Subgroups — C₁₉×#11214 #18017173

Order 4864.

646 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2905	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1733	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#338	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	C₂²×M₁₆×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	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#428	—	2	2	no	—
16	C₁₉×#428	—	2	2	no	—
17	C₂×C₁₉×#107	C₄	1	2	yes	complemented
18	C₂×C₁₉×#106	C₄	1	2	yes	complemented
19	C₁₉×#424	—	2	2	no	—
20	C₁₉×#424	—	2	2	no	—
21	C₁₉×#423	—	2	2	no	—
22	C₁₉×#344	—	2	2	no	—
23	C₁₉×#343	—	2	2	no	—
24	C₁₉×#340	—	2	2	no	—
25	C₁₉×#339	—	2	2	no	—
26	C₁₉×#338	—	2	2	no	—
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
38	C₂×M₁₆×C₁₉	—	2	1	no	—
39	C₂×M₁₆×C₁₉	—	2	1	no	—
40	C₂×M₁₆×C₁₉	—	2	1	no	—
41	C₂×M₁₆×C₁₉	—	2	1	no	—
42	C₂×M₁₆×C₁₉	—	2	1	no	—
43	C₂×M₁₆×C₁₉	—	2	1	no	—
44	C₂×M₁₆×C₁₉	—	2	1	no	—
45	C₂×M₁₆×C₁₉	—	2	1	no	—
46	C₂×M₁₆×C₁₉	—	2	1	no	—
47	C₂×M₁₆×C₁₉	—	2	1	no	—
48	C₂×M₁₆×C₁₉	—	2	1	no	—
49	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
50	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
51	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
52	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
53	C₂²×C₈×C₁₉	—	2	1	no	—
54	C₂²×C₈×C₁₉	—	2	1	no	—
55	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
56	C₂²×C₈×C₁₉	D₄	1	2	yes	—
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	D₄	1	2	yes	—
63	C₁₉×#117	D₄	1	2	yes	—
64	C₁₉×#117	Q₈	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄²×C₁₉	—	2	1	no	—
77	C₂×C₄²×C₁₉	—	2	1	no	—
78	C₁₉×#107	—	2	4	no	—
79	C₁₉×#106	—	2	4	no	—
80	C₁₉×C₄⋊C₈	—	2	8	no	—
81	C₂⁴×C₁₉	#41	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	8	2	no	—
89	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
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	—	2	2	no	—
109	M₁₆×C₁₉	—	2	2	no	—
110	M₁₆×C₁₉	—	2	2	no	—
111	M₁₆×C₁₉	—	4	1	no	—
112	M₁₆×C₁₉	—	4	1	no	—
113	M₁₆×C₁₉	—	4	1	no	—
114	M₁₆×C₁₉	—	4	1	no	—
115	M₁₆×C₁₉	—	4	1	no	—
116	M₁₆×C₁₉	—	4	1	no	—
117	M₁₆×C₁₉	—	4	1	no	—
118	M₁₆×C₁₉	—	4	1	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	2	2	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	—	4	1	no	—
127	C₂×C₈×C₁₉	—	4	1	no	—
128	C₂×C₈×C₁₉	—	4	1	no	—
129	C₂×C₈×C₁₉	—	4	1	no	—
130	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	4	1	no	—
137	C₄⋊C₄×C₁₉	—	4	1	no	—
138	C₄⋊C₄×C₁₉	—	4	1	no	—
139	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
140	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
141	C₂²⋊C₄×C₁₉	—	2	2	no	—
142	C₂²⋊C₄×C₁₉	—	2	2	no	—
143	C₂²⋊C₄×C₁₉	—	2	2	no	—
144	C₂²⋊C₄×C₁₉	—	4	1	no	—
145	C₄²×C₁₉	—	2	2	no	—
146	C₄²×C₁₉	—	2	2	no	—
147	C₄²×C₁₉	—	2	2	no	—
148	C₄²×C₁₉	—	4	1	no	—
149	#11214	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	C₄×D₄	1	1	yes	characteristic
153	C₂³×C₁₉	#121	1	1	yes	characteristic
154	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂³×C₁₉	#123	1	1	yes	characteristic
156	C₂³×C₁₉	#125	1	1	yes	characteristic
157	C₂³×C₁₉	#125	1	1	yes	characteristic
158	C₂³×C₁₉	#126	1	1	yes	characteristic
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	8	1	no	—
164	C₂×C₄×C₁₉	—	8	1	no	—
165	C₂×C₄×C₁₉	—	8	1	no	—
166	C₂×C₄×C₁₉	—	8	1	no	—
167	C₂×C₄×C₁₉	—	8	2	no	—
168	C₂×C₄×C₁₉	—	8	2	no	—
169	C₂×C₄×C₁₉	—	8	2	no	—
170	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂²⋊Q₈	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	C₂²⋊Q₈	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
198	C₈×C₁₉	—	2	4	no	—
199	C₈×C₁₉	—	4	2	no	—
200	C₈×C₁₉	—	4	2	no	—
201	C₈×C₁₉	—	4	2	no	—
202	C₂×#428	C₂×C₁₉	1	1	yes	characteristic
203	#2905	C₂×C₁₉	1	1	yes	characteristic
204	C₂×#344	C₂×C₁₉	1	1	yes	characteristic
205	C₂×#343	C₂×C₁₉	1	1	yes	characteristic
206	#1736	C₂×C₁₉	1	1	yes	characteristic
207	#1733	C₂×C₁₉	1	1	yes	characteristic
208	C₂×#338	C₂×C₁₉	1	1	yes	characteristic
209	C₂²×C₁₉	—	2	1	no	—
210	C₂²×C₁₉	—	2	1	no	—
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	—	2	1	no	—
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	4	1	no	—
216	C₂²×C₁₉	—	4	1	no	—
217	C₂²×C₁₉	—	4	1	no	—
218	C₂²×C₁₉	—	4	1	no	—
219	C₂²×C₁₉	#386	1	1	yes	characteristic
220	C₂²×C₁₉	#387	1	1	yes	characteristic
221	C₂²×C₁₉	#389	1	1	yes	characteristic
222	C₂²×C₁₉	#396	1	1	yes	characteristic
223	C₂²×C₁₉	#398	1	1	yes	characteristic
224	C₂²×C₁₉	#398	1	1	yes	characteristic
225	C₂²×C₁₉	#400	1	1	yes	characteristic
226	C₄×C₁₉	—	4	2	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	8	2	no	—
229	C₄×C₁₉	—	8	2	no	—
230	C₄×C₁₉	#380	1	1	yes	characteristic
231	C₄×C₁₉	#387	1	1	yes	characteristic
232	C₄×C₁₉	#389	1	1	yes	characteristic
233	C₄×C₁₉	#391	1	1	yes	characteristic
234	C₄×C₁₉	#394	1	1	yes	characteristic
235	C₄×C₁₉	#395	1	1	yes	characteristic
236	C₄×C₁₉	#396	1	1	yes	characteristic
237	C₄×C₁₉	#398	1	1	yes	characteristic
238	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
239	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
240	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
241	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
242	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
243	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
244	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
245	#428	—	2	2	no	—
246	#428	—	2	2	no	—
247	C₂×#107	C₄×C₁₉	1	2	yes	complemented
248	C₂×#106	C₄×C₁₉	1	2	yes	complemented
249	#424	—	2	2	no	—
250	#424	—	2	2	no	—
251	#423	—	2	2	no	—
252	#344	—	2	2	no	—
253	#343	—	2	2	no	—
254	#340	—	2	2	no	—
255	#339	—	2	2	no	—
256	#338	—	2	2	no	—
257	C₂×C₁₉	—	2	1	no	—
258	C₂×C₁₉	—	2	1	no	—
259	C₂×C₁₉	—	2	1	no	—
260	C₂×C₁₉	—	2	1	no	—
261	C₂×C₁₉	—	2	1	no	—
262	C₂×C₁₉	—	2	1	no	—
263	C₂×C₁₉	#1441	1	1	yes	characteristic
264	C₂×C₁₉	#1902	1	1	yes	characteristic
265	C₂×C₁₉	#1903	1	1	yes	characteristic
266	C₂³×C₄	—	2	1	no	—
267	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	2	1	no	—
273	C₂×M₁₆	—	2	1	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	2	1	no	—
281	C₂×M₁₆	—	2	1	no	—
282	C₂×M₁₆	—	2	1	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	2	1	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	—	2	1	no	—
287	C₂×M₁₆	—	2	1	no	—
288	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
289	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
290	C₂×M₁₆	Q₈×C₁₉	1	2	yes	—
291	C₂×M₁₆	Q₈×C₁₉	1	2	yes	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
295	C₂²×C₈	D₄×C₁₉	1	2	yes	—
296	#117	—	2	1	no	—
297	#117	—	2	1	no	—
298	#117	—	2	1	no	—
299	#117	—	2	1	no	—
300	#117	—	2	1	no	—
301	#117	D₄×C₁₉	1	2	yes	—
302	#117	D₄×C₁₉	1	2	yes	—
303	#117	Q₈×C₁₉	1	2	yes	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
311	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	—	2	1	no	—
317	#107	—	2	4	no	—
318	#106	—	2	4	no	—
319	C₄⋊C₈	—	2	8	no	—
320	C₁₉	#11214	1	1	yes	characteristic, direct product factor, Sylow
321	C₂⁴	#41×C₁₉	1	1	yes	characteristic
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	8	2	no	—
329	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
338	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
339	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
340	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
341	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
343	M₁₆	—	2	2	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	2	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	4	1	no	—
352	M₁₆	—	4	1	no	—
353	M₁₆	—	4	1	no	—
354	M₁₆	—	4	1	no	—
355	M₁₆	—	4	1	no	—
356	M₁₆	—	4	1	no	—
357	M₁₆	—	4	1	no	—
358	M₁₆	—	4	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	4	1	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	C₄⋊C₄×C₁₉	1	4	yes	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
380	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
392	C₂³	C₁₉×#121	1	1	yes	characteristic
393	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
394	C₂³	C₁₉×#123	1	1	yes	characteristic
395	C₂³	C₁₉×#125	1	1	yes	characteristic
396	C₂³	C₁₉×#125	1	1	yes	characteristic
397	C₂³	C₁₉×#126	1	1	yes	characteristic
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	8	1	no	—
403	C₂×C₄	—	8	1	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	—	8	1	no	—
407	C₂×C₄	—	8	1	no	—
408	C₂×C₄	—	8	2	no	—
409	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
411	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
412	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
413	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
414	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
415	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
416	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
417	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
418	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
419	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
420	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
421	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
422	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
423	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
424	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
425	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
426	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
427	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
428	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
429	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
430	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
431	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
432	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
433	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
434	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
435	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
436	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
437	C₈	—	2	4	no	—
438	C₈	—	4	2	no	—
439	C₈	—	4	2	no	—
440	C₈	—	4	2	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	1	no	—
451	C₂²	C₁₉×#386	1	1	yes	characteristic
452	C₂²	C₁₉×#387	1	1	yes	characteristic
453	C₂²	C₁₉×#389	1	1	yes	characteristic
454	C₂²	C₁₉×#396	1	1	yes	characteristic
455	C₂²	C₁₉×#398	1	1	yes	characteristic
456	C₂²	C₁₉×#398	1	1	yes	characteristic
457	C₂²	C₁₉×#400	1	1	yes	characteristic
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	8	2	no	—
461	C₄	—	8	2	no	—
462	C₄	C₁₉×#380	1	1	yes	characteristic
463	C₄	C₁₉×#387	1	1	yes	characteristic
464	C₄	C₁₉×#389	1	1	yes	characteristic
465	C₄	C₁₉×#391	1	1	yes	characteristic
466	C₄	C₁₉×#394	1	1	yes	characteristic
467	C₄	C₁₉×#395	1	1	yes	characteristic
468	C₄	C₁₉×#396	1	1	yes	characteristic
469	C₄	C₁₉×#398	1	1	yes	characteristic
470	C₂	—	2	1	no	—
471	C₂	—	2	1	no	—
472	C₂	—	2	1	no	—
473	C₂	—	2	1	no	—
474	C₂	—	2	1	no	—
475	C₂	—	2	1	no	—
476	C₂	C₁₉×#1441	1	1	yes	characteristic
477	C₂	C₁₉×#1902	1	1	yes	characteristic
478	C₂	C₁₉×#1903	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×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
17. C₂×C₁₉×#107	C₄	semidirect
18. C₂×C₁₉×#106	C₄	semidirect
149. #11214	C₁₉	direct (N × H)
247. C₂×#107	C₄×C₁₉	semidirect
248. C₂×#106	C₄×C₁₉	semidirect
320. C₁₉	#11214	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×#428	2
C₁₉×#2905	2
C₂×C₁₉×#344	2
C₂×C₁₉×#343	2
C₁₉×#1736	2
C₁₉×#1733	2
C₂×C₁₉×#338	2
#11214	19

Subgroups — C19×#11214 #18017173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11214 #18017173