Subgroups — C₁₉×#9997 #18015956

Order 4864.

622 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3100	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3037	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1517	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1486	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1286	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#137	—	2	1	no	—
9	C₁₉×#532	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
11	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#480	—	2	1	no	—
14	C₁₉×#474	—	2	1	no	—
15	C₁₉×#464	—	2	2	no	—
16	C₁₉×#462	—	2	1	no	—
17	C₁₉×#460	—	2	1	no	—
18	C₁₉×#459	—	2	1	no	—
19	C₁₉×#447	—	2	1	no	—
20	C₄×D₈×C₁₉	—	2	2	no	—
21	C₁₉×#431	C₂²	1	1	yes	characteristic
22	C₁₉×#431	C₂²	1	1	yes	characteristic
23	C₁₉×#423	C₂²	1	1	yes	characteristic
24	C₁₉×#417	—	2	1	no	—
25	C₁₉×#398	—	2	1	no	—
26	C₁₉×#394	—	2	1	no	—
27	C₁₉×#388	—	2	2	no	—
28	C₁₉×#382	C₂²	1	1	yes	characteristic
29	C₁₉×#380	—	2	1	no	—
30	C₁₉×#327	—	2	2	no	—
31	C₁₉×Q₈⋊C₈	—	2	2	no	—
32	C₁₉×D₄⋊C₈	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	—	2	1	no	—
37	C₁₉×#137	—	4	2	no	—
38	C₁₉×#137	—	4	2	no	—
39	C₂×Q₁₆×C₁₉	—	2	2	no	—
40	C₂×SD₁₆×C₁₉	—	2	2	no	—
41	C₂×D₈×C₁₉	—	2	2	no	—
42	C₂×M₁₆×C₁₉	—	2	1	no	—
43	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
44	C₁₉×#127	D₄	1	1	yes	characteristic
45	C₁₉×#124	—	2	1	no	—
46	C₁₉×C₂²⋊Q₈	—	4	2	no	—
47	C₁₉×C₂²⋊Q₈	—	4	2	no	—
48	C₁₉×#121	—	2	1	no	—
49	C₁₉×#121	—	2	1	no	—
50	C₄×Q₈×C₁₉	—	2	1	no	—
51	C₄×Q₈×C₁₉	—	2	1	no	—
52	C₄×Q₈×C₁₉	—	2	1	no	—
53	C₄×Q₈×C₁₉	—	2	1	no	—
54	C₄×D₄×C₁₉	—	2	1	no	—
55	C₄×D₄×C₁₉	—	2	1	no	—
56	C₄×D₄×C₁₉	—	2	1	no	—
57	C₄×D₄×C₁₉	—	2	1	no	—
58	C₄×D₄×C₁₉	—	2	1	no	—
59	C₄×D₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×#107	—	2	2	no	—
71	C₁₉×C₄⋊C₈	—	2	1	no	—
72	C₁₉×C₄⋊C₈	—	2	1	no	—
73	C₁₉×C₄⋊C₈	—	2	1	no	—
74	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
75	C₁₉×#103	—	2	2	no	—
76	C₁₉×#102	—	2	2	no	—
77	C₁₉×#102	—	2	2	no	—
78	C₁₉×#102	—	2	2	no	—
79	C₁₉×C₂²⋊C₈	—	2	1	no	—
80	C₁₉×C₂²⋊C₈	—	2	1	no	—
81	C₄×C₈×C₁₉	—	2	1	no	—
82	C₄×C₈×C₁₉	D₄	1	2	yes	—
83	C₁₉×#95	—	2	2	no	—
84	C₁₉×#95	—	2	1	no	—
85	C₁₉×#95	D₄	1	2	yes	—
86	C₂⁴×C₁₉	—	2	1	no	—
87	#41×C₁₉	—	4	1	no	—
88	#41×C₁₉	—	4	1	no	—
89	#41×C₁₉	—	4	1	no	—
90	#41×C₁₉	—	4	1	no	—
91	C₂×Q₈×C₁₉	—	2	1	no	—
92	C₂×Q₈×C₁₉	—	2	1	no	—
93	C₂×Q₈×C₁₉	—	2	1	no	—
94	C₂×Q₈×C₁₉	—	2	1	no	—
95	C₂×Q₈×C₁₉	—	2	1	no	—
96	C₂×Q₈×C₁₉	—	2	1	no	—
97	C₂×Q₈×C₁₉	D₈	1	2	yes	complemented
98	C₂×D₄×C₁₉	—	2	1	no	—
99	C₂×D₄×C₁₉	—	2	1	no	—
100	C₂×D₄×C₁₉	—	2	1	no	—
101	C₂×D₄×C₁₉	—	2	1	no	—
102	C₂×D₄×C₁₉	—	2	1	no	—
103	C₂×D₄×C₁₉	—	4	2	no	—
104	C₂×D₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	4	1	no	—
110	C₂²×C₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	—	4	1	no	—
112	C₂²×C₄×C₁₉	—	4	1	no	—
113	C₂²×C₄×C₁₉	—	4	1	no	—
114	C₂²×C₄×C₁₉	—	4	1	no	—
115	C₂²×C₄×C₁₉	—	4	1	no	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	Q₁₆×C₁₉	—	4	4	no	—
120	SD₁₆×C₁₉	—	4	4	no	—
121	D₈×C₁₉	—	4	4	no	—
122	M₁₆×C₁₉	—	4	1	no	—
123	M₁₆×C₁₉	—	4	1	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	4	1	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	4	4	no	—
134	C₄⋊C₄×C₁₉	—	4	1	no	—
135	C₄⋊C₄×C₁₉	—	4	1	no	—
136	C₄⋊C₄×C₁₉	—	4	1	no	—
137	C₄⋊C₄×C₁₉	—	4	1	no	—
138	C₂²⋊C₄×C₁₉	—	4	4	no	—
139	C₂²⋊C₄×C₁₉	—	4	4	no	—
140	C₂²⋊C₄×C₁₉	—	4	1	no	—
141	C₂²⋊C₄×C₁₉	—	4	1	no	—
142	C₂²⋊C₄×C₁₉	—	4	1	no	—
143	C₂²⋊C₄×C₁₉	—	4	1	no	—
144	C₄²×C₁₉	—	4	1	no	—
145	C₄²×C₁₉	—	4	1	no	—
146	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₉	#41	1	1	yes	characteristic
150	#9997	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	—	4	1	no	—
154	C₂³×C₁₉	—	4	1	no	—
155	C₂³×C₁₉	—	4	1	no	—
156	C₂³×C₁₉	—	4	1	no	—
157	C₂³×C₁₉	—	4	1	no	—
158	C₂³×C₁₉	—	4	1	no	—
159	C₂³×C₁₉	#120	1	1	yes	characteristic
160	Q₈×C₁₉	—	2	2	no	—
161	Q₈×C₁₉	—	2	2	no	—
162	Q₈×C₁₉	—	4	1	no	—
163	Q₈×C₁₉	—	4	1	no	—
164	Q₈×C₁₉	—	4	1	no	—
165	Q₈×C₁₉	—	4	1	no	—
166	D₄×C₁₉	—	2	2	no	—
167	D₄×C₁₉	—	2	2	no	—
168	D₄×C₁₉	—	4	1	no	—
169	D₄×C₁₉	—	4	1	no	—
170	D₄×C₁₉	—	4	2	no	—
171	D₄×C₁₉	—	4	1	no	—
172	D₄×C₁₉	—	4	1	no	—
173	D₄×C₁₉	—	8	1	no	—
174	D₄×C₁₉	—	8	1	no	—
175	D₄×C₁₉	—	8	1	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	8	1	no	—
191	C₂×C₄×C₁₉	—	8	1	no	—
192	C₂×C₄×C₁₉	—	8	1	no	—
193	C₂×C₄×C₁₉	—	8	1	no	—
194	C₂×C₄×C₁₉	—	8	1	no	—
195	C₂×C₄×C₁₉	—	8	1	no	—
196	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
200	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
201	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
204	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
205	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
206	C₈×C₁₉	—	4	2	no	—
207	C₈×C₁₉	—	4	2	no	—
208	C₈×C₁₉	—	8	1	no	—
209	#3100	C₂×C₁₉	1	1	yes	characteristic
210	#3037	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#2536	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#1517	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#1486	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#1479	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#1286	C₂×C₁₉	1	1	yes	characteristic, complemented
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	4	2	no	—
219	C₂²×C₁₉	—	4	2	no	—
220	C₂²×C₁₉	—	4	2	no	—
221	C₂²×C₁₉	—	8	1	no	—
222	C₂²×C₁₉	—	8	1	no	—
223	C₂²×C₁₉	—	8	1	no	—
224	C₂²×C₁₉	—	8	1	no	—
225	C₂²×C₁₉	—	8	1	no	—
226	C₂²×C₁₉	—	8	1	no	—
227	C₂²×C₁₉	—	8	1	no	—
228	C₂²×C₁₉	#392	1	1	yes	characteristic
229	C₂²×C₁₉	#447	1	1	yes	characteristic
230	C₂²×C₁₉	#449	1	1	yes	characteristic
231	C₄×C₁₉	—	2	1	no	—
232	C₄×C₁₉	—	2	1	no	—
233	C₄×C₁₉	—	2	1	no	—
234	C₄×C₁₉	—	2	1	no	—
235	C₄×C₁₉	—	4	2	no	—
236	C₄×C₁₉	—	8	2	no	—
237	C₄×C₁₉	—	8	1	no	—
238	C₄×C₁₉	—	8	1	no	—
239	C₄×C₁₉	—	8	1	no	—
240	C₄×C₁₉	#447	1	1	yes	characteristic
241	C₄×C₁₉	#449	1	1	yes	characteristic
242	C₄×C₁₉	#466	1	1	yes	characteristic
243	C₄×C₁₉	#469	1	1	yes	characteristic
244	C₂×#137	—	2	1	no	—
245	#532	C₂²×C₁₉	1	1	yes	characteristic
246	C₂×C₂²⋊Q₈	—	2	1	no	—
247	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
249	#480	—	2	1	no	—
250	#474	—	2	1	no	—
251	#464	—	2	2	no	—
252	#462	—	2	1	no	—
253	#460	—	2	1	no	—
254	#459	—	2	1	no	—
255	#447	—	2	1	no	—
256	C₄×D₈	—	2	2	no	—
257	#431	C₂²×C₁₉	1	1	yes	characteristic
258	#431	C₂²×C₁₉	1	1	yes	characteristic
259	#423	C₂²×C₁₉	1	1	yes	characteristic
260	#417	—	2	1	no	—
261	#398	—	2	1	no	—
262	#394	—	2	1	no	—
263	#388	—	2	2	no	—
264	#382	C₂²×C₁₉	1	1	yes	characteristic
265	#380	—	2	1	no	—
266	#327	—	2	2	no	—
267	Q₈⋊C₈	—	2	2	no	—
268	D₄⋊C₈	—	2	2	no	—
269	C₂×C₁₉	—	2	1	no	—
270	C₂×C₁₉	—	2	1	no	—
271	C₂×C₁₉	—	8	2	no	—
272	C₂×C₁₉	—	16	1	no	—
273	C₂×C₁₉	#1999	1	1	yes	characteristic
274	C₂×C₁₉	#2009	1	1	yes	characteristic
275	C₂×C₁₉	#2010	1	1	yes	characteristic
276	C₂×#41	—	2	1	no	—
277	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
278	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
279	C₂³×C₄	—	2	1	no	—
280	#137	—	4	2	no	—
281	#137	—	4	2	no	—
282	C₂×Q₁₆	—	2	2	no	—
283	C₂×SD₁₆	—	2	2	no	—
284	C₂×D₈	—	2	2	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
287	#127	D₄×C₁₉	1	1	yes	characteristic
288	#124	—	2	1	no	—
289	C₂²⋊Q₈	—	4	2	no	—
290	C₂²⋊Q₈	—	4	2	no	—
291	#121	—	2	1	no	—
292	#121	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×Q₈	—	2	1	no	—
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
307	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
313	#107	—	2	2	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	—	2	1	no	—
316	C₄⋊C₈	—	2	1	no	—
317	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
318	#103	—	2	2	no	—
319	#102	—	2	2	no	—
320	#102	—	2	2	no	—
321	#102	—	2	2	no	—
322	C₂²⋊C₈	—	2	1	no	—
323	C₂²⋊C₈	—	2	1	no	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	D₄×C₁₉	1	2	yes	—
326	#95	—	2	2	no	—
327	#95	—	2	1	no	—
328	#95	D₄×C₁₉	1	2	yes	—
329	C₁₉	#9997	1	1	yes	characteristic, direct product factor, Sylow
330	C₂⁴	—	2	1	no	—
331	#41	—	4	1	no	—
332	#41	—	4	1	no	—
333	#41	—	4	1	no	—
334	#41	—	4	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	D₈×C₁₉	1	2	yes	complemented
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	—	4	1	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	—	4	1	no	—
360	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
363	Q₁₆	—	4	4	no	—
364	SD₁₆	—	4	4	no	—
365	D₈	—	4	4	no	—
366	M₁₆	—	4	1	no	—
367	M₁₆	—	4	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	4	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	4	4	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	4	1	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₂²⋊C₄	—	4	4	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₂²⋊C₄	—	4	1	no	—
387	C₂²⋊C₄	—	4	1	no	—
388	C₄²	—	4	1	no	—
389	C₄²	—	4	1	no	—
390	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
391	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
392	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
393	C₄²	#41×C₁₉	1	1	yes	characteristic
394	C₂³	—	2	2	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	C₁₉×#120	1	1	yes	characteristic
403	Q₈	—	2	2	no	—
404	Q₈	—	2	2	no	—
405	Q₈	—	4	1	no	—
406	Q₈	—	4	1	no	—
407	Q₈	—	4	1	no	—
408	Q₈	—	4	1	no	—
409	D₄	—	2	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	4	1	no	—
412	D₄	—	4	1	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	1	no	—
415	D₄	—	4	1	no	—
416	D₄	—	8	1	no	—
417	D₄	—	8	1	no	—
418	D₄	—	8	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	8	1	no	—
434	C₂×C₄	—	8	1	no	—
435	C₂×C₄	—	8	1	no	—
436	C₂×C₄	—	8	1	no	—
437	C₂×C₄	—	8	1	no	—
438	C₂×C₄	—	8	1	no	—
439	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
440	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
441	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
442	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
443	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
444	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
445	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
446	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
447	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
448	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
449	C₈	—	4	2	no	—
450	C₈	—	4	2	no	—
451	C₈	—	8	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	8	1	no	—
463	C₂²	—	8	1	no	—
464	C₂²	C₁₉×#392	1	1	yes	characteristic
465	C₂²	C₁₉×#447	1	1	yes	characteristic
466	C₂²	C₁₉×#449	1	1	yes	characteristic
467	C₄	—	2	1	no	—
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	4	2	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	1	no	—
474	C₄	—	8	1	no	—
475	C₄	—	8	1	no	—
476	C₄	C₁₉×#447	1	1	yes	characteristic
477	C₄	C₁₉×#449	1	1	yes	characteristic
478	C₄	C₁₉×#466	1	1	yes	characteristic
479	C₄	C₁₉×#469	1	1	yes	characteristic
480	C₂	—	2	1	no	—
481	C₂	—	2	1	no	—
482	C₂	—	8	2	no	—
483	C₂	—	16	1	no	—
484	C₂	C₁₉×#1999	1	1	yes	characteristic
485	C₂	C₁₉×#2009	1	1	yes	characteristic
486	C₂	C₁₉×#2010	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3100	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3037	C₂	semidirect
3. C₁₉×#2536	C₂	semidirect
4. C₁₉×#1517	C₂	semidirect
5. C₁₉×#1486	C₂	semidirect
6. C₁₉×#1479	C₂	semidirect
7. C₁₉×#1286	C₂	semidirect
97. C₂×Q₈×C₁₉	D₈	semidirect
150. #9997	C₁₉	direct (N × H)
210. #3037	C₂×C₁₉	semidirect
211. #2536	C₂×C₁₉	semidirect
212. #1517	C₂×C₁₉	semidirect
213. #1486	C₂×C₁₉	semidirect
214. #1479	C₂×C₁₉	semidirect
215. #1286	C₂×C₁₉	semidirect
329. C₁₉	#9997	direct (N × H)
341. C₂×Q₈	D₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3100	2
C₁₉×#3037	2
C₁₉×#2536	2
C₁₉×#1517	2
C₁₉×#1486	2
C₁₉×#1479	2
C₁₉×#1286	2
#9997	19

Subgroups — C19×#9997 #18015956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9997 #18015956