Subgroups — C₁₉×#18315 #18024274

Order 4864.

868 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3461	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3232	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2634	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1617	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1616	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1615	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1611	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1610	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1609	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1521	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1461	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#544	C₂²	1	1	yes	characteristic
13	C₁₉×#542	—	2	2	no	—
14	C₁₉×#541	—	2	2	no	—
15	C₁₉×#539	—	2	1	no	—
16	C₁₉×#539	C₂²	1	2	yes	—
17	C₁₉×#537	C₂²	1	1	yes	characteristic
18	C₁₉×#536	—	2	1	no	—
19	C₁₉×#533	—	2	2	no	—
20	C₁₉×#529	—	2	2	no	—
21	C₁₉×#529	—	2	1	no	—
22	C₁₉×#529	C₂²	1	2	yes	—
23	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
24	C₄×#41×C₁₉	—	2	1	no	—
25	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#499	—	2	2	no	—
27	C₁₉×#488	—	2	2	no	—
28	C₁₉×#484	C₂²	1	2	yes	—
29	C₁₉×#483	C₂²	1	2	yes	—
30	C₁₉×#481	C₂²	1	2	yes	—
31	C₁₉×#480	C₂²	1	2	yes	—
32	C₁₉×#479	—	2	2	no	—
33	C₁₉×#478	—	2	2	no	—
34	C₁₉×#431	C₂²	1	2	yes	—
35	C₁₉×#400	—	2	1	no	—
36	C₁₉×#400	C₂²	1	1	yes	characteristic
37	C₁₉×#400	C₂²	1	1	yes	characteristic
38	C₁₉×#398	C₂²	1	1	yes	characteristic
39	C₁₉×#398	C₂²	1	1	yes	characteristic
40	C₁₉×#395	—	2	1	no	—
41	C₁₉×#387	—	2	1	no	—
42	C₁₉×#387	—	2	1	no	—
43	C₁₉×#383	C₂²	1	1	yes	characteristic
44	C₁₉×#328	C₂²	1	2	yes	—
45	C₁₉×#328	C₂²	1	2	yes	—
46	C₁₉×#327	C₂²	1	2	yes	—
47	C₁₉×#327	C₂²	1	2	yes	—
48	C₁₉×#324	C₂²	1	2	yes	—
49	C₁₉×#324	C₂²	1	1	yes	characteristic
50	C₁₉×#324	C₂²	1	1	yes	characteristic
51	C₂×#41×C₁₉	—	2	1	no	—
52	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
53	C₁₉×C₄⋊Q₈	—	2	2	no	—
54	C₁₉×C₄⋊Q₈	—	2	2	no	—
55	C₁₉×#126	—	2	2	no	—
56	C₁₉×#126	—	2	2	no	—
57	C₁₉×#126	—	2	2	no	—
58	C₁₉×#126	—	2	2	no	—
59	C₁₉×#125	—	2	1	no	—
60	C₁₉×#125	—	2	2	no	—
61	C₁₉×#125	—	2	2	no	—
62	C₁₉×#125	—	2	2	no	—
63	C₁₉×#125	—	2	2	no	—
64	C₁₉×#125	—	2	2	no	—
65	C₁₉×#125	D₄	1	2	yes	—
66	C₁₉×#124	—	2	2	no	—
67	C₁₉×#124	—	2	1	no	—
68	C₁₉×#124	D₄	1	2	yes	—
69	C₁₉×#123	—	2	2	no	—
70	C₁₉×#123	—	2	2	no	—
71	C₁₉×#123	—	2	2	no	—
72	C₁₉×#123	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	—	2	2	no	—
74	C₁₉×C₂²⋊Q₈	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	2	1	no	—
78	C₁₉×C₂²⋊Q₈	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
80	C₁₉×#121	—	2	2	no	—
81	C₁₉×#121	—	2	1	no	—
82	C₁₉×#121	C₂³	1	2	yes	—
83	C₄×Q₈×C₁₉	—	2	1	no	—
84	C₄×Q₈×C₁₉	—	2	1	no	—
85	C₄×Q₈×C₁₉	—	2	1	no	—
86	C₄×Q₈×C₁₉	—	2	2	no	—
87	C₄×Q₈×C₁₉	—	2	2	no	—
88	C₄×Q₈×C₁₉	D₄	1	2	yes	—
89	C₄×D₄×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	—	2	1	no	—
91	C₄×D₄×C₁₉	—	2	1	no	—
92	C₄×D₄×C₁₉	—	2	2	no	—
93	C₄×D₄×C₁₉	—	2	2	no	—
94	C₄×D₄×C₁₉	D₄	1	2	yes	—
95	C₁₉×#117	—	2	2	no	—
96	C₁₉×#117	—	2	2	no	—
97	C₁₉×#117	—	2	1	no	—
98	C₁₉×#117	—	2	2	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₉	—	2	2	no	—
109	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
112	C₁₉×#107	—	2	2	no	—
113	C₁₉×#107	—	2	2	no	—
114	C₁₉×#106	—	2	2	no	—
115	C₁₉×#106	—	2	2	no	—
116	C₁₉×C₄⋊C₈	—	2	2	no	—
117	C₁₉×#103	—	2	2	no	—
118	C₁₉×#103	—	2	2	no	—
119	C₁₉×#102	—	2	2	no	—
120	C₁₉×#102	—	2	2	no	—
121	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
122	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
123	C₄×C₈×C₁₉	—	2	2	no	—
124	C₁₉×#95	—	2	1	no	—
125	C₁₉×#95	—	2	1	no	—
126	C₁₉×#95	—	2	1	no	—
127	C₁₉×#95	—	2	1	no	—
128	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	—	2	1	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	C₂³	1	1	yes	characteristic
133	C₁₉×#95	C₂³	1	1	yes	characteristic
134	#41×C₁₉	—	4	2	no	—
135	#41×C₁₉	—	4	2	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	2	2	no	—
139	C₂×Q₈×C₁₉	—	2	2	no	—
140	C₂×Q₈×C₁₉	—	4	1	no	—
141	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	4	2	no	—
180	C₄⋊C₄×C₁₉	—	4	1	no	—
181	C₄⋊C₄×C₁₉	—	4	1	no	—
182	C₄⋊C₄×C₁₉	—	4	2	no	—
183	C₄⋊C₄×C₁₉	—	4	2	no	—
184	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
185	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
186	C₂²⋊C₄×C₁₉	—	2	2	no	—
187	C₂²⋊C₄×C₁₉	—	2	2	no	—
188	C₂²⋊C₄×C₁₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₉	—	2	2	no	—
192	C₂²⋊C₄×C₁₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	2	2	no	—
195	C₄²×C₁₉	—	2	2	no	—
196	C₄²×C₁₉	—	2	2	no	—
197	C₄²×C₁₉	—	2	1	no	—
198	C₄²×C₁₉	—	2	2	no	—
199	C₄²×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	—	2	1	no	—
201	C₄²×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	C₂×D₄	1	2	yes	—
203	C₄²×C₁₉	C₂×D₄	1	2	yes	—
204	#18315	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂³×C₁₉	—	2	2	no	—
206	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
207	Q₈×C₁₉	—	4	4	no	—
208	Q₈×C₁₉	—	4	2	no	—
209	Q₈×C₁₉	—	4	2	no	—
210	Q₈×C₁₉	—	8	1	no	—
211	D₄×C₁₉	—	4	2	no	—
212	D₄×C₁₉	—	4	2	no	—
213	D₄×C₁₉	—	4	2	no	—
214	D₄×C₁₉	—	4	2	no	—
215	D₄×C₁₉	—	8	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	4	no	—
231	C₂×C₄×C₁₉	—	4	4	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	8	2	no	—
246	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#120	1	2	yes	—
249	C₂×C₄×C₁₉	#135	1	2	yes	—
250	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
251	C₈×C₁₉	—	4	2	no	—
252	C₈×C₁₉	—	4	2	no	—
253	#3461	C₂×C₁₉	1	1	yes	characteristic
254	#3232	C₂×C₁₉	1	2	yes	complemented
255	#2634	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1617	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1616	C₂×C₁₉	1	1	yes	characteristic
258	#1615	C₂×C₁₉	1	2	yes	complemented
259	#1611	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1610	C₂×C₁₉	1	1	yes	characteristic
261	#1609	C₂×C₁₉	1	2	yes	complemented
262	#1521	C₂×C₁₉	1	2	yes	complemented
263	#1461	C₂×C₁₉	1	1	yes	characteristic, complemented
264	C₂²×C₁₉	—	2	1	no	—
265	C₂²×C₁₉	—	2	1	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	4	2	no	—
268	C₂²×C₁₉	—	4	2	no	—
269	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
270	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
271	C₂²×C₁₉	#575	1	1	yes	characteristic
272	C₄×C₁₉	—	2	2	no	—
273	C₄×C₁₉	—	2	2	no	—
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	2	2	no	—
277	C₄×C₁₉	—	4	1	no	—
278	C₄×C₁₉	—	4	2	no	—
279	C₄×C₁₉	—	4	2	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	4	1	no	—
282	C₄×C₁₉	—	4	2	no	—
283	C₄×C₁₉	—	8	1	no	—
284	C₄×C₁₉	—	8	1	no	—
285	C₄×C₁₉	—	8	1	no	—
286	C₄×C₁₉	—	8	1	no	—
287	#544	C₂²×C₁₉	1	1	yes	characteristic
288	#542	—	2	2	no	—
289	#541	—	2	2	no	—
290	#539	—	2	1	no	—
291	#539	C₂²×C₁₉	1	2	yes	—
292	#537	C₂²×C₁₉	1	1	yes	characteristic
293	#536	—	2	1	no	—
294	#533	—	2	2	no	—
295	#529	—	2	2	no	—
296	#529	—	2	1	no	—
297	#529	C₂²×C₁₉	1	2	yes	—
298	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
299	C₄×#41	—	2	1	no	—
300	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
301	#499	—	2	2	no	—
302	#488	—	2	2	no	—
303	#484	C₂²×C₁₉	1	2	yes	—
304	#483	C₂²×C₁₉	1	2	yes	—
305	#481	C₂²×C₁₉	1	2	yes	—
306	#480	C₂²×C₁₉	1	2	yes	—
307	#479	—	2	2	no	—
308	#478	—	2	2	no	—
309	#431	C₂²×C₁₉	1	2	yes	—
310	#400	—	2	1	no	—
311	#400	C₂²×C₁₉	1	1	yes	characteristic
312	#400	C₂²×C₁₉	1	1	yes	characteristic
313	#398	C₂²×C₁₉	1	1	yes	characteristic
314	#398	C₂²×C₁₉	1	1	yes	characteristic
315	#395	—	2	1	no	—
316	#387	—	2	1	no	—
317	#387	—	2	1	no	—
318	#383	C₂²×C₁₉	1	1	yes	characteristic
319	#328	C₂²×C₁₉	1	2	yes	—
320	#328	C₂²×C₁₉	1	2	yes	—
321	#327	C₂²×C₁₉	1	2	yes	—
322	#327	C₂²×C₁₉	1	2	yes	—
323	#324	C₂²×C₁₉	1	2	yes	—
324	#324	C₂²×C₁₉	1	1	yes	characteristic
325	#324	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×C₁₉	—	2	1	no	—
327	C₂×C₁₉	—	2	1	no	—
328	C₂×C₁₉	—	8	2	no	—
329	C₂×C₁₉	#3002	1	1	yes	characteristic
330	C₂×C₁₉	#3020	1	1	yes	characteristic
331	C₂×C₁₉	#3028	1	1	yes	characteristic
332	C₂×#41	—	2	1	no	—
333	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
334	C₄⋊Q₈	—	2	2	no	—
335	C₄⋊Q₈	—	2	2	no	—
336	#126	—	2	2	no	—
337	#126	—	2	2	no	—
338	#126	—	2	2	no	—
339	#126	—	2	2	no	—
340	#125	—	2	1	no	—
341	#125	—	2	2	no	—
342	#125	—	2	2	no	—
343	#125	—	2	2	no	—
344	#125	—	2	2	no	—
345	#125	—	2	2	no	—
346	#125	D₄×C₁₉	1	2	yes	—
347	#124	—	2	2	no	—
348	#124	—	2	1	no	—
349	#124	D₄×C₁₉	1	2	yes	—
350	#123	—	2	2	no	—
351	#123	—	2	2	no	—
352	#123	—	2	2	no	—
353	#123	—	2	2	no	—
354	C₂²⋊Q₈	—	2	2	no	—
355	C₂²⋊Q₈	—	2	2	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	1	no	—
359	C₂²⋊Q₈	—	2	2	no	—
360	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
361	#121	—	2	2	no	—
362	#121	—	2	1	no	—
363	#121	C₂³×C₁₉	1	2	yes	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	—	2	2	no	—
368	C₄×Q₈	—	2	2	no	—
369	C₄×Q₈	D₄×C₁₉	1	2	yes	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	—	2	2	no	—
375	C₄×D₄	D₄×C₁₉	1	2	yes	—
376	#117	—	2	2	no	—
377	#117	—	2	2	no	—
378	#117	—	2	1	no	—
379	#117	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
389	C₂×C₄²	—	2	2	no	—
390	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
391	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
393	#107	—	2	2	no	—
394	#107	—	2	2	no	—
395	#106	—	2	2	no	—
396	#106	—	2	2	no	—
397	C₄⋊C₈	—	2	2	no	—
398	#103	—	2	2	no	—
399	#103	—	2	2	no	—
400	#102	—	2	2	no	—
401	#102	—	2	2	no	—
402	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
403	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
404	C₄×C₈	—	2	2	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	C₂³×C₁₉	1	1	yes	characteristic
414	#95	C₂³×C₁₉	1	1	yes	characteristic
415	C₁₉	#18315	1	1	yes	characteristic, direct product factor, Sylow
416	#41	—	4	2	no	—
417	#41	—	4	2	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	—	4	1	no	—
423	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
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	C₂×D₄×C₁₉	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	4	2	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	—	4	2	no	—
465	C₄⋊C₄	—	4	2	no	—
466	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
467	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	2	2	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	C₂×D₄×C₁₉	1	2	yes	—
485	C₄²	C₂×D₄×C₁₉	1	2	yes	—
486	C₂³	—	2	2	no	—
487	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
488	Q₈	—	4	4	no	—
489	Q₈	—	4	2	no	—
490	Q₈	—	4	2	no	—
491	Q₈	—	8	1	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	2	no	—
496	D₄	—	8	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	8	2	no	—
527	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
528	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
529	C₂×C₄	C₁₉×#120	1	2	yes	—
530	C₂×C₄	C₁₉×#135	1	2	yes	—
531	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
532	C₈	—	4	2	no	—
533	C₈	—	4	2	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
540	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
541	C₂²	C₁₉×#575	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	2	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	2	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	2	no	—
553	C₄	—	8	1	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₂	—	2	1	no	—
558	C₂	—	2	1	no	—
559	C₂	—	8	2	no	—
560	C₂	C₁₉×#3002	1	1	yes	characteristic
561	C₂	C₁₉×#3020	1	1	yes	characteristic
562	C₂	C₁₉×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#537	C₂²
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×#3232	C₂	semidirect
3. C₁₉×#2634	C₂	semidirect
4. C₁₉×#1617	C₂	semidirect
6. C₁₉×#1615	C₂	semidirect
7. C₁₉×#1611	C₂	semidirect
9. C₁₉×#1609	C₂	semidirect
10. C₁₉×#1521	C₂	semidirect
11. C₁₉×#1461	C₂	semidirect
204. #18315	C₁₉	direct (N × H)
254. #3232	C₂×C₁₉	semidirect
255. #2634	C₂×C₁₉	semidirect
256. #1617	C₂×C₁₉	semidirect
258. #1615	C₂×C₁₉	semidirect
259. #1611	C₂×C₁₉	semidirect
261. #1609	C₂×C₁₉	semidirect
262. #1521	C₂×C₁₉	semidirect
263. #1461	C₂×C₁₉	semidirect
415. C₁₉	#18315	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×#3461	2
C₁₉×#3232	2
C₁₉×#2634	2
C₁₉×#1617	2
C₁₉×#1616	2
C₁₉×#1615	2
C₁₉×#1611	2
C₁₉×#1610	2
C₁₉×#1609	2
C₁₉×#1521	2
C₁₉×#1461	2
#18315	19

Subgroups — C19×#18315 #18024274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18315 #18024274