Subgroups — C₁₉×#19025 #18024984

Order 4864.

872 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3561	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, complemented
4	C₁₉×#3140	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1664	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1664	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1662	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1661	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1529	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1527	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1526	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#563	C₂²	1	2	yes	—
13	C₁₉×#562	C₂²	1	2	yes	—
14	C₁₉×#556	—	2	1	no	—
15	C₁₉×#551	—	2	2	no	—
16	D₄×Q₈×C₁₉	—	2	1	no	—
17	C₁₉×#548	—	2	1	no	—
18	C₁₉×#546	—	2	1	no	—
19	C₁₉×#543	—	2	1	no	—
20	C₁₉×#542	—	2	1	no	—
21	C₁₉×#542	—	2	2	no	—
22	C₁₉×#538	—	2	1	no	—
23	C₁₉×#536	—	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×#124	C₂²	1	1	yes	characteristic
28	C₁₉×#501	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#501	C₂²	1	2	yes	complemented
30	C₁₉×#497	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#491	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#491	C₂²	1	2	yes	complemented
33	C₁₉×#489	C₂²	1	2	yes	—
34	C₁₉×#489	C₂²	1	2	yes	—
35	C₁₉×#489	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#488	—	2	2	no	—
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×#419	—	2	1	no	—
46	C₁₉×#418	—	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	complemented
50	C₁₉×#330	C₂²	1	2	yes	complemented
51	C₁₉×#330	C₂²	1	2	yes	complemented
52	C₁₉×#329	C₂²	1	2	yes	—
53	C₁₉×#329	C₂²	1	2	yes	—
54	C₁₉×#329	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂²×Q₈×C₁₉	—	2	1	no	—
57	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
58	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂×Q₁₆×C₁₉	—	2	1	no	—
60	C₂×SD₁₆×C₁₉	—	2	1	no	—
61	C₂×M₁₆×C₁₉	—	2	1	no	—
62	C₂×M₁₆×C₁₉	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	—	2	2	no	—
65	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
67	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
69	C₁₉×#126	—	2	2	no	—
70	C₁₉×#126	—	2	2	no	—
71	C₁₉×#126	—	2	2	no	—
72	C₁₉×#126	—	2	1	no	—
73	C₁₉×#125	—	2	1	no	—
74	C₁₉×#125	C₂³	1	1	yes	characteristic
75	C₁₉×#125	C₂³	1	2	yes	—
76	C₁₉×#124	—	2	1	no	—
77	C₁₉×#124	—	2	2	no	—
78	C₁₉×#124	—	2	2	no	—
79	C₁₉×#124	—	2	1	no	—
80	C₁₉×#124	—	2	1	no	—
81	C₁₉×#124	D₄	1	2	yes	—
82	C₁₉×#124	C₂³	1	2	yes	—
83	C₁₉×#124	C₂³	1	1	yes	characteristic
84	C₁₉×#123	—	2	2	no	—
85	C₁₉×#123	—	2	2	no	—
86	C₁₉×#123	—	2	1	no	—
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	2	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	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	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	—	2	1	no	—
103	C₁₉×#121	—	2	2	no	—
104	C₁₉×#121	—	2	2	no	—
105	C₁₉×#121	D₄	1	1	yes	characteristic
106	C₁₉×#120	—	2	2	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	D₄	1	1	yes	characteristic
113	C₄×D₄×C₁₉	—	2	2	no	—
114	C₄×D₄×C₁₉	—	2	1	no	—
115	C₄×D₄×C₁₉	—	2	2	no	—
116	C₄×D₄×C₁₉	—	2	1	no	—
117	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
118	C₁₉×#117	—	2	2	no	—
119	C₁₉×#117	—	2	1	no	—
120	C₁₉×#117	—	2	1	no	—
121	C₁₉×#117	D₄	1	2	yes	—
122	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
123	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
126	C₁₉×#107	—	2	1	no	—
127	C₁₉×#107	—	2	2	no	—
128	C₁₉×#106	—	2	1	no	—
129	C₁₉×#106	—	2	2	no	—
130	C₁₉×C₄⋊C₈	—	2	1	no	—
131	C₁₉×#103	—	2	2	no	—
132	C₁₉×#103	—	2	2	no	—
133	C₁₉×#103	—	2	1	no	—
134	C₁₉×#103	—	2	1	no	—
135	C₁₉×#103	—	2	1	no	—
136	C₁₉×#103	—	2	2	no	—
137	C₁₉×#103	—	2	2	no	—
138	C₁₉×#102	—	2	2	no	—
139	C₁₉×#102	—	2	2	no	—
140	C₁₉×#102	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₁₉×#97	C₂³	1	2	yes	—
143	C₁₉×#97	C₂³	1	1	yes	characteristic
144	C₁₉×#97	C₂³	1	1	yes	characteristic
145	C₁₉×#97	C₂³	1	2	yes	—
146	C₄×C₈×C₁₉	—	2	1	no	—
147	C₄×C₈×C₁₉	—	2	1	no	—
148	C₂⁴×C₁₉	—	2	1	no	—
149	#41×C₁₉	—	8	2	no	—
150	C₂×Q₈×C₁₉	—	2	2	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	2	1	no	—
156	C₂×Q₈×C₁₉	—	4	2	no	—
157	C₂×Q₈×C₁₉	—	8	2	no	—
158	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	4	2	no	—
165	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₉	—	2	2	no	—
168	C₂²×C₄×C₁₉	—	2	2	no	—
169	C₂²×C₄×C₁₉	—	2	2	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	Q₁₆×C₁₉	—	4	2	no	—
176	SD₁₆×C₁₉	—	4	2	no	—
177	M₁₆×C₁₉	—	4	2	no	—
178	M₁₆×C₁₉	—	4	2	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	2	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	4	1	no	—
200	C₄⋊C₄×C₁₉	—	4	1	no	—
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	2	no	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	1	no	—
211	C₂²⋊C₄×C₁₉	—	2	2	no	—
212	C₂²⋊C₄×C₁₉	—	2	2	no	—
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₉	—	2	1	no	—
215	C₂²⋊C₄×C₁₉	—	2	1	no	—
216	C₂²⋊C₄×C₁₉	—	2	2	no	—
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	1	no	—
219	C₂²⋊C₄×C₁₉	—	2	1	no	—
220	C₂²⋊C₄×C₁₉	—	4	1	no	—
221	C₄²×C₁₉	—	2	2	no	—
222	C₄²×C₁₉	—	2	2	no	—
223	C₄²×C₁₉	—	2	1	no	—
224	C₄²×C₁₉	—	4	1	no	—
225	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
227	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
228	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
229	#19025	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂³×C₁₉	—	2	2	no	—
231	C₂³×C₁₉	—	2	1	no	—
232	C₂³×C₁₉	—	4	2	no	—
233	C₂³×C₁₉	—	8	1	no	—
234	C₂³×C₁₉	—	8	1	no	—
235	C₂³×C₁₉	#120	1	1	yes	characteristic
236	Q₈×C₁₉	—	4	1	no	—
237	Q₈×C₁₉	—	4	2	no	—
238	Q₈×C₁₉	—	4	1	no	—
239	Q₈×C₁₉	—	4	1	no	—
240	Q₈×C₁₉	—	4	2	no	—
241	Q₈×C₁₉	—	4	2	no	—
242	Q₈×C₁₉	—	4	2	no	—
243	Q₈×C₁₉	—	8	1	no	—
244	Q₈×C₁₉	—	8	2	no	—
245	D₄×C₁₉	—	4	1	no	—
246	D₄×C₁₉	—	4	2	no	—
247	D₄×C₁₉	—	4	2	no	—
248	D₄×C₁₉	—	4	2	no	—
249	D₄×C₁₉	—	8	2	no	—
250	D₄×C₁₉	—	8	2	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	2	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	2	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	8	1	no	—
264	C₂×C₄×C₁₉	—	8	2	no	—
265	C₂×C₄×C₁₉	—	8	2	no	—
266	C₂×C₄×C₁₉	—	8	2	no	—
267	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
268	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
269	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
270	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
273	C₈×C₁₉	—	2	2	no	—
274	C₈×C₁₉	—	4	2	no	—
275	C₈×C₁₉	—	4	2	no	—
276	C₈×C₁₉	—	4	1	no	—
277	#3561	C₂×C₁₉	1	1	yes	characteristic
278	#3237	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#3172	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#3140	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1664	C₂×C₁₉	1	2	yes	complemented
282	#1664	C₂×C₁₉	1	2	yes	complemented
283	#1662	C₂×C₁₉	1	2	yes	complemented
284	#1661	C₂×C₁₉	1	2	yes	complemented
285	#1529	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1527	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1526	C₂×C₁₉	1	1	yes	characteristic, complemented
288	C₂²×C₁₉	—	2	1	no	—
289	C₂²×C₁₉	—	2	1	no	—
290	C₂²×C₁₉	—	2	1	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	—	4	2	no	—
293	C₂²×C₁₉	—	4	2	no	—
294	C₂²×C₁₉	—	4	1	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	—	4	2	no	—
297	C₂²×C₁₉	—	16	2	no	—
298	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	2	1	no	—
301	C₄×C₁₉	—	2	1	no	—
302	C₄×C₁₉	—	2	1	no	—
303	C₄×C₁₉	—	2	1	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	—	4	2	no	—
306	C₄×C₁₉	—	4	2	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	4	2	no	—
309	C₄×C₁₉	—	4	1	no	—
310	C₄×C₁₉	—	8	1	no	—
311	C₄×C₁₉	—	8	1	no	—
312	C₄×C₁₉	#455	1	2	yes	—
313	#563	C₂²×C₁₉	1	2	yes	—
314	#562	C₂²×C₁₉	1	2	yes	—
315	#556	—	2	1	no	—
316	#551	—	2	2	no	—
317	D₄×Q₈	—	2	1	no	—
318	#548	—	2	1	no	—
319	#546	—	2	1	no	—
320	#543	—	2	1	no	—
321	#542	—	2	1	no	—
322	#542	—	2	2	no	—
323	#538	—	2	1	no	—
324	#536	—	2	1	no	—
325	#533	C₂²×C₁₉	1	1	yes	characteristic
326	#533	C₂²×C₁₉	1	1	yes	characteristic
327	#529	C₂²×C₁₉	1	1	yes	characteristic
328	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
329	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
330	#501	C₂²×C₁₉	1	2	yes	complemented
331	#497	C₂²×C₁₉	1	1	yes	characteristic, complemented
332	#491	C₂²×C₁₉	1	1	yes	characteristic, complemented
333	#491	C₂²×C₁₉	1	2	yes	complemented
334	#489	C₂²×C₁₉	1	2	yes	—
335	#489	C₂²×C₁₉	1	2	yes	—
336	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
337	#488	—	2	2	no	—
338	#485	—	2	2	no	—
339	#477	—	2	1	no	—
340	#475	—	2	1	no	—
341	#470	—	2	1	no	—
342	#468	—	2	1	no	—
343	C₄×Q₁₆	—	2	1	no	—
344	C₄×SD₁₆	—	2	1	no	—
345	#432	C₂²×C₁₉	1	1	yes	characteristic
346	#419	—	2	1	no	—
347	#418	—	2	1	no	—
348	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
349	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
350	#330	C₂²×C₁₉	1	2	yes	complemented
351	#330	C₂²×C₁₉	1	2	yes	complemented
352	#330	C₂²×C₁₉	1	2	yes	complemented
353	#329	C₂²×C₁₉	1	2	yes	—
354	#329	C₂²×C₁₉	1	2	yes	—
355	#329	C₂²×C₁₉	1	2	yes	complemented
356	C₂×C₁₉	—	4	1	no	—
357	C₂×C₁₉	—	8	1	no	—
358	C₂×C₁₉	—	8	2	no	—
359	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
360	C₂×C₁₉	#3018	1	1	yes	characteristic
361	C₂×C₁₉	#3020	1	1	yes	characteristic
362	C₂×#41	—	2	1	no	—
363	C₂²×Q₈	—	2	1	no	—
364	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
365	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
366	C₂×Q₁₆	—	2	1	no	—
367	C₂×SD₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₄⋊Q₈	—	2	1	no	—
371	C₄⋊Q₈	—	2	2	no	—
372	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
373	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
374	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
375	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
376	#126	—	2	2	no	—
377	#126	—	2	2	no	—
378	#126	—	2	2	no	—
379	#126	—	2	1	no	—
380	#125	—	2	1	no	—
381	#125	C₂³×C₁₉	1	1	yes	characteristic
382	#125	C₂³×C₁₉	1	2	yes	—
383	#124	—	2	1	no	—
384	#124	—	2	2	no	—
385	#124	—	2	2	no	—
386	#124	—	2	1	no	—
387	#124	—	2	1	no	—
388	#124	D₄×C₁₉	1	2	yes	—
389	#124	C₂³×C₁₉	1	2	yes	—
390	#124	C₂³×C₁₉	1	1	yes	characteristic
391	#123	—	2	2	no	—
392	#123	—	2	2	no	—
393	#123	—	2	1	no	—
394	#123	—	2	2	no	—
395	#123	—	2	2	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	2	2	no	—
398	C₂²⋊Q₈	—	2	1	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	2	2	no	—
401	C₂²⋊Q₈	—	2	2	no	—
402	C₂²⋊Q₈	—	2	1	no	—
403	C₂²⋊Q₈	—	2	1	no	—
404	C₂²⋊Q₈	—	2	2	no	—
405	C₂²⋊Q₈	—	2	2	no	—
406	C₂²⋊Q₈	—	2	1	no	—
407	C₂²⋊Q₈	—	2	1	no	—
408	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
409	#121	—	2	1	no	—
410	#121	—	2	2	no	—
411	#121	—	2	2	no	—
412	#121	D₄×C₁₉	1	1	yes	characteristic
413	#120	—	2	2	no	—
414	C₄×Q₈	—	2	1	no	—
415	C₄×Q₈	—	2	1	no	—
416	C₄×Q₈	—	2	1	no	—
417	C₄×Q₈	—	2	1	no	—
418	C₄×Q₈	—	2	1	no	—
419	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	—	2	2	no	—
423	C₄×D₄	—	2	1	no	—
424	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
425	#117	—	2	2	no	—
426	#117	—	2	1	no	—
427	#117	—	2	1	no	—
428	#117	D₄×C₁₉	1	2	yes	—
429	C₂×C₂²⋊C₄	—	2	2	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
433	#107	—	2	1	no	—
434	#107	—	2	2	no	—
435	#106	—	2	1	no	—
436	#106	—	2	2	no	—
437	C₄⋊C₈	—	2	1	no	—
438	#103	—	2	2	no	—
439	#103	—	2	2	no	—
440	#103	—	2	1	no	—
441	#103	—	2	1	no	—
442	#103	—	2	1	no	—
443	#103	—	2	2	no	—
444	#103	—	2	2	no	—
445	#102	—	2	2	no	—
446	#102	—	2	2	no	—
447	#102	—	2	1	no	—
448	C₂²⋊C₈	—	2	1	no	—
449	#97	C₂³×C₁₉	1	2	yes	—
450	#97	C₂³×C₁₉	1	1	yes	characteristic
451	#97	C₂³×C₁₉	1	1	yes	characteristic
452	#97	C₂³×C₁₉	1	2	yes	—
453	C₄×C₈	—	2	1	no	—
454	C₄×C₈	—	2	1	no	—
455	C₁₉	#19025	1	1	yes	characteristic, direct product factor, Sylow
456	C₂⁴	—	2	1	no	—
457	#41	—	8	2	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	4	2	no	—
465	C₂×Q₈	—	8	2	no	—
466	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
467	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	4	2	no	—
473	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
474	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
483	Q₁₆	—	4	2	no	—
484	SD₁₆	—	4	2	no	—
485	M₁₆	—	4	2	no	—
486	M₁₆	—	4	2	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	4	1	no	—
508	C₄⋊C₄	—	4	1	no	—
509	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
510	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
511	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
512	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	1	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	1	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	2	1	no	—
528	C₂²⋊C₄	—	4	1	no	—
529	C₄²	—	2	2	no	—
530	C₄²	—	2	2	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	4	1	no	—
533	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
534	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
535	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
536	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
537	C₂³	—	2	2	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	4	2	no	—
540	C₂³	—	8	1	no	—
541	C₂³	—	8	1	no	—
542	C₂³	C₁₉×#120	1	1	yes	characteristic
543	Q₈	—	4	1	no	—
544	Q₈	—	4	2	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	4	1	no	—
547	Q₈	—	4	2	no	—
548	Q₈	—	4	2	no	—
549	Q₈	—	4	2	no	—
550	Q₈	—	8	1	no	—
551	Q₈	—	8	2	no	—
552	D₄	—	4	1	no	—
553	D₄	—	4	2	no	—
554	D₄	—	4	2	no	—
555	D₄	—	4	2	no	—
556	D₄	—	8	2	no	—
557	D₄	—	8	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	8	1	no	—
571	C₂×C₄	—	8	2	no	—
572	C₂×C₄	—	8	2	no	—
573	C₂×C₄	—	8	2	no	—
574	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
575	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
576	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
577	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
578	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
579	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
580	C₈	—	2	2	no	—
581	C₈	—	4	2	no	—
582	C₈	—	4	1	no	—
583	C₈	—	4	2	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	2	no	—
589	C₂²	—	4	2	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	16	2	no	—
594	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	2	no	—
605	C₄	—	4	1	no	—
606	C₄	—	8	1	no	—
607	C₄	—	8	1	no	—
608	C₄	C₁₉×#455	1	2	yes	—
609	C₂	—	4	1	no	—
610	C₂	—	8	2	no	—
611	C₂	—	8	1	no	—
612	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
613	C₂	C₁₉×#3018	1	1	yes	characteristic
614	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×#3561	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×#3237	C₂	semidirect
3. C₁₉×#3172	C₂	semidirect
4. C₁₉×#3140	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1664	C₂	semidirect
7. C₁₉×#1662	C₂	semidirect
8. C₁₉×#1661	C₂	semidirect
9. C₁₉×#1529	C₂	semidirect
10. C₁₉×#1527	C₂	semidirect
11. C₁₉×#1526	C₂	semidirect
28. C₁₉×#501	C₂²	semidirect
29. C₁₉×#501	C₂²	semidirect
30. C₁₉×#497	C₂²	semidirect
31. C₁₉×#491	C₂²	semidirect
32. C₁₉×#491	C₂²	semidirect
35. C₁₉×#489	C₂²	semidirect
49. C₁₉×#330	C₂²	semidirect
50. C₁₉×#330	C₂²	semidirect
51. C₁₉×#330	C₂²	semidirect
54. C₁₉×#329	C₂²	semidirect
229. #19025	C₁₉	direct (N × H)
278. #3237	C₂×C₁₉	semidirect
279. #3172	C₂×C₁₉	semidirect
280. #3140	C₂×C₁₉	semidirect
281. #1664	C₂×C₁₉	semidirect
282. #1664	C₂×C₁₉	semidirect
283. #1662	C₂×C₁₉	semidirect
284. #1661	C₂×C₁₉	semidirect
285. #1529	C₂×C₁₉	semidirect
286. #1527	C₂×C₁₉	semidirect
287. #1526	C₂×C₁₉	semidirect
329. #501	C₂²×C₁₉	semidirect
330. #501	C₂²×C₁₉	semidirect
331. #497	C₂²×C₁₉	semidirect
332. #491	C₂²×C₁₉	semidirect
333. #491	C₂²×C₁₉	semidirect
336. #489	C₂²×C₁₉	semidirect
350. #330	C₂²×C₁₉	semidirect
351. #330	C₂²×C₁₉	semidirect
352. #330	C₂²×C₁₉	semidirect
355. #329	C₂²×C₁₉	semidirect
455. C₁₉	#19025	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×#3561	2
C₁₉×#3237	2
C₁₉×#3172	2
C₁₉×#3140	2
C₁₉×#1664	2
C₁₉×#1662	2
C₁₉×#1661	2
C₁₉×#1529	2
C₁₉×#1527	2
C₁₉×#1526	2
#19025	19

Subgroups — C19×#19025 #18024984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19025 #18024984