Subgroups — C₁₉×#9525 #18015484

Order 4864.

538 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3094	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2333	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1826	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1820	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1510	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1306	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1284	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
10	C₁₉×#482	—	2	2	no	—
11	C₁₉×#481	C₄	1	2	yes	complemented
12	C₁₉×#480	C₄	1	2	yes	complemented
13	C₁₉×#428	—	2	1	no	—
14	C₁₉×#418	—	2	1	no	—
15	C₁₉×#407	C₂²	1	1	yes	characteristic
16	C₁₉×#407	C₂²	1	1	yes	characteristic
17	C₁₉×#390	—	2	1	no	—
18	C₁₉×#388	—	2	1	no	—
19	C₁₉×#387	—	2	1	no	—
20	C₁₉×#386	—	2	1	no	—
21	C₁₉×#386	—	2	1	no	—
22	C₁₉×#381	C₂²	1	1	yes	characteristic
23	C₁₉×#381	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
25	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#342	—	2	1	no	—
27	C₁₉×#342	—	2	1	no	—
28	C₁₉×#339	—	2	1	no	—
29	C₁₉×#339	—	2	1	no	—
30	C₁₉×#327	—	2	2	no	—
31	C₂²×D₄×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	—	2	1	no	—
34	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₁₉×#121	—	2	1	no	—
38	C₁₉×#121	—	2	1	no	—
39	C₁₉×#121	C₂×C₄	1	2	yes	—
40	C₁₉×#121	D₄	1	2	yes	—
41	C₁₉×#117	—	2	1	no	—
42	C₁₉×#117	—	2	1	no	—
43	C₁₉×#117	—	2	1	no	—
44	C₁₉×#117	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
47	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₉	—	2	1	no	—
59	C₂×C₄²×C₁₉	—	2	1	no	—
60	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
62	C₁₉×#107	—	2	2	no	—
63	C₁₉×#106	—	2	2	no	—
64	C₁₉×#102	—	2	2	no	—
65	C₁₉×#102	—	2	2	no	—
66	C₁₉×C₂²⋊C₈	—	2	1	no	—
67	C₁₉×C₂²⋊C₈	—	2	1	no	—
68	C₁₉×C₂²⋊C₈	—	2	1	no	—
69	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	complemented
70	C₁₉×#95	—	2	1	no	—
71	C₁₉×#95	—	2	1	no	—
72	C₁₉×#95	—	2	1	no	—
73	C₁₉×#95	—	2	1	no	—
74	C₁₉×#95	—	2	1	no	—
75	C₁₉×#95	—	2	1	no	—
76	C₁₉×#95	—	2	1	no	—
77	C₂⁴×C₁₉	—	2	1	no	—
78	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂×D₄×C₁₉	—	2	2	no	—
80	C₂×D₄×C₁₉	—	2	2	no	—
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	4	1	no	—
83	C₂×D₄×C₁₉	—	4	1	no	—
84	C₂×D₄×C₁₉	—	8	1	no	—
85	C₂×D₄×C₁₉	—	8	1	no	—
86	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	—	4	2	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	8	1	no	—
99	C₂²×C₄×C₁₉	—	8	1	no	—
100	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
106	M₁₆×C₁₉	—	4	1	no	—
107	M₁₆×C₁₉	—	4	1	no	—
108	M₁₆×C₁₉	—	4	1	no	—
109	M₁₆×C₁₉	—	4	1	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	4	1	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	8	1	no	—
118	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
119	C₂²⋊C₄×C₁₉	—	2	2	no	—
120	C₂²⋊C₄×C₁₉	—	2	2	no	—
121	C₂²⋊C₄×C₁₉	—	4	2	no	—
122	C₂²⋊C₄×C₁₉	—	4	2	no	—
123	C₂²⋊C₄×C₁₉	—	4	1	no	—
124	C₂²⋊C₄×C₁₉	—	4	1	no	—
125	C₂²⋊C₄×C₁₉	—	4	1	no	—
126	C₂²⋊C₄×C₁₉	—	4	1	no	—
127	C₂²⋊C₄×C₁₉	—	4	1	no	—
128	C₂²⋊C₄×C₁₉	—	4	1	no	—
129	C₂²⋊C₄×C₁₉	—	8	1	no	—
130	C₂²⋊C₄×C₁₉	—	8	1	no	—
131	C₄²×C₁₉	—	4	1	no	—
132	C₄²×C₁₉	—	4	1	no	—
133	C₄²×C₁₉	—	4	1	no	—
134	C₄²×C₁₉	—	4	1	no	—
135	C₄²×C₁₉	—	8	1	no	—
136	#9525	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	2	1	no	—
139	C₂³×C₁₉	—	2	2	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	4	1	no	—
142	C₂³×C₁₉	—	4	1	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	—	4	1	no	—
147	C₂³×C₁₉	—	4	1	no	—
148	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
149	C₂³×C₁₉	#120	1	1	yes	characteristic
150	C₂³×C₁₉	#121	1	1	yes	characteristic
151	D₄×C₁₉	—	4	2	no	—
152	D₄×C₁₉	—	8	1	no	—
153	D₄×C₁₉	—	8	2	no	—
154	D₄×C₁₉	—	8	2	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	1	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	—	8	4	no	—
181	C₂×C₄×C₁₉	—	8	1	no	—
182	C₂×C₄×C₁₉	—	8	1	no	—
183	C₂×C₄×C₁₉	—	8	1	no	—
184	C₂×C₄×C₁₉	—	8	1	no	—
185	C₂×C₄×C₁₉	—	8	1	no	—
186	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
190	C₈×C₁₉	—	4	2	no	—
191	C₈×C₁₉	—	8	1	no	—
192	#3094	C₂×C₁₉	1	1	yes	characteristic
193	#2333	C₂×C₁₉	1	1	yes	characteristic
194	#1826	C₂×C₁₉	1	1	yes	characteristic, complemented
195	#1820	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#1510	C₂×C₁₉	1	1	yes	characteristic
197	#1306	C₂×C₁₉	1	1	yes	characteristic, complemented
198	#1284	C₂×C₁₉	1	1	yes	characteristic, complemented
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	2	1	no	—
203	C₂²×C₁₉	—	2	1	no	—
204	C₂²×C₁₉	—	2	1	no	—
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	2	1	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	—	4	2	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	8	1	no	—
211	C₂²×C₁₉	—	8	1	no	—
212	C₂²×C₁₉	—	8	1	no	—
213	C₂²×C₁₉	—	8	1	no	—
214	C₂²×C₁₉	—	8	1	no	—
215	C₂²×C₁₉	—	8	1	no	—
216	C₂²×C₁₉	#386	1	1	yes	characteristic
217	C₂²×C₁₉	#458	1	1	yes	characteristic
218	C₂²×C₁₉	#458	1	1	yes	characteristic
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	—	8	1	no	—
226	C₄×C₁₉	—	8	1	no	—
227	C₄×C₁₉	—	8	1	no	—
228	C₄×C₁₉	—	8	1	no	—
229	C₄×C₁₉	—	8	1	no	—
230	C₄×C₁₉	—	16	1	no	—
231	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
232	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
233	#482	—	2	2	no	—
234	#481	C₄×C₁₉	1	2	yes	complemented
235	#480	C₄×C₁₉	1	2	yes	complemented
236	#428	—	2	1	no	—
237	#418	—	2	1	no	—
238	#407	C₂²×C₁₉	1	1	yes	characteristic
239	#407	C₂²×C₁₉	1	1	yes	characteristic
240	#390	—	2	1	no	—
241	#388	—	2	1	no	—
242	#387	—	2	1	no	—
243	#386	—	2	1	no	—
244	#386	—	2	1	no	—
245	#381	C₂²×C₁₉	1	1	yes	characteristic
246	#381	C₂²×C₁₉	1	1	yes	characteristic
247	C₄×C₂²⋊C₄	—	2	1	no	—
248	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
249	#342	—	2	1	no	—
250	#342	—	2	1	no	—
251	#339	—	2	1	no	—
252	#339	—	2	1	no	—
253	#327	—	2	2	no	—
254	C₂×C₁₉	—	2	1	no	—
255	C₂×C₁₉	—	2	1	no	—
256	C₂×C₁₉	—	4	1	no	—
257	C₂×C₁₉	—	4	1	no	—
258	C₂×C₁₉	—	8	2	no	—
259	C₂×C₁₉	#1890	1	1	yes	characteristic
260	C₂×C₁₉	#1904	1	1	yes	characteristic
261	C₂×C₁₉	#1906	1	1	yes	characteristic
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
264	C₂³×C₄	—	2	1	no	—
265	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	1	no	—
268	#121	—	2	1	no	—
269	#121	—	2	1	no	—
270	#121	C₂×C₄×C₁₉	1	2	yes	—
271	#121	D₄×C₁₉	1	2	yes	—
272	#117	—	2	1	no	—
273	#117	—	2	1	no	—
274	#117	—	2	1	no	—
275	#117	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
278	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
279	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
292	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
293	#107	—	2	2	no	—
294	#106	—	2	2	no	—
295	#102	—	2	2	no	—
296	#102	—	2	2	no	—
297	C₂²⋊C₈	—	2	1	no	—
298	C₂²⋊C₈	—	2	1	no	—
299	C₂²⋊C₈	—	2	1	no	—
300	C₂²⋊C₈	C₂×C₄×C₁₉	1	2	yes	complemented
301	#95	—	2	1	no	—
302	#95	—	2	1	no	—
303	#95	—	2	1	no	—
304	#95	—	2	1	no	—
305	#95	—	2	1	no	—
306	#95	—	2	1	no	—
307	#95	—	2	1	no	—
308	C₁₉	#9525	1	1	yes	characteristic, direct product factor, Sylow
309	C₂⁴	—	2	1	no	—
310	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	8	1	no	—
317	C₂×D₄	—	8	1	no	—
318	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	8	1	no	—
331	C₂²×C₄	—	8	1	no	—
332	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
338	M₁₆	—	4	1	no	—
339	M₁₆	—	4	1	no	—
340	M₁₆	—	4	1	no	—
341	M₁₆	—	4	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	4	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	8	1	no	—
350	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	4	2	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	—	4	1	no	—
361	C₂²⋊C₄	—	8	1	no	—
362	C₂²⋊C₄	—	8	1	no	—
363	C₄²	—	4	1	no	—
364	C₄²	—	4	1	no	—
365	C₄²	—	4	1	no	—
366	C₄²	—	4	1	no	—
367	C₄²	—	8	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
380	C₂³	C₁₉×#120	1	1	yes	characteristic
381	C₂³	C₁₉×#121	1	1	yes	characteristic
382	D₄	—	4	2	no	—
383	D₄	—	8	1	no	—
384	D₄	—	8	2	no	—
385	D₄	—	8	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	8	4	no	—
412	C₂×C₄	—	8	1	no	—
413	C₂×C₄	—	8	1	no	—
414	C₂×C₄	—	8	1	no	—
415	C₂×C₄	—	8	1	no	—
416	C₂×C₄	—	8	1	no	—
417	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
418	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
419	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
420	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
421	C₈	—	4	2	no	—
422	C₈	—	8	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	8	1	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	C₁₉×#386	1	1	yes	characteristic
441	C₂²	C₁₉×#458	1	1	yes	characteristic
442	C₂²	C₁₉×#458	1	1	yes	characteristic
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	8	1	no	—
450	C₄	—	8	1	no	—
451	C₄	—	8	1	no	—
452	C₄	—	8	1	no	—
453	C₄	—	8	1	no	—
454	C₄	—	16	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	2	1	no	—
457	C₂	—	4	1	no	—
458	C₂	—	4	1	no	—
459	C₂	—	8	2	no	—
460	C₂	C₁₉×#1890	1	1	yes	characteristic
461	C₂	C₁₉×#1904	1	1	yes	characteristic
462	C₂	C₁₉×#1906	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1826	C₂	semidirect
4. C₁₉×#1820	C₂	semidirect
6. C₁₉×#1306	C₂	semidirect
7. C₁₉×#1284	C₂	semidirect
11. C₁₉×#481	C₄	semidirect
12. C₁₉×#480	C₄	semidirect
46. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
47. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
69. C₁₉×C₂²⋊C₈	C₂×C₄	semidirect
136. #9525	C₁₉	direct (N × H)
194. #1826	C₂×C₁₉	semidirect
195. #1820	C₂×C₁₉	semidirect
197. #1306	C₂×C₁₉	semidirect
198. #1284	C₂×C₁₉	semidirect
234. #481	C₄×C₁₉	semidirect
235. #480	C₄×C₁₉	semidirect
277. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
278. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
300. C₂²⋊C₈	C₂×C₄×C₁₉	semidirect
308. C₁₉	#9525	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×#3094	2
C₁₉×#2333	2
C₁₉×#1826	2
C₁₉×#1820	2
C₁₉×#1510	2
C₁₉×#1306	2
C₁₉×#1284	2
#9525	19

Subgroups — C19×#9525 #18015484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9525 #18015484