Subgroups — C₁₉×#10340 #18016299

Order 4864.

900 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2659	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#1786	C₂	1	2	yes	maximal
3	C₁₉×#1438	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1294	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1280	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
8	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
9	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
10	C₂×C₁₉×#102	—	2	2	no	—
11	C₂×C₁₉×#102	—	2	2	no	—
12	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
13	C₁₉×#398	—	2	2	no	—
14	C₁₉×#395	—	2	2	no	—
15	C₁₉×#380	—	2	1	no	—
16	C₁₉×#380	C₂²	1	2	yes	—
17	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
19	C₂⁵×C₁₉	—	2	1	no	—
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂²×D₄×C₁₉	—	2	2	no	—
22	C₂²×D₄×C₁₉	—	2	2	no	—
23	C₂²×D₄×C₁₉	—	2	1	no	—
24	C₂²×D₄×C₁₉	—	4	2	no	—
25	C₂²×D₄×C₁₉	—	4	2	no	—
26	C₂²×D₄×C₁₉	Q₈	1	2	yes	complemented
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×C₈×C₁₉	—	2	2	no	—
32	C₁₉×C₂²⋊Q₈	—	4	2	no	—
33	C₁₉×C₂²⋊Q₈	—	4	2	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
39	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
47	C₁₉×#102	—	4	4	no	—
48	C₁₉×#102	—	4	4	no	—
49	C₁₉×C₂²⋊C₈	—	2	2	no	—
50	C₁₉×C₂²⋊C₈	—	2	2	no	—
51	C₁₉×#95	—	2	2	no	—
52	C₁₉×#95	—	2	2	no	—
53	C₁₉×#95	—	2	2	no	—
54	C₁₉×#95	—	2	2	no	—
55	C₂⁴×C₁₉	—	2	2	no	—
56	C₂⁴×C₁₉	—	2	2	no	—
57	C₂⁴×C₁₉	—	2	2	no	—
58	C₂⁴×C₁₉	—	4	1	no	—
59	C₂⁴×C₁₉	—	4	1	no	—
60	C₂⁴×C₁₉	—	4	1	no	—
61	C₂⁴×C₁₉	—	4	1	no	—
62	C₂⁴×C₁₉	—	4	1	no	—
63	C₂⁴×C₁₉	—	4	1	no	—
64	C₂⁴×C₁₉	—	4	1	no	—
65	C₂⁴×C₁₉	—	4	1	no	—
66	C₂⁴×C₁₉	—	4	1	no	—
67	C₂⁴×C₁₉	—	4	1	no	—
68	C₂⁴×C₁₉	—	4	1	no	—
69	C₂⁴×C₁₉	—	4	1	no	—
70	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂×Q₈×C₁₉	—	4	2	no	—
72	C₂×Q₈×C₁₉	—	8	1	no	—
73	C₂×Q₈×C₁₉	—	8	1	no	—
74	C₂×D₄×C₁₉	—	2	4	no	—
75	C₂×D₄×C₁₉	—	2	4	no	—
76	C₂×D₄×C₁₉	—	2	4	no	—
77	C₂×D₄×C₁₉	—	4	2	no	—
78	C₂×D₄×C₁₉	—	4	2	no	—
79	C₂×D₄×C₁₉	—	4	4	no	—
80	C₂×D₄×C₁₉	—	4	8	no	—
81	C₂×D₄×C₁₉	—	4	4	no	—
82	C₂×D₄×C₁₉	—	4	2	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	4	1	no	—
92	C₂²×C₄×C₁₉	—	4	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	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	D₈	1	2	yes	—
103	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	#41	1	2	yes	—
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
108	C₂×C₈×C₁₉	—	4	2	no	—
109	C₂×C₈×C₁₉	—	4	2	no	—
110	C₂×C₈×C₁₉	—	4	2	no	—
111	C₄⋊C₄×C₁₉	—	4	2	no	—
112	C₄⋊C₄×C₁₉	—	4	2	no	—
113	C₄⋊C₄×C₁₉	—	4	2	no	—
114	C₄⋊C₄×C₁₉	—	4	4	no	—
115	C₄⋊C₄×C₁₉	—	8	1	no	—
116	C₄⋊C₄×C₁₉	—	8	1	no	—
117	C₂²⋊C₄×C₁₉	—	4	8	no	—
118	C₂²⋊C₄×C₁₉	—	4	8	no	—
119	C₂²⋊C₄×C₁₉	—	4	2	no	—
120	C₂²⋊C₄×C₁₉	—	4	2	no	—
121	#10340	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂³×C₁₉	—	2	1	no	—
123	C₂³×C₁₉	—	2	1	no	—
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	—	2	1	no	—
126	C₂³×C₁₉	—	2	4	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	—	4	2	no	—
130	C₂³×C₁₉	—	4	2	no	—
131	C₂³×C₁₉	—	4	2	no	—
132	C₂³×C₁₉	—	4	2	no	—
133	C₂³×C₁₉	—	4	2	no	—
134	C₂³×C₁₉	—	4	2	no	—
135	C₂³×C₁₉	—	4	2	no	—
136	C₂³×C₁₉	—	4	2	no	—
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	—	4	2	no	—
143	C₂³×C₁₉	—	4	2	no	—
144	C₂³×C₁₉	—	4	2	no	—
145	C₂³×C₁₉	—	8	1	no	—
146	C₂³×C₁₉	—	8	1	no	—
147	C₂³×C₁₉	—	8	1	no	—
148	C₂³×C₁₉	—	8	1	no	—
149	C₂³×C₁₉	—	8	1	no	—
150	C₂³×C₁₉	—	8	1	no	—
151	C₂³×C₁₉	—	8	1	no	—
152	C₂³×C₁₉	—	8	1	no	—
153	C₂³×C₁₉	—	8	1	no	—
154	C₂³×C₁₉	—	8	1	no	—
155	C₂³×C₁₉	—	8	1	no	—
156	C₂³×C₁₉	—	8	1	no	—
157	C₂³×C₁₉	—	8	1	no	—
158	C₂³×C₁₉	—	8	1	no	—
159	C₂³×C₁₉	—	8	1	no	—
160	C₂³×C₁₉	—	8	1	no	—
161	C₂³×C₁₉	#120	1	1	yes	characteristic
162	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
163	C₂³×C₁₉	#124	1	1	yes	characteristic
164	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
165	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
166	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂³×C₁₉	#137	1	1	yes	characteristic
168	Q₈×C₁₉	—	8	4	no	—
169	D₄×C₁₉	—	2	8	no	—
170	D₄×C₁₉	—	4	4	no	—
171	D₄×C₁₉	—	4	4	no	—
172	D₄×C₁₉	—	4	4	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	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	2	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	8	1	no	—
196	C₂×C₄×C₁₉	—	8	1	no	—
197	C₂×C₄×C₁₉	—	8	1	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	C₂²⋊Q₈	1	2	yes	—
202	C₂×C₄×C₁₉	#124	1	2	yes	—
203	C₈×C₁₉	—	8	2	no	—
204	#2659	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#1786	C₂×C₁₉	1	2	yes	—
206	#1438	C₂×C₁₉	1	1	yes	characteristic
207	#1294	C₂×C₁₉	1	2	yes	complemented
208	#1280	C₂×C₁₉	1	1	yes	characteristic, complemented
209	C₂²×C₁₉	—	2	1	no	—
210	C₂²×C₁₉	—	2	1	no	—
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	—	2	1	no	—
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	2	1	no	—
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	2	1	no	—
221	C₂²×C₁₉	—	4	4	no	—
222	C₂²×C₁₉	—	4	4	no	—
223	C₂²×C₁₉	—	4	4	no	—
224	C₂²×C₁₉	—	8	2	no	—
225	C₂²×C₁₉	—	8	2	no	—
226	C₂²×C₁₉	—	8	2	no	—
227	C₂²×C₁₉	—	8	2	no	—
228	C₂²×C₁₉	—	8	2	no	—
229	C₂²×C₁₉	—	8	2	no	—
230	C₂²×C₁₉	—	8	2	no	—
231	C₂²×C₁₉	—	8	2	no	—
232	C₂²×C₁₉	—	8	2	no	—
233	C₂²×C₁₉	—	8	2	no	—
234	C₂²×C₁₉	—	8	2	no	—
235	C₂²×C₁₉	—	8	2	no	—
236	C₂²×C₁₉	#393	1	1	yes	characteristic
237	C₂²×C₁₉	#447	1	1	yes	characteristic
238	C₂²×C₁₉	#448	1	1	yes	characteristic
239	C₂²×C₁₉	#453	1	1	yes	characteristic
240	C₂²×C₁₉	#454	1	1	yes	characteristic
241	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
242	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
243	C₂²×C₁₉	#474	1	1	yes	characteristic
244	C₂²×C₁₉	#476	1	1	yes	characteristic
245	C₂²×C₁₉	#486	1	1	yes	characteristic
246	C₂²×C₁₉	#489	1	1	yes	characteristic
247	C₄×C₁₉	—	2	2	no	—
248	C₄×C₁₉	—	2	2	no	—
249	C₄×C₁₉	—	4	2	no	—
250	C₄×C₁₉	—	4	2	no	—
251	C₄×C₁₉	—	8	2	no	—
252	C₄×C₁₉	—	8	2	no	—
253	C₄×C₁₉	—	8	2	no	—
254	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×C₂²⋊Q₈	—	2	1	no	—
256	C₂²×C₂²⋊C₄	—	2	1	no	—
257	C₂²×C₂²⋊C₄	—	2	1	no	—
258	C₂×#102	—	2	2	no	—
259	C₂×#102	—	2	2	no	—
260	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
261	#398	—	2	2	no	—
262	#395	—	2	2	no	—
263	#380	—	2	1	no	—
264	#380	C₂²×C₁₉	1	2	yes	—
265	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
267	C₂×C₁₉	—	2	1	no	—
268	C₂×C₁₉	—	2	1	no	—
269	C₂×C₁₉	—	2	1	no	—
270	C₂×C₁₉	—	2	1	no	—
271	C₂×C₁₉	—	8	4	no	—
272	C₂×C₁₉	#1595	1	1	yes	characteristic
273	C₂×C₁₉	#1596	1	1	yes	characteristic
274	C₂×C₁₉	#1598	1	1	yes	characteristic
275	C₂×C₁₉	#1599	1	1	yes	characteristic
276	C₂×C₁₉	#2023	1	1	yes	characteristic
277	C₂×C₁₉	#2027	1	1	yes	characteristic
278	C₂×C₁₉	#2029	1	1	yes	characteristic
279	C₂⁵	—	2	1	no	—
280	C₂²×Q₈	—	2	1	no	—
281	C₂²×D₄	—	2	2	no	—
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	—	2	1	no	—
284	C₂²×D₄	—	4	2	no	—
285	C₂²×D₄	—	4	2	no	—
286	C₂²×D₄	Q₈×C₁₉	1	2	yes	complemented
287	C₂³×C₄	—	2	1	no	—
288	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
289	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
291	C₂²×C₈	—	2	2	no	—
292	C₂²⋊Q₈	—	4	2	no	—
293	C₂²⋊Q₈	—	4	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
299	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	4	2	no	—
302	C₂×C₂²⋊C₄	—	4	2	no	—
303	C₂×C₂²⋊C₄	—	4	2	no	—
304	C₂×C₂²⋊C₄	—	4	2	no	—
305	C₂×C₂²⋊C₄	—	4	2	no	—
306	C₂×C₂²⋊C₄	—	4	2	no	—
307	#102	—	4	4	no	—
308	#102	—	4	4	no	—
309	C₂²⋊C₈	—	2	2	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	C₁₉	#10340	1	1	yes	characteristic, direct product factor, Sylow
316	C₂⁴	—	2	2	no	—
317	C₂⁴	—	2	2	no	—
318	C₂⁴	—	2	2	no	—
319	C₂⁴	—	4	1	no	—
320	C₂⁴	—	4	1	no	—
321	C₂⁴	—	4	1	no	—
322	C₂⁴	—	4	1	no	—
323	C₂⁴	—	4	1	no	—
324	C₂⁴	—	4	1	no	—
325	C₂⁴	—	4	1	no	—
326	C₂⁴	—	4	1	no	—
327	C₂⁴	—	4	1	no	—
328	C₂⁴	—	4	1	no	—
329	C₂⁴	—	4	1	no	—
330	C₂⁴	—	4	1	no	—
331	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	—	8	1	no	—
334	C₂×Q₈	—	8	1	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	4	no	—
341	C₂×D₄	—	4	8	no	—
342	C₂×D₄	—	4	4	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×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	—	4	1	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	—	4	1	no	—
362	C₂²×C₄	—	4	1	no	—
363	C₂²×C₄	D₈×C₁₉	1	2	yes	—
364	C₂²×C₄	SD₁₆×C₁₉	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
366	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
367	C₂²×C₄	#41×C₁₉	1	2	yes	—
368	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
369	C₂×C₈	—	4	2	no	—
370	C₂×C₈	—	4	2	no	—
371	C₂×C₈	—	4	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	4	no	—
376	C₄⋊C₄	—	8	1	no	—
377	C₄⋊C₄	—	8	1	no	—
378	C₂²⋊C₄	—	4	8	no	—
379	C₂²⋊C₄	—	4	8	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	8	1	no	—
406	C₂³	—	8	1	no	—
407	C₂³	—	8	1	no	—
408	C₂³	—	8	1	no	—
409	C₂³	—	8	1	no	—
410	C₂³	—	8	1	no	—
411	C₂³	—	8	1	no	—
412	C₂³	—	8	1	no	—
413	C₂³	—	8	1	no	—
414	C₂³	—	8	1	no	—
415	C₂³	—	8	1	no	—
416	C₂³	—	8	1	no	—
417	C₂³	—	8	1	no	—
418	C₂³	—	8	1	no	—
419	C₂³	—	8	1	no	—
420	C₂³	—	8	1	no	—
421	C₂³	C₁₉×#120	1	1	yes	characteristic
422	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
423	C₂³	C₁₉×#124	1	1	yes	characteristic
424	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
425	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
426	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
427	C₂³	C₁₉×#137	1	1	yes	characteristic
428	Q₈	—	8	4	no	—
429	D₄	—	2	8	no	—
430	D₄	—	4	4	no	—
431	D₄	—	4	4	no	—
432	D₄	—	4	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	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	—	8	1	no	—
461	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
462	C₂×C₄	C₁₉×#124	1	2	yes	—
463	C₈	—	8	2	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	2	no	—
481	C₂²	—	8	2	no	—
482	C₂²	—	8	2	no	—
483	C₂²	—	8	2	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	—	8	2	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	C₁₉×#393	1	1	yes	characteristic
492	C₂²	C₁₉×#447	1	1	yes	characteristic
493	C₂²	C₁₉×#448	1	1	yes	characteristic
494	C₂²	C₁₉×#453	1	1	yes	characteristic
495	C₂²	C₁₉×#454	1	1	yes	characteristic
496	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
497	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
498	C₂²	C₁₉×#474	1	1	yes	characteristic
499	C₂²	C₁₉×#476	1	1	yes	characteristic
500	C₂²	C₁₉×#486	1	1	yes	characteristic
501	C₂²	C₁₉×#489	1	1	yes	characteristic
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	8	2	no	—
507	C₄	—	8	2	no	—
508	C₄	—	8	2	no	—
509	C₂	—	2	1	no	—
510	C₂	—	2	1	no	—
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	8	4	no	—
514	C₂	C₁₉×#1595	1	1	yes	characteristic
515	C₂	C₁₉×#1596	1	1	yes	characteristic
516	C₂	C₁₉×#1598	1	1	yes	characteristic
517	C₂	C₁₉×#1599	1	1	yes	characteristic
518	C₂	C₁₉×#2023	1	1	yes	characteristic
519	C₂	C₁₉×#2027	1	1	yes	characteristic
520	C₂	C₁₉×#2029	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂³×D₄×C₁₉	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. C₁₉×#2659	C₂	semidirect
4. C₁₉×#1294	C₂	semidirect
5. C₁₉×#1280	C₂	semidirect
26. C₂²×D₄×C₁₉	Q₈	semidirect
121. #10340	C₁₉	direct (N × H)
204. #2659	C₂×C₁₉	semidirect
207. #1294	C₂×C₁₉	semidirect
208. #1280	C₂×C₁₉	semidirect
286. C₂²×D₄	Q₈×C₁₉	semidirect
315. C₁₉	#10340	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×#2659	2
C₁₉×#1786	2
C₁₉×#1438	2
C₁₉×#1294	2
C₁₉×#1280	2
#10340	19

Subgroups — C19×#10340 #18016299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10340 #18016299