Subgroups — C₁₉×#22219 #18028178

Order 4864.

990 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#486	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉×#127	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1957	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1926	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1864	C₂	1	4	yes	maximal, complemented
8	C₁₉×#1844	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1744	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
13	C₂×C₄×D₄×C₁₉	—	2	1	no	—
14	C₂×C₄×D₄×C₁₉	—	2	1	no	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
16	C₁₉×#486	C₄	1	8	yes	complemented
17	C₂×C₁₉×#106	C₂²	1	4	yes	—
18	C₂×C₁₉×#102	C₂²	1	4	yes	—
19	C₂×C₁₉×#102	C₂²	1	4	yes	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#391	—	2	1	no	—
23	C₁₉×#390	—	2	1	no	—
24	C₁₉×#390	—	2	1	no	—
25	C₁₉×#390	C₂²	1	2	yes	—
26	C₁₉×#389	—	2	1	no	—
27	C₁₉×#389	C₂²	1	2	yes	—
28	C₁₉×#384	C₂²	1	1	yes	characteristic
29	C₁₉×#384	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
32	C₄³×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#340	C₂²	1	4	yes	—
34	C₁₉×#336	C₂²	1	2	yes	—
35	C₁₉×#336	C₂²	1	2	yes	—
36	C₂²×Q₈×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	—	2	1	no	—
39	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₉	—	2	2	no	—
41	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
43	C₁₉×C₄⋊Q₈	—	2	2	no	—
44	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
45	C₁₉×#127	—	2	2	no	—
46	C₁₉×#127	C₂×C₄	1	4	yes	—
47	C₄×Q₈×C₁₉	—	4	4	no	—
48	C₄×D₄×C₁₉	—	4	4	no	—
49	C₄×D₄×C₁₉	—	4	4	no	—
50	C₄×D₄×C₁₉	—	4	4	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₄²×C₁₉	—	2	2	no	—
64	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
71	C₁₉×#106	—	4	4	no	—
72	C₁₉×#102	—	4	4	no	—
73	C₁₉×#102	C₂×C₄	1	16	yes	complemented
74	C₄×C₈×C₁₉	—	2	2	no	—
75	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	complemented
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₂⁴×C₁₉	—	2	2	no	—
79	C₂×Q₈×C₁₉	—	2	4	no	—
80	C₂×Q₈×C₁₉	—	4	2	no	—
81	C₂×Q₈×C₁₉	—	4	2	no	—
82	C₂×D₄×C₁₉	—	2	4	no	—
83	C₂×D₄×C₁₉	—	2	4	no	—
84	C₂×D₄×C₁₉	—	2	2	no	—
85	C₂×D₄×C₁₉	—	2	4	no	—
86	C₂×D₄×C₁₉	—	2	4	no	—
87	C₂×D₄×C₁₉	—	4	2	no	—
88	C₂×D₄×C₁₉	—	4	2	no	—
89	C₂×D₄×C₁₉	—	4	2	no	—
90	C₂×D₄×C₁₉	—	4	2	no	—
91	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	4	4	no	—
96	C₂²×C₄×C₁₉	—	4	4	no	—
97	C₂²×C₄×C₁₉	—	4	4	no	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
111	C₄⋊C₄×C₁₉	—	2	4	no	—
112	C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	—	2	4	no	—
114	C₄⋊C₄×C₁₉	—	2	4	no	—
115	C₄⋊C₄×C₁₉	—	4	4	no	—
116	C₄⋊C₄×C₁₉	—	4	2	no	—
117	C₄⋊C₄×C₁₉	—	4	2	no	—
118	C₄⋊C₄×C₁₉	—	4	2	no	—
119	C₄⋊C₄×C₁₉	—	4	2	no	—
120	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
121	C₂²⋊C₄×C₁₉	—	4	4	no	—
122	C₂²⋊C₄×C₁₉	—	4	4	no	—
123	C₂²⋊C₄×C₁₉	—	4	4	no	—
124	C₄²×C₁₉	—	2	2	no	—
125	C₄²×C₁₉	—	2	2	no	—
126	C₄²×C₁₉	—	2	2	no	—
127	C₄²×C₁₉	—	2	2	no	—
128	C₄²×C₁₉	—	2	2	no	—
129	C₄²×C₁₉	—	4	4	no	—
130	C₄²×C₁₉	SD₁₆	1	4	yes	—
131	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
132	C₄²×C₁₉	#41	1	2	yes	—
133	#22219	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₁₉	—	2	4	no	—
135	C₂³×C₁₉	—	4	2	no	—
136	C₂³×C₁₉	—	4	2	no	—
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
142	Q₈×C₁₉	—	4	8	no	—
143	D₄×C₁₉	—	2	8	no	—
144	D₄×C₁₉	—	4	4	no	—
145	D₄×C₁₉	—	4	8	no	—
146	D₄×C₁₉	—	4	8	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	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	—	8	8	no	—
167	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
170	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
171	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
172	C₂×C₄×C₁₉	#135	1	2	yes	—
173	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
174	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
175	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
178	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
179	C₈×C₁₉	—	2	4	no	—
180	C₈×C₁₉	—	4	2	no	—
181	C₂×#486	C₂×C₁₉	1	1	yes	characteristic
182	C₄×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
183	C₄×#127	C₂×C₁₉	1	1	yes	characteristic
184	#1990	C₂×C₁₉	1	1	yes	characteristic, complemented
185	#1957	C₂×C₁₉	1	1	yes	characteristic
186	#1926	C₂×C₁₉	1	4	yes	complemented
187	#1864	C₂×C₁₉	1	4	yes	complemented
188	#1844	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#1744	C₂×C₁₉	1	1	yes	characteristic, complemented
190	C₂²×C₁₉	—	4	4	no	—
191	C₂²×C₁₉	—	4	4	no	—
192	C₂²×C₁₉	—	4	4	no	—
193	C₂²×C₁₉	—	8	2	no	—
194	C₂²×C₁₉	—	8	2	no	—
195	C₂²×C₁₉	—	8	2	no	—
196	C₂²×C₁₉	—	8	2	no	—
197	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₁₉	#535	1	1	yes	characteristic
199	C₂²×C₁₉	#536	1	1	yes	characteristic
200	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
201	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
202	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₄×C₁₉	—	2	2	no	—
205	C₄×C₁₉	—	2	2	no	—
206	C₄×C₁₉	—	4	4	no	—
207	C₄×C₁₉	—	4	1	no	—
208	C₄×C₁₉	—	4	1	no	—
209	C₄×C₁₉	—	8	2	no	—
210	C₄×C₁₉	—	8	2	no	—
211	C₄×C₁₉	C₄×SD₁₆	1	4	yes	—
212	C₄×C₁₉	#442	1	4	yes	—
213	C₄×C₁₉	#520	1	2	yes	—
214	C₄×C₁₉	#542	1	2	yes	—
215	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
216	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×C₄×Q₈	—	2	1	no	—
218	C₂×C₄×D₄	—	2	1	no	—
219	C₂×C₄×D₄	—	2	1	no	—
220	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
221	#486	C₄×C₁₉	1	8	yes	complemented
222	C₂×#106	C₂²×C₁₉	1	4	yes	—
223	C₂×#102	C₂²×C₁₉	1	4	yes	—
224	C₂×#102	C₂²×C₁₉	1	4	yes	—
225	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
226	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
227	#391	—	2	1	no	—
228	#390	—	2	1	no	—
229	#390	—	2	1	no	—
230	#390	C₂²×C₁₉	1	2	yes	—
231	#389	—	2	1	no	—
232	#389	C₂²×C₁₉	1	2	yes	—
233	#384	C₂²×C₁₉	1	1	yes	characteristic
234	#384	C₂²×C₁₉	1	1	yes	characteristic
235	C₄×C₄⋊C₄	—	2	1	no	—
236	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
237	C₄³	C₂²×C₁₉	1	1	yes	characteristic
238	#340	C₂²×C₁₉	1	4	yes	—
239	#336	C₂²×C₁₉	1	2	yes	—
240	#336	C₂²×C₁₉	1	2	yes	—
241	C₂×C₁₉	—	8	4	no	—
242	C₂×C₁₉	#2326	1	1	yes	characteristic
243	C₂×C₁₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
244	C₂×C₁₉	C₂×#442	1	1	yes	characteristic
245	C₂×C₁₉	#3207	1	1	yes	characteristic
246	C₂×C₁₉	#3208	1	1	yes	characteristic
247	C₂×C₁₉	#3227	1	1	yes	characteristic
248	C₂×C₁₉	#3228	1	1	yes	characteristic
249	C₂²×Q₈	—	2	1	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
253	C₂³×C₄	—	2	2	no	—
254	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
255	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
256	C₄⋊Q₈	—	2	2	no	—
257	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
258	#127	—	2	2	no	—
259	#127	C₂×C₄×C₁₉	1	4	yes	—
260	C₄×Q₈	—	4	4	no	—
261	C₄×D₄	—	4	4	no	—
262	C₄×D₄	—	4	4	no	—
263	C₄×D₄	—	4	4	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
278	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
279	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
280	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
284	#106	—	4	4	no	—
285	#102	—	4	4	no	—
286	#102	C₂×C₄×C₁₉	1	16	yes	complemented
287	C₄×C₈	—	2	2	no	—
288	C₄×C₈	C₂×C₄×C₁₉	1	4	yes	complemented
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	C₁₉	#22219	1	1	yes	characteristic, direct product factor, Sylow
292	C₂⁴	—	2	2	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	4	2	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	4	4	no	—
310	C₂²×C₄	—	4	4	no	—
311	C₂²×C₄	—	4	4	no	—
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×D₄×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
335	C₂²⋊C₄	—	4	4	no	—
336	C₂²⋊C₄	—	4	4	no	—
337	C₂²⋊C₄	—	4	4	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	4	4	no	—
344	C₄²	SD₁₆×C₁₉	1	4	yes	—
345	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
346	C₄²	#41×C₁₉	1	2	yes	—
347	C₂³	—	2	4	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
355	Q₈	—	4	8	no	—
356	D₄	—	2	8	no	—
357	D₄	—	4	8	no	—
358	D₄	—	4	8	no	—
359	D₄	—	4	4	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	8	8	no	—
380	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
381	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
382	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
383	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
384	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
385	C₂×C₄	C₁₉×#135	1	2	yes	—
386	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
387	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
388	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
389	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
390	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
391	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
392	C₈	—	2	4	no	—
393	C₈	—	4	2	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
402	C₂²	C₁₉×#535	1	1	yes	characteristic
403	C₂²	C₁₉×#536	1	1	yes	characteristic
404	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
405	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
406	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
407	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	8	2	no	—
414	C₄	—	8	2	no	—
415	C₄	C₄×SD₁₆×C₁₉	1	4	yes	—
416	C₄	C₁₉×#442	1	4	yes	—
417	C₄	C₁₉×#520	1	2	yes	—
418	C₄	C₁₉×#542	1	2	yes	—
419	C₂	—	8	4	no	—
420	C₂	C₁₉×#2326	1	1	yes	characteristic
421	C₂	C₂×C₄×SD₁₆×C₁₉	1	1	yes	characteristic
422	C₂	C₂×C₁₉×#442	1	1	yes	characteristic
423	C₂	C₁₉×#3207	1	1	yes	characteristic
424	C₂	C₁₉×#3208	1	1	yes	characteristic
425	C₂	C₁₉×#3227	1	1	yes	characteristic
426	C₂	C₁₉×#3228	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₉×C₄⋊Q₈	C₂	semidirect
4. C₁₉×#1990	C₂	semidirect
6. C₁₉×#1926	C₂	semidirect
7. C₁₉×#1864	C₂	semidirect
8. C₁₉×#1844	C₂	semidirect
9. C₁₉×#1744	C₂	semidirect
16. C₁₉×#486	C₄	semidirect
44. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
73. C₁₉×#102	C₂×C₄	semidirect
75. C₄×C₈×C₁₉	C₂×C₄	semidirect
133. #22219	C₁₉	direct (N × H)
182. C₄×C₄⋊Q₈	C₂×C₁₉	semidirect
184. #1990	C₂×C₁₉	semidirect
186. #1926	C₂×C₁₉	semidirect
187. #1864	C₂×C₁₉	semidirect
188. #1844	C₂×C₁₉	semidirect
189. #1744	C₂×C₁₉	semidirect
221. #486	C₄×C₁₉	semidirect
257. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
286. #102	C₂×C₄×C₁₉	semidirect
288. C₄×C₈	C₂×C₄×C₁₉	semidirect
291. C₁₉	#22219	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×#486	2
C₄×C₁₉×C₄⋊Q₈	2
C₄×C₁₉×#127	2
C₁₉×#1990	2
C₁₉×#1957	2
C₁₉×#1926	2
C₁₉×#1864	2
C₁₉×#1844	2
C₁₉×#1744	2
#22219	19

Subgroups — C19×#22219 #18028178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22219 #18028178