Subgroups — C₁₉×#9971 #18015930

Order 4864.

658 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#480	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2639	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#328	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#327	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1445	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1280	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#483	—	2	2	no	—
12	C₁₉×#483	—	2	2	no	—
13	C₁₉×#480	—	2	2	no	—
14	C₁₉×#480	—	2	2	no	—
15	C₂×C₁₉×#107	—	2	1	no	—
16	C₂×C₁₉×#106	—	2	1	no	—
17	C₂×C₁₉×#103	—	2	1	no	—
18	C₂×C₁₉×#102	—	2	1	no	—
19	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₁₉×#400	—	2	1	no	—
22	C₁₉×#397	—	2	1	no	—
23	C₁₉×#394	—	2	1	no	—
24	C₁₉×#393	—	2	1	no	—
25	C₁₉×#386	—	2	2	no	—
26	C₂×C₁₉×#95	—	2	2	no	—
27	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
29	C₁₉×#328	—	2	2	no	—
30	C₁₉×#327	—	2	2	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	—	2	1	no	—
35	C₂³×C₄×C₁₉	—	2	1	no	—
36	C₂³×C₄×C₁₉	D₄	1	2	yes	—
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₁₉×C₂²⋊Q₈	—	2	1	no	—
41	C₁₉×C₂²⋊Q₈	—	2	1	no	—
42	C₁₉×C₂²⋊Q₈	—	2	1	no	—
43	C₁₉×C₂²⋊Q₈	—	2	1	no	—
44	C₁₉×#121	—	2	1	no	—
45	C₁₉×#121	—	2	1	no	—
46	C₁₉×#121	—	2	1	no	—
47	C₁₉×#121	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	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×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
61	C₁₉×#107	—	2	4	no	—
62	C₁₉×#106	—	2	4	no	—
63	C₁₉×#103	—	2	4	no	—
64	C₁₉×#102	—	2	4	no	—
65	C₁₉×C₂²⋊C₈	—	2	1	no	—
66	C₁₉×C₂²⋊C₈	—	2	1	no	—
67	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
68	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
69	C₁₉×#95	—	2	2	no	—
70	C₁₉×#95	—	2	2	no	—
71	C₁₉×#95	—	2	1	no	—
72	C₁₉×#95	—	2	1	no	—
73	C₁₉×#95	—	2	1	no	—
74	C₁₉×#95	—	2	1	no	—
75	C₁₉×#95	—	4	4	no	—
76	C₂⁴×C₁₉	—	2	1	no	—
77	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂×Q₈×C₁₉	—	2	1	no	—
79	C₂×Q₈×C₁₉	—	2	1	no	—
80	C₂×Q₈×C₁₉	—	4	2	no	—
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	—	4	2	no	—
84	C₂×D₄×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	2	no	—
87	C₂×D₄×C₁₉	—	4	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	4	2	no	—
97	C₂²×C₄×C₁₉	—	4	2	no	—
98	C₂²×C₄×C₁₉	—	4	2	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	—	4	2	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	—	4	2	no	—
105	C₂²×C₄×C₁₉	—	4	2	no	—
106	C₂²×C₄×C₁₉	—	4	2	no	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	4	2	no	—
116	C₂×C₈×C₁₉	—	4	2	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₄⋊C₄×C₁₉	—	2	1	no	—
123	C₄⋊C₄×C₁₉	—	4	1	no	—
124	C₄⋊C₄×C₁₉	—	4	1	no	—
125	C₄⋊C₄×C₁₉	—	4	1	no	—
126	C₄⋊C₄×C₁₉	—	4	1	no	—
127	C₂²⋊C₄×C₁₉	—	4	1	no	—
128	C₂²⋊C₄×C₁₉	—	4	1	no	—
129	C₂²⋊C₄×C₁₉	—	4	1	no	—
130	C₂²⋊C₄×C₁₉	—	4	1	no	—
131	C₂²⋊C₄×C₁₉	—	8	2	no	—
132	C₂²⋊C₄×C₁₉	—	8	2	no	—
133	#9971	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₁₉	—	2	1	no	—
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	—	4	1	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	#120	1	1	yes	characteristic
143	C₂³×C₁₉	#121	1	1	yes	characteristic
144	C₂³×C₁₉	#127	1	1	yes	characteristic
145	C₂³×C₁₉	#135	1	2	yes	—
146	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
147	Q₈×C₁₉	—	4	2	no	—
148	Q₈×C₁₉	—	8	1	no	—
149	D₄×C₁₉	—	4	2	no	—
150	D₄×C₁₉	—	8	1	no	—
151	D₄×C₁₉	—	8	2	no	—
152	D₄×C₁₉	—	8	1	no	—
153	D₄×C₁₉	—	8	1	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	4	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	4	no	—
175	C₂×C₄×C₁₉	—	8	2	no	—
176	C₂×C₄×C₁₉	—	8	1	no	—
177	C₂×C₄×C₁₉	—	8	2	no	—
178	C₂×C₄×C₁₉	—	8	1	no	—
179	C₂×C₄×C₁₉	—	8	1	no	—
180	C₂×C₄×C₁₉	—	8	1	no	—
181	C₂×C₄×C₁₉	—	8	2	no	—
182	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
186	C₈×C₁₉	—	4	2	no	—
187	C₈×C₁₉	—	4	2	no	—
188	C₂×#483	C₂×C₁₉	1	1	yes	characteristic, complemented
189	C₂×#480	C₂×C₁₉	1	1	yes	characteristic
190	#2639	C₂×C₁₉	1	1	yes	characteristic
191	C₂×#328	C₂×C₁₉	1	1	yes	characteristic, complemented
192	C₂×#327	C₂×C₁₉	1	1	yes	characteristic
193	#1445	C₂×C₁₉	1	1	yes	characteristic, complemented
194	#1280	C₂×C₁₉	1	1	yes	characteristic, complemented
195	C₂²×C₁₉	—	2	2	no	—
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	—	2	2	no	—
198	C₂²×C₁₉	—	2	2	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	2	1	no	—
203	C₂²×C₁₉	—	8	2	no	—
204	C₂²×C₁₉	—	8	2	no	—
205	C₂²×C₁₉	—	8	1	no	—
206	C₂²×C₁₉	—	8	1	no	—
207	C₂²×C₁₉	—	8	1	no	—
208	C₂²×C₁₉	#392	1	1	yes	characteristic
209	C₂²×C₁₉	#449	1	2	yes	—
210	C₂²×C₁₉	#455	1	1	yes	characteristic
211	C₂²×C₁₉	#456	1	1	yes	characteristic
212	C₂²×C₁₉	#458	1	2	yes	—
213	C₂²×C₁₉	#463	1	2	yes	—
214	C₂²×C₁₉	#495	1	1	yes	characteristic
215	C₂²×C₁₉	#496	1	1	yes	characteristic
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	8	2	no	—
221	C₄×C₁₉	—	8	2	no	—
222	C₄×C₁₉	—	8	1	no	—
223	C₄×C₁₉	—	8	2	no	—
224	C₄×C₁₉	—	8	1	no	—
225	C₄×C₁₉	—	8	1	no	—
226	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
229	#483	—	2	2	no	—
230	#483	—	2	2	no	—
231	#480	—	2	2	no	—
232	#480	—	2	2	no	—
233	C₂×#107	—	2	1	no	—
234	C₂×#106	—	2	1	no	—
235	C₂×#103	—	2	1	no	—
236	C₂×#102	—	2	1	no	—
237	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
239	#400	—	2	1	no	—
240	#397	—	2	1	no	—
241	#394	—	2	1	no	—
242	#393	—	2	1	no	—
243	#386	—	2	2	no	—
244	C₂×#95	—	2	2	no	—
245	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
246	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
247	#328	—	2	2	no	—
248	#327	—	2	2	no	—
249	C₂×C₁₉	—	2	1	no	—
250	C₂×C₁₉	—	2	2	no	—
251	C₂×C₁₉	—	2	1	no	—
252	C₂×C₁₉	—	16	1	no	—
253	C₂×C₁₉	#1609	1	2	yes	—
254	C₂×C₁₉	#1612	1	2	yes	—
255	C₂×C₁₉	#2007	1	1	yes	characteristic
256	C₂×C₁₉	#2012	1	1	yes	characteristic
257	C₂×C₁₉	#2022	1	1	yes	characteristic
258	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
261	C₂³×C₄	—	2	1	no	—
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	D₄×C₁₉	1	2	yes	—
264	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²⋊Q₈	—	2	1	no	—
268	C₂²⋊Q₈	—	2	1	no	—
269	C₂²⋊Q₈	—	2	1	no	—
270	C₂²⋊Q₈	—	2	1	no	—
271	#121	—	2	1	no	—
272	#121	—	2	1	no	—
273	#121	—	2	1	no	—
274	#121	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
282	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
283	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	#107	—	2	4	no	—
289	#106	—	2	4	no	—
290	#103	—	2	4	no	—
291	#102	—	2	4	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₂²⋊C₈	—	2	1	no	—
294	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
295	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	1	no	—
299	#95	—	2	1	no	—
300	#95	—	2	1	no	—
301	#95	—	2	1	no	—
302	#95	—	4	4	no	—
303	C₁₉	#9971	1	1	yes	characteristic, direct product factor, Sylow
304	C₂⁴	—	2	1	no	—
305	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	4	2	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
340	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	4	2	no	—
344	C₂×C₈	—	4	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₂²⋊C₄	—	4	1	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	8	2	no	—
360	C₂²⋊C₄	—	8	2	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	2	no	—
369	C₂³	C₁₉×#120	1	1	yes	characteristic
370	C₂³	C₁₉×#121	1	1	yes	characteristic
371	C₂³	C₁₉×#127	1	1	yes	characteristic
372	C₂³	C₁₉×#135	1	2	yes	—
373	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
374	Q₈	—	4	2	no	—
375	Q₈	—	8	1	no	—
376	D₄	—	4	2	no	—
377	D₄	—	8	1	no	—
378	D₄	—	8	2	no	—
379	D₄	—	8	1	no	—
380	D₄	—	8	1	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	8	1	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	—	8	1	no	—
406	C₂×C₄	—	8	1	no	—
407	C₂×C₄	—	8	1	no	—
408	C₂×C₄	—	8	2	no	—
409	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
410	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
411	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
412	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
413	C₈	—	4	2	no	—
414	C₈	—	4	2	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	C₁₉×#392	1	1	yes	characteristic
429	C₂²	C₁₉×#449	1	2	yes	—
430	C₂²	C₁₉×#455	1	1	yes	characteristic
431	C₂²	C₁₉×#456	1	1	yes	characteristic
432	C₂²	C₁₉×#458	1	2	yes	—
433	C₂²	C₁₉×#463	1	2	yes	—
434	C₂²	C₁₉×#495	1	1	yes	characteristic
435	C₂²	C₁₉×#496	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	2	no	—
443	C₄	—	8	1	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	2	no	—
446	C₂	—	2	1	no	—
447	C₂	—	2	2	no	—
448	C₂	—	2	1	no	—
449	C₂	—	16	1	no	—
450	C₂	C₁₉×#1609	1	2	yes	—
451	C₂	C₁₉×#1612	1	2	yes	—
452	C₂	C₁₉×#2007	1	1	yes	characteristic
453	C₂	C₁₉×#2012	1	1	yes	characteristic
454	C₂	C₁₉×#2022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#483	C₂	semidirect
4. C₂×C₁₉×#328	C₂	semidirect
6. C₁₉×#1445	C₂	semidirect
7. C₁₉×#1280	C₂	semidirect
133. #9971	C₁₉	direct (N × H)
188. C₂×#483	C₂×C₁₉	semidirect
191. C₂×#328	C₂×C₁₉	semidirect
193. #1445	C₂×C₁₉	semidirect
194. #1280	C₂×C₁₉	semidirect
303. C₁₉	#9971	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#483	2
C₂×C₁₉×#480	2
C₁₉×#2639	2
C₂×C₁₉×#328	2
C₂×C₁₉×#327	2
C₁₉×#1445	2
C₁₉×#1280	2
#9971	19

Subgroups — C19×#9971 #18015930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9971 #18015930