	—	2	4	no	—
303	#107	—	2	4	no	—
304	#107	—	2	2	no	—
305	#107	—	2	2	no	—
306	#106	—	2	4	no	—
307	#106	—	2	4	no	—
308	#106	—	2	2	no	—
309	#106	—	2	2	no	—
310	C₄⋊C₈	—	2	8	no	—
311	C₁₉	#23675	1	1	yes	characteristic, direct product factor, Sylow
312	C₂⁴	#41×C₁₉	1	1	yes	characteristic
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	8	2	no	—
321	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
325	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
326	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
327	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
328	C₂²×C₄	#41×C₁₉	1	2	yes	—
329	C₂²×C₄	#41×C₁₉	1	2	yes	—
330	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
331	M₁₆	—	2	4	no	—
332	M₁₆	—	2	4	no	—
333	M₁₆	—	2	4	no	—
334	M₁₆	—	2	4	no	—
335	M₁₆	—	2	2	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	2	2	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	4	2	no	—
340	M₁₆	C₂×Q₈×C₁₉	1	4	yes	—
341	M₁₆	C₂×Q₈×C₁₉	1	4	yes	—
342	C₂×C₈	—	2	4	no	—
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
362	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	4	1	no	—
370	C₄²	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	C₁₉×#121	1	1	yes	characteristic
374	C₂³	C₁₉×#121	1	1	yes	characteristic
375	C₂³	C₁₉×#125	1	2	yes	—
376	C₂³	C₁₉×#125	1	2	yes	—
377	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	8	1	no	—
384	C₂×C₄	—	8	1	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	8	2	no	—
387	C₂×C₄	—	8	2	no	—
388	C₂×C₄	—	8	1	no	—
389	C₂×C₄	—	8	1	no	—
390	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
391	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
392	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
393	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
394	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
395	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
396	C₂×C₄	C₁₉×#123	1	2	yes	—
397	C₂×C₄	C₁₉×#123	1	2	yes	—
398	C₂×C₄	C₁₉×#125	1	2	yes	—
399	C₂×C₄	C₁₉×#125	1	2	yes	—
400	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
401	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
402	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
403	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
404	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
405	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
406	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
407	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
408	C₈	—	2	4	no	—
409	C₈	—	2	4	no	—
410	C₈	—	2	4	no	—
411	C₈	—	4	2	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	C₁₉×#398	1	2	yes	—
421	C₂²	C₁₉×#398	1	2	yes	—
422	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
423	C₂²	C₂×C₁₉×#125	1	1	yes	characteristic
424	C₂²	C₂×C₁₉×#125	1	1	yes	characteristic
425	C₄	—	4	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	1	no	—
429	C₄	—	8	1	no	—
430	C₄	C₁₉×#398	1	2	yes	—
431	C₄	C₁₉×#398	1	2	yes	—
432	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
433	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
434	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
435	C₄	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
436	C₂	—	2	2	no	—
437	C₂	—	2	2	no	—
438	C₂	—	2	1	no	—
439	C₂	—	2	1	no	—
440	C₂	C₂×C₁₉×#398	1	1	yes	characteristic
441	C₂	C₁₉×#3068	1	1	yes	characteristic
442	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₉×#2090	C₂	semidirect
6. C₁₉×#2089	C₂	semidirect
149. #23675	C₁₉	direct (N × H)
195. #2090	C₂×C₁₉	semidirect
196. #2089	C₂×C₁₉	semidirect
311. C₁₉	#23675	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×#2911	2
C₂×C₁₉×#428	2
C₁₉×#2905	2
C₁₉×#2090	2
C₁₉×#2089	2
C₁₉×#1742	2
C₂×C₁₉×#343	2
C₁₉×#1738	2
#23675	19

Subgroups — C19×#23675 #18029634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23675 #18029634