Subgroups — C₁₉×#23096 #18029055

Order 4864.

826 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	C₂×C₁₉×#462	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2365	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2355	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1969	C₂	1	2	yes	maximal
5	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1947	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1928	C₂	1	2	yes	maximal
8	C₁₉×#1878	C₂	1	2	yes	maximal
9	C₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
10	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₉×#103	C₂	1	2	yes	maximal
12	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#462	C₄	1	8	yes	complemented
17	C₂×C₁₉×#107	C₂²	1	2	yes	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#103	C₂²	1	2	yes	—
20	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#103	C₂²	1	2	yes	—
23	C₂×C₁₉×#103	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
26	C₁₉×#391	C₂²	1	2	yes	—
27	C₁₉×#391	C₂²	1	2	yes	—
28	C₁₉×#389	—	2	1	no	—
29	C₁₉×#387	—	2	2	no	—
30	C₁₉×#387	—	2	2	no	—
31	C₁₉×#384	C₂²	1	1	yes	characteristic
32	C₁₉×#382	—	2	1	no	—
33	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₁₉×#340	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	1	yes	characteristic
41	C₁₉×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
44	C₂×Q₁₆×C₁₉	—	4	2	no	—
45	C₂×Q₁₆×C₁₉	—	4	2	no	—
46	C₂×Q₁₆×C₁₉	C₂×C₄	1	8	yes	—
47	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₁₉×C₄⋊Q₈	—	2	2	no	—
51	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
52	C₄×Q₈×C₁₉	—	2	2	no	—
53	C₄×Q₈×C₁₉	—	2	4	no	—
54	C₄×Q₈×C₁₉	—	4	2	no	—
55	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	—	2	1	no	—
70	C₂×C₄²×C₁₉	—	2	2	no	—
71	C₂×C₄²×C₁₉	—	2	2	no	—
72	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
73	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×#107	—	4	2	no	—
75	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
76	C₁₉×#103	—	2	4	no	—
77	C₁₉×#103	—	2	2	no	—
78	C₁₉×#103	—	2	2	no	—
79	C₁₉×#103	—	4	2	no	—
80	C₁₉×#103	C₂×C₄	1	8	yes	—
81	C₄×C₈×C₁₉	—	2	2	no	—
82	C₄×C₈×C₁₉	—	4	2	no	—
83	C₁₉×#95	—	2	2	no	—
84	C₁₉×#95	—	2	2	no	—
85	C₁₉×#95	—	2	2	no	—
86	C₁₉×#95	—	2	1	no	—
87	C₁₉×#95	—	2	2	no	—
88	C₁₉×#95	—	2	2	no	—
89	C₁₉×#95	D₄	1	2	yes	—
90	C₂×Q₈×C₁₉	—	2	1	no	—
91	C₂×Q₈×C₁₉	—	2	2	no	—
92	C₂×Q₈×C₁₉	—	2	2	no	—
93	C₂×Q₈×C₁₉	—	2	1	no	—
94	C₂×Q₈×C₁₉	—	2	1	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	1	no	—
98	C₂×Q₈×C₁₉	—	2	1	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
101	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
113	Q₁₆×C₁₉	—	4	8	no	—
114	C₂×C₈×C₁₉	—	2	1	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	2	1	no	—
118	C₂×C₈×C₁₉	—	2	1	no	—
119	C₂×C₈×C₁₉	—	2	1	no	—
120	C₂×C₈×C₁₉	—	2	1	no	—
121	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
122	C₂×C₈×C₁₉	#41	1	2	yes	—
123	C₄⋊C₄×C₁₉	—	2	4	no	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	—	2	4	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	4	4	no	—
134	C₄⋊C₄×C₁₉	—	4	2	no	—
135	C₄⋊C₄×C₁₉	—	8	1	no	—
136	C₄⋊C₄×C₁₉	Q₁₆	1	4	yes	complemented
137	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
138	C₄⋊C₄×C₁₉	#41	1	2	yes	—
139	C₄²×C₁₉	—	2	4	no	—
140	C₄²×C₁₉	—	2	2	no	—
141	C₄²×C₁₉	—	2	2	no	—
142	C₄²×C₁₉	—	4	4	no	—
143	C₄²×C₁₉	—	4	2	no	—
144	C₄²×C₁₉	—	8	2	no	—
145	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
146	C₄²×C₁₉	#41	1	2	yes	—
147	#23096	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₁₉	—	2	4	no	—
150	Q₈×C₁₉	—	2	2	no	—
151	Q₈×C₁₉	—	2	2	no	—
152	Q₈×C₁₉	—	2	4	no	—
153	Q₈×C₁₉	—	4	1	no	—
154	Q₈×C₁₉	—	4	2	no	—
155	Q₈×C₁₉	—	4	1	no	—
156	Q₈×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
183	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₁₉	C₂×Q₁₆	1	4	yes	—
185	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
186	C₂×C₄×C₁₉	#135	1	2	yes	—
187	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
193	C₈×C₁₉	—	2	4	no	—
194	C₈×C₁₉	—	2	2	no	—
195	C₈×C₁₉	—	4	1	no	—
196	C₂×#462	C₂×C₁₉	1	1	yes	characteristic
197	#2365	C₂×C₁₉	1	1	yes	characteristic
198	#2355	C₂×C₁₉	1	1	yes	characteristic
199	#1969	C₂×C₁₉	1	2	yes	—
200	#1956	C₂×C₁₉	1	1	yes	characteristic
201	#1947	C₂×C₁₉	1	1	yes	characteristic
202	#1928	C₂×C₁₉	1	2	yes	—
203	#1878	C₂×C₁₉	1	2	yes	—
204	C₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
205	C₄×#103	C₂×C₁₉	1	2	yes	—
206	C₄×#103	C₂×C₁₉	1	1	yes	characteristic
207	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂²×C₁₉	#546	1	1	yes	characteristic
209	C₂²×C₁₉	#550	1	1	yes	characteristic
210	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
211	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
212	C₂²×C₁₉	#577	1	1	yes	characteristic
213	C₂²×C₁₉	#578	1	1	yes	characteristic
214	C₄×C₁₉	—	2	2	no	—
215	C₄×C₁₉	—	2	4	no	—
216	C₄×C₁₉	—	4	2	no	—
217	C₄×C₁₉	—	4	4	no	—
218	C₄×C₁₉	—	4	2	no	—
219	C₄×C₁₉	—	4	2	no	—
220	C₄×C₁₉	—	4	2	no	—
221	C₄×C₁₉	—	8	1	no	—
222	C₄×C₁₉	—	8	2	no	—
223	C₄×C₁₉	C₄×Q₁₆	1	4	yes	—
224	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
225	C₄×C₁₉	#518	1	1	yes	characteristic
226	C₄×C₁₉	#553	1	1	yes	characteristic
227	C₄×C₁₉	#555	1	1	yes	characteristic
228	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	—
229	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
230	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
231	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
232	#462	C₄×C₁₉	1	8	yes	complemented
233	C₂×#107	C₂²×C₁₉	1	2	yes	—
234	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×#103	C₂²×C₁₉	1	2	yes	—
237	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×#103	C₂²×C₁₉	1	2	yes	—
239	C₂×#103	C₂²×C₁₉	1	2	yes	—
240	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
241	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
242	#391	C₂²×C₁₉	1	2	yes	—
243	#391	C₂²×C₁₉	1	2	yes	—
244	#389	—	2	1	no	—
245	#387	—	2	2	no	—
246	#387	—	2	2	no	—
247	#384	C₂²×C₁₉	1	1	yes	characteristic
248	#382	—	2	1	no	—
249	C₄×C₄⋊C₄	—	2	1	no	—
250	C₄×C₄⋊C₄	—	2	1	no	—
251	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
252	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
253	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
254	#340	C₂²×C₁₉	1	2	yes	—
255	#340	C₂²×C₁₉	1	1	yes	characteristic
256	#340	C₂²×C₁₉	1	1	yes	characteristic
257	#336	C₂²×C₁₉	1	2	yes	—
258	C₂×C₁₉	#2363	1	1	yes	characteristic
259	C₂×C₁₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
260	C₂×C₁₉	#2947	1	1	yes	characteristic
261	C₂×C₁₉	#3299	1	1	yes	characteristic
262	C₂×C₁₉	#3302	1	1	yes	characteristic
263	C₂×C₁₉	#3394	1	1	yes	characteristic
264	C₂×C₁₉	#3395	1	1	yes	characteristic
265	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
266	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
267	C₂×Q₁₆	—	4	2	no	—
268	C₂×Q₁₆	—	4	2	no	—
269	C₂×Q₁₆	C₂×C₄×C₁₉	1	8	yes	—
270	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
272	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
273	C₄⋊Q₈	—	2	2	no	—
274	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×Q₈	—	2	4	no	—
277	C₄×Q₈	—	4	2	no	—
278	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
286	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
296	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
297	#107	—	4	2	no	—
298	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
299	#103	—	2	4	no	—
300	#103	—	2	2	no	—
301	#103	—	2	2	no	—
302	#103	—	4	2	no	—
303	#103	C₂×C₄×C₁₉	1	8	yes	—
304	C₄×C₈	—	2	2	no	—
305	C₄×C₈	—	4	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	1	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	D₄×C₁₉	1	2	yes	—
313	C₁₉	#23096	1	1	yes	characteristic, direct product factor, Sylow
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
325	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
337	Q₁₆	—	4	8	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
346	C₂×C₈	#41×C₁₉	1	2	yes	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	4	4	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	8	1	no	—
360	C₄⋊C₄	Q₁₆×C₁₉	1	4	yes	complemented
361	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
362	C₄⋊C₄	#41×C₁₉	1	2	yes	—
363	C₄²	—	2	4	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	4	4	no	—
367	C₄²	—	4	2	no	—
368	C₄²	—	8	2	no	—
369	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
370	C₄²	#41×C₁₉	1	2	yes	—
371	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
372	Q₈	—	2	2	no	—
373	Q₈	—	2	4	no	—
374	Q₈	—	2	2	no	—
375	Q₈	—	2	4	no	—
376	Q₈	—	4	1	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	4	1	no	—
379	Q₈	—	4	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
406	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
407	C₂×C₄	C₂×Q₁₆×C₁₉	1	4	yes	—
408	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
409	C₂×C₄	C₁₉×#135	1	2	yes	—
410	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
412	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
414	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
415	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
416	C₈	—	2	4	no	—
417	C₈	—	2	2	no	—
418	C₈	—	4	1	no	—
419	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
420	C₂²	C₁₉×#546	1	1	yes	characteristic
421	C₂²	C₁₉×#550	1	1	yes	characteristic
422	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
423	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
424	C₂²	C₁₉×#577	1	1	yes	characteristic
425	C₂²	C₁₉×#578	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	4	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	4	no	—
433	C₄	—	8	1	no	—
434	C₄	—	8	2	no	—
435	C₄	C₄×Q₁₆×C₁₉	1	4	yes	—
436	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
437	C₄	C₁₉×#518	1	1	yes	characteristic
438	C₄	C₁₉×#553	1	1	yes	characteristic
439	C₄	C₁₉×#555	1	1	yes	characteristic
440	C₂	C₁₉×#2363	1	1	yes	characteristic
441	C₂	C₂×C₄×Q₁₆×C₁₉	1	1	yes	characteristic
442	C₂	C₁₉×#2947	1	1	yes	characteristic
443	C₂	C₁₉×#3299	1	1	yes	characteristic
444	C₂	C₁₉×#3302	1	1	yes	characteristic
445	C₂	C₁₉×#3394	1	1	yes	characteristic
446	C₂	C₁₉×#3395	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
16. C₁₉×#462	C₄	semidirect
136. C₄⋊C₄×C₁₉	Q₁₆	semidirect
147. #23096	C₁₉	direct (N × H)
232. #462	C₄×C₁₉	semidirect
313. C₁₉	#23096	direct (N × H)
360. C₄⋊C₄	Q₁₆×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×#462	2
C₁₉×#2365	2
C₁₉×#2355	2
C₁₉×#1969	2
C₁₉×#1956	2
C₁₉×#1947	2
C₁₉×#1928	2
C₁₉×#1878	2
C₈×C₄⋊C₄×C₁₉	2
C₄×C₁₉×#103	2
#23096	19

Subgroups — C19×#23096 #18029055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23096 #18029055