Subgroups — C₁₉×#18344 #18024303

Order 4864.

924 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3461	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3238	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2546	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1611	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1610	C₂	1	2	yes	maximal
6	C₁₉×#1609	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1509	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1467	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#544	C₂²	1	1	yes	characteristic
10	C₁₉×#542	—	2	2	no	—
11	C₁₉×#541	—	2	2	no	—
12	C₁₉×#539	—	2	1	no	—
13	C₁₉×#539	C₂²	1	2	yes	—
14	C₁₉×#537	C₂²	1	1	yes	characteristic
15	C₁₉×#536	—	2	1	no	—
16	C₁₉×#533	—	2	2	no	—
17	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
18	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₁₉×#529	—	2	2	no	—
20	C₁₉×#529	—	2	1	no	—
21	C₁₉×#529	C₂²	1	2	yes	—
22	C₄×#41×C₁₉	—	2	1	no	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#501	—	2	2	no	—
25	C₁₉×#489	—	2	2	no	—
26	C₁₉×#483	C₂²	1	4	yes	—
27	C₁₉×#480	C₂²	1	4	yes	—
28	C₁₉×#477	—	2	2	no	—
29	C₁₉×#476	—	2	2	no	—
30	C₁₉×#432	C₂²	1	2	yes	—
31	C₁₉×#398	C₂²	1	2	yes	—
32	C₁₉×#398	C₂²	1	2	yes	—
33	C₁₉×#391	—	2	1	no	—
34	C₁₉×#389	—	2	1	no	—
35	C₁₉×#389	—	2	1	no	—
36	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#328	C₂²	1	4	yes	—
38	C₁₉×#327	C₂²	1	4	yes	—
39	C₁₉×#324	C₂²	1	2	yes	—
40	C₁₉×#324	C₂²	1	2	yes	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
44	C₁₉×C₄⋊Q₈	—	2	2	no	—
45	C₁₉×C₄⋊Q₈	—	2	2	no	—
46	C₁₉×C₄⋊Q₈	—	2	2	no	—
47	C₁₉×C₄⋊Q₈	—	2	2	no	—
48	C₁₉×C₄⋊Q₈	—	4	4	no	—
49	C₁₉×#126	—	2	2	no	—
50	C₁₉×#126	—	2	2	no	—
51	C₁₉×#126	—	2	2	no	—
52	C₁₉×#126	—	2	2	no	—
53	C₁₉×#125	—	2	1	no	—
54	C₁₉×#125	—	2	2	no	—
55	C₁₉×#125	—	2	2	no	—
56	C₁₉×#125	—	2	2	no	—
57	C₁₉×#125	D₄	1	2	yes	—
58	C₁₉×#124	—	2	2	no	—
59	C₁₉×#124	—	2	1	no	—
60	C₁₉×#124	D₄	1	2	yes	—
61	C₁₉×#123	—	2	2	no	—
62	C₁₉×#123	—	2	2	no	—
63	C₁₉×#123	—	2	2	no	—
64	C₁₉×#123	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₁₉×C₂²⋊Q₈	—	2	2	no	—
67	C₁₉×C₂²⋊Q₈	—	2	2	no	—
68	C₁₉×C₂²⋊Q₈	—	2	2	no	—
69	C₁₉×C₂²⋊Q₈	—	2	1	no	—
70	C₁₉×C₂²⋊Q₈	—	2	2	no	—
71	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
72	C₁₉×#121	—	2	2	no	—
73	C₁₉×#121	—	2	1	no	—
74	C₁₉×#121	C₂³	1	2	yes	—
75	C₄×Q₈×C₁₉	—	2	1	no	—
76	C₄×Q₈×C₁₉	—	2	1	no	—
77	C₄×Q₈×C₁₉	—	2	1	no	—
78	C₄×Q₈×C₁₉	—	2	2	no	—
79	C₄×Q₈×C₁₉	—	2	2	no	—
80	C₄×Q₈×C₁₉	D₄	1	2	yes	—
81	C₄×D₄×C₁₉	—	2	1	no	—
82	C₄×D₄×C₁₉	—	2	1	no	—
83	C₄×D₄×C₁₉	—	2	1	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	—	2	2	no	—
86	C₄×D₄×C₁₉	D₄	1	2	yes	—
87	C₁₉×#117	—	2	2	no	—
88	C₁₉×#117	—	2	2	no	—
89	C₁₉×#117	—	2	1	no	—
90	C₁₉×#117	—	2	2	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₉	—	2	2	no	—
100	C₂×C₄²×C₁₉	—	2	1	no	—
101	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₁₉×#107	—	2	4	no	—
105	C₁₉×#106	—	2	4	no	—
106	C₁₉×C₄⋊C₈	—	2	2	no	—
107	C₁₉×#103	—	2	4	no	—
108	C₁₉×#102	—	2	4	no	—
109	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
110	C₁₉×#97	—	2	2	no	—
111	C₁₉×#95	—	2	2	no	—
112	C₁₉×#95	—	2	2	no	—
113	C₁₉×#95	C₂³	1	2	yes	—
114	#41×C₁₉	—	4	2	no	—
115	#41×C₁₉	—	4	2	no	—
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	—	2	2	no	—
119	C₂×Q₈×C₁₉	—	2	2	no	—
120	C₂×Q₈×C₁₉	—	4	1	no	—
121	C₂×Q₈×C₁₉	—	4	2	no	—
122	C₂×Q₈×C₁₉	—	4	2	no	—
123	C₂×Q₈×C₁₉	—	4	2	no	—
124	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
125	C₂×D₄×C₁₉	—	2	1	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
141	C₂×C₈×C₁₉	—	2	4	no	—
142	C₄⋊C₄×C₁₉	—	2	4	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	4	no	—
159	C₄⋊C₄×C₁₉	—	4	4	no	—
160	C₄⋊C₄×C₁₉	—	4	1	no	—
161	C₄⋊C₄×C₁₉	—	4	1	no	—
162	C₄⋊C₄×C₁₉	—	4	4	no	—
163	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
165	C₂²⋊C₄×C₁₉	—	2	2	no	—
166	C₂²⋊C₄×C₁₉	—	2	2	no	—
167	C₂²⋊C₄×C₁₉	—	2	2	no	—
168	C₂²⋊C₄×C₁₉	—	2	2	no	—
169	C₂²⋊C₄×C₁₉	—	2	2	no	—
170	C₂²⋊C₄×C₁₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₄²×C₁₉	—	2	2	no	—
175	C₄²×C₁₉	—	2	2	no	—
176	C₄²×C₁₉	—	2	1	no	—
177	C₄²×C₁₉	—	2	2	no	—
178	C₄²×C₁₉	—	2	1	no	—
179	C₄²×C₁₉	—	2	1	no	—
180	C₄²×C₁₉	—	2	1	no	—
181	C₄²×C₁₉	—	4	2	no	—
182	C₄²×C₁₉	C₂×D₄	1	2	yes	—
183	C₄²×C₁₉	C₂×D₄	1	2	yes	—
184	#18344	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂³×C₁₉	—	2	2	no	—
186	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₁₉	—	4	4	no	—
188	Q₈×C₁₉	—	4	2	no	—
189	Q₈×C₁₉	—	4	2	no	—
190	Q₈×C₁₉	—	8	4	no	—
191	Q₈×C₁₉	—	8	1	no	—
192	D₄×C₁₉	—	4	2	no	—
193	D₄×C₁₉	—	4	2	no	—
194	D₄×C₁₉	—	4	2	no	—
195	D₄×C₁₉	—	4	2	no	—
196	D₄×C₁₉	—	8	1	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	4	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	4	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	8	2	no	—
222	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#120	1	2	yes	—
224	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
225	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
226	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
227	C₈×C₁₉	—	4	4	no	—
228	#3461	C₂×C₁₉	1	1	yes	characteristic
229	#3238	C₂×C₁₉	1	2	yes	complemented
230	#2546	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#1611	C₂×C₁₉	1	2	yes	complemented
232	#1610	C₂×C₁₉	1	2	yes	—
233	#1609	C₂×C₁₉	1	4	yes	complemented
234	#1509	C₂×C₁₉	1	2	yes	complemented
235	#1467	C₂×C₁₉	1	1	yes	characteristic, complemented
236	C₂²×C₁₉	—	2	1	no	—
237	C₂²×C₁₉	—	2	1	no	—
238	C₂²×C₁₉	—	4	2	no	—
239	C₂²×C₁₉	—	4	2	no	—
240	C₂²×C₁₉	—	4	2	no	—
241	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
242	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₂²×C₁₉	#575	1	1	yes	characteristic
244	C₄×C₁₉	—	2	2	no	—
245	C₄×C₁₉	—	2	2	no	—
246	C₄×C₁₉	—	2	1	no	—
247	C₄×C₁₉	—	2	2	no	—
248	C₄×C₁₉	—	4	4	no	—
249	C₄×C₁₉	—	4	1	no	—
250	C₄×C₁₉	—	4	2	no	—
251	C₄×C₁₉	—	4	2	no	—
252	C₄×C₁₉	—	4	1	no	—
253	C₄×C₁₉	—	4	1	no	—
254	C₄×C₁₉	—	4	2	no	—
255	C₄×C₁₉	—	8	2	no	—
256	C₄×C₁₉	#456	1	2	yes	—
257	#544	C₂²×C₁₉	1	1	yes	characteristic
258	#542	—	2	2	no	—
259	#541	—	2	2	no	—
260	#539	—	2	1	no	—
261	#539	C₂²×C₁₉	1	2	yes	—
262	#537	C₂²×C₁₉	1	1	yes	characteristic
263	#536	—	2	1	no	—
264	#533	—	2	2	no	—
265	C₂×C₄⋊Q₈	—	2	1	no	—
266	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
267	#529	—	2	2	no	—
268	#529	—	2	1	no	—
269	#529	C₂²×C₁₉	1	2	yes	—
270	C₄×#41	—	2	1	no	—
271	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
272	#501	—	2	2	no	—
273	#489	—	2	2	no	—
274	#483	C₂²×C₁₉	1	4	yes	—
275	#480	C₂²×C₁₉	1	4	yes	—
276	#477	—	2	2	no	—
277	#476	—	2	2	no	—
278	#432	C₂²×C₁₉	1	2	yes	—
279	#398	C₂²×C₁₉	1	2	yes	—
280	#398	C₂²×C₁₉	1	2	yes	—
281	#391	—	2	1	no	—
282	#389	—	2	1	no	—
283	#389	—	2	1	no	—
284	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
285	#328	C₂²×C₁₉	1	4	yes	—
286	#327	C₂²×C₁₉	1	4	yes	—
287	#324	C₂²×C₁₉	1	2	yes	—
288	#324	C₂²×C₁₉	1	2	yes	—
289	C₂×C₁₉	—	2	1	no	—
290	C₂×C₁₉	—	2	1	no	—
291	C₂×C₁₉	—	8	2	no	—
292	C₂×C₁₉	#3006	1	1	yes	characteristic
293	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
294	C₂×C₁₉	#3028	1	1	yes	characteristic
295	C₂×#41	—	2	1	no	—
296	C₂²×Q₈	—	2	1	no	—
297	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
298	C₄⋊Q₈	—	2	2	no	—
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	—	2	2	no	—
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	—	4	4	no	—
303	#126	—	2	2	no	—
304	#126	—	2	2	no	—
305	#126	—	2	2	no	—
306	#126	—	2	2	no	—
307	#125	—	2	1	no	—
308	#125	—	2	2	no	—
309	#125	—	2	2	no	—
310	#125	—	2	2	no	—
311	#125	D₄×C₁₉	1	2	yes	—
312	#124	—	2	2	no	—
313	#124	—	2	1	no	—
314	#124	D₄×C₁₉	1	2	yes	—
315	#123	—	2	2	no	—
316	#123	—	2	2	no	—
317	#123	—	2	2	no	—
318	#123	—	2	2	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	—	2	2	no	—
323	C₂²⋊Q₈	—	2	1	no	—
324	C₂²⋊Q₈	—	2	2	no	—
325	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
326	#121	—	2	2	no	—
327	#121	—	2	1	no	—
328	#121	C₂³×C₁₉	1	2	yes	—
329	C₄×Q₈	—	2	1	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	—	2	1	no	—
332	C₄×Q₈	—	2	2	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	D₄×C₁₉	1	2	yes	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	2	1	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	D₄×C₁₉	1	2	yes	—
341	#117	—	2	2	no	—
342	#117	—	2	2	no	—
343	#117	—	2	1	no	—
344	#117	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
353	C₂×C₄²	—	2	2	no	—
354	C₂×C₄²	—	2	1	no	—
355	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
356	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
358	#107	—	2	4	no	—
359	#106	—	2	4	no	—
360	C₄⋊C₈	—	2	2	no	—
361	#103	—	2	4	no	—
362	#102	—	2	4	no	—
363	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
364	#97	—	2	2	no	—
365	#95	—	2	2	no	—
366	#95	—	2	2	no	—
367	#95	C₂³×C₁₉	1	2	yes	—
368	C₁₉	#18344	1	1	yes	characteristic, direct product factor, Sylow
369	#41	—	4	2	no	—
370	#41	—	4	2	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	4	1	no	—
376	C₂×Q₈	—	4	2	no	—
377	C₂×Q₈	—	4	2	no	—
378	C₂×Q₈	—	4	2	no	—
379	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
396	C₂×C₈	—	2	4	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	4	4	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	—	4	1	no	—
417	C₄⋊C₄	—	4	4	no	—
418	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
419	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
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	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	2	2	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	1	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	4	2	no	—
437	C₄²	C₂×D₄×C₁₉	1	2	yes	—
438	C₄²	C₂×D₄×C₁₉	1	2	yes	—
439	C₂³	—	2	2	no	—
440	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
441	Q₈	—	4	4	no	—
442	Q₈	—	4	2	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	8	4	no	—
445	Q₈	—	8	1	no	—
446	D₄	—	4	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	8	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	8	2	no	—
476	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
477	C₂×C₄	C₁₉×#120	1	2	yes	—
478	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
479	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
480	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
481	C₈	—	4	4	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
488	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
489	C₂²	C₁₉×#575	1	1	yes	characteristic
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	2	no	—
494	C₄	—	4	4	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	1	no	—
499	C₄	—	4	1	no	—
500	C₄	—	4	2	no	—
501	C₄	—	8	2	no	—
502	C₄	C₁₉×#456	1	2	yes	—
503	C₂	—	2	1	no	—
504	C₂	—	2	1	no	—
505	C₂	—	8	2	no	—
506	C₂	C₁₉×#3006	1	1	yes	characteristic
507	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
508	C₂	C₁₉×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#537	C₂²
LCS	G ▷ C₂²×C₄ ▷ 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×#3238	C₂	semidirect
3. C₁₉×#2546	C₂	semidirect
4. C₁₉×#1611	C₂	semidirect
6. C₁₉×#1609	C₂	semidirect
7. C₁₉×#1509	C₂	semidirect
8. C₁₉×#1467	C₂	semidirect
184. #18344	C₁₉	direct (N × H)
229. #3238	C₂×C₁₉	semidirect
230. #2546	C₂×C₁₉	semidirect
231. #1611	C₂×C₁₉	semidirect
233. #1609	C₂×C₁₉	semidirect
234. #1509	C₂×C₁₉	semidirect
235. #1467	C₂×C₁₉	semidirect
368. C₁₉	#18344	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3461	2
C₁₉×#3238	2
C₁₉×#2546	2
C₁₉×#1611	2
C₁₉×#1610	2
C₁₉×#1609	2
C₁₉×#1509	2
C₁₉×#1467	2
#18344	19

Subgroups — C19×#18344 #18024303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18344 #18024303