Subgroups — C₁₉×#34389 #18040348

Order 4864.

1926 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2381	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2381	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2368	C₂	1	4	yes	maximal
5	C₁₉×#2356	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2343	C₂	1	4	yes	maximal
7	C₁₉×#2336	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2329	C₂	1	4	yes	maximal
9	C₁₉×#2320	C₂	1	4	yes	maximal, complemented
10	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic
11	C₂×C₁₉×#383	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#533	C₄	1	16	yes	complemented
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#125	C₂²	1	2	yes	—
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
20	C₂×C₁₉×#117	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#391	C₂²	1	8	yes	—
23	C₁₉×#391	C₂²	1	8	yes	—
24	C₁₉×#389	C₂²	1	8	yes	—
25	C₁₉×#387	C₂²	1	8	yes	—
26	C₁₉×#387	C₂²	1	8	yes	—
27	C₁₉×#387	C₂²	1	8	yes	—
28	C₁₉×#387	C₂²	1	8	yes	—
29	C₁₉×#387	C₂²	1	8	yes	—
30	C₁₉×#387	C₂²	1	8	yes	—
31	C₁₉×#385	C₂²	1	8	yes	—
32	C₁₉×#383	C₂²	1	2	yes	—
33	C₁₉×#383	C₂²	1	2	yes	—
34	C₁₉×#383	C₂²	1	2	yes	—
35	C₁₉×#383	C₂²	1	2	yes	—
36	C₁₉×#383	C₂²	1	2	yes	—
37	C₁₉×#383	C₂²	1	4	yes	—
38	C₁₉×#382	C₂²	1	2	yes	—
39	C₁₉×#382	C₂²	1	4	yes	—
40	C₁₉×#381	C₂²	1	2	yes	—
41	C₁₉×#380	C₂²	1	2	yes	—
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
43	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
44	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
45	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
46	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
47	C₁₉×#376	C₂²	1	2	yes	—
48	C₁₉×#376	C₂²	1	4	yes	—
49	C₂×C₁₉×#95	C₂²	1	2	yes	—
50	C₂×C₁₉×#95	C₂²	1	2	yes	—
51	C₂×C₁₉×#95	C₂²	1	2	yes	—
52	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
53	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
56	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
59	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
60	C₁₉×#125	C₂×C₄	1	16	yes	complemented
61	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
62	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
63	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	complemented
64	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	complemented
65	C₁₉×#117	C₂×C₄	1	16	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
75	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
77	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	—
78	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
79	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
80	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
81	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
83	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₁₉×#95	C₂³	1	4	yes	—
87	C₁₉×#95	C₂³	1	4	yes	—
88	C₁₉×#95	C₂³	1	4	yes	—
89	C₁₉×#95	C₂³	1	4	yes	—
90	C₁₉×#95	C₂³	1	4	yes	—
91	C₁₉×#95	C₂³	1	4	yes	—
92	C₁₉×#95	C₂³	1	4	yes	—
93	C₁₉×#95	C₂³	1	4	yes	—
94	C₁₉×#95	C₂³	1	8	yes	—
95	C₁₉×#95	C₂³	1	4	yes	—
96	C₁₉×#95	C₂³	1	8	yes	—
97	C₁₉×#95	C₂³	1	8	yes	—
98	C₁₉×#95	C₂³	1	4	yes	—
99	C₁₉×#95	C₂³	1	8	yes	—
100	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
101	C₂×Q₈×C₁₉	—	4	2	no	—
102	C₂×Q₈×C₁₉	—	4	4	no	—
103	C₂×Q₈×C₁₉	—	4	2	no	—
104	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
105	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
106	C₂²×C₄×C₁₉	—	2	4	no	—
107	C₂²×C₄×C₁₉	—	2	8	no	—
108	C₂²×C₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	—	4	2	no	—
110	C₂²×C₄×C₁₉	—	4	4	no	—
111	C₂²×C₄×C₁₉	—	4	4	no	—
112	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
113	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
114	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
115	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
116	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
117	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
125	C₄⋊C₄×C₁₉	—	4	8	no	—
126	C₄⋊C₄×C₁₉	—	4	4	no	—
127	C₄⋊C₄×C₁₉	—	4	8	no	—
128	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
129	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
130	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
131	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
132	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
133	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
134	C₂²⋊C₄×C₁₉	—	2	8	no	—
135	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
136	C₄²×C₁₉	—	4	4	no	—
137	C₄²×C₁₉	—	4	8	no	—
138	C₄²×C₁₉	—	4	8	no	—
139	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
140	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
141	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
142	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
143	C₄²×C₁₉	C₂²×C₄	1	16	yes	—
144	#34389	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	2	2	no	—
147	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
148	C₂³×C₁₉	2₋¹⁺⁴	1	4	yes	—
149	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
150	Q₈×C₁₉	—	4	8	no	—
151	Q₈×C₁₉	—	4	8	no	—
152	C₂×C₄×C₁₉	—	2	8	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	8	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	8	no	—
163	C₂×C₄×C₁₉	—	2	8	no	—
164	C₂×C₄×C₁₉	—	2	8	no	—
165	C₂×C₄×C₁₉	—	2	8	no	—
166	C₂×C₄×C₁₉	—	2	8	no	—
167	C₂×C₄×C₁₉	—	2	8	no	—
168	C₂×C₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	4	4	no	—
170	C₂×C₄×C₁₉	—	8	8	no	—
171	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
172	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
173	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
174	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
175	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
176	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
177	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
178	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
179	C₂×#533	C₂×C₁₉	1	1	yes	characteristic
180	#2381	C₂×C₁₉	1	2	yes	complemented
181	#2381	C₂×C₁₉	1	2	yes	complemented
182	#2368	C₂×C₁₉	1	4	yes	—
183	#2356	C₂×C₁₉	1	4	yes	complemented
184	#2343	C₂×C₁₉	1	4	yes	—
185	#2336	C₂×C₁₉	1	4	yes	complemented
186	#2329	C₂×C₁₉	1	4	yes	—
187	#2320	C₂×C₁₉	1	4	yes	complemented
188	#2283	C₂×C₁₉	1	1	yes	characteristic
189	C₂×#383	C₂×C₁₉	1	1	yes	characteristic
190	C₂²×C₁₉	—	2	2	no	—
191	C₂²×C₁₉	—	2	2	no	—
192	C₂²×C₁₉	—	2	8	no	—
193	C₂²×C₁₉	#519	1	4	yes	—
194	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
195	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
196	C₂²×C₁₉	#585	1	2	yes	—
197	C₂²×C₁₉	#585	1	2	yes	—
198	C₄×C₁₉	—	2	2	no	—
199	C₄×C₁₉	—	2	2	no	—
200	C₄×C₁₉	—	2	2	no	—
201	C₄×C₁₉	—	2	2	no	—
202	C₄×C₁₉	—	2	2	no	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	2	8	no	—
205	C₄×C₁₉	—	2	8	no	—
206	C₄×C₁₉	—	4	8	no	—
207	C₄×C₁₉	—	4	8	no	—
208	#533	C₄×C₁₉	1	16	yes	complemented
209	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
210	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×#125	C₂²×C₁₉	1	2	yes	—
212	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
213	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
214	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
215	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
216	C₂×#117	C₂²×C₁₉	1	2	yes	—
217	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
218	#391	C₂²×C₁₉	1	8	yes	—
219	#391	C₂²×C₁₉	1	8	yes	—
220	#389	C₂²×C₁₉	1	8	yes	—
221	#387	C₂²×C₁₉	1	8	yes	—
222	#387	C₂²×C₁₉	1	8	yes	—
223	#387	C₂²×C₁₉	1	8	yes	—
224	#387	C₂²×C₁₉	1	8	yes	—
225	#387	C₂²×C₁₉	1	8	yes	—
226	#387	C₂²×C₁₉	1	8	yes	—
227	#385	C₂²×C₁₉	1	8	yes	—
228	#383	C₂²×C₁₉	1	2	yes	—
229	#383	C₂²×C₁₉	1	4	yes	—
230	#383	C₂²×C₁₉	1	2	yes	—
231	#383	C₂²×C₁₉	1	2	yes	—
232	#383	C₂²×C₁₉	1	2	yes	—
233	#383	C₂²×C₁₉	1	2	yes	—
234	#382	C₂²×C₁₉	1	2	yes	—
235	#382	C₂²×C₁₉	1	4	yes	—
236	#381	C₂²×C₁₉	1	2	yes	—
237	#380	C₂²×C₁₉	1	2	yes	—
238	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
239	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
240	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
241	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
242	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
243	#376	C₂²×C₁₉	1	4	yes	—
244	#376	C₂²×C₁₉	1	2	yes	—
245	C₂×#95	C₂²×C₁₉	1	2	yes	—
246	C₂×#95	C₂²×C₁₉	1	2	yes	—
247	C₂×#95	C₂²×C₁₉	1	2	yes	—
248	C₂×C₁₉	—	2	4	no	—
249	C₂×C₁₉	C₂×#519	1	1	yes	characteristic
250	C₂×C₁₉	#3428	1	1	yes	characteristic
251	C₂×C₁₉	#3428	1	1	yes	characteristic
252	C₂×C₁₉	#3564	1	4	yes	—
253	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
254	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
255	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
256	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
257	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
259	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
260	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
261	#125	C₂×C₄×C₁₉	1	16	yes	complemented
262	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
263	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
264	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	complemented
265	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	complemented
266	#117	C₂×C₄×C₁₉	1	16	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
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	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
276	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
277	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
278	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	—
279	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
280	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
281	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
282	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
283	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
284	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
287	#95	C₂³×C₁₉	1	4	yes	—
288	#95	C₂³×C₁₉	1	4	yes	—
289	#95	C₂³×C₁₉	1	4	yes	—
290	#95	C₂³×C₁₉	1	4	yes	—
291	#95	C₂³×C₁₉	1	4	yes	—
292	#95	C₂³×C₁₉	1	4	yes	—
293	#95	C₂³×C₁₉	1	4	yes	—
294	#95	C₂³×C₁₉	1	4	yes	—
295	#95	C₂³×C₁₉	1	8	yes	—
296	#95	C₂³×C₁₉	1	4	yes	—
297	#95	C₂³×C₁₉	1	8	yes	—
298	#95	C₂³×C₁₉	1	8	yes	—
299	#95	C₂³×C₁₉	1	4	yes	—
300	#95	C₂³×C₁₉	1	8	yes	—
301	C₁₉	#34389	1	1	yes	characteristic, direct product factor, Sylow
302	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
303	C₂×Q₈	—	4	2	no	—
304	C₂×Q₈	—	4	4	no	—
305	C₂×Q₈	—	4	2	no	—
306	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
307	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	8	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	4	4	no	—
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
315	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
316	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
317	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
318	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
319	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
321	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
323	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
325	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
326	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
327	C₄⋊C₄	—	4	8	no	—
328	C₄⋊C₄	—	4	4	no	—
329	C₄⋊C₄	—	4	8	no	—
330	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
331	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
332	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
333	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
334	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
335	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
336	C₂²⋊C₄	—	2	8	no	—
337	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
338	C₄²	—	4	4	no	—
339	C₄²	—	4	8	no	—
340	C₄²	—	4	8	no	—
341	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
342	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
343	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
344	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
345	C₄²	C₂²×C₄×C₁₉	1	16	yes	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
349	C₂³	C₁₉×2₋¹⁺⁴	1	4	yes	—
350	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
351	Q₈	—	4	8	no	—
352	Q₈	—	4	8	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	8	8	no	—
372	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
373	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
374	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
375	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
376	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
377	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
378	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
379	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	8	no	—
383	C₂²	C₁₉×#519	1	4	yes	—
384	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
385	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
386	C₂²	C₁₉×#585	1	2	yes	—
387	C₂²	C₁₉×#585	1	2	yes	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	8	no	—
395	C₄	—	2	8	no	—
396	C₄	—	4	8	no	—
397	C₄	—	4	8	no	—
398	C₂	—	2	4	no	—
399	C₂	C₂×C₁₉×#519	1	1	yes	characteristic
400	C₂	C₁₉×#3428	1	1	yes	characteristic
401	C₂	C₁₉×#3428	1	1	yes	characteristic
402	C₂	C₁₉×#3564	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂⁴×C₁₉	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2381	C₂	semidirect
3. C₁₉×#2381	C₂	semidirect
5. C₁₉×#2356	C₂	semidirect
7. C₁₉×#2336	C₂	semidirect
9. C₁₉×#2320	C₂	semidirect
12. C₁₉×#533	C₄	semidirect
58. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
59. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
60. C₁₉×#125	C₂×C₄	semidirect
63. C₄×Q₈×C₁₉	C₂×C₄	semidirect
64. C₄×Q₈×C₁₉	C₂×C₄	semidirect
144. #34389	C₁₉	direct (N × H)
180. #2381	C₂×C₁₉	semidirect
181. #2381	C₂×C₁₉	semidirect
183. #2356	C₂×C₁₉	semidirect
185. #2336	C₂×C₁₉	semidirect
187. #2320	C₂×C₁₉	semidirect
208. #533	C₄×C₁₉	semidirect
259. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
260. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
261. #125	C₂×C₄×C₁₉	semidirect
264. C₄×Q₈	C₂×C₄×C₁₉	semidirect
265. C₄×Q₈	C₂×C₄×C₁₉	semidirect
301. C₁₉	#34389	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×#533	2
C₁₉×#2381	2
C₁₉×#2368	2
C₁₉×#2356	2
C₁₉×#2343	2
C₁₉×#2336	2
C₁₉×#2329	2
C₁₉×#2320	2
C₁₉×#2283	2
C₂×C₁₉×#383	2
#34389	19

Subgroups — C19×#34389 #18040348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34389 #18040348