Subgroups — C₁₉×#10746 #18016705

Order 4864.

1246 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#568	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#413	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2297	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#344	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1728	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#568	—	2	2	no	—
8	C₁₉×#568	—	2	4	no	—
9	C₁₉×#568	C₄	1	4	yes	complemented
10	C₂×C₁₉×#131	—	2	4	no	—
11	C₂²×M₁₆×C₁₉	—	2	2	no	—
12	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#413	—	2	2	no	—
17	C₁₉×#413	C₄	1	4	yes	complemented
18	C₂×C₁₉×#101	—	2	1	no	—
19	C₂×C₁₉×#100	—	2	1	no	—
20	C₁₉×#391	—	2	1	no	—
21	C₁₉×#390	—	2	1	no	—
22	C₁₉×#386	C₄	1	4	yes	—
23	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
24	C₁₉×#344	—	2	4	no	—
25	C₁₉×#336	—	2	4	no	—
26	C₂×#41×C₁₉	—	2	2	no	—
27	C₂×#41×C₁₉	—	2	2	no	—
28	C₂×#41×C₁₉	—	2	2	no	—
29	C₂×#41×C₁₉	—	2	2	no	—
30	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×#41×C₁₉	D₄	1	2	yes	—
33	C₂×#41×C₁₉	Q₈	1	2	yes	—
34	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
36	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₉	D₄	1	2	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₁₉×#131	—	2	16	no	—
41	C₁₉×#131	—	2	16	no	—
42	C₂×M₁₆×C₁₉	—	2	4	no	—
43	C₂×M₁₆×C₁₉	—	2	8	no	—
44	C₂×M₁₆×C₁₉	—	2	8	no	—
45	C₂×M₁₆×C₁₉	—	2	2	no	—
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	2	2	no	—
49	C₂×M₁₆×C₁₉	—	2	2	no	—
50	C₂×M₁₆×C₁₉	—	2	2	no	—
51	C₂×M₁₆×C₁₉	—	2	2	no	—
52	C₂×M₁₆×C₁₉	—	2	2	no	—
53	C₂×M₁₆×C₁₉	—	2	2	no	—
54	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
55	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
56	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
57	C₂²×C₈×C₁₉	—	2	4	no	—
58	C₂²×C₈×C₁₉	—	2	2	no	—
59	C₂²×C₈×C₁₉	D₄	1	4	yes	—
60	C₁₉×#117	—	2	2	no	—
61	C₁₉×#117	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	—	2	2	no	—
69	C₂×C₄²×C₁₉	—	2	2	no	—
70	C₁₉×#101	—	2	4	no	—
71	C₁₉×#100	—	2	4	no	—
72	C₁₉×#95	—	2	4	no	—
73	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
74	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
75	#41×C₁₉	—	2	4	no	—
76	#41×C₁₉	—	2	4	no	—
77	#41×C₁₉	—	2	4	no	—
78	#41×C₁₉	—	2	4	no	—
79	#41×C₁₉	—	2	4	no	—
80	#41×C₁₉	—	2	4	no	—
81	#41×C₁₉	—	2	4	no	—
82	#41×C₁₉	—	2	4	no	—
83	C₂×Q₈×C₁₉	—	2	2	no	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
86	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
87	C₂×D₄×C₁₉	—	2	4	no	—
88	C₂×D₄×C₁₉	—	2	4	no	—
89	C₂×D₄×C₁₉	—	2	2	no	—
90	C₂×D₄×C₁₉	—	2	2	no	—
91	C₂×D₄×C₁₉	C₄²	1	4	yes	—
92	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
93	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
94	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	4	4	no	—
103	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
105	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
106	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	#41	1	2	yes	—
115	C₂²×C₄×C₁₉	#41	1	2	yes	—
116	M₁₆×C₁₉	—	2	16	no	—
117	M₁₆×C₁₉	—	2	4	no	—
118	M₁₆×C₁₉	—	2	4	no	—
119	M₁₆×C₁₉	—	2	4	no	—
120	M₁₆×C₁₉	—	2	4	no	—
121	M₁₆×C₁₉	—	2	4	no	—
122	M₁₆×C₁₉	—	2	4	no	—
123	M₁₆×C₁₉	—	4	2	no	—
124	M₁₆×C₁₉	—	4	2	no	—
125	C₂×C₈×C₁₉	—	2	16	no	—
126	C₂×C₈×C₁₉	—	2	4	no	—
127	C₂×C₈×C₁₉	—	2	4	no	—
128	C₂×C₈×C₁₉	—	2	4	no	—
129	C₂×C₈×C₁₉	—	4	2	no	—
130	C₂×C₈×C₁₉	—	4	2	no	—
131	C₂×C₈×C₁₉	C₂²⋊C₄	1	8	yes	complemented
132	C₄⋊C₄×C₁₉	—	4	2	no	—
133	C₂²⋊C₄×C₁₉	—	2	4	no	—
134	C₂²⋊C₄×C₁₉	—	4	8	no	—
135	C₄²×C₁₉	—	4	1	no	—
136	C₄²×C₁₉	—	4	1	no	—
137	C₄²×C₁₉	—	4	2	no	—
138	C₄²×C₁₉	—	4	1	no	—
139	C₄²×C₁₉	—	4	1	no	—
140	#10746	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₁₉	—	2	2	no	—
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	4	2	no	—
144	C₂³×C₁₉	—	4	4	no	—
145	C₂³×C₁₉	#95	1	4	yes	—
146	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
147	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂³×C₁₉	C₄×D₄	1	2	yes	—
150	C₂³×C₁₉	C₄×D₄	1	2	yes	—
151	Q₈×C₁₉	—	2	4	no	—
152	Q₈×C₁₉	—	2	4	no	—
153	D₄×C₁₉	—	2	8	no	—
154	D₄×C₁₉	—	2	8	no	—
155	D₄×C₁₉	—	2	4	no	—
156	D₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	2	4	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	8	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	#95	1	4	yes	—
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#117	1	2	yes	—
177	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#120	1	2	yes	—
181	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#121	1	2	yes	—
183	C₂×C₄×C₁₉	#121	1	2	yes	—
184	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
185	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
186	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#123	1	2	yes	—
189	C₈×C₁₉	—	2	8	no	—
190	C₈×C₁₉	—	4	4	no	—
191	C₂×#568	C₂×C₁₉	1	1	yes	characteristic
192	C₂×#413	C₂×C₁₉	1	1	yes	characteristic
193	#2297	C₂×C₁₉	1	1	yes	characteristic
194	C₂×#344	C₂×C₁₉	1	2	yes	complemented
195	#1728	C₂×C₁₉	1	2	yes	complemented
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	—	2	4	no	—
198	C₂²×C₁₉	—	2	4	no	—
199	C₂²×C₁₉	—	4	1	no	—
200	C₂²×C₁₉	—	4	1	no	—
201	C₂²×C₁₉	—	4	2	no	—
202	C₂²×C₁₉	—	4	4	no	—
203	C₂²×C₁₉	—	4	4	no	—
204	C₂²×C₁₉	—	8	2	no	—
205	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
206	C₂²×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
207	C₂²×C₁₉	#385	1	2	yes	—
208	C₂²×C₁₉	#386	1	1	yes	characteristic
209	C₂²×C₁₉	#386	1	1	yes	characteristic
210	C₄×C₁₉	—	2	4	no	—
211	C₄×C₁₉	—	4	4	no	—
212	C₄×C₁₉	—	8	2	no	—
213	C₄×C₁₉	#379	1	1	yes	characteristic
214	C₄×C₁₉	#380	1	2	yes	—
215	C₄×C₁₉	#381	1	1	yes	characteristic
216	C₄×C₁₉	#385	1	1	yes	characteristic
217	C₄×C₁₉	#385	1	1	yes	characteristic
218	C₄×C₁₉	#386	1	2	yes	—
219	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
220	#568	—	2	2	no	—
221	#568	—	2	4	no	—
222	#568	C₄×C₁₉	1	4	yes	complemented
223	C₂×#131	—	2	4	no	—
224	C₂²×M₁₆	—	2	2	no	—
225	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
226	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
227	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
228	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
229	#413	—	2	2	no	—
230	#413	C₄×C₁₉	1	4	yes	complemented
231	C₂×#101	—	2	1	no	—
232	C₂×#100	—	2	1	no	—
233	#391	—	2	1	no	—
234	#390	—	2	1	no	—
235	#386	C₄×C₁₉	1	4	yes	—
236	C₄×C₂²⋊C₄	—	2	2	no	—
237	#344	—	2	4	no	—
238	#336	—	2	4	no	—
239	C₂×C₁₉	—	2	1	no	—
240	C₂×C₁₉	—	2	1	no	—
241	C₂×C₁₉	—	2	2	no	—
242	C₂×C₁₉	—	2	2	no	—
243	C₂×C₁₉	—	4	4	no	—
244	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
245	C₂×C₁₉	#1891	1	2	yes	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	—	2	2	no	—
248	C₂×#41	—	2	2	no	—
249	C₂×#41	—	2	2	no	—
250	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
251	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
252	C₂×#41	D₄×C₁₉	1	2	yes	—
253	C₂×#41	Q₈×C₁₉	1	2	yes	—
254	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
255	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
256	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
257	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
258	C₂³×C₄	D₄×C₁₉	1	2	yes	—
259	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
260	#131	—	2	16	no	—
261	#131	—	2	16	no	—
262	C₂×M₁₆	—	2	4	no	—
263	C₂×M₁₆	—	2	8	no	—
264	C₂×M₁₆	—	2	8	no	—
265	C₂×M₁₆	—	2	2	no	—
266	C₂×M₁₆	—	2	2	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	—
275	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	—
276	C₂×M₁₆	D₄×C₁₉	1	4	yes	—
277	C₂²×C₈	—	2	4	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	D₄×C₁₉	1	4	yes	—
280	#117	—	2	2	no	—
281	#117	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	4	no	—
284	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	2	2	no	—
290	#101	—	2	4	no	—
291	#100	—	2	4	no	—
292	#95	—	2	4	no	—
293	C₁₉	#10746	1	1	yes	characteristic, direct product factor, Sylow
294	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
295	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
296	#41	—	2	4	no	—
297	#41	—	2	4	no	—
298	#41	—	2	4	no	—
299	#41	—	2	4	no	—
300	#41	—	2	4	no	—
301	#41	—	2	4	no	—
302	#41	—	2	4	no	—
303	#41	—	2	4	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
307	C₂×Q₈	C₄⋊C₄×C₁₉	1	2	yes	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	C₄²×C₁₉	1	4	yes	—
313	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
314	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	—
315	C₂×D₄	C₄⋊C₄×C₁₉	1	4	yes	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	4	4	no	—
324	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
325	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
326	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
327	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
328	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
334	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
335	C₂²×C₄	#41×C₁₉	1	2	yes	—
336	C₂²×C₄	#41×C₁₉	1	2	yes	—
337	M₁₆	—	2	16	no	—
338	M₁₆	—	2	4	no	—
339	M₁₆	—	2	4	no	—
340	M₁₆	—	2	4	no	—
341	M₁₆	—	2	4	no	—
342	M₁₆	—	2	4	no	—
343	M₁₆	—	2	4	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	—	4	2	no	—
346	C₂×C₈	—	2	16	no	—
347	C₂×C₈	—	2	4	no	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	4	no	—
350	C₂×C₈	—	4	2	no	—
351	C₂×C₈	—	4	2	no	—
352	C₂×C₈	C₂²⋊C₄×C₁₉	1	8	yes	complemented
353	C₄⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	2	4	no	—
355	C₂²⋊C₄	—	4	8	no	—
356	C₄²	—	4	1	no	—
357	C₄²	—	4	1	no	—
358	C₄²	—	4	2	no	—
359	C₄²	—	4	1	no	—
360	C₄²	—	4	1	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	4	no	—
365	C₂³	C₁₉×#95	1	4	yes	—
366	C₂³	C₂×C₄²×C₁₉	1	1	yes	characteristic
367	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
368	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
369	C₂³	C₄×D₄×C₁₉	1	2	yes	—
370	C₂³	C₄×D₄×C₁₉	1	2	yes	—
371	Q₈	—	2	4	no	—
372	Q₈	—	2	4	no	—
373	D₄	—	2	8	no	—
374	D₄	—	2	8	no	—
375	D₄	—	2	4	no	—
376	D₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	C₁₉×#95	1	4	yes	—
391	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
392	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
393	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
394	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
395	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
396	C₂×C₄	C₁₉×#117	1	2	yes	—
397	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
398	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
399	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
400	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
401	C₂×C₄	C₁₉×#120	1	2	yes	—
402	C₂×C₄	C₁₉×#121	1	2	yes	—
403	C₂×C₄	C₁₉×#121	1	2	yes	—
404	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
405	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
406	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
407	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
408	C₂×C₄	C₁₉×#123	1	2	yes	—
409	C₈	—	2	8	no	—
410	C₈	—	4	4	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	8	2	no	—
420	C₂²	C₂×C₁₉×#95	1	1	yes	characteristic
421	C₂²	C₄×C₂²⋊C₄×C₁₉	1	2	yes	—
422	C₂²	C₁₉×#385	1	2	yes	—
423	C₂²	C₁₉×#386	1	1	yes	characteristic
424	C₂²	C₁₉×#386	1	1	yes	characteristic
425	C₄	—	2	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	8	2	no	—
428	C₄	C₁₉×#379	1	1	yes	characteristic
429	C₄	C₁₉×#380	1	2	yes	—
430	C₄	C₁₉×#381	1	1	yes	characteristic
431	C₄	C₁₉×#385	1	1	yes	characteristic
432	C₄	C₁₉×#385	1	1	yes	characteristic
433	C₄	C₁₉×#386	1	2	yes	—
434	C₂	—	2	1	no	—
435	C₂	—	2	1	no	—
436	C₂	—	2	2	no	—
437	C₂	—	2	2	no	—
438	C₂	—	4	4	no	—
439	C₂	C₁₉×C₂²⋊#95	1	1	yes	characteristic
440	C₂	C₁₉×#1891	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator	C₂³	C₂×C₄²×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	#386
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₁₉×#344	C₂	semidirect
5. C₁₉×#1728	C₂	semidirect
9. C₁₉×#568	C₄	semidirect
17. C₁₉×#413	C₄	semidirect
131. C₂×C₈×C₁₉	C₂²⋊C₄	semidirect
140. #10746	C₁₉	direct (N × H)
194. C₂×#344	C₂×C₁₉	semidirect
195. #1728	C₂×C₁₉	semidirect
222. #568	C₄×C₁₉	semidirect
230. #413	C₄×C₁₉	semidirect
293. C₁₉	#10746	direct (N × H)
352. C₂×C₈	C₂²⋊C₄×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×#568	2
C₂×C₁₉×#413	2
C₁₉×#2297	2
C₂×C₁₉×#344	2
C₁₉×#1728	2
#10746	19

Subgroups — C19×#10746 #18016705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10746 #18016705