Subgroups — C₁₉×#19023 #18024982

Order 4864.

880 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3559	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3239	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#491	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1664	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1662	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1530	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, complemented
10	C₁₉×#563	C₂²	1	2	yes	—
11	C₁₉×#562	C₂²	1	2	yes	—
12	C₁₉×#554	—	2	1	no	—
13	C₁₉×#553	—	2	1	no	—
14	C₁₉×#553	—	2	1	no	—
15	C₁₉×#547	—	2	2	no	—
16	C₁₉×#547	—	2	1	no	—
17	C₁₉×#544	—	2	1	no	—
18	C₁₉×#540	—	2	1	no	—
19	C₁₉×#539	—	2	2	no	—
20	C₁₉×#539	—	2	1	no	—
21	C₁₉×#537	—	2	1	no	—
22	C₁₉×#532	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	C₂²	1	2	yes	—
27	C₁₉×#491	—	2	2	no	—
28	C₁₉×#491	C₂²	1	4	yes	—
29	C₁₉×#489	C₂²	1	2	yes	—
30	C₁₉×#489	C₂²	1	4	yes	—
31	C₁₉×#487	—	2	1	no	—
32	C₁₉×#486	—	2	1	no	—
33	C₁₉×#484	—	2	1	no	—
34	C₁₉×#481	—	2	1	no	—
35	C₁₉×#475	—	2	1	no	—
36	C₁₉×#474	—	2	1	no	—
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#417	—	2	2	no	—
39	C₂×C₁₉×#103	—	2	1	no	—
40	C₂×C₁₉×#103	—	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	2	yes	—
45	C₁₉×#329	C₂²	1	2	yes	—
46	C₁₉×#329	C₂²	1	4	yes	—
47	C₂×#41×C₁₉	—	2	2	no	—
48	C₂×#41×C₁₉	D₄	1	2	yes	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂²×C₈×C₁₉	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	2	no	—
54	C₁₉×C₄⋊Q₈	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
58	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₁₉×#127	D₄	1	1	yes	characteristic
60	C₁₉×#126	—	2	2	no	—
61	C₁₉×#126	—	2	2	no	—
62	C₁₉×#126	—	2	1	no	—
63	C₁₉×#125	—	2	2	no	—
64	C₁₉×#125	—	2	1	no	—
65	C₁₉×#125	—	2	1	no	—
66	C₁₉×#125	—	2	1	no	—
67	C₁₉×#125	D₄	1	2	yes	—
68	C₁₉×#125	C₂³	1	2	yes	—
69	C₁₉×#125	C₂³	1	1	yes	characteristic
70	C₁₉×#124	C₂³	1	1	yes	characteristic
71	C₁₉×#124	C₂³	1	2	yes	—
72	C₁₉×#123	—	2	2	no	—
73	C₁₉×#123	—	2	2	no	—
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×#123	—	2	2	no	—
76	C₁₉×#123	—	2	1	no	—
77	C₁₉×#123	—	2	2	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
86	C₁₉×#121	—	2	2	no	—
87	C₁₉×#121	—	2	2	no	—
88	C₁₉×#121	—	2	1	no	—
89	C₁₉×#121	—	2	1	no	—
90	C₁₉×#121	—	2	2	no	—
91	C₁₉×#121	—	2	2	no	—
92	C₁₉×#121	—	2	1	no	—
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#121	D₄	1	1	yes	characteristic
95	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
96	C₄×D₄×C₁₉	—	2	2	no	—
97	C₄×D₄×C₁₉	—	2	2	no	—
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
104	C₁₉×#117	—	2	1	no	—
105	C₁₉×#117	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
107	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
115	C₁₉×#107	—	2	2	no	—
116	C₁₉×#106	—	2	2	no	—
117	C₁₉×C₄⋊C₈	—	2	1	no	—
118	C₁₉×#103	—	2	4	no	—
119	C₁₉×#103	—	2	2	no	—
120	C₁₉×#103	—	2	4	no	—
121	C₁₉×#103	—	2	4	no	—
122	C₁₉×#102	—	2	4	no	—
123	C₁₉×#102	—	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	#41×C₁₉	—	4	4	no	—
131	#41×C₁₉	—	8	4	no	—
132	C₂×Q₈×C₁₉	—	2	2	no	—
133	C₂×Q₈×C₁₉	—	2	2	no	—
134	C₂×Q₈×C₁₉	—	4	4	no	—
135	C₂×Q₈×C₁₉	—	4	1	no	—
136	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	—	2	1	no	—
140	C₂×D₄×C₁₉	—	2	2	no	—
141	C₂×D₄×C₁₉	—	2	2	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	4	1	no	—
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	M₁₆×C₁₉	—	4	2	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	—	4	2	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	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	1	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	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	4	1	no	—
181	C₄⋊C₄×C₁₉	—	4	1	no	—
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	2	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	C₂²⋊C₄×C₁₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₉	—	2	2	no	—
197	C₂²⋊C₄×C₁₉	—	2	1	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	#19023	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂³×C₁₉	—	2	2	no	—
206	C₂³×C₁₉	—	2	1	no	—
207	C₂³×C₁₉	#120	1	1	yes	characteristic
208	Q₈×C₁₉	—	4	1	no	—
209	Q₈×C₁₉	—	4	2	no	—
210	Q₈×C₁₉	—	4	4	no	—
211	Q₈×C₁₉	—	8	2	no	—
212	Q₈×C₁₉	—	8	2	no	—
213	D₄×C₁₉	—	4	1	no	—
214	D₄×C₁₉	—	4	2	no	—
215	D₄×C₁₉	—	4	4	no	—
216	D₄×C₁₉	—	4	2	no	—
217	D₄×C₁₉	—	4	2	no	—
218	D₄×C₁₉	—	8	1	no	—
219	D₄×C₁₉	—	8	2	no	—
220	D₄×C₁₉	—	8	2	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	8	2	no	—
234	C₂×C₄×C₁₉	—	8	1	no	—
235	C₂×C₄×C₁₉	—	8	2	no	—
236	C₂×C₄×C₁₉	—	8	2	no	—
237	C₂×C₄×C₁₉	—	8	2	no	—
238	C₂×C₄×C₁₉	—	8	2	no	—
239	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
245	C₈×C₁₉	—	4	2	no	—
246	C₈×C₁₉	—	4	2	no	—
247	C₈×C₁₉	—	4	2	no	—
248	#3559	C₂×C₁₉	1	1	yes	characteristic
249	#3239	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#3141	C₂×C₁₉	1	1	yes	characteristic, complemented
251	C₂×#491	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#1664	C₂×C₁₉	1	4	yes	complemented
253	#1662	C₂×C₁₉	1	4	yes	complemented
254	#1530	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#1528	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1524	C₂×C₁₉	1	1	yes	characteristic, complemented
257	C₂²×C₁₉	—	2	1	no	—
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	—	4	2	no	—
260	C₂²×C₁₉	—	4	1	no	—
261	C₂²×C₁₉	—	4	1	no	—
262	C₂²×C₁₉	—	4	2	no	—
263	C₂²×C₁₉	—	4	2	no	—
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	#455	1	2	yes	—
266	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
267	C₄×C₁₉	—	2	1	no	—
268	C₄×C₁₉	—	2	1	no	—
269	C₄×C₁₉	—	2	1	no	—
270	C₄×C₁₉	—	2	1	no	—
271	C₄×C₁₉	—	2	1	no	—
272	C₄×C₁₉	—	4	2	no	—
273	C₄×C₁₉	—	4	2	no	—
274	C₄×C₁₉	—	4	1	no	—
275	C₄×C₁₉	—	4	1	no	—
276	C₄×C₁₉	—	4	2	no	—
277	C₄×C₁₉	—	4	1	no	—
278	C₄×C₁₉	—	8	2	no	—
279	C₄×C₁₉	#454	1	2	yes	—
280	#563	C₂²×C₁₉	1	2	yes	—
281	#562	C₂²×C₁₉	1	2	yes	—
282	#554	—	2	1	no	—
283	#553	—	2	1	no	—
284	#553	—	2	1	no	—
285	#547	—	2	2	no	—
286	#547	—	2	1	no	—
287	#544	—	2	1	no	—
288	#540	—	2	1	no	—
289	#539	—	2	2	no	—
290	#539	—	2	1	no	—
291	#537	—	2	1	no	—
292	#532	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
294	#529	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
296	#501	C₂²×C₁₉	1	2	yes	—
297	#491	—	2	2	no	—
298	#491	C₂²×C₁₉	1	4	yes	—
299	#489	C₂²×C₁₉	1	4	yes	—
300	#489	C₂²×C₁₉	1	2	yes	—
301	#487	—	2	1	no	—
302	#486	—	2	1	no	—
303	#484	—	2	1	no	—
304	#481	—	2	1	no	—
305	#475	—	2	1	no	—
306	#474	—	2	1	no	—
307	#432	C₂²×C₁₉	1	1	yes	characteristic
308	#417	—	2	2	no	—
309	C₂×#103	—	2	1	no	—
310	C₂×#103	—	2	1	no	—
311	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
312	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
313	#330	C₂²×C₁₉	1	4	yes	—
314	#330	C₂²×C₁₉	1	2	yes	—
315	#329	C₂²×C₁₉	1	2	yes	—
316	#329	C₂²×C₁₉	1	4	yes	—
317	C₂×C₁₉	—	2	2	no	—
318	C₂×C₁₉	—	8	2	no	—
319	C₂×C₁₉	—	8	1	no	—
320	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
321	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
322	C₂×C₁₉	#3022	1	1	yes	characteristic
323	C₂×#41	—	2	2	no	—
324	C₂×#41	D₄×C₁₉	1	2	yes	—
325	C₂²×Q₈	—	2	1	no	—
326	C₂×M₁₆	—	2	1	no	—
327	C₂²×C₈	—	2	1	no	—
328	C₄⋊Q₈	—	2	1	no	—
329	C₄⋊Q₈	—	2	2	no	—
330	C₄⋊Q₈	—	2	1	no	—
331	C₄⋊Q₈	—	2	1	no	—
332	C₄⋊Q₈	—	2	1	no	—
333	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
334	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
335	#127	D₄×C₁₉	1	1	yes	characteristic
336	#126	—	2	2	no	—
337	#126	—	2	2	no	—
338	#126	—	2	1	no	—
339	#125	—	2	2	no	—
340	#125	—	2	1	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	#124	C₂³×C₁₉	1	1	yes	characteristic
347	#124	C₂³×C₁₉	1	2	yes	—
348	#123	—	2	2	no	—
349	#123	—	2	2	no	—
350	#123	—	2	2	no	—
351	#123	—	2	2	no	—
352	#123	—	2	1	no	—
353	#123	—	2	2	no	—
354	#123	—	2	2	no	—
355	C₂²⋊Q₈	—	2	2	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₂²⋊Q₈	—	2	2	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
362	#121	—	2	2	no	—
363	#121	—	2	2	no	—
364	#121	—	2	1	no	—
365	#121	—	2	1	no	—
366	#121	—	2	2	no	—
367	#121	—	2	2	no	—
368	#121	—	2	1	no	—
369	#121	—	2	1	no	—
370	#121	D₄×C₁₉	1	1	yes	characteristic
371	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
380	#117	—	2	1	no	—
381	#117	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	2	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
389	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
391	#107	—	2	2	no	—
392	#106	—	2	2	no	—
393	C₄⋊C₈	—	2	1	no	—
394	#103	—	2	4	no	—
395	#103	—	2	2	no	—
396	#103	—	2	4	no	—
397	#103	—	2	4	no	—
398	#102	—	2	4	no	—
399	#102	—	2	2	no	—
400	C₂²⋊C₈	—	2	1	no	—
401	#97	—	2	1	no	—
402	#97	C₂³×C₁₉	1	2	yes	—
403	#97	C₂³×C₁₉	1	2	yes	—
404	#97	C₂³×C₁₉	1	2	yes	—
405	C₄×C₈	—	2	1	no	—
406	C₁₉	#19023	1	1	yes	characteristic, direct product factor, Sylow
407	#41	—	4	4	no	—
408	#41	—	8	4	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	4	4	no	—
412	C₂×Q₈	—	4	1	no	—
413	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
422	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
434	M₁₆	—	4	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	4	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
460	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
461	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₄²	—	2	2	no	—
476	C₄²	—	2	1	no	—
477	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
481	C₂³	—	2	2	no	—
482	C₂³	—	2	1	no	—
483	C₂³	C₁₉×#120	1	1	yes	characteristic
484	Q₈	—	4	2	no	—
485	Q₈	—	4	1	no	—
486	Q₈	—	4	4	no	—
487	Q₈	—	8	2	no	—
488	Q₈	—	8	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	1	no	—
491	D₄	—	4	4	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	8	1	no	—
495	D₄	—	8	2	no	—
496	D₄	—	8	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	8	2	no	—
510	C₂×C₄	—	8	1	no	—
511	C₂×C₄	—	8	2	no	—
512	C₂×C₄	—	8	2	no	—
513	C₂×C₄	—	8	2	no	—
514	C₂×C₄	—	8	2	no	—
515	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
516	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
517	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
521	C₈	—	4	2	no	—
522	C₈	—	4	2	no	—
523	C₈	—	4	2	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	1	no	—
532	C₂²	C₁₉×#455	1	2	yes	—
533	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	1	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	1	no	—
545	C₄	—	8	2	no	—
546	C₄	C₁₉×#454	1	2	yes	—
547	C₂	—	2	2	no	—
548	C₂	—	8	2	no	—
549	C₂	—	8	1	no	—
550	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
551	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
552	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×#3559	C₂
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
2. C₁₉×#3239	C₂	semidirect
3. C₁₉×#3141	C₂	semidirect
4. C₂×C₁₉×#491	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1662	C₂	semidirect
7. C₁₉×#1530	C₂	semidirect
8. C₁₉×#1528	C₂	semidirect
9. C₁₉×#1524	C₂	semidirect
204. #19023	C₁₉	direct (N × H)
249. #3239	C₂×C₁₉	semidirect
250. #3141	C₂×C₁₉	semidirect
251. C₂×#491	C₂×C₁₉	semidirect
252. #1664	C₂×C₁₉	semidirect
253. #1662	C₂×C₁₉	semidirect
254. #1530	C₂×C₁₉	semidirect
255. #1528	C₂×C₁₉	semidirect
256. #1524	C₂×C₁₉	semidirect
406. C₁₉	#19023	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×#3559	2
C₁₉×#3239	2
C₁₉×#3141	2
C₂×C₁₉×#491	2
C₁₉×#1664	2
C₁₉×#1662	2
C₁₉×#1530	2
C₁₉×#1528	2
C₁₉×#1524	2
#19023	19

Subgroups — C19×#19023 #18024982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19023 #18024982