Subgroups — C₁₉×#19034 #18024993

Order 4864.

836 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3563	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3218	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1663	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1660	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1531	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1528	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1524	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#564	C₂²	1	2	yes	—
11	C₁₉×#563	C₂²	1	2	yes	—
12	C₁₉×#557	—	2	1	no	—
13	C₁₉×#554	—	2	1	no	—
14	C₁₉×#552	—	2	1	no	—
15	C₁₉×#552	—	2	2	no	—
16	C₁₉×#552	—	2	1	no	—
17	C₁₉×#544	—	2	1	no	—
18	C₁₉×#544	—	2	1	no	—
19	C₁₉×#541	—	2	1	no	—
20	C₁₉×#541	—	2	2	no	—
21	C₁₉×#539	—	2	1	no	—
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₉×#529	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
26	C₁₉×#501	—	2	2	no	—
27	C₁₉×#501	C₂²	1	4	yes	—
28	C₁₉×#501	C₂²	1	4	yes	—
29	C₁₉×#500	—	2	1	no	—
30	C₁₉×#498	—	2	1	no	—
31	C₁₉×#497	C₂²	1	2	yes	—
32	C₁₉×#491	C₂²	1	2	yes	—
33	C₁₉×#462	—	2	1	no	—
34	C₁₉×#461	—	2	1	no	—
35	C₁₉×#451	—	2	1	no	—
36	C₁₉×#448	—	2	1	no	—
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#428	—	2	2	no	—
39	C₂×C₁₉×#107	—	2	1	no	—
40	C₂×C₁₉×#106	—	2	1	no	—
41	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
43	C₁₉×#330	C₂²	1	4	yes	—
44	C₁₉×#330	C₂²	1	4	yes	—
45	C₁₉×#330	C₂²	1	2	yes	—
46	C₁₉×#329	C₂²	1	2	yes	—
47	C₂²×Q₈×C₁₉	—	2	1	no	—
48	C₂×Q₁₆×C₁₉	—	2	2	no	—
49	C₂×SD₁₆×C₁₉	—	2	2	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂²×C₈×C₁₉	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	2	no	—
53	C₁₉×C₄⋊Q₈	—	2	1	no	—
54	C₁₉×C₄⋊Q₈	—	2	2	no	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
59	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₁₉×#126	—	2	2	no	—
62	C₁₉×#126	—	2	2	no	—
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#126	—	2	2	no	—
65	C₁₉×#126	—	2	1	no	—
66	C₁₉×#125	—	2	2	no	—
67	C₁₉×#125	—	2	2	no	—
68	C₁₉×#125	—	2	1	no	—
69	C₁₉×#125	—	2	2	no	—
70	C₁₉×#125	—	2	2	no	—
71	C₁₉×#125	—	2	2	no	—
72	C₁₉×#125	—	2	2	no	—
73	C₁₉×#125	—	2	2	no	—
74	C₁₉×#125	—	2	2	no	—
75	C₁₉×#125	—	2	1	no	—
76	C₁₉×#125	—	2	1	no	—
77	C₁₉×#125	D₄	1	2	yes	—
78	C₁₉×#125	C₂³	1	1	yes	characteristic
79	C₁₉×#125	C₂³	1	2	yes	—
80	C₁₉×#125	C₂³	1	2	yes	—
81	C₁₉×#124	C₂³	1	1	yes	characteristic
82	C₁₉×#123	—	2	2	no	—
83	C₁₉×#123	—	2	2	no	—
84	C₁₉×#123	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	1	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
94	C₁₉×#121	D₄	1	1	yes	characteristic
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	—	2	2	no	—
97	C₄×Q₈×C₁₉	—	2	1	no	—
98	C₄×Q₈×C₁₉	—	2	1	no	—
99	C₄×Q₈×C₁₉	—	2	1	no	—
100	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
101	C₄×D₄×C₁₉	—	2	2	no	—
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
104	C₁₉×#117	—	2	2	no	—
105	C₁₉×#117	—	2	1	no	—
106	C₁₉×#117	—	2	2	no	—
107	C₁₉×#117	—	2	1	no	—
108	C₁₉×#117	D₄	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
117	C₁₉×#107	—	2	4	no	—
118	C₁₉×#107	—	2	4	no	—
119	C₁₉×#106	—	2	4	no	—
120	C₁₉×#106	—	2	4	no	—
121	C₁₉×C₄⋊C₈	—	2	1	no	—
122	C₁₉×#103	—	2	2	no	—
123	C₁₉×#103	—	2	2	no	—
124	C₁₉×C₂²⋊C₈	—	2	1	no	—
125	C₁₉×#97	—	2	1	no	—
126	C₁₉×#97	C₂³	1	2	yes	—
127	C₁₉×#97	C₂³	1	2	yes	—
128	C₁₉×#97	C₂³	1	2	yes	—
129	C₄×C₈×C₁₉	—	2	1	no	—
130	C₂×Q₈×C₁₉	—	2	2	no	—
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	—	2	1	no	—
133	C₂×Q₈×C₁₉	—	2	2	no	—
134	C₂×Q₈×C₁₉	—	4	1	no	—
135	C₂×Q₈×C₁₉	—	8	2	no	—
136	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	4	1	no	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	Q₁₆×C₁₉	—	8	2	no	—
148	SD₁₆×C₁₉	—	8	2	no	—
149	M₁₆×C₁₉	—	2	4	no	—
150	C₂×C₈×C₁₉	—	2	4	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	—	2	2	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	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	2	no	—
178	C₄⋊C₄×C₁₉	—	4	1	no	—
179	C₄⋊C₄×C₁₉	—	4	1	no	—
180	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
181	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
182	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
183	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
184	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂²⋊C₄×C₁₉	—	2	2	no	—
187	C₂²⋊C₄×C₁₉	—	2	2	no	—
188	C₂²⋊C₄×C₁₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₉	—	2	1	no	—
190	C₂²⋊C₄×C₁₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₉	—	2	1	no	—
192	C₂²⋊C₄×C₁₉	—	2	1	no	—
193	C₂²⋊C₄×C₁₉	—	2	1	no	—
194	C₂²⋊C₄×C₁₉	—	2	1	no	—
195	C₄²×C₁₉	—	2	2	no	—
196	C₄²×C₁₉	—	2	2	no	—
197	C₄²×C₁₉	—	2	2	no	—
198	C₄²×C₁₉	—	2	2	no	—
199	C₄²×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
204	#19034	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂³×C₁₉	—	2	1	no	—
206	C₂³×C₁₉	#120	1	1	yes	characteristic
207	Q₈×C₁₉	—	4	1	no	—
208	Q₈×C₁₉	—	4	2	no	—
209	Q₈×C₁₉	—	4	2	no	—
210	Q₈×C₁₉	—	4	2	no	—
211	Q₈×C₁₉	—	8	1	no	—
212	Q₈×C₁₉	—	8	2	no	—
213	Q₈×C₁₉	—	8	2	no	—
214	D₄×C₁₉	—	4	1	no	—
215	D₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	8	1	no	—
230	C₂×C₄×C₁₉	—	8	2	no	—
231	C₂×C₄×C₁₉	—	8	2	no	—
232	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
238	C₈×C₁₉	—	2	4	no	—
239	C₈×C₁₉	—	2	4	no	—
240	C₈×C₁₉	—	4	2	no	—
241	#3563	C₂×C₁₉	1	1	yes	characteristic
242	#3218	C₂×C₁₉	1	1	yes	characteristic
243	#3165	C₂×C₁₉	1	1	yes	characteristic, complemented
244	C₂×#501	C₂×C₁₉	1	1	yes	characteristic, complemented
245	#1663	C₂×C₁₉	1	4	yes	complemented
246	#1660	C₂×C₁₉	1	4	yes	complemented
247	#1531	C₂×C₁₉	1	1	yes	characteristic, complemented
248	#1528	C₂×C₁₉	1	1	yes	characteristic, complemented
249	#1524	C₂×C₁₉	1	1	yes	characteristic
250	C₂²×C₁₉	—	2	1	no	—
251	C₂²×C₁₉	—	2	1	no	—
252	C₂²×C₁₉	—	4	1	no	—
253	C₂²×C₁₉	—	4	1	no	—
254	C₂²×C₁₉	—	4	1	no	—
255	C₂²×C₁₉	#456	1	2	yes	—
256	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
257	C₄×C₁₉	—	2	1	no	—
258	C₄×C₁₉	—	2	1	no	—
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	2	1	no	—
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	4	2	no	—
263	C₄×C₁₉	—	4	1	no	—
264	C₄×C₁₉	—	4	1	no	—
265	C₄×C₁₉	—	4	2	no	—
266	C₄×C₁₉	—	4	2	no	—
267	C₄×C₁₉	—	4	2	no	—
268	C₄×C₁₉	—	4	1	no	—
269	C₄×C₁₉	—	8	2	no	—
270	C₄×C₁₉	#456	1	2	yes	—
271	#564	C₂²×C₁₉	1	2	yes	—
272	#563	C₂²×C₁₉	1	2	yes	—
273	#557	—	2	1	no	—
274	#554	—	2	1	no	—
275	#552	—	2	1	no	—
276	#552	—	2	2	no	—
277	#552	—	2	1	no	—
278	#544	—	2	1	no	—
279	#544	—	2	1	no	—
280	#541	—	2	1	no	—
281	#541	—	2	2	no	—
282	#539	—	2	1	no	—
283	#533	C₂²×C₁₉	1	1	yes	characteristic
284	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
285	#529	C₂²×C₁₉	1	1	yes	characteristic
286	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
287	#501	—	2	2	no	—
288	#501	C₂²×C₁₉	1	4	yes	—
289	#501	C₂²×C₁₉	1	4	yes	—
290	#500	—	2	1	no	—
291	#498	—	2	1	no	—
292	#497	C₂²×C₁₉	1	2	yes	—
293	#491	C₂²×C₁₉	1	2	yes	—
294	#462	—	2	1	no	—
295	#461	—	2	1	no	—
296	#451	—	2	1	no	—
297	#448	—	2	1	no	—
298	#432	C₂²×C₁₉	1	1	yes	characteristic
299	#428	—	2	2	no	—
300	C₂×#107	—	2	1	no	—
301	C₂×#106	—	2	1	no	—
302	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
303	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
304	#330	C₂²×C₁₉	1	4	yes	—
305	#330	C₂²×C₁₉	1	4	yes	—
306	#330	C₂²×C₁₉	1	2	yes	—
307	#329	C₂²×C₁₉	1	2	yes	—
308	C₂×C₁₉	—	2	2	no	—
309	C₂×C₁₉	—	8	1	no	—
310	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
311	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
312	C₂×C₁₉	#3021	1	1	yes	characteristic
313	C₂²×Q₈	—	2	1	no	—
314	C₂×Q₁₆	—	2	2	no	—
315	C₂×SD₁₆	—	2	2	no	—
316	C₂×M₁₆	—	2	1	no	—
317	C₂²×C₈	—	2	1	no	—
318	C₄⋊Q₈	—	2	2	no	—
319	C₄⋊Q₈	—	2	1	no	—
320	C₄⋊Q₈	—	2	2	no	—
321	C₄⋊Q₈	—	2	1	no	—
322	C₄⋊Q₈	—	2	1	no	—
323	C₄⋊Q₈	—	2	1	no	—
324	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
325	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
326	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
327	#126	—	2	2	no	—
328	#126	—	2	2	no	—
329	#126	—	2	2	no	—
330	#126	—	2	2	no	—
331	#126	—	2	1	no	—
332	#125	—	2	2	no	—
333	#125	—	2	2	no	—
334	#125	—	2	1	no	—
335	#125	—	2	2	no	—
336	#125	—	2	2	no	—
337	#125	—	2	2	no	—
338	#125	—	2	2	no	—
339	#125	—	2	2	no	—
340	#125	—	2	2	no	—
341	#125	—	2	1	no	—
342	#125	—	2	1	no	—
343	#125	D₄×C₁₉	1	2	yes	—
344	#125	C₂³×C₁₉	1	2	yes	—
345	#125	C₂³×C₁₉	1	1	yes	characteristic
346	#125	C₂³×C₁₉	1	2	yes	—
347	#124	C₂³×C₁₉	1	1	yes	characteristic
348	#123	—	2	2	no	—
349	#123	—	2	2	no	—
350	#123	—	2	1	no	—
351	C₂²⋊Q₈	—	2	2	no	—
352	C₂²⋊Q₈	—	2	1	no	—
353	C₂²⋊Q₈	—	2	1	no	—
354	C₂²⋊Q₈	—	2	2	no	—
355	C₂²⋊Q₈	—	2	1	no	—
356	C₂²⋊Q₈	—	2	1	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
360	#121	D₄×C₁₉	1	1	yes	characteristic
361	C₄×Q₈	—	2	1	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
370	#117	—	2	2	no	—
371	#117	—	2	1	no	—
372	#117	—	2	2	no	—
373	#117	—	2	1	no	—
374	#117	D₄×C₁₉	1	2	yes	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
381	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
383	#107	—	2	4	no	—
384	#107	—	2	4	no	—
385	#106	—	2	4	no	—
386	#106	—	2	4	no	—
387	C₄⋊C₈	—	2	1	no	—
388	#103	—	2	2	no	—
389	#103	—	2	2	no	—
390	C₂²⋊C₈	—	2	1	no	—
391	#97	—	2	1	no	—
392	#97	C₂³×C₁₉	1	2	yes	—
393	#97	C₂³×C₁₉	1	2	yes	—
394	#97	C₂³×C₁₉	1	2	yes	—
395	C₄×C₈	—	2	1	no	—
396	C₁₉	#19034	1	1	yes	characteristic, direct product factor, Sylow
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	4	1	no	—
402	C₂×Q₈	—	8	2	no	—
403	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	4	1	no	—
411	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
414	Q₁₆	—	8	2	no	—
415	SD₁₆	—	8	2	no	—
416	M₁₆	—	2	4	no	—
417	C₂×C₈	—	2	4	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	4	1	no	—
446	C₄⋊C₄	—	4	1	no	—
447	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
450	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
451	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
452	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₄²	—	2	2	no	—
463	C₄²	—	2	2	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	2	1	no	—
467	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
470	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
471	C₂³	—	2	1	no	—
472	C₂³	C₁₉×#120	1	1	yes	characteristic
473	Q₈	—	4	1	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	4	2	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	8	1	no	—
478	Q₈	—	8	2	no	—
479	Q₈	—	8	2	no	—
480	D₄	—	4	1	no	—
481	D₄	—	4	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	8	1	no	—
496	C₂×C₄	—	8	2	no	—
497	C₂×C₄	—	8	2	no	—
498	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
499	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
500	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
502	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
504	C₈	—	2	4	no	—
505	C₈	—	2	4	no	—
506	C₈	—	4	2	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	C₁₉×#456	1	2	yes	—
513	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	1	no	—
526	C₄	—	8	2	no	—
527	C₄	C₁₉×#456	1	2	yes	—
528	C₂	—	2	2	no	—
529	C₂	—	8	1	no	—
530	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
531	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
532	C₂	C₁₉×#3021	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×#3165	C₂	semidirect
4. C₂×C₁₉×#501	C₂	semidirect
5. C₁₉×#1663	C₂	semidirect
6. C₁₉×#1660	C₂	semidirect
7. C₁₉×#1531	C₂	semidirect
8. C₁₉×#1528	C₂	semidirect
204. #19034	C₁₉	direct (N × H)
243. #3165	C₂×C₁₉	semidirect
244. C₂×#501	C₂×C₁₉	semidirect
245. #1663	C₂×C₁₉	semidirect
246. #1660	C₂×C₁₉	semidirect
247. #1531	C₂×C₁₉	semidirect
248. #1528	C₂×C₁₉	semidirect
396. C₁₉	#19034	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×#3563	2
C₁₉×#3218	2
C₁₉×#3165	2
C₂×C₁₉×#501	2
C₁₉×#1663	2
C₁₉×#1660	2
C₁₉×#1531	2
C₁₉×#1528	2
C₁₉×#1524	2
#19034	19

Subgroups — C19×#19034 #18024993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19034 #18024993