Subgroups — C₁₉×#9924 #18015883

Order 4864.

890 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#451	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2626	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#393	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1787	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#328	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#323	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1294	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Q₁₆×C₁₉	—	2	1	no	—
10	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
12	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#451	—	2	2	no	—
14	C₁₉×#451	—	2	2	no	—
15	C₂×C₁₉×#103	—	2	1	no	—
16	C₂×C₁₉×#103	—	2	2	no	—
17	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
19	C₁₉×#399	—	2	1	no	—
20	C₁₉×#396	—	2	2	no	—
21	C₁₉×#393	—	2	2	no	—
22	C₁₉×#393	—	2	1	no	—
23	C₁₉×#393	—	2	2	no	—
24	C₁₉×#385	—	2	1	no	—
25	C₁₉×#380	C₂²	1	1	yes	characteristic
26	C₁₉×#379	—	2	1	no	—
27	C₂×C₁₉×#95	—	2	1	no	—
28	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
29	C₁₉×#328	—	2	2	no	—
30	C₁₉×#323	—	2	2	no	—
31	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂²×Q₈×C₁₉	—	2	1	no	—
34	C₂²×Q₈×C₁₉	—	2	1	no	—
35	C₂²×Q₈×C₁₉	—	2	1	no	—
36	C₂²×Q₈×C₁₉	—	2	1	no	—
37	C₂²×Q₈×C₁₉	—	4	4	no	—
38	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
39	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	—	2	1	no	—
41	C₂³×C₄×C₁₉	—	2	1	no	—
42	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆×C₁₉	—	2	4	no	—
45	C₂×Q₁₆×C₁₉	—	4	4	no	—
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₂²×C₈×C₁₉	—	2	1	no	—
48	C₁₉×C₂²⋊Q₈	—	2	1	no	—
49	C₁₉×C₂²⋊Q₈	—	2	1	no	—
50	C₁₉×C₂²⋊Q₈	—	2	1	no	—
51	C₁₉×C₂²⋊Q₈	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
68	C₁₉×#103	—	2	4	no	—
69	C₁₉×#103	—	4	4	no	—
70	C₁₉×C₂²⋊C₈	—	2	1	no	—
71	C₁₉×C₂²⋊C₈	—	2	1	no	—
72	C₁₉×C₂²⋊C₈	—	2	1	no	—
73	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
74	C₁₉×#95	—	2	4	no	—
75	C₁₉×#95	—	2	2	no	—
76	C₁₉×#95	—	2	1	no	—
77	C₁₉×#95	—	2	1	no	—
78	C₁₉×#95	D₄	1	2	yes	—
79	C₂⁴×C₁₉	—	2	1	no	—
80	C₂⁴×C₁₉	—	2	1	no	—
81	C₂⁴×C₁₉	—	2	1	no	—
82	C₂⁴×C₁₉	—	2	1	no	—
83	C₂⁴×C₁₉	—	2	1	no	—
84	C₂⁴×C₁₉	—	2	1	no	—
85	C₂⁴×C₁₉	—	4	2	no	—
86	C₂⁴×C₁₉	—	4	2	no	—
87	C₂⁴×C₁₉	Q₁₆	1	2	yes	complemented
88	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂×Q₈×C₁₉	—	2	4	no	—
90	C₂×Q₈×C₁₉	—	2	4	no	—
91	C₂×Q₈×C₁₉	—	2	2	no	—
92	C₂×Q₈×C₁₉	—	2	1	no	—
93	C₂×Q₈×C₁₉	—	2	2	no	—
94	C₂×Q₈×C₁₉	—	2	1	no	—
95	C₂×Q₈×C₁₉	—	4	4	no	—
96	C₂×Q₈×C₁₉	—	4	2	no	—
97	C₂×Q₈×C₁₉	—	4	2	no	—
98	C₂×Q₈×C₁₉	—	4	4	no	—
99	C₂×Q₈×C₁₉	—	4	2	no	—
100	C₂×Q₈×C₁₉	—	4	4	no	—
101	C₂×Q₈×C₁₉	—	4	4	no	—
102	C₂×Q₈×C₁₉	—	4	1	no	—
103	C₂×Q₈×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	2	4	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	2	1	no	—
112	C₂²×C₄×C₁₉	—	2	1	no	—
113	C₂²×C₄×C₁₉	—	4	2	no	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	—	4	1	no	—
116	C₂²×C₄×C₁₉	—	4	1	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	—	4	2	no	—
119	C₂²×C₄×C₁₉	—	4	2	no	—
120	C₂²×C₄×C₁₉	—	4	1	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	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
128	Q₁₆×C₁₉	—	4	8	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	4	2	no	—
131	C₂×C₈×C₁₉	—	4	2	no	—
132	C₂×C₈×C₁₉	—	4	1	no	—
133	C₄⋊C₄×C₁₉	—	2	1	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	4	2	no	—
136	C₄⋊C₄×C₁₉	—	4	1	no	—
137	C₄⋊C₄×C₁₉	—	4	1	no	—
138	C₄⋊C₄×C₁₉	—	8	2	no	—
139	C₂²⋊C₄×C₁₉	—	4	8	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	C₂²⋊C₄×C₁₉	—	4	1	no	—
145	C₂²⋊C₄×C₁₉	—	4	1	no	—
146	C₂²⋊C₄×C₁₉	—	4	1	no	—
147	C₂²⋊C₄×C₁₉	—	4	1	no	—
148	C₂²⋊C₄×C₁₉	—	8	2	no	—
149	C₂²⋊C₄×C₁₉	—	8	2	no	—
150	#9924	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	2	2	no	—
153	C₂³×C₁₉	—	2	2	no	—
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	4	4	no	—
157	C₂³×C₁₉	—	4	2	no	—
158	C₂³×C₁₉	—	4	4	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	4	1	no	—
161	C₂³×C₁₉	—	4	1	no	—
162	C₂³×C₁₉	—	4	1	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	—	4	2	no	—
165	C₂³×C₁₉	—	4	1	no	—
166	C₂³×C₁₉	—	8	2	no	—
167	C₂³×C₁₉	—	8	2	no	—
168	C₂³×C₁₉	—	8	1	no	—
169	C₂³×C₁₉	—	8	1	no	—
170	C₂³×C₁₉	#120	1	1	yes	characteristic
171	C₂³×C₁₉	#120	1	1	yes	characteristic
172	C₂³×C₁₉	#121	1	1	yes	characteristic
173	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
174	C₂³×C₁₉	#135	1	1	yes	characteristic
175	C₂³×C₁₉	#137	1	1	yes	characteristic
176	C₂³×C₁₉	#137	1	1	yes	characteristic
177	Q₈×C₁₉	—	2	4	no	—
178	Q₈×C₁₉	—	2	4	no	—
179	Q₈×C₁₉	—	4	2	no	—
180	Q₈×C₁₉	—	4	4	no	—
181	Q₈×C₁₉	—	4	2	no	—
182	Q₈×C₁₉	—	4	4	no	—
183	Q₈×C₁₉	—	4	2	no	—
184	Q₈×C₁₉	—	8	1	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	4	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	2	no	—
193	C₂×C₄×C₁₉	—	4	4	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	4	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	8	2	no	—
210	C₂×C₄×C₁₉	—	8	2	no	—
211	C₂×C₄×C₁₉	—	8	1	no	—
212	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
213	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
215	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
216	C₈×C₁₉	—	4	2	no	—
217	C₈×C₁₉	—	8	1	no	—
218	C₂×#451	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#2626	C₂×C₁₉	1	1	yes	characteristic
220	C₂×#393	C₂×C₁₉	1	1	yes	characteristic
221	#1787	C₂×C₁₉	1	1	yes	characteristic, complemented
222	C₂×#328	C₂×C₁₉	1	1	yes	characteristic, complemented
223	C₂×#323	C₂×C₁₉	1	1	yes	characteristic
224	#1294	C₂×C₁₉	1	1	yes	characteristic, complemented
225	C₂²×C₁₉	—	2	2	no	—
226	C₂²×C₁₉	—	2	2	no	—
227	C₂²×C₁₉	—	2	2	no	—
228	C₂²×C₁₉	—	2	2	no	—
229	C₂²×C₁₉	—	2	1	no	—
230	C₂²×C₁₉	—	2	1	no	—
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	4	4	no	—
234	C₂²×C₁₉	—	4	4	no	—
235	C₂²×C₁₉	—	4	2	no	—
236	C₂²×C₁₉	—	8	2	no	—
237	C₂²×C₁₉	—	8	2	no	—
238	C₂²×C₁₉	—	8	2	no	—
239	C₂²×C₁₉	—	8	2	no	—
240	C₂²×C₁₉	—	8	1	no	—
241	C₂²×C₁₉	—	8	1	no	—
242	C₂²×C₁₉	#392	1	1	yes	characteristic
243	C₂²×C₁₉	#451	1	1	yes	characteristic
244	C₂²×C₁₉	#451	1	1	yes	characteristic
245	C₂²×C₁₉	#452	1	1	yes	characteristic
246	C₂²×C₁₉	#452	1	1	yes	characteristic
247	C₂²×C₁₉	#455	1	2	yes	—
248	C₂²×C₁₉	B(4,𝔽₂)	1	2	yes	—
249	C₂²×C₁₉	#467	1	1	yes	characteristic
250	C₂²×C₁₉	#470	1	1	yes	characteristic
251	C₄×C₁₉	—	2	1	no	—
252	C₄×C₁₉	—	2	1	no	—
253	C₄×C₁₉	—	2	1	no	—
254	C₄×C₁₉	—	2	1	no	—
255	C₄×C₁₉	—	4	4	no	—
256	C₄×C₁₉	—	8	2	no	—
257	C₄×C₁₉	—	8	2	no	—
258	C₄×C₁₉	—	8	1	no	—
259	C₄×C₁₉	—	8	1	no	—
260	C₄×C₁₉	—	8	1	no	—
261	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
262	C₂²×Q₁₆	—	2	1	no	—
263	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
264	C₂²×C₂²⋊C₄	—	2	1	no	—
265	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
266	#451	—	2	2	no	—
267	#451	—	2	2	no	—
268	C₂×#103	—	2	1	no	—
269	C₂×#103	—	2	2	no	—
270	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
271	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
272	#399	—	2	1	no	—
273	#396	—	2	2	no	—
274	#393	—	2	1	no	—
275	#393	—	2	2	no	—
276	#393	—	2	2	no	—
277	#385	—	2	1	no	—
278	#380	C₂²×C₁₉	1	1	yes	characteristic
279	#379	—	2	1	no	—
280	C₂×#95	—	2	1	no	—
281	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
282	#328	—	2	2	no	—
283	#323	—	2	2	no	—
284	C₂×C₁₉	—	2	1	no	—
285	C₂×C₁₉	—	2	1	no	—
286	C₂×C₁₉	—	2	1	no	—
287	C₂×C₁₉	—	2	1	no	—
288	C₂×C₁₉	—	8	2	no	—
289	C₂×C₁₉	#1602	1	2	yes	—
290	C₂×C₁₉	#1606	1	2	yes	—
291	C₂×C₁₉	#2001	1	1	yes	characteristic
292	C₂×C₁₉	#2004	1	1	yes	characteristic
293	C₂×C₁₉	#2021	1	1	yes	characteristic
294	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
295	C₂²×Q₈	—	2	1	no	—
296	C₂²×Q₈	—	2	1	no	—
297	C₂²×Q₈	—	2	1	no	—
298	C₂²×Q₈	—	2	1	no	—
299	C₂²×Q₈	—	2	1	no	—
300	C₂²×Q₈	—	4	4	no	—
301	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
302	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
303	C₂³×C₄	—	2	1	no	—
304	C₂³×C₄	—	2	1	no	—
305	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
307	C₂×Q₁₆	—	2	4	no	—
308	C₂×Q₁₆	—	4	4	no	—
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	—	2	1	no	—
311	C₂²⋊Q₈	—	2	1	no	—
312	C₂²⋊Q₈	—	2	1	no	—
313	C₂²⋊Q₈	—	2	1	no	—
314	C₂²⋊Q₈	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
318	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
319	C₂×C₂²⋊C₄	—	2	4	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	4	4	no	—
331	#103	—	2	4	no	—
332	#103	—	4	4	no	—
333	C₂²⋊C₈	—	2	1	no	—
334	C₂²⋊C₈	—	2	1	no	—
335	C₂²⋊C₈	—	2	1	no	—
336	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
337	#95	—	2	4	no	—
338	#95	—	2	2	no	—
339	#95	—	2	1	no	—
340	#95	—	2	1	no	—
341	#95	D₄×C₁₉	1	2	yes	—
342	C₁₉	#9924	1	1	yes	characteristic, direct product factor, Sylow
343	C₂⁴	—	2	1	no	—
344	C₂⁴	—	2	1	no	—
345	C₂⁴	—	2	1	no	—
346	C₂⁴	—	2	1	no	—
347	C₂⁴	—	2	1	no	—
348	C₂⁴	—	2	1	no	—
349	C₂⁴	—	4	2	no	—
350	C₂⁴	—	4	2	no	—
351	C₂⁴	Q₁₆×C₁₉	1	2	yes	complemented
352	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
353	C₂×Q₈	—	2	4	no	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	4	4	no	—
360	C₂×Q₈	—	4	2	no	—
361	C₂×Q₈	—	4	2	no	—
362	C₂×Q₈	—	4	4	no	—
363	C₂×Q₈	—	4	2	no	—
364	C₂×Q₈	—	4	4	no	—
365	C₂×Q₈	—	4	4	no	—
366	C₂×Q₈	—	4	1	no	—
367	C₂×Q₈	—	4	1	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	1	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	—	4	1	no	—
386	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
391	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
392	Q₁₆	—	4	8	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	4	2	no	—
395	C₂×C₈	—	4	2	no	—
396	C₂×C₈	—	4	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	4	2	no	—
400	C₄⋊C₄	—	4	1	no	—
401	C₄⋊C₄	—	4	1	no	—
402	C₄⋊C₄	—	8	2	no	—
403	C₂²⋊C₄	—	4	8	no	—
404	C₂²⋊C₄	—	4	1	no	—
405	C₂²⋊C₄	—	4	1	no	—
406	C₂²⋊C₄	—	4	1	no	—
407	C₂²⋊C₄	—	4	1	no	—
408	C₂²⋊C₄	—	4	1	no	—
409	C₂²⋊C₄	—	4	1	no	—
410	C₂²⋊C₄	—	4	1	no	—
411	C₂²⋊C₄	—	4	1	no	—
412	C₂²⋊C₄	—	8	2	no	—
413	C₂²⋊C₄	—	8	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	4	4	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	4	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	8	2	no	—
430	C₂³	—	8	1	no	—
431	C₂³	—	8	1	no	—
432	C₂³	—	8	2	no	—
433	C₂³	C₁₉×#120	1	1	yes	characteristic
434	C₂³	C₁₉×#120	1	1	yes	characteristic
435	C₂³	C₁₉×#121	1	1	yes	characteristic
436	C₂³	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
437	C₂³	C₁₉×#135	1	1	yes	characteristic
438	C₂³	C₁₉×#137	1	1	yes	characteristic
439	C₂³	C₁₉×#137	1	1	yes	characteristic
440	Q₈	—	2	4	no	—
441	Q₈	—	2	4	no	—
442	Q₈	—	4	2	no	—
443	Q₈	—	4	4	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	4	no	—
446	Q₈	—	4	2	no	—
447	Q₈	—	8	1	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	8	2	no	—
473	C₂×C₄	—	8	2	no	—
474	C₂×C₄	—	8	1	no	—
475	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
476	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
477	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
478	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
479	C₈	—	4	2	no	—
480	C₈	—	8	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	2	no	—
494	C₂²	—	8	2	no	—
495	C₂²	—	8	1	no	—
496	C₂²	—	8	1	no	—
497	C₂²	—	8	2	no	—
498	C₂²	C₁₉×#392	1	1	yes	characteristic
499	C₂²	C₁₉×#451	1	1	yes	characteristic
500	C₂²	C₁₉×#451	1	1	yes	characteristic
501	C₂²	C₁₉×#452	1	1	yes	characteristic
502	C₂²	C₁₉×#452	1	1	yes	characteristic
503	C₂²	C₁₉×#455	1	2	yes	—
504	C₂²	C₁₉×B(4,𝔽₂)	1	2	yes	—
505	C₂²	C₁₉×#467	1	1	yes	characteristic
506	C₂²	C₁₉×#470	1	1	yes	characteristic
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	1	no	—
511	C₄	—	4	4	no	—
512	C₄	—	8	2	no	—
513	C₄	—	8	1	no	—
514	C₄	—	8	1	no	—
515	C₄	—	8	1	no	—
516	C₄	—	8	2	no	—
517	C₂	—	2	1	no	—
518	C₂	—	2	1	no	—
519	C₂	—	2	1	no	—
520	C₂	—	2	1	no	—
521	C₂	—	8	2	no	—
522	C₂	C₁₉×#1602	1	2	yes	—
523	C₂	C₁₉×#1606	1	2	yes	—
524	C₂	C₁₉×#2001	1	1	yes	characteristic
525	C₂	C₁₉×#2004	1	1	yes	characteristic
526	C₂	C₁₉×#2021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#451	C₂	semidirect
4. C₁₉×#1787	C₂	semidirect
5. C₂×C₁₉×#328	C₂	semidirect
7. C₁₉×#1294	C₂	semidirect
87. C₂⁴×C₁₉	Q₁₆	semidirect
150. #9924	C₁₉	direct (N × H)
218. C₂×#451	C₂×C₁₉	semidirect
221. #1787	C₂×C₁₉	semidirect
222. C₂×#328	C₂×C₁₉	semidirect
224. #1294	C₂×C₁₉	semidirect
342. C₁₉	#9924	direct (N × H)
351. C₂⁴	Q₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#451	2
C₁₉×#2626	2
C₂×C₁₉×#393	2
C₁₉×#1787	2
C₂×C₁₉×#328	2
C₂×C₁₉×#323	2
C₁₉×#1294	2
#9924	19

Subgroups — C19×#9924 #18015883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9924 #18015883