Subgroups — C₁₉×#9996 #18015955

Order 4864.

686 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3100	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3036	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2535	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1517	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1486	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1478	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1286	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
9	C₁₉×#532	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#121	—	2	1	no	—
11	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#480	—	2	1	no	—
14	C₁₉×#474	—	2	1	no	—
15	C₁₉×#463	—	2	2	no	—
16	C₁₉×#461	—	2	1	no	—
17	C₁₉×#459	—	2	1	no	—
18	C₁₉×#459	—	2	1	no	—
19	C₁₉×#447	—	2	1	no	—
20	C₄×D₈×C₁₉	—	2	2	no	—
21	C₁₉×#431	C₂²	1	1	yes	characteristic
22	C₁₉×#431	C₂²	1	1	yes	characteristic
23	C₁₉×#423	C₂²	1	1	yes	characteristic
24	C₁₉×#417	—	2	1	no	—
25	C₁₉×#397	—	2	1	no	—
26	C₁₉×#392	—	2	1	no	—
27	C₁₉×#386	—	2	2	no	—
28	C₁₉×#382	C₂²	1	1	yes	characteristic
29	C₁₉×#380	—	2	1	no	—
30	C₁₉×#327	—	2	2	no	—
31	C₁₉×D₄⋊C₈	—	2	2	no	—
32	C₁₉×D₄⋊C₈	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	2	no	—
35	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	—	2	1	no	—
38	C₂³×C₄×C₁₉	—	2	1	no	—
39	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
40	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
41	C₂×SD₁₆×C₁₉	—	2	2	no	—
42	C₂×D₈×C₁₉	—	2	2	no	—
43	C₂×D₈×C₁₉	—	2	2	no	—
44	C₂×M₁₆×C₁₉	—	2	1	no	—
45	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
46	C₁₉×#127	D₄	1	1	yes	characteristic, complemented
47	C₁₉×#124	—	2	1	no	—
48	C₁₉×#121	—	2	1	no	—
49	C₁₉×#121	—	2	1	no	—
50	C₁₉×#121	—	4	2	no	—
51	C₁₉×#121	—	4	2	no	—
52	C₄×D₄×C₁₉	—	2	1	no	—
53	C₄×D₄×C₁₉	—	2	1	no	—
54	C₄×D₄×C₁₉	—	2	1	no	—
55	C₄×D₄×C₁₉	—	2	1	no	—
56	C₄×D₄×C₁₉	—	2	1	no	—
57	C₄×D₄×C₁₉	—	2	1	no	—
58	C₄×D₄×C₁₉	—	2	1	no	—
59	C₄×D₄×C₁₉	—	2	1	no	—
60	C₄×D₄×C₁₉	—	2	1	no	—
61	C₄×D₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×#107	—	2	2	no	—
71	C₁₉×C₄⋊C₈	—	2	1	no	—
72	C₁₉×C₄⋊C₈	—	2	1	no	—
73	C₁₉×C₄⋊C₈	—	2	1	no	—
74	C₁₉×C₄⋊C₈	D₄	1	2	yes	complemented
75	C₁₉×#103	—	2	2	no	—
76	C₁₉×#102	—	2	2	no	—
77	C₁₉×#102	—	2	2	no	—
78	C₁₉×#102	—	2	2	no	—
79	C₁₉×C₂²⋊C₈	—	2	1	no	—
80	C₁₉×C₂²⋊C₈	—	2	1	no	—
81	C₄×C₈×C₁₉	—	2	1	no	—
82	C₄×C₈×C₁₉	D₄	1	2	yes	complemented
83	C₁₉×#95	—	2	2	no	—
84	C₁₉×#95	—	2	1	no	—
85	C₁₉×#95	D₄	1	2	yes	—
86	C₂⁴×C₁₉	—	2	1	no	—
87	C₂⁴×C₁₉	—	2	1	no	—
88	#41×C₁₉	—	4	1	no	—
89	#41×C₁₉	—	4	1	no	—
90	#41×C₁₉	—	4	1	no	—
91	#41×C₁₉	—	4	1	no	—
92	C₂×Q₈×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	—	2	1	no	—
96	C₂×D₄×C₁₉	—	2	1	no	—
97	C₂×D₄×C₁₉	—	2	1	no	—
98	C₂×D₄×C₁₉	—	2	1	no	—
99	C₂×D₄×C₁₉	—	2	1	no	—
100	C₂×D₄×C₁₉	—	2	1	no	—
101	C₂×D₄×C₁₉	—	2	1	no	—
102	C₂×D₄×C₁₉	—	2	1	no	—
103	C₂×D₄×C₁₉	—	4	2	no	—
104	C₂×D₄×C₁₉	—	4	4	no	—
105	C₂×D₄×C₁₉	—	4	4	no	—
106	C₂×D₄×C₁₉	—	4	1	no	—
107	C₂×D₄×C₁₉	—	8	2	no	—
108	C₂×D₄×C₁₉	D₈	1	2	yes	complemented
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	4	1	no	—
113	C₂²×C₄×C₁₉	—	4	1	no	—
114	C₂²×C₄×C₁₉	—	4	1	no	—
115	C₂²×C₄×C₁₉	—	4	1	no	—
116	C₂²×C₄×C₁₉	—	4	1	no	—
117	C₂²×C₄×C₁₉	—	4	1	no	—
118	C₂²×C₄×C₁₉	—	4	1	no	—
119	C₂²×C₄×C₁₉	—	4	1	no	—
120	C₂²×C₄×C₁₉	—	4	1	no	—
121	C₂²×C₄×C₁₉	—	8	2	no	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	SD₁₆×C₁₉	—	4	4	no	—
126	D₈×C₁₉	—	4	4	no	—
127	D₈×C₁₉	—	4	4	no	—
128	M₁₆×C₁₉	—	4	1	no	—
129	M₁₆×C₁₉	—	4	1	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	4	1	no	—
133	C₄⋊C₄×C₁₉	—	2	1	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	4	1	no	—
140	C₄⋊C₄×C₁₉	—	4	1	no	—
141	C₂²⋊C₄×C₁₉	—	4	4	no	—
142	C₂²⋊C₄×C₁₉	—	4	1	no	—
143	C₂²⋊C₄×C₁₉	—	4	1	no	—
144	C₂²⋊C₄×C₁₉	—	4	1	no	—
145	C₂²⋊C₄×C₁₉	—	4	1	no	—
146	C₂²⋊C₄×C₁₉	—	4	1	no	—
147	C₂²⋊C₄×C₁₉	—	4	1	no	—
148	C₂²⋊C₄×C₁₉	—	8	2	no	—
149	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₁₉	#41	1	1	yes	characteristic
153	#9996	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	4	1	no	—
157	C₂³×C₁₉	—	4	2	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	4	1	no	—
160	C₂³×C₁₉	—	4	1	no	—
161	C₂³×C₁₉	—	4	1	no	—
162	C₂³×C₁₉	—	4	1	no	—
163	C₂³×C₁₉	—	4	1	no	—
164	C₂³×C₁₉	—	4	1	no	—
165	C₂³×C₁₉	—	4	1	no	—
166	C₂³×C₁₉	—	4	1	no	—
167	C₂³×C₁₉	#120	1	1	yes	characteristic
168	Q₈×C₁₉	—	4	1	no	—
169	Q₈×C₁₉	—	4	1	no	—
170	D₄×C₁₉	—	2	2	no	—
171	D₄×C₁₉	—	2	2	no	—
172	D₄×C₁₉	—	2	2	no	—
173	D₄×C₁₉	—	2	2	no	—
174	D₄×C₁₉	—	4	1	no	—
175	D₄×C₁₉	—	4	1	no	—
176	D₄×C₁₉	—	4	2	no	—
177	D₄×C₁₉	—	4	1	no	—
178	D₄×C₁₉	—	4	1	no	—
179	D₄×C₁₉	—	4	1	no	—
180	D₄×C₁₉	—	4	1	no	—
181	D₄×C₁₉	—	8	1	no	—
182	D₄×C₁₉	—	8	8	no	—
183	D₄×C₁₉	—	8	1	no	—
184	D₄×C₁₉	—	8	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	8	2	no	—
197	C₂×C₄×C₁₉	—	8	2	no	—
198	C₂×C₄×C₁₉	—	8	1	no	—
199	C₂×C₄×C₁₉	—	8	1	no	—
200	C₂×C₄×C₁₉	—	8	1	no	—
201	C₂×C₄×C₁₉	—	8	1	no	—
202	C₂×C₄×C₁₉	—	8	1	no	—
203	C₂×C₄×C₁₉	—	8	1	no	—
204	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
205	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
206	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
209	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
211	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
212	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₈×C₁₉	—	4	2	no	—
215	C₈×C₁₉	—	4	2	no	—
216	C₈×C₁₉	—	8	1	no	—
217	#3100	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#3036	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#2535	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#1517	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#1486	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#1478	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#1286	C₂×C₁₉	1	1	yes	characteristic, complemented
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	4	2	no	—
227	C₂²×C₁₉	—	4	4	no	—
228	C₂²×C₁₉	—	4	2	no	—
229	C₂²×C₁₉	—	4	2	no	—
230	C₂²×C₁₉	—	4	2	no	—
231	C₂²×C₁₉	—	8	1	no	—
232	C₂²×C₁₉	—	8	2	no	—
233	C₂²×C₁₉	—	8	1	no	—
234	C₂²×C₁₉	—	8	1	no	—
235	C₂²×C₁₉	—	8	1	no	—
236	C₂²×C₁₉	—	8	1	no	—
237	C₂²×C₁₉	—	8	1	no	—
238	C₂²×C₁₉	—	8	1	no	—
239	C₂²×C₁₉	—	8	1	no	—
240	C₂²×C₁₉	—	8	1	no	—
241	C₂²×C₁₉	#392	1	1	yes	characteristic
242	C₂²×C₁₉	#447	1	1	yes	characteristic
243	C₂²×C₁₉	#449	1	1	yes	characteristic
244	C₄×C₁₉	—	2	1	no	—
245	C₄×C₁₉	—	2	1	no	—
246	C₄×C₁₉	—	2	1	no	—
247	C₄×C₁₉	—	2	1	no	—
248	C₄×C₁₉	—	8	2	no	—
249	C₄×C₁₉	—	8	1	no	—
250	C₄×C₁₉	—	8	1	no	—
251	C₄×C₁₉	—	8	1	no	—
252	C₄×C₁₉	#447	1	1	yes	characteristic
253	C₄×C₁₉	#449	1	1	yes	characteristic
254	C₄×C₁₉	#466	1	1	yes	characteristic
255	C₄×C₁₉	#469	1	1	yes	characteristic
256	C₂×AGL(1,ℤ/8)	—	2	1	no	—
257	#532	C₂²×C₁₉	1	1	yes	characteristic
258	C₂×#121	—	2	1	no	—
259	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
260	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
261	#480	—	2	1	no	—
262	#474	—	2	1	no	—
263	#463	—	2	2	no	—
264	#461	—	2	1	no	—
265	#459	—	2	1	no	—
266	#459	—	2	1	no	—
267	#447	—	2	1	no	—
268	C₄×D₈	—	2	2	no	—
269	#431	C₂²×C₁₉	1	1	yes	characteristic
270	#431	C₂²×C₁₉	1	1	yes	characteristic
271	#423	C₂²×C₁₉	1	1	yes	characteristic
272	#417	—	2	1	no	—
273	#397	—	2	1	no	—
274	#392	—	2	1	no	—
275	#386	—	2	2	no	—
276	#382	C₂²×C₁₉	1	1	yes	characteristic
277	#380	—	2	1	no	—
278	#327	—	2	2	no	—
279	D₄⋊C₈	—	2	2	no	—
280	D₄⋊C₈	—	2	2	no	—
281	C₂×C₁₉	—	2	1	no	—
282	C₂×C₁₉	—	2	1	no	—
283	C₂×C₁₉	—	8	2	no	—
284	C₂×C₁₉	—	8	2	no	—
285	C₂×C₁₉	—	16	1	no	—
286	C₂×C₁₉	#1999	1	1	yes	characteristic
287	C₂×C₁₉	#2008	1	1	yes	characteristic
288	C₂×C₁₉	#2010	1	1	yes	characteristic
289	C₂×#41	—	2	1	no	—
290	C₂²×D₄	—	2	2	no	—
291	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
292	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
293	C₂³×C₄	—	2	1	no	—
294	C₂³×C₄	—	2	1	no	—
295	AGL(1,ℤ/8)	—	4	2	no	—
296	AGL(1,ℤ/8)	—	4	2	no	—
297	C₂×SD₁₆	—	2	2	no	—
298	C₂×D₈	—	2	2	no	—
299	C₂×D₈	—	2	2	no	—
300	C₂×M₁₆	—	2	1	no	—
301	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
302	#127	D₄×C₁₉	1	1	yes	characteristic, complemented
303	#124	—	2	1	no	—
304	#121	—	2	1	no	—
305	#121	—	2	1	no	—
306	#121	—	4	2	no	—
307	#121	—	4	2	no	—
308	C₄×D₄	—	2	1	no	—
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
320	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
326	#107	—	2	2	no	—
327	C₄⋊C₈	—	2	1	no	—
328	C₄⋊C₈	—	2	1	no	—
329	C₄⋊C₈	—	2	1	no	—
330	C₄⋊C₈	D₄×C₁₉	1	2	yes	complemented
331	#103	—	2	2	no	—
332	#102	—	2	2	no	—
333	#102	—	2	2	no	—
334	#102	—	2	2	no	—
335	C₂²⋊C₈	—	2	1	no	—
336	C₂²⋊C₈	—	2	1	no	—
337	C₄×C₈	—	2	1	no	—
338	C₄×C₈	D₄×C₁₉	1	2	yes	complemented
339	#95	—	2	2	no	—
340	#95	—	2	1	no	—
341	#95	D₄×C₁₉	1	2	yes	—
342	C₁₉	#9996	1	1	yes	characteristic, direct product factor, Sylow
343	C₂⁴	—	2	1	no	—
344	C₂⁴	—	2	1	no	—
345	#41	—	4	1	no	—
346	#41	—	4	1	no	—
347	#41	—	4	1	no	—
348	#41	—	4	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	4	4	no	—
362	C₂×D₄	—	4	4	no	—
363	C₂×D₄	—	4	1	no	—
364	C₂×D₄	—	8	2	no	—
365	C₂×D₄	D₈×C₁₉	1	2	yes	complemented
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	4	1	no	—
370	C₂²×C₄	—	4	1	no	—
371	C₂²×C₄	—	4	1	no	—
372	C₂²×C₄	—	4	1	no	—
373	C₂²×C₄	—	4	1	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	—	4	1	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	—	8	2	no	—
379	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
382	SD₁₆	—	4	4	no	—
383	D₈	—	4	4	no	—
384	D₈	—	4	4	no	—
385	M₁₆	—	4	1	no	—
386	M₁₆	—	4	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	4	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	—	4	1	no	—
398	C₂²⋊C₄	—	4	4	no	—
399	C₂²⋊C₄	—	4	1	no	—
400	C₂²⋊C₄	—	4	1	no	—
401	C₂²⋊C₄	—	4	1	no	—
402	C₂²⋊C₄	—	4	1	no	—
403	C₂²⋊C₄	—	4	1	no	—
404	C₂²⋊C₄	—	4	1	no	—
405	C₂²⋊C₄	—	8	2	no	—
406	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
407	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
408	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
409	C₄²	#41×C₁₉	1	1	yes	characteristic
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	C₁₉×#120	1	1	yes	characteristic
424	Q₈	—	4	1	no	—
425	Q₈	—	4	1	no	—
426	D₄	—	2	2	no	—
427	D₄	—	2	2	no	—
428	D₄	—	2	2	no	—
429	D₄	—	2	2	no	—
430	D₄	—	4	1	no	—
431	D₄	—	4	1	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	1	no	—
434	D₄	—	4	1	no	—
435	D₄	—	4	1	no	—
436	D₄	—	4	1	no	—
437	D₄	—	8	1	no	—
438	D₄	—	8	8	no	—
439	D₄	—	8	1	no	—
440	D₄	—	8	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	8	2	no	—
453	C₂×C₄	—	8	2	no	—
454	C₂×C₄	—	8	1	no	—
455	C₂×C₄	—	8	1	no	—
456	C₂×C₄	—	8	1	no	—
457	C₂×C₄	—	8	1	no	—
458	C₂×C₄	—	8	1	no	—
459	C₂×C₄	—	8	1	no	—
460	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
461	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
462	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
463	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
464	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
465	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
466	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
467	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
468	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
469	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
470	C₈	—	4	2	no	—
471	C₈	—	4	2	no	—
472	C₈	—	8	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	8	1	no	—
481	C₂²	—	8	2	no	—
482	C₂²	—	8	1	no	—
483	C₂²	—	8	1	no	—
484	C₂²	—	8	1	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	—	8	1	no	—
488	C₂²	—	8	1	no	—
489	C₂²	—	8	1	no	—
490	C₂²	C₁₉×#392	1	1	yes	characteristic
491	C₂²	C₁₉×#447	1	1	yes	characteristic
492	C₂²	C₁₉×#449	1	1	yes	characteristic
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	8	2	no	—
498	C₄	—	8	1	no	—
499	C₄	—	8	1	no	—
500	C₄	—	8	1	no	—
501	C₄	C₁₉×#447	1	1	yes	characteristic
502	C₄	C₁₉×#449	1	1	yes	characteristic
503	C₄	C₁₉×#466	1	1	yes	characteristic
504	C₄	C₁₉×#469	1	1	yes	characteristic
505	C₂	—	2	1	no	—
506	C₂	—	2	1	no	—
507	C₂	—	8	2	no	—
508	C₂	—	8	2	no	—
509	C₂	—	16	1	no	—
510	C₂	C₁₉×#1999	1	1	yes	characteristic
511	C₂	C₁₉×#2008	1	1	yes	characteristic
512	C₂	C₁₉×#2010	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
LCS	G ▷ C₂×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×#3100	C₂	semidirect
2. C₁₉×#3036	C₂	semidirect
3. C₁₉×#2535	C₂	semidirect
4. C₁₉×#1517	C₂	semidirect
5. C₁₉×#1486	C₂	semidirect
6. C₁₉×#1478	C₂	semidirect
7. C₁₉×#1286	C₂	semidirect
45. C₁₉×C₄⋊Q₈	D₄	semidirect
46. C₁₉×#127	D₄	semidirect
74. C₁₉×C₄⋊C₈	D₄	semidirect
82. C₄×C₈×C₁₉	D₄	semidirect
108. C₂×D₄×C₁₉	D₈	semidirect
153. #9996	C₁₉	direct (N × H)
217. #3100	C₂×C₁₉	semidirect
218. #3036	C₂×C₁₉	semidirect
219. #2535	C₂×C₁₉	semidirect
220. #1517	C₂×C₁₉	semidirect
221. #1486	C₂×C₁₉	semidirect
222. #1478	C₂×C₁₉	semidirect
223. #1286	C₂×C₁₉	semidirect
301. C₄⋊Q₈	D₄×C₁₉	semidirect
302. #127	D₄×C₁₉	semidirect
330. C₄⋊C₈	D₄×C₁₉	semidirect
338. C₄×C₈	D₄×C₁₉	semidirect
342. C₁₉	#9996	direct (N × H)
365. C₂×D₄	D₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3100	2
C₁₉×#3036	2
C₁₉×#2535	2
C₁₉×#1517	2
C₁₉×#1486	2
C₁₉×#1478	2
C₁₉×#1286	2
#9996	19

Subgroups — C19×#9996 #18015955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9996 #18015955