Subgroups — C₁₉×#10473 #18016432

Order 4864.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#459	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1957	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1954	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1802	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#331	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₈×C₁₉	—	2	1	no	—
9	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#459	—	2	2	no	—
12	C₁₉×#459	—	2	2	no	—
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#102	—	2	1	no	—
17	C₂×C₁₉×#102	—	2	1	no	—
18	C₂×C₁₉×#102	—	2	1	no	—
19	C₂×C₁₉×#102	—	2	1	no	—
20	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
21	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
22	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#384	C₂²	1	1	yes	characteristic
24	C₁₉×#340	—	2	1	no	—
25	C₁₉×#334	—	2	2	no	—
26	C₁₉×#331	—	2	2	no	—
27	C₂²×D₄×C₁₉	—	2	1	no	—
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂×D₈×C₁₉	—	2	4	no	—
33	C₂×D₈×C₁₉	—	4	2	no	—
34	C₂×D₈×C₁₉	—	4	2	no	—
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
40	C₁₉×#127	—	2	1	no	—
41	C₁₉×#127	—	2	1	no	—
42	C₁₉×#127	—	2	1	no	—
43	C₁₉×#127	D₄	1	2	yes	—
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	—	2	1	no	—
46	C₄×D₄×C₁₉	—	2	1	no	—
47	C₄×D₄×C₁₉	—	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	D₄	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×C₄⋊C₈	—	2	1	no	—
57	C₁₉×C₄⋊C₈	—	2	1	no	—
58	C₁₉×C₄⋊C₈	—	2	1	no	—
59	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
60	C₁₉×#102	—	2	4	no	—
61	C₁₉×#102	—	4	2	no	—
62	C₁₉×#102	—	4	2	no	—
63	C₁₉×#102	—	4	2	no	—
64	C₁₉×C₂²⋊C₈	—	4	2	no	—
65	C₁₉×C₂²⋊C₈	—	4	2	no	—
66	C₄×C₈×C₁₉	—	2	1	no	—
67	C₄×C₈×C₁₉	—	2	1	no	—
68	C₂⁴×C₁₉	—	2	1	no	—
69	C₂⁴×C₁₉	—	4	1	no	—
70	C₂×D₄×C₁₉	—	2	1	no	—
71	C₂×D₄×C₁₉	—	2	2	no	—
72	C₂×D₄×C₁₉	—	2	2	no	—
73	C₂×D₄×C₁₉	—	2	1	no	—
74	C₂×D₄×C₁₉	—	2	2	no	—
75	C₂×D₄×C₁₉	—	2	1	no	—
76	C₂×D₄×C₁₉	—	2	1	no	—
77	C₂×D₄×C₁₉	—	2	1	no	—
78	C₂×D₄×C₁₉	—	4	1	no	—
79	C₂×D₄×C₁₉	—	4	1	no	—
80	C₂×D₄×C₁₉	—	4	1	no	—
81	C₂×D₄×C₁₉	—	4	1	no	—
82	C₂×D₄×C₁₉	—	4	1	no	—
83	C₂×D₄×C₁₉	—	4	1	no	—
84	C₂×D₄×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	8	1	no	—
90	C₂×D₄×C₁₉	—	8	1	no	—
91	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	4	1	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
103	D₈×C₁₉	—	4	8	no	—
104	C₂×C₈×C₁₉	—	2	1	no	—
105	C₂×C₈×C₁₉	—	2	1	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	2	1	no	—
108	C₂×C₈×C₁₉	—	2	1	no	—
109	C₂×C₈×C₁₉	—	2	1	no	—
110	C₂×C₈×C₁₉	—	4	1	no	—
111	C₂×C₈×C₁₉	—	4	1	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₂×C₈×C₁₉	—	4	1	no	—
116	C₂×C₈×C₁₉	—	4	1	no	—
117	C₂×C₈×C₁₉	—	4	1	no	—
118	C₂×C₈×C₁₉	D₈	1	2	yes	complemented
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₄⋊C₄×C₁₉	—	4	1	no	—
122	C₄⋊C₄×C₁₉	—	4	1	no	—
123	C₄⋊C₄×C₁₉	—	4	1	no	—
124	C₄⋊C₄×C₁₉	—	4	1	no	—
125	C₄⋊C₄×C₁₉	—	8	1	no	—
126	C₂²⋊C₄×C₁₉	—	4	1	no	—
127	C₂²⋊C₄×C₁₉	—	4	1	no	—
128	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₉	#41	1	1	yes	characteristic
131	C₄²×C₁₉	#41	1	1	yes	characteristic
132	#10473	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₁₉	—	2	2	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	4	1	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	—	4	1	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	—	8	1	no	—
142	C₂³×C₁₉	—	8	1	no	—
143	C₂³×C₁₉	—	8	1	no	—
144	C₂³×C₁₉	—	8	1	no	—
145	C₂³×C₁₉	—	8	1	no	—
146	C₂³×C₁₉	—	8	1	no	—
147	C₂³×C₁₉	#121	1	1	yes	characteristic
148	D₄×C₁₉	—	2	2	no	—
149	D₄×C₁₉	—	2	2	no	—
150	D₄×C₁₉	—	4	1	no	—
151	D₄×C₁₉	—	4	2	no	—
152	D₄×C₁₉	—	4	2	no	—
153	D₄×C₁₉	—	4	2	no	—
154	D₄×C₁₉	—	4	2	no	—
155	D₄×C₁₉	—	4	1	no	—
156	D₄×C₁₉	—	8	2	no	—
157	D₄×C₁₉	—	8	2	no	—
158	D₄×C₁₉	—	8	1	no	—
159	D₄×C₁₉	—	8	1	no	—
160	D₄×C₁₉	—	8	1	no	—
161	D₄×C₁₉	—	8	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	8	1	no	—
168	C₂×C₄×C₁₉	—	8	1	no	—
169	C₂×C₄×C₁₉	—	8	1	no	—
170	C₂×C₄×C₁₉	—	8	1	no	—
171	C₂×C₄×C₁₉	—	8	1	no	—
172	C₂×C₄×C₁₉	—	8	1	no	—
173	C₂×C₄×C₁₉	—	8	1	no	—
174	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
184	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₈×C₁₉	—	2	2	no	—
189	C₈×C₁₉	—	4	2	no	—
190	C₈×C₁₉	—	4	1	no	—
191	C₈×C₁₉	—	8	1	no	—
192	C₈×C₁₉	—	8	1	no	—
193	C₂×#459	C₂×C₁₉	1	1	yes	characteristic
194	#1957	C₂×C₁₉	1	1	yes	characteristic, complemented
195	#1954	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#1802	C₂×C₁₉	1	1	yes	characteristic, complemented
197	C₂×#334	C₂×C₁₉	1	1	yes	characteristic, complemented
198	C₂×#331	C₂×C₁₉	1	1	yes	characteristic, complemented
199	#1296	C₂×C₁₉	1	1	yes	characteristic, complemented
200	C₂²×C₁₉	—	4	2	no	—
201	C₂²×C₁₉	—	4	2	no	—
202	C₂²×C₁₉	—	4	2	no	—
203	C₂²×C₁₉	—	8	1	no	—
204	C₂²×C₁₉	—	8	1	no	—
205	C₂²×C₁₉	—	8	1	no	—
206	C₂²×C₁₉	—	8	1	no	—
207	C₂²×C₁₉	—	8	2	no	—
208	C₂²×C₁₉	—	8	2	no	—
209	C₂²×C₁₉	—	8	2	no	—
210	C₂²×C₁₉	—	16	1	no	—
211	C₂²×C₁₉	—	16	1	no	—
212	C₂²×C₁₉	—	16	1	no	—
213	C₂²×C₁₉	—	16	1	no	—
214	C₂²×C₁₉	#394	1	1	yes	characteristic
215	C₂²×C₁₉	#459	1	1	yes	characteristic
216	C₂²×C₁₉	#463	1	1	yes	characteristic
217	C₂²×C₁₉	#465	1	1	yes	characteristic
218	C₂²×C₁₉	#469	1	1	yes	characteristic
219	C₂²×C₁₉	#471	1	1	yes	characteristic
220	C₂²×C₁₉	#472	1	1	yes	characteristic
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	8	1	no	—
224	C₄×C₁₉	—	16	1	no	—
225	C₄×C₁₉	#449	1	1	yes	characteristic
226	C₄×C₁₉	#450	1	1	yes	characteristic
227	C₄×C₁₉	#459	1	1	yes	characteristic
228	C₄×C₁₉	#463	1	1	yes	characteristic
229	C₄×C₁₉	#466	1	1	yes	characteristic
230	C₄×C₁₉	#469	1	1	yes	characteristic
231	C₄×C₁₉	#481	1	1	yes	characteristic
232	C₄×C₁₉	#482	1	1	yes	characteristic
233	C₂²×D₈	—	2	1	no	—
234	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
236	#459	—	2	2	no	—
237	#459	—	2	2	no	—
238	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
241	C₂×#102	—	2	1	no	—
242	C₂×#102	—	2	1	no	—
243	C₂×#102	—	2	1	no	—
244	C₂×#102	—	2	1	no	—
245	C₂×C₂²⋊C₈	—	2	1	no	—
246	C₂×C₂²⋊C₈	—	2	1	no	—
247	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
248	#384	C₂²×C₁₉	1	1	yes	characteristic
249	#340	—	2	1	no	—
250	#334	—	2	2	no	—
251	#331	—	2	2	no	—
252	C₂×C₁₉	—	8	2	no	—
253	C₂×C₁₉	—	16	2	no	—
254	C₂×C₁₉	#1665	1	1	yes	characteristic
255	C₂×C₁₉	#1677	1	1	yes	characteristic
256	C₂×C₁₉	#1687	1	1	yes	characteristic
257	C₂×C₁₉	#1701	1	1	yes	characteristic
258	C₂×C₁₉	#2034	1	1	yes	characteristic
259	C₂×C₁₉	#2051	1	1	yes	characteristic
260	C₂×C₁₉	#2054	1	1	yes	characteristic
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
265	C₂³×C₄	—	2	1	no	—
266	C₂×D₈	—	2	4	no	—
267	C₂×D₈	—	4	2	no	—
268	C₂×D₈	—	4	2	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
273	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
274	#127	—	2	1	no	—
275	#127	—	2	1	no	—
276	#127	—	2	1	no	—
277	#127	D₄×C₁₉	1	2	yes	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
294	#102	—	2	4	no	—
295	#102	—	4	2	no	—
296	#102	—	4	2	no	—
297	#102	—	4	2	no	—
298	C₂²⋊C₈	—	4	2	no	—
299	C₂²⋊C₈	—	4	2	no	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	—	2	1	no	—
302	C₁₉	#10473	1	1	yes	characteristic, direct product factor, Sylow
303	C₂⁴	—	2	1	no	—
304	C₂⁴	—	4	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	8	1	no	—
325	C₂×D₄	—	8	1	no	—
326	C₂×D₄	SD₁₆×C₁₉	1	2	yes	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	4	1	no	—
335	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
338	D₈	—	4	8	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	1	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	D₈×C₁₉	1	2	yes	complemented
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	8	1	no	—
361	C₂²⋊C₄	—	4	1	no	—
362	C₂²⋊C₄	—	4	1	no	—
363	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
364	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
365	C₄²	#41×C₁₉	1	1	yes	characteristic
366	C₄²	#41×C₁₉	1	1	yes	characteristic
367	C₂³	—	2	2	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	8	1	no	—
376	C₂³	—	8	1	no	—
377	C₂³	—	8	1	no	—
378	C₂³	—	8	1	no	—
379	C₂³	—	8	1	no	—
380	C₂³	—	8	1	no	—
381	C₂³	C₁₉×#121	1	1	yes	characteristic
382	D₄	—	2	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	1	no	—
390	D₄	—	8	2	no	—
391	D₄	—	8	2	no	—
392	D₄	—	8	1	no	—
393	D₄	—	8	1	no	—
394	D₄	—	8	1	no	—
395	D₄	—	8	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	8	1	no	—
402	C₂×C₄	—	8	1	no	—
403	C₂×C₄	—	8	1	no	—
404	C₂×C₄	—	8	1	no	—
405	C₂×C₄	—	8	1	no	—
406	C₂×C₄	—	8	1	no	—
407	C₂×C₄	—	8	1	no	—
408	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
409	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
410	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
411	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
412	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
413	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
414	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
415	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
416	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
417	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
418	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
419	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
420	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
421	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
422	C₈	—	2	2	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	1	no	—
425	C₈	—	8	1	no	—
426	C₈	—	8	1	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	—	8	1	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	16	1	no	—
438	C₂²	—	16	1	no	—
439	C₂²	—	16	1	no	—
440	C₂²	—	16	1	no	—
441	C₂²	C₁₉×#394	1	1	yes	characteristic
442	C₂²	C₁₉×#459	1	1	yes	characteristic
443	C₂²	C₁₉×#463	1	1	yes	characteristic
444	C₂²	C₁₉×#465	1	1	yes	characteristic
445	C₂²	C₁₉×#469	1	1	yes	characteristic
446	C₂²	C₁₉×#471	1	1	yes	characteristic
447	C₂²	C₁₉×#472	1	1	yes	characteristic
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	8	1	no	—
451	C₄	—	16	1	no	—
452	C₄	C₁₉×#449	1	1	yes	characteristic
453	C₄	C₁₉×#450	1	1	yes	characteristic
454	C₄	C₁₉×#459	1	1	yes	characteristic
455	C₄	C₁₉×#463	1	1	yes	characteristic
456	C₄	C₁₉×#466	1	1	yes	characteristic
457	C₄	C₁₉×#469	1	1	yes	characteristic
458	C₄	C₁₉×#481	1	1	yes	characteristic
459	C₄	C₁₉×#482	1	1	yes	characteristic
460	C₂	—	8	2	no	—
461	C₂	—	16	2	no	—
462	C₂	C₁₉×#1665	1	1	yes	characteristic
463	C₂	C₁₉×#1677	1	1	yes	characteristic
464	C₂	C₁₉×#1687	1	1	yes	characteristic
465	C₂	C₁₉×#1701	1	1	yes	characteristic
466	C₂	C₁₉×#2034	1	1	yes	characteristic
467	C₂	C₁₉×#2051	1	1	yes	characteristic
468	C₂	C₁₉×#2054	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂×C₁₉×#459	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1957	C₂	semidirect
3. C₁₉×#1954	C₂	semidirect
4. C₁₉×#1802	C₂	semidirect
5. C₂×C₁₉×#334	C₂	semidirect
6. C₂×C₁₉×#331	C₂	semidirect
7. C₁₉×#1296	C₂	semidirect
118. C₂×C₈×C₁₉	D₈	semidirect
132. #10473	C₁₉	direct (N × H)
194. #1957	C₂×C₁₉	semidirect
195. #1954	C₂×C₁₉	semidirect
196. #1802	C₂×C₁₉	semidirect
197. C₂×#334	C₂×C₁₉	semidirect
198. C₂×#331	C₂×C₁₉	semidirect
199. #1296	C₂×C₁₉	semidirect
302. C₁₉	#10473	direct (N × H)
353. C₂×C₈	D₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#459	2
C₁₉×#1957	2
C₁₉×#1954	2
C₁₉×#1802	2
C₂×C₁₉×#334	2
C₂×C₁₉×#331	2
C₁₉×#1296	2
#10473	19

Subgroups — C19×#10473 #18016432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10473 #18016432