Subgroups — C₁₉×#11231 #18017190

Order 4864.

870 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#340	C₂	1	2	yes	maximal
5	C₁₉×C₄⋊#95	C₂	1	2	yes	maximal
6	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
10	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#106	—	2	2	no	—
12	C₂×C₁₉×#106	—	2	4	no	—
13	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
14	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
15	C₂×C₁₉×C₄⋊C₈	C₄	1	4	yes	complemented
16	C₂×C₁₉×#95	—	2	2	no	—
17	C₂×C₁₉×#95	—	2	2	no	—
18	C₁₉×#340	—	2	2	no	—
19	C₁₉×#340	—	2	4	no	—
20	C₂³×C₄×C₁₉	—	2	2	no	—
21	C₂³×C₄×C₁₉	—	2	2	no	—
22	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	—	2	2	no	—
26	C₂²×C₈×C₁₉	—	2	2	no	—
27	C₂²×C₈×C₁₉	—	2	2	no	—
28	C₂²×C₈×C₁₉	—	2	1	no	—
29	C₂²×C₈×C₁₉	—	2	1	no	—
30	C₂²×C₈×C₁₉	—	2	2	no	—
31	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₁₉	D₄	1	2	yes	—
34	C₂²×C₈×C₁₉	D₄	1	2	yes	—
35	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₉	Q₈	1	4	yes	—
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
53	C₁₉×#106	—	2	8	no	—
54	C₁₉×C₄⋊C₈	—	2	8	no	—
55	C₁₉×#95	—	4	4	no	—
56	C₁₉×#95	—	4	4	no	—
57	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	—	2	1	no	—
59	C₂²×C₄×C₁₉	—	2	1	no	—
60	C₂²×C₄×C₁₉	—	2	2	no	—
61	C₂²×C₄×C₁₉	—	2	1	no	—
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂²×C₄×C₁₉	—	2	2	no	—
64	C₂²×C₄×C₁₉	—	2	2	no	—
65	C₂²×C₄×C₁₉	—	2	4	no	—
66	C₂²×C₄×C₁₉	—	2	4	no	—
67	C₂²×C₄×C₁₉	—	4	2	no	—
68	C₂²×C₄×C₁₉	—	4	2	no	—
69	C₂²×C₄×C₁₉	—	4	2	no	—
70	C₂²×C₄×C₁₉	—	4	2	no	—
71	C₂²×C₄×C₁₉	—	4	2	no	—
72	C₂²×C₄×C₁₉	—	4	2	no	—
73	C₂²×C₄×C₁₉	—	4	2	no	—
74	C₂²×C₄×C₁₉	—	4	2	no	—
75	C₂²×C₄×C₁₉	—	4	2	no	—
76	C₂²×C₄×C₁₉	—	4	2	no	—
77	C₂²×C₄×C₁₉	—	4	2	no	—
78	C₂²×C₄×C₁₉	—	4	2	no	—
79	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
80	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
81	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	—
82	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	#41	1	2	yes	—
91	C₂²×C₄×C₁₉	#41	1	2	yes	—
92	C₂×C₈×C₁₉	—	2	4	no	—
93	C₂×C₈×C₁₉	—	2	2	no	—
94	C₂×C₈×C₁₉	—	2	4	no	—
95	C₂×C₈×C₁₉	—	2	2	no	—
96	C₂×C₈×C₁₉	—	2	2	no	—
97	C₂×C₈×C₁₉	—	2	4	no	—
98	C₂×C₈×C₁₉	—	4	1	no	—
99	C₂×C₈×C₁₉	—	4	2	no	—
100	C₂×C₈×C₁₉	—	4	1	no	—
101	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
102	C₄⋊C₄×C₁₉	—	2	4	no	—
103	C₄⋊C₄×C₁₉	—	2	4	no	—
104	C₄⋊C₄×C₁₉	—	2	4	no	—
105	C₄⋊C₄×C₁₉	—	2	4	no	—
106	C₄⋊C₄×C₁₉	—	4	2	no	—
107	C₄⋊C₄×C₁₉	—	4	2	no	—
108	C₄⋊C₄×C₁₉	—	4	2	no	—
109	C₄⋊C₄×C₁₉	—	4	2	no	—
110	C₄²×C₁₉	—	2	2	no	—
111	C₄²×C₁₉	—	2	2	no	—
112	C₄²×C₁₉	—	2	2	no	—
113	C₄²×C₁₉	—	2	2	no	—
114	#11231	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
116	C₂³×C₁₉	#121	1	1	yes	characteristic
117	C₂³×C₁₉	#121	1	1	yes	characteristic
118	C₂³×C₁₉	#121	1	2	yes	—
119	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
120	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
121	C₂³×C₁₉	#135	1	2	yes	—
122	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
123	C₂³×C₁₉	#137	1	2	yes	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	2	2	no	—
126	C₂×C₄×C₁₉	—	2	4	no	—
127	C₂×C₄×C₁₉	—	2	4	no	—
128	C₂×C₄×C₁₉	—	2	2	no	—
129	C₂×C₄×C₁₉	—	2	4	no	—
130	C₂×C₄×C₁₉	—	4	2	no	—
131	C₂×C₄×C₁₉	—	4	1	no	—
132	C₂×C₄×C₁₉	—	4	1	no	—
133	C₂×C₄×C₁₉	—	4	4	no	—
134	C₂×C₄×C₁₉	—	4	4	no	—
135	C₂×C₄×C₁₉	—	4	4	no	—
136	C₂×C₄×C₁₉	—	4	4	no	—
137	C₂×C₄×C₁₉	—	4	4	no	—
138	C₂×C₄×C₁₉	—	4	4	no	—
139	C₂×C₄×C₁₉	—	8	2	no	—
140	C₂×C₄×C₁₉	—	8	2	no	—
141	C₂×C₄×C₁₉	—	8	2	no	—
142	C₂×C₄×C₁₉	—	8	2	no	—
143	C₂×C₄×C₁₉	—	8	2	no	—
144	C₂×C₄×C₁₉	—	8	2	no	—
145	C₂×C₄×C₁₉	—	8	2	no	—
146	C₂×C₄×C₁₉	—	8	2	no	—
147	C₂×C₄×C₁₉	#106	1	4	yes	complemented
148	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
151	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
152	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#121	1	2	yes	—
154	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
155	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
156	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#123	1	2	yes	—
160	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#125	1	2	yes	—
162	C₂×C₄×C₁₉	#125	1	2	yes	—
163	C₂×C₄×C₁₉	#126	1	2	yes	—
164	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
166	C₈×C₁₉	—	2	4	no	—
167	C₈×C₁₉	—	4	2	no	—
168	C₂²×#106	C₂×C₁₉	1	1	yes	characteristic
169	C₂²×C₄⋊C₈	C₂×C₁₉	1	1	yes	characteristic
170	C₂×#340	C₂×C₁₉	1	2	yes	—
171	C₂×#340	C₂×C₁₉	1	1	yes	characteristic
172	C₄⋊#95	C₂×C₁₉	1	2	yes	—
173	C₂²×C₁₉	#380	1	1	yes	characteristic
174	C₂²×C₁₉	#389	1	2	yes	—
175	C₂²×C₁₉	#394	1	1	yes	characteristic
176	C₂²×C₁₉	#396	1	2	yes	—
177	C₂²×C₁₉	#398	1	1	yes	characteristic
178	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
179	C₂²×C₁₉	#427	1	1	yes	characteristic
180	C₂²×C₁₉	#428	1	2	yes	—
181	C₂²×C₁₉	#460	1	2	yes	—
182	C₂²×C₁₉	#461	1	2	yes	—
183	C₂²×C₁₉	#463	1	2	yes	—
184	C₂²×C₁₉	#464	1	2	yes	—
185	C₂²×C₁₉	#465	1	2	yes	—
186	C₂²×C₁₉	#465	1	2	yes	—
187	C₂²×C₁₉	#468	1	2	yes	—
188	C₂²×C₁₉	#469	1	1	yes	characteristic
189	C₂²×C₁₉	#470	1	1	yes	characteristic
190	C₂²×C₁₉	#475	1	2	yes	—
191	C₂²×C₁₉	#476	1	2	yes	—
192	C₂²×C₁₉	#478	1	2	yes	—
193	C₂²×C₁₉	#479	1	2	yes	—
194	C₄×C₁₉	—	2	4	no	—
195	C₄×C₁₉	—	4	2	no	—
196	C₄×C₁₉	—	8	4	no	—
197	C₄×C₁₉	—	8	4	no	—
198	C₄×C₁₉	#386	1	1	yes	characteristic
199	C₄×C₁₉	#387	1	2	yes	—
200	C₄×C₁₉	#391	1	1	yes	characteristic
201	C₄×C₁₉	#395	1	1	yes	characteristic
202	C₄×C₁₉	#398	1	2	yes	—
203	C₄×C₁₉	#400	1	1	yes	characteristic
204	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
205	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
206	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
207	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
208	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
209	C₂×#106	—	2	2	no	—
210	C₂×#106	—	2	4	no	—
211	C₂×C₄⋊C₈	—	2	2	no	—
212	C₂×C₄⋊C₈	—	2	2	no	—
213	C₂×C₄⋊C₈	C₄×C₁₉	1	4	yes	complemented
214	C₂×#95	—	2	2	no	—
215	C₂×#95	—	2	2	no	—
216	#340	—	2	2	no	—
217	#340	—	2	4	no	—
218	C₂×C₁₉	#1441	1	1	yes	characteristic
219	C₂×C₁₉	#1807	1	1	yes	characteristic
220	C₂×C₁₉	#1809	1	1	yes	characteristic
221	C₂×C₁₉	#1948	1	2	yes	—
222	C₂×C₁₉	#1949	1	2	yes	—
223	C₂×C₁₉	#2055	1	2	yes	—
224	C₂×C₁₉	#2065	1	2	yes	—
225	C₂×C₁₉	#2066	1	2	yes	—
226	C₂×C₁₉	#2088	1	2	yes	—
227	C₂³×C₄	—	2	2	no	—
228	C₂³×C₄	—	2	2	no	—
229	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
230	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
231	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	—	2	2	no	—
234	C₂²×C₈	—	2	2	no	—
235	C₂²×C₈	—	2	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
239	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
240	C₂²×C₈	D₄×C₁₉	1	2	yes	—
241	C₂²×C₈	D₄×C₁₉	1	2	yes	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
253	C₂×C₄⋊C₄	Q₈×C₁₉	1	4	yes	—
254	C₂×C₄²	—	2	1	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
259	C₂×C₄²	Q₈×C₁₉	1	2	yes	—
260	#106	—	2	8	no	—
261	C₄⋊C₈	—	2	8	no	—
262	#95	—	4	4	no	—
263	#95	—	4	4	no	—
264	C₁₉	#11231	1	1	yes	characteristic, direct product factor, Sylow
265	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	C₄⋊C₄×C₁₉	1	2	yes	—
288	C₂²×C₄	C₄⋊C₄×C₁₉	1	2	yes	—
289	C₂²×C₄	SD₁₆×C₁₉	1	4	yes	—
290	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
294	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
295	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
296	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
297	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
298	C₂²×C₄	#41×C₁₉	1	2	yes	—
299	C₂²×C₄	#41×C₁₉	1	2	yes	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	2	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	C₂²⋊C₄×C₁₉	1	4	yes	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
323	C₂³	C₁₉×#121	1	1	yes	characteristic
324	C₂³	C₁₉×#121	1	1	yes	characteristic
325	C₂³	C₁₉×#121	1	2	yes	—
326	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
327	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
328	C₂³	C₁₉×#135	1	2	yes	—
329	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
330	C₂³	C₁₉×#137	1	2	yes	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	—	8	2	no	—
352	C₂×C₄	—	8	2	no	—
353	C₂×C₄	—	8	2	no	—
354	C₂×C₄	C₁₉×#106	1	4	yes	complemented
355	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
356	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
357	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
358	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
359	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
360	C₂×C₄	C₁₉×#121	1	2	yes	—
361	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
362	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
363	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
364	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
365	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
366	C₂×C₄	C₁₉×#123	1	2	yes	—
367	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
368	C₂×C₄	C₁₉×#125	1	2	yes	—
369	C₂×C₄	C₁₉×#125	1	2	yes	—
370	C₂×C₄	C₁₉×#126	1	2	yes	—
371	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
372	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
373	C₈	—	2	4	no	—
374	C₈	—	4	2	no	—
375	C₂²	C₁₉×#380	1	1	yes	characteristic
376	C₂²	C₁₉×#389	1	2	yes	—
377	C₂²	C₁₉×#394	1	1	yes	characteristic
378	C₂²	C₁₉×#396	1	2	yes	—
379	C₂²	C₁₉×#398	1	1	yes	characteristic
380	C₂²	C₂×C₁₉×#106	1	1	yes	characteristic
381	C₂²	C₁₉×#427	1	1	yes	characteristic
382	C₂²	C₁₉×#428	1	2	yes	—
383	C₂²	C₁₉×#460	1	2	yes	—
384	C₂²	C₁₉×#461	1	2	yes	—
385	C₂²	C₁₉×#463	1	2	yes	—
386	C₂²	C₁₉×#464	1	2	yes	—
387	C₂²	C₁₉×#465	1	2	yes	—
388	C₂²	C₁₉×#465	1	2	yes	—
389	C₂²	C₁₉×#468	1	2	yes	—
390	C₂²	C₁₉×#469	1	1	yes	characteristic
391	C₂²	C₁₉×#470	1	1	yes	characteristic
392	C₂²	C₁₉×#475	1	2	yes	—
393	C₂²	C₁₉×#476	1	2	yes	—
394	C₂²	C₁₉×#478	1	2	yes	—
395	C₂²	C₁₉×#479	1	2	yes	—
396	C₄	—	2	4	no	—
397	C₄	—	4	2	no	—
398	C₄	—	8	4	no	—
399	C₄	—	8	4	no	—
400	C₄	C₁₉×#386	1	1	yes	characteristic
401	C₄	C₁₉×#387	1	2	yes	—
402	C₄	C₁₉×#391	1	1	yes	characteristic
403	C₄	C₁₉×#395	1	1	yes	characteristic
404	C₄	C₁₉×#398	1	2	yes	—
405	C₄	C₁₉×#400	1	1	yes	characteristic
406	C₂	C₁₉×#1441	1	1	yes	characteristic
407	C₂	C₁₉×#1807	1	1	yes	characteristic
408	C₂	C₁₉×#1809	1	1	yes	characteristic
409	C₂	C₁₉×#1948	1	2	yes	—
410	C₂	C₁₉×#1949	1	2	yes	—
411	C₂	C₁₉×#2055	1	2	yes	—
412	C₂	C₁₉×#2065	1	2	yes	—
413	C₂	C₁₉×#2066	1	2	yes	—
414	C₂	C₁₉×#2088	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₂×C₁₉×C₄⋊C₈	C₄	semidirect
114. #11231	C₁₉	direct (N × H)
147. C₂×C₄×C₁₉	#106	semidirect
213. C₂×C₄⋊C₈	C₄×C₁₉	semidirect
264. C₁₉	#11231	direct (N × H)
354. C₂×C₄	C₁₉×#106	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₉×#106	2
C₂²×C₁₉×C₄⋊C₈	2
C₂×C₁₉×#340	2
C₁₉×C₄⋊#95	2
#11231	19

Subgroups — C19×#11231 #18017190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11231 #18017190