Subgroups — C₄×C₁₉×#487 #18027600

Order 4864.

878 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#487	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1933	C₂	1	4	yes	maximal
7	C₁₉×#1834	C₂	1	1	yes	maximal, characteristic
8	C₄×C₁₉×#103	C₂	1	4	yes	maximal
9	C₄²×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
13	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
14	C₁₉×#487	C₄	1	8	yes	direct product factor
15	C₂×C₁₉×#103	C₂²	1	4	yes	—
16	C₂×C₁₉×#103	C₂²	1	4	yes	—
17	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#391	—	2	1	no	—
22	C₁₉×#391	C₂²	1	2	yes	—
23	C₁₉×#389	—	2	1	no	—
24	C₁₉×#389	—	2	1	no	—
25	C₁₉×#389	—	2	1	no	—
26	C₁₉×#389	C₂²	1	2	yes	—
27	C₁₉×#384	C₂²	1	1	yes	characteristic
28	C₁₉×#384	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
33	C₄³×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#340	C₂²	1	4	yes	—
35	C₁₉×#340	C₂²	1	4	yes	—
36	C₂²×Q₈×C₁₉	—	2	1	no	—
37	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
40	C₁₉×C₄⋊Q₈	—	2	2	no	—
41	C₁₉×C₄⋊Q₈	—	2	2	no	—
42	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
43	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
44	C₄×Q₈×C₁₉	—	2	8	no	—
45	C₄×Q₈×C₁₉	—	4	4	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
58	C₂×C₄²×C₁₉	—	2	2	no	—
59	C₂×C₄²×C₁₉	—	2	2	no	—
60	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
67	C₁₉×#103	—	2	8	no	—
68	C₁₉×#103	C₂×C₄	1	16	yes	—
69	C₄×C₈×C₁₉	—	2	4	no	—
70	C₄×C₈×C₁₉	—	2	2	no	—
71	C₄×C₈×C₁₉	—	2	4	no	—
72	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
73	C₁₉×#95	—	2	2	no	—
74	C₁₉×#95	—	2	2	no	—
75	C₁₉×#95	—	2	2	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₂×Q₈×C₁₉	—	2	4	no	—
78	C₂×Q₈×C₁₉	—	2	2	no	—
79	C₂×Q₈×C₁₉	—	2	4	no	—
80	C₂×Q₈×C₁₉	—	2	4	no	—
81	C₂×Q₈×C₁₉	—	4	2	no	—
82	C₂×Q₈×C₁₉	—	4	2	no	—
83	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
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	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
95	C₂×C₈×C₁₉	—	2	2	no	—
96	C₂×C₈×C₁₉	—	2	2	no	—
97	C₂×C₈×C₁₉	—	2	2	no	—
98	C₂×C₈×C₁₉	—	2	2	no	—
99	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₁₉	#41	1	4	yes	—
101	C₄⋊C₄×C₁₉	—	2	4	no	—
102	C₄⋊C₄×C₁₉	—	2	4	no	—
103	C₄⋊C₄×C₁₉	—	2	4	no	—
104	C₄⋊C₄×C₁₉	—	2	2	no	—
105	C₄⋊C₄×C₁₉	—	2	4	no	—
106	C₄⋊C₄×C₁₉	—	2	4	no	—
107	C₄⋊C₄×C₁₉	—	4	4	no	—
108	C₄⋊C₄×C₁₉	—	4	4	no	—
109	C₄⋊C₄×C₁₉	—	4	2	no	—
110	C₄⋊C₄×C₁₉	—	4	2	no	—
111	C₄⋊C₄×C₁₉	—	4	2	no	—
112	C₄⋊C₄×C₁₉	—	4	2	no	—
113	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
114	C₄²×C₁₉	—	2	2	no	—
115	C₄²×C₁₉	—	2	2	no	—
116	C₄²×C₁₉	—	2	2	no	—
117	C₄²×C₁₉	—	4	4	no	—
118	C₄²×C₁₉	—	4	4	no	—
119	C₄²×C₁₉	SD₁₆	1	4	yes	—
120	C₄²×C₁₉	Q₁₆	1	4	yes	—
121	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
122	C₄²×C₁₉	#41	1	2	yes	—
123	C₄²×C₁₉	#41	1	4	yes	—
124	C₄×#487	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
126	Q₈×C₁₉	—	2	8	no	—
127	Q₈×C₁₉	—	4	4	no	—
128	Q₈×C₁₉	—	4	8	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	4	no	—
136	C₂×C₄×C₁₉	—	2	4	no	—
137	C₂×C₄×C₁₉	—	4	2	no	—
138	C₂×C₄×C₁₉	—	4	2	no	—
139	C₂×C₄×C₁₉	—	4	2	no	—
140	C₂×C₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	2	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
148	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₁₉	#124	1	2	yes	—
150	C₂×C₄×C₁₉	#124	1	2	yes	—
151	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
152	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
153	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
154	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
155	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
156	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
157	C₂×C₄×C₁₉	#135	1	2	yes	—
158	C₂×C₄×C₁₉	#135	1	2	yes	—
159	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
161	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
162	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
163	C₈×C₁₉	—	2	4	no	—
164	C₈×C₁₉	—	2	4	no	—
165	C₂×#487	C₂×C₁₉	1	1	yes	characteristic
166	C₄×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
167	C₄×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
168	#1990	C₂×C₁₉	1	1	yes	characteristic
169	#1956	C₂×C₁₉	1	1	yes	characteristic
170	#1933	C₂×C₁₉	1	4	yes	—
171	#1834	C₂×C₁₉	1	1	yes	characteristic
172	C₄×#103	C₂×C₁₉	1	4	yes	—
173	C₄²×C₈	C₂×C₁₉	1	1	yes	characteristic
174	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
175	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
176	C₂²×C₁₉	#532	1	1	yes	characteristic
177	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
178	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
179	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
180	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
181	C₄×C₁₉	—	2	2	no	—
182	C₄×C₁₉	—	2	2	no	—
183	C₄×C₁₉	—	2	2	no	—
184	C₄×C₁₉	—	4	4	no	—
185	C₄×C₁₉	—	4	4	no	—
186	C₄×C₁₉	—	8	2	no	—
187	C₄×C₁₉	—	8	2	no	—
188	C₄×C₁₉	C₄×SD₁₆	1	4	yes	—
189	C₄×C₁₉	C₄×Q₁₆	1	4	yes	—
190	C₄×C₁₉	#487	1	4	yes	direct product factor
191	C₄×C₁₉	C₄×#41	1	2	yes	—
192	C₄×C₁₉	#529	1	2	yes	—
193	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
194	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
195	C₂×C₄×Q₈	—	2	1	no	—
196	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
197	#487	C₄×C₁₉	1	8	yes	direct product factor
198	C₂×#103	C₂²×C₁₉	1	4	yes	—
199	C₂×#103	C₂²×C₁₉	1	4	yes	—
200	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
201	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
202	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
203	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
204	#391	—	2	1	no	—
205	#391	C₂²×C₁₉	1	2	yes	—
206	#389	—	2	1	no	—
207	#389	—	2	1	no	—
208	#389	—	2	1	no	—
209	#389	C₂²×C₁₉	1	2	yes	—
210	#384	C₂²×C₁₉	1	1	yes	characteristic
211	#384	C₂²×C₁₉	1	1	yes	characteristic
212	C₄×C₄⋊C₄	—	2	1	no	—
213	C₄×C₄⋊C₄	—	2	1	no	—
214	C₄×C₄⋊C₄	—	2	1	no	—
215	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
216	C₄³	C₂²×C₁₉	1	1	yes	characteristic
217	#340	C₂²×C₁₉	1	4	yes	—
218	#340	C₂²×C₁₉	1	4	yes	—
219	C₂×C₁₉	C₄×#124	1	1	yes	characteristic
220	C₂×C₁₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
221	C₂×C₁₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
222	C₂×C₁₉	C₂×#487	1	1	yes	characteristic
223	C₂×C₁₉	#3131	1	1	yes	characteristic
224	C₂×C₁₉	#3167	1	1	yes	characteristic
225	C₂×C₁₉	#3170	1	1	yes	characteristic
226	C₂²×Q₈	—	2	1	no	—
227	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
228	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
229	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
230	C₄⋊Q₈	—	2	2	no	—
231	C₄⋊Q₈	—	2	2	no	—
232	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
233	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
234	C₄×Q₈	—	2	8	no	—
235	C₄×Q₈	—	4	4	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
248	C₂×C₄²	—	2	2	no	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
251	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
252	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
253	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
254	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
257	#103	—	2	8	no	—
258	#103	C₂×C₄×C₁₉	1	16	yes	—
259	C₄×C₈	—	2	4	no	—
260	C₄×C₈	—	2	2	no	—
261	C₄×C₈	—	2	4	no	—
262	C₄×C₈	C₂×C₄×C₁₉	1	4	yes	—
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	#95	—	2	2	no	—
266	#95	—	2	2	no	—
267	C₁₉	C₄×#487	1	1	yes	characteristic, direct product factor, Sylow
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	2	4	no	—
272	C₂×Q₈	—	4	2	no	—
273	C₂×Q₈	—	4	2	no	—
274	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
291	C₂×C₈	#41×C₁₉	1	4	yes	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	4	4	no	—
299	C₄⋊C₄	—	4	4	no	—
300	C₄⋊C₄	—	4	2	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	4	4	no	—
309	C₄²	—	4	4	no	—
310	C₄²	SD₁₆×C₁₉	1	4	yes	—
311	C₄²	Q₁₆×C₁₉	1	4	yes	—
312	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
313	C₄²	#41×C₁₉	1	2	yes	—
314	C₄²	#41×C₁₉	1	4	yes	—
315	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
316	Q₈	—	2	8	no	—
317	Q₈	—	4	8	no	—
318	Q₈	—	4	4	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
338	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
339	C₂×C₄	C₁₉×#124	1	2	yes	—
340	C₂×C₄	C₁₉×#124	1	2	yes	—
341	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
342	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
343	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
344	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
345	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
346	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
347	C₂×C₄	C₁₉×#135	1	2	yes	—
348	C₂×C₄	C₁₉×#135	1	2	yes	—
349	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
350	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
351	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
352	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
353	C₈	—	2	4	no	—
354	C₈	—	2	4	no	—
355	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
356	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
357	C₂²	C₁₉×#532	1	1	yes	characteristic
358	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
359	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
360	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
361	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	4	4	no	—
366	C₄	—	4	4	no	—
367	C₄	—	8	2	no	—
368	C₄	—	8	2	no	—
369	C₄	C₄×SD₁₆×C₁₉	1	4	yes	—
370	C₄	C₄×Q₁₆×C₁₉	1	4	yes	—
371	C₄	C₁₉×#487	1	4	yes	direct product factor
372	C₄	C₄×#41×C₁₉	1	2	yes	—
373	C₄	C₁₉×#529	1	2	yes	—
374	C₂	C₄×C₁₉×#124	1	1	yes	characteristic
375	C₂	C₂×C₄×SD₁₆×C₁₉	1	1	yes	characteristic
376	C₂	C₂×C₄×Q₁₆×C₁₉	1	1	yes	characteristic
377	C₂	C₂×C₁₉×#487	1	1	yes	characteristic
378	C₂	C₁₉×#3131	1	1	yes	characteristic
379	C₂	C₁₉×#3167	1	1	yes	characteristic
380	C₂	C₁₉×#3170	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
14. C₁₉×#487	C₄	direct (N × H)
124. C₄×#487	C₁₉	direct (N × H)
190. C₄×C₁₉	#487	direct (N × H)
197. #487	C₄×C₁₉	direct (N × H)
267. C₁₉	C₄×#487	direct (N × H)
371. C₄	C₁₉×#487	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×#487	2
C₄×C₁₉×C₄⋊Q₈	2
C₁₉×#1990	2
C₁₉×#1956	2
C₁₉×#1933	2
C₁₉×#1834	2
C₄×C₁₉×#103	2
C₄²×C₈×C₁₉	2
C₄×#487	19

Subgroups — C4×C19×#487 #18027600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉×#487 #18027600