Subgroups — C₁₉×#8400 #18014359

Order 4864.

858 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3460	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1871	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1870	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₉×#99	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1501	C₂	1	2	yes	maximal, complemented
6	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#544	C₄	1	1	yes	characteristic, complemented
8	C₁₉×#542	—	2	2	no	—
9	C₁₉×#540	—	2	2	no	—
10	C₁₉×#538	—	2	1	no	—
11	C₁₉×#538	C₄	1	2	yes	complemented
12	C₁₉×#537	C₄	1	1	yes	characteristic, complemented
13	C₁₉×#535	—	2	1	no	—
14	C₁₉×#532	—	2	2	no	—
15	C₁₉×#529	—	2	2	no	—
16	C₁₉×#525	—	2	1	no	—
17	C₁₉×#525	C₂²	1	2	yes	—
18	C₄×#41×C₁₉	—	2	1	no	—
19	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#104	—	2	2	no	—
21	C₂×C₁₉×#99	—	2	1	no	—
22	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
23	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
25	C₁₉×#342	—	2	1	no	—
26	C₁₉×#339	—	2	2	no	—
27	C₁₉×#336	—	2	1	no	—
28	C₁₉×#328	—	2	2	no	—
29	C₁₉×#327	—	2	2	no	—
30	C₂×#41×C₁₉	—	2	1	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂×#41×C₁₉	D₄	1	2	yes	—
33	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₁₉	—	2	2	no	—
37	C₂×M₁₆×C₁₉	—	4	2	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₁₉×C₄⋊Q₈	—	2	2	no	—
41	C₁₉×#127	—	2	2	no	—
42	C₁₉×#126	—	2	2	no	—
43	C₁₉×#126	—	2	2	no	—
44	C₁₉×#125	—	2	2	no	—
45	C₁₉×#124	—	2	2	no	—
46	C₁₉×#124	—	2	2	no	—
47	C₁₉×#124	—	2	2	no	—
48	C₁₉×#123	—	2	2	no	—
49	C₁₉×#123	—	2	2	no	—
50	C₁₉×#123	—	2	2	no	—
51	C₁₉×#123	—	2	2	no	—
52	C₁₉×C₂²⋊Q₈	—	2	1	no	—
53	C₁₉×C₂²⋊Q₈	—	2	1	no	—
54	C₁₉×C₂²⋊Q₈	—	2	2	no	—
55	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
56	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
57	C₁₉×#121	—	2	1	no	—
58	C₁₉×#121	—	2	2	no	—
59	C₁₉×#121	—	2	2	no	—
60	C₁₉×#121	—	2	2	no	—
61	C₁₉×#121	—	2	2	no	—
62	C₁₉×#121	—	2	2	no	—
63	C₁₉×#121	—	2	1	no	—
64	C₁₉×#121	C₂×C₄	1	2	yes	—
65	C₁₉×#121	D₄	1	2	yes	—
66	C₁₉×#120	—	2	2	no	—
67	C₁₉×#120	—	2	2	no	—
68	C₄×Q₈×C₁₉	—	2	1	no	—
69	C₄×Q₈×C₁₉	—	2	1	no	—
70	C₄×D₄×C₁₉	—	2	1	no	—
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	—	2	2	no	—
73	C₄×D₄×C₁₉	—	2	2	no	—
74	C₄×D₄×C₁₉	—	2	2	no	—
75	C₄×D₄×C₁₉	—	2	2	no	—
76	C₄×D₄×C₁₉	—	2	2	no	—
77	C₄×D₄×C₁₉	—	2	2	no	—
78	C₁₉×#117	—	2	2	no	—
79	C₁₉×#117	—	2	1	no	—
80	C₁₉×#117	—	2	1	no	—
81	C₁₉×#117	D₄	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₉	—	2	2	no	—
87	C₂×C₄²×C₁₉	—	2	2	no	—
88	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
89	C₁₉×#104	—	4	4	no	—
90	C₁₉×#99	—	2	4	no	—
91	C₁₉×C₂²⋊C₈	—	2	2	no	—
92	C₁₉×C₂²⋊C₈	—	4	2	no	—
93	C₁₉×#95	—	2	2	no	—
94	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
96	#41×C₁₉	—	4	2	no	—
97	#41×C₁₉	—	4	2	no	—
98	#41×C₁₉	—	4	2	no	—
99	#41×C₁₉	—	4	2	no	—
100	#41×C₁₉	—	8	1	no	—
101	#41×C₁₉	—	8	1	no	—
102	C₂×Q₈×C₁₉	—	2	1	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
105	C₂×D₄×C₁₉	—	2	1	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	2	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	4	1	no	—
115	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	4	1	no	—
122	C₂²×C₄×C₁₉	—	4	1	no	—
123	C₂²×C₄×C₁₉	—	4	1	no	—
124	C₂²×C₄×C₁₉	—	4	1	no	—
125	C₂²×C₄×C₁₉	—	4	2	no	—
126	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
133	M₁₆×C₁₉	—	2	4	no	—
134	M₁₆×C₁₉	—	4	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	4	1	no	—
137	C₂×C₈×C₁₉	—	4	1	no	—
138	C₂×C₈×C₁₉	—	4	1	no	—
139	C₂×C₈×C₁₉	—	4	1	no	—
140	C₂×C₈×C₁₉	—	4	1	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
151	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
152	C₂²⋊C₄×C₁₉	—	2	2	no	—
153	C₂²⋊C₄×C₁₉	—	2	2	no	—
154	C₂²⋊C₄×C₁₉	—	2	2	no	—
155	C₂²⋊C₄×C₁₉	—	2	2	no	—
156	C₂²⋊C₄×C₁₉	—	2	2	no	—
157	C₂²⋊C₄×C₁₉	—	2	2	no	—
158	C₂²⋊C₄×C₁₉	—	2	2	no	—
159	C₂²⋊C₄×C₁₉	—	2	2	no	—
160	C₂²⋊C₄×C₁₉	—	2	2	no	—
161	C₂²⋊C₄×C₁₉	—	2	2	no	—
162	C₂²⋊C₄×C₁₉	—	2	2	no	—
163	C₂²⋊C₄×C₁₉	—	2	4	no	—
164	C₂²⋊C₄×C₁₉	—	4	2	no	—
165	C₄²×C₁₉	—	2	2	no	—
166	C₄²×C₁₉	—	2	2	no	—
167	C₄²×C₁₉	—	2	1	no	—
168	C₄²×C₁₉	—	2	1	no	—
169	C₄²×C₁₉	—	2	2	no	—
170	C₄²×C₁₉	—	4	2	no	—
171	C₄²×C₁₉	—	4	2	no	—
172	#8400	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂³×C₁₉	—	2	1	no	—
174	C₂³×C₁₉	—	2	1	no	—
175	C₂³×C₁₉	—	2	1	no	—
176	C₂³×C₁₉	—	2	2	no	—
177	C₂³×C₁₉	—	2	1	no	—
178	C₂³×C₁₉	—	2	1	no	—
179	C₂³×C₁₉	—	4	1	no	—
180	C₂³×C₁₉	—	4	1	no	—
181	C₂³×C₁₉	—	4	1	no	—
182	C₂³×C₁₉	—	4	1	no	—
183	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂³×C₁₉	#120	1	2	yes	—
185	Q₈×C₁₉	—	4	2	no	—
186	Q₈×C₁₉	—	4	2	no	—
187	Q₈×C₁₉	—	8	1	no	—
188	D₄×C₁₉	—	4	4	no	—
189	D₄×C₁₉	—	4	2	no	—
190	D₄×C₁₉	—	4	2	no	—
191	D₄×C₁₉	—	4	2	no	—
192	D₄×C₁₉	—	4	2	no	—
193	D₄×C₁₉	—	8	2	no	—
194	D₄×C₁₉	—	8	2	no	—
195	D₄×C₁₉	—	8	2	no	—
196	D₄×C₁₉	—	8	1	no	—
197	D₄×C₁₉	—	8	2	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	4	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	4	no	—
219	C₂×C₄×C₁₉	—	8	1	no	—
220	C₂×C₄×C₁₉	—	8	2	no	—
221	C₂×C₄×C₁₉	—	8	2	no	—
222	C₂×C₄×C₁₉	—	8	2	no	—
223	C₂×C₄×C₁₉	#104	1	2	yes	complemented
224	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
225	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
226	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
227	C₈×C₁₉	—	4	2	no	—
228	C₈×C₁₉	—	8	1	no	—
229	#3460	C₂×C₁₉	1	1	yes	characteristic
230	#1871	C₂×C₁₉	1	2	yes	complemented
231	#1870	C₂×C₁₉	1	1	yes	characteristic, complemented
232	C₄×#99	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#1501	C₂×C₁₉	1	2	yes	complemented
234	C₂²×C₁₉	—	2	1	no	—
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	2	2	no	—
237	C₂²×C₁₉	—	2	2	no	—
238	C₂²×C₁₉	—	2	2	no	—
239	C₂²×C₁₉	—	4	2	no	—
240	C₂²×C₁₉	—	4	2	no	—
241	C₂²×C₁₉	—	4	1	no	—
242	C₂²×C₁₉	—	4	2	no	—
243	C₂²×C₁₉	—	4	1	no	—
244	C₂²×C₁₉	—	4	1	no	—
245	C₂²×C₁₉	—	4	2	no	—
246	C₂²×C₁₉	—	8	1	no	—
247	C₂²×C₁₉	—	8	1	no	—
248	C₂²×C₁₉	—	8	1	no	—
249	C₂²×C₁₉	#379	1	1	yes	characteristic
250	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
251	C₂²×C₁₉	#421	1	1	yes	characteristic
252	C₄×C₁₉	—	2	2	no	—
253	C₄×C₁₉	—	2	1	no	—
254	C₄×C₁₉	—	2	2	no	—
255	C₄×C₁₉	—	4	1	no	—
256	C₄×C₁₉	—	4	2	no	—
257	C₄×C₁₉	—	4	2	no	—
258	C₄×C₁₉	—	4	1	no	—
259	C₄×C₁₉	—	4	2	no	—
260	C₄×C₁₉	—	8	4	no	—
261	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
262	C₄×C₁₉	#458	1	1	yes	characteristic
263	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
264	#544	C₄×C₁₉	1	1	yes	characteristic, complemented
265	#542	—	2	2	no	—
266	#540	—	2	2	no	—
267	#538	—	2	1	no	—
268	#538	C₄×C₁₉	1	2	yes	complemented
269	#537	C₄×C₁₉	1	1	yes	characteristic, complemented
270	#535	—	2	1	no	—
271	#532	—	2	2	no	—
272	#529	—	2	2	no	—
273	#525	—	2	1	no	—
274	#525	C₂²×C₁₉	1	2	yes	—
275	C₄×#41	—	2	1	no	—
276	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
277	C₂×#104	—	2	2	no	—
278	C₂×#99	—	2	1	no	—
279	C₂×C₂²⋊C₈	—	2	1	no	—
280	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
281	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
282	#342	—	2	1	no	—
283	#339	—	2	2	no	—
284	#336	—	2	1	no	—
285	#328	—	2	2	no	—
286	#327	—	2	2	no	—
287	C₂×C₁₉	—	2	1	no	—
288	C₂×C₁₉	—	2	1	no	—
289	C₂×C₁₉	—	4	2	no	—
290	C₂×C₁₉	—	8	2	no	—
291	C₂×C₁₉	—	8	1	no	—
292	C₂×C₁₉	#1789	1	1	yes	characteristic
293	C₂×C₁₉	#1790	1	1	yes	characteristic
294	C₂×C₁₉	#1794	1	1	yes	characteristic
295	C₂×#41	—	2	1	no	—
296	C₂×#41	—	2	1	no	—
297	C₂×#41	D₄×C₁₉	1	2	yes	—
298	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
299	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
300	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
301	C₂×M₁₆	—	2	2	no	—
302	C₂×M₁₆	—	4	2	no	—
303	C₂²×C₈	—	2	1	no	—
304	C₂²×C₈	—	2	1	no	—
305	C₄⋊Q₈	—	2	2	no	—
306	#127	—	2	2	no	—
307	#126	—	2	2	no	—
308	#126	—	2	2	no	—
309	#125	—	2	2	no	—
310	#124	—	2	2	no	—
311	#124	—	2	2	no	—
312	#124	—	2	2	no	—
313	#123	—	2	2	no	—
314	#123	—	2	2	no	—
315	#123	—	2	2	no	—
316	#123	—	2	2	no	—
317	C₂²⋊Q₈	—	2	1	no	—
318	C₂²⋊Q₈	—	2	1	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
321	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
322	#121	—	2	1	no	—
323	#121	—	2	2	no	—
324	#121	—	2	2	no	—
325	#121	—	2	2	no	—
326	#121	—	2	2	no	—
327	#121	—	2	2	no	—
328	#121	—	2	1	no	—
329	#121	C₂×C₄×C₁₉	1	2	yes	—
330	#121	D₄×C₁₉	1	2	yes	—
331	#120	—	2	2	no	—
332	#120	—	2	2	no	—
333	C₄×Q₈	—	2	1	no	—
334	C₄×Q₈	—	2	1	no	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	—	2	2	no	—
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	—	2	2	no	—
343	#117	—	2	2	no	—
344	#117	—	2	1	no	—
345	#117	—	2	1	no	—
346	#117	D₄×C₁₉	1	2	yes	—
347	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
351	C₂×C₄²	—	2	2	no	—
352	C₂×C₄²	—	2	2	no	—
353	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
354	#104	—	4	4	no	—
355	#99	—	2	4	no	—
356	C₂²⋊C₈	—	2	2	no	—
357	C₂²⋊C₈	—	4	2	no	—
358	#95	—	2	2	no	—
359	C₁₉	#8400	1	1	yes	characteristic, direct product factor, Sylow
360	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
361	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
362	#41	—	4	2	no	—
363	#41	—	4	2	no	—
364	#41	—	4	2	no	—
365	#41	—	4	2	no	—
366	#41	—	8	1	no	—
367	#41	—	8	1	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	4	1	no	—
381	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	—	4	1	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
393	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
394	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
395	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
399	M₁₆	—	2	4	no	—
400	M₁₆	—	4	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	4	1	no	—
403	C₂×C₈	—	4	1	no	—
404	C₂×C₈	—	4	1	no	—
405	C₂×C₈	—	4	1	no	—
406	C₂×C₈	—	4	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
417	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	4	no	—
430	C₂²⋊C₄	—	4	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	2	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	4	2	no	—
437	C₄²	—	4	2	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	2	1	no	—
444	C₂³	—	4	1	no	—
445	C₂³	—	4	1	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
449	C₂³	C₁₉×#120	1	2	yes	—
450	Q₈	—	4	2	no	—
451	Q₈	—	4	2	no	—
452	Q₈	—	8	1	no	—
453	D₄	—	4	4	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	8	2	no	—
459	D₄	—	8	2	no	—
460	D₄	—	8	1	no	—
461	D₄	—	8	2	no	—
462	D₄	—	8	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	8	1	no	—
485	C₂×C₄	—	8	2	no	—
486	C₂×C₄	—	8	2	no	—
487	C₂×C₄	—	8	2	no	—
488	C₂×C₄	C₁₉×#104	1	2	yes	complemented
489	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
490	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
491	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
492	C₈	—	4	2	no	—
493	C₈	—	8	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	8	1	no	—
508	C₂²	—	8	1	no	—
509	C₂²	C₁₉×#379	1	1	yes	characteristic
510	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
511	C₂²	C₁₉×#421	1	1	yes	characteristic
512	C₄	—	2	2	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	2	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	2	no	—
520	C₄	—	8	4	no	—
521	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
522	C₄	C₁₉×#458	1	1	yes	characteristic
523	C₂	—	2	1	no	—
524	C₂	—	2	1	no	—
525	C₂	—	4	2	no	—
526	C₂	—	8	1	no	—
527	C₂	—	8	2	no	—
528	C₂	C₁₉×#1789	1	1	yes	characteristic
529	C₂	C₁₉×#1790	1	1	yes	characteristic
530	C₂	C₁₉×#1794	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	#379
prime radical	C₁₉×#3460	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ 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
2. C₁₉×#1871	C₂	semidirect
3. C₁₉×#1870	C₂	semidirect
4. C₄×C₁₉×#99	C₂	semidirect
5. C₁₉×#1501	C₂	semidirect
7. C₁₉×#544	C₄	semidirect
11. C₁₉×#538	C₄	semidirect
12. C₁₉×#537	C₄	semidirect
172. #8400	C₁₉	direct (N × H)
223. C₂×C₄×C₁₉	#104	semidirect
230. #1871	C₂×C₁₉	semidirect
231. #1870	C₂×C₁₉	semidirect
232. C₄×#99	C₂×C₁₉	semidirect
233. #1501	C₂×C₁₉	semidirect
264. #544	C₄×C₁₉	semidirect
268. #538	C₄×C₁₉	semidirect
269. #537	C₄×C₁₉	semidirect
359. C₁₉	#8400	direct (N × H)
488. C₂×C₄	C₁₉×#104	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3460	2
C₁₉×#1871	2
C₁₉×#1870	2
C₄×C₁₉×#99	2
C₁₉×#1501	2
#8400	19

Subgroups — C19×#8400 #18014359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8400 #18014359