Subgroups — C₁₉×#10900 #18016859

Order 4864.

686 conjugacy classes of subgroups.

The subgroup lattice has 448 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	C₁₉×#2873	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#341	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1735	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1733	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic
8	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₁₉×#428	—	2	2	no	—
16	C₁₉×#428	C₄	1	4	yes	complemented
17	C₁₉×#427	—	2	2	no	—
18	C₁₉×#405	—	2	2	no	—
19	C₁₉×#405	—	2	2	no	—
20	C₄×M₁₆×C₁₉	—	2	2	no	—
21	C₁₉×#344	C₄	1	4	yes	complemented
22	C₁₉×#341	C₄	1	4	yes	complemented
23	C₁₉×#340	—	2	2	no	—
24	C₁₉×#339	—	2	2	no	—
25	C₁₉×#336	—	2	2	no	—
26	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×M₁₆×C₁₉	—	2	1	no	—
28	C₂×M₁₆×C₁₉	—	2	1	no	—
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₂×M₁₆×C₁₉	—	2	1	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
39	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
40	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
42	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
43	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
44	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
45	C₂²×C₈×C₁₉	—	2	1	no	—
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₂²×C₈×C₁₉	—	2	1	no	—
48	C₂²×C₈×C₁₉	—	2	1	no	—
49	C₂²×C₈×C₁₉	—	2	1	no	—
50	C₂²×C₈×C₁₉	—	2	1	no	—
51	C₂²×C₈×C₁₉	—	2	1	no	—
52	C₂²×C₈×C₁₉	—	2	1	no	—
53	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₁₉	D₄	1	2	yes	—
55	C₁₉×#117	—	2	1	no	—
56	C₁₉×#117	—	2	1	no	—
57	C₁₉×#117	—	2	1	no	—
58	C₁₉×#117	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
65	C₁₉×#117	C₂×C₄	1	2	yes	—
66	C₁₉×#117	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄²×C₁₉	—	2	1	no	—
74	C₂×C₄²×C₁₉	—	2	1	no	—
75	C₂×C₄²×C₁₉	—	2	1	no	—
76	C₁₉×#107	—	2	4	no	—
77	C₁₉×#106	—	2	4	no	—
78	C₁₉×#97	—	2	4	no	—
79	C₄×C₈×C₁₉	—	2	4	no	—
80	C₂⁴×C₁₉	#41	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
98	M₁₆×C₁₉	—	2	2	no	—
99	M₁₆×C₁₉	—	2	2	no	—
100	M₁₆×C₁₉	—	2	2	no	—
101	M₁₆×C₁₉	—	2	2	no	—
102	M₁₆×C₁₉	—	2	2	no	—
103	M₁₆×C₁₉	—	2	2	no	—
104	M₁₆×C₁₉	—	2	2	no	—
105	M₁₆×C₁₉	—	2	2	no	—
106	M₁₆×C₁₉	—	2	2	no	—
107	M₁₆×C₁₉	—	2	2	no	—
108	M₁₆×C₁₉	C₄²	1	4	yes	—
109	M₁₆×C₁₉	C₄⋊C₄	1	4	yes	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	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	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	4	1	no	—
122	C₂×C₈×C₁₉	—	4	1	no	—
123	C₂×C₈×C₁₉	—	4	1	no	—
124	C₂×C₈×C₁₉	—	4	1	no	—
125	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	4	1	no	—
131	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
132	C₂²⋊C₄×C₁₉	—	2	2	no	—
133	C₂²⋊C₄×C₁₉	—	2	2	no	—
134	C₂²⋊C₄×C₁₉	—	2	2	no	—
135	C₂²⋊C₄×C₁₉	—	4	1	no	—
136	C₂²⋊C₄×C₁₉	—	4	1	no	—
137	C₂²⋊C₄×C₁₉	—	4	1	no	—
138	C₄²×C₁₉	—	2	2	no	—
139	C₄²×C₁₉	—	2	2	no	—
140	C₄²×C₁₉	—	2	2	no	—
141	C₄²×C₁₉	—	4	1	no	—
142	C₄²×C₁₉	—	4	1	no	—
143	C₄²×C₁₉	—	4	1	no	—
144	#10900	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₁₉	—	4	2	no	—
146	C₂³×C₁₉	#117	1	1	yes	characteristic
147	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
148	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
149	C₂³×C₁₉	#121	1	1	yes	characteristic
150	C₂³×C₁₉	#123	1	1	yes	characteristic
151	C₂³×C₁₉	#125	1	1	yes	characteristic
152	C₂³×C₁₉	#126	1	1	yes	characteristic
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	4	4	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	8	2	no	—
158	C₂×C₄×C₁₉	—	8	2	no	—
159	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₄⋊Q₈	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	#2873	C₂×C₁₉	1	1	yes	characteristic
193	C₂×#344	C₂×C₁₉	1	1	yes	characteristic
194	C₂×#341	C₂×C₁₉	1	1	yes	characteristic
195	#1735	C₂×C₁₉	1	1	yes	characteristic
196	#1733	C₂×C₁₉	1	1	yes	characteristic
197	#1729	C₂×C₁₉	1	1	yes	characteristic
198	C₂²×C₁₉	—	2	2	no	—
199	C₂²×C₁₉	—	2	2	no	—
200	C₂²×C₁₉	—	2	2	no	—
201	C₂²×C₁₉	—	4	1	no	—
202	C₂²×C₁₉	—	4	1	no	—
203	C₂²×C₁₉	—	4	1	no	—
204	C₂²×C₁₉	—	4	1	no	—
205	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
206	C₂²×C₁₉	#386	1	1	yes	characteristic
207	C₂²×C₁₉	#387	1	1	yes	characteristic
208	C₂²×C₁₉	#387	1	1	yes	characteristic
209	C₂²×C₁₉	#387	1	1	yes	characteristic
210	C₂²×C₁₉	#388	1	1	yes	characteristic
211	C₂²×C₁₉	#389	1	1	yes	characteristic
212	C₄×C₁₉	—	4	4	no	—
213	C₄×C₁₉	—	8	2	no	—
214	C₄×C₁₉	—	8	2	no	—
215	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
216	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
217	C₄×C₁₉	#385	1	1	yes	characteristic
218	C₄×C₁₉	#385	1	1	yes	characteristic
219	C₄×C₁₉	#387	1	1	yes	characteristic
220	C₄×C₁₉	#388	1	1	yes	characteristic
221	C₄×C₁₉	#389	1	1	yes	characteristic
222	C₄×C₁₉	#391	1	1	yes	characteristic
223	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
224	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
225	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
226	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×#117	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	#428	—	2	2	no	—
231	#428	C₄×C₁₉	1	4	yes	complemented
232	#427	—	2	2	no	—
233	#405	—	2	2	no	—
234	#405	—	2	2	no	—
235	C₄×M₁₆	—	2	2	no	—
236	#344	C₄×C₁₉	1	4	yes	complemented
237	#341	C₄×C₁₉	1	4	yes	complemented
238	#340	—	2	2	no	—
239	#339	—	2	2	no	—
240	#336	—	2	2	no	—
241	C₂×C₁₉	—	2	1	no	—
242	C₂×C₁₉	—	2	1	no	—
243	C₂×C₁₉	—	2	1	no	—
244	C₂×C₁₉	—	2	1	no	—
245	C₂×C₁₉	—	2	1	no	—
246	C₂×C₁₉	—	2	1	no	—
247	C₂×C₁₉	#1436	1	1	yes	characteristic
248	C₂×C₁₉	#1881	1	2	yes	—
249	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	2	1	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
261	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
262	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
263	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
264	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
265	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
266	C₂×M₁₆	Q₈×C₁₉	1	2	yes	—
267	C₂×M₁₆	Q₈×C₁₉	1	2	yes	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	—	2	1	no	—
275	C₂²×C₈	—	2	1	no	—
276	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
277	C₂²×C₈	D₄×C₁₉	1	2	yes	—
278	#117	—	2	1	no	—
279	#117	—	2	1	no	—
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	—	2	1	no	—
287	#117	C₂×C₄×C₁₉	1	2	yes	—
288	#117	C₂×C₄×C₁₉	1	2	yes	—
289	#117	D₄×C₁₉	1	2	yes	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
292	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	—	2	1	no	—
299	#107	—	2	4	no	—
300	#106	—	2	4	no	—
301	#97	—	2	4	no	—
302	C₄×C₈	—	2	4	no	—
303	C₁₉	#10900	1	1	yes	characteristic, direct product factor, Sylow
304	C₂⁴	#41×C₁₉	1	1	yes	characteristic
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
309	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
315	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
317	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
320	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
321	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	2	2	no	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	C₄²×C₁₉	1	4	yes	—
333	M₁₆	C₄⋊C₄×C₁₉	1	4	yes	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	1	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	C₄⋊C₄×C₁₉	1	4	yes	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₂²⋊C₄	—	4	1	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	4	1	no	—
366	C₄²	—	4	1	no	—
367	C₄²	—	4	1	no	—
368	C₂³	—	4	2	no	—
369	C₂³	C₁₉×#117	1	1	yes	characteristic
370	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
371	C₂³	C₄×Q₈×C₁₉	1	1	yes	characteristic
372	C₂³	C₁₉×#121	1	1	yes	characteristic
373	C₂³	C₁₉×#123	1	1	yes	characteristic
374	C₂³	C₁₉×#125	1	1	yes	characteristic
375	C₂³	C₁₉×#126	1	1	yes	characteristic
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	8	2	no	—
381	C₂×C₄	—	8	2	no	—
382	C₂×C₄	C₂×C₄²×C₁₉	1	1	yes	characteristic
383	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
384	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
385	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
386	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
387	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
388	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
389	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
390	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
391	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
392	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
393	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
394	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
395	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
396	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
397	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
398	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
399	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
400	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
401	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
402	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
403	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
404	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
405	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
406	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
407	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
408	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
409	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
410	C₈	—	2	4	no	—
411	C₈	—	2	4	no	—
412	C₈	—	2	4	no	—
413	C₈	—	4	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	C₄×C₄⋊C₄×C₁₉	1	1	yes	characteristic
422	C₂²	C₁₉×#386	1	1	yes	characteristic
423	C₂²	C₁₉×#387	1	1	yes	characteristic
424	C₂²	C₁₉×#387	1	1	yes	characteristic
425	C₂²	C₁₉×#387	1	1	yes	characteristic
426	C₂²	C₁₉×#388	1	1	yes	characteristic
427	C₂²	C₁₉×#389	1	1	yes	characteristic
428	C₄	—	4	4	no	—
429	C₄	—	8	2	no	—
430	C₄	—	8	2	no	—
431	C₄	C₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
432	C₄	C₄×C₄⋊C₄×C₁₉	1	1	yes	characteristic
433	C₄	C₁₉×#385	1	1	yes	characteristic
434	C₄	C₁₉×#385	1	1	yes	characteristic
435	C₄	C₁₉×#387	1	1	yes	characteristic
436	C₄	C₁₉×#388	1	1	yes	characteristic
437	C₄	C₁₉×#389	1	1	yes	characteristic
438	C₄	C₁₉×#391	1	1	yes	characteristic
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	C₁₉×#1436	1	1	yes	characteristic
446	C₂	C₁₉×#1881	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator	C₂×C₄	C₂×C₄²×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	#386
prime radical	C₂⁴×C₁₉	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
16. C₁₉×#428	C₄	semidirect
21. C₁₉×#344	C₄	semidirect
22. C₁₉×#341	C₄	semidirect
144. #10900	C₁₉	direct (N × H)
231. #428	C₄×C₁₉	semidirect
236. #344	C₄×C₁₉	semidirect
237. #341	C₄×C₁₉	semidirect
303. C₁₉	#10900	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
C₁₉×#2873	2
C₂×C₁₉×#344	2
C₂×C₁₉×#341	2
C₁₉×#1735	2
C₁₉×#1733	2
C₁₉×#1729	2
#10900	19

Subgroups — C19×#10900 #18016859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10900 #18016859