Subgroups — C₁₉×#9520 #18015479

Order 4864.

772 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3003	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2976	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1786	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1783	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1513	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1305	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1293	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
10	C₁₉×#525	C₂²	1	1	yes	characteristic
11	C₁₉×#450	—	2	1	no	—
12	C₁₉×#450	C₄	1	2	yes	complemented
13	C₁₉×#447	—	2	1	no	—
14	C₁₉×#447	C₄	1	2	yes	complemented
15	C₁₉×#436	—	2	1	no	—
16	C₁₉×#435	—	2	1	no	—
17	C₁₉×#435	—	2	1	no	—
18	C₈×D₄×C₁₉	—	2	1	no	—
19	C₁₉×#433	—	2	1	no	—
20	C₁₉×#418	—	2	1	no	—
21	C₂×C₁₉×#102	—	2	1	no	—
22	C₂×C₁₉×#102	—	2	1	no	—
23	C₂×C₁₉×#100	—	2	1	no	—
24	C₂×C₁₉×#100	—	2	1	no	—
25	C₁₉×#408	—	2	1	no	—
26	C₁₉×#407	C₂²	1	1	yes	characteristic
27	C₁₉×#407	C₂²	1	1	yes	characteristic
28	C₁₉×#407	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₁₉×#380	C₂²	1	1	yes	characteristic
31	C₁₉×#328	—	2	1	no	—
32	C₁₉×#327	—	2	1	no	—
33	C₂⁵×C₁₉	—	2	1	no	—
34	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₉	—	2	1	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	—	2	1	no	—
39	C₂²×D₄×C₁₉	—	2	1	no	—
40	C₂²×D₄×C₁₉	—	4	2	no	—
41	C₂²×D₄×C₁₉	—	4	2	no	—
42	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
45	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
46	C₂×SD₁₆×C₁₉	—	2	2	no	—
47	C₂×D₈×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	2	1	no	—
49	C₂×M₁₆×C₁₉	—	2	1	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
52	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₉	—	2	1	no	—
54	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
56	C₁₉×#123	—	2	1	no	—
57	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
58	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
59	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
60	C₁₉×#121	D₄	1	1	yes	characteristic
61	C₁₉×#120	—	2	1	no	—
62	C₄×D₄×C₁₉	—	2	1	no	—
63	C₄×D₄×C₁₉	—	2	1	no	—
64	C₁₉×#117	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
67	C₁₉×C₄⋊C₈	—	2	1	no	—
68	C₁₉×C₄⋊C₈	—	2	1	no	—
69	C₁₉×#102	—	2	2	no	—
70	C₁₉×#102	—	2	2	no	—
71	C₁₉×#102	—	4	2	no	—
72	C₁₉×#102	—	4	2	no	—
73	C₁₉×#100	—	4	2	no	—
74	C₁₉×#100	—	4	2	no	—
75	C₁₉×C₂²⋊C₈	—	2	1	no	—
76	C₁₉×C₂²⋊C₈	—	2	1	no	—
77	C₁₉×C₂²⋊C₈	—	2	1	no	—
78	C₁₉×C₂²⋊C₈	—	2	1	no	—
79	C₁₉×C₂²⋊C₈	—	2	1	no	—
80	C₁₉×C₂²⋊C₈	—	2	1	no	—
81	C₁₉×C₂²⋊C₈	—	2	1	no	—
82	C₁₉×C₂²⋊C₈	—	2	1	no	—
83	C₁₉×C₂²⋊C₈	—	2	1	no	—
84	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
85	C₁₉×#97	—	2	1	no	—
86	C₄×C₈×C₁₉	—	2	1	no	—
87	C₁₉×#95	—	2	1	no	—
88	C₂⁴×C₁₉	—	2	2	no	—
89	C₂⁴×C₁₉	—	4	4	no	—
90	C₂⁴×C₁₉	—	4	1	no	—
91	C₂⁴×C₁₉	—	4	1	no	—
92	C₂⁴×C₁₉	—	8	1	no	—
93	C₂⁴×C₁₉	—	8	1	no	—
94	C₂⁴×C₁₉	—	8	2	no	—
95	C₂⁴×C₁₉	#41	1	1	yes	characteristic
96	#41×C₁₉	—	4	1	no	—
97	#41×C₁₉	—	4	1	no	—
98	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×D₄×C₁₉	—	2	2	no	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	2	2	no	—
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	1	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	2	no	—
110	C₂×D₄×C₁₉	—	4	1	no	—
111	C₂×D₄×C₁₉	—	4	1	no	—
112	C₂×D₄×C₁₉	—	4	1	no	—
113	C₂×D₄×C₁₉	—	4	1	no	—
114	C₂×D₄×C₁₉	—	4	1	no	—
115	C₂×D₄×C₁₉	—	4	1	no	—
116	C₂×D₄×C₁₉	—	4	4	no	—
117	C₂×D₄×C₁₉	—	4	4	no	—
118	C₂×D₄×C₁₉	—	4	4	no	—
119	C₂×D₄×C₁₉	—	4	1	no	—
120	C₂×D₄×C₁₉	—	4	1	no	—
121	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	4	1	no	—
124	C₂²×C₄×C₁₉	—	4	1	no	—
125	C₂²×C₄×C₁₉	—	4	1	no	—
126	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
132	SD₁₆×C₁₉	—	4	4	no	—
133	D₈×C₁₉	—	4	4	no	—
134	M₁₆×C₁₉	—	4	1	no	—
135	M₁₆×C₁₉	—	4	1	no	—
136	M₁₆×C₁₉	—	4	1	no	—
137	M₁₆×C₁₉	—	4	1	no	—
138	M₁₆×C₁₉	—	4	1	no	—
139	M₁₆×C₁₉	—	4	1	no	—
140	M₁₆×C₁₉	—	8	1	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	2	1	no	—
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	—	2	1	no	—
145	C₂×C₈×C₁₉	—	2	1	no	—
146	C₂×C₈×C₁₉	—	4	1	no	—
147	C₂×C₈×C₁₉	—	4	1	no	—
148	C₂×C₈×C₁₉	—	4	1	no	—
149	C₂×C₈×C₁₉	—	8	1	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	4	1	no	—
153	C₄⋊C₄×C₁₉	—	4	1	no	—
154	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
155	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²⋊C₄×C₁₉	—	2	1	no	—
157	C₂²⋊C₄×C₁₉	—	2	1	no	—
158	C₂²⋊C₄×C₁₉	—	2	1	no	—
159	C₂²⋊C₄×C₁₉	—	2	1	no	—
160	C₂²⋊C₄×C₁₉	—	2	1	no	—
161	C₂²⋊C₄×C₁₉	—	8	1	no	—
162	C₄²×C₁₉	—	2	1	no	—
163	#9520	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₁₉	—	2	1	no	—
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	—	2	4	no	—
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	—	4	1	no	—
169	C₂³×C₁₉	—	4	1	no	—
170	C₂³×C₁₉	—	4	2	no	—
171	C₂³×C₁₉	—	4	2	no	—
172	C₂³×C₁₉	—	4	2	no	—
173	C₂³×C₁₉	—	4	2	no	—
174	C₂³×C₁₉	—	4	2	no	—
175	C₂³×C₁₉	—	4	2	no	—
176	C₂³×C₁₉	—	8	2	no	—
177	C₂³×C₁₉	—	8	2	no	—
178	C₂³×C₁₉	—	8	2	no	—
179	C₂³×C₁₉	—	8	1	no	—
180	C₂³×C₁₉	—	8	1	no	—
181	C₂³×C₁₉	—	8	2	no	—
182	C₂³×C₁₉	—	8	8	no	—
183	C₂³×C₁₉	—	8	8	no	—
184	C₂³×C₁₉	—	8	1	no	—
185	C₂³×C₁₉	—	8	1	no	—
186	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
187	C₂³×C₁₉	#121	1	1	yes	characteristic
188	C₂³×C₁₉	#123	1	1	yes	characteristic
189	Q₈×C₁₉	—	4	1	no	—
190	D₄×C₁₉	—	2	4	no	—
191	D₄×C₁₉	—	2	4	no	—
192	D₄×C₁₉	—	4	1	no	—
193	D₄×C₁₉	—	4	2	no	—
194	D₄×C₁₉	—	4	2	no	—
195	D₄×C₁₉	—	4	2	no	—
196	D₄×C₁₉	—	4	2	no	—
197	D₄×C₁₉	—	4	1	no	—
198	D₄×C₁₉	—	4	1	no	—
199	D₄×C₁₉	—	4	2	no	—
200	D₄×C₁₉	—	4	2	no	—
201	D₄×C₁₉	—	8	1	no	—
202	D₄×C₁₉	—	8	1	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	8	1	no	—
218	C₂×C₄×C₁₉	—	8	1	no	—
219	C₂×C₄×C₁₉	—	8	1	no	—
220	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
224	C₈×C₁₉	—	4	2	no	—
225	C₈×C₁₉	—	4	1	no	—
226	C₈×C₁₉	—	4	1	no	—
227	C₈×C₁₉	—	4	1	no	—
228	C₈×C₁₉	—	4	1	no	—
229	C₈×C₁₉	—	8	1	no	—
230	#3003	C₂×C₁₉	1	1	yes	characteristic
231	#2976	C₂×C₁₉	1	1	yes	characteristic, complemented
232	#1786	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#1783	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#1513	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#1305	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#1293	C₂×C₁₉	1	1	yes	characteristic, complemented
237	C₂²×C₁₉	—	2	1	no	—
238	C₂²×C₁₉	—	2	1	no	—
239	C₂²×C₁₉	—	2	1	no	—
240	C₂²×C₁₉	—	2	1	no	—
241	C₂²×C₁₉	—	2	1	no	—
242	C₂²×C₁₉	—	2	1	no	—
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	2	1	no	—
245	C₂²×C₁₉	—	4	2	no	—
246	C₂²×C₁₉	—	4	2	no	—
247	C₂²×C₁₉	—	4	1	no	—
248	C₂²×C₁₉	—	4	4	no	—
249	C₂²×C₁₉	—	4	1	no	—
250	C₂²×C₁₉	—	4	1	no	—
251	C₂²×C₁₉	—	8	2	no	—
252	C₂²×C₁₉	—	8	2	no	—
253	C₂²×C₁₉	—	8	2	no	—
254	C₂²×C₁₉	—	8	2	no	—
255	C₂²×C₁₉	—	8	4	no	—
256	C₂²×C₁₉	—	8	4	no	—
257	C₂²×C₁₉	—	8	4	no	—
258	C₂²×C₁₉	—	8	4	no	—
259	C₂²×C₁₉	—	8	2	no	—
260	C₂²×C₁₉	—	8	2	no	—
261	C₂²×C₁₉	#386	1	1	yes	characteristic
262	C₂²×C₁₉	#471	1	1	yes	characteristic
263	C₂²×C₁₉	#472	1	1	yes	characteristic
264	C₄×C₁₉	—	2	1	no	—
265	C₄×C₁₉	—	2	1	no	—
266	C₄×C₁₉	—	2	1	no	—
267	C₄×C₁₉	—	4	1	no	—
268	C₄×C₁₉	—	4	1	no	—
269	C₄×C₁₉	—	4	1	no	—
270	C₄×C₁₉	—	16	1	no	—
271	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
272	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
273	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
274	C₂×AGL(1,ℤ/8)	—	2	1	no	—
275	#525	C₂²×C₁₉	1	1	yes	characteristic
276	#450	—	2	1	no	—
277	#450	C₄×C₁₉	1	2	yes	complemented
278	#447	—	2	1	no	—
279	#447	C₄×C₁₉	1	2	yes	complemented
280	#436	—	2	1	no	—
281	#435	—	2	1	no	—
282	#435	—	2	1	no	—
283	C₈×D₄	—	2	1	no	—
284	#433	—	2	1	no	—
285	#418	—	2	1	no	—
286	C₂×#102	—	2	1	no	—
287	C₂×#102	—	2	1	no	—
288	C₂×#100	—	2	1	no	—
289	C₂×#100	—	2	1	no	—
290	#408	—	2	1	no	—
291	#407	C₂²×C₁₉	1	1	yes	characteristic
292	#407	C₂²×C₁₉	1	1	yes	characteristic
293	#407	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
295	#380	C₂²×C₁₉	1	1	yes	characteristic
296	#328	—	2	1	no	—
297	#327	—	2	1	no	—
298	C₂×C₁₉	—	2	1	no	—
299	C₂×C₁₉	—	2	1	no	—
300	C₂×C₁₉	—	4	1	no	—
301	C₂×C₁₉	—	4	1	no	—
302	C₂×C₁₉	—	8	1	no	—
303	C₂×C₁₉	—	8	4	no	—
304	C₂×C₁₉	#1889	1	1	yes	characteristic
305	C₂×C₁₉	#1903	1	1	yes	characteristic
306	C₂×C₁₉	#1907	1	1	yes	characteristic
307	C₂⁵	—	2	1	no	—
308	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
309	C₂²×D₄	—	2	1	no	—
310	C₂²×D₄	—	2	1	no	—
311	C₂²×D₄	—	2	1	no	—
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	—	2	1	no	—
314	C₂²×D₄	—	4	2	no	—
315	C₂²×D₄	—	4	2	no	—
316	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
317	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
318	AGL(1,ℤ/8)	—	4	2	no	—
319	AGL(1,ℤ/8)	—	4	2	no	—
320	C₂×SD₁₆	—	2	2	no	—
321	C₂×D₈	—	2	2	no	—
322	C₂×M₁₆	—	2	1	no	—
323	C₂×M₁₆	—	2	1	no	—
324	C₂×M₁₆	—	2	1	no	—
325	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
326	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
327	C₂²×C₈	—	2	1	no	—
328	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
329	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
330	#123	—	2	1	no	—
331	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
332	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
333	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
334	#121	D₄×C₁₉	1	1	yes	characteristic
335	#120	—	2	1	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	2	1	no	—
338	#117	D₄×C₁₉	1	1	yes	characteristic
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₄⋊C₈	—	2	1	no	—
342	C₄⋊C₈	—	2	1	no	—
343	#102	—	2	2	no	—
344	#102	—	2	2	no	—
345	#102	—	4	2	no	—
346	#102	—	4	2	no	—
347	#100	—	4	2	no	—
348	#100	—	4	2	no	—
349	C₂²⋊C₈	—	2	1	no	—
350	C₂²⋊C₈	—	2	1	no	—
351	C₂²⋊C₈	—	2	1	no	—
352	C₂²⋊C₈	—	2	1	no	—
353	C₂²⋊C₈	—	2	1	no	—
354	C₂²⋊C₈	—	2	1	no	—
355	C₂²⋊C₈	—	2	1	no	—
356	C₂²⋊C₈	—	2	1	no	—
357	C₂²⋊C₈	—	2	1	no	—
358	C₂²⋊C₈	C₂×C₄×C₁₉	1	2	yes	—
359	#97	—	2	1	no	—
360	C₄×C₈	—	2	1	no	—
361	#95	—	2	1	no	—
362	C₁₉	#9520	1	1	yes	characteristic, direct product factor, Sylow
363	C₂⁴	—	2	2	no	—
364	C₂⁴	—	4	4	no	—
365	C₂⁴	—	4	1	no	—
366	C₂⁴	—	4	1	no	—
367	C₂⁴	—	8	1	no	—
368	C₂⁴	—	8	1	no	—
369	C₂⁴	—	8	2	no	—
370	C₂⁴	#41×C₁₉	1	1	yes	characteristic
371	#41	—	4	1	no	—
372	#41	—	4	1	no	—
373	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	4	1	no	—
386	C₂×D₄	—	4	1	no	—
387	C₂×D₄	—	4	1	no	—
388	C₂×D₄	—	4	1	no	—
389	C₂×D₄	—	4	1	no	—
390	C₂×D₄	—	4	1	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	—	4	4	no	—
393	C₂×D₄	—	4	4	no	—
394	C₂×D₄	—	4	1	no	—
395	C₂×D₄	—	4	1	no	—
396	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	4	1	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
407	SD₁₆	—	4	4	no	—
408	D₈	—	4	4	no	—
409	M₁₆	—	4	1	no	—
410	M₁₆	—	4	1	no	—
411	M₁₆	—	4	1	no	—
412	M₁₆	—	4	1	no	—
413	M₁₆	—	4	1	no	—
414	M₁₆	—	4	1	no	—
415	M₁₆	—	8	1	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	4	1	no	—
422	C₂×C₈	—	4	1	no	—
423	C₂×C₈	—	4	1	no	—
424	C₂×C₈	—	8	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	4	1	no	—
428	C₄⋊C₄	—	4	1	no	—
429	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
430	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	8	1	no	—
437	C₄²	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	1	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	8	2	no	—
451	C₂³	—	8	2	no	—
452	C₂³	—	8	1	no	—
453	C₂³	—	8	1	no	—
454	C₂³	—	8	2	no	—
455	C₂³	—	8	2	no	—
456	C₂³	—	8	8	no	—
457	C₂³	—	8	8	no	—
458	C₂³	—	8	1	no	—
459	C₂³	—	8	1	no	—
460	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
461	C₂³	C₁₉×#121	1	1	yes	characteristic
462	C₂³	C₁₉×#123	1	1	yes	characteristic
463	Q₈	—	4	1	no	—
464	D₄	—	2	4	no	—
465	D₄	—	2	4	no	—
466	D₄	—	4	1	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	1	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	8	1	no	—
476	D₄	—	8	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	8	1	no	—
492	C₂×C₄	—	8	1	no	—
493	C₂×C₄	—	8	1	no	—
494	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
495	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
496	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
497	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
498	C₈	—	4	2	no	—
499	C₈	—	4	1	no	—
500	C₈	—	4	1	no	—
501	C₈	—	4	1	no	—
502	C₈	—	4	1	no	—
503	C₈	—	8	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	1	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	8	2	no	—
519	C₂²	—	8	2	no	—
520	C₂²	—	8	2	no	—
521	C₂²	—	8	2	no	—
522	C₂²	—	8	4	no	—
523	C₂²	—	8	4	no	—
524	C₂²	—	8	4	no	—
525	C₂²	—	8	4	no	—
526	C₂²	—	8	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	C₁₉×#386	1	1	yes	characteristic
529	C₂²	C₁₉×#471	1	1	yes	characteristic
530	C₂²	C₁₉×#472	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	16	1	no	—
538	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
539	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
540	C₂	—	2	1	no	—
541	C₂	—	2	1	no	—
542	C₂	—	4	1	no	—
543	C₂	—	4	1	no	—
544	C₂	—	8	1	no	—
545	C₂	—	8	4	no	—
546	C₂	C₁₉×#1889	1	1	yes	characteristic
547	C₂	C₁₉×#1903	1	1	yes	characteristic
548	C₂	C₁₉×#1907	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₁₉×#3003	C₂
LCS	G ▷ C₂²×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×#2976	C₂	semidirect
3. C₁₉×#1786	C₂	semidirect
4. C₁₉×#1783	C₂	semidirect
5. C₁₉×#1513	C₂	semidirect
6. C₁₉×#1305	C₂	semidirect
7. C₁₉×#1293	C₂	semidirect
12. C₁₉×#450	C₄	semidirect
14. C₁₉×#447	C₄	semidirect
163. #9520	C₁₉	direct (N × H)
231. #2976	C₂×C₁₉	semidirect
232. #1786	C₂×C₁₉	semidirect
233. #1783	C₂×C₁₉	semidirect
234. #1513	C₂×C₁₉	semidirect
235. #1305	C₂×C₁₉	semidirect
236. #1293	C₂×C₁₉	semidirect
277. #450	C₄×C₁₉	semidirect
279. #447	C₄×C₁₉	semidirect
362. C₁₉	#9520	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×#3003	2
C₁₉×#2976	2
C₁₉×#1786	2
C₁₉×#1783	2
C₁₉×#1513	2
C₁₉×#1305	2
C₁₉×#1293	2
#9520	19

Subgroups — C19×#9520 #18015479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9520 #18015479