Subgroups — C₁₉×#18400 #18024359

Order 4864.

978 conjugacy classes of subgroups.

The subgroup lattice has 644 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, complemented
2	C₁₉×#3211	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2610	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1606	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1605	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1604	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1600	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1599	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1598	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×#124	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×#495	—	2	2	no	—
27	C₁₉×#488	—	2	2	no	—
28	C₁₉×#464	—	2	2	no	—
29	C₁₉×#463	—	2	2	no	—
30	C₁₉×#451	C₂²	1	2	yes	—
31	C₁₉×#450	C₂²	1	2	yes	—
32	C₁₉×#448	C₂²	1	2	yes	—
33	C₁₉×#447	C₂²	1	2	yes	—
34	C₁₉×#431	C₂²	1	2	yes	—
35	C₁₉×#395	C₂²	1	1	yes	characteristic
36	C₁₉×#394	C₂²	1	1	yes	characteristic
37	C₁₉×#393	C₂²	1	1	yes	characteristic
38	C₁₉×#392	C₂²	1	1	yes	characteristic
39	C₁₉×#390	—	2	1	no	—
40	C₁₉×#388	—	2	1	no	—
41	C₁₉×#388	—	2	1	no	—
42	C₁₉×#386	—	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	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₉	—	2	1	no	—
54	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
56	C₂×Q₁₆×C₁₉	—	2	2	no	—
57	C₂×SD₁₆×C₁₉	—	2	2	no	—
58	C₂×SD₁₆×C₁₉	—	2	2	no	—
59	C₂×D₈×C₁₉	—	2	2	no	—
60	C₁₉×C₄⋊Q₈	—	2	2	no	—
61	C₁₉×#126	—	2	2	no	—
62	C₁₉×#126	—	2	2	no	—
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#126	—	2	2	no	—
65	C₁₉×#125	—	2	1	no	—
66	C₁₉×#125	—	2	2	no	—
67	C₁₉×#125	D₄	1	2	yes	complemented
68	C₁₉×#124	—	2	1	no	—
69	C₁₉×#124	—	2	2	no	—
70	C₁₉×#124	—	2	2	no	—
71	C₁₉×#124	—	2	2	no	—
72	C₁₉×#124	—	2	2	no	—
73	C₁₉×#124	D₄	1	2	yes	complemented
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×#123	—	2	2	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	2	1	no	—
78	C₁₉×C₂²⋊Q₈	—	2	1	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
82	C₁₉×#121	—	2	1	no	—
83	C₁₉×#121	—	2	1	no	—
84	C₁₉×#121	—	2	2	no	—
85	C₁₉×#121	—	2	2	no	—
86	C₁₉×#121	—	2	2	no	—
87	C₁₉×#121	—	2	1	no	—
88	C₁₉×#121	C₂³	1	2	yes	—
89	C₁₉×#120	—	2	2	no	—
90	C₄×Q₈×C₁₉	—	2	2	no	—
91	C₄×Q₈×C₁₉	—	2	1	no	—
92	C₄×Q₈×C₁₉	D₄	1	2	yes	complemented
93	C₄×D₄×C₁₉	—	2	2	no	—
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	—	2	2	no	—
98	C₄×D₄×C₁₉	—	2	2	no	—
99	C₄×D₄×C₁₉	D₄	1	2	yes	complemented
100	C₁₉×#117	—	2	2	no	—
101	C₁₉×#117	—	2	2	no	—
102	C₁₉×#117	—	2	1	no	—
103	C₁₉×#117	—	2	2	no	—
104	C₁₉×#117	—	2	2	no	—
105	C₁₉×#117	—	2	2	no	—
106	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
107	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₉	—	2	1	no	—
119	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	—	2	2	no	—
122	C₁₉×#103	—	2	2	no	—
123	C₁₉×#103	—	2	2	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×#102	—	2	2	no	—
126	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
127	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
128	C₄×C₈×C₁₉	—	2	2	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	—	2	1	no	—
135	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
136	#41×C₁₉	—	4	2	no	—
137	#41×C₁₉	—	4	2	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	2	2	no	—
141	C₂×Q₈×C₁₉	—	8	1	no	—
142	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	2	no	—
147	C₂×D₄×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	4	2	no	—
150	C₂×D₄×C₁₉	—	4	2	no	—
151	C₂×D₄×C₁₉	—	8	1	no	—
152	C₂×D₄×C₁₉	—	8	1	no	—
153	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	4	1	no	—
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
170	Q₁₆×C₁₉	—	8	2	no	—
171	SD₁₆×C₁₉	—	8	2	no	—
172	SD₁₆×C₁₉	—	8	2	no	—
173	D₈×C₁₉	—	8	2	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₂×C₈×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	8	1	no	—
189	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
190	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
198	C₂²⋊C₄×C₁₉	—	2	2	no	—
199	C₂²⋊C₄×C₁₉	—	2	2	no	—
200	C₂²⋊C₄×C₁₉	—	2	2	no	—
201	C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₉	—	4	2	no	—
203	C₂²⋊C₄×C₁₉	—	4	1	no	—
204	C₂²⋊C₄×C₁₉	—	4	1	no	—
205	C₂²⋊C₄×C₁₉	—	4	2	no	—
206	C₂²⋊C₄×C₁₉	—	4	2	no	—
207	C₂²⋊C₄×C₁₉	—	8	1	no	—
208	C₂²⋊C₄×C₁₉	—	8	1	no	—
209	C₄²×C₁₉	—	2	2	no	—
210	C₄²×C₁₉	—	2	2	no	—
211	C₄²×C₁₉	—	2	1	no	—
212	C₄²×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	—	2	2	no	—
214	C₄²×C₁₉	—	4	2	no	—
215	C₄²×C₁₉	C₂×D₄	1	2	yes	—
216	C₄²×C₁₉	C₂×D₄	1	2	yes	—
217	#18400	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	2	2	no	—
220	C₂³×C₁₉	—	2	1	no	—
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	4	1	no	—
223	C₂³×C₁₉	—	4	1	no	—
224	C₂³×C₁₉	—	4	1	no	—
225	C₂³×C₁₉	—	4	1	no	—
226	C₂³×C₁₉	—	4	1	no	—
227	C₂³×C₁₉	—	4	1	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
232	Q₈×C₁₉	—	4	2	no	—
233	Q₈×C₁₉	—	4	2	no	—
234	Q₈×C₁₉	—	4	2	no	—
235	Q₈×C₁₉	—	4	2	no	—
236	Q₈×C₁₉	—	8	1	no	—
237	D₄×C₁₉	—	4	2	no	—
238	D₄×C₁₉	—	4	2	no	—
239	D₄×C₁₉	—	4	2	no	—
240	D₄×C₁₉	—	4	2	no	—
241	D₄×C₁₉	—	4	2	no	—
242	D₄×C₁₉	—	4	2	no	—
243	D₄×C₁₉	—	8	2	no	—
244	D₄×C₁₉	—	8	1	no	—
245	D₄×C₁₉	—	8	2	no	—
246	D₄×C₁₉	—	8	4	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	2	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	2	no	—
260	C₂×C₄×C₁₉	—	4	2	no	—
261	C₂×C₄×C₁₉	—	4	4	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	8	2	no	—
273	C₂×C₄×C₁₉	—	8	2	no	—
274	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
275	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
276	C₂×C₄×C₁₉	#120	1	2	yes	—
277	C₂×C₄×C₁₉	#135	1	2	yes	—
278	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
279	C₈×C₁₉	—	4	2	no	—
280	C₈×C₁₉	—	4	2	no	—
281	#3493	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#3211	C₂×C₁₉	1	2	yes	complemented
283	#2610	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1606	C₂×C₁₉	1	2	yes	complemented
285	#1605	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1604	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1600	C₂×C₁₉	1	2	yes	complemented
288	#1599	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1598	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1500	C₂×C₁₉	1	2	yes	complemented
291	#1458	C₂×C₁₉	1	1	yes	characteristic, complemented
292	C₂²×C₁₉	—	2	1	no	—
293	C₂²×C₁₉	—	2	1	no	—
294	C₂²×C₁₉	—	4	2	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	—	4	2	no	—
297	C₂²×C₁₉	—	4	2	no	—
298	C₂²×C₁₉	—	4	1	no	—
299	C₂²×C₁₉	—	4	2	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	—	8	1	no	—
302	C₂²×C₁₉	—	8	1	no	—
303	C₂²×C₁₉	—	8	1	no	—
304	C₂²×C₁₉	—	8	1	no	—
305	C₂²×C₁₉	—	8	1	no	—
306	C₂²×C₁₉	—	8	1	no	—
307	C₂²×C₁₉	—	8	1	no	—
308	C₂²×C₁₉	—	8	1	no	—
309	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
310	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
311	C₂²×C₁₉	#575	1	1	yes	characteristic
312	C₄×C₁₉	—	2	2	no	—
313	C₄×C₁₉	—	2	1	no	—
314	C₄×C₁₉	—	2	1	no	—
315	C₄×C₁₉	—	2	2	no	—
316	C₄×C₁₉	—	2	2	no	—
317	C₄×C₁₉	—	4	2	no	—
318	C₄×C₁₉	—	4	2	no	—
319	C₄×C₁₉	—	4	1	no	—
320	C₄×C₁₉	—	4	2	no	—
321	C₄×C₁₉	—	4	1	no	—
322	C₄×C₁₉	—	4	2	no	—
323	C₄×C₁₉	—	8	1	no	—
324	C₄×C₁₉	—	8	1	no	—
325	#556	—	2	2	no	—
326	#555	—	2	2	no	—
327	#553	—	2	2	no	—
328	#552	—	2	2	no	—
329	#544	C₂²×C₁₉	1	1	yes	characteristic
330	#538	—	2	1	no	—
331	#538	C₂²×C₁₉	1	2	yes	—
332	#537	C₂²×C₁₉	1	1	yes	characteristic
333	#529	—	2	1	no	—
334	#529	C₂²×C₁₉	1	2	yes	—
335	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
336	#525	—	2	1	no	—
337	#520	—	2	1	no	—
338	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
339	#495	—	2	2	no	—
340	#488	—	2	2	no	—
341	#464	—	2	2	no	—
342	#463	—	2	2	no	—
343	#451	C₂²×C₁₉	1	2	yes	—
344	#450	C₂²×C₁₉	1	2	yes	—
345	#448	C₂²×C₁₉	1	2	yes	—
346	#447	C₂²×C₁₉	1	2	yes	—
347	#431	C₂²×C₁₉	1	2	yes	—
348	#395	C₂²×C₁₉	1	1	yes	characteristic
349	#394	C₂²×C₁₉	1	1	yes	characteristic
350	#393	C₂²×C₁₉	1	1	yes	characteristic
351	#392	C₂²×C₁₉	1	1	yes	characteristic
352	#390	—	2	1	no	—
353	#388	—	2	1	no	—
354	#388	—	2	1	no	—
355	#386	—	2	1	no	—
356	#376	C₂²×C₁₉	1	1	yes	characteristic
357	#328	C₂²×C₁₉	1	2	yes	—
358	#328	C₂²×C₁₉	1	2	yes	—
359	#327	C₂²×C₁₉	1	2	yes	—
360	#327	C₂²×C₁₉	1	2	yes	—
361	#324	C₂²×C₁₉	1	1	yes	characteristic
362	#324	C₂²×C₁₉	1	1	yes	characteristic
363	#323	C₂²×C₁₉	1	2	yes	—
364	C₂×C₁₉	—	2	1	no	—
365	C₂×C₁₉	—	2	1	no	—
366	C₂×C₁₉	—	8	2	no	—
367	C₂×C₁₉	—	8	1	no	—
368	C₂×C₁₉	—	16	1	no	—
369	C₂×C₁₉	#3002	1	1	yes	characteristic
370	C₂×C₁₉	#3018	1	1	yes	characteristic
371	C₂×C₁₉	#3027	1	1	yes	characteristic
372	C₂×#41	—	2	1	no	—
373	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
374	C₂²×D₄	—	2	1	no	—
375	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
376	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
377	C₂×Q₁₆	—	2	2	no	—
378	C₂×SD₁₆	—	2	2	no	—
379	C₂×SD₁₆	—	2	2	no	—
380	C₂×D₈	—	2	2	no	—
381	C₄⋊Q₈	—	2	2	no	—
382	#126	—	2	2	no	—
383	#126	—	2	2	no	—
384	#126	—	2	2	no	—
385	#126	—	2	2	no	—
386	#125	—	2	1	no	—
387	#125	—	2	2	no	—
388	#125	D₄×C₁₉	1	2	yes	complemented
389	#124	—	2	1	no	—
390	#124	—	2	2	no	—
391	#124	—	2	2	no	—
392	#124	—	2	2	no	—
393	#124	—	2	2	no	—
394	#124	D₄×C₁₉	1	2	yes	complemented
395	#123	—	2	2	no	—
396	#123	—	2	2	no	—
397	#123	—	2	2	no	—
398	C₂²⋊Q₈	—	2	1	no	—
399	C₂²⋊Q₈	—	2	1	no	—
400	C₂²⋊Q₈	—	2	1	no	—
401	C₂²⋊Q₈	—	2	2	no	—
402	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
403	#121	—	2	1	no	—
404	#121	—	2	1	no	—
405	#121	—	2	2	no	—
406	#121	—	2	2	no	—
407	#121	—	2	2	no	—
408	#121	—	2	1	no	—
409	#121	C₂³×C₁₉	1	2	yes	—
410	#120	—	2	2	no	—
411	C₄×Q₈	—	2	2	no	—
412	C₄×Q₈	—	2	1	no	—
413	C₄×Q₈	D₄×C₁₉	1	2	yes	complemented
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
421	#117	—	2	2	no	—
422	#117	—	2	2	no	—
423	#117	—	2	1	no	—
424	#117	—	2	2	no	—
425	#117	—	2	2	no	—
426	#117	—	2	2	no	—
427	C₂×C₄⋊C₄	—	2	2	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	1	no	—
437	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
442	C₄⋊C₈	—	2	2	no	—
443	#103	—	2	2	no	—
444	#103	—	2	2	no	—
445	#102	—	2	2	no	—
446	#102	—	2	2	no	—
447	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
448	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
449	C₄×C₈	—	2	2	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	—	2	1	no	—
453	#95	C₂³×C₁₉	1	1	yes	characteristic
454	#95	C₂³×C₁₉	1	1	yes	characteristic
455	C₁₉	#18400	1	1	yes	characteristic, direct product factor, Sylow
456	C₂⁴	—	2	1	no	—
457	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
458	#41	—	4	2	no	—
459	#41	—	4	2	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	2	no	—
463	C₂×Q₈	—	8	1	no	—
464	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	4	2	no	—
472	C₂×D₄	—	4	2	no	—
473	C₂×D₄	—	8	1	no	—
474	C₂×D₄	—	8	1	no	—
475	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	4	1	no	—
486	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
492	Q₁₆	—	8	2	no	—
493	SD₁₆	—	8	2	no	—
494	SD₁₆	—	8	2	no	—
495	D₈	—	8	2	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	—	2	2	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	8	1	no	—
511	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
512	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	4	2	no	—
525	C₂²⋊C₄	—	4	1	no	—
526	C₂²⋊C₄	—	4	1	no	—
527	C₂²⋊C₄	—	4	2	no	—
528	C₂²⋊C₄	—	4	2	no	—
529	C₂²⋊C₄	—	8	1	no	—
530	C₂²⋊C₄	—	8	1	no	—
531	C₄²	—	2	2	no	—
532	C₄²	—	2	2	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	4	2	no	—
537	C₄²	C₂×D₄×C₁₉	1	2	yes	—
538	C₄²	C₂×D₄×C₁₉	1	2	yes	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	1	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	1	no	—
551	C₂³	—	4	1	no	—
552	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
553	Q₈	—	4	2	no	—
554	Q₈	—	4	2	no	—
555	Q₈	—	4	2	no	—
556	Q₈	—	4	2	no	—
557	Q₈	—	8	1	no	—
558	D₄	—	4	2	no	—
559	D₄	—	4	2	no	—
560	D₄	—	4	2	no	—
561	D₄	—	4	2	no	—
562	D₄	—	4	2	no	—
563	D₄	—	4	2	no	—
564	D₄	—	8	2	no	—
565	D₄	—	8	1	no	—
566	D₄	—	8	2	no	—
567	D₄	—	8	4	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	4	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	8	2	no	—
594	C₂×C₄	—	8	2	no	—
595	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
596	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
597	C₂×C₄	C₁₉×#120	1	2	yes	—
598	C₂×C₄	C₁₉×#135	1	2	yes	—
599	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
600	C₈	—	4	2	no	—
601	C₈	—	4	2	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	—	8	1	no	—
616	C₂²	—	8	1	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	1	no	—
619	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
620	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
621	C₂²	C₁₉×#575	1	1	yes	characteristic
622	C₄	—	2	2	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	2	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	2	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	2	no	—
633	C₄	—	8	1	no	—
634	C₄	—	8	1	no	—
635	C₂	—	2	1	no	—
636	C₂	—	2	1	no	—
637	C₂	—	8	1	no	—
638	C₂	—	8	2	no	—
639	C₂	—	16	1	no	—
640	C₂	C₁₉×#3002	1	1	yes	characteristic
641	C₂	C₁₉×#3018	1	1	yes	characteristic
642	C₂	C₁₉×#3027	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
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
1. C₁₉×#3493	C₂	semidirect
2. C₁₉×#3211	C₂	semidirect
3. C₁₉×#2610	C₂	semidirect
4. C₁₉×#1606	C₂	semidirect
5. C₁₉×#1605	C₂	semidirect
6. C₁₉×#1604	C₂	semidirect
7. C₁₉×#1600	C₂	semidirect
8. C₁₉×#1599	C₂	semidirect
9. C₁₉×#1598	C₂	semidirect
10. C₁₉×#1500	C₂	semidirect
11. C₁₉×#1458	C₂	semidirect
67. C₁₉×#125	D₄	semidirect
73. C₁₉×#124	D₄	semidirect
92. C₄×Q₈×C₁₉	D₄	semidirect
99. C₄×D₄×C₁₉	D₄	semidirect
217. #18400	C₁₉	direct (N × H)
281. #3493	C₂×C₁₉	semidirect
282. #3211	C₂×C₁₉	semidirect
283. #2610	C₂×C₁₉	semidirect
284. #1606	C₂×C₁₉	semidirect
285. #1605	C₂×C₁₉	semidirect
286. #1604	C₂×C₁₉	semidirect
287. #1600	C₂×C₁₉	semidirect
288. #1599	C₂×C₁₉	semidirect
289. #1598	C₂×C₁₉	semidirect
290. #1500	C₂×C₁₉	semidirect
291. #1458	C₂×C₁₉	semidirect
388. #125	D₄×C₁₉	semidirect
394. #124	D₄×C₁₉	semidirect
413. C₄×Q₈	D₄×C₁₉	semidirect
420. C₄×D₄	D₄×C₁₉	semidirect
455. C₁₉	#18400	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×#3211	2
C₁₉×#2610	2
C₁₉×#1606	2
C₁₉×#1605	2
C₁₉×#1604	2
C₁₉×#1600	2
C₁₉×#1599	2
C₁₉×#1598	2
C₁₉×#1500	2
C₁₉×#1458	2
#18400	19

Subgroups — C19×#18400 #18024359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18400 #18024359