Subgroups — C₁₉×#9259 #18015218

Order 4864.

966 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#447	C₂	1	1	yes	maximal, characteristic
2	D₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1964	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1786	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1519	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1289	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1282	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×D₈×C₁₉	C₄	1	2	yes	complemented
10	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₉	—	2	1	no	—
12	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
13	C₁₉×#447	—	2	1	no	—
14	C₁₉×#447	—	2	2	no	—
15	C₁₉×#447	—	2	1	no	—
16	C₂×C₁₉×#102	—	2	2	no	—
17	C₂×C₁₉×#102	C₄	1	2	yes	complemented
18	C₂×C₁₉×#99	—	2	1	no	—
19	C₂×C₁₉×#99	—	2	1	no	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₁₉×#390	—	2	1	no	—
23	C₁₉×#386	—	2	2	no	—
24	C₁₉×#380	C₂²	1	1	yes	characteristic
25	C₁₉×#380	C₂²	1	1	yes	characteristic
26	C₁₉×#379	—	2	1	no	—
27	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#327	—	2	2	no	—
29	C₂⁵×C₁₉	—	2	1	no	—
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	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	4	4	no	—
35	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
36	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
37	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₉	D₄	1	2	yes	—
39	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	—	2	2	no	—
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂×D₈×C₁₉	—	2	2	no	—
43	C₂×D₈×C₁₉	—	2	2	no	—
44	C₂×D₈×C₁₉	—	4	4	no	—
45	C₂²×C₈×C₁₉	—	2	1	no	—
46	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	complemented
47	C₁₉×#121	—	2	1	no	—
48	C₁₉×#121	—	2	1	no	—
49	C₁₉×#121	—	2	1	no	—
50	C₁₉×#121	—	2	1	no	—
51	C₄×D₄×C₁₉	—	4	4	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
55	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	2	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	2	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
63	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₁₉×#102	—	2	2	no	—
67	C₁₉×#102	—	2	2	no	—
68	C₁₉×#102	—	4	4	no	—
69	C₁₉×#99	—	4	2	no	—
70	C₁₉×#99	—	4	2	no	—
71	C₁₉×C₂²⋊C₈	—	2	1	no	—
72	C₁₉×C₂²⋊C₈	—	2	1	no	—
73	C₁₉×C₂²⋊C₈	—	2	1	no	—
74	C₁₉×C₂²⋊C₈	—	2	1	no	—
75	C₁₉×#95	—	2	1	no	—
76	C₁₉×#95	—	2	1	no	—
77	C₁₉×#95	D₄	1	2	yes	—
78	C₂⁴×C₁₉	—	2	1	no	—
79	C₂⁴×C₁₉	—	2	1	no	—
80	C₂⁴×C₁₉	—	2	2	no	—
81	C₂⁴×C₁₉	—	2	2	no	—
82	C₂⁴×C₁₉	—	2	1	no	—
83	C₂⁴×C₁₉	—	4	4	no	—
84	C₂⁴×C₁₉	—	4	1	no	—
85	C₂⁴×C₁₉	—	4	1	no	—
86	C₂⁴×C₁₉	—	4	1	no	—
87	C₂⁴×C₁₉	—	4	1	no	—
88	C₂⁴×C₁₉	—	8	2	no	—
89	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂×D₄×C₁₉	—	2	4	no	—
91	C₂×D₄×C₁₉	—	2	4	no	—
92	C₂×D₄×C₁₉	—	2	4	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂×D₄×C₁₉	—	2	2	no	—
95	C₂×D₄×C₁₉	—	2	1	no	—
96	C₂×D₄×C₁₉	—	2	2	no	—
97	C₂×D₄×C₁₉	—	2	1	no	—
98	C₂×D₄×C₁₉	—	2	1	no	—
99	C₂×D₄×C₁₉	—	4	2	no	—
100	C₂×D₄×C₁₉	—	4	2	no	—
101	C₂×D₄×C₁₉	—	4	2	no	—
102	C₂×D₄×C₁₉	—	4	2	no	—
103	C₂×D₄×C₁₉	—	4	4	no	—
104	C₂×D₄×C₁₉	—	4	4	no	—
105	C₂×D₄×C₁₉	—	4	4	no	—
106	C₂×D₄×C₁₉	—	4	1	no	—
107	C₂×D₄×C₁₉	—	4	1	no	—
108	C₂×D₄×C₁₉	—	4	1	no	—
109	C₂×D₄×C₁₉	—	4	1	no	—
110	C₂×D₄×C₁₉	—	4	1	no	—
111	C₂×D₄×C₁₉	—	4	1	no	—
112	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
113	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	2	1	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	4	2	no	—
119	C₂²×C₄×C₁₉	—	4	4	no	—
120	C₂²×C₄×C₁₉	—	4	4	no	—
121	C₂²×C₄×C₁₉	—	4	1	no	—
122	C₂²×C₄×C₁₉	—	8	2	no	—
123	C₂²×C₄×C₁₉	C₂²×C₄	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	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
129	D₈×C₁₉	—	4	4	no	—
130	D₈×C₁₉	—	4	4	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	4	2	no	—
133	C₂×C₈×C₁₉	—	4	2	no	—
134	C₂×C₈×C₁₉	—	4	1	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	4	2	no	—
138	C₄⋊C₄×C₁₉	—	4	2	no	—
139	C₂²⋊C₄×C₁₉	—	2	1	no	—
140	C₂²⋊C₄×C₁₉	—	2	1	no	—
141	C₂²⋊C₄×C₁₉	—	2	1	no	—
142	C₂²⋊C₄×C₁₉	—	4	4	no	—
143	C₂²⋊C₄×C₁₉	—	4	4	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	—	4	1	no	—
149	C₂²⋊C₄×C₁₉	—	4	1	no	—
150	C₂²⋊C₄×C₁₉	—	8	2	no	—
151	C₂²⋊C₄×C₁₉	D₈	1	2	yes	complemented
152	C₄²×C₁₉	—	4	2	no	—
153	#9259	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₁₉	—	2	4	no	—
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	4	1	no	—
158	C₂³×C₁₉	—	4	1	no	—
159	C₂³×C₁₉	—	4	4	no	—
160	C₂³×C₁₉	—	4	4	no	—
161	C₂³×C₁₉	—	4	2	no	—
162	C₂³×C₁₉	—	4	2	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	—	4	1	no	—
165	C₂³×C₁₉	—	4	1	no	—
166	C₂³×C₁₉	—	4	2	no	—
167	C₂³×C₁₉	—	4	2	no	—
168	C₂³×C₁₉	—	4	1	no	—
169	C₂³×C₁₉	—	4	1	no	—
170	C₂³×C₁₉	—	4	2	no	—
171	C₂³×C₁₉	—	4	2	no	—
172	C₂³×C₁₉	—	4	1	no	—
173	C₂³×C₁₉	—	4	1	no	—
174	C₂³×C₁₉	—	4	1	no	—
175	C₂³×C₁₉	—	8	2	no	—
176	C₂³×C₁₉	—	8	2	no	—
177	C₂³×C₁₉	—	8	1	no	—
178	C₂³×C₁₉	—	8	1	no	—
179	C₂³×C₁₉	—	8	4	no	—
180	C₂³×C₁₉	—	8	4	no	—
181	C₂³×C₁₉	—	8	4	no	—
182	C₂³×C₁₉	—	8	4	no	—
183	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
184	C₂³×C₁₉	#120	1	1	yes	characteristic
185	C₂³×C₁₉	#121	1	1	yes	characteristic
186	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
187	C₂³×C₁₉	#135	1	1	yes	characteristic
188	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
190	D₄×C₁₉	—	2	4	no	—
191	D₄×C₁₉	—	2	2	no	—
192	D₄×C₁₉	—	2	2	no	—
193	D₄×C₁₉	—	2	2	no	—
194	D₄×C₁₉	—	4	4	no	—
195	D₄×C₁₉	—	4	4	no	—
196	D₄×C₁₉	—	4	2	no	—
197	D₄×C₁₉	—	4	2	no	—
198	D₄×C₁₉	—	8	1	no	—
199	D₄×C₁₉	—	8	1	no	—
200	D₄×C₁₉	—	8	1	no	—
201	D₄×C₁₉	—	8	1	no	—
202	D₄×C₁₉	—	8	1	no	—
203	D₄×C₁₉	#99	1	4	yes	complemented
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	8	8	no	—
223	C₂×C₄×C₁₉	—	8	1	no	—
224	C₂×C₄×C₁₉	—	8	1	no	—
225	C₂×C₄×C₁₉	—	8	1	no	—
226	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
230	C₈×C₁₉	—	4	2	no	—
231	C₈×C₁₉	—	8	1	no	—
232	C₂×#447	C₂×C₁₉	1	1	yes	characteristic
233	D₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#1964	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#1786	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#1519	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#1289	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#1282	C₂×C₁₉	1	1	yes	characteristic, complemented
239	C₂²×C₁₉	—	2	1	no	—
240	C₂²×C₁₉	—	2	1	no	—
241	C₂²×C₁₉	—	2	1	no	—
242	C₂²×C₁₉	—	2	1	no	—
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	2	1	no	—
245	C₂²×C₁₉	—	2	4	no	—
246	C₂²×C₁₉	—	4	1	no	—
247	C₂²×C₁₉	—	4	1	no	—
248	C₂²×C₁₉	—	4	1	no	—
249	C₂²×C₁₉	—	4	1	no	—
250	C₂²×C₁₉	—	4	4	no	—
251	C₂²×C₁₉	—	4	4	no	—
252	C₂²×C₁₉	—	4	2	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	—	4	2	no	—
255	C₂²×C₁₉	—	4	2	no	—
256	C₂²×C₁₉	—	4	2	no	—
257	C₂²×C₁₉	—	8	4	no	—
258	C₂²×C₁₉	—	8	4	no	—
259	C₂²×C₁₉	—	8	4	no	—
260	C₂²×C₁₉	—	8	4	no	—
261	C₂²×C₁₉	—	8	2	no	—
262	C₂²×C₁₉	—	8	2	no	—
263	C₂²×C₁₉	—	8	1	no	—
264	C₂²×C₁₉	—	8	1	no	—
265	C₂²×C₁₉	—	8	1	no	—
266	C₂²×C₁₉	—	16	1	no	—
267	C₂²×C₁₉	—	16	1	no	—
268	C₂²×C₁₉	#386	1	1	yes	characteristic
269	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
270	C₂²×C₁₉	#442	1	1	yes	characteristic
271	C₂²×C₁₉	#447	1	1	yes	characteristic
272	C₂²×C₁₉	#449	1	1	yes	characteristic
273	C₂²×C₁₉	#459	1	1	yes	characteristic
274	C₂²×C₁₉	#463	1	1	yes	characteristic
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	2	1	no	—
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	4	2	no	—
279	C₄×C₁₉	—	8	1	no	—
280	C₄×C₁₉	—	8	2	no	—
281	C₄×C₁₉	—	8	1	no	—
282	C₄×C₁₉	—	16	1	no	—
283	C₄×C₁₉	C₂×#99	1	2	yes	—
284	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
285	C₂²×D₈	C₄×C₁₉	1	2	yes	complemented
286	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
287	C₂×C₄×D₄	—	2	1	no	—
288	C₂²×C₂²⋊C₄	—	2	1	no	—
289	#447	—	2	1	no	—
290	#447	—	2	2	no	—
291	#447	—	2	1	no	—
292	C₂×#102	—	2	2	no	—
293	C₂×#102	C₄×C₁₉	1	2	yes	complemented
294	C₂×#99	—	2	1	no	—
295	C₂×#99	—	2	1	no	—
296	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
298	#390	—	2	1	no	—
299	#386	—	2	2	no	—
300	#380	C₂²×C₁₉	1	1	yes	characteristic
301	#380	C₂²×C₁₉	1	1	yes	characteristic
302	#379	—	2	1	no	—
303	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
304	#327	—	2	2	no	—
305	C₂×C₁₉	—	2	1	no	—
306	C₂×C₁₉	—	2	1	no	—
307	C₂×C₁₉	—	2	1	no	—
308	C₂×C₁₉	—	2	1	no	—
309	C₂×C₁₉	—	2	1	no	—
310	C₂×C₁₉	—	2	1	no	—
311	C₂×C₁₉	—	4	4	no	—
312	C₂×C₁₉	—	8	2	no	—
313	C₂×C₁₉	—	16	1	no	—
314	C₂×C₁₉	#1879	1	1	yes	characteristic
315	C₂×C₁₉	#1898	1	1	yes	characteristic
316	C₂×C₁₉	#1904	1	1	yes	characteristic
317	C₂⁵	—	2	1	no	—
318	C₂²×D₄	—	2	1	no	—
319	C₂²×D₄	—	2	1	no	—
320	C₂²×D₄	—	2	1	no	—
321	C₂²×D₄	—	2	1	no	—
322	C₂²×D₄	—	4	4	no	—
323	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
324	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
325	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
326	C₂²×D₄	D₄×C₁₉	1	2	yes	—
327	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
328	C₂³×C₄	—	2	2	no	—
329	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
330	C₂×D₈	—	2	2	no	—
331	C₂×D₈	—	2	2	no	—
332	C₂×D₈	—	4	4	no	—
333	C₂²×C₈	—	2	1	no	—
334	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	complemented
335	#121	—	2	1	no	—
336	#121	—	2	1	no	—
337	#121	—	2	1	no	—
338	#121	—	2	1	no	—
339	C₄×D₄	—	4	4	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	—	4	2	no	—
350	C₂×C₂²⋊C₄	—	4	2	no	—
351	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
353	C₂×C₄²	—	2	1	no	—
354	#102	—	2	2	no	—
355	#102	—	2	2	no	—
356	#102	—	4	4	no	—
357	#99	—	4	2	no	—
358	#99	—	4	2	no	—
359	C₂²⋊C₈	—	2	1	no	—
360	C₂²⋊C₈	—	2	1	no	—
361	C₂²⋊C₈	—	2	1	no	—
362	C₂²⋊C₈	—	2	1	no	—
363	#95	—	2	1	no	—
364	#95	—	2	1	no	—
365	#95	D₄×C₁₉	1	2	yes	—
366	C₁₉	#9259	1	1	yes	characteristic, direct product factor, Sylow
367	C₂⁴	—	2	1	no	—
368	C₂⁴	—	2	1	no	—
369	C₂⁴	—	2	2	no	—
370	C₂⁴	—	2	2	no	—
371	C₂⁴	—	2	1	no	—
372	C₂⁴	—	4	4	no	—
373	C₂⁴	—	4	1	no	—
374	C₂⁴	—	4	1	no	—
375	C₂⁴	—	4	1	no	—
376	C₂⁴	—	4	1	no	—
377	C₂⁴	—	8	2	no	—
378	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂×D₄	—	4	2	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	4	4	no	—
393	C₂×D₄	—	4	4	no	—
394	C₂×D₄	—	4	4	no	—
395	C₂×D₄	—	4	1	no	—
396	C₂×D₄	—	4	1	no	—
397	C₂×D₄	—	4	1	no	—
398	C₂×D₄	—	4	1	no	—
399	C₂×D₄	—	4	1	no	—
400	C₂×D₄	—	4	1	no	—
401	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
402	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	4	2	no	—
408	C₂²×C₄	—	4	4	no	—
409	C₂²×C₄	—	4	4	no	—
410	C₂²×C₄	—	4	1	no	—
411	C₂²×C₄	—	8	2	no	—
412	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
416	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
417	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
418	D₈	—	4	4	no	—
419	D₈	—	4	4	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	4	2	no	—
422	C₂×C₈	—	4	2	no	—
423	C₂×C₈	—	4	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	4	2	no	—
427	C₄⋊C₄	—	4	2	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	4	4	no	—
432	C₂²⋊C₄	—	4	4	no	—
433	C₂²⋊C₄	—	4	1	no	—
434	C₂²⋊C₄	—	4	1	no	—
435	C₂²⋊C₄	—	4	1	no	—
436	C₂²⋊C₄	—	4	1	no	—
437	C₂²⋊C₄	—	4	1	no	—
438	C₂²⋊C₄	—	4	1	no	—
439	C₂²⋊C₄	—	8	2	no	—
440	C₂²⋊C₄	D₈×C₁₉	1	2	yes	complemented
441	C₄²	—	4	2	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	4	1	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	4	no	—
448	C₂³	—	4	4	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	1	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	1	no	—
461	C₂³	—	4	1	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	8	2	no	—
464	C₂³	—	8	2	no	—
465	C₂³	—	8	1	no	—
466	C₂³	—	8	1	no	—
467	C₂³	—	8	4	no	—
468	C₂³	—	8	4	no	—
469	C₂³	—	8	4	no	—
470	C₂³	—	8	4	no	—
471	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
472	C₂³	C₁₉×#120	1	1	yes	characteristic
473	C₂³	C₁₉×#121	1	1	yes	characteristic
474	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
475	C₂³	C₁₉×#135	1	1	yes	characteristic
476	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
477	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
478	D₄	—	2	4	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	2	no	—
481	D₄	—	2	2	no	—
482	D₄	—	4	4	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	2	no	—
485	D₄	—	4	2	no	—
486	D₄	—	8	1	no	—
487	D₄	—	8	1	no	—
488	D₄	—	8	1	no	—
489	D₄	—	8	1	no	—
490	D₄	—	8	1	no	—
491	D₄	C₁₉×#99	1	4	yes	complemented
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	8	8	no	—
511	C₂×C₄	—	8	1	no	—
512	C₂×C₄	—	8	1	no	—
513	C₂×C₄	—	8	1	no	—
514	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
515	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
516	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
517	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
518	C₈	—	4	2	no	—
519	C₈	—	8	1	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	4	no	—
532	C₂²	—	4	4	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	8	4	no	—
539	C₂²	—	8	4	no	—
540	C₂²	—	8	4	no	—
541	C₂²	—	8	4	no	—
542	C₂²	—	8	2	no	—
543	C₂²	—	8	2	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	—	8	1	no	—
547	C₂²	—	16	1	no	—
548	C₂²	—	16	1	no	—
549	C₂²	C₁₉×#386	1	1	yes	characteristic
550	C₂²	C₄×D₈×C₁₉	1	1	yes	characteristic
551	C₂²	C₁₉×#442	1	1	yes	characteristic
552	C₂²	C₁₉×#447	1	1	yes	characteristic
553	C₂²	C₁₉×#449	1	1	yes	characteristic
554	C₂²	C₁₉×#459	1	1	yes	characteristic
555	C₂²	C₁₉×#463	1	1	yes	characteristic
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	4	2	no	—
560	C₄	—	8	2	no	—
561	C₄	—	8	1	no	—
562	C₄	—	8	1	no	—
563	C₄	—	16	1	no	—
564	C₄	C₂×C₁₉×#99	1	2	yes	—
565	C₂	—	2	1	no	—
566	C₂	—	2	1	no	—
567	C₂	—	2	1	no	—
568	C₂	—	2	1	no	—
569	C₂	—	2	1	no	—
570	C₂	—	2	1	no	—
571	C₂	—	4	4	no	—
572	C₂	—	8	2	no	—
573	C₂	—	16	1	no	—
574	C₂	C₁₉×#1879	1	1	yes	characteristic
575	C₂	C₁₉×#1898	1	1	yes	characteristic
576	C₂	C₁₉×#1904	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×#447	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
2. D₄×C₂²⋊C₄×C₁₉	C₂	semidirect
3. C₁₉×#1964	C₂	semidirect
4. C₁₉×#1786	C₂	semidirect
5. C₁₉×#1519	C₂	semidirect
6. C₁₉×#1289	C₂	semidirect
7. C₁₉×#1282	C₂	semidirect
9. C₂²×D₈×C₁₉	C₄	semidirect
17. C₂×C₁₉×#102	C₄	semidirect
36. C₂²×D₄×C₁₉	C₂×C₄	semidirect
46. C₂²×C₈×C₁₉	C₂×C₄	semidirect
54. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
151. C₂²⋊C₄×C₁₉	D₈	semidirect
153. #9259	C₁₉	direct (N × H)
203. D₄×C₁₉	#99	semidirect
233. D₄×C₂²⋊C₄	C₂×C₁₉	semidirect
234. #1964	C₂×C₁₉	semidirect
235. #1786	C₂×C₁₉	semidirect
236. #1519	C₂×C₁₉	semidirect
237. #1289	C₂×C₁₉	semidirect
238. #1282	C₂×C₁₉	semidirect
285. C₂²×D₈	C₄×C₁₉	semidirect
293. C₂×#102	C₄×C₁₉	semidirect
324. C₂²×D₄	C₂×C₄×C₁₉	semidirect
334. C₂²×C₈	C₂×C₄×C₁₉	semidirect
342. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
366. C₁₉	#9259	direct (N × H)
440. C₂²⋊C₄	D₈×C₁₉	semidirect
491. D₄	C₁₉×#99	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#447	2
D₄×C₂²⋊C₄×C₁₉	2
C₁₉×#1964	2
C₁₉×#1786	2
C₁₉×#1519	2
C₁₉×#1289	2
C₁₉×#1282	2
#9259	19

Subgroups — C19×#9259 #18015218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9259 #18015218