Subgroups — C₁₉×#29119 #18035078

Order 4864.

842 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2629	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2311	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2072	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2071	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2026	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2025	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1936	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1935	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1934	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1933	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1824	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1823	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1788	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1788	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×#398	—	2	1	no	—
33	C₁₉×#398	—	2	1	no	—
34	C₁₉×#396	—	2	1	no	—
35	C₁₉×#396	—	2	1	no	—
36	C₁₉×#391	C₂²	1	1	yes	characteristic
37	C₁₉×#391	C₂²	1	1	yes	characteristic
38	C₁₉×#390	C₂²	1	1	yes	characteristic
39	C₁₉×#390	C₂²	1	1	yes	characteristic
40	C₁₉×#389	C₂²	1	1	yes	characteristic
41	C₁₉×#389	C₂²	1	1	yes	characteristic
42	C₁₉×#386	—	2	1	no	—
43	C₁₉×#386	—	2	1	no	—
44	C₁₉×#384	C₂²	1	1	yes	characteristic
45	C₁₉×#380	—	2	1	no	—
46	C₁₉×#380	—	2	1	no	—
47	C₁₉×#380	C₂²	1	1	yes	characteristic
48	C₁₉×#380	C₂²	1	1	yes	characteristic
49	C₁₉×#340	C₂²	1	1	yes	characteristic
50	C₁₉×#340	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	C₂²	1	1	yes	characteristic
57	C₁₉×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₂×#41×C₁₉	—	2	2	no	—
60	C₂×#41×C₁₉	—	2	2	no	—
61	C₂×#41×C₁₉	—	2	2	no	—
62	C₂×#41×C₁₉	—	2	2	no	—
63	C₂×#41×C₁₉	—	4	1	no	—
64	C₂×#41×C₁₉	—	4	1	no	—
65	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₉	—	2	1	no	—
67	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₉	—	2	1	no	—
69	C₂³×C₄×C₁₉	—	2	1	no	—
70	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×#125	—	4	1	no	—
76	C₁₉×#125	—	4	1	no	—
77	C₁₉×#117	—	4	1	no	—
78	C₁₉×#117	—	4	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₁₉×#103	—	2	2	no	—
107	C₁₉×#103	—	2	2	no	—
108	C₁₉×#103	—	4	1	no	—
109	C₁₉×#103	—	4	1	no	—
110	C₁₉×#102	—	2	2	no	—
111	C₁₉×#102	—	2	2	no	—
112	C₁₉×#102	—	4	1	no	—
113	C₁₉×#102	—	4	1	no	—
114	C₁₉×C₂²⋊C₈	—	2	2	no	—
115	C₁₉×C₂²⋊C₈	—	2	2	no	—
116	C₁₉×#97	—	4	1	no	—
117	C₄×C₈×C₁₉	—	4	1	no	—
118	C₁₉×#95	—	2	1	no	—
119	C₁₉×#95	—	2	1	no	—
120	C₁₉×#95	—	2	1	no	—
121	C₁₉×#95	—	2	1	no	—
122	C₁₉×#95	—	2	1	no	—
123	C₁₉×#95	—	2	1	no	—
124	C₁₉×#95	—	2	1	no	—
125	C₁₉×#95	—	2	1	no	—
126	C₂⁴×C₁₉	—	2	1	no	—
127	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
128	#41×C₁₉	—	4	4	no	—
129	#41×C₁₉	—	4	4	no	—
130	#41×C₁₉	—	4	4	no	—
131	#41×C₁₉	—	4	4	no	—
132	C₂×Q₈×C₁₉	—	2	1	no	—
133	C₂×Q₈×C₁₉	—	2	1	no	—
134	C₂×Q₈×C₁₉	—	2	1	no	—
135	C₂×Q₈×C₁₉	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	#41	1	2	yes	—
138	C₂×D₄×C₁₉	—	2	4	no	—
139	C₂×D₄×C₁₉	—	2	1	no	—
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	—	2	1	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	4	2	no	—
145	C₂×D₄×C₁₉	—	4	2	no	—
146	C₂×D₄×C₁₉	#41	1	2	yes	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	4	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	4	2	no	—
160	C₂²×C₄×C₁₉	—	4	2	no	—
161	C₂²×C₄×C₁₉	—	4	2	no	—
162	C₂²×C₄×C₁₉	—	8	1	no	—
163	C₂²×C₄×C₁₉	—	8	1	no	—
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	#41	1	2	yes	—
170	C₂²×C₄×C₁₉	#41	1	2	yes	—
171	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
178	C₂×C₈×C₁₉	—	2	1	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	4	1	no	—
197	C₄⋊C₄×C₁₉	—	4	1	no	—
198	C₄⋊C₄×C₁₉	—	4	2	no	—
199	C₄⋊C₄×C₁₉	—	4	2	no	—
200	C₄⋊C₄×C₁₉	—	4	2	no	—
201	C₄⋊C₄×C₁₉	—	8	1	no	—
202	C₄⋊C₄×C₁₉	—	8	1	no	—
203	C₄⋊C₄×C₁₉	—	8	1	no	—
204	C₄⋊C₄×C₁₉	—	8	1	no	—
205	C₂²⋊C₄×C₁₉	—	4	1	no	—
206	C₂²⋊C₄×C₁₉	—	4	1	no	—
207	C₂²⋊C₄×C₁₉	—	8	1	no	—
208	C₂²⋊C₄×C₁₉	—	8	1	no	—
209	C₂²⋊C₄×C₁₉	—	8	1	no	—
210	C₂²⋊C₄×C₁₉	—	8	1	no	—
211	C₂²⋊C₄×C₁₉	—	8	1	no	—
212	C₂²⋊C₄×C₁₉	—	8	1	no	—
213	C₄²×C₁₉	—	2	1	no	—
214	C₄²×C₁₉	—	2	1	no	—
215	C₄²×C₁₉	—	2	1	no	—
216	C₄²×C₁₉	—	2	1	no	—
217	#29119	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	2	1	no	—
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	2	1	no	—
223	C₂³×C₁₉	—	2	1	no	—
224	C₂³×C₁₉	—	2	2	no	—
225	C₂³×C₁₉	—	4	1	no	—
226	C₂³×C₁₉	—	4	1	no	—
227	C₂³×C₁₉	—	4	1	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	#124	1	2	yes	—
232	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
233	Q₈×C₁₉	—	2	2	no	—
234	Q₈×C₁₉	—	2	2	no	—
235	Q₈×C₁₉	—	4	1	no	—
236	Q₈×C₁₉	—	4	1	no	—
237	D₄×C₁₉	—	2	2	no	—
238	D₄×C₁₉	—	2	2	no	—
239	D₄×C₁₉	—	4	8	no	—
240	D₄×C₁₉	—	4	1	no	—
241	D₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	4	8	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	8	4	no	—
283	C₂×C₄×C₁₉	#124	1	2	yes	—
284	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
285	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
289	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
290	C₈×C₁₉	—	4	1	no	—
291	C₈×C₁₉	—	4	1	no	—
292	C₈×C₁₉	—	4	1	no	—
293	C₈×C₁₉	—	4	1	no	—
294	#2629	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#2311	C₂×C₁₉	1	1	yes	characteristic
296	#2072	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#2071	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#2026	C₂×C₁₉	1	1	yes	characteristic, complemented
299	#2025	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#1936	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#1935	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1934	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#1933	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#1824	C₂×C₁₉	1	1	yes	characteristic, complemented
305	#1823	C₂×C₁₉	1	1	yes	characteristic, complemented
306	#1788	C₂×C₁₉	1	1	yes	characteristic
307	#1788	C₂×C₁₉	1	1	yes	characteristic
308	#1750	C₂×C₁₉	1	1	yes	characteristic, complemented
309	C₂²×C₁₉	—	2	2	no	—
310	C₂²×C₁₉	—	2	2	no	—
311	C₂²×C₁₉	—	2	2	no	—
312	C₂²×C₁₉	—	4	1	no	—
313	C₂²×C₁₉	—	4	1	no	—
314	C₂²×C₁₉	—	4	1	no	—
315	C₂²×C₁₉	—	4	1	no	—
316	C₂²×C₁₉	—	4	2	no	—
317	C₂²×C₁₉	—	4	2	no	—
318	C₂²×C₁₉	—	4	2	no	—
319	C₂²×C₁₉	—	8	1	no	—
320	C₂²×C₁₉	—	8	1	no	—
321	C₂²×C₁₉	—	8	1	no	—
322	C₂²×C₁₉	—	8	1	no	—
323	C₂²×C₁₉	#525	1	1	yes	characteristic
324	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
325	C₂²×C₁₉	#534	1	1	yes	characteristic
326	C₂²×C₁₉	#576	1	1	yes	characteristic
327	C₂²×C₁₉	#577	1	1	yes	characteristic
328	C₂²×C₁₉	#577	1	1	yes	characteristic
329	C₂²×C₁₉	#578	1	1	yes	characteristic
330	C₄×C₁₉	—	2	2	no	—
331	C₄×C₁₉	—	4	2	no	—
332	C₄×C₁₉	—	4	1	no	—
333	C₄×C₁₉	—	4	1	no	—
334	C₄×C₁₉	—	4	1	no	—
335	C₄×C₁₉	—	4	1	no	—
336	C₄×C₁₉	—	8	1	no	—
337	C₄×C₁₉	—	8	1	no	—
338	C₄×C₁₉	—	8	1	no	—
339	C₄×C₁₉	—	8	1	no	—
340	C₄×C₁₉	—	8	1	no	—
341	C₄×C₁₉	—	8	1	no	—
342	C₄×C₁₉	#551	1	1	yes	characteristic
343	C₄×C₁₉	#551	1	1	yes	characteristic
344	C₄×C₁₉	#551	1	1	yes	characteristic
345	C₄×C₁₉	#551	1	1	yes	characteristic
346	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
347	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
348	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
349	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
350	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
351	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
352	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
353	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
354	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
355	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
361	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
362	#398	—	2	1	no	—
363	#398	—	2	1	no	—
364	#396	—	2	1	no	—
365	#396	—	2	1	no	—
366	#391	C₂²×C₁₉	1	1	yes	characteristic
367	#391	C₂²×C₁₉	1	1	yes	characteristic
368	#390	C₂²×C₁₉	1	1	yes	characteristic
369	#390	C₂²×C₁₉	1	1	yes	characteristic
370	#389	C₂²×C₁₉	1	1	yes	characteristic
371	#389	C₂²×C₁₉	1	1	yes	characteristic
372	#386	—	2	1	no	—
373	#386	—	2	1	no	—
374	#384	C₂²×C₁₉	1	1	yes	characteristic
375	#380	—	2	1	no	—
376	#380	—	2	1	no	—
377	#380	C₂²×C₁₉	1	1	yes	characteristic
378	#380	C₂²×C₁₉	1	1	yes	characteristic
379	#340	C₂²×C₁₉	1	1	yes	characteristic
380	#340	C₂²×C₁₉	1	1	yes	characteristic
381	#340	C₂²×C₁₉	1	1	yes	characteristic
382	#340	C₂²×C₁₉	1	1	yes	characteristic
383	#340	C₂²×C₁₉	1	1	yes	characteristic
384	#340	C₂²×C₁₉	1	1	yes	characteristic
385	#340	C₂²×C₁₉	1	1	yes	characteristic
386	#340	C₂²×C₁₉	1	1	yes	characteristic
387	#336	C₂²×C₁₉	1	1	yes	characteristic
388	#336	C₂²×C₁₉	1	1	yes	characteristic
389	C₂×C₁₉	—	4	2	no	—
390	C₂×C₁₉	—	8	2	no	—
391	C₂×C₁₉	#2561	1	1	yes	characteristic
392	C₂×C₁₉	#3119	1	1	yes	characteristic
393	C₂×C₁₉	#3120	1	1	yes	characteristic
394	C₂×C₁₉	#3136	1	1	yes	characteristic
395	C₂×C₁₉	#3137	1	1	yes	characteristic
396	C₂×C₁₉	#3203	1	1	yes	characteristic
397	C₂×C₁₉	#3204	1	1	yes	characteristic
398	C₂×#41	—	2	2	no	—
399	C₂×#41	—	2	2	no	—
400	C₂×#41	—	2	2	no	—
401	C₂×#41	—	2	2	no	—
402	C₂×#41	—	4	1	no	—
403	C₂×#41	—	4	1	no	—
404	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
405	C₂²×D₄	—	2	1	no	—
406	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
407	C₂³×C₄	—	2	1	no	—
408	C₂³×C₄	—	2	1	no	—
409	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
413	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
414	#125	—	4	1	no	—
415	#125	—	4	1	no	—
416	#117	—	4	1	no	—
417	#117	—	4	1	no	—
418	C₂×C₄⋊C₄	—	2	2	no	—
419	C₂×C₄⋊C₄	—	2	2	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
428	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	1	no	—
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
442	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
445	#103	—	2	2	no	—
446	#103	—	2	2	no	—
447	#103	—	4	1	no	—
448	#103	—	4	1	no	—
449	#102	—	2	2	no	—
450	#102	—	2	2	no	—
451	#102	—	4	1	no	—
452	#102	—	4	1	no	—
453	C₂²⋊C₈	—	2	2	no	—
454	C₂²⋊C₈	—	2	2	no	—
455	#97	—	4	1	no	—
456	C₄×C₈	—	4	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	C₁₉	#29119	1	1	yes	characteristic, direct product factor, Sylow
466	C₂⁴	—	2	1	no	—
467	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
468	#41	—	4	4	no	—
469	#41	—	4	4	no	—
470	#41	—	4	4	no	—
471	#41	—	4	4	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	#41×C₁₉	1	2	yes	—
478	C₂×D₄	—	2	4	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	4	2	no	—
485	C₂×D₄	—	4	2	no	—
486	C₂×D₄	#41×C₁₉	1	2	yes	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	—	4	2	no	—
501	C₂²×C₄	—	4	2	no	—
502	C₂²×C₄	—	8	1	no	—
503	C₂²×C₄	—	8	1	no	—
504	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
509	C₂²×C₄	#41×C₁₉	1	2	yes	—
510	C₂²×C₄	#41×C₁₉	1	2	yes	—
511	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	4	1	no	—
537	C₄⋊C₄	—	4	1	no	—
538	C₄⋊C₄	—	4	2	no	—
539	C₄⋊C₄	—	4	2	no	—
540	C₄⋊C₄	—	4	2	no	—
541	C₄⋊C₄	—	8	1	no	—
542	C₄⋊C₄	—	8	1	no	—
543	C₄⋊C₄	—	8	1	no	—
544	C₄⋊C₄	—	8	1	no	—
545	C₂²⋊C₄	—	4	1	no	—
546	C₂²⋊C₄	—	4	1	no	—
547	C₂²⋊C₄	—	8	1	no	—
548	C₂²⋊C₄	—	8	1	no	—
549	C₂²⋊C₄	—	8	1	no	—
550	C₂²⋊C₄	—	8	1	no	—
551	C₂²⋊C₄	—	8	1	no	—
552	C₂²⋊C₄	—	8	1	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	2	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	1	no	—
570	C₂³	C₁₉×#124	1	2	yes	—
571	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
572	Q₈	—	2	2	no	—
573	Q₈	—	2	2	no	—
574	Q₈	—	4	1	no	—
575	Q₈	—	4	1	no	—
576	D₄	—	2	2	no	—
577	D₄	—	2	2	no	—
578	D₄	—	4	8	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	4	8	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	8	4	no	—
622	C₂×C₄	C₁₉×#124	1	2	yes	—
623	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
624	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
625	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
626	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
627	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
628	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
629	C₈	—	4	1	no	—
630	C₈	—	4	1	no	—
631	C₈	—	4	1	no	—
632	C₈	—	4	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	2	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	8	1	no	—
644	C₂²	—	8	1	no	—
645	C₂²	—	8	1	no	—
646	C₂²	—	8	1	no	—
647	C₂²	C₁₉×#525	1	1	yes	characteristic
648	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
649	C₂²	C₁₉×#534	1	1	yes	characteristic
650	C₂²	C₁₉×#576	1	1	yes	characteristic
651	C₂²	C₁₉×#577	1	1	yes	characteristic
652	C₂²	C₁₉×#577	1	1	yes	characteristic
653	C₂²	C₁₉×#578	1	1	yes	characteristic
654	C₄	—	2	2	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	2	no	—
660	C₄	—	8	1	no	—
661	C₄	—	8	1	no	—
662	C₄	—	8	1	no	—
663	C₄	—	8	1	no	—
664	C₄	—	8	1	no	—
665	C₄	—	8	1	no	—
666	C₄	C₁₉×#551	1	1	yes	characteristic
667	C₄	C₁₉×#551	1	1	yes	characteristic
668	C₄	C₁₉×#551	1	1	yes	characteristic
669	C₄	C₁₉×#551	1	1	yes	characteristic
670	C₂	—	4	2	no	—
671	C₂	—	8	2	no	—
672	C₂	C₁₉×#2561	1	1	yes	characteristic
673	C₂	C₁₉×#3119	1	1	yes	characteristic
674	C₂	C₁₉×#3120	1	1	yes	characteristic
675	C₂	C₁₉×#3136	1	1	yes	characteristic
676	C₂	C₁₉×#3137	1	1	yes	characteristic
677	C₂	C₁₉×#3203	1	1	yes	characteristic
678	C₂	C₁₉×#3204	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2629	C₂	semidirect
3. C₁₉×#2072	C₂	semidirect
4. C₁₉×#2071	C₂	semidirect
5. C₁₉×#2026	C₂	semidirect
6. C₁₉×#2025	C₂	semidirect
7. C₁₉×#1936	C₂	semidirect
8. C₁₉×#1935	C₂	semidirect
9. C₁₉×#1934	C₂	semidirect
10. C₁₉×#1933	C₂	semidirect
11. C₁₉×#1824	C₂	semidirect
12. C₁₉×#1823	C₂	semidirect
15. C₁₉×#1750	C₂	semidirect
217. #29119	C₁₉	direct (N × H)
294. #2629	C₂×C₁₉	semidirect
296. #2072	C₂×C₁₉	semidirect
297. #2071	C₂×C₁₉	semidirect
298. #2026	C₂×C₁₉	semidirect
299. #2025	C₂×C₁₉	semidirect
300. #1936	C₂×C₁₉	semidirect
301. #1935	C₂×C₁₉	semidirect
302. #1934	C₂×C₁₉	semidirect
303. #1933	C₂×C₁₉	semidirect
304. #1824	C₂×C₁₉	semidirect
305. #1823	C₂×C₁₉	semidirect
308. #1750	C₂×C₁₉	semidirect
465. C₁₉	#29119	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×#2629	2
C₁₉×#2311	2
C₁₉×#2072	2
C₁₉×#2071	2
C₁₉×#2026	2
C₁₉×#2025	2
C₁₉×#1936	2
C₁₉×#1935	2
C₁₉×#1934	2
C₁₉×#1933	2
C₁₉×#1824	2
C₁₉×#1823	2
C₁₉×#1788	2
C₁₉×#1750	2
#29119	19

Subgroups — C19×#29119 #18035078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#29119 #18035078