Subgroups — C₁₉×#21414 #18027373

Order 4864.

1198 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#540	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2314	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1992	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1991	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1961	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1895	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1893	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1762	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×#102	C₂	1	2	yes	maximal, complemented
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#540	—	2	4	no	—
15	C₁₉×#540	C₄	1	8	yes	complemented
16	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#123	—	2	2	no	—
19	C₂×C₁₉×#121	—	2	2	no	—
20	C₂×C₁₉×#121	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#102	C₂²	1	2	yes	—
24	C₂×C₁₉×#102	C₂²	1	2	yes	—
25	C₂×C₁₉×#102	C₂²	1	2	yes	—
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₁₉×#405	—	2	4	no	—
28	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×#388	—	2	2	no	—
33	C₁₉×#387	—	2	2	no	—
34	C₁₉×#384	C₂²	1	1	yes	characteristic
35	C₁₉×#382	C₂²	1	1	yes	characteristic
36	C₁₉×#380	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₂²×D₄×C₁₉	—	2	2	no	—
43	C₂²×D₄×C₁₉	—	2	2	no	—
44	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	—	2	2	no	—
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	2	2	no	—
49	C₂×M₁₆×C₁₉	—	2	2	no	—
50	C₂²×C₈×C₁₉	—	2	2	no	—
51	C₂²×C₈×C₁₉	—	2	2	no	—
52	C₂²×C₈×C₁₉	—	2	2	no	—
53	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₁₉×#127	—	2	2	no	—
58	C₁₉×#127	C₂×C₄	1	4	yes	—
59	C₁₉×#125	—	2	2	no	—
60	C₁₉×#125	C₂×C₄	1	4	yes	—
61	C₁₉×#123	—	2	16	no	—
62	C₁₉×#121	—	2	4	no	—
63	C₁₉×#121	—	2	16	no	—
64	C₁₉×#121	C₂×C₄	1	8	yes	—
65	C₄×D₄×C₁₉	—	2	4	no	—
66	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	—
67	C₁₉×#117	C₂×C₄	1	4	yes	—
68	C₁₉×#117	D₄	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₉	D₄	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	2	yes	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
79	C₂×C₄²×C₁₉	—	2	2	no	—
80	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
82	C₁₉×#102	—	2	4	no	—
83	C₁₉×#102	—	2	4	no	—
84	C₁₉×#102	—	2	4	no	—
85	C₁₉×#102	—	2	4	no	—
86	C₁₉×#97	—	2	2	no	—
87	C₁₉×#97	—	2	2	no	—
88	C₄×C₈×C₁₉	—	2	2	no	—
89	C₄×C₈×C₁₉	—	2	2	no	—
90	C₁₉×#95	—	2	2	no	—
91	C₁₉×#95	—	2	2	no	—
92	C₁₉×#95	—	2	2	no	—
93	C₂⁴×C₁₉	—	2	2	no	—
94	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂×D₄×C₁₉	—	2	8	no	—
96	C₂×D₄×C₁₉	—	2	8	no	—
97	C₂×D₄×C₁₉	—	2	2	no	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	—	2	2	no	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	2	2	no	—
102	C₂×D₄×C₁₉	—	8	2	no	—
103	C₂×D₄×C₁₉	—	8	2	no	—
104	C₂×D₄×C₁₉	—	8	2	no	—
105	C₂×D₄×C₁₉	—	8	2	no	—
106	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	8	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	8	2	no	—
116	C₂²×C₄×C₁₉	—	8	2	no	—
117	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
123	M₁₆×C₁₉	—	2	8	no	—
124	C₂×C₈×C₁₉	—	2	8	no	—
125	C₂×C₈×C₁₉	—	2	1	no	—
126	C₂×C₈×C₁₉	—	2	1	no	—
127	C₂×C₈×C₁₉	—	2	1	no	—
128	C₂×C₈×C₁₉	—	2	1	no	—
129	C₂×C₈×C₁₉	—	2	1	no	—
130	C₂×C₈×C₁₉	—	2	1	no	—
131	C₂×C₈×C₁₉	—	2	1	no	—
132	C₂×C₈×C₁₉	—	2	1	no	—
133	C₂×C₈×C₁₉	#41	1	2	yes	—
134	C₂×C₈×C₁₉	#41	1	2	yes	—
135	C₂×C₈×C₁₉	#41	1	2	yes	—
136	C₂×C₈×C₁₉	#41	1	2	yes	—
137	C₄⋊C₄×C₁₉	—	2	8	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	8	2	no	—
144	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
145	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
146	C₂²⋊C₄×C₁₉	—	2	8	no	—
147	C₂²⋊C₄×C₁₉	—	2	8	no	—
148	C₂²⋊C₄×C₁₉	—	8	2	no	—
149	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
150	C₄²×C₁₉	—	8	2	no	—
151	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
152	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
153	C₄²×C₁₉	C₂×D₄	1	2	yes	—
154	C₄²×C₁₉	C₂×D₄	1	2	yes	—
155	#21414	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂³×C₁₉	—	2	1	no	—
157	C₂³×C₁₉	—	2	1	no	—
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	—	2	4	no	—
161	C₂³×C₁₉	—	4	2	no	—
162	C₂³×C₁₉	—	4	2	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	—	4	2	no	—
165	C₂³×C₁₉	—	4	2	no	—
166	C₂³×C₁₉	—	4	2	no	—
167	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
169	D₄×C₁₉	—	2	4	no	—
170	D₄×C₁₉	—	2	4	no	—
171	D₄×C₁₉	—	4	2	no	—
172	D₄×C₁₉	—	4	2	no	—
173	D₄×C₁₉	—	8	8	no	—
174	D₄×C₁₉	—	8	8	no	—
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	8	8	no	—
195	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
196	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
197	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
198	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
204	C₈×C₁₉	—	2	2	no	—
205	C₈×C₁₉	—	2	2	no	—
206	C₈×C₁₉	—	2	2	no	—
207	C₈×C₁₉	—	2	2	no	—
208	C₂×#540	C₂×C₁₉	1	1	yes	characteristic
209	C₂×#405	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#2314	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#1992	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#1991	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#1961	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#1957	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#1895	C₂×C₁₉	1	2	yes	complemented
216	#1893	C₂×C₁₉	1	2	yes	complemented
217	#1762	C₂×C₁₉	1	2	yes	complemented
218	C₄×#102	C₂×C₁₉	1	2	yes	complemented
219	C₂²×C₁₉	—	2	4	no	—
220	C₂²×C₁₉	—	2	2	no	—
221	C₂²×C₁₉	—	4	1	no	—
222	C₂²×C₁₉	—	4	1	no	—
223	C₂²×C₁₉	—	4	2	no	—
224	C₂²×C₁₉	—	4	4	no	—
225	C₂²×C₁₉	—	4	4	no	—
226	C₂²×C₁₉	—	4	4	no	—
227	C₂²×C₁₉	—	8	2	no	—
228	C₂²×C₁₉	—	8	2	no	—
229	C₂²×C₁₉	—	8	2	no	—
230	C₂²×C₁₉	—	8	2	no	—
231	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
232	C₂²×C₁₉	#532	1	1	yes	characteristic
233	C₂²×C₁₉	#532	1	1	yes	characteristic
234	C₂²×C₁₉	#576	1	2	yes	—
235	C₂²×C₁₉	#577	1	2	yes	—
236	C₄×C₁₉	—	2	4	no	—
237	C₄×C₁₉	—	2	4	no	—
238	C₄×C₁₉	—	2	2	no	—
239	C₄×C₁₉	—	4	4	no	—
240	C₄×C₁₉	—	8	2	no	—
241	C₄×C₁₉	—	8	2	no	—
242	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
243	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
244	C₄×C₁₉	#525	1	1	yes	characteristic
245	C₄×C₁₉	#525	1	1	yes	characteristic
246	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
247	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
248	#540	—	2	4	no	—
249	#540	C₄×C₁₉	1	8	yes	complemented
250	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×#123	—	2	2	no	—
253	C₂×#121	—	2	2	no	—
254	C₂×#121	C₂²×C₁₉	1	2	yes	—
255	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
256	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
257	C₂×#102	C₂²×C₁₉	1	2	yes	—
258	C₂×#102	C₂²×C₁₉	1	2	yes	—
259	C₂×#102	C₂²×C₁₉	1	2	yes	—
260	C₂×#102	C₂²×C₁₉	1	2	yes	—
261	#405	—	2	4	no	—
262	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
263	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
266	#388	—	2	2	no	—
267	#387	—	2	2	no	—
268	#384	C₂²×C₁₉	1	1	yes	characteristic
269	#382	C₂²×C₁₉	1	1	yes	characteristic
270	#380	C₂²×C₁₉	1	2	yes	—
271	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
272	#340	C₂²×C₁₉	1	2	yes	—
273	#340	C₂²×C₁₉	1	2	yes	—
274	#340	C₂²×C₁₉	1	2	yes	—
275	#340	C₂²×C₁₉	1	2	yes	—
276	C₂×C₁₉	—	4	2	no	—
277	C₂×C₁₉	—	8	4	no	—
278	C₂×C₁₉	#2297	1	1	yes	characteristic
279	C₂×C₁₉	#2897	1	2	yes	—
280	C₂×C₁₉	#3174	1	1	yes	characteristic
281	C₂×C₁₉	#3176	1	1	yes	characteristic
282	C₂×C₁₉	#3179	1	2	yes	—
283	C₂²×D₄	—	2	2	no	—
284	C₂²×D₄	—	2	2	no	—
285	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
286	C₂³×C₄	—	2	2	no	—
287	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
298	#127	—	2	2	no	—
299	#127	C₂×C₄×C₁₉	1	4	yes	—
300	#125	—	2	2	no	—
301	#125	C₂×C₄×C₁₉	1	4	yes	—
302	#123	—	2	16	no	—
303	#121	—	2	4	no	—
304	#121	—	2	16	no	—
305	#121	C₂×C₄×C₁₉	1	8	yes	—
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	—
308	#117	C₂×C₄×C₁₉	1	4	yes	—
309	#117	D₄×C₁₉	1	4	yes	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
323	#102	—	2	4	no	—
324	#102	—	2	4	no	—
325	#102	—	2	4	no	—
326	#102	—	2	4	no	—
327	#97	—	2	2	no	—
328	#97	—	2	2	no	—
329	C₄×C₈	—	2	2	no	—
330	C₄×C₈	—	2	2	no	—
331	#95	—	2	2	no	—
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	C₁₉	#21414	1	1	yes	characteristic, direct product factor, Sylow
335	C₂⁴	—	2	2	no	—
336	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
337	C₂×D₄	—	2	8	no	—
338	C₂×D₄	—	2	8	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	8	2	no	—
345	C₂×D₄	—	8	2	no	—
346	C₂×D₄	—	8	2	no	—
347	C₂×D₄	—	8	2	no	—
348	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	8	2	no	—
358	C₂²×C₄	—	8	2	no	—
359	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
365	M₁₆	—	2	8	no	—
366	C₂×C₈	—	2	8	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	#41×C₁₉	1	2	yes	—
376	C₂×C₈	#41×C₁₉	1	2	yes	—
377	C₂×C₈	#41×C₁₉	1	2	yes	—
378	C₂×C₈	#41×C₁₉	1	2	yes	—
379	C₄⋊C₄	—	2	8	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	8	2	no	—
386	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
387	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	2	8	no	—
390	C₂²⋊C₄	—	8	2	no	—
391	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
392	C₄²	—	8	2	no	—
393	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
394	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
395	C₄²	C₂×D₄×C₁₉	1	2	yes	—
396	C₄²	C₂×D₄×C₁₉	1	2	yes	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
409	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
410	D₄	—	2	4	no	—
411	D₄	—	2	4	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	D₄	—	8	8	no	—
415	D₄	—	8	8	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	8	8	no	—
436	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
437	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
438	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
439	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
441	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
442	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
443	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
445	C₈	—	2	2	no	—
446	C₈	—	2	2	no	—
447	C₈	—	2	2	no	—
448	C₈	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	4	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
462	C₂²	C₁₉×#532	1	1	yes	characteristic
463	C₂²	C₁₉×#532	1	1	yes	characteristic
464	C₂²	C₁₉×#576	1	2	yes	—
465	C₂²	C₁₉×#577	1	2	yes	—
466	C₄	—	2	2	no	—
467	C₄	—	2	4	no	—
468	C₄	—	2	4	no	—
469	C₄	—	4	4	no	—
470	C₄	—	8	2	no	—
471	C₄	—	8	2	no	—
472	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
473	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
474	C₄	C₁₉×#525	1	1	yes	characteristic
475	C₄	C₁₉×#525	1	1	yes	characteristic
476	C₂	—	4	2	no	—
477	C₂	—	8	4	no	—
478	C₂	C₁₉×#2297	1	1	yes	characteristic
479	C₂	C₁₉×#2897	1	2	yes	—
480	C₂	C₁₉×#3174	1	1	yes	characteristic
481	C₂	C₁₉×#3176	1	1	yes	characteristic
482	C₂	C₁₉×#3179	1	2	yes	—

	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×#540	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#405	C₂	semidirect
3. C₁₉×#2314	C₂	semidirect
4. C₁₉×#1992	C₂	semidirect
5. C₁₉×#1991	C₂	semidirect
6. C₁₉×#1961	C₂	semidirect
7. C₁₉×#1957	C₂	semidirect
8. C₁₉×#1895	C₂	semidirect
9. C₁₉×#1893	C₂	semidirect
10. C₁₉×#1762	C₂	semidirect
11. C₄×C₁₉×#102	C₂	semidirect
15. C₁₉×#540	C₄	semidirect
155. #21414	C₁₉	direct (N × H)
209. C₂×#405	C₂×C₁₉	semidirect
210. #2314	C₂×C₁₉	semidirect
211. #1992	C₂×C₁₉	semidirect
212. #1991	C₂×C₁₉	semidirect
213. #1961	C₂×C₁₉	semidirect
214. #1957	C₂×C₁₉	semidirect
215. #1895	C₂×C₁₉	semidirect
216. #1893	C₂×C₁₉	semidirect
217. #1762	C₂×C₁₉	semidirect
218. C₄×#102	C₂×C₁₉	semidirect
249. #540	C₄×C₁₉	semidirect
334. C₁₉	#21414	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×#540	2
C₂×C₁₉×#405	2
C₁₉×#2314	2
C₁₉×#1992	2
C₁₉×#1991	2
C₁₉×#1961	2
C₁₉×#1957	2
C₁₉×#1895	2
C₁₉×#1893	2
C₁₉×#1762	2
C₄×C₁₉×#102	2
#21414	19

Subgroups — C19×#21414 #18027373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21414 #18027373