Subgroups — C₁₉×#8475 #18014434

Order 4864.

932 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3500	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1543	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1488	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1469	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×2₋¹⁺⁴	C₄	1	1	yes	characteristic
7	C₂×C₁₉×H(5,𝔽₂)	C₄	1	1	yes	characteristic
8	C₁₉×#548	—	2	2	no	—
9	C₁₉×#546	—	2	2	no	—
10	C₁₉×#546	—	2	4	no	—
11	C₁₉×#536	—	2	1	no	—
12	C₁₉×#536	C₄	1	1	yes	characteristic
13	C₁₉×#535	—	2	1	no	—
14	C₁₉×#535	C₄	1	1	yes	characteristic
15	C₁₉×#532	—	2	1	no	—
16	C₁₉×#532	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#124	—	2	1	no	—
18	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
19	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#432	C₂²	1	2	yes	complemented
21	C₁₉×#431	C₂²	1	2	yes	complemented
22	C₁₉×#333	—	2	1	no	—
23	C₁₉×#331	—	2	1	no	—
24	C₁₉×#329	—	2	1	no	—
25	C₁₉×#329	—	2	1	no	—
26	C₁₉×Q₈⋊C₈	—	2	2	no	—
27	C₁₉×D₄⋊C₈	—	2	2	no	—
28	C₁₉×#323	—	2	4	no	—
29	C₁₉×2₋¹⁺⁴	—	4	2	no	—
30	C₁₉×2₋¹⁺⁴	—	4	2	no	—
31	C₁₉×H(5,𝔽₂)	—	4	2	no	—
32	C₁₉×H(5,𝔽₂)	—	4	2	no	—
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂×#41×C₁₉	—	2	1	no	—
35	C₂×#41×C₁₉	—	2	1	no	—
36	C₂×#41×C₁₉	—	2	1	no	—
37	C₂×#41×C₁₉	—	2	2	no	—
38	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₁₉×C₄⋊Q₈	—	2	1	no	—
49	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
50	C₁₉×#127	—	2	1	no	—
51	C₁₉×#127	D₄	1	1	yes	characteristic
52	C₁₉×#124	—	2	4	no	—
53	C₁₉×#124	—	2	1	no	—
54	C₁₉×#124	—	2	1	no	—
55	C₁₉×#124	—	2	1	no	—
56	C₁₉×#124	—	2	1	no	—
57	C₁₉×#124	—	2	2	no	—
58	C₁₉×#124	D₄	1	1	yes	characteristic
59	C₁₉×#124	D₄	1	1	yes	characteristic
60	C₁₉×#123	—	2	4	no	—
61	C₁₉×#123	—	2	2	no	—
62	C₁₉×C₂²⋊Q₈	—	2	4	no	—
63	C₁₉×C₂²⋊Q₈	—	2	2	no	—
64	C₁₉×#121	—	2	4	no	—
65	C₁₉×#121	—	2	4	no	—
66	C₁₉×#121	—	2	2	no	—
67	C₁₉×#121	—	2	2	no	—
68	C₁₉×#120	—	2	4	no	—
69	C₁₉×#120	—	2	2	no	—
70	C₄×Q₈×C₁₉	D₄	1	2	yes	—
71	C₄×D₄×C₁₉	—	2	4	no	—
72	C₄×D₄×C₁₉	—	2	2	no	—
73	C₄×D₄×C₁₉	—	2	2	no	—
74	C₄×D₄×C₁₉	D₄	1	2	yes	—
75	C₁₉×#117	—	2	1	no	—
76	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
79	C₂×C₄²×C₁₉	—	2	1	no	—
80	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
81	C₁₉×C₄⋊C₈	—	2	2	no	—
82	C₁₉×C₄⋊C₈	—	2	2	no	—
83	C₁₉×C₂²⋊C₈	—	2	2	no	—
84	C₁₉×C₂²⋊C₈	—	2	2	no	—
85	C₁₉×#97	—	2	2	no	—
86	C₄×C₈×C₁₉	—	2	2	no	—
87	C₂⁴×C₁₉	—	2	2	no	—
88	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
89	#41×C₁₉	—	2	2	no	—
90	#41×C₁₉	—	2	2	no	—
91	#41×C₁₉	—	4	4	no	—
92	#41×C₁₉	—	4	4	no	—
93	#41×C₁₉	—	4	1	no	—
94	#41×C₁₉	—	4	1	no	—
95	#41×C₁₉	—	4	1	no	—
96	#41×C₁₉	—	4	1	no	—
97	#41×C₁₉	—	4	8	no	—
98	#41×C₁₉	—	4	2	no	—
99	#41×C₁₉	—	4	2	no	—
100	#41×C₁₉	—	4	2	no	—
101	#41×C₁₉	—	4	2	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	2	1	no	—
105	C₂×Q₈×C₁₉	—	4	1	no	—
106	C₂×Q₈×C₁₉	—	4	1	no	—
107	C₂×Q₈×C₁₉	—	4	4	no	—
108	C₂×Q₈×C₁₉	—	4	2	no	—
109	C₂×Q₈×C₁₉	—	4	2	no	—
110	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×C₁₉	—	2	1	no	—
119	C₂×D₄×C₁₉	—	2	4	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	4	4	no	—
124	C₂×D₄×C₁₉	—	4	1	no	—
125	C₂×D₄×C₁₉	—	4	1	no	—
126	C₂×D₄×C₁₉	—	4	8	no	—
127	C₂×D₄×C₁₉	—	4	2	no	—
128	C₂×D₄×C₁₉	—	4	2	no	—
129	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
140	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₁₉	—	4	2	no	—
143	C₂×C₈×C₁₉	—	4	2	no	—
144	C₄⋊C₄×C₁₉	—	2	4	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
148	C₂²⋊C₄×C₁₉	—	2	4	no	—
149	C₂²⋊C₄×C₁₉	—	2	4	no	—
150	C₂²⋊C₄×C₁₉	—	2	1	no	—
151	C₂²⋊C₄×C₁₉	—	2	2	no	—
152	C₂²⋊C₄×C₁₉	—	2	4	no	—
153	C₂²⋊C₄×C₁₉	—	2	4	no	—
154	C₂²⋊C₄×C₁₉	—	2	2	no	—
155	C₂²⋊C₄×C₁₉	—	2	2	no	—
156	C₄²×C₁₉	—	2	1	no	—
157	C₄²×C₁₉	—	2	2	no	—
158	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₉	C₂×D₄	1	2	yes	—
161	#8475	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂³×C₁₉	—	2	1	no	—
163	C₂³×C₁₉	—	2	2	no	—
164	C₂³×C₁₉	—	2	1	no	—
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	—	4	4	no	—
167	C₂³×C₁₉	—	4	2	no	—
168	C₂³×C₁₉	—	4	4	no	—
169	C₂³×C₁₉	—	8	4	no	—
170	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	Q₈×C₁₉	—	2	1	no	—
172	Q₈×C₁₉	—	4	1	no	—
173	Q₈×C₁₉	—	4	1	no	—
174	Q₈×C₁₉	—	4	2	no	—
175	Q₈×C₁₉	—	4	4	no	—
176	Q₈×C₁₉	—	4	1	no	—
177	Q₈×C₁₉	—	4	1	no	—
178	Q₈×C₁₉	#100	1	2	yes	—
179	D₄×C₁₉	—	2	4	no	—
180	D₄×C₁₉	—	2	1	no	—
181	D₄×C₁₉	—	4	1	no	—
182	D₄×C₁₉	—	4	1	no	—
183	D₄×C₁₉	—	4	2	no	—
184	D₄×C₁₉	—	4	4	no	—
185	D₄×C₁₉	—	4	2	no	—
186	D₄×C₁₉	—	4	4	no	—
187	D₄×C₁₉	—	4	2	no	—
188	D₄×C₁₉	—	4	4	no	—
189	D₄×C₁₉	—	4	1	no	—
190	D₄×C₁₉	—	4	1	no	—
191	D₄×C₁₉	—	8	2	no	—
192	D₄×C₁₉	—	8	4	no	—
193	D₄×C₁₉	#100	1	2	yes	—
194	C₂×C₄×C₁₉	—	2	4	no	—
195	C₂×C₄×C₁₉	—	2	1	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	4	no	—
204	C₂×C₄×C₁₉	—	4	4	no	—
205	C₂×C₄×C₁₉	—	4	4	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	8	2	no	—
212	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#120	1	2	yes	—
215	C₂×C₄×C₁₉	#120	1	2	yes	—
216	C₈×C₁₉	—	8	2	no	—
217	C₈×C₁₉	—	8	2	no	—
218	#3500	C₂×C₁₉	1	1	yes	characteristic
219	#1543	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#1536	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#1488	C₂×C₁₉	1	2	yes	complemented
222	#1469	C₂×C₁₉	1	2	yes	complemented
223	C₂²×C₁₉	—	2	2	no	—
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	2	2	no	—
226	C₂²×C₁₉	—	4	2	no	—
227	C₂²×C₁₉	—	4	2	no	—
228	C₂²×C₁₉	—	4	4	no	—
229	C₂²×C₁₉	—	4	2	no	—
230	C₂²×C₁₉	—	4	1	no	—
231	C₂²×C₁₉	—	4	2	no	—
232	C₂²×C₁₉	—	4	1	no	—
233	C₂²×C₁₉	—	16	2	no	—
234	C₂²×C₁₉	—	16	4	no	—
235	C₂²×C₁₉	#379	1	1	yes	characteristic
236	C₄×C₁₉	—	2	2	no	—
237	C₄×C₁₉	—	2	2	no	—
238	C₄×C₁₉	—	2	1	no	—
239	C₄×C₁₉	—	2	2	no	—
240	C₄×C₁₉	—	4	2	no	—
241	C₄×C₁₉	—	4	1	no	—
242	C₄×C₁₉	—	4	1	no	—
243	C₄×C₁₉	—	4	2	no	—
244	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
245	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
246	C₂×2₋¹⁺⁴	C₄×C₁₉	1	1	yes	characteristic
247	C₂×H(5,𝔽₂)	C₄×C₁₉	1	1	yes	characteristic
248	#548	—	2	2	no	—
249	#546	—	2	2	no	—
250	#546	—	2	4	no	—
251	#536	—	2	1	no	—
252	#536	C₄×C₁₉	1	1	yes	characteristic
253	#535	—	2	1	no	—
254	#535	C₄×C₁₉	1	1	yes	characteristic
255	#532	—	2	1	no	—
256	#532	C₂²×C₁₉	1	1	yes	characteristic
257	C₂×#124	—	2	1	no	—
258	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
259	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
260	#432	C₂²×C₁₉	1	2	yes	complemented
261	#431	C₂²×C₁₉	1	2	yes	complemented
262	#333	—	2	1	no	—
263	#331	—	2	1	no	—
264	#329	—	2	1	no	—
265	#329	—	2	1	no	—
266	Q₈⋊C₈	—	2	2	no	—
267	D₄⋊C₈	—	2	2	no	—
268	#323	—	2	4	no	—
269	C₂×C₁₉	—	4	1	no	—
270	C₂×C₁₉	—	4	2	no	—
271	C₂×C₁₉	—	8	1	no	—
272	C₂×C₁₉	—	8	2	no	—
273	C₂×C₁₉	—	8	1	no	—
274	C₂×C₁₉	#1783	1	1	yes	characteristic
275	C₂×C₁₉	#1794	1	2	yes	—
276	2₋¹⁺⁴	—	4	2	no	—
277	2₋¹⁺⁴	—	4	2	no	—
278	H(5,𝔽₂)	—	4	2	no	—
279	H(5,𝔽₂)	—	4	2	no	—
280	C₂×#41	—	2	1	no	—
281	C₂×#41	—	2	1	no	—
282	C₂×#41	—	2	1	no	—
283	C₂×#41	—	2	1	no	—
284	C₂×#41	—	2	2	no	—
285	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
286	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
287	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
288	C₂²×Q₈	—	2	1	no	—
289	C₂²×Q₈	—	2	1	no	—
290	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
295	C₄⋊Q₈	—	2	1	no	—
296	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
297	#127	—	2	1	no	—
298	#127	D₄×C₁₉	1	1	yes	characteristic
299	#124	—	2	4	no	—
300	#124	—	2	1	no	—
301	#124	—	2	1	no	—
302	#124	—	2	1	no	—
303	#124	—	2	1	no	—
304	#124	—	2	2	no	—
305	#124	D₄×C₁₉	1	1	yes	characteristic
306	#124	D₄×C₁₉	1	1	yes	characteristic
307	#123	—	2	4	no	—
308	#123	—	2	2	no	—
309	C₂²⋊Q₈	—	2	4	no	—
310	C₂²⋊Q₈	—	2	2	no	—
311	#121	—	2	4	no	—
312	#121	—	2	4	no	—
313	#121	—	2	2	no	—
314	#121	—	2	2	no	—
315	#120	—	2	4	no	—
316	#120	—	2	2	no	—
317	C₄×Q₈	D₄×C₁₉	1	2	yes	—
318	C₄×D₄	—	2	4	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	D₄×C₁₉	1	2	yes	—
322	#117	—	2	1	no	—
323	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
324	C₂×C₂²⋊C₄	—	2	4	no	—
325	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
328	C₄⋊C₈	—	2	2	no	—
329	C₄⋊C₈	—	2	2	no	—
330	C₂²⋊C₈	—	2	2	no	—
331	C₂²⋊C₈	—	2	2	no	—
332	#97	—	2	2	no	—
333	C₄×C₈	—	2	2	no	—
334	C₁₉	#8475	1	1	yes	characteristic, direct product factor, Sylow
335	C₂⁴	—	2	2	no	—
336	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
337	#41	—	2	2	no	—
338	#41	—	2	2	no	—
339	#41	—	4	4	no	—
340	#41	—	4	4	no	—
341	#41	—	4	1	no	—
342	#41	—	4	1	no	—
343	#41	—	4	1	no	—
344	#41	—	4	1	no	—
345	#41	—	4	8	no	—
346	#41	—	4	2	no	—
347	#41	—	4	2	no	—
348	#41	—	4	2	no	—
349	#41	—	4	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	4	1	no	—
354	C₂×Q₈	—	4	1	no	—
355	C₂×Q₈	—	4	4	no	—
356	C₂×Q₈	—	4	2	no	—
357	C₂×Q₈	—	4	2	no	—
358	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
359	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
360	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	1	no	—
373	C₂×D₄	—	4	1	no	—
374	C₂×D₄	—	4	8	no	—
375	C₂×D₄	—	4	2	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
378	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
379	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
388	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
390	C₂×C₈	—	4	2	no	—
391	C₂×C₈	—	4	2	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	2	4	no	—
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	4	no	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	2	no	—
406	C₄²	C₂×D₄×C₁₉	1	2	yes	—
407	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
408	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
409	C₂³	—	2	1	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	4	4	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	4	no	—
416	C₂³	—	8	4	no	—
417	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
418	Q₈	—	2	1	no	—
419	Q₈	—	4	1	no	—
420	Q₈	—	4	1	no	—
421	Q₈	—	4	2	no	—
422	Q₈	—	4	4	no	—
423	Q₈	—	4	1	no	—
424	Q₈	—	4	1	no	—
425	Q₈	C₁₉×#100	1	2	yes	—
426	D₄	—	2	4	no	—
427	D₄	—	2	1	no	—
428	D₄	—	4	1	no	—
429	D₄	—	4	1	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	4	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	4	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	4	no	—
436	D₄	—	4	1	no	—
437	D₄	—	4	1	no	—
438	D₄	—	8	2	no	—
439	D₄	—	8	4	no	—
440	D₄	C₁₉×#100	1	2	yes	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	8	2	no	—
459	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
460	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
461	C₂×C₄	C₁₉×#120	1	2	yes	—
462	C₂×C₄	C₁₉×#120	1	2	yes	—
463	C₈	—	8	2	no	—
464	C₈	—	8	2	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	16	2	no	—
476	C₂²	—	16	4	no	—
477	C₂²	C₁₉×#379	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	4	1	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	C₂×C₁₉×#100	1	1	yes	characteristic
487	C₄	C₂×C₁₉×#100	1	1	yes	characteristic
488	C₂	—	4	1	no	—
489	C₂	—	4	2	no	—
490	C₂	—	8	1	no	—
491	C₂	—	8	2	no	—
492	C₂	—	8	1	no	—
493	C₂	C₁₉×#1783	1	1	yes	characteristic
494	C₂	C₁₉×#1794	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3500	C₂
LCS	G ▷ C₂²×C₄ ▷ 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
2. C₁₉×#1543	C₂	semidirect
3. C₁₉×#1536	C₂	semidirect
4. C₁₉×#1488	C₂	semidirect
5. C₁₉×#1469	C₂	semidirect
20. C₁₉×#432	C₂²	semidirect
21. C₁₉×#431	C₂²	semidirect
161. #8475	C₁₉	direct (N × H)
219. #1543	C₂×C₁₉	semidirect
220. #1536	C₂×C₁₉	semidirect
221. #1488	C₂×C₁₉	semidirect
222. #1469	C₂×C₁₉	semidirect
260. #432	C₂²×C₁₉	semidirect
261. #431	C₂²×C₁₉	semidirect
334. C₁₉	#8475	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×#3500	2
C₁₉×#1543	2
C₁₉×#1536	2
C₁₉×#1488	2
C₁₉×#1469	2
#8475	19

Subgroups — C19×#8475 #18014434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8475 #18014434