Subgroups — C₁₉×#19045 #18025004

Order 4864.

870 conjugacy classes of subgroups.

The subgroup lattice has 606 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×#3236	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3181	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3135	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×#1532	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1530	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#330	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#563	C₂²	1	2	yes	—
13	C₁₉×#562	C₂²	1	2	yes	—
14	C₁₉×#554	—	2	1	no	—
15	C₁₉×#553	—	2	1	no	—
16	C₁₉×#553	—	2	1	no	—
17	C₁₉×#547	—	2	2	no	—
18	C₁₉×#547	—	2	1	no	—
19	C₁₉×#544	—	2	1	no	—
20	C₁₉×#540	—	2	1	no	—
21	C₁₉×#539	—	2	2	no	—
22	C₁₉×#539	—	2	1	no	—
23	C₁₉×#537	—	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×#497	C₂²	1	1	yes	characteristic
31	C₁₉×#491	—	2	1	no	—
32	C₁₉×#491	C₂²	1	1	yes	characteristic
33	C₁₉×#491	C₂²	1	2	yes	—
34	C₁₉×#490	—	2	1	no	—
35	C₁₉×#489	C₂²	1	1	yes	characteristic
36	C₁₉×#489	C₂²	1	2	yes	—
37	C₁₉×#489	C₂²	1	2	yes	—
38	C₁₉×#484	—	2	1	no	—
39	C₁₉×#483	—	2	1	no	—
40	C₁₉×#479	—	2	2	no	—
41	C₁₉×#467	—	2	1	no	—
42	C₁₉×#465	—	2	1	no	—
43	C₁₉×#441	—	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×#329	C₂²	1	2	yes	—
53	C₁₉×#329	C₂²	1	2	yes	—
54	C₁₉×#329	C₂²	1	2	yes	—
55	C₂×#41×C₁₉	—	2	2	no	—
56	C₂×#41×C₁₉	D₄	1	2	yes	—
57	C₂×Q₁₆×C₁₉	—	2	1	no	—
58	C₂×SD₁₆×C₁₉	—	2	1	no	—
59	C₂²×C₈×C₁₉	—	2	1	no	—
60	C₂²×C₈×C₁₉	—	2	1	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	C₂³	1	1	yes	characteristic
65	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₁₉×#127	D₄	1	1	yes	characteristic
67	C₁₉×#126	—	2	2	no	—
68	C₁₉×#126	—	2	2	no	—
69	C₁₉×#126	—	2	1	no	—
70	C₁₉×#125	—	2	2	no	—
71	C₁₉×#125	—	2	1	no	—
72	C₁₉×#125	—	2	1	no	—
73	C₁₉×#125	—	2	1	no	—
74	C₁₉×#125	—	2	1	no	—
75	C₁₉×#125	D₄	1	2	yes	—
76	C₁₉×#125	C₂³	1	2	yes	—
77	C₁₉×#125	C₂³	1	1	yes	characteristic
78	C₁₉×#124	C₂³	1	2	yes	—
79	C₁₉×#124	C₂³	1	1	yes	characteristic
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×#123	—	2	2	no	—
82	C₁₉×#123	—	2	2	no	—
83	C₁₉×#123	—	2	2	no	—
84	C₁₉×#123	—	2	1	no	—
85	C₁₉×#123	—	2	2	no	—
86	C₁₉×#123	—	2	2	no	—
87	C₁₉×C₂²⋊Q₈	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	2	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	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	D₄	1	1	yes	characteristic
96	C₁₉×#121	—	2	2	no	—
97	C₁₉×#121	—	2	2	no	—
98	C₁₉×#121	—	2	1	no	—
99	C₁₉×#121	—	2	1	no	—
100	C₁₉×#121	—	2	2	no	—
101	C₁₉×#121	—	2	2	no	—
102	C₁₉×#121	—	2	1	no	—
103	C₁₉×#121	—	2	1	no	—
104	C₁₉×#121	D₄	1	1	yes	characteristic
105	C₄×Q₈×C₁₉	—	2	1	no	—
106	C₄×Q₈×C₁₉	—	2	1	no	—
107	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
108	C₄×D₄×C₁₉	—	2	2	no	—
109	C₄×D₄×C₁₉	—	2	2	no	—
110	C₄×D₄×C₁₉	—	2	1	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	—	2	1	no	—
115	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
116	C₁₉×#117	—	2	1	no	—
117	C₁₉×#117	—	2	1	no	—
118	C₁₉×#117	—	2	1	no	—
119	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
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	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	—	2	1	no	—
143	C₁₉×#97	—	2	1	no	—
144	C₁₉×#97	C₂³	1	2	yes	—
145	C₁₉×#97	C₂³	1	1	yes	characteristic
146	C₁₉×#97	C₂³	1	1	yes	characteristic
147	C₁₉×#97	C₂³	1	2	yes	—
148	#41×C₁₉	—	4	4	no	—
149	#41×C₁₉	—	8	4	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	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
155	C₂×D₄×C₁₉	—	2	2	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	2	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	2	no	—
165	C₂²×C₄×C₁₉	—	2	2	no	—
166	C₂²×C₄×C₁₉	—	2	2	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	2	no	—
170	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	Q₁₆×C₁₉	—	4	2	no	—
174	SD₁₆×C₁₉	—	4	2	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	2	2	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
178	C₂×C₈×C₁₉	—	2	2	no	—
179	C₂×C₈×C₁₉	—	4	2	no	—
180	C₂×C₈×C₁₉	—	4	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	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	4	1	no	—
202	C₄⋊C₄×C₁₉	—	4	1	no	—
203	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
204	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
205	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	2	no	—
211	C₂²⋊C₄×C₁₉	—	2	2	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	—	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	—	4	1	no	—
220	C₄²×C₁₉	—	2	2	no	—
221	C₄²×C₁₉	—	2	1	no	—
222	C₄²×C₁₉	—	4	1	no	—
223	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
224	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
225	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
227	#19045	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂³×C₁₉	—	2	2	no	—
229	C₂³×C₁₉	—	2	1	no	—
230	C₂³×C₁₉	#120	1	1	yes	characteristic
231	Q₈×C₁₉	—	4	1	no	—
232	Q₈×C₁₉	—	4	2	no	—
233	Q₈×C₁₉	—	4	1	no	—
234	Q₈×C₁₉	—	4	1	no	—
235	Q₈×C₁₉	—	4	2	no	—
236	Q₈×C₁₉	—	8	2	no	—
237	D₄×C₁₉	—	4	1	no	—
238	D₄×C₁₉	—	4	2	no	—
239	D₄×C₁₉	—	4	2	no	—
240	D₄×C₁₉	—	4	4	no	—
241	D₄×C₁₉	—	4	2	no	—
242	D₄×C₁₉	—	8	1	no	—
243	D₄×C₁₉	—	8	2	no	—
244	D₄×C₁₉	—	8	2	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	2	1	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	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	—	4	2	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	8	2	no	—
259	C₂×C₄×C₁₉	—	8	1	no	—
260	C₂×C₄×C₁₉	—	8	2	no	—
261	C₂×C₄×C₁₉	—	8	2	no	—
262	C₂×C₄×C₁₉	—	8	2	no	—
263	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
264	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
265	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
269	C₈×C₁₉	—	2	2	no	—
270	C₈×C₁₉	—	4	2	no	—
271	C₈×C₁₉	—	4	2	no	—
272	C₈×C₁₉	—	4	1	no	—
273	#3559	C₂×C₁₉	1	1	yes	characteristic
274	#3236	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#3181	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#3135	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1664	C₂×C₁₉	1	2	yes	complemented
278	#1664	C₂×C₁₉	1	2	yes	complemented
279	#1662	C₂×C₁₉	1	2	yes	complemented
280	#1661	C₂×C₁₉	1	2	yes	complemented
281	#1532	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1530	C₂×C₁₉	1	1	yes	characteristic, complemented
283	C₂×#330	C₂×C₁₉	1	1	yes	characteristic, complemented
284	C₂²×C₁₉	—	2	1	no	—
285	C₂²×C₁₉	—	2	1	no	—
286	C₂²×C₁₉	—	4	2	no	—
287	C₂²×C₁₉	—	4	1	no	—
288	C₂²×C₁₉	—	4	2	no	—
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	2	no	—
292	C₂²×C₁₉	#455	1	2	yes	—
293	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
294	C₄×C₁₉	—	2	1	no	—
295	C₄×C₁₉	—	2	1	no	—
296	C₄×C₁₉	—	2	1	no	—
297	C₄×C₁₉	—	2	1	no	—
298	C₄×C₁₉	—	2	1	no	—
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	4	2	no	—
301	C₄×C₁₉	—	4	2	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	4	2	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	8	1	no	—
307	C₄×C₁₉	—	8	1	no	—
308	#563	C₂²×C₁₉	1	2	yes	—
309	#562	C₂²×C₁₉	1	2	yes	—
310	#554	—	2	1	no	—
311	#553	—	2	1	no	—
312	#553	—	2	1	no	—
313	#547	—	2	2	no	—
314	#547	—	2	1	no	—
315	#544	—	2	1	no	—
316	#540	—	2	1	no	—
317	#539	—	2	2	no	—
318	#539	—	2	1	no	—
319	#537	—	2	1	no	—
320	#533	C₂²×C₁₉	1	1	yes	characteristic
321	#532	C₂²×C₁₉	1	1	yes	characteristic
322	#529	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
324	#501	C₂²×C₁₉	1	1	yes	characteristic
325	#501	C₂²×C₁₉	1	2	yes	—
326	#497	C₂²×C₁₉	1	1	yes	characteristic
327	#491	—	2	1	no	—
328	#491	C₂²×C₁₉	1	1	yes	characteristic
329	#491	C₂²×C₁₉	1	2	yes	—
330	#490	—	2	1	no	—
331	#489	C₂²×C₁₉	1	2	yes	—
332	#489	C₂²×C₁₉	1	2	yes	—
333	#489	C₂²×C₁₉	1	1	yes	characteristic
334	#484	—	2	1	no	—
335	#483	—	2	1	no	—
336	#479	—	2	2	no	—
337	#467	—	2	1	no	—
338	#465	—	2	1	no	—
339	#441	—	2	1	no	—
340	#440	—	2	1	no	—
341	#432	C₂²×C₁₉	1	1	yes	characteristic
342	#416	—	2	2	no	—
343	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
345	#330	C₂²×C₁₉	1	2	yes	—
346	#330	C₂²×C₁₉	1	2	yes	—
347	#330	C₂²×C₁₉	1	2	yes	—
348	#329	C₂²×C₁₉	1	2	yes	—
349	#329	C₂²×C₁₉	1	2	yes	—
350	#329	C₂²×C₁₉	1	2	yes	—
351	C₂×C₁₉	—	2	2	no	—
352	C₂×C₁₉	—	8	2	no	—
353	C₂×C₁₉	—	8	1	no	—
354	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
355	C₂×C₁₉	#3018	1	1	yes	characteristic
356	C₂×C₁₉	#3020	1	1	yes	characteristic
357	C₂×#41	—	2	2	no	—
358	C₂×#41	D₄×C₁₉	1	2	yes	—
359	C₂×Q₁₆	—	2	1	no	—
360	C₂×SD₁₆	—	2	1	no	—
361	C₂²×C₈	—	2	1	no	—
362	C₂²×C₈	—	2	1	no	—
363	C₄⋊Q₈	—	2	1	no	—
364	C₄⋊Q₈	—	2	2	no	—
365	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
366	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
367	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
368	#127	D₄×C₁₉	1	1	yes	characteristic
369	#126	—	2	2	no	—
370	#126	—	2	2	no	—
371	#126	—	2	1	no	—
372	#125	—	2	2	no	—
373	#125	—	2	1	no	—
374	#125	—	2	1	no	—
375	#125	—	2	1	no	—
376	#125	—	2	1	no	—
377	#125	D₄×C₁₉	1	2	yes	—
378	#125	C₂³×C₁₉	1	2	yes	—
379	#125	C₂³×C₁₉	1	1	yes	characteristic
380	#124	C₂³×C₁₉	1	1	yes	characteristic
381	#124	C₂³×C₁₉	1	2	yes	—
382	#123	—	2	2	no	—
383	#123	—	2	2	no	—
384	#123	—	2	2	no	—
385	#123	—	2	2	no	—
386	#123	—	2	1	no	—
387	#123	—	2	2	no	—
388	#123	—	2	2	no	—
389	C₂²⋊Q₈	—	2	2	no	—
390	C₂²⋊Q₈	—	2	2	no	—
391	C₂²⋊Q₈	—	2	2	no	—
392	C₂²⋊Q₈	—	2	2	no	—
393	C₂²⋊Q₈	—	2	2	no	—
394	C₂²⋊Q₈	—	2	2	no	—
395	C₂²⋊Q₈	—	2	1	no	—
396	C₂²⋊Q₈	—	2	1	no	—
397	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
398	#121	—	2	2	no	—
399	#121	—	2	2	no	—
400	#121	—	2	1	no	—
401	#121	—	2	1	no	—
402	#121	—	2	2	no	—
403	#121	—	2	2	no	—
404	#121	—	2	1	no	—
405	#121	—	2	1	no	—
406	#121	D₄×C₁₉	1	1	yes	characteristic
407	C₄×Q₈	—	2	1	no	—
408	C₄×Q₈	—	2	1	no	—
409	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	—	2	1	no	—
415	C₄×D₄	—	2	1	no	—
416	C₄×D₄	—	2	1	no	—
417	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
418	#117	—	2	1	no	—
419	#117	—	2	1	no	—
420	#117	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	2	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
426	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
428	#107	—	2	1	no	—
429	#107	—	2	2	no	—
430	#106	—	2	1	no	—
431	#106	—	2	2	no	—
432	C₄⋊C₈	—	2	1	no	—
433	#103	—	2	2	no	—
434	#103	—	2	2	no	—
435	#103	—	2	1	no	—
436	#103	—	2	1	no	—
437	#103	—	2	1	no	—
438	#103	—	2	2	no	—
439	#103	—	2	2	no	—
440	#102	—	2	2	no	—
441	#102	—	2	2	no	—
442	#102	—	2	1	no	—
443	C₂²⋊C₈	—	2	1	no	—
444	#97	—	2	1	no	—
445	#97	—	2	1	no	—
446	#97	C₂³×C₁₉	1	2	yes	—
447	#97	C₂³×C₁₉	1	1	yes	characteristic
448	#97	C₂³×C₁₉	1	1	yes	characteristic
449	#97	C₂³×C₁₉	1	2	yes	—
450	C₁₉	#19045	1	1	yes	characteristic, direct product factor, Sylow
451	#41	—	4	4	no	—
452	#41	—	8	4	no	—
453	C₂×Q₈	—	2	2	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
457	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
465	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	Q₁₆	—	4	2	no	—
477	SD₁₆	—	4	2	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	4	2	no	—
483	C₂×C₈	—	4	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	4	1	no	—
505	C₄⋊C₄	—	4	1	no	—
506	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
507	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
508	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
509	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	1	no	—
518	C₂²⋊C₄	—	2	1	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	4	1	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	4	1	no	—
526	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
527	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
530	C₂³	—	2	2	no	—
531	C₂³	—	2	1	no	—
532	C₂³	C₁₉×#120	1	1	yes	characteristic
533	Q₈	—	4	1	no	—
534	Q₈	—	4	2	no	—
535	Q₈	—	4	1	no	—
536	Q₈	—	4	1	no	—
537	Q₈	—	4	2	no	—
538	Q₈	—	8	2	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	2	no	—
541	D₄	—	4	2	no	—
542	D₄	—	4	4	no	—
543	D₄	—	4	2	no	—
544	D₄	—	8	1	no	—
545	D₄	—	8	2	no	—
546	D₄	—	8	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	8	2	no	—
561	C₂×C₄	—	8	1	no	—
562	C₂×C₄	—	8	2	no	—
563	C₂×C₄	—	8	2	no	—
564	C₂×C₄	—	8	2	no	—
565	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
566	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
567	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
571	C₈	—	2	2	no	—
572	C₈	—	4	2	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	2	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	2	no	—
583	C₂²	C₁₉×#455	1	2	yes	—
584	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	2	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	8	1	no	—
598	C₄	—	8	1	no	—
599	C₂	—	2	2	no	—
600	C₂	—	8	2	no	—
601	C₂	—	8	1	no	—
602	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
603	C₂	C₁₉×#3018	1	1	yes	characteristic
604	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×#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×#3236	C₂	semidirect
3. C₁₉×#3181	C₂	semidirect
4. C₁₉×#3135	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1664	C₂	semidirect
7. C₁₉×#1662	C₂	semidirect
8. C₁₉×#1661	C₂	semidirect
9. C₁₉×#1532	C₂	semidirect
10. C₁₉×#1530	C₂	semidirect
11. C₂×C₁₉×#330	C₂	semidirect
227. #19045	C₁₉	direct (N × H)
274. #3236	C₂×C₁₉	semidirect
275. #3181	C₂×C₁₉	semidirect
276. #3135	C₂×C₁₉	semidirect
277. #1664	C₂×C₁₉	semidirect
278. #1664	C₂×C₁₉	semidirect
279. #1662	C₂×C₁₉	semidirect
280. #1661	C₂×C₁₉	semidirect
281. #1532	C₂×C₁₉	semidirect
282. #1530	C₂×C₁₉	semidirect
283. C₂×#330	C₂×C₁₉	semidirect
450. C₁₉	#19045	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×#3236	2
C₁₉×#3181	2
C₁₉×#3135	2
C₁₉×#1664	2
C₁₉×#1662	2
C₁₉×#1661	2
C₁₉×#1532	2
C₁₉×#1530	2
C₂×C₁₉×#330	2
#19045	19

Subgroups — C19×#19045 #18025004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19045 #18025004