Subgroups — C₁₉×#19037 #18024996

Order 4864.

812 conjugacy classes of subgroups.

The subgroup lattice has 580 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×#3237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3172	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3166	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1664	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1663	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1663	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1660	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1529	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1528	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1526	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#564	C₂²	1	2	yes	—
13	C₁₉×#563	C₂²	1	2	yes	—
14	C₁₉×#557	—	2	1	no	—
15	C₁₉×#554	—	2	1	no	—
16	C₁₉×#552	—	2	1	no	—
17	C₁₉×#552	—	2	2	no	—
18	C₁₉×#552	—	2	1	no	—
19	C₁₉×#544	—	2	1	no	—
20	C₁₉×#544	—	2	1	no	—
21	C₁₉×#541	—	2	1	no	—
22	C₁₉×#541	—	2	2	no	—
23	C₁₉×#539	—	2	1	no	—
24	C₁₉×#533	C₂²	1	1	yes	characteristic
25	C₁₉×#533	C₂²	1	1	yes	characteristic
26	C₁₉×#529	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
28	C₁₉×#501	C₂²	1	1	yes	characteristic
29	C₁₉×#501	C₂²	1	2	yes	—
30	C₁₉×#501	C₂²	1	2	yes	—
31	C₁₉×#501	C₂²	1	2	yes	—
32	C₁₉×#499	—	2	2	no	—
33	C₁₉×#497	C₂²	1	1	yes	characteristic
34	C₁₉×#491	C₂²	1	1	yes	characteristic
35	C₁₉×#491	C₂²	1	2	yes	—
36	C₁₉×#489	C₂²	1	1	yes	characteristic
37	C₁₉×#485	—	2	2	no	—
38	C₁₉×#477	—	2	1	no	—
39	C₁₉×#475	—	2	1	no	—
40	C₁₉×#470	—	2	1	no	—
41	C₁₉×#468	—	2	1	no	—
42	C₄×Q₁₆×C₁₉	—	2	1	no	—
43	C₄×SD₁₆×C₁₉	—	2	1	no	—
44	C₁₉×#432	C₂²	1	1	yes	characteristic
45	C₁₉×#428	—	2	1	no	—
46	C₁₉×#428	—	2	1	no	—
47	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
48	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#330	C₂²	1	2	yes	—
50	C₁₉×#330	C₂²	1	2	yes	—
51	C₁₉×#330	C₂²	1	2	yes	—
52	C₁₉×#330	C₂²	1	2	yes	—
53	C₁₉×#330	C₂²	1	2	yes	—
54	C₁₉×#329	C₂²	1	2	yes	—
55	C₂×Q₁₆×C₁₉	—	2	1	no	—
56	C₂×SD₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	—	2	2	no	—
60	C₁₉×C₄⋊Q₈	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	—	2	2	no	—
62	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
63	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
64	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₁₉×#126	—	2	2	no	—
67	C₁₉×#126	—	2	2	no	—
68	C₁₉×#126	—	2	2	no	—
69	C₁₉×#126	—	2	2	no	—
70	C₁₉×#126	—	2	1	no	—
71	C₁₉×#125	—	2	2	no	—
72	C₁₉×#125	—	2	2	no	—
73	C₁₉×#125	—	2	1	no	—
74	C₁₉×#125	—	2	2	no	—
75	C₁₉×#125	—	2	2	no	—
76	C₁₉×#125	—	2	2	no	—
77	C₁₉×#125	—	2	2	no	—
78	C₁₉×#125	—	2	2	no	—
79	C₁₉×#125	—	2	2	no	—
80	C₁₉×#125	—	2	1	no	—
81	C₁₉×#125	—	2	1	no	—
82	C₁₉×#125	—	2	1	no	—
83	C₁₉×#125	D₄	1	2	yes	—
84	C₁₉×#125	C₂³	1	1	yes	characteristic
85	C₁₉×#125	C₂³	1	2	yes	—
86	C₁₉×#125	C₂³	1	2	yes	—
87	C₁₉×#124	C₂³	1	1	yes	characteristic
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×#123	—	2	2	no	—
90	C₁₉×#123	—	2	1	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	—	2	1	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	2	no	—
99	C₁₉×C₂²⋊Q₈	—	2	1	no	—
100	C₁₉×C₂²⋊Q₈	—	2	1	no	—
101	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
102	C₁₉×#121	D₄	1	1	yes	characteristic
103	C₄×Q₈×C₁₉	—	2	1	no	—
104	C₄×Q₈×C₁₉	—	2	2	no	—
105	C₄×Q₈×C₁₉	—	2	1	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	D₄	1	1	yes	characteristic
111	C₄×D₄×C₁₉	—	2	2	no	—
112	C₄×D₄×C₁₉	—	2	1	no	—
113	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
114	C₁₉×#117	—	2	2	no	—
115	C₁₉×#117	—	2	1	no	—
116	C₁₉×#117	—	2	2	no	—
117	C₁₉×#117	—	2	1	no	—
118	C₁₉×#117	—	2	1	no	—
119	C₁₉×#117	D₄	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
123	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
126	C₁₉×#107	—	2	2	no	—
127	C₁₉×#107	—	2	2	no	—
128	C₁₉×#107	—	2	1	no	—
129	C₁₉×#107	—	2	2	no	—
130	C₁₉×#106	—	2	2	no	—
131	C₁₉×#106	—	2	2	no	—
132	C₁₉×#106	—	2	1	no	—
133	C₁₉×#106	—	2	2	no	—
134	C₁₉×C₄⋊C₈	—	2	1	no	—
135	C₁₉×#103	—	2	1	no	—
136	C₁₉×#103	—	2	1	no	—
137	C₁₉×#103	—	2	1	no	—
138	C₁₉×#103	—	2	2	no	—
139	C₁₉×#103	—	2	2	no	—
140	C₁₉×#102	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₁₉×#97	C₂³	1	1	yes	characteristic
143	C₁₉×#97	C₂³	1	1	yes	characteristic
144	C₁₉×#97	C₂³	1	2	yes	—
145	C₁₉×#97	C₂³	1	2	yes	—
146	C₄×C₈×C₁₉	—	2	1	no	—
147	C₄×C₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	2	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	Q₁₆×C₁₉	—	4	2	no	—
164	SD₁₆×C₁₉	—	4	2	no	—
165	M₁₆×C₁₉	—	2	4	no	—
166	M₁₆×C₁₉	—	4	2	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	2	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×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	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×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	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	4	1	no	—
198	C₄⋊C₄×C₁₉	—	4	1	no	—
199	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
200	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
201	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
202	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
203	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₂²⋊C₄×C₁₉	—	2	2	no	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	2	1	no	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	1	no	—
211	C₂²⋊C₄×C₁₉	—	2	1	no	—
212	C₂²⋊C₄×C₁₉	—	2	1	no	—
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₂²⋊C₄×C₁₉	—	4	1	no	—
215	C₄²×C₁₉	—	2	2	no	—
216	C₄²×C₁₉	—	2	2	no	—
217	C₄²×C₁₉	—	2	2	no	—
218	C₄²×C₁₉	—	2	2	no	—
219	C₄²×C₁₉	—	2	1	no	—
220	C₄²×C₁₉	—	4	1	no	—
221	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
222	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
223	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
224	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
225	#19037	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂³×C₁₉	—	2	1	no	—
227	C₂³×C₁₉	#120	1	1	yes	characteristic
228	Q₈×C₁₉	—	4	1	no	—
229	Q₈×C₁₉	—	4	1	no	—
230	Q₈×C₁₉	—	4	1	no	—
231	Q₈×C₁₉	—	4	2	no	—
232	Q₈×C₁₉	—	4	2	no	—
233	Q₈×C₁₉	—	8	1	no	—
234	Q₈×C₁₉	—	8	2	no	—
235	D₄×C₁₉	—	4	1	no	—
236	D₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	8	1	no	—
252	C₂×C₄×C₁₉	—	8	2	no	—
253	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
254	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
255	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
259	C₈×C₁₉	—	2	4	no	—
260	C₈×C₁₉	—	2	2	no	—
261	C₈×C₁₉	—	4	2	no	—
262	C₈×C₁₉	—	4	1	no	—
263	#3563	C₂×C₁₉	1	1	yes	characteristic
264	#3237	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#3172	C₂×C₁₉	1	1	yes	characteristic
266	#3166	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1664	C₂×C₁₉	1	2	yes	complemented
268	#1663	C₂×C₁₉	1	2	yes	complemented
269	#1663	C₂×C₁₉	1	2	yes	complemented
270	#1660	C₂×C₁₉	1	2	yes	complemented
271	#1529	C₂×C₁₉	1	1	yes	characteristic
272	#1528	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1526	C₂×C₁₉	1	1	yes	characteristic, complemented
274	C₂²×C₁₉	—	2	1	no	—
275	C₂²×C₁₉	—	2	1	no	—
276	C₂²×C₁₉	—	2	1	no	—
277	C₂²×C₁₉	—	4	1	no	—
278	C₂²×C₁₉	—	4	1	no	—
279	C₂²×C₁₉	—	4	1	no	—
280	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
281	C₄×C₁₉	—	2	1	no	—
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	2	no	—
288	C₄×C₁₉	—	4	2	no	—
289	C₄×C₁₉	—	4	2	no	—
290	C₄×C₁₉	—	4	1	no	—
291	C₄×C₁₉	—	4	2	no	—
292	C₄×C₁₉	—	4	1	no	—
293	C₄×C₁₉	—	8	1	no	—
294	C₄×C₁₉	—	8	1	no	—
295	C₄×C₁₉	#456	1	2	yes	—
296	#564	C₂²×C₁₉	1	2	yes	—
297	#563	C₂²×C₁₉	1	2	yes	—
298	#557	—	2	1	no	—
299	#554	—	2	1	no	—
300	#552	—	2	1	no	—
301	#552	—	2	2	no	—
302	#552	—	2	1	no	—
303	#544	—	2	1	no	—
304	#544	—	2	1	no	—
305	#541	—	2	1	no	—
306	#541	—	2	2	no	—
307	#539	—	2	1	no	—
308	#533	C₂²×C₁₉	1	1	yes	characteristic
309	#533	C₂²×C₁₉	1	1	yes	characteristic
310	#529	C₂²×C₁₉	1	1	yes	characteristic
311	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
312	#501	C₂²×C₁₉	1	2	yes	—
313	#501	C₂²×C₁₉	1	2	yes	—
314	#501	C₂²×C₁₉	1	1	yes	characteristic
315	#501	C₂²×C₁₉	1	2	yes	—
316	#499	—	2	2	no	—
317	#497	C₂²×C₁₉	1	1	yes	characteristic
318	#491	C₂²×C₁₉	1	1	yes	characteristic
319	#491	C₂²×C₁₉	1	2	yes	—
320	#489	C₂²×C₁₉	1	1	yes	characteristic
321	#485	—	2	2	no	—
322	#477	—	2	1	no	—
323	#475	—	2	1	no	—
324	#470	—	2	1	no	—
325	#468	—	2	1	no	—
326	C₄×Q₁₆	—	2	1	no	—
327	C₄×SD₁₆	—	2	1	no	—
328	#432	C₂²×C₁₉	1	1	yes	characteristic
329	#428	—	2	1	no	—
330	#428	—	2	1	no	—
331	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
332	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
333	#330	C₂²×C₁₉	1	2	yes	—
334	#330	C₂²×C₁₉	1	2	yes	—
335	#330	C₂²×C₁₉	1	2	yes	—
336	#330	C₂²×C₁₉	1	2	yes	—
337	#330	C₂²×C₁₉	1	2	yes	—
338	#329	C₂²×C₁₉	1	2	yes	—
339	C₂×C₁₉	—	4	1	no	—
340	C₂×C₁₉	—	8	1	no	—
341	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
342	C₂×C₁₉	#3018	1	1	yes	characteristic
343	C₂×C₁₉	#3020	1	1	yes	characteristic
344	C₂×Q₁₆	—	2	1	no	—
345	C₂×SD₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₄⋊Q₈	—	2	2	no	—
349	C₄⋊Q₈	—	2	1	no	—
350	C₄⋊Q₈	—	2	2	no	—
351	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
352	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
353	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
354	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
355	#126	—	2	2	no	—
356	#126	—	2	2	no	—
357	#126	—	2	2	no	—
358	#126	—	2	2	no	—
359	#126	—	2	1	no	—
360	#125	—	2	2	no	—
361	#125	—	2	2	no	—
362	#125	—	2	1	no	—
363	#125	—	2	2	no	—
364	#125	—	2	2	no	—
365	#125	—	2	2	no	—
366	#125	—	2	2	no	—
367	#125	—	2	2	no	—
368	#125	—	2	2	no	—
369	#125	—	2	1	no	—
370	#125	—	2	1	no	—
371	#125	—	2	1	no	—
372	#125	D₄×C₁₉	1	2	yes	—
373	#125	C₂³×C₁₉	1	2	yes	—
374	#125	C₂³×C₁₉	1	1	yes	characteristic
375	#125	C₂³×C₁₉	1	2	yes	—
376	#124	C₂³×C₁₉	1	1	yes	characteristic
377	#123	—	2	2	no	—
378	#123	—	2	2	no	—
379	#123	—	2	1	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	C₂²⋊Q₈	—	2	1	no	—
383	C₂²⋊Q₈	—	2	2	no	—
384	C₂²⋊Q₈	—	2	1	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	C₂²⋊Q₈	—	2	2	no	—
388	C₂²⋊Q₈	—	2	1	no	—
389	C₂²⋊Q₈	—	2	1	no	—
390	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
391	#121	D₄×C₁₉	1	1	yes	characteristic
392	C₄×Q₈	—	2	1	no	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	1	no	—
395	C₄×Q₈	—	2	1	no	—
396	C₄×Q₈	—	2	1	no	—
397	C₄×Q₈	—	2	1	no	—
398	C₄×Q₈	—	2	1	no	—
399	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
403	#117	—	2	2	no	—
404	#117	—	2	1	no	—
405	#117	—	2	2	no	—
406	#117	—	2	1	no	—
407	#117	—	2	1	no	—
408	#117	D₄×C₁₉	1	2	yes	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
413	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
414	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
415	#107	—	2	2	no	—
416	#107	—	2	2	no	—
417	#107	—	2	1	no	—
418	#107	—	2	2	no	—
419	#106	—	2	2	no	—
420	#106	—	2	2	no	—
421	#106	—	2	1	no	—
422	#106	—	2	2	no	—
423	C₄⋊C₈	—	2	1	no	—
424	#103	—	2	1	no	—
425	#103	—	2	1	no	—
426	#103	—	2	1	no	—
427	#103	—	2	2	no	—
428	#103	—	2	2	no	—
429	#102	—	2	1	no	—
430	C₂²⋊C₈	—	2	1	no	—
431	#97	C₂³×C₁₉	1	2	yes	—
432	#97	C₂³×C₁₉	1	2	yes	—
433	#97	C₂³×C₁₉	1	1	yes	characteristic
434	#97	C₂³×C₁₉	1	1	yes	characteristic
435	C₄×C₈	—	2	1	no	—
436	C₄×C₈	—	2	1	no	—
437	C₁₉	#19037	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	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
453	Q₁₆	—	4	2	no	—
454	SD₁₆	—	4	2	no	—
455	M₁₆	—	2	4	no	—
456	M₁₆	—	4	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	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	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
490	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
492	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
494	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	2	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	—	4	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	—	4	1	no	—
511	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
512	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
514	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
515	C₂³	—	2	1	no	—
516	C₂³	C₁₉×#120	1	1	yes	characteristic
517	Q₈	—	4	1	no	—
518	Q₈	—	4	1	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	4	2	no	—
521	Q₈	—	4	2	no	—
522	Q₈	—	8	1	no	—
523	Q₈	—	8	2	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	8	1	no	—
541	C₂×C₄	—	8	2	no	—
542	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
543	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
544	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
545	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
548	C₈	—	2	4	no	—
549	C₈	—	2	2	no	—
550	C₈	—	4	1	no	—
551	C₈	—	4	2	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	2	no	—
570	C₄	—	4	1	no	—
571	C₄	—	8	1	no	—
572	C₄	—	8	1	no	—
573	C₄	C₁₉×#456	1	2	yes	—
574	C₂	—	4	1	no	—
575	C₂	—	8	1	no	—
576	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
577	C₂	C₁₉×#3018	1	1	yes	characteristic
578	C₂	C₁₉×#3020	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
2. C₁₉×#3237	C₂	semidirect
4. C₁₉×#3166	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1663	C₂	semidirect
7. C₁₉×#1663	C₂	semidirect
8. C₁₉×#1660	C₂	semidirect
10. C₁₉×#1528	C₂	semidirect
11. C₁₉×#1526	C₂	semidirect
225. #19037	C₁₉	direct (N × H)
264. #3237	C₂×C₁₉	semidirect
266. #3166	C₂×C₁₉	semidirect
267. #1664	C₂×C₁₉	semidirect
268. #1663	C₂×C₁₉	semidirect
269. #1663	C₂×C₁₉	semidirect
270. #1660	C₂×C₁₉	semidirect
272. #1528	C₂×C₁₉	semidirect
273. #1526	C₂×C₁₉	semidirect
437. C₁₉	#19037	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×#3237	2
C₁₉×#3172	2
C₁₉×#3166	2
C₁₉×#1664	2
C₁₉×#1663	2
C₁₉×#1660	2
C₁₉×#1529	2
C₁₉×#1528	2
C₁₉×#1526	2
#19037	19

Subgroups — C19×#19037 #18024996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19037 #18024996