Subgroups — C₁₉×#19874 #18025833

Order 4864.

608 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3400	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3396	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1721	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1688	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1682	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1668	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1666	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1640	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1626	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1620	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1620	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1579	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#559	C₂²	1	1	yes	characteristic
17	C₁₉×#559	C₂²	1	1	yes	characteristic
18	C₁₉×#559	C₂²	1	1	yes	characteristic
19	C₁₉×#557	C₂²	1	1	yes	characteristic
20	C₁₉×#497	—	2	1	no	—
21	C₁₉×#495	—	2	1	no	—
22	C₁₉×#495	—	2	1	no	—
23	C₁₉×#493	C₂²	1	1	yes	characteristic
24	C₁₉×#493	C₂²	1	1	yes	characteristic
25	C₁₉×#493	C₂²	1	1	yes	characteristic
26	C₁₉×#492	C₂²	1	1	yes	characteristic
27	C₁₉×#488	—	2	1	no	—
28	C₁₉×#486	C₂²	1	1	yes	characteristic
29	C₁₉×#486	C₂²	1	1	yes	characteristic
30	C₁₉×#478	—	2	1	no	—
31	C₁₉×#475	C₂²	1	1	yes	characteristic
32	C₁₉×#464	—	2	1	no	—
33	C₁₉×#464	—	2	1	no	—
34	C₁₉×#463	—	2	1	no	—
35	C₁₉×#463	—	2	1	no	—
36	C₁₉×#463	—	2	1	no	—
37	C₁₉×#463	—	2	1	no	—
38	C₁₉×#462	C₂²	1	1	yes	characteristic
39	C₁₉×#461	—	2	1	no	—
40	C₁₉×#460	C₂²	1	1	yes	characteristic
41	C₁₉×#460	C₂²	1	1	yes	characteristic
42	C₁₉×#460	C₂²	1	1	yes	characteristic
43	C₁₉×#460	C₂²	1	1	yes	characteristic
44	C₁₉×#460	C₂²	1	1	yes	characteristic
45	C₁₉×#460	C₂²	1	1	yes	characteristic
46	C₁₉×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
50	C₁₉×#440	—	2	1	no	—
51	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
52	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
53	C₄×SD₁₆×C₁₉	—	2	1	no	—
54	C₄×D₈×C₁₉	—	2	1	no	—
55	C₄×D₈×C₁₉	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#332	C₂²	1	1	yes	characteristic
59	C₁₉×#331	C₂²	1	1	yes	characteristic
60	C₁₉×#331	C₂²	1	1	yes	characteristic
61	C₁₉×#331	C₂²	1	1	yes	characteristic
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₉×#322	C₂²	1	1	yes	characteristic
67	C₂×Q₁₆×C₁₉	—	2	1	no	—
68	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
69	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
70	C₂×SD₁₆×C₁₉	—	2	1	no	—
71	C₂×SD₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×SD₁₆×C₁₉	—	2	1	no	—
75	C₂×SD₁₆×C₁₉	—	2	1	no	—
76	C₂×SD₁₆×C₁₉	—	2	1	no	—
77	C₂×SD₁₆×C₁₉	—	2	1	no	—
78	C₂×D₈×C₁₉	—	2	1	no	—
79	C₂×D₈×C₁₉	—	2	1	no	—
80	C₂×D₈×C₁₉	—	2	1	no	—
81	C₂×D₈×C₁₉	—	2	1	no	—
82	C₂×D₈×C₁₉	—	4	1	no	—
83	C₁₉×C₄⋊Q₈	—	2	1	no	—
84	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₉×#127	C₂³	1	1	yes	characteristic
86	C₁₉×#127	C₂³	1	1	yes	characteristic
87	C₁₉×#127	C₂³	1	1	yes	characteristic
88	C₁₉×#125	—	2	1	no	—
89	C₁₉×#125	—	4	1	no	—
90	C₁₉×#124	—	2	1	no	—
91	C₁₉×#124	—	2	1	no	—
92	C₁₉×#124	—	2	1	no	—
93	C₁₉×#124	—	2	1	no	—
94	C₁₉×#124	—	2	1	no	—
95	C₁₉×#124	—	2	1	no	—
96	C₁₉×#123	—	4	1	no	—
97	C₁₉×#123	—	4	1	no	—
98	C₁₉×#123	—	4	1	no	—
99	C₄×Q₈×C₁₉	—	2	1	no	—
100	C₄×Q₈×C₁₉	—	2	1	no	—
101	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
102	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
103	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
104	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₁₉	—	2	1	no	—
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	—	2	1	no	—
108	C₄×D₄×C₁₉	—	2	1	no	—
109	C₄×D₄×C₁₉	—	2	1	no	—
110	C₄×D₄×C₁₉	—	2	1	no	—
111	C₁₉×#107	D₄	1	1	yes	characteristic
112	C₁₉×#107	D₄	1	1	yes	characteristic
113	C₁₉×#106	—	2	1	no	—
114	C₁₉×C₄⋊C₈	—	2	1	no	—
115	C₁₉×C₄⋊C₈	—	2	1	no	—
116	C₁₉×C₄⋊C₈	—	2	1	no	—
117	C₁₉×C₄⋊C₈	—	2	1	no	—
118	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₉×#103	—	2	1	no	—
123	C₁₉×#103	—	2	1	no	—
124	C₁₉×#103	D₄	1	1	yes	characteristic
125	C₁₉×#103	D₄	1	1	yes	characteristic
126	C₁₉×#103	D₄	1	1	yes	characteristic
127	C₁₉×#103	D₄	1	1	yes	characteristic
128	C₁₉×#102	—	2	1	no	—
129	C₁₉×#102	—	2	1	no	—
130	C₁₉×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	2	1	no	—
134	C₁₉×#102	—	2	1	no	—
135	C₁₉×#102	—	2	1	no	—
136	C₁₉×#102	—	4	1	no	—
137	C₁₉×#97	—	2	1	no	—
138	C₄×C₈×C₁₉	—	2	1	no	—
139	C₄×C₈×C₁₉	—	2	1	no	—
140	C₄×C₈×C₁₉	—	2	1	no	—
141	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₂×Q₈×C₁₉	—	2	1	no	—
145	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
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	C₂²×C₄×C₁₉	—	4	1	no	—
159	C₂²×C₄×C₁₉	—	4	1	no	—
160	C₂²×C₄×C₁₉	—	4	1	no	—
161	Q₁₆×C₁₉	—	2	2	no	—
162	Q₁₆×C₁₉	—	4	1	no	—
163	Q₁₆×C₁₉	—	8	1	no	—
164	SD₁₆×C₁₉	—	4	2	no	—
165	SD₁₆×C₁₉	—	4	2	no	—
166	SD₁₆×C₁₉	—	8	1	no	—
167	SD₁₆×C₁₉	—	8	1	no	—
168	SD₁₆×C₁₉	—	8	1	no	—
169	SD₁₆×C₁₉	—	8	1	no	—
170	SD₁₆×C₁₉	—	8	1	no	—
171	SD₁₆×C₁₉	—	8	1	no	—
172	D₈×C₁₉	—	4	2	no	—
173	D₈×C₁₉	—	4	2	no	—
174	D₈×C₁₉	—	8	1	no	—
175	D₈×C₁₉	—	8	1	no	—
176	D₈×C₁₉	—	8	2	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
178	C₂×C₈×C₁₉	—	2	1	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	4	1	no	—
193	C₄⋊C₄×C₁₉	—	4	1	no	—
194	C₄⋊C₄×C₁₉	—	4	1	no	—
195	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₂²⋊C₄×C₁₉	—	4	1	no	—
200	C₂²⋊C₄×C₁₉	—	4	1	no	—
201	C₂²⋊C₄×C₁₉	—	4	1	no	—
202	C₂²⋊C₄×C₁₉	—	4	1	no	—
203	C₂²⋊C₄×C₁₉	—	4	1	no	—
204	C₂²⋊C₄×C₁₉	—	4	1	no	—
205	C₂²⋊C₄×C₁₉	—	4	1	no	—
206	C₂²⋊C₄×C₁₉	—	4	1	no	—
207	C₂²⋊C₄×C₁₉	—	4	1	no	—
208	C₄²×C₁₉	—	2	1	no	—
209	C₄²×C₁₉	—	2	1	no	—
210	C₄²×C₁₉	—	2	1	no	—
211	C₄²×C₁₉	—	2	1	no	—
212	C₄²×C₁₉	—	4	1	no	—
213	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
214	#19874	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂³×C₁₉	—	4	1	no	—
216	C₂³×C₁₉	—	4	1	no	—
217	C₂³×C₁₉	—	4	1	no	—
218	Q₈×C₁₉	—	2	1	no	—
219	Q₈×C₁₉	—	2	1	no	—
220	Q₈×C₁₉	—	2	1	no	—
221	Q₈×C₁₉	—	2	1	no	—
222	Q₈×C₁₉	—	2	1	no	—
223	Q₈×C₁₉	—	2	1	no	—
224	Q₈×C₁₉	—	2	1	no	—
225	Q₈×C₁₉	—	2	1	no	—
226	Q₈×C₁₉	—	4	1	no	—
227	Q₈×C₁₉	—	4	1	no	—
228	D₄×C₁₉	—	4	1	no	—
229	D₄×C₁₉	—	4	1	no	—
230	D₄×C₁₉	—	4	1	no	—
231	D₄×C₁₉	—	4	1	no	—
232	D₄×C₁₉	—	4	1	no	—
233	D₄×C₁₉	—	4	1	no	—
234	D₄×C₁₉	—	4	1	no	—
235	D₄×C₁₉	—	4	1	no	—
236	D₄×C₁₉	—	4	1	no	—
237	D₄×C₁₉	—	4	1	no	—
238	D₄×C₁₉	—	4	1	no	—
239	D₄×C₁₉	—	4	1	no	—
240	D₄×C₁₉	—	8	1	no	—
241	D₄×C₁₉	—	8	1	no	—
242	D₄×C₁₉	—	8	1	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	16	1	no	—
253	C₂×C₄×C₁₉	—	16	1	no	—
254	C₂×C₄×C₁₉	—	16	1	no	—
255	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
258	C₈×C₁₉	—	2	1	no	—
259	C₈×C₁₉	—	2	1	no	—
260	C₈×C₁₉	—	2	1	no	—
261	C₈×C₁₉	—	4	1	no	—
262	C₈×C₁₉	—	4	1	no	—
263	C₈×C₁₉	—	4	1	no	—
264	C₈×C₁₉	—	4	1	no	—
265	C₈×C₁₉	—	4	1	no	—
266	C₈×C₁₉	#135	1	2	yes	—
267	#3400	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#3396	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#3396	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#3365	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#1721	C₂×C₁₉	1	1	yes	characteristic
272	#1688	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1682	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1668	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1666	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1640	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1626	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1620	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1620	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1584	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1579	C₂×C₁₉	1	1	yes	characteristic, complemented
282	C₂²×C₁₉	—	8	1	no	—
283	C₂²×C₁₉	—	8	1	no	—
284	C₂²×C₁₉	—	8	1	no	—
285	C₂²×C₁₉	—	8	1	no	—
286	C₂²×C₁₉	—	8	1	no	—
287	C₂²×C₁₉	—	8	1	no	—
288	C₂²×C₁₉	—	8	1	no	—
289	C₂²×C₁₉	—	8	1	no	—
290	C₂²×C₁₉	—	8	1	no	—
291	C₂²×C₁₉	D₄²	1	1	yes	characteristic
292	C₄×C₁₉	—	2	1	no	—
293	C₄×C₁₉	—	4	1	no	—
294	C₄×C₁₉	—	4	1	no	—
295	C₄×C₁₉	—	4	1	no	—
296	C₄×C₁₉	—	4	1	no	—
297	C₄×C₁₉	—	4	1	no	—
298	C₄×C₁₉	—	4	1	no	—
299	C₄×C₁₉	—	4	1	no	—
300	C₄×C₁₉	—	4	1	no	—
301	C₄×C₁₉	—	8	1	no	—
302	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
303	C₄×C₁₉	#575	1	1	yes	characteristic
304	C₄×C₁₉	#576	1	1	yes	characteristic
305	C₄×C₁₉	#577	1	1	yes	characteristic
306	#559	C₂²×C₁₉	1	1	yes	characteristic
307	#559	C₂²×C₁₉	1	1	yes	characteristic
308	#559	C₂²×C₁₉	1	1	yes	characteristic
309	#557	C₂²×C₁₉	1	1	yes	characteristic
310	#497	—	2	1	no	—
311	#495	—	2	1	no	—
312	#495	—	2	1	no	—
313	#493	C₂²×C₁₉	1	1	yes	characteristic
314	#493	C₂²×C₁₉	1	1	yes	characteristic
315	#493	C₂²×C₁₉	1	1	yes	characteristic
316	#492	C₂²×C₁₉	1	1	yes	characteristic
317	#488	—	2	1	no	—
318	#486	C₂²×C₁₉	1	1	yes	characteristic
319	#486	C₂²×C₁₉	1	1	yes	characteristic
320	#478	—	2	1	no	—
321	#475	C₂²×C₁₉	1	1	yes	characteristic
322	#464	—	2	1	no	—
323	#464	—	2	1	no	—
324	#463	—	2	1	no	—
325	#463	—	2	1	no	—
326	#463	—	2	1	no	—
327	#463	—	2	1	no	—
328	#462	C₂²×C₁₉	1	1	yes	characteristic
329	#461	—	2	1	no	—
330	#460	C₂²×C₁₉	1	1	yes	characteristic
331	#460	C₂²×C₁₉	1	1	yes	characteristic
332	#460	C₂²×C₁₉	1	1	yes	characteristic
333	#460	C₂²×C₁₉	1	1	yes	characteristic
334	#460	C₂²×C₁₉	1	1	yes	characteristic
335	#460	C₂²×C₁₉	1	1	yes	characteristic
336	#446	C₂²×C₁₉	1	1	yes	characteristic
337	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
338	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
339	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
340	#440	—	2	1	no	—
341	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
342	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
343	C₄×SD₁₆	—	2	1	no	—
344	C₄×D₈	—	2	1	no	—
345	C₄×D₈	—	2	1	no	—
346	#335	C₂²×C₁₉	1	1	yes	characteristic
347	#334	C₂²×C₁₉	1	1	yes	characteristic
348	#332	C₂²×C₁₉	1	1	yes	characteristic
349	#331	C₂²×C₁₉	1	1	yes	characteristic
350	#331	C₂²×C₁₉	1	1	yes	characteristic
351	#331	C₂²×C₁₉	1	1	yes	characteristic
352	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
353	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
354	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
355	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
356	#322	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×C₁₉	—	16	1	no	—
358	C₂×C₁₉	—	16	1	no	—
359	C₂×C₁₉	—	16	1	no	—
360	C₂×C₁₉	#3271	1	1	yes	characteristic
361	C₂×C₁₉	#3287	1	1	yes	characteristic
362	C₂×C₁₉	#3288	1	1	yes	characteristic
363	C₂×Q₁₆	—	2	1	no	—
364	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
365	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
366	C₂×SD₁₆	—	2	1	no	—
367	C₂×SD₁₆	—	2	1	no	—
368	C₂×SD₁₆	—	2	1	no	—
369	C₂×SD₁₆	—	2	1	no	—
370	C₂×SD₁₆	—	2	1	no	—
371	C₂×SD₁₆	—	2	1	no	—
372	C₂×SD₁₆	—	2	1	no	—
373	C₂×SD₁₆	—	2	1	no	—
374	C₂×D₈	—	2	1	no	—
375	C₂×D₈	—	2	1	no	—
376	C₂×D₈	—	2	1	no	—
377	C₂×D₈	—	2	1	no	—
378	C₂×D₈	—	4	1	no	—
379	C₄⋊Q₈	—	2	1	no	—
380	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
381	#127	C₂³×C₁₉	1	1	yes	characteristic
382	#127	C₂³×C₁₉	1	1	yes	characteristic
383	#127	C₂³×C₁₉	1	1	yes	characteristic
384	#125	—	2	1	no	—
385	#125	—	4	1	no	—
386	#124	—	2	1	no	—
387	#124	—	2	1	no	—
388	#124	—	2	1	no	—
389	#124	—	2	1	no	—
390	#124	—	2	1	no	—
391	#124	—	2	1	no	—
392	#123	—	4	1	no	—
393	#123	—	4	1	no	—
394	#123	—	4	1	no	—
395	C₄×Q₈	—	2	1	no	—
396	C₄×Q₈	—	2	1	no	—
397	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
398	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
399	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
400	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	#107	D₄×C₁₉	1	1	yes	characteristic
408	#107	D₄×C₁₉	1	1	yes	characteristic
409	#106	—	2	1	no	—
410	C₄⋊C₈	—	2	1	no	—
411	C₄⋊C₈	—	2	1	no	—
412	C₄⋊C₈	—	2	1	no	—
413	C₄⋊C₈	—	2	1	no	—
414	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
415	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
416	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
418	#103	—	2	1	no	—
419	#103	—	2	1	no	—
420	#103	D₄×C₁₉	1	1	yes	characteristic
421	#103	D₄×C₁₉	1	1	yes	characteristic
422	#103	D₄×C₁₉	1	1	yes	characteristic
423	#103	D₄×C₁₉	1	1	yes	characteristic
424	#102	—	2	1	no	—
425	#102	—	2	1	no	—
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	—	2	1	no	—
429	#102	—	2	1	no	—
430	#102	—	2	1	no	—
431	#102	—	2	1	no	—
432	#102	—	4	1	no	—
433	#97	—	2	1	no	—
434	C₄×C₈	—	2	1	no	—
435	C₄×C₈	—	2	1	no	—
436	C₄×C₈	—	2	1	no	—
437	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
438	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
439	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
440	C₁₉	#19874	1	1	yes	characteristic, direct product factor, Sylow
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
445	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	Q₁₆	—	2	2	no	—
459	Q₁₆	—	4	1	no	—
460	Q₁₆	—	8	1	no	—
461	SD₁₆	—	4	2	no	—
462	SD₁₆	—	4	2	no	—
463	SD₁₆	—	8	1	no	—
464	SD₁₆	—	8	1	no	—
465	SD₁₆	—	8	1	no	—
466	SD₁₆	—	8	1	no	—
467	SD₁₆	—	8	1	no	—
468	SD₁₆	—	8	1	no	—
469	D₈	—	4	2	no	—
470	D₈	—	4	2	no	—
471	D₈	—	8	1	no	—
472	D₈	—	8	1	no	—
473	D₈	—	8	2	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	—	4	1	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₂²⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	—	4	1	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₂²⋊C₄	—	4	1	no	—
503	C₂²⋊C₄	—	4	1	no	—
504	C₂²⋊C₄	—	4	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	4	1	no	—
510	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
511	C₂³	—	4	1	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	4	1	no	—
514	Q₈	—	2	1	no	—
515	Q₈	—	2	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	2	1	no	—
518	Q₈	—	2	1	no	—
519	Q₈	—	2	1	no	—
520	Q₈	—	2	1	no	—
521	Q₈	—	2	1	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	4	1	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	1	no	—
531	D₄	—	4	1	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	1	no	—
534	D₄	—	4	1	no	—
535	D₄	—	4	1	no	—
536	D₄	—	8	1	no	—
537	D₄	—	8	1	no	—
538	D₄	—	8	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	16	1	no	—
549	C₂×C₄	—	16	1	no	—
550	C₂×C₄	—	16	1	no	—
551	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
553	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	C₁₉×#135	1	2	yes	—
563	C₂²	—	8	1	no	—
564	C₂²	—	8	1	no	—
565	C₂²	—	8	1	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	8	1	no	—
569	C₂²	—	8	1	no	—
570	C₂²	—	8	1	no	—
571	C₂²	—	8	1	no	—
572	C₂²	D₄²×C₁₉	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	8	1	no	—
583	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
584	C₄	C₁₉×#575	1	1	yes	characteristic
585	C₄	C₁₉×#576	1	1	yes	characteristic
586	C₄	C₁₉×#577	1	1	yes	characteristic
587	C₂	—	16	1	no	—
588	C₂	—	16	1	no	—
589	C₂	—	16	1	no	—
590	C₂	C₁₉×#3271	1	1	yes	characteristic
591	C₂	C₁₉×#3287	1	1	yes	characteristic
592	C₂	C₁₉×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#1721	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₉×#3400	C₂	semidirect
2. C₁₉×#3396	C₂	semidirect
3. C₁₉×#3396	C₂	semidirect
4. C₁₉×#3365	C₂	semidirect
6. C₁₉×#1688	C₂	semidirect
7. C₁₉×#1682	C₂	semidirect
8. C₁₉×#1668	C₂	semidirect
9. C₁₉×#1666	C₂	semidirect
10. C₁₉×#1640	C₂	semidirect
11. C₁₉×#1626	C₂	semidirect
12. C₁₉×#1620	C₂	semidirect
13. C₁₉×#1620	C₂	semidirect
14. C₁₉×#1584	C₂	semidirect
15. C₁₉×#1579	C₂	semidirect
214. #19874	C₁₉	direct (N × H)
267. #3400	C₂×C₁₉	semidirect
268. #3396	C₂×C₁₉	semidirect
269. #3396	C₂×C₁₉	semidirect
270. #3365	C₂×C₁₉	semidirect
272. #1688	C₂×C₁₉	semidirect
273. #1682	C₂×C₁₉	semidirect
274. #1668	C₂×C₁₉	semidirect
275. #1666	C₂×C₁₉	semidirect
276. #1640	C₂×C₁₉	semidirect
277. #1626	C₂×C₁₉	semidirect
278. #1620	C₂×C₁₉	semidirect
279. #1620	C₂×C₁₉	semidirect
280. #1584	C₂×C₁₉	semidirect
281. #1579	C₂×C₁₉	semidirect
440. C₁₉	#19874	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×#3400	2
C₁₉×#3396	2
C₁₉×#3365	2
C₁₉×#1721	2
C₁₉×#1688	2
C₁₉×#1682	2
C₁₉×#1668	2
C₁₉×#1666	2
C₁₉×#1640	2
C₁₉×#1626	2
C₁₉×#1620	2
C₁₉×#1584	2
C₁₉×#1579	2
#19874	19

Subgroups — C19×#19874 #18025833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19874 #18025833