Subgroups — C₁₉×#10565 #18016524

Order 4864.

532 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3187	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1996	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1964	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1893	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1289	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
11	C₁₉×#483	—	2	1	no	—
12	C₁₉×#481	—	2	1	no	—
13	C₁₉×#465	—	2	1	no	—
14	C₁₉×#465	—	2	1	no	—
15	C₁₉×#450	—	2	1	no	—
16	C₁₉×#448	—	2	1	no	—
17	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
18	C₂×C₁₉×#103	—	2	1	no	—
19	C₂×C₁₉×#102	—	2	1	no	—
20	C₂×C₁₉×#99	—	2	1	no	—
21	C₂×C₁₉×#99	—	2	1	no	—
22	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₁₉×#380	C₂²	1	1	yes	characteristic
24	C₁₉×#380	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#342	—	2	1	no	—
27	C₁₉×#342	—	2	1	no	—
28	C₁₉×#340	—	2	1	no	—
29	C₁₉×#340	—	2	1	no	—
30	C₁₉×#336	—	2	1	no	—
31	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×SD₁₆×C₁₉	—	2	1	no	—
36	C₂×SD₁₆×C₁₉	—	2	1	no	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₂²×C₈×C₁₉	—	4	2	no	—
41	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₁₉×C₂²⋊Q₈	—	2	1	no	—
44	C₁₉×C₂²⋊Q₈	—	2	1	no	—
45	C₁₉×C₂²⋊Q₈	—	2	1	no	—
46	C₁₉×C₂²⋊Q₈	—	2	1	no	—
47	C₁₉×#121	—	2	1	no	—
48	C₁₉×#121	—	2	1	no	—
49	C₁₉×#121	—	2	1	no	—
50	C₁₉×#121	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₉	—	2	1	no	—
63	C₁₉×#106	—	2	1	no	—
64	C₁₉×#106	—	2	1	no	—
65	C₁₉×C₄⋊C₈	—	4	2	no	—
66	C₁₉×#103	—	2	1	no	—
67	C₁₉×#103	—	2	1	no	—
68	C₁₉×#103	—	4	2	no	—
69	C₁₉×#102	—	2	1	no	—
70	C₁₉×#102	—	2	1	no	—
71	C₁₉×#102	—	4	2	no	—
72	C₁₉×#99	—	4	2	no	—
73	C₁₉×#99	—	4	2	no	—
74	C₁₉×C₂²⋊C₈	—	2	1	no	—
75	C₁₉×C₂²⋊C₈	—	2	1	no	—
76	C₁₉×#95	—	2	1	no	—
77	C₁₉×#95	—	2	1	no	—
78	C₁₉×#95	—	2	1	no	—
79	C₂⁴×C₁₉	—	2	1	no	—
80	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂×Q₈×C₁₉	—	2	1	no	—
82	C₂×Q₈×C₁₉	—	2	1	no	—
83	C₂×Q₈×C₁₉	—	4	1	no	—
84	C₂×Q₈×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	2	1	no	—
86	C₂×D₄×C₁₉	—	2	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	4	1	no	—
92	C₂×D₄×C₁₉	—	4	1	no	—
93	C₂×D₄×C₁₉	—	4	1	no	—
94	C₂×D₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
110	SD₁₆×C₁₉	—	8	1	no	—
111	SD₁₆×C₁₉	—	8	1	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	1	no	—
116	C₂×C₈×C₁₉	—	2	1	no	—
117	C₂×C₈×C₁₉	—	4	1	no	—
118	C₂×C₈×C₁₉	—	4	1	no	—
119	C₂×C₈×C₁₉	—	4	1	no	—
120	C₂×C₈×C₁₉	—	4	1	no	—
121	C₂×C₈×C₁₉	—	4	1	no	—
122	C₂×C₈×C₁₉	—	4	1	no	—
123	C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	4	1	no	—
128	C₄⋊C₄×C₁₉	—	4	1	no	—
129	C₄⋊C₄×C₁₉	—	4	1	no	—
130	C₄⋊C₄×C₁₉	—	4	1	no	—
131	C₄⋊C₄×C₁₉	—	4	1	no	—
132	C₄⋊C₄×C₁₉	—	4	1	no	—
133	C₂²⋊C₄×C₁₉	—	2	1	no	—
134	C₂²⋊C₄×C₁₉	—	2	1	no	—
135	C₂²⋊C₄×C₁₉	—	2	1	no	—
136	C₂²⋊C₄×C₁₉	—	4	1	no	—
137	C₂²⋊C₄×C₁₉	—	4	1	no	—
138	C₂²⋊C₄×C₁₉	—	4	1	no	—
139	C₂²⋊C₄×C₁₉	—	4	1	no	—
140	C₂²⋊C₄×C₁₉	—	4	1	no	—
141	C₂²⋊C₄×C₁₉	—	4	1	no	—
142	C₂²⋊C₄×C₁₉	—	4	1	no	—
143	C₂²⋊C₄×C₁₉	—	4	1	no	—
144	C₂²⋊C₄×C₁₉	SD₁₆	1	2	yes	complemented
145	C₄²×C₁₉	—	4	1	no	—
146	C₄²×C₁₉	—	4	1	no	—
147	#10565	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₁₉	—	4	1	no	—
149	C₂³×C₁₉	—	4	1	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	—	8	1	no	—
154	C₂³×C₁₉	—	8	1	no	—
155	C₂³×C₁₉	#121	1	1	yes	characteristic
156	C₂³×C₁₉	#121	1	1	yes	characteristic
157	C₂³×C₁₉	#121	1	1	yes	characteristic
158	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
159	C₂³×C₁₉	#135	1	1	yes	characteristic
160	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂³×C₁₉	#137	1	1	yes	characteristic
162	Q₈×C₁₉	—	4	2	no	—
163	Q₈×C₁₉	—	4	1	no	—
164	Q₈×C₁₉	—	4	1	no	—
165	D₄×C₁₉	—	4	2	no	—
166	D₄×C₁₉	—	4	1	no	—
167	D₄×C₁₉	—	4	1	no	—
168	D₄×C₁₉	—	8	1	no	—
169	D₄×C₁₉	—	8	1	no	—
170	D₄×C₁₉	—	8	1	no	—
171	D₄×C₁₉	—	8	1	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	8	1	no	—
193	C₂×C₄×C₁₉	—	8	1	no	—
194	C₂×C₄×C₁₉	—	8	1	no	—
195	C₂×C₄×C₁₉	—	8	1	no	—
196	C₂×C₄×C₁₉	—	8	1	no	—
197	C₂×C₄×C₁₉	—	8	1	no	—
198	C₂×C₄×C₁₉	—	8	1	no	—
199	C₂×C₄×C₁₉	—	8	1	no	—
200	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
201	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
204	C₈×C₁₉	—	4	2	no	—
205	C₈×C₁₉	—	4	1	no	—
206	C₈×C₁₉	—	4	1	no	—
207	#3187	C₂×C₁₉	1	1	yes	characteristic
208	#1996	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#1964	C₂×C₁₉	1	1	yes	characteristic
210	#1893	C₂×C₁₉	1	1	yes	characteristic
211	#1892	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#1850	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#1289	C₂×C₁₉	1	1	yes	characteristic, complemented
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	2	1	no	—
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	4	1	no	—
221	C₂²×C₁₉	—	4	1	no	—
222	C₂²×C₁₉	—	4	1	no	—
223	C₂²×C₁₉	—	4	1	no	—
224	C₂²×C₁₉	—	8	1	no	—
225	C₂²×C₁₉	—	8	1	no	—
226	C₂²×C₁₉	—	8	1	no	—
227	C₂²×C₁₉	—	16	1	no	—
228	C₂²×C₁₉	—	16	1	no	—
229	C₂²×C₁₉	#394	1	1	yes	characteristic
230	C₂²×C₁₉	#460	1	1	yes	characteristic
231	C₂²×C₁₉	#461	1	1	yes	characteristic
232	C₂²×C₁₉	#463	1	1	yes	characteristic
233	C₂²×C₁₉	#464	1	1	yes	characteristic
234	C₂²×C₁₉	#465	1	1	yes	characteristic
235	C₂²×C₁₉	#468	1	1	yes	characteristic
236	C₄×C₁₉	—	2	1	no	—
237	C₄×C₁₉	—	2	1	no	—
238	C₄×C₁₉	—	2	1	no	—
239	C₄×C₁₉	—	4	2	no	—
240	C₄×C₁₉	—	8	1	no	—
241	C₄×C₁₉	—	8	1	no	—
242	C₄×C₁₉	—	8	1	no	—
243	C₄×C₁₉	—	8	1	no	—
244	C₄×C₁₉	—	16	1	no	—
245	C₄×C₁₉	—	16	1	no	—
246	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
247	C₄×C₁₉	#458	1	1	yes	characteristic
248	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
249	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
251	#483	—	2	1	no	—
252	#481	—	2	1	no	—
253	#465	—	2	1	no	—
254	#465	—	2	1	no	—
255	#450	—	2	1	no	—
256	#448	—	2	1	no	—
257	C₂×C₄⋊C₈	—	2	1	no	—
258	C₂×#103	—	2	1	no	—
259	C₂×#102	—	2	1	no	—
260	C₂×#99	—	2	1	no	—
261	C₂×#99	—	2	1	no	—
262	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
263	#380	C₂²×C₁₉	1	1	yes	characteristic
264	#380	C₂²×C₁₉	1	1	yes	characteristic
265	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
266	#342	—	2	1	no	—
267	#342	—	2	1	no	—
268	#340	—	2	1	no	—
269	#340	—	2	1	no	—
270	#336	—	2	1	no	—
271	C₂×C₁₉	—	2	1	no	—
272	C₂×C₁₉	—	2	1	no	—
273	C₂×C₁₉	—	2	1	no	—
274	C₂×C₁₉	—	2	1	no	—
275	C₂×C₁₉	—	2	1	no	—
276	C₂×C₁₉	—	2	1	no	—
277	C₂×C₁₉	—	16	1	no	—
278	C₂×C₁₉	#2044	1	1	yes	characteristic
279	C₂×C₁₉	#2053	1	1	yes	characteristic
280	C₂×C₁₉	#2055	1	1	yes	characteristic
281	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
282	C₂²×D₄	—	2	1	no	—
283	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
285	C₂×SD₁₆	—	2	1	no	—
286	C₂×SD₁₆	—	2	1	no	—
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	4	2	no	—
291	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
292	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
293	C₂²⋊Q₈	—	2	1	no	—
294	C₂²⋊Q₈	—	2	1	no	—
295	C₂²⋊Q₈	—	2	1	no	—
296	C₂²⋊Q₈	—	2	1	no	—
297	#121	—	2	1	no	—
298	#121	—	2	1	no	—
299	#121	—	2	1	no	—
300	#121	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
305	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
312	C₂×C₄²	—	2	1	no	—
313	#106	—	2	1	no	—
314	#106	—	2	1	no	—
315	C₄⋊C₈	—	4	2	no	—
316	#103	—	2	1	no	—
317	#103	—	2	1	no	—
318	#103	—	4	2	no	—
319	#102	—	2	1	no	—
320	#102	—	2	1	no	—
321	#102	—	4	2	no	—
322	#99	—	4	2	no	—
323	#99	—	4	2	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	2	1	no	—
326	#95	—	2	1	no	—
327	#95	—	2	1	no	—
328	#95	—	2	1	no	—
329	C₁₉	#10565	1	1	yes	characteristic, direct product factor, Sylow
330	C₂⁴	—	2	1	no	—
331	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	4	1	no	—
335	C₂×Q₈	—	4	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	—	4	1	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
358	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
360	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
361	SD₁₆	—	8	1	no	—
362	SD₁₆	—	8	1	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	1	no	—
371	C₂×C₈	—	4	1	no	—
372	C₂×C₈	—	4	1	no	—
373	C₂×C₈	—	4	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	4	1	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₂²⋊C₄	—	4	1	no	—
388	C₂²⋊C₄	—	4	1	no	—
389	C₂²⋊C₄	—	4	1	no	—
390	C₂²⋊C₄	—	4	1	no	—
391	C₂²⋊C₄	—	4	1	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₂²⋊C₄	SD₁₆×C₁₉	1	2	yes	complemented
396	C₄²	—	4	1	no	—
397	C₄²	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	8	1	no	—
404	C₂³	—	8	1	no	—
405	C₂³	C₁₉×#121	1	1	yes	characteristic
406	C₂³	C₁₉×#121	1	1	yes	characteristic
407	C₂³	C₁₉×#121	1	1	yes	characteristic
408	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
409	C₂³	C₁₉×#135	1	1	yes	characteristic
410	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
411	C₂³	C₁₉×#137	1	1	yes	characteristic
412	Q₈	—	4	2	no	—
413	Q₈	—	4	1	no	—
414	Q₈	—	4	1	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	1	no	—
417	D₄	—	4	1	no	—
418	D₄	—	8	1	no	—
419	D₄	—	8	1	no	—
420	D₄	—	8	1	no	—
421	D₄	—	8	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	8	1	no	—
443	C₂×C₄	—	8	1	no	—
444	C₂×C₄	—	8	1	no	—
445	C₂×C₄	—	8	1	no	—
446	C₂×C₄	—	8	1	no	—
447	C₂×C₄	—	8	1	no	—
448	C₂×C₄	—	8	1	no	—
449	C₂×C₄	—	8	1	no	—
450	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
451	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
452	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
453	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
454	C₈	—	4	2	no	—
455	C₈	—	4	1	no	—
456	C₈	—	4	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	8	1	no	—
468	C₂²	—	8	1	no	—
469	C₂²	—	8	1	no	—
470	C₂²	—	16	1	no	—
471	C₂²	—	16	1	no	—
472	C₂²	C₁₉×#394	1	1	yes	characteristic
473	C₂²	C₁₉×#460	1	1	yes	characteristic
474	C₂²	C₁₉×#461	1	1	yes	characteristic
475	C₂²	C₁₉×#463	1	1	yes	characteristic
476	C₂²	C₁₉×#464	1	1	yes	characteristic
477	C₂²	C₁₉×#465	1	1	yes	characteristic
478	C₂²	C₁₉×#468	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	8	1	no	—
484	C₄	—	8	1	no	—
485	C₄	—	8	1	no	—
486	C₄	—	8	1	no	—
487	C₄	—	16	1	no	—
488	C₄	—	16	1	no	—
489	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
490	C₄	C₁₉×#458	1	1	yes	characteristic
491	C₂	—	2	1	no	—
492	C₂	—	2	1	no	—
493	C₂	—	2	1	no	—
494	C₂	—	2	1	no	—
495	C₂	—	2	1	no	—
496	C₂	—	2	1	no	—
497	C₂	—	16	1	no	—
498	C₂	C₁₉×#2044	1	1	yes	characteristic
499	C₂	C₁₉×#2053	1	1	yes	characteristic
500	C₂	C₁₉×#2055	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#394
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1996	C₂	semidirect
5. C₁₉×#1892	C₂	semidirect
6. C₁₉×#1850	C₂	semidirect
7. C₁₉×#1289	C₂	semidirect
144. C₂²⋊C₄×C₁₉	SD₁₆	semidirect
147. #10565	C₁₉	direct (N × H)
208. #1996	C₂×C₁₉	semidirect
211. #1892	C₂×C₁₉	semidirect
212. #1850	C₂×C₁₉	semidirect
213. #1289	C₂×C₁₉	semidirect
329. C₁₉	#10565	direct (N × H)
395. C₂²⋊C₄	SD₁₆×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3187	2
C₁₉×#1996	2
C₁₉×#1964	2
C₁₉×#1893	2
C₁₉×#1892	2
C₁₉×#1850	2
C₁₉×#1289	2
#10565	19

Subgroups — C19×#10565 #18016524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10565 #18016524