Subgroups — C₁₉×#18972 #18024931

Order 4864.

818 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3555	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3239	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3229	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1653	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1652	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1645	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1644	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1554	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1497	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1482	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#563	—	2	2	no	—
13	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#557	—	2	1	no	—
15	C₁₉×#557	C₂²	1	1	yes	characteristic
16	C₁₉×#556	—	2	1	no	—
17	C₁₉×#556	—	2	1	no	—
18	C₁₉×#556	C₂²	1	1	yes	characteristic
19	C₁₉×#554	C₂²	1	1	yes	characteristic
20	C₁₉×#552	—	2	1	no	—
21	C₁₉×#544	—	2	1	no	—
22	C₁₉×#542	—	2	1	no	—
23	C₁₉×#541	—	2	1	no	—
24	C₁₉×#541	—	2	1	no	—
25	C₁₉×#541	—	2	2	no	—
26	C₁₉×#533	C₂²	1	1	yes	characteristic
27	C₁₉×#533	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₁₉×#529	C₂²	1	1	yes	characteristic
30	C₁₉×#501	—	2	1	no	—
31	C₁₉×#498	C₂²	1	2	yes	—
32	C₁₉×#494	—	2	1	no	—
33	C₁₉×#489	—	2	1	no	—
34	C₁₉×#487	—	2	1	no	—
35	C₁₉×#487	C₂²	1	2	yes	—
36	C₁₉×#484	—	2	1	no	—
37	C₁₉×#483	—	2	2	no	—
38	C₁₉×#481	—	2	1	no	—
39	C₁₉×#475	—	2	2	no	—
40	C₁₉×#475	C₂²	1	2	yes	—
41	C₁₉×#474	C₂²	1	2	yes	—
42	C₁₉×#462	C₂²	1	2	yes	—
43	C₁₉×#462	C₂²	1	2	yes	—
44	C₁₉×#451	—	2	1	no	—
45	C₁₉×#451	—	2	1	no	—
46	C₁₉×#432	C₂²	1	1	yes	characteristic
47	C₁₉×#431	C₂²	1	1	yes	characteristic
48	C₁₉×#431	C₂²	1	1	yes	characteristic
49	C₁₉×#333	C₂²	1	2	yes	—
50	C₁₉×#332	C₂²	1	2	yes	—
51	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
52	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
53	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
54	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
55	C₂²×Q₈×C₁₉	—	2	1	no	—
56	C₂×Q₁₆×C₁₉	—	2	2	no	—
57	C₂×Q₁₆×C₁₉	—	2	2	no	—
58	C₁₉×C₄⋊Q₈	—	2	2	no	—
59	C₁₉×C₄⋊Q₈	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	—	2	2	no	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	—	2	1	no	—
65	C₁₉×C₄⋊Q₈	—	2	1	no	—
66	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
67	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
68	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
70	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₁₉×#126	—	2	2	no	—
72	C₁₉×#126	—	2	2	no	—
73	C₁₉×#126	—	2	2	no	—
74	C₁₉×#126	—	2	2	no	—
75	C₁₉×#126	—	2	2	no	—
76	C₁₉×#126	—	2	2	no	—
77	C₁₉×#126	—	2	1	no	—
78	C₁₉×#125	—	2	2	no	—
79	C₁₉×#125	—	2	2	no	—
80	C₁₉×#125	—	2	2	no	—
81	C₁₉×#125	—	2	2	no	—
82	C₁₉×#125	—	2	1	no	—
83	C₁₉×#125	—	2	2	no	—
84	C₁₉×#125	—	2	1	no	—
85	C₁₉×#125	—	2	1	no	—
86	C₁₉×#125	—	2	1	no	—
87	C₁₉×#125	D₄	1	1	yes	characteristic
88	C₁₉×#124	—	2	2	no	—
89	C₁₉×#124	—	2	1	no	—
90	C₁₉×#124	D₄	1	1	yes	characteristic
91	C₁₉×#123	—	2	2	no	—
92	C₁₉×#123	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	—	2	1	no	—
96	C₁₉×C₂²⋊Q₈	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	—	2	2	no	—
98	C₁₉×C₂²⋊Q₈	—	2	1	no	—
99	C₁₉×C₂²⋊Q₈	—	2	1	no	—
100	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
101	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
102	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
103	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
104	C₁₉×#121	D₄	1	1	yes	characteristic
105	C₄×Q₈×C₁₉	—	2	2	no	—
106	C₄×Q₈×C₁₉	—	2	1	no	—
107	C₄×Q₈×C₁₉	—	2	1	no	—
108	C₄×Q₈×C₁₉	—	2	1	no	—
109	C₄×Q₈×C₁₉	—	2	1	no	—
110	C₄×Q₈×C₁₉	—	2	1	no	—
111	C₄×Q₈×C₁₉	—	2	1	no	—
112	C₄×Q₈×C₁₉	—	2	1	no	—
113	C₄×Q₈×C₁₉	D₄	1	2	yes	—
114	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
115	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
116	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
117	C₄×D₄×C₁₉	—	2	1	no	—
118	C₄×D₄×C₁₉	—	2	1	no	—
119	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
120	C₁₉×#117	—	2	2	no	—
121	C₁₉×#117	—	2	1	no	—
122	C₁₉×#117	—	2	1	no	—
123	C₁₉×#117	—	2	1	no	—
124	C₁₉×#117	—	2	1	no	—
125	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
129	C₁₉×#107	—	2	2	no	—
130	C₁₉×#106	—	2	4	no	—
131	C₁₉×#106	—	2	2	no	—
132	C₁₉×C₄⋊C₈	—	2	1	no	—
133	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
134	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
135	C₁₉×#103	—	2	4	no	—
136	C₁₉×#103	—	2	2	no	—
137	C₁₉×#103	—	2	2	no	—
138	C₁₉×#103	—	2	2	no	—
139	C₁₉×#102	—	2	2	no	—
140	C₁₉×C₂²⋊C₈	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₁₉×C₂²⋊C₈	—	2	1	no	—
143	C₁₉×#97	—	2	1	no	—
144	C₄×C₈×C₁₉	—	2	1	no	—
145	C₄×C₈×C₁₉	C₂³	1	2	yes	—
146	C₂×Q₈×C₁₉	—	2	2	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	2	no	—
150	C₂×Q₈×C₁₉	—	4	1	no	—
151	C₂×Q₈×C₁₉	—	8	2	no	—
152	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	4	1	no	—
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	Q₁₆×C₁₉	—	8	2	no	—
165	Q₁₆×C₁₉	—	8	2	no	—
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₂×C₈×C₁₉	—	2	2	no	—
168	C₂×C₈×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	2	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	2	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	4	1	no	—
196	C₄⋊C₄×C₁₉	—	4	1	no	—
197	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
202	C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	1	no	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	1	no	—
208	C₂²⋊C₄×C₁₉	—	2	1	no	—
209	C₂²⋊C₄×C₁₉	—	2	1	no	—
210	C₂²⋊C₄×C₁₉	—	2	1	no	—
211	C₂²⋊C₄×C₁₉	—	2	1	no	—
212	C₂²⋊C₄×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	—	2	2	no	—
214	C₄²×C₁₉	—	2	2	no	—
215	C₄²×C₁₉	—	2	2	no	—
216	C₄²×C₁₉	—	2	2	no	—
217	C₄²×C₁₉	—	2	1	no	—
218	C₄²×C₁₉	—	2	1	no	—
219	C₄²×C₁₉	—	2	1	no	—
220	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
222	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
223	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
224	#18972	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂³×C₁₉	—	2	1	no	—
226	C₂³×C₁₉	#120	1	1	yes	characteristic
227	Q₈×C₁₉	—	2	2	no	—
228	Q₈×C₁₉	—	2	2	no	—
229	Q₈×C₁₉	—	2	2	no	—
230	Q₈×C₁₉	—	4	2	no	—
231	Q₈×C₁₉	—	4	2	no	—
232	Q₈×C₁₉	—	4	2	no	—
233	Q₈×C₁₉	—	4	2	no	—
234	Q₈×C₁₉	—	8	1	no	—
235	Q₈×C₁₉	—	8	2	no	—
236	Q₈×C₁₉	—	8	2	no	—
237	D₄×C₁₉	—	2	2	no	—
238	D₄×C₁₉	—	8	1	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	—	2	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	1	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	2	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	8	2	no	—
254	C₂×C₄×C₁₉	—	8	2	no	—
255	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
257	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
261	C₈×C₁₉	—	4	2	no	—
262	C₈×C₁₉	—	4	2	no	—
263	C₈×C₁₉	—	4	2	no	—
264	#3555	C₂×C₁₉	1	1	yes	characteristic
265	#3239	C₂×C₁₉	1	1	yes	characteristic
266	#3229	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#3209	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#1653	C₂×C₁₉	1	2	yes	complemented
269	#1652	C₂×C₁₉	1	2	yes	complemented
270	#1645	C₂×C₁₉	1	2	yes	complemented
271	#1644	C₂×C₁₉	1	2	yes	complemented
272	#1554	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1497	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1482	C₂×C₁₉	1	1	yes	characteristic
275	C₂²×C₁₉	—	2	1	no	—
276	C₂²×C₁₉	—	2	1	no	—
277	C₂²×C₁₉	—	2	1	no	—
278	C₂²×C₁₉	—	4	1	no	—
279	C₂²×C₁₉	—	4	1	no	—
280	C₂²×C₁₉	—	4	1	no	—
281	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
282	C₄×C₁₉	—	2	1	no	—
283	C₄×C₁₉	—	2	1	no	—
284	C₄×C₁₉	—	2	1	no	—
285	C₄×C₁₉	—	2	1	no	—
286	C₄×C₁₉	—	4	1	no	—
287	C₄×C₁₉	—	4	1	no	—
288	C₄×C₁₉	—	4	1	no	—
289	C₄×C₁₉	—	4	1	no	—
290	C₄×C₁₉	—	4	2	no	—
291	C₄×C₁₉	—	4	1	no	—
292	C₄×C₁₉	—	4	2	no	—
293	C₄×C₁₉	—	4	1	no	—
294	C₄×C₁₉	—	4	1	no	—
295	C₄×C₁₉	—	8	2	no	—
296	C₄×C₁₉	#577	1	2	yes	—
297	C₄×C₁₉	#578	1	2	yes	—
298	#563	—	2	2	no	—
299	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
300	#557	—	2	1	no	—
301	#557	C₂²×C₁₉	1	1	yes	characteristic
302	#556	—	2	1	no	—
303	#556	—	2	1	no	—
304	#556	C₂²×C₁₉	1	1	yes	characteristic
305	#554	C₂²×C₁₉	1	1	yes	characteristic
306	#552	—	2	1	no	—
307	#544	—	2	1	no	—
308	#542	—	2	1	no	—
309	#541	—	2	1	no	—
310	#541	—	2	1	no	—
311	#541	—	2	2	no	—
312	#533	C₂²×C₁₉	1	1	yes	characteristic
313	#533	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
315	#529	C₂²×C₁₉	1	1	yes	characteristic
316	#501	—	2	1	no	—
317	#498	C₂²×C₁₉	1	2	yes	—
318	#494	—	2	1	no	—
319	#489	—	2	1	no	—
320	#487	—	2	1	no	—
321	#487	C₂²×C₁₉	1	2	yes	—
322	#484	—	2	1	no	—
323	#483	—	2	2	no	—
324	#481	—	2	1	no	—
325	#475	—	2	2	no	—
326	#475	C₂²×C₁₉	1	2	yes	—
327	#474	C₂²×C₁₉	1	2	yes	—
328	#462	C₂²×C₁₉	1	2	yes	—
329	#462	C₂²×C₁₉	1	2	yes	—
330	#451	—	2	1	no	—
331	#451	—	2	1	no	—
332	#432	C₂²×C₁₉	1	1	yes	characteristic
333	#431	C₂²×C₁₉	1	1	yes	characteristic
334	#431	C₂²×C₁₉	1	1	yes	characteristic
335	#333	C₂²×C₁₉	1	2	yes	—
336	#332	C₂²×C₁₉	1	2	yes	—
337	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
338	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
339	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
340	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
341	C₂×C₁₉	—	4	1	no	—
342	C₂×C₁₉	—	8	1	no	—
343	C₂×C₁₉	#3010	1	1	yes	characteristic
344	C₂×C₁₉	#3011	1	1	yes	characteristic
345	C₂×C₁₉	#3022	1	1	yes	characteristic
346	C₂²×Q₈	—	2	1	no	—
347	C₂×Q₁₆	—	2	2	no	—
348	C₂×Q₁₆	—	2	2	no	—
349	C₄⋊Q₈	—	2	2	no	—
350	C₄⋊Q₈	—	2	1	no	—
351	C₄⋊Q₈	—	2	2	no	—
352	C₄⋊Q₈	—	2	1	no	—
353	C₄⋊Q₈	—	2	1	no	—
354	C₄⋊Q₈	—	2	1	no	—
355	C₄⋊Q₈	—	2	1	no	—
356	C₄⋊Q₈	—	2	1	no	—
357	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
358	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
359	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
360	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
361	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
362	#126	—	2	2	no	—
363	#126	—	2	2	no	—
364	#126	—	2	2	no	—
365	#126	—	2	2	no	—
366	#126	—	2	2	no	—
367	#126	—	2	2	no	—
368	#126	—	2	1	no	—
369	#125	—	2	2	no	—
370	#125	—	2	2	no	—
371	#125	—	2	2	no	—
372	#125	—	2	2	no	—
373	#125	—	2	1	no	—
374	#125	—	2	2	no	—
375	#125	—	2	1	no	—
376	#125	—	2	1	no	—
377	#125	—	2	1	no	—
378	#125	D₄×C₁₉	1	1	yes	characteristic
379	#124	—	2	2	no	—
380	#124	—	2	1	no	—
381	#124	D₄×C₁₉	1	1	yes	characteristic
382	#123	—	2	2	no	—
383	#123	—	2	1	no	—
384	C₂²⋊Q₈	—	2	2	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	—	2	1	no	—
387	C₂²⋊Q₈	—	2	1	no	—
388	C₂²⋊Q₈	—	2	2	no	—
389	C₂²⋊Q₈	—	2	1	no	—
390	C₂²⋊Q₈	—	2	1	no	—
391	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
392	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
393	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
394	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
395	#121	D₄×C₁₉	1	1	yes	characteristic
396	C₄×Q₈	—	2	2	no	—
397	C₄×Q₈	—	2	1	no	—
398	C₄×Q₈	—	2	1	no	—
399	C₄×Q₈	—	2	1	no	—
400	C₄×Q₈	—	2	1	no	—
401	C₄×Q₈	—	2	1	no	—
402	C₄×Q₈	—	2	1	no	—
403	C₄×Q₈	—	2	1	no	—
404	C₄×Q₈	D₄×C₁₉	1	2	yes	—
405	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
406	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
407	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
411	#117	—	2	2	no	—
412	#117	—	2	1	no	—
413	#117	—	2	1	no	—
414	#117	—	2	1	no	—
415	#117	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
420	#107	—	2	2	no	—
421	#106	—	2	4	no	—
422	#106	—	2	2	no	—
423	C₄⋊C₈	—	2	1	no	—
424	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
425	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
426	#103	—	2	4	no	—
427	#103	—	2	2	no	—
428	#103	—	2	2	no	—
429	#103	—	2	2	no	—
430	#102	—	2	2	no	—
431	C₂²⋊C₈	—	2	1	no	—
432	C₂²⋊C₈	—	2	1	no	—
433	C₂²⋊C₈	—	2	1	no	—
434	#97	—	2	1	no	—
435	C₄×C₈	—	2	1	no	—
436	C₄×C₈	C₂³×C₁₉	1	2	yes	—
437	C₁₉	#18972	1	1	yes	characteristic, direct product factor, Sylow
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	4	1	no	—
443	C₂×Q₈	—	8	2	no	—
444	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
445	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	4	1	no	—
453	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
456	Q₁₆	—	8	2	no	—
457	Q₁₆	—	8	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
492	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
493	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₄²	—	2	2	no	—
506	C₄²	—	2	2	no	—
507	C₄²	—	2	2	no	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
514	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
515	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
516	C₂³	—	2	1	no	—
517	C₂³	C₁₉×#120	1	1	yes	characteristic
518	Q₈	—	2	2	no	—
519	Q₈	—	2	2	no	—
520	Q₈	—	2	2	no	—
521	Q₈	—	4	2	no	—
522	Q₈	—	4	2	no	—
523	Q₈	—	4	2	no	—
524	Q₈	—	4	2	no	—
525	Q₈	—	8	1	no	—
526	Q₈	—	8	2	no	—
527	Q₈	—	8	2	no	—
528	D₄	—	2	2	no	—
529	D₄	—	8	1	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	—	8	2	no	—
546	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
547	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
548	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
549	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
552	C₈	—	4	2	no	—
553	C₈	—	4	2	no	—
554	C₈	—	4	2	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	8	2	no	—
576	C₄	C₁₉×#577	1	2	yes	—
577	C₄	C₁₉×#578	1	2	yes	—
578	C₂	—	4	1	no	—
579	C₂	—	8	1	no	—
580	C₂	C₁₉×#3010	1	1	yes	characteristic
581	C₂	C₁₉×#3011	1	1	yes	characteristic
582	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#121	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#3229	C₂	semidirect
4. C₁₉×#3209	C₂	semidirect
5. C₁₉×#1653	C₂	semidirect
6. C₁₉×#1652	C₂	semidirect
7. C₁₉×#1645	C₂	semidirect
8. C₁₉×#1644	C₂	semidirect
9. C₁₉×#1554	C₂	semidirect
10. C₁₉×#1497	C₂	semidirect
224. #18972	C₁₉	direct (N × H)
266. #3229	C₂×C₁₉	semidirect
267. #3209	C₂×C₁₉	semidirect
268. #1653	C₂×C₁₉	semidirect
269. #1652	C₂×C₁₉	semidirect
270. #1645	C₂×C₁₉	semidirect
271. #1644	C₂×C₁₉	semidirect
272. #1554	C₂×C₁₉	semidirect
273. #1497	C₂×C₁₉	semidirect
437. C₁₉	#18972	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×#3555	2
C₁₉×#3239	2
C₁₉×#3229	2
C₁₉×#3209	2
C₁₉×#1653	2
C₁₉×#1652	2
C₁₉×#1645	2
C₁₉×#1644	2
C₁₉×#1554	2
C₁₉×#1497	2
C₁₉×#1482	2
#18972	19

Subgroups — C19×#18972 #18024931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18972 #18024931