Subgroups — C₁₉×#18407 #18024366

Order 4864.

904 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3493	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3232	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2611	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1618	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1617	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1616	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1612	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1611	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1610	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1500	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1458	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#556	—	2	2	no	—
13	C₁₉×#555	—	2	2	no	—
14	C₁₉×#553	—	2	2	no	—
15	C₁₉×#552	—	2	2	no	—
16	C₁₉×#544	C₂²	1	1	yes	characteristic
17	C₁₉×#538	—	2	1	no	—
18	C₁₉×#538	C₂²	1	2	yes	—
19	C₁₉×#537	C₂²	1	1	yes	characteristic
20	C₁₉×#529	—	2	1	no	—
21	C₁₉×#529	C₂²	1	2	yes	—
22	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
23	C₁₉×#525	—	2	1	no	—
24	C₁₉×#520	—	2	1	no	—
25	C₂×C₁₉×#117	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	C₂²	1	1	yes	characteristic
36	C₁₉×#399	C₂²	1	1	yes	characteristic
37	C₁₉×#398	C₂²	1	1	yes	characteristic
38	C₁₉×#397	C₂²	1	1	yes	characteristic
39	C₁₉×#389	—	2	1	no	—
40	C₁₉×#388	—	2	1	no	—
41	C₁₉×#387	—	2	1	no	—
42	C₁₉×#385	—	2	1	no	—
43	C₁₉×#376	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	1	yes	characteristic
49	C₁₉×#324	C₂²	1	1	yes	characteristic
50	C₁₉×#323	C₂²	1	2	yes	—
51	C₂×#41×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
53	C₁₉×C₄⋊Q₈	—	2	2	no	—
54	C₁₉×#126	—	2	2	no	—
55	C₁₉×#126	—	2	2	no	—
56	C₁₉×#126	—	2	2	no	—
57	C₁₉×#126	—	2	2	no	—
58	C₁₉×#125	—	2	1	no	—
59	C₁₉×#125	—	2	2	no	—
60	C₁₉×#125	—	2	2	no	—
61	C₁₉×#125	—	2	2	no	—
62	C₁₉×#125	D₄	1	2	yes	—
63	C₁₉×#124	—	2	1	no	—
64	C₁₉×#124	—	2	2	no	—
65	C₁₉×#124	—	2	2	no	—
66	C₁₉×#124	D₄	1	2	yes	—
67	C₁₉×#123	—	2	2	no	—
68	C₁₉×#123	—	2	2	no	—
69	C₁₉×#123	—	2	2	no	—
70	C₁₉×C₂²⋊Q₈	—	2	1	no	—
71	C₁₉×C₂²⋊Q₈	—	2	1	no	—
72	C₁₉×C₂²⋊Q₈	—	2	1	no	—
73	C₁₉×C₂²⋊Q₈	—	2	2	no	—
74	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
75	C₁₉×#121	—	2	1	no	—
76	C₁₉×#121	—	2	1	no	—
77	C₁₉×#121	—	2	2	no	—
78	C₁₉×#121	—	2	2	no	—
79	C₁₉×#121	—	2	2	no	—
80	C₁₉×#121	—	2	1	no	—
81	C₁₉×#121	C₂³	1	2	yes	—
82	C₁₉×#120	—	2	2	no	—
83	C₄×Q₈×C₁₉	—	2	2	no	—
84	C₄×Q₈×C₁₉	—	2	1	no	—
85	C₄×Q₈×C₁₉	D₄	1	2	yes	—
86	C₄×D₄×C₁₉	—	2	2	no	—
87	C₄×D₄×C₁₉	—	2	2	no	—
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₄×D₄×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	—	2	2	no	—
91	C₄×D₄×C₁₉	—	2	2	no	—
92	C₄×D₄×C₁₉	D₄	1	2	yes	—
93	C₁₉×#117	—	2	2	no	—
94	C₁₉×#117	—	2	2	no	—
95	C₁₉×#117	—	2	1	no	—
96	C₁₉×#117	—	2	2	no	—
97	C₁₉×#117	—	2	2	no	—
98	C₁₉×#117	—	2	2	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
104	C₂×C₄⋊C₄×C₁₉	D₄	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×C₂²⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₉	—	2	1	no	—
113	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
115	C₁₉×#107	—	2	2	no	—
116	C₁₉×#107	—	2	2	no	—
117	C₁₉×#106	—	2	2	no	—
118	C₁₉×#106	—	2	2	no	—
119	C₁₉×C₄⋊C₈	—	2	2	no	—
120	C₁₉×#103	—	2	2	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#102	—	2	2	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
125	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
126	C₄×C₈×C₁₉	—	2	2	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	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
135	#41×C₁₉	—	4	2	no	—
136	#41×C₁₉	—	4	2	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	—	2	2	no	—
142	C₂×D₄×C₁₉	—	2	2	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	1	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	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	4	1	no	—
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	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	C₂²⋊C₄×C₁₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₉	—	2	2	no	—
197	C₂²⋊C₄×C₁₉	—	4	2	no	—
198	C₂²⋊C₄×C₁₉	—	4	2	no	—
199	C₄²×C₁₉	—	2	2	no	—
200	C₄²×C₁₉	—	2	2	no	—
201	C₄²×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	—	2	1	no	—
203	C₄²×C₁₉	—	2	2	no	—
204	C₄²×C₁₉	—	4	2	no	—
205	C₄²×C₁₉	C₂×D₄	1	2	yes	—
206	C₄²×C₁₉	C₂×D₄	1	2	yes	—
207	#18407	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×C₁₉	—	2	2	no	—
210	C₂³×C₁₉	—	2	1	no	—
211	C₂³×C₁₉	—	2	1	no	—
212	C₂³×C₁₉	—	4	1	no	—
213	C₂³×C₁₉	—	4	1	no	—
214	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
215	Q₈×C₁₉	—	4	2	no	—
216	Q₈×C₁₉	—	4	2	no	—
217	Q₈×C₁₉	—	8	1	no	—
218	D₄×C₁₉	—	4	2	no	—
219	D₄×C₁₉	—	4	2	no	—
220	D₄×C₁₉	—	4	2	no	—
221	D₄×C₁₉	—	4	2	no	—
222	D₄×C₁₉	—	8	2	no	—
223	D₄×C₁₉	—	8	1	no	—
224	D₄×C₁₉	—	8	2	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	4	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	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	8	2	no	—
254	C₂×C₄×C₁₉	—	8	2	no	—
255	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
257	C₂×C₄×C₁₉	#120	1	2	yes	—
258	C₂×C₄×C₁₉	#135	1	2	yes	—
259	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
260	C₈×C₁₉	—	4	2	no	—
261	C₈×C₁₉	—	4	2	no	—
262	#3493	C₂×C₁₉	1	1	yes	characteristic
263	#3232	C₂×C₁₉	1	2	yes	complemented
264	#2611	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1618	C₂×C₁₉	1	2	yes	complemented
266	#1617	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1616	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#1612	C₂×C₁₉	1	2	yes	complemented
269	#1611	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#1610	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#1500	C₂×C₁₉	1	2	yes	complemented
272	#1458	C₂×C₁₉	1	1	yes	characteristic, complemented
273	C₂²×C₁₉	—	2	1	no	—
274	C₂²×C₁₉	—	2	1	no	—
275	C₂²×C₁₉	—	4	2	no	—
276	C₂²×C₁₉	—	4	1	no	—
277	C₂²×C₁₉	—	4	2	no	—
278	C₂²×C₁₉	—	4	2	no	—
279	C₂²×C₁₉	—	4	1	no	—
280	C₂²×C₁₉	—	4	2	no	—
281	C₂²×C₁₉	—	4	1	no	—
282	C₂²×C₁₉	—	8	1	no	—
283	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
284	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
285	C₂²×C₁₉	#575	1	1	yes	characteristic
286	C₄×C₁₉	—	2	2	no	—
287	C₄×C₁₉	—	2	1	no	—
288	C₄×C₁₉	—	2	1	no	—
289	C₄×C₁₉	—	2	2	no	—
290	C₄×C₁₉	—	2	2	no	—
291	C₄×C₁₉	—	4	2	no	—
292	C₄×C₁₉	—	4	2	no	—
293	C₄×C₁₉	—	4	1	no	—
294	C₄×C₁₉	—	4	2	no	—
295	C₄×C₁₉	—	4	1	no	—
296	C₄×C₁₉	—	4	2	no	—
297	C₄×C₁₉	—	8	1	no	—
298	C₄×C₁₉	—	8	1	no	—
299	C₄×C₁₉	—	8	1	no	—
300	#556	—	2	2	no	—
301	#555	—	2	2	no	—
302	#553	—	2	2	no	—
303	#552	—	2	2	no	—
304	#544	C₂²×C₁₉	1	1	yes	characteristic
305	#538	—	2	1	no	—
306	#538	C₂²×C₁₉	1	2	yes	—
307	#537	C₂²×C₁₉	1	1	yes	characteristic
308	#529	—	2	1	no	—
309	#529	C₂²×C₁₉	1	2	yes	—
310	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
311	#525	—	2	1	no	—
312	#520	—	2	1	no	—
313	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
314	#499	—	2	2	no	—
315	#488	—	2	2	no	—
316	#484	C₂²×C₁₉	1	2	yes	—
317	#483	C₂²×C₁₉	1	2	yes	—
318	#481	C₂²×C₁₉	1	2	yes	—
319	#480	C₂²×C₁₉	1	2	yes	—
320	#479	—	2	2	no	—
321	#478	—	2	2	no	—
322	#431	C₂²×C₁₉	1	2	yes	—
323	#400	C₂²×C₁₉	1	1	yes	characteristic
324	#399	C₂²×C₁₉	1	1	yes	characteristic
325	#398	C₂²×C₁₉	1	1	yes	characteristic
326	#397	C₂²×C₁₉	1	1	yes	characteristic
327	#389	—	2	1	no	—
328	#388	—	2	1	no	—
329	#387	—	2	1	no	—
330	#385	—	2	1	no	—
331	#376	C₂²×C₁₉	1	1	yes	characteristic
332	#328	C₂²×C₁₉	1	2	yes	—
333	#328	C₂²×C₁₉	1	2	yes	—
334	#327	C₂²×C₁₉	1	2	yes	—
335	#327	C₂²×C₁₉	1	2	yes	—
336	#324	C₂²×C₁₉	1	1	yes	characteristic
337	#324	C₂²×C₁₉	1	1	yes	characteristic
338	#323	C₂²×C₁₉	1	2	yes	—
339	C₂×C₁₉	—	2	1	no	—
340	C₂×C₁₉	—	2	1	no	—
341	C₂×C₁₉	—	8	2	no	—
342	C₂×C₁₉	—	8	1	no	—
343	C₂×C₁₉	#3002	1	1	yes	characteristic
344	C₂×C₁₉	#3018	1	1	yes	characteristic
345	C₂×C₁₉	#3028	1	1	yes	characteristic
346	C₂×#41	—	2	1	no	—
347	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
348	C₄⋊Q₈	—	2	2	no	—
349	#126	—	2	2	no	—
350	#126	—	2	2	no	—
351	#126	—	2	2	no	—
352	#126	—	2	2	no	—
353	#125	—	2	1	no	—
354	#125	—	2	2	no	—
355	#125	—	2	2	no	—
356	#125	—	2	2	no	—
357	#125	D₄×C₁₉	1	2	yes	—
358	#124	—	2	1	no	—
359	#124	—	2	2	no	—
360	#124	—	2	2	no	—
361	#124	D₄×C₁₉	1	2	yes	—
362	#123	—	2	2	no	—
363	#123	—	2	2	no	—
364	#123	—	2	2	no	—
365	C₂²⋊Q₈	—	2	1	no	—
366	C₂²⋊Q₈	—	2	1	no	—
367	C₂²⋊Q₈	—	2	1	no	—
368	C₂²⋊Q₈	—	2	2	no	—
369	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
370	#121	—	2	1	no	—
371	#121	—	2	1	no	—
372	#121	—	2	2	no	—
373	#121	—	2	2	no	—
374	#121	—	2	2	no	—
375	#121	—	2	1	no	—
376	#121	C₂³×C₁₉	1	2	yes	—
377	#120	—	2	2	no	—
378	C₄×Q₈	—	2	2	no	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	D₄×C₁₉	1	2	yes	—
381	C₄×D₄	—	2	2	no	—
382	C₄×D₄	—	2	2	no	—
383	C₄×D₄	—	2	2	no	—
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	D₄×C₁₉	1	2	yes	—
388	#117	—	2	2	no	—
389	#117	—	2	2	no	—
390	#117	—	2	1	no	—
391	#117	—	2	2	no	—
392	#117	—	2	2	no	—
393	#117	—	2	2	no	—
394	C₂×C₄⋊C₄	—	2	2	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
406	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
409	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
410	#107	—	2	2	no	—
411	#107	—	2	2	no	—
412	#106	—	2	2	no	—
413	#106	—	2	2	no	—
414	C₄⋊C₈	—	2	2	no	—
415	#103	—	2	2	no	—
416	#103	—	2	2	no	—
417	#102	—	2	2	no	—
418	#102	—	2	2	no	—
419	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
420	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
421	C₄×C₈	—	2	2	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	C₂³×C₁₉	1	1	yes	characteristic
428	#95	C₂³×C₁₉	1	1	yes	characteristic
429	C₁₉	#18407	1	1	yes	characteristic, direct product factor, Sylow
430	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
431	#41	—	4	2	no	—
432	#41	—	4	2	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	4	1	no	—
453	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	4	2	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	2	no	—
479	C₄⋊C₄	—	4	2	no	—
480	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
481	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	4	2	no	—
494	C₂²⋊C₄	—	4	2	no	—
495	C₄²	—	2	2	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	4	2	no	—
501	C₄²	C₂×D₄×C₁₉	1	2	yes	—
502	C₄²	C₂×D₄×C₁₉	1	2	yes	—
503	C₂³	—	2	1	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	4	1	no	—
509	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
510	Q₈	—	4	2	no	—
511	Q₈	—	4	2	no	—
512	Q₈	—	8	1	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	8	2	no	—
518	D₄	—	8	1	no	—
519	D₄	—	8	2	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	8	2	no	—
549	C₂×C₄	—	8	2	no	—
550	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
551	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
552	C₂×C₄	C₁₉×#120	1	2	yes	—
553	C₂×C₄	C₁₉×#135	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
555	C₈	—	4	2	no	—
556	C₈	—	4	2	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	8	1	no	—
567	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
568	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
569	C₂²	C₁₉×#575	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	2	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	2	no	—
581	C₄	—	8	1	no	—
582	C₄	—	8	1	no	—
583	C₄	—	8	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	2	1	no	—
586	C₂	—	8	1	no	—
587	C₂	—	8	2	no	—
588	C₂	C₁₉×#3002	1	1	yes	characteristic
589	C₂	C₁₉×#3018	1	1	yes	characteristic
590	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×#3493	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×#3232	C₂	semidirect
3. C₁₉×#2611	C₂	semidirect
4. C₁₉×#1618	C₂	semidirect
5. C₁₉×#1617	C₂	semidirect
6. C₁₉×#1616	C₂	semidirect
7. C₁₉×#1612	C₂	semidirect
8. C₁₉×#1611	C₂	semidirect
9. C₁₉×#1610	C₂	semidirect
10. C₁₉×#1500	C₂	semidirect
11. C₁₉×#1458	C₂	semidirect
207. #18407	C₁₉	direct (N × H)
263. #3232	C₂×C₁₉	semidirect
264. #2611	C₂×C₁₉	semidirect
265. #1618	C₂×C₁₉	semidirect
266. #1617	C₂×C₁₉	semidirect
267. #1616	C₂×C₁₉	semidirect
268. #1612	C₂×C₁₉	semidirect
269. #1611	C₂×C₁₉	semidirect
270. #1610	C₂×C₁₉	semidirect
271. #1500	C₂×C₁₉	semidirect
272. #1458	C₂×C₁₉	semidirect
429. C₁₉	#18407	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×#3493	2
C₁₉×#3232	2
C₁₉×#2611	2
C₁₉×#1618	2
C₁₉×#1617	2
C₁₉×#1616	2
C₁₉×#1612	2
C₁₉×#1611	2
C₁₉×#1610	2
C₁₉×#1500	2
C₁₉×#1458	2
#18407	19

Subgroups — C19×#18407 #18024366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18407 #18024366