Subgroups — C₁₉×#8528 #18014487

Order 4864.

728 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3545	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1958	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1533	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1512	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1494	C₂	1	2	yes	maximal, complemented
6	C₁₉×#563	C₄	1	1	yes	characteristic, complemented
7	C₁₉×#562	C₄	1	2	yes	complemented
8	C₁₉×H(3,𝔽₄)	C₄	1	1	yes	characteristic, complemented
9	C₁₉×#555	—	2	1	no	—
10	C₁₉×#551	—	2	1	no	—
11	C₁₉×#551	—	2	2	no	—
12	C₁₉×#546	—	2	2	no	—
13	C₁₉×#542	—	2	2	no	—
14	C₁₉×#538	—	2	2	no	—
15	C₁₉×#536	—	2	1	no	—
16	C₁₉×#534	—	2	1	no	—
17	C₁₉×#529	C₂²	1	2	yes	—
18	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
19	C₁₉×#432	C₂²	1	2	yes	complemented
20	C₂×C₁₉×#103	—	2	1	no	—
21	C₂×C₁₉×#102	—	2	1	no	—
22	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#382	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#329	—	2	1	no	—
25	C₁₉×#329	—	2	1	no	—
26	C₁₉×#328	—	2	2	no	—
27	C₁₉×#327	—	2	2	no	—
28	C₁₉×Q₈⋊C₈	—	2	2	no	—
29	C₁₉×D₄⋊C₈	—	2	2	no	—
30	C₂×#41×C₁₉	—	2	1	no	—
31	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	—	2	1	no	—
37	C₁₉×#126	—	2	2	no	—
38	C₁₉×#126	—	2	2	no	—
39	C₁₉×#126	—	2	2	no	—
40	C₁₉×#125	C₂×C₄	1	2	yes	—
41	C₁₉×#124	—	2	1	no	—
42	C₁₉×#124	—	2	2	no	—
43	C₁₉×#124	—	2	1	no	—
44	C₁₉×#124	—	2	2	no	—
45	C₁₉×#124	—	2	2	no	—
46	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
47	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
48	C₁₉×#124	C₂×C₄	1	2	yes	—
49	C₁₉×#124	D₄	1	1	yes	characteristic
50	C₁₉×#124	D₄	1	1	yes	characteristic
51	C₁₉×#123	—	2	1	no	—
52	C₁₉×#123	—	2	2	no	—
53	C₁₉×#123	—	2	2	no	—
54	C₁₉×#123	—	2	1	no	—
55	C₁₉×#123	—	2	2	no	—
56	C₁₉×#123	—	2	2	no	—
57	C₁₉×#123	—	2	2	no	—
58	C₁₉×C₂²⋊Q₈	—	2	2	no	—
59	C₁₉×C₂²⋊Q₈	—	2	2	no	—
60	C₁₉×C₂²⋊Q₈	—	2	2	no	—
61	C₁₉×C₂²⋊Q₈	—	2	2	no	—
62	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
63	C₁₉×#121	—	2	2	no	—
64	C₁₉×#121	—	2	2	no	—
65	C₁₉×#121	—	2	2	no	—
66	C₁₉×#121	—	2	2	no	—
67	C₁₉×#121	D₄	1	2	yes	—
68	C₁₉×#120	—	2	1	no	—
69	C₁₉×#120	—	2	2	no	—
70	C₁₉×#120	—	2	1	no	—
71	C₁₉×#120	—	2	2	no	—
72	C₄×Q₈×C₁₉	D₄	1	2	yes	—
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	D₄	1	2	yes	—
77	C₁₉×#117	—	2	1	no	—
78	C₁₉×#117	—	2	2	no	—
79	C₁₉×#117	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₁₉×C₄⋊C₈	—	2	2	no	—
86	C₁₉×#103	—	4	2	no	—
87	C₁₉×#102	—	4	2	no	—
88	C₁₉×C₂²⋊C₈	—	2	2	no	—
89	C₁₉×#97	—	2	2	no	—
90	C₄×C₈×C₁₉	—	2	2	no	—
91	C₁₉×#95	—	2	2	no	—
92	C₂⁴×C₁₉	—	2	1	no	—
93	C₂⁴×C₁₉	—	2	1	no	—
94	#41×C₁₉	—	8	1	no	—
95	#41×C₁₉	—	8	1	no	—
96	C₂×Q₈×C₁₉	—	2	1	no	—
97	C₂×Q₈×C₁₉	—	2	1	no	—
98	C₂×Q₈×C₁₉	—	4	1	no	—
99	C₂×Q₈×C₁₉	—	4	1	no	—
100	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
101	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	4	1	no	—
110	C₂×D₄×C₁₉	—	4	1	no	—
111	C₂×D₄×C₁₉	—	8	1	no	—
112	C₂×D₄×C₁₉	—	8	1	no	—
113	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
114	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	—	2	1	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	2	no	—
121	C₂²×C₄×C₁₉	—	4	1	no	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	4	1	no	—
126	C₂×C₈×C₁₉	—	4	1	no	—
127	C₂×C₈×C₁₉	—	4	2	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	4	1	no	—
136	C₄⋊C₄×C₁₉	—	4	1	no	—
137	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
138	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
139	C₂²⋊C₄×C₁₉	—	2	2	no	—
140	C₂²⋊C₄×C₁₉	—	2	1	no	—
141	C₂²⋊C₄×C₁₉	—	2	1	no	—
142	C₂²⋊C₄×C₁₉	—	2	2	no	—
143	C₂²⋊C₄×C₁₉	—	2	2	no	—
144	C₂²⋊C₄×C₁₉	—	2	2	no	—
145	C₂²⋊C₄×C₁₉	—	2	2	no	—
146	C₂²⋊C₄×C₁₉	—	2	2	no	—
147	C₂²⋊C₄×C₁₉	—	2	2	no	—
148	C₂²⋊C₄×C₁₉	—	2	2	no	—
149	C₂²⋊C₄×C₁₉	—	2	2	no	—
150	C₂²⋊C₄×C₁₉	—	2	2	no	—
151	C₂²⋊C₄×C₁₉	—	2	2	no	—
152	C₂²⋊C₄×C₁₉	—	2	2	no	—
153	C₂²⋊C₄×C₁₉	—	2	2	no	—
154	C₄²×C₁₉	—	2	1	no	—
155	C₄²×C₁₉	—	2	1	no	—
156	C₄²×C₁₉	—	2	2	no	—
157	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₉	C₂×D₄	1	2	yes	—
160	#8528	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂³×C₁₉	—	2	1	no	—
162	C₂³×C₁₉	—	2	2	no	—
163	C₂³×C₁₉	—	2	1	no	—
164	C₂³×C₁₉	—	4	1	no	—
165	C₂³×C₁₉	—	4	1	no	—
166	C₂³×C₁₉	—	8	2	no	—
167	C₂³×C₁₉	—	8	1	no	—
168	C₂³×C₁₉	—	8	2	no	—
169	C₂³×C₁₉	#120	1	1	yes	characteristic
170	Q₈×C₁₉	—	4	1	no	—
171	Q₈×C₁₉	—	4	1	no	—
172	Q₈×C₁₉	—	4	2	no	—
173	Q₈×C₁₉	—	8	1	no	—
174	Q₈×C₁₉	—	8	1	no	—
175	D₄×C₁₉	—	4	1	no	—
176	D₄×C₁₉	—	4	1	no	—
177	D₄×C₁₉	—	4	2	no	—
178	D₄×C₁₉	—	4	2	no	—
179	D₄×C₁₉	—	4	2	no	—
180	D₄×C₁₉	—	8	1	no	—
181	D₄×C₁₉	—	8	2	no	—
182	D₄×C₁₉	—	8	2	no	—
183	D₄×C₁₉	—	8	2	no	—
184	D₄×C₁₉	—	8	1	no	—
185	C₂×C₄×C₁₉	—	2	1	no	—
186	C₂×C₄×C₁₉	—	2	1	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	8	2	no	—
196	C₂×C₄×C₁₉	—	8	2	no	—
197	C₂×C₄×C₁₉	—	8	1	no	—
198	C₂×C₄×C₁₉	—	8	2	no	—
199	C₂×C₄×C₁₉	—	8	2	no	—
200	C₂×C₄×C₁₉	—	8	1	no	—
201	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
202	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#120	1	2	yes	—
204	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
205	C₈×C₁₉	—	4	2	no	—
206	C₈×C₁₉	—	8	2	no	—
207	#3545	C₂×C₁₉	1	1	yes	characteristic
208	#1958	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#1533	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#1512	C₂×C₁₉	1	2	yes	complemented
211	#1494	C₂×C₁₉	1	2	yes	complemented
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	4	2	no	—
214	C₂²×C₁₉	—	4	1	no	—
215	C₂²×C₁₉	—	4	1	no	—
216	C₂²×C₁₉	—	4	2	no	—
217	C₂²×C₁₉	—	4	2	no	—
218	C₂²×C₁₉	—	4	2	no	—
219	C₂²×C₁₉	—	4	2	no	—
220	C₂²×C₁₉	—	16	1	no	—
221	C₂²×C₁₉	—	16	1	no	—
222	C₂²×C₁₉	—	16	2	no	—
223	C₂²×C₁₉	#379	1	1	yes	characteristic
224	C₂²×C₁₉	#453	1	1	yes	characteristic
225	C₂²×C₁₉	#455	1	1	yes	characteristic
226	C₄×C₁₉	—	2	1	no	—
227	C₄×C₁₉	—	2	1	no	—
228	C₄×C₁₉	—	2	2	no	—
229	C₄×C₁₉	—	2	2	no	—
230	C₄×C₁₉	—	4	1	no	—
231	C₄×C₁₉	—	4	1	no	—
232	C₄×C₁₉	—	4	2	no	—
233	C₄×C₁₉	—	4	2	no	—
234	C₄×C₁₉	—	4	2	no	—
235	C₄×C₁₉	—	16	1	no	—
236	#563	C₄×C₁₉	1	1	yes	characteristic, complemented
237	#562	C₄×C₁₉	1	2	yes	complemented
238	H(3,𝔽₄)	C₄×C₁₉	1	1	yes	characteristic, complemented
239	#555	—	2	1	no	—
240	#551	—	2	1	no	—
241	#551	—	2	2	no	—
242	#546	—	2	2	no	—
243	#542	—	2	2	no	—
244	#538	—	2	2	no	—
245	#536	—	2	1	no	—
246	#534	—	2	1	no	—
247	#529	C₂²×C₁₉	1	2	yes	—
248	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
249	#432	C₂²×C₁₉	1	2	yes	complemented
250	C₂×#103	—	2	1	no	—
251	C₂×#102	—	2	1	no	—
252	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
253	#382	C₂²×C₁₉	1	1	yes	characteristic, complemented
254	#329	—	2	1	no	—
255	#329	—	2	1	no	—
256	#328	—	2	2	no	—
257	#327	—	2	2	no	—
258	Q₈⋊C₈	—	2	2	no	—
259	D₄⋊C₈	—	2	2	no	—
260	C₂×C₁₉	—	2	1	no	—
261	C₂×C₁₉	—	2	1	no	—
262	C₂×C₁₉	—	8	2	no	—
263	C₂×C₁₉	—	8	1	no	—
264	C₂×C₁₉	—	8	1	no	—
265	C₂×C₁₉	#1792	1	1	yes	characteristic
266	C₂×C₁₉	#1794	1	2	yes	—
267	C₂×#41	—	2	1	no	—
268	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
271	C₂²×C₈	—	2	1	no	—
272	C₄⋊Q₈	—	2	1	no	—
273	C₄⋊Q₈	—	2	1	no	—
274	#126	—	2	2	no	—
275	#126	—	2	2	no	—
276	#126	—	2	2	no	—
277	#125	C₂×C₄×C₁₉	1	2	yes	—
278	#124	—	2	1	no	—
279	#124	—	2	2	no	—
280	#124	—	2	1	no	—
281	#124	—	2	2	no	—
282	#124	—	2	2	no	—
283	#124	C₂×C₄×C₁₉	1	1	yes	characteristic
284	#124	C₂×C₄×C₁₉	1	1	yes	characteristic
285	#124	C₂×C₄×C₁₉	1	2	yes	—
286	#124	D₄×C₁₉	1	1	yes	characteristic
287	#124	D₄×C₁₉	1	1	yes	characteristic
288	#123	—	2	1	no	—
289	#123	—	2	2	no	—
290	#123	—	2	2	no	—
291	#123	—	2	1	no	—
292	#123	—	2	2	no	—
293	#123	—	2	2	no	—
294	#123	—	2	2	no	—
295	C₂²⋊Q₈	—	2	2	no	—
296	C₂²⋊Q₈	—	2	2	no	—
297	C₂²⋊Q₈	—	2	2	no	—
298	C₂²⋊Q₈	—	2	2	no	—
299	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
300	#121	—	2	2	no	—
301	#121	—	2	2	no	—
302	#121	—	2	2	no	—
303	#121	—	2	2	no	—
304	#121	D₄×C₁₉	1	2	yes	—
305	#120	—	2	1	no	—
306	#120	—	2	2	no	—
307	#120	—	2	1	no	—
308	#120	—	2	2	no	—
309	C₄×Q₈	D₄×C₁₉	1	2	yes	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	—	2	2	no	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	D₄×C₁₉	1	2	yes	—
314	#117	—	2	1	no	—
315	#117	—	2	2	no	—
316	#117	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
322	C₄⋊C₈	—	2	2	no	—
323	#103	—	4	2	no	—
324	#102	—	4	2	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	#97	—	2	2	no	—
327	C₄×C₈	—	2	2	no	—
328	#95	—	2	2	no	—
329	C₁₉	#8528	1	1	yes	characteristic, direct product factor, Sylow
330	C₂⁴	—	2	1	no	—
331	C₂⁴	—	2	1	no	—
332	#41	—	8	1	no	—
333	#41	—	8	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	4	1	no	—
337	C₂×Q₈	—	4	1	no	—
338	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
339	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
340	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	8	1	no	—
350	C₂×D₄	—	8	1	no	—
351	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
352	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
353	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	4	1	no	—
360	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	4	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
376	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	1	no	—
379	C₂²⋊C₄	—	2	1	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
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	—	2	2	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	2	no	—
395	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
396	C₄²	C₂×D₄×C₁₉	1	2	yes	—
397	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₂³	—	2	1	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	8	2	no	—
404	C₂³	—	8	1	no	—
405	C₂³	—	8	2	no	—
406	C₂³	C₁₉×#120	1	1	yes	characteristic
407	Q₈	—	4	1	no	—
408	Q₈	—	4	1	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	8	1	no	—
411	Q₈	—	8	1	no	—
412	D₄	—	4	1	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	8	1	no	—
418	D₄	—	8	2	no	—
419	D₄	—	8	1	no	—
420	D₄	—	8	2	no	—
421	D₄	—	8	2	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	8	2	no	—
433	C₂×C₄	—	8	1	no	—
434	C₂×C₄	—	8	2	no	—
435	C₂×C₄	—	8	2	no	—
436	C₂×C₄	—	8	2	no	—
437	C₂×C₄	—	8	1	no	—
438	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
439	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
440	C₂×C₄	C₁₉×#120	1	2	yes	—
441	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
442	C₈	—	4	2	no	—
443	C₈	—	8	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	16	1	no	—
453	C₂²	—	16	1	no	—
454	C₂²	—	16	2	no	—
455	C₂²	C₁₉×#379	1	1	yes	characteristic
456	C₂²	C₁₉×#453	1	1	yes	characteristic
457	C₂²	C₁₉×#455	1	1	yes	characteristic
458	C₄	—	2	1	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	2	no	—
467	C₄	—	16	1	no	—
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	—	8	1	no	—
471	C₂	—	8	2	no	—
472	C₂	—	8	1	no	—
473	C₂	C₁₉×#1792	1	1	yes	characteristic
474	C₂	C₁₉×#1794	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3545	C₂
LCS	G ▷ 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×#1958	C₂	semidirect
3. C₁₉×#1533	C₂	semidirect
4. C₁₉×#1512	C₂	semidirect
5. C₁₉×#1494	C₂	semidirect
6. C₁₉×#563	C₄	semidirect
7. C₁₉×#562	C₄	semidirect
8. C₁₉×H(3,𝔽₄)	C₄	semidirect
19. C₁₉×#432	C₂²	semidirect
22. C₂×C₄×C₈×C₁₉	C₂²	semidirect
23. C₁₉×#382	C₂²	semidirect
160. #8528	C₁₉	direct (N × H)
208. #1958	C₂×C₁₉	semidirect
209. #1533	C₂×C₁₉	semidirect
210. #1512	C₂×C₁₉	semidirect
211. #1494	C₂×C₁₉	semidirect
236. #563	C₄×C₁₉	semidirect
237. #562	C₄×C₁₉	semidirect
238. H(3,𝔽₄)	C₄×C₁₉	semidirect
249. #432	C₂²×C₁₉	semidirect
252. C₂×C₄×C₈	C₂²×C₁₉	semidirect
253. #382	C₂²×C₁₉	semidirect
329. C₁₉	#8528	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×#3545	2
C₁₉×#1958	2
C₁₉×#1533	2
C₁₉×#1512	2
C₁₉×#1494	2
#8528	19

Subgroups — C19×#8528 #18014487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8528 #18014487