Subgroups — C₁₉×#11213 #18017172

Order 4864.

682 conjugacy classes of subgroups.

The subgroup lattice has 496 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×#2316	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1740	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×H(3,ℤ/4)	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	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#117	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×#389	—	2	2	no	—
20	C₁₉×#389	—	2	2	no	—
21	C₁₉×#380	—	2	2	no	—
22	C₁₉×#344	—	2	2	no	—
23	C₁₉×#342	—	2	2	no	—
24	C₁₉×#340	—	2	2	no	—
25	C₁₉×#339	—	2	2	no	—
26	C₁₉×H(3,ℤ/4)	—	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	D₄	1	2	yes	—
39	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
40	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
41	C₂²×C₈×C₁₉	—	2	1	no	—
42	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
43	C₁₉×#117	—	2	1	no	—
44	C₁₉×#117	—	2	1	no	—
45	C₁₉×#117	—	2	1	no	—
46	C₁₉×#117	—	2	1	no	—
47	C₁₉×#117	—	2	1	no	—
48	C₁₉×#117	—	2	1	no	—
49	C₁₉×#117	—	2	1	no	—
50	C₁₉×#117	—	2	1	no	—
51	C₁₉×#117	—	2	1	no	—
52	C₁₉×#117	—	2	1	no	—
53	C₁₉×#117	—	2	1	no	—
54	C₁₉×#117	—	2	1	no	—
55	C₁₉×#117	—	2	1	no	—
56	C₁₉×#117	—	2	1	no	—
57	C₁₉×#117	—	2	1	no	—
58	C₁₉×#117	Q₈	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
66	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
75	C₂×C₄²×C₁₉	—	2	1	no	—
76	C₂×C₄²×C₁₉	—	2	1	no	—
77	C₂×C₄²×C₁₉	—	2	1	no	—
78	C₂×C₄²×C₁₉	D₄	1	2	yes	—
79	C₁₉×#107	—	2	4	no	—
80	C₁₉×#106	—	2	4	no	—
81	C₁₉×#95	—	2	4	no	—
82	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	8	2	no	—
92	C₂²×C₄×C₁₉	C₂²×C₄	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×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×Q₈	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	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
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	—	2	2	no	—
112	M₁₆×C₁₉	—	4	1	no	—
113	M₁₆×C₁₉	—	4	1	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	—	4	1	no	—
118	C₂×C₈×C₁₉	—	4	1	no	—
119	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	complemented
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	4	1	no	—
129	C₄⋊C₄×C₁₉	—	4	1	no	—
130	C₄⋊C₄×C₁₉	—	4	1	no	—
131	C₄⋊C₄×C₁₉	—	4	1	no	—
132	C₄⋊C₄×C₁₉	—	4	1	no	—
133	C₄⋊C₄×C₁₉	—	8	4	no	—
134	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
135	C₂²⋊C₄×C₁₉	—	2	2	no	—
136	C₂²⋊C₄×C₁₉	—	2	2	no	—
137	C₂²⋊C₄×C₁₉	—	2	2	no	—
138	C₂²⋊C₄×C₁₉	—	4	1	no	—
139	C₂²⋊C₄×C₁₉	—	4	1	no	—
140	C₂²⋊C₄×C₁₉	—	4	1	no	—
141	C₂²⋊C₄×C₁₉	—	4	1	no	—
142	C₂²⋊C₄×C₁₉	—	4	1	no	—
143	C₄²×C₁₉	—	2	2	no	—
144	C₄²×C₁₉	—	2	2	no	—
145	C₄²×C₁₉	—	2	2	no	—
146	C₄²×C₁₉	—	4	1	no	—
147	C₄²×C₁₉	—	4	1	no	—
148	C₄²×C₁₉	—	4	1	no	—
149	C₄²×C₁₉	—	4	1	no	—
150	C₄²×C₁₉	—	4	1	no	—
151	#11213	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	—	4	1	no	—
154	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
155	C₂³×C₁₉	#120	1	1	yes	characteristic
156	C₂³×C₁₉	#121	1	1	yes	characteristic
157	C₂³×C₁₉	#121	1	1	yes	characteristic
158	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂³×C₁₉	#123	1	1	yes	characteristic
160	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	8	2	no	—
173	C₂×C₄×C₁₉	—	8	2	no	—
174	C₂×C₄×C₁₉	—	8	1	no	—
175	C₂×C₄×C₁₉	—	8	1	no	—
176	C₂×C₄×C₁₉	—	8	1	no	—
177	C₂×C₄×C₁₉	—	8	1	no	—
178	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
200	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
201	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
206	C₈×C₁₉	—	2	4	no	—
207	C₈×C₁₉	—	4	2	no	—
208	C₂×#428	C₂×C₁₉	1	1	yes	characteristic
209	#2316	C₂×C₁₉	1	1	yes	characteristic
210	C₂×#344	C₂×C₁₉	1	1	yes	characteristic
211	#1740	C₂×C₁₉	1	1	yes	characteristic
212	#1736	C₂×C₁₉	1	1	yes	characteristic
213	#1733	C₂×C₁₉	1	1	yes	characteristic
214	C₂×H(3,ℤ/4)	C₂×C₁₉	1	1	yes	characteristic
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	2	1	no	—
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	2	1	no	—
221	C₂²×C₁₉	—	4	1	no	—
222	C₂²×C₁₉	—	4	1	no	—
223	C₂²×C₁₉	—	4	1	no	—
224	C₂²×C₁₉	—	4	1	no	—
225	C₂²×C₁₉	#386	1	1	yes	characteristic
226	C₂²×C₁₉	#387	1	1	yes	characteristic
227	C₂²×C₁₉	#389	1	1	yes	characteristic
228	C₂²×C₁₉	#394	1	1	yes	characteristic
229	C₂²×C₁₉	#395	1	1	yes	characteristic
230	C₂²×C₁₉	#396	1	1	yes	characteristic
231	C₂²×C₁₉	#398	1	1	yes	characteristic
232	C₄×C₁₉	—	4	4	no	—
233	C₄×C₁₉	—	8	2	no	—
234	C₄×C₁₉	—	8	2	no	—
235	C₄×C₁₉	—	8	2	no	—
236	C₄×C₁₉	—	8	1	no	—
237	C₄×C₁₉	—	8	1	no	—
238	C₄×C₁₉	#380	1	1	yes	characteristic
239	C₄×C₁₉	#387	1	1	yes	characteristic
240	C₄×C₁₉	#389	1	1	yes	characteristic
241	C₄×C₁₉	#391	1	1	yes	characteristic
242	C₄×C₁₉	#396	1	1	yes	characteristic
243	C₄×C₁₉	#398	1	1	yes	characteristic
244	C₄×C₁₉	#398	1	1	yes	characteristic
245	C₄×C₁₉	#400	1	1	yes	characteristic
246	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
247	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
249	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
252	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
253	#428	—	2	2	no	—
254	#428	—	2	2	no	—
255	C₂×#107	C₄×C₁₉	1	2	yes	complemented
256	C₂×#106	C₄×C₁₉	1	2	yes	complemented
257	#389	—	2	2	no	—
258	#389	—	2	2	no	—
259	#380	—	2	2	no	—
260	#344	—	2	2	no	—
261	#342	—	2	2	no	—
262	#340	—	2	2	no	—
263	#339	—	2	2	no	—
264	H(3,ℤ/4)	—	2	2	no	—
265	C₂×C₁₉	—	2	1	no	—
266	C₂×C₁₉	—	2	1	no	—
267	C₂×C₁₉	—	2	1	no	—
268	C₂×C₁₉	—	2	1	no	—
269	C₂×C₁₉	—	2	1	no	—
270	C₂×C₁₉	—	2	1	no	—
271	C₂×C₁₉	#1441	1	1	yes	characteristic
272	C₂×C₁₉	#1904	1	1	yes	characteristic
273	C₂×C₁₉	#1905	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
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	D₄×C₁₉	1	2	yes	—
286	C₂×M₁₆	Q₈×C₁₉	1	2	yes	—
287	C₂×M₁₆	Q₈×C₁₉	1	2	yes	—
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
290	#117	—	2	1	no	—
291	#117	—	2	1	no	—
292	#117	—	2	1	no	—
293	#117	—	2	1	no	—
294	#117	—	2	1	no	—
295	#117	—	2	1	no	—
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	—	2	1	no	—
302	#117	—	2	1	no	—
303	#117	—	2	1	no	—
304	#117	—	2	1	no	—
305	#117	Q₈×C₁₉	1	2	yes	—
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	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	4	no	—
313	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
316	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
317	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	D₄×C₁₉	1	2	yes	—
326	#107	—	2	4	no	—
327	#106	—	2	4	no	—
328	#95	—	2	4	no	—
329	C₁₉	#11213	1	1	yes	characteristic, direct product factor, Sylow
330	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	8	2	no	—
340	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
345	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
347	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
348	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
349	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
350	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
352	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
353	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	2	no	—
358	M₁₆	—	2	2	no	—
359	M₁₆	—	2	2	no	—
360	M₁₆	—	4	1	no	—
361	M₁₆	—	4	1	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	4	1	no	—
367	C₂×C₈	C₄⋊C₄×C₁₉	1	4	yes	complemented
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	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	—	4	1	no	—
380	C₄⋊C₄	—	4	1	no	—
381	C₄⋊C₄	—	8	4	no	—
382	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	4	1	no	—
387	C₂²⋊C₄	—	4	1	no	—
388	C₂²⋊C₄	—	4	1	no	—
389	C₂²⋊C₄	—	4	1	no	—
390	C₂²⋊C₄	—	4	1	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	4	1	no	—
395	C₄²	—	4	1	no	—
396	C₄²	—	4	1	no	—
397	C₄²	—	4	1	no	—
398	C₄²	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
402	C₂³	C₁₉×#120	1	1	yes	characteristic
403	C₂³	C₁₉×#121	1	1	yes	characteristic
404	C₂³	C₁₉×#121	1	1	yes	characteristic
405	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
406	C₂³	C₁₉×#123	1	1	yes	characteristic
407	C₂³	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	8	2	no	—
420	C₂×C₄	—	8	2	no	—
421	C₂×C₄	—	8	1	no	—
422	C₂×C₄	—	8	1	no	—
423	C₂×C₄	—	8	1	no	—
424	C₂×C₄	—	8	1	no	—
425	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
426	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
427	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
428	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
429	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
430	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
431	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
432	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
433	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
434	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
435	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
436	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
437	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
438	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
439	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
440	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
441	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
442	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
443	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
444	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
445	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
446	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
447	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
448	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
449	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
450	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
451	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
452	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
453	C₈	—	2	4	no	—
454	C₈	—	4	2	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	C₁₉×#386	1	1	yes	characteristic
466	C₂²	C₁₉×#387	1	1	yes	characteristic
467	C₂²	C₁₉×#389	1	1	yes	characteristic
468	C₂²	C₁₉×#394	1	1	yes	characteristic
469	C₂²	C₁₉×#395	1	1	yes	characteristic
470	C₂²	C₁₉×#396	1	1	yes	characteristic
471	C₂²	C₁₉×#398	1	1	yes	characteristic
472	C₄	—	4	4	no	—
473	C₄	—	8	2	no	—
474	C₄	—	8	2	no	—
475	C₄	—	8	2	no	—
476	C₄	—	8	1	no	—
477	C₄	—	8	1	no	—
478	C₄	C₁₉×#380	1	1	yes	characteristic
479	C₄	C₁₉×#387	1	1	yes	characteristic
480	C₄	C₁₉×#389	1	1	yes	characteristic
481	C₄	C₁₉×#391	1	1	yes	characteristic
482	C₄	C₁₉×#396	1	1	yes	characteristic
483	C₄	C₁₉×#398	1	1	yes	characteristic
484	C₄	C₁₉×#398	1	1	yes	characteristic
485	C₄	C₁₉×#400	1	1	yes	characteristic
486	C₂	—	2	1	no	—
487	C₂	—	2	1	no	—
488	C₂	—	2	1	no	—
489	C₂	—	2	1	no	—
490	C₂	—	2	1	no	—
491	C₂	—	2	1	no	—
492	C₂	C₁₉×#1441	1	1	yes	characteristic
493	C₂	C₁₉×#1904	1	1	yes	characteristic
494	C₂	C₁₉×#1905	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	C₂×D₄
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
119. C₂×C₈×C₁₉	C₄⋊C₄	semidirect
151. #11213	C₁₉	direct (N × H)
255. C₂×#107	C₄×C₁₉	semidirect
256. C₂×#106	C₄×C₁₉	semidirect
329. C₁₉	#11213	direct (N × H)
367. C₂×C₈	C₄⋊C₄×C₁₉	semidirect

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×#2316	2
C₂×C₁₉×#344	2
C₁₉×#1740	2
C₁₉×#1736	2
C₁₉×#1733	2
C₂×C₁₉×H(3,ℤ/4)	2
#11213	19

Subgroups — C19×#11213 #18017172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11213 #18017172