Subgroups — C₁₉×#9445 #18015404

Order 4864.

770 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2879	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2431	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1782	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1510	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1284	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₉	—	2	1	no	—
8	C₂×C₁₉×#127	C₄	1	1	yes	characteristic, complemented
9	C₂×C₁₉×#124	C₄	1	1	yes	characteristic, complemented
10	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#99	—	2	1	no	—
12	C₂×C₁₉×#99	—	2	1	no	—
13	C₁₉×#408	—	2	4	no	—
14	C₁₉×#407	—	2	1	no	—
15	C₁₉×#407	C₂²	1	2	yes	—
16	C₁₉×#392	—	2	1	no	—
17	C₁₉×#392	—	2	1	no	—
18	C₁₉×#391	C₄	1	1	yes	characteristic, complemented
19	C₁₉×#390	C₄	1	1	yes	characteristic, complemented
20	C₁₉×#386	—	2	1	no	—
21	C₁₉×#386	—	2	1	no	—
22	C₁₉×#381	C₂²	1	2	yes	—
23	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#327	—	2	4	no	—
25	C₂×#41×C₁₉	—	2	2	no	—
26	C₂×#41×C₁₉	—	2	2	no	—
27	C₂×#41×C₁₉	—	4	2	no	—
28	C₂×#41×C₁₉	—	4	2	no	—
29	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×M₁₆×C₁₉	—	2	2	no	—
41	C₂×M₁₆×C₁₉	—	2	2	no	—
42	C₂×M₁₆×C₁₉	—	4	2	no	—
43	C₂×M₁₆×C₁₉	—	4	2	no	—
44	C₂²×C₈×C₁₉	—	2	2	no	—
45	C₁₉×#127	—	4	2	no	—
46	C₁₉×#124	—	4	2	no	—
47	C₁₉×#121	—	2	2	no	—
48	C₁₉×#121	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
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	2	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
59	C₁₉×#99	—	4	2	no	—
60	C₁₉×#99	—	4	2	no	—
61	C₁₉×C₂²⋊C₈	—	2	4	no	—
62	C₁₉×C₂²⋊C₈	—	2	2	no	—
63	C₁₉×C₂²⋊C₈	D₄	1	4	yes	complemented
64	C₁₉×#95	—	2	1	no	—
65	C₁₉×#95	—	2	1	no	—
66	C₁₉×#95	—	2	1	no	—
67	C₁₉×#95	—	2	2	no	—
68	C₁₉×#95	—	2	2	no	—
69	C₂⁴×C₁₉	—	2	1	no	—
70	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
73	#41×C₁₉	—	4	4	no	—
74	#41×C₁₉	—	4	4	no	—
75	#41×C₁₉	—	4	8	no	—
76	C₂×Q₈×C₁₉	—	2	2	no	—
77	C₂×Q₈×C₁₉	—	2	2	no	—
78	C₂×Q₈×C₁₉	—	4	1	no	—
79	C₂×D₄×C₁₉	—	2	2	no	—
80	C₂×D₄×C₁₉	—	2	2	no	—
81	C₂×D₄×C₁₉	—	2	2	no	—
82	C₂×D₄×C₁₉	—	2	2	no	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	—	2	2	no	—
85	C₂×D₄×C₁₉	—	2	2	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	4	2	no	—
92	C₂×D₄×C₁₉	—	4	2	no	—
93	C₂×D₄×C₁₉	—	4	2	no	—
94	C₂×D₄×C₁₉	—	4	2	no	—
95	C₂×D₄×C₁₉	—	4	2	no	—
96	C₂×D₄×C₁₉	—	8	1	no	—
97	C₂×D₄×C₁₉	—	8	1	no	—
98	C₂×D₄×C₁₉	—	8	1	no	—
99	C₂×D₄×C₁₉	—	8	1	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	1	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	2	no	—
114	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₉	#41	1	2	yes	—
120	M₁₆×C₁₉	—	4	4	no	—
121	M₁₆×C₁₉	—	4	2	no	—
122	M₁₆×C₁₉	—	4	2	no	—
123	C₂×C₈×C₁₉	—	2	4	no	—
124	C₂×C₈×C₁₉	—	4	4	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₂²⋊C₄×C₁₉	—	4	2	no	—
127	C₂²⋊C₄×C₁₉	—	4	2	no	—
128	C₂²⋊C₄×C₁₉	—	4	2	no	—
129	C₂²⋊C₄×C₁₉	—	4	1	no	—
130	C₂²⋊C₄×C₁₉	—	4	1	no	—
131	C₂²⋊C₄×C₁₉	—	4	2	no	—
132	C₂²⋊C₄×C₁₉	—	4	2	no	—
133	C₂²⋊C₄×C₁₉	—	8	1	no	—
134	C₂²⋊C₄×C₁₉	—	8	1	no	—
135	C₄²×C₁₉	—	4	1	no	—
136	C₄²×C₁₉	—	4	1	no	—
137	#9445	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₁₉	—	2	1	no	—
139	C₂³×C₁₉	—	2	1	no	—
140	C₂³×C₁₉	—	2	1	no	—
141	C₂³×C₁₉	—	2	1	no	—
142	C₂³×C₁₉	—	2	1	no	—
143	C₂³×C₁₉	—	2	1	no	—
144	C₂³×C₁₉	—	2	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	—	4	1	no	—
147	C₂³×C₁₉	—	4	1	no	—
148	C₂³×C₁₉	—	4	1	no	—
149	C₂³×C₁₉	—	4	1	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	4	1	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	#99	1	2	yes	—
159	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂³×C₁₉	#121	1	2	yes	—
161	Q₈×C₁₉	—	4	4	no	—
162	D₄×C₁₉	—	4	4	no	—
163	D₄×C₁₉	—	4	4	no	—
164	D₄×C₁₉	—	4	4	no	—
165	D₄×C₁₉	—	8	2	no	—
166	D₄×C₁₉	—	8	4	no	—
167	D₄×C₁₉	—	8	4	no	—
168	D₄×C₁₉	—	8	4	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	8	2	no	—
195	C₂×C₄×C₁₉	—	8	2	no	—
196	C₂×C₄×C₁₉	—	8	2	no	—
197	C₂×C₄×C₁₉	#99	1	2	yes	—
198	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
199	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
200	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
201	C₈×C₁₉	—	4	4	no	—
202	#2879	C₂×C₁₉	1	1	yes	characteristic, complemented
203	#2431	C₂×C₁₉	1	1	yes	characteristic
204	#1782	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#1510	C₂×C₁₉	1	2	yes	complemented
206	#1284	C₂×C₁₉	1	2	yes	complemented
207	C₂²×C₁₉	—	2	1	no	—
208	C₂²×C₁₉	—	2	1	no	—
209	C₂²×C₁₉	—	2	2	no	—
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	4	2	no	—
214	C₂²×C₁₉	—	4	2	no	—
215	C₂²×C₁₉	—	4	1	no	—
216	C₂²×C₁₉	—	4	1	no	—
217	C₂²×C₁₉	—	4	1	no	—
218	C₂²×C₁₉	—	4	1	no	—
219	C₂²×C₁₉	—	4	1	no	—
220	C₂²×C₁₉	—	8	1	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	—	8	1	no	—
229	C₂²×C₁₉	—	8	1	no	—
230	C₂²×C₁₉	—	8	1	no	—
231	C₂²×C₁₉	#386	1	1	yes	characteristic
232	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
233	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
234	C₄×C₁₉	—	2	1	no	—
235	C₄×C₁₉	—	2	1	no	—
236	C₄×C₁₉	—	2	2	no	—
237	C₄×C₁₉	—	2	2	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	4	1	no	—
240	C₄×C₁₉	—	8	1	no	—
241	C₄×C₁₉	—	8	1	no	—
242	C₄×C₁₉	—	16	2	no	—
243	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
244	C₂²×M₁₆	—	2	1	no	—
245	C₂×#127	C₄×C₁₉	1	1	yes	characteristic, complemented
246	C₂×#124	C₄×C₁₉	1	1	yes	characteristic, complemented
247	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×#99	—	2	1	no	—
249	C₂×#99	—	2	1	no	—
250	#408	—	2	4	no	—
251	#407	—	2	1	no	—
252	#407	C₂²×C₁₉	1	2	yes	—
253	#392	—	2	1	no	—
254	#392	—	2	1	no	—
255	#391	C₄×C₁₉	1	1	yes	characteristic, complemented
256	#390	C₄×C₁₉	1	1	yes	characteristic, complemented
257	#386	—	2	1	no	—
258	#386	—	2	1	no	—
259	#381	C₂²×C₁₉	1	2	yes	—
260	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
261	#327	—	2	4	no	—
262	C₂×C₁₉	—	2	1	no	—
263	C₂×C₁₉	—	2	1	no	—
264	C₂×C₁₉	—	4	2	no	—
265	C₂×C₁₉	—	4	2	no	—
266	C₂×C₁₉	—	8	1	no	—
267	C₂×C₁₉	—	16	1	no	—
268	C₂×C₁₉	#1884	1	1	yes	characteristic
269	C₂×C₁₉	#1898	1	1	yes	characteristic
270	C₂×C₁₉	#1910	1	1	yes	characteristic
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	4	2	no	—
274	C₂×#41	—	4	2	no	—
275	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	—	2	1	no	—
278	C₂²×D₄	—	2	1	no	—
279	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
280	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
281	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
282	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
283	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
284	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₂×M₁₆	—	4	2	no	—
289	C₂×M₁₆	—	4	2	no	—
290	C₂²×C₈	—	2	2	no	—
291	#127	—	4	2	no	—
292	#124	—	4	2	no	—
293	#121	—	2	2	no	—
294	#121	—	2	2	no	—
295	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
304	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
305	#99	—	4	2	no	—
306	#99	—	4	2	no	—
307	C₂²⋊C₈	—	2	4	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	C₂²⋊C₈	D₄×C₁₉	1	4	yes	complemented
310	#95	—	2	1	no	—
311	#95	—	2	1	no	—
312	#95	—	2	1	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	C₁₉	#9445	1	1	yes	characteristic, direct product factor, Sylow
316	C₂⁴	—	2	1	no	—
317	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
318	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
319	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
320	#41	—	4	4	no	—
321	#41	—	4	4	no	—
322	#41	—	4	8	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	4	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂×D₄	—	4	1	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂×D₄	—	4	1	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	8	1	no	—
344	C₂×D₄	—	8	1	no	—
345	C₂×D₄	—	8	1	no	—
346	C₂×D₄	—	8	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	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	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	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	2	no	—
361	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
362	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
363	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
366	C₂²×C₄	#41×C₁₉	1	2	yes	—
367	M₁₆	—	4	4	no	—
368	M₁₆	—	4	2	no	—
369	M₁₆	—	4	2	no	—
370	C₂×C₈	—	2	4	no	—
371	C₂×C₈	—	4	4	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	4	2	no	—
374	C₂²⋊C₄	—	4	2	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	4	2	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	8	1	no	—
381	C₂²⋊C₄	—	8	1	no	—
382	C₄²	—	4	1	no	—
383	C₄²	—	4	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	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	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	C₁₉×#99	1	2	yes	—
405	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
406	C₂³	C₁₉×#121	1	2	yes	—
407	Q₈	—	4	4	no	—
408	D₄	—	4	4	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	4	no	—
411	D₄	—	8	2	no	—
412	D₄	—	8	4	no	—
413	D₄	—	8	4	no	—
414	D₄	—	8	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	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	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	8	2	no	—
441	C₂×C₄	—	8	2	no	—
442	C₂×C₄	—	8	2	no	—
443	C₂×C₄	C₁₉×#99	1	2	yes	—
444	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
445	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
446	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
447	C₈	—	4	4	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	8	1	no	—
463	C₂²	—	8	1	no	—
464	C₂²	—	8	1	no	—
465	C₂²	—	8	1	no	—
466	C₂²	—	8	1	no	—
467	C₂²	—	8	1	no	—
468	C₂²	—	8	1	no	—
469	C₂²	—	8	1	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	C₁₉×#386	1	1	yes	characteristic
473	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
474	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	1	no	—
481	C₄	—	8	1	no	—
482	C₄	—	8	1	no	—
483	C₄	—	16	2	no	—
484	C₂	—	2	1	no	—
485	C₂	—	2	1	no	—
486	C₂	—	4	2	no	—
487	C₂	—	4	2	no	—
488	C₂	—	8	1	no	—
489	C₂	—	16	1	no	—
490	C₂	C₁₉×#1884	1	1	yes	characteristic
491	C₂	C₁₉×#1898	1	1	yes	characteristic
492	C₂	C₁₉×#1910	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	C₁₉×#2431	C₂
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
1. C₁₉×#2879	C₂	semidirect
3. C₁₉×#1782	C₂	semidirect
4. C₁₉×#1510	C₂	semidirect
5. C₁₉×#1284	C₂	semidirect
8. C₂×C₁₉×#127	C₄	semidirect
9. C₂×C₁₉×#124	C₄	semidirect
18. C₁₉×#391	C₄	semidirect
19. C₁₉×#390	C₄	semidirect
63. C₁₉×C₂²⋊C₈	D₄	semidirect
137. #9445	C₁₉	direct (N × H)
202. #2879	C₂×C₁₉	semidirect
204. #1782	C₂×C₁₉	semidirect
205. #1510	C₂×C₁₉	semidirect
206. #1284	C₂×C₁₉	semidirect
245. C₂×#127	C₄×C₁₉	semidirect
246. C₂×#124	C₄×C₁₉	semidirect
255. #391	C₄×C₁₉	semidirect
256. #390	C₄×C₁₉	semidirect
309. C₂²⋊C₈	D₄×C₁₉	semidirect
315. C₁₉	#9445	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×#2879	2
C₁₉×#2431	2
C₁₉×#1782	2
C₁₉×#1510	2
C₁₉×#1284	2
#9445	19

Subgroups — C19×#9445 #18015404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9445 #18015404