Subgroups — C₁₉×#33678 #18039637

Order 4864.

568 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3175	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2237	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2234	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2226	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2224	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2210	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2210	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2187	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2184	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#2177	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2175	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₉×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₉×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#2164	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#542	—	2	1	no	—
18	C₁₉×#518	—	2	1	no	—
19	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×D₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×D₁₆	C₂²	1	1	yes	characteristic
23	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#495	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#489	—	2	1	no	—
26	C₁₉×#468	—	2	1	no	—
27	C₁₉×#467	C₂²	1	1	yes	characteristic
28	C₁₉×#466	C₂²	1	1	yes	characteristic
29	C₁₉×#442	—	2	1	no	—
30	C₁₉×#442	—	2	1	no	—
31	C₁₉×#440	—	2	1	no	—
32	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
33	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
34	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
35	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
36	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
37	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#427	C₂²	1	1	yes	characteristic
39	C₁₉×#418	—	2	1	no	—
40	C₁₉×#405	C₂²	1	1	yes	characteristic
41	C₁₉×#367	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#367	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#366	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#366	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#358	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#358	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#357	C₂²	1	1	yes	characteristic
50	C₁₉×#357	C₂²	1	1	yes	characteristic
51	C₁₉×#357	C₂²	1	1	yes	characteristic
52	C₁₉×#357	C₂²	1	1	yes	characteristic
53	C₁₉×#357	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#357	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
56	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₁₉×#346	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×SD₁₆×C₁₉	—	2	1	no	—
62	C₂×D₈×C₁₉	—	2	2	no	—
63	C₂×D₈×C₁₉	—	2	2	no	—
64	C₂×D₈×C₁₉	—	2	1	no	—
65	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×C₄⋊Q₈	—	2	1	no	—
71	C₁₉×#126	—	4	1	no	—
72	C₁₉×#124	—	2	1	no	—
73	C₁₉×#124	—	4	1	no	—
74	C₁₉×#123	—	4	1	no	—
75	C₁₉×C₂²⋊Q₈	—	2	1	no	—
76	C₁₉×C₂²⋊Q₈	—	4	1	no	—
77	C₁₉×#121	—	2	1	no	—
78	C₄×Q₈×C₁₉	—	2	1	no	—
79	C₄×D₄×C₁₉	—	2	1	no	—
80	C₄×D₄×C₁₉	—	2	1	no	—
81	C₄×D₄×C₁₉	—	2	1	no	—
82	C₄×D₄×C₁₉	—	2	1	no	—
83	C₄×D₄×C₁₉	—	2	1	no	—
84	C₄×D₄×C₁₉	—	4	1	no	—
85	C₄×D₄×C₁₉	—	4	1	no	—
86	C₁₉×#117	—	2	1	no	—
87	C₁₉×#117	D₄	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
90	C₁₉×SD₃₂	—	2	2	no	—
91	C₁₉×SD₃₂	—	2	2	no	—
92	C₁₉×D₁₆	—	2	2	no	—
93	C₁₉×D₁₆	—	2	2	no	—
94	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
98	C₁₉×#107	—	2	1	no	—
99	C₁₉×#107	C₂³	1	1	yes	characteristic
100	C₁₉×#107	C₂³	1	1	yes	characteristic
101	C₁₉×#107	C₂³	1	1	yes	characteristic
102	C₁₉×#107	C₂³	1	1	yes	characteristic
103	C₁₉×#106	—	2	1	no	—
104	C₁₉×#103	—	2	1	no	—
105	C₁₉×#103	—	2	1	no	—
106	C₁₉×#102	—	2	1	no	—
107	C₁₉×#102	—	2	1	no	—
108	C₁₉×#102	—	2	1	no	—
109	C₁₉×#102	—	2	1	no	—
110	C₁₉×#102	—	2	1	no	—
111	C₁₉×#102	—	2	1	no	—
112	C₁₉×#97	D₄	1	1	yes	characteristic
113	C₁₉×#97	D₄	1	1	yes	characteristic
114	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
115	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
116	C₂⁴×C₁₉	—	4	1	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	—	4	1	no	—
119	C₂×D₄×C₁₉	—	2	4	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	4	2	no	—
124	C₂×D₄×C₁₉	—	4	1	no	—
125	C₂×D₄×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	—	4	1	no	—
130	C₂²×C₄×C₁₉	—	4	1	no	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	Q₁₆×C₁₉	—	2	1	no	—
133	Q₁₆×C₁₉	—	2	1	no	—
134	SD₁₆×C₁₉	—	4	2	no	—
135	D₈×C₁₉	—	2	4	no	—
136	D₈×C₁₉	—	2	1	no	—
137	D₈×C₁₉	—	2	1	no	—
138	D₈×C₁₉	—	2	1	no	—
139	D₈×C₁₉	—	2	1	no	—
140	D₈×C₁₉	#41	1	2	yes	—
141	D₈×C₁₉	#41	1	2	yes	—
142	M₁₆×C₁₉	—	4	1	no	—
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	—	2	1	no	—
145	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	4	1	no	—
154	C₄⋊C₄×C₁₉	—	4	1	no	—
155	C₄⋊C₄×C₁₉	—	4	1	no	—
156	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
157	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
158	C₂²⋊C₄×C₁₉	—	4	1	no	—
159	C₂²⋊C₄×C₁₉	—	4	1	no	—
160	C₂²⋊C₄×C₁₉	—	4	1	no	—
161	C₂²⋊C₄×C₁₉	—	4	1	no	—
162	C₂²⋊C₄×C₁₉	—	4	1	no	—
163	C₂²⋊C₄×C₁₉	—	4	1	no	—
164	C₂²⋊C₄×C₁₉	—	4	1	no	—
165	C₂²⋊C₄×C₁₉	—	4	1	no	—
166	C₂²⋊C₄×C₁₉	—	4	1	no	—
167	C₂²⋊C₄×C₁₉	—	4	1	no	—
168	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
169	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
170	C₄²×C₁₉	—	4	1	no	—
171	C₄²×C₁₉	—	4	1	no	—
172	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₁₆×C₁₉	—	2	1	no	—
175	C₁₆×C₁₉	—	2	1	no	—
176	C₁₆×C₁₉	—	2	1	no	—
177	C₁₆×C₁₉	—	2	1	no	—
178	#33678	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂³×C₁₉	—	4	4	no	—
180	C₂³×C₁₉	—	4	1	no	—
181	C₂³×C₁₉	—	4	1	no	—
182	C₂³×C₁₉	—	4	1	no	—
183	C₂³×C₁₉	—	16	1	no	—
184	C₂³×C₁₉	—	16	1	no	—
185	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
186	Q₈×C₁₉	—	4	1	no	—
187	Q₈×C₁₉	—	4	1	no	—
188	Q₈×C₁₉	—	16	1	no	—
189	D₄×C₁₉	—	2	2	no	—
190	D₄×C₁₉	—	2	2	no	—
191	D₄×C₁₉	—	4	4	no	—
192	D₄×C₁₉	—	4	1	no	—
193	D₄×C₁₉	—	4	1	no	—
194	D₄×C₁₉	—	4	1	no	—
195	D₄×C₁₉	—	4	1	no	—
196	D₄×C₁₉	—	16	1	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	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	1	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	16	1	no	—
205	C₂×C₄×C₁₉	—	16	1	no	—
206	C₂×C₄×C₁₉	—	16	1	no	—
207	C₂×C₄×C₁₉	—	16	1	no	—
208	C₂×C₄×C₁₉	—	16	1	no	—
209	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
215	C₈×C₁₉	—	2	1	no	—
216	C₈×C₁₉	—	2	1	no	—
217	C₈×C₁₉	—	2	1	no	—
218	C₈×C₁₉	C₂×#41	1	1	yes	characteristic
219	C₈×C₁₉	C₂×#41	1	1	yes	characteristic
220	#3175	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#2948	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#2237	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#2234	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#2226	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#2224	C₂×C₁₉	1	1	yes	characteristic, complemented
226	#2210	C₂×C₁₉	1	1	yes	characteristic, complemented
227	#2210	C₂×C₁₉	1	1	yes	characteristic, complemented
228	#2187	C₂×C₁₉	1	1	yes	characteristic, complemented
229	#2184	C₂×C₁₉	1	1	yes	characteristic
230	#2177	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#2175	C₂×C₁₉	1	1	yes	characteristic, complemented
232	C₄×SD₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
233	C₄×D₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#2164	C₂×C₁₉	1	1	yes	characteristic, complemented
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	2	1	no	—
237	C₂²×C₁₉	—	2	1	no	—
238	C₂²×C₁₉	—	4	2	no	—
239	C₂²×C₁₉	—	4	2	no	—
240	C₂²×C₁₉	—	8	1	no	—
241	C₂²×C₁₉	—	8	1	no	—
242	C₂²×C₁₉	—	8	1	no	—
243	C₂²×C₁₉	—	8	1	no	—
244	C₂²×C₁₉	—	8	1	no	—
245	C₂²×C₁₉	—	8	1	no	—
246	C₂²×C₁₉	—	8	1	no	—
247	C₂²×C₁₉	—	16	4	no	—
248	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
249	C₄×C₁₉	—	2	1	no	—
250	C₄×C₁₉	—	2	1	no	—
251	C₄×C₁₉	—	2	1	no	—
252	C₄×C₁₉	—	2	1	no	—
253	C₄×C₁₉	—	2	1	no	—
254	C₄×C₁₉	—	8	1	no	—
255	C₄×C₁₉	—	8	1	no	—
256	C₄×C₁₉	—	8	1	no	—
257	C₄×C₁₉	—	8	1	no	—
258	C₄×C₁₉	—	8	1	no	—
259	C₄×C₁₉	#525	1	1	yes	characteristic
260	C₄×C₁₉	#575	1	1	yes	characteristic
261	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
262	#542	—	2	1	no	—
263	#518	—	2	1	no	—
264	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×D₁₆	C₂²×C₁₉	1	1	yes	characteristic
267	C₂×D₁₆	C₂²×C₁₉	1	1	yes	characteristic
268	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
269	#495	C₂²×C₁₉	1	1	yes	characteristic, complemented
270	#489	—	2	1	no	—
271	#468	—	2	1	no	—
272	#467	C₂²×C₁₉	1	1	yes	characteristic
273	#466	C₂²×C₁₉	1	1	yes	characteristic
274	#442	—	2	1	no	—
275	#442	—	2	1	no	—
276	#440	—	2	1	no	—
277	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
278	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
279	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
280	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
281	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
282	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
283	#427	C₂²×C₁₉	1	1	yes	characteristic
284	#418	—	2	1	no	—
285	#405	C₂²×C₁₉	1	1	yes	characteristic
286	#367	C₂²×C₁₉	1	1	yes	characteristic, complemented
287	#367	C₂²×C₁₉	1	1	yes	characteristic, complemented
288	#366	C₂²×C₁₉	1	1	yes	characteristic, complemented
289	#366	C₂²×C₁₉	1	1	yes	characteristic, complemented
290	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
291	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
292	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
293	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
294	#357	C₂²×C₁₉	1	1	yes	characteristic
295	#357	C₂²×C₁₉	1	1	yes	characteristic
296	#357	C₂²×C₁₉	1	1	yes	characteristic
297	#357	C₂²×C₁₉	1	1	yes	characteristic
298	#357	C₂²×C₁₉	1	1	yes	characteristic, complemented
299	#357	C₂²×C₁₉	1	1	yes	characteristic, complemented
300	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
301	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
302	#346	C₂²×C₁₉	1	1	yes	characteristic, complemented
303	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
304	C₂×C₁₉	—	4	1	no	—
305	C₂×C₁₉	—	8	2	no	—
306	C₂×C₁₉	—	8	2	no	—
307	C₂×C₁₉	—	16	1	no	—
308	C₂×C₁₉	#3100	1	1	yes	characteristic
309	C₂×C₁₉	#3415	1	1	yes	characteristic
310	C₂×C₁₉	#3416	1	1	yes	characteristic
311	C₂²×D₄	—	2	1	no	—
312	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
313	C₂×SD₁₆	—	2	1	no	—
314	C₂×D₈	—	2	2	no	—
315	C₂×D₈	—	2	2	no	—
316	C₂×D₈	—	2	1	no	—
317	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
318	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
319	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
320	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
321	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
322	C₄⋊Q₈	—	2	1	no	—
323	#126	—	4	1	no	—
324	#124	—	2	1	no	—
325	#124	—	4	1	no	—
326	#123	—	4	1	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₂²⋊Q₈	—	4	1	no	—
329	#121	—	2	1	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×D₄	—	2	1	no	—
332	C₄×D₄	—	2	1	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	4	1	no	—
337	C₄×D₄	—	4	1	no	—
338	#117	—	2	1	no	—
339	#117	D₄×C₁₉	1	1	yes	characteristic
340	C₂×C₂²⋊C₄	—	4	1	no	—
341	C₂×C₂²⋊C₄	—	4	1	no	—
342	SD₃₂	—	2	2	no	—
343	SD₃₂	—	2	2	no	—
344	D₁₆	—	2	2	no	—
345	D₁₆	—	2	2	no	—
346	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
347	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
348	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
349	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
350	#107	—	2	1	no	—
351	#107	C₂³×C₁₉	1	1	yes	characteristic
352	#107	C₂³×C₁₉	1	1	yes	characteristic
353	#107	C₂³×C₁₉	1	1	yes	characteristic
354	#107	C₂³×C₁₉	1	1	yes	characteristic
355	#106	—	2	1	no	—
356	#103	—	2	1	no	—
357	#103	—	2	1	no	—
358	#102	—	2	1	no	—
359	#102	—	2	1	no	—
360	#102	—	2	1	no	—
361	#102	—	2	1	no	—
362	#102	—	2	1	no	—
363	#102	—	2	1	no	—
364	#97	D₄×C₁₉	1	1	yes	characteristic
365	#97	D₄×C₁₉	1	1	yes	characteristic
366	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
367	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
368	C₁₉	#33678	1	1	yes	characteristic, direct product factor, Sylow
369	C₂⁴	—	4	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	4	1	no	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	—	4	1	no	—
378	C₂×D₄	—	4	1	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	4	1	no	—
384	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
385	Q₁₆	—	2	1	no	—
386	Q₁₆	—	2	1	no	—
387	SD₁₆	—	4	2	no	—
388	D₈	—	2	4	no	—
389	D₈	—	2	1	no	—
390	D₈	—	2	1	no	—
391	D₈	—	2	1	no	—
392	D₈	—	2	1	no	—
393	D₈	#41×C₁₉	1	2	yes	—
394	D₈	#41×C₁₉	1	2	yes	—
395	M₁₆	—	4	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
399	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
400	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
401	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	4	1	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
410	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
411	C₂²⋊C₄	—	4	1	no	—
412	C₂²⋊C₄	—	4	1	no	—
413	C₂²⋊C₄	—	4	1	no	—
414	C₂²⋊C₄	—	4	1	no	—
415	C₂²⋊C₄	—	4	1	no	—
416	C₂²⋊C₄	—	4	1	no	—
417	C₂²⋊C₄	—	4	1	no	—
418	C₂²⋊C₄	—	4	1	no	—
419	C₂²⋊C₄	—	4	1	no	—
420	C₂²⋊C₄	—	4	1	no	—
421	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
422	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
423	C₄²	—	4	1	no	—
424	C₄²	—	4	1	no	—
425	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₁₆	—	2	1	no	—
428	C₁₆	—	2	1	no	—
429	C₁₆	—	2	1	no	—
430	C₁₆	—	2	1	no	—
431	C₂³	—	4	4	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	16	1	no	—
436	C₂³	—	16	1	no	—
437	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
438	Q₈	—	4	1	no	—
439	Q₈	—	4	1	no	—
440	Q₈	—	16	1	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	2	no	—
443	D₄	—	4	4	no	—
444	D₄	—	4	1	no	—
445	D₄	—	4	1	no	—
446	D₄	—	4	1	no	—
447	D₄	—	4	1	no	—
448	D₄	—	16	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	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	1	no	—
456	C₂×C₄	—	16	1	no	—
457	C₂×C₄	—	16	1	no	—
458	C₂×C₄	—	16	1	no	—
459	C₂×C₄	—	16	1	no	—
460	C₂×C₄	—	16	1	no	—
461	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
462	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
463	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
464	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
465	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
466	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
467	C₈	—	2	1	no	—
468	C₈	—	2	1	no	—
469	C₈	—	2	1	no	—
470	C₈	C₂×#41×C₁₉	1	1	yes	characteristic
471	C₈	C₂×#41×C₁₉	1	1	yes	characteristic
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	8	1	no	—
478	C₂²	—	8	1	no	—
479	C₂²	—	8	1	no	—
480	C₂²	—	8	1	no	—
481	C₂²	—	8	1	no	—
482	C₂²	—	8	1	no	—
483	C₂²	—	8	1	no	—
484	C₂²	—	16	4	no	—
485	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	8	1	no	—
492	C₄	—	8	1	no	—
493	C₄	—	8	1	no	—
494	C₄	—	8	1	no	—
495	C₄	—	8	1	no	—
496	C₄	C₁₉×#525	1	1	yes	characteristic
497	C₄	C₁₉×#575	1	1	yes	characteristic
498	C₂	—	4	1	no	—
499	C₂	—	8	2	no	—
500	C₂	—	8	2	no	—
501	C₂	—	16	1	no	—
502	C₂	C₁₉×#3100	1	1	yes	characteristic
503	C₂	C₁₉×#3415	1	1	yes	characteristic
504	C₂	C₁₉×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₁₉×#2184	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#117 ◁ C₁₉×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3175	C₂	semidirect
2. C₁₉×#2948	C₂	semidirect
3. C₁₉×#2237	C₂	semidirect
4. C₁₉×#2234	C₂	semidirect
5. C₁₉×#2226	C₂	semidirect
6. C₁₉×#2224	C₂	semidirect
7. C₁₉×#2210	C₂	semidirect
8. C₁₉×#2210	C₂	semidirect
9. C₁₉×#2187	C₂	semidirect
11. C₁₉×#2177	C₂	semidirect
12. C₁₉×#2175	C₂	semidirect
13. C₄×C₁₉×SD₃₂	C₂	semidirect
14. C₄×C₁₉×D₁₆	C₂	semidirect
15. C₁₉×#2164	C₂	semidirect
23. C₁₉×#500	C₂²	semidirect
24. C₁₉×#495	C₂²	semidirect
32. C₄×Q₁₆×C₁₉	C₂²	semidirect
37. C₄×D₈×C₁₉	C₂²	semidirect
41. C₁₉×#367	C₂²	semidirect
42. C₁₉×#367	C₂²	semidirect
43. C₁₉×#366	C₂²	semidirect
44. C₁₉×#366	C₂²	semidirect
45. C₁₉×C₄⋊C₁₆	C₂²	semidirect
46. C₁₉×C₄⋊C₁₆	C₂²	semidirect
47. C₁₉×#358	C₂²	semidirect
48. C₁₉×#358	C₂²	semidirect
53. C₁₉×#357	C₂²	semidirect
54. C₁₉×#357	C₂²	semidirect
57. C₁₉×#346	C₂²	semidirect
58. C₄×C₁₆×C₁₉	C₂²	semidirect
178. #33678	C₁₉	direct (N × H)
220. #3175	C₂×C₁₉	semidirect
221. #2948	C₂×C₁₉	semidirect
222. #2237	C₂×C₁₉	semidirect
223. #2234	C₂×C₁₉	semidirect
224. #2226	C₂×C₁₉	semidirect
225. #2224	C₂×C₁₉	semidirect
226. #2210	C₂×C₁₉	semidirect
227. #2210	C₂×C₁₉	semidirect
228. #2187	C₂×C₁₉	semidirect
230. #2177	C₂×C₁₉	semidirect
231. #2175	C₂×C₁₉	semidirect
232. C₄×SD₃₂	C₂×C₁₉	semidirect
233. C₄×D₁₆	C₂×C₁₉	semidirect
234. #2164	C₂×C₁₉	semidirect
268. #500	C₂²×C₁₉	semidirect
269. #495	C₂²×C₁₉	semidirect
277. C₄×Q₁₆	C₂²×C₁₉	semidirect
282. C₄×D₈	C₂²×C₁₉	semidirect
286. #367	C₂²×C₁₉	semidirect
287. #367	C₂²×C₁₉	semidirect
288. #366	C₂²×C₁₉	semidirect
289. #366	C₂²×C₁₉	semidirect
290. C₄⋊C₁₆	C₂²×C₁₉	semidirect
291. C₄⋊C₁₆	C₂²×C₁₉	semidirect
292. #358	C₂²×C₁₉	semidirect
293. #358	C₂²×C₁₉	semidirect
298. #357	C₂²×C₁₉	semidirect
299. #357	C₂²×C₁₉	semidirect
302. #346	C₂²×C₁₉	semidirect
303. C₄×C₁₆	C₂²×C₁₉	semidirect
368. C₁₉	#33678	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×#3175	2
C₁₉×#2948	2
C₁₉×#2237	2
C₁₉×#2234	2
C₁₉×#2226	2
C₁₉×#2224	2
C₁₉×#2210	2
C₁₉×#2187	2
C₁₉×#2184	2
C₁₉×#2177	2
C₁₉×#2175	2
C₄×C₁₉×SD₃₂	2
C₄×C₁₉×D₁₆	2
C₁₉×#2164	2
#33678	19

Subgroups — C19×#33678 #18039637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33678 #18039637