Subgroups — C₁₉×#19046 #18025005

Order 4864.

836 conjugacy classes of subgroups.

The subgroup lattice has 596 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, complemented
2	C₁₉×#3234	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3180	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3135	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×#1658	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1657	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1532	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1531	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#330	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×#532	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×#496	C₂²	1	1	yes	characteristic
31	C₁₉×#491	C₂²	1	2	yes	—
32	C₁₉×#490	C₂²	1	1	yes	characteristic
33	C₁₉×#490	C₂²	1	2	yes	—
34	C₁₉×#490	C₂²	1	2	yes	—
35	C₁₉×#489	—	2	1	no	—
36	C₁₉×#489	—	2	1	no	—
37	C₁₉×#489	C₂²	1	1	yes	characteristic
38	C₁₉×#481	—	2	1	no	—
39	C₁₉×#480	—	2	1	no	—
40	C₁₉×#478	—	2	2	no	—
41	C₁₉×#466	—	2	1	no	—
42	C₁₉×#465	—	2	1	no	—
43	C₁₉×#442	—	2	1	no	—
44	C₁₉×#440	—	2	1	no	—
45	C₁₉×#432	C₂²	1	1	yes	characteristic
46	C₁₉×#416	—	2	2	no	—
47	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×#97	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×#41×C₁₉	—	2	1	no	—
56	C₂×SD₁₆×C₁₉	—	2	1	no	—
57	C₂×D₈×C₁₉	—	2	1	no	—
58	C₂²×C₈×C₁₉	—	2	1	no	—
59	C₂²×C₈×C₁₉	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	—	2	2	no	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	2	no	—
63	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
64	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₁₉×#127	C₂³	1	1	yes	characteristic
67	C₁₉×#126	—	2	2	no	—
68	C₁₉×#126	—	2	2	no	—
69	C₁₉×#126	—	2	2	no	—
70	C₁₉×#126	—	2	2	no	—
71	C₁₉×#126	—	2	1	no	—
72	C₁₉×#125	—	2	2	no	—
73	C₁₉×#125	—	2	2	no	—
74	C₁₉×#125	—	2	1	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	2	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	2	yes	—
85	C₁₉×#125	C₂³	1	2	yes	—
86	C₁₉×#125	C₂³	1	1	yes	characteristic
87	C₁₉×#124	—	2	1	no	—
88	C₁₉×#124	C₂³	1	1	yes	characteristic
89	C₁₉×#123	—	2	2	no	—
90	C₁₉×#123	—	2	2	no	—
91	C₁₉×#123	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	—	2	1	no	—
94	C₁₉×C₂²⋊Q₈	—	2	1	no	—
95	C₁₉×C₂²⋊Q₈	—	2	2	no	—
96	C₁₉×C₂²⋊Q₈	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	—	2	1	no	—
98	C₁₉×C₂²⋊Q₈	—	2	2	no	—
99	C₁₉×C₂²⋊Q₈	—	2	2	no	—
100	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
101	C₁₉×#121	—	2	1	no	—
102	C₁₉×#121	—	2	1	no	—
103	C₁₉×#121	D₄	1	1	yes	characteristic
104	C₄×Q₈×C₁₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
110	C₄×D₄×C₁₉	—	2	2	no	—
111	C₄×D₄×C₁₉	—	2	1	no	—
112	C₄×D₄×C₁₉	—	2	1	no	—
113	C₄×D₄×C₁₉	—	2	1	no	—
114	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
115	C₁₉×#117	—	2	2	no	—
116	C₁₉×#117	—	2	1	no	—
117	C₁₉×#117	—	2	2	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	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	1	no	—
132	C₁₉×#103	—	2	2	no	—
133	C₁₉×#103	—	2	2	no	—
134	C₁₉×#102	—	2	1	no	—
135	C₁₉×#102	—	2	2	no	—
136	C₁₉×#102	—	2	2	no	—
137	C₁₉×#102	—	2	1	no	—
138	C₁₉×#102	—	2	1	no	—
139	C₁₉×#102	—	2	2	no	—
140	C₁₉×#102	—	2	2	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₁₉×#97	—	2	1	no	—
143	C₁₉×#97	—	2	1	no	—
144	C₁₉×#97	C₂³	1	1	yes	characteristic
145	C₁₉×#97	C₂³	1	2	yes	—
146	C₁₉×#97	C₂³	1	1	yes	characteristic
147	C₁₉×#97	C₂³	1	2	yes	—
148	#41×C₁₉	—	4	4	no	—
149	C₂×Q₈×C₁₉	—	2	2	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	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	4	1	no	—
159	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	4	1	no	—
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	SD₁₆×C₁₉	—	4	2	no	—
169	D₈×C₁₉	—	4	2	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	4	2	no	—
175	C₂×C₈×C₁₉	—	4	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	2	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	2	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	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₄⋊C₄×C₁₉	—	2	2	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
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	2	yes	—
204	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	1	no	—
210	C₂²⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
215	C₂²⋊C₄×C₁₉	—	4	1	no	—
216	C₂²⋊C₄×C₁₉	—	4	1	no	—
217	C₄²×C₁₉	—	2	2	no	—
218	C₄²×C₁₉	—	2	2	no	—
219	C₄²×C₁₉	—	2	2	no	—
220	C₄²×C₁₉	—	2	2	no	—
221	C₄²×C₁₉	—	2	1	no	—
222	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
223	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
224	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
225	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
226	#19046	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂³×C₁₉	—	2	1	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	#120	1	1	yes	characteristic
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	1	no	—
237	D₄×C₁₉	—	4	1	no	—
238	D₄×C₁₉	—	4	2	no	—
239	D₄×C₁₉	—	4	2	no	—
240	D₄×C₁₉	—	4	2	no	—
241	D₄×C₁₉	—	8	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	4	2	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	8	2	no	—
256	C₂×C₄×C₁₉	—	8	1	no	—
257	C₂×C₄×C₁₉	—	8	2	no	—
258	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
259	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
260	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
264	C₈×C₁₉	—	2	2	no	—
265	C₈×C₁₉	—	4	2	no	—
266	C₈×C₁₉	—	4	2	no	—
267	C₈×C₁₉	—	4	1	no	—
268	#3563	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#3234	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#3180	C₂×C₁₉	1	1	yes	characteristic
271	#3135	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1664	C₂×C₁₉	1	2	yes	complemented
273	#1663	C₂×C₁₉	1	2	yes	complemented
274	#1658	C₂×C₁₉	1	2	yes	complemented
275	#1657	C₂×C₁₉	1	2	yes	complemented
276	#1532	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1531	C₂×C₁₉	1	1	yes	characteristic, complemented
278	C₂×#330	C₂×C₁₉	1	1	yes	characteristic, complemented
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	2	1	no	—
281	C₂²×C₁₉	—	4	1	no	—
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	1	no	—
284	C₂²×C₁₉	—	8	1	no	—
285	C₂²×C₁₉	—	8	1	no	—
286	C₂²×C₁₉	—	8	1	no	—
287	C₂²×C₁₉	#454	1	2	yes	—
288	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
289	C₄×C₁₉	—	2	1	no	—
290	C₄×C₁₉	—	2	1	no	—
291	C₄×C₁₉	—	2	1	no	—
292	C₄×C₁₉	—	2	1	no	—
293	C₄×C₁₉	—	2	1	no	—
294	C₄×C₁₉	—	2	1	no	—
295	C₄×C₁₉	—	4	2	no	—
296	C₄×C₁₉	—	4	1	no	—
297	C₄×C₁₉	—	4	2	no	—
298	C₄×C₁₉	—	4	2	no	—
299	C₄×C₁₉	—	4	1	no	—
300	C₄×C₁₉	—	4	1	no	—
301	C₄×C₁₉	—	4	2	no	—
302	C₄×C₁₉	—	8	1	no	—
303	#564	C₂²×C₁₉	1	2	yes	—
304	#563	C₂²×C₁₉	1	2	yes	—
305	#557	—	2	1	no	—
306	#554	—	2	1	no	—
307	#552	—	2	1	no	—
308	#552	—	2	2	no	—
309	#552	—	2	1	no	—
310	#544	—	2	1	no	—
311	#544	—	2	1	no	—
312	#541	—	2	1	no	—
313	#541	—	2	2	no	—
314	#539	—	2	1	no	—
315	#533	C₂²×C₁₉	1	1	yes	characteristic
316	#532	C₂²×C₁₉	1	1	yes	characteristic
317	#529	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
319	#501	C₂²×C₁₉	1	1	yes	characteristic
320	#501	C₂²×C₁₉	1	2	yes	—
321	#496	C₂²×C₁₉	1	1	yes	characteristic
322	#491	C₂²×C₁₉	1	2	yes	—
323	#490	C₂²×C₁₉	1	2	yes	—
324	#490	C₂²×C₁₉	1	1	yes	characteristic
325	#490	C₂²×C₁₉	1	2	yes	—
326	#489	—	2	1	no	—
327	#489	—	2	1	no	—
328	#489	C₂²×C₁₉	1	1	yes	characteristic
329	#481	—	2	1	no	—
330	#480	—	2	1	no	—
331	#478	—	2	2	no	—
332	#466	—	2	1	no	—
333	#465	—	2	1	no	—
334	#442	—	2	1	no	—
335	#440	—	2	1	no	—
336	#432	C₂²×C₁₉	1	1	yes	characteristic
337	#416	—	2	2	no	—
338	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
339	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
340	#330	C₂²×C₁₉	1	2	yes	—
341	#330	C₂²×C₁₉	1	2	yes	—
342	#330	C₂²×C₁₉	1	2	yes	—
343	#330	C₂²×C₁₉	1	2	yes	—
344	#330	C₂²×C₁₉	1	2	yes	—
345	#329	C₂²×C₁₉	1	2	yes	—
346	C₂×C₁₉	—	2	2	no	—
347	C₂×C₁₉	—	8	1	no	—
348	C₂×C₁₉	—	16	1	no	—
349	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
350	C₂×C₁₉	#3018	1	1	yes	characteristic
351	C₂×C₁₉	#3020	1	1	yes	characteristic
352	C₂×#41	—	2	1	no	—
353	C₂×SD₁₆	—	2	1	no	—
354	C₂×D₈	—	2	1	no	—
355	C₂²×C₈	—	2	1	no	—
356	C₂²×C₈	—	2	1	no	—
357	C₄⋊Q₈	—	2	2	no	—
358	C₄⋊Q₈	—	2	1	no	—
359	C₄⋊Q₈	—	2	2	no	—
360	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
361	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
362	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
363	#127	C₂³×C₁₉	1	1	yes	characteristic
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	1	no	—
372	#125	—	2	2	no	—
373	#125	—	2	2	no	—
374	#125	—	2	2	no	—
375	#125	—	2	2	no	—
376	#125	—	2	2	no	—
377	#125	—	2	2	no	—
378	#125	—	2	1	no	—
379	#125	—	2	1	no	—
380	#125	D₄×C₁₉	1	2	yes	—
381	#125	C₂³×C₁₉	1	2	yes	—
382	#125	C₂³×C₁₉	1	1	yes	characteristic
383	#125	C₂³×C₁₉	1	2	yes	—
384	#124	—	2	1	no	—
385	#124	C₂³×C₁₉	1	1	yes	characteristic
386	#123	—	2	2	no	—
387	#123	—	2	2	no	—
388	#123	—	2	1	no	—
389	C₂²⋊Q₈	—	2	2	no	—
390	C₂²⋊Q₈	—	2	1	no	—
391	C₂²⋊Q₈	—	2	1	no	—
392	C₂²⋊Q₈	—	2	2	no	—
393	C₂²⋊Q₈	—	2	1	no	—
394	C₂²⋊Q₈	—	2	1	no	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
398	#121	—	2	1	no	—
399	#121	—	2	1	no	—
400	#121	D₄×C₁₉	1	1	yes	characteristic
401	C₄×Q₈	—	2	1	no	—
402	C₄×Q₈	—	2	2	no	—
403	C₄×Q₈	—	2	1	no	—
404	C₄×Q₈	—	2	1	no	—
405	C₄×Q₈	—	2	1	no	—
406	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
412	#117	—	2	2	no	—
413	#117	—	2	1	no	—
414	#117	—	2	2	no	—
415	#117	—	2	1	no	—
416	#117	D₄×C₁₉	1	2	yes	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
421	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
423	#107	—	2	1	no	—
424	#107	—	2	2	no	—
425	#106	—	2	1	no	—
426	#106	—	2	2	no	—
427	C₄⋊C₈	—	2	1	no	—
428	#103	—	2	1	no	—
429	#103	—	2	2	no	—
430	#103	—	2	2	no	—
431	#102	—	2	1	no	—
432	#102	—	2	2	no	—
433	#102	—	2	2	no	—
434	#102	—	2	1	no	—
435	#102	—	2	1	no	—
436	#102	—	2	2	no	—
437	#102	—	2	2	no	—
438	C₂²⋊C₈	—	2	1	no	—
439	#97	—	2	1	no	—
440	#97	—	2	1	no	—
441	#97	C₂³×C₁₉	1	2	yes	—
442	#97	C₂³×C₁₉	1	2	yes	—
443	#97	C₂³×C₁₉	1	1	yes	characteristic
444	#97	C₂³×C₁₉	1	1	yes	characteristic
445	C₁₉	#19046	1	1	yes	characteristic, direct product factor, Sylow
446	#41	—	4	4	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	4	1	no	—
463	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
466	SD₁₆	—	4	2	no	—
467	D₈	—	4	2	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	4	2	no	—
473	C₂×C₈	—	4	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
499	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
500	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
501	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
502	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
503	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	4	1	no	—
514	C₂²⋊C₄	—	4	1	no	—
515	C₄²	—	2	2	no	—
516	C₄²	—	2	2	no	—
517	C₄²	—	2	2	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	1	no	—
520	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
521	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
522	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
523	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
524	C₂³	—	2	1	no	—
525	C₂³	—	4	1	no	—
526	C₂³	C₁₉×#120	1	1	yes	characteristic
527	Q₈	—	4	1	no	—
528	Q₈	—	4	2	no	—
529	Q₈	—	4	2	no	—
530	Q₈	—	8	1	no	—
531	Q₈	—	8	2	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	1	no	—
534	D₄	—	4	1	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	8	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	8	2	no	—
553	C₂×C₄	—	8	1	no	—
554	C₂×C₄	—	8	2	no	—
555	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
556	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
557	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
558	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
560	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
561	C₈	—	2	2	no	—
562	C₈	—	4	2	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	2	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	8	1	no	—
571	C₂²	—	8	1	no	—
572	C₂²	—	8	1	no	—
573	C₂²	C₁₉×#454	1	2	yes	—
574	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	2	1	no	—
580	C₄	—	2	1	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	2	no	—
584	C₄	—	4	2	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	2	no	—
588	C₄	—	8	1	no	—
589	C₂	—	2	2	no	—
590	C₂	—	8	1	no	—
591	C₂	—	16	1	no	—
592	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
593	C₂	C₁₉×#3018	1	1	yes	characteristic
594	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×#3180	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
1. C₁₉×#3563	C₂	semidirect
2. C₁₉×#3234	C₂	semidirect
4. C₁₉×#3135	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1663	C₂	semidirect
7. C₁₉×#1658	C₂	semidirect
8. C₁₉×#1657	C₂	semidirect
9. C₁₉×#1532	C₂	semidirect
10. C₁₉×#1531	C₂	semidirect
11. C₂×C₁₉×#330	C₂	semidirect
226. #19046	C₁₉	direct (N × H)
268. #3563	C₂×C₁₉	semidirect
269. #3234	C₂×C₁₉	semidirect
271. #3135	C₂×C₁₉	semidirect
272. #1664	C₂×C₁₉	semidirect
273. #1663	C₂×C₁₉	semidirect
274. #1658	C₂×C₁₉	semidirect
275. #1657	C₂×C₁₉	semidirect
276. #1532	C₂×C₁₉	semidirect
277. #1531	C₂×C₁₉	semidirect
278. C₂×#330	C₂×C₁₉	semidirect
445. C₁₉	#19046	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×#3234	2
C₁₉×#3180	2
C₁₉×#3135	2
C₁₉×#1664	2
C₁₉×#1663	2
C₁₉×#1658	2
C₁₉×#1657	2
C₁₉×#1532	2
C₁₉×#1531	2
C₂×C₁₉×#330	2
#19046	19

Subgroups — C19×#19046 #18025005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19046 #18025005