Subgroups — C₁₉×#18126 #18024085

Order 4864.

1034 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3101	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1612	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1609	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1600	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1597	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1503	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1502	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1458	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#542	—	2	1	no	—
13	C₁₉×#542	—	2	1	no	—
14	C₁₉×#541	—	2	1	no	—
15	C₁₉×#540	—	2	1	no	—
16	C₁₉×#539	—	2	1	no	—
17	C₁₉×#539	C₂²	1	2	yes	—
18	C₁₉×#538	—	2	1	no	—
19	C₁₉×#538	C₂²	1	2	yes	—
20	C₁₉×#533	C₂²	1	1	yes	characteristic
21	C₁₉×#532	C₂²	1	1	yes	characteristic
22	C₁₉×#529	—	2	2	no	—
23	C₁₉×#529	—	2	2	no	—
24	C₁₉×#525	—	2	1	no	—
25	C₄×#41×C₁₉	—	2	1	no	—
26	C₂×C₄×D₄×C₁₉	—	2	1	no	—
27	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
29	C₁₉×#483	C₂²	1	2	yes	—
30	C₁₉×#480	C₂²	1	2	yes	—
31	C₁₉×#476	—	2	1	no	—
32	C₁₉×#474	—	2	1	no	—
33	C₁₉×#461	—	2	1	no	—
34	C₁₉×#459	—	2	1	no	—
35	C₁₉×#450	C₂²	1	2	yes	—
36	C₁₉×#447	C₂²	1	2	yes	—
37	C₄×SD₁₆×C₁₉	—	2	2	no	—
38	C₄×D₈×C₁₉	—	2	2	no	—
39	C₁₉×#431	C₂²	1	1	yes	characteristic
40	C₁₉×#431	C₂²	1	1	yes	characteristic
41	C₁₉×#398	C₂²	1	1	yes	characteristic
42	C₁₉×#397	C₂²	1	1	yes	characteristic
43	C₁₉×#396	—	2	1	no	—
44	C₁₉×#394	—	2	1	no	—
45	C₁₉×#394	C₂²	1	1	yes	characteristic
46	C₁₉×#392	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
49	C₁₉×#328	C₂²	1	2	yes	—
50	C₁₉×#328	C₂²	1	2	yes	—
51	C₁₉×#327	C₂²	1	2	yes	—
52	C₁₉×#327	C₂²	1	2	yes	—
53	C₁₉×#324	C₂²	1	2	yes	—
54	C₁₉×#323	C₂²	1	2	yes	—
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂²×D₄×C₁₉	—	2	1	no	—
57	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₉	—	2	1	no	—
59	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂×SD₁₆×C₁₉	—	2	2	no	—
61	C₂×D₈×C₁₉	—	2	2	no	—
62	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
63	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
64	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
65	C₁₉×#127	D₄	1	1	yes	characteristic, complemented
66	C₁₉×#126	—	2	2	no	—
67	C₁₉×#126	—	2	2	no	—
68	C₁₉×#126	—	2	2	no	—
69	C₁₉×#126	—	2	2	no	—
70	C₁₉×#125	—	2	2	no	—
71	C₁₉×#125	—	2	2	no	—
72	C₁₉×#125	—	2	1	no	—
73	C₁₉×#124	—	2	2	no	—
74	C₁₉×#124	—	2	2	no	—
75	C₁₉×#124	—	2	1	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×#123	—	2	2	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×#123	—	2	2	no	—
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	—	2	1	no	—
82	C₁₉×C₂²⋊Q₈	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	1	no	—
86	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
87	C₁₉×#121	—	2	1	no	—
88	C₁₉×#121	—	2	1	no	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	—	2	2	no	—
91	C₁₉×#121	—	2	1	no	—
92	C₁₉×#121	C₂³	1	2	yes	—
93	C₁₉×#120	—	2	2	no	—
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	—	2	1	no	—
97	C₄×Q₈×C₁₉	D₄	1	2	yes	complemented
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	2	2	no	—
101	C₄×D₄×C₁₉	—	2	2	no	—
102	C₄×D₄×C₁₉	—	2	2	no	—
103	C₄×D₄×C₁₉	—	2	2	no	—
104	C₄×D₄×C₁₉	—	2	1	no	—
105	C₄×D₄×C₁₉	—	2	1	no	—
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	—	2	1	no	—
108	C₄×D₄×C₁₉	—	2	1	no	—
109	C₄×D₄×C₁₉	—	4	4	no	—
110	C₄×D₄×C₁₉	D₄	1	2	yes	complemented
111	C₁₉×#117	—	2	2	no	—
112	C₁₉×#117	—	2	1	no	—
113	C₁₉×#117	—	2	1	no	—
114	C₁₉×#117	—	2	1	no	—
115	C₁₉×#117	—	2	1	no	—
116	C₁₉×#117	—	2	1	no	—
117	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₉	—	2	2	no	—
130	C₂×C₄²×C₁₉	—	2	1	no	—
131	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
132	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
133	C₁₉×#107	—	2	2	no	—
134	C₁₉×#106	—	2	2	no	—
135	C₁₉×C₄⋊C₈	—	2	1	no	—
136	C₁₉×C₄⋊C₈	—	2	1	no	—
137	C₁₉×#103	—	2	2	no	—
138	C₁₉×#102	—	2	2	no	—
139	C₁₉×#102	—	2	2	no	—
140	C₁₉×#102	—	2	2	no	—
141	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
142	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
143	C₄×C₈×C₁₉	—	2	1	no	—
144	C₄×C₈×C₁₉	—	2	1	no	—
145	C₁₉×#95	—	2	1	no	—
146	C₁₉×#95	—	2	1	no	—
147	C₁₉×#95	C₂³	1	1	yes	characteristic
148	C₁₉×#95	C₂³	1	1	yes	characteristic
149	C₂⁴×C₁₉	—	2	1	no	—
150	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
151	#41×C₁₉	—	4	2	no	—
152	#41×C₁₉	—	4	2	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₁₉	—	2	2	no	—
157	C₂×D₄×C₁₉	—	2	2	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	4	2	no	—
164	C₂×D₄×C₁₉	—	4	2	no	—
165	C₂×D₄×C₁₉	—	4	2	no	—
166	C₂×D₄×C₁₉	—	4	2	no	—
167	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	2	no	—
170	C₂²×C₄×C₁₉	—	2	2	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	2	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	2	no	—
175	C₂²×C₄×C₁₉	—	2	2	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	4	1	no	—
179	C₂²×C₄×C₁₉	—	4	1	no	—
180	C₂²×C₄×C₁₉	—	4	2	no	—
181	C₂²×C₄×C₁₉	—	4	2	no	—
182	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
188	SD₁₆×C₁₉	—	4	4	no	—
189	D₈×C₁₉	—	4	4	no	—
190	C₂×C₈×C₁₉	—	2	2	no	—
191	C₂×C₈×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	2	2	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	2	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	2	2	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	2	1	no	—
208	C₄⋊C₄×C₁₉	—	4	2	no	—
209	C₄⋊C₄×C₁₉	—	4	2	no	—
210	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
211	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
212	C₂²⋊C₄×C₁₉	—	2	2	no	—
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₉	—	2	2	no	—
215	C₂²⋊C₄×C₁₉	—	2	2	no	—
216	C₂²⋊C₄×C₁₉	—	2	2	no	—
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
219	C₂²⋊C₄×C₁₉	—	2	1	no	—
220	C₂²⋊C₄×C₁₉	—	2	1	no	—
221	C₂²⋊C₄×C₁₉	—	2	2	no	—
222	C₂²⋊C₄×C₁₉	—	2	1	no	—
223	C₂²⋊C₄×C₁₉	—	2	1	no	—
224	C₂²⋊C₄×C₁₉	—	2	2	no	—
225	C₂²⋊C₄×C₁₉	—	4	2	no	—
226	C₂²⋊C₄×C₁₉	—	4	2	no	—
227	C₂²⋊C₄×C₁₉	—	4	2	no	—
228	C₂²⋊C₄×C₁₉	—	4	2	no	—
229	C₂²⋊C₄×C₁₉	—	4	1	no	—
230	C₂²⋊C₄×C₁₉	—	4	1	no	—
231	C₄²×C₁₉	—	2	2	no	—
232	C₄²×C₁₉	—	2	2	no	—
233	C₄²×C₁₉	—	2	1	no	—
234	C₄²×C₁₉	—	2	1	no	—
235	C₄²×C₁₉	—	2	2	no	—
236	C₄²×C₁₉	—	4	2	no	—
237	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
238	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
239	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
240	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
241	#18126	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂³×C₁₉	—	2	2	no	—
243	C₂³×C₁₉	—	2	1	no	—
244	C₂³×C₁₉	—	2	2	no	—
245	C₂³×C₁₉	—	2	1	no	—
246	C₂³×C₁₉	—	2	1	no	—
247	C₂³×C₁₉	—	4	1	no	—
248	C₂³×C₁₉	—	4	1	no	—
249	C₂³×C₁₉	—	4	1	no	—
250	C₂³×C₁₉	—	4	1	no	—
251	C₂³×C₁₉	—	4	1	no	—
252	C₂³×C₁₉	—	4	1	no	—
253	C₂³×C₁₉	—	4	1	no	—
254	C₂³×C₁₉	—	4	1	no	—
255	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
256	Q₈×C₁₉	—	4	2	no	—
257	Q₈×C₁₉	—	4	2	no	—
258	Q₈×C₁₉	—	8	1	no	—
259	D₄×C₁₉	—	2	2	no	—
260	D₄×C₁₉	—	2	2	no	—
261	D₄×C₁₉	—	4	2	no	—
262	D₄×C₁₉	—	4	1	no	—
263	D₄×C₁₉	—	4	1	no	—
264	D₄×C₁₉	—	4	8	no	—
265	D₄×C₁₉	—	4	2	no	—
266	D₄×C₁₉	—	4	2	no	—
267	D₄×C₁₉	—	4	2	no	—
268	D₄×C₁₉	—	8	1	no	—
269	D₄×C₁₉	—	8	2	no	—
270	D₄×C₁₉	—	8	2	no	—
271	C₂×C₄×C₁₉	—	2	2	no	—
272	C₂×C₄×C₁₉	—	2	1	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	2	2	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	2	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	1	no	—
279	C₂×C₄×C₁₉	—	2	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	4	1	no	—
284	C₂×C₄×C₁₉	—	4	2	no	—
285	C₂×C₄×C₁₉	—	4	2	no	—
286	C₂×C₄×C₁₉	—	4	4	no	—
287	C₂×C₄×C₁₉	—	4	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	1	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	4	1	no	—
294	C₂×C₄×C₁₉	—	4	1	no	—
295	C₂×C₄×C₁₉	—	8	2	no	—
296	C₂×C₄×C₁₉	—	8	2	no	—
297	C₂×C₄×C₁₉	—	8	2	no	—
298	C₂×C₄×C₁₉	—	8	2	no	—
299	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
300	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
301	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
302	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
303	C₂×C₄×C₁₉	#135	1	2	yes	—
304	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
305	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
307	C₈×C₁₉	—	4	2	no	—
308	C₈×C₁₉	—	4	2	no	—
309	#3455	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#3101	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#3100	C₂×C₁₉	1	1	yes	characteristic, complemented
312	#2392	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1612	C₂×C₁₉	1	2	yes	complemented
314	#1609	C₂×C₁₉	1	2	yes	complemented
315	#1600	C₂×C₁₉	1	2	yes	complemented
316	#1597	C₂×C₁₉	1	2	yes	complemented
317	#1503	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#1502	C₂×C₁₉	1	1	yes	characteristic, complemented
319	#1458	C₂×C₁₉	1	1	yes	characteristic, complemented
320	C₂²×C₁₉	—	2	1	no	—
321	C₂²×C₁₉	—	2	1	no	—
322	C₂²×C₁₉	—	4	2	no	—
323	C₂²×C₁₉	—	4	2	no	—
324	C₂²×C₁₉	—	4	2	no	—
325	C₂²×C₁₉	—	4	1	no	—
326	C₂²×C₁₉	—	4	2	no	—
327	C₂²×C₁₉	—	4	2	no	—
328	C₂²×C₁₉	—	4	1	no	—
329	C₂²×C₁₉	—	4	2	no	—
330	C₂²×C₁₉	—	4	2	no	—
331	C₂²×C₁₉	—	4	1	no	—
332	C₂²×C₁₉	—	8	1	no	—
333	C₂²×C₁₉	—	8	1	no	—
334	C₂²×C₁₉	—	8	1	no	—
335	C₂²×C₁₉	—	8	1	no	—
336	C₂²×C₁₉	—	8	1	no	—
337	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
338	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
339	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
340	C₄×C₁₉	—	2	1	no	—
341	C₄×C₁₉	—	2	1	no	—
342	C₄×C₁₉	—	2	1	no	—
343	C₄×C₁₉	—	2	1	no	—
344	C₄×C₁₉	—	4	2	no	—
345	C₄×C₁₉	—	4	1	no	—
346	C₄×C₁₉	—	4	2	no	—
347	C₄×C₁₉	—	4	1	no	—
348	C₄×C₁₉	—	4	2	no	—
349	C₄×C₁₉	—	4	1	no	—
350	C₄×C₁₉	—	4	2	no	—
351	C₄×C₁₉	—	8	1	no	—
352	C₄×C₁₉	—	8	1	no	—
353	C₄×C₁₉	#449	1	2	yes	—
354	C₄×C₁₉	#449	1	2	yes	—
355	#542	—	2	1	no	—
356	#542	—	2	1	no	—
357	#541	—	2	1	no	—
358	#540	—	2	1	no	—
359	#539	—	2	1	no	—
360	#539	C₂²×C₁₉	1	2	yes	—
361	#538	—	2	1	no	—
362	#538	C₂²×C₁₉	1	2	yes	—
363	#533	C₂²×C₁₉	1	1	yes	characteristic
364	#532	C₂²×C₁₉	1	1	yes	characteristic
365	#529	—	2	2	no	—
366	#529	—	2	2	no	—
367	#525	—	2	1	no	—
368	C₄×#41	—	2	1	no	—
369	C₂×C₄×D₄	—	2	1	no	—
370	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
371	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
372	#483	C₂²×C₁₉	1	2	yes	—
373	#480	C₂²×C₁₉	1	2	yes	—
374	#476	—	2	1	no	—
375	#474	—	2	1	no	—
376	#461	—	2	1	no	—
377	#459	—	2	1	no	—
378	#450	C₂²×C₁₉	1	2	yes	—
379	#447	C₂²×C₁₉	1	2	yes	—
380	C₄×SD₁₆	—	2	2	no	—
381	C₄×D₈	—	2	2	no	—
382	#431	C₂²×C₁₉	1	1	yes	characteristic
383	#431	C₂²×C₁₉	1	1	yes	characteristic
384	#398	C₂²×C₁₉	1	1	yes	characteristic
385	#397	C₂²×C₁₉	1	1	yes	characteristic
386	#396	—	2	1	no	—
387	#394	—	2	1	no	—
388	#394	C₂²×C₁₉	1	1	yes	characteristic
389	#392	C₂²×C₁₉	1	1	yes	characteristic
390	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
391	C₄×C₂²⋊C₄	—	2	1	no	—
392	#328	C₂²×C₁₉	1	2	yes	—
393	#328	C₂²×C₁₉	1	2	yes	—
394	#327	C₂²×C₁₉	1	2	yes	—
395	#327	C₂²×C₁₉	1	2	yes	—
396	#324	C₂²×C₁₉	1	2	yes	—
397	#323	C₂²×C₁₉	1	2	yes	—
398	C₂×C₁₉	—	2	1	no	—
399	C₂×C₁₉	—	2	1	no	—
400	C₂×C₁₉	—	8	2	no	—
401	C₂×C₁₉	—	8	1	no	—
402	C₂×C₁₉	—	8	2	no	—
403	C₂×C₁₉	C₂×#449	1	1	yes	characteristic
404	C₂×C₁₉	#3018	1	1	yes	characteristic
405	C₂×C₁₉	#3025	1	1	yes	characteristic
406	C₂×#41	—	2	1	no	—
407	C₂²×D₄	—	2	1	no	—
408	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
409	C₂³×C₄	—	2	1	no	—
410	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
411	C₂×SD₁₆	—	2	2	no	—
412	C₂×D₈	—	2	2	no	—
413	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
414	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
415	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
416	#127	D₄×C₁₉	1	1	yes	characteristic, complemented
417	#126	—	2	2	no	—
418	#126	—	2	2	no	—
419	#126	—	2	2	no	—
420	#126	—	2	2	no	—
421	#125	—	2	2	no	—
422	#125	—	2	2	no	—
423	#125	—	2	1	no	—
424	#124	—	2	2	no	—
425	#124	—	2	2	no	—
426	#124	—	2	1	no	—
427	#123	—	2	2	no	—
428	#123	—	2	2	no	—
429	#123	—	2	2	no	—
430	#123	—	2	2	no	—
431	#123	—	2	2	no	—
432	C₂²⋊Q₈	—	2	1	no	—
433	C₂²⋊Q₈	—	2	1	no	—
434	C₂²⋊Q₈	—	2	2	no	—
435	C₂²⋊Q₈	—	2	2	no	—
436	C₂²⋊Q₈	—	2	1	no	—
437	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
438	#121	—	2	1	no	—
439	#121	—	2	1	no	—
440	#121	—	2	2	no	—
441	#121	—	2	2	no	—
442	#121	—	2	1	no	—
443	#121	C₂³×C₁₉	1	2	yes	—
444	#120	—	2	2	no	—
445	C₄×Q₈	—	2	1	no	—
446	C₄×Q₈	—	2	1	no	—
447	C₄×Q₈	—	2	1	no	—
448	C₄×Q₈	D₄×C₁₉	1	2	yes	complemented
449	C₄×D₄	—	2	1	no	—
450	C₄×D₄	—	2	1	no	—
451	C₄×D₄	—	2	2	no	—
452	C₄×D₄	—	2	2	no	—
453	C₄×D₄	—	2	2	no	—
454	C₄×D₄	—	2	2	no	—
455	C₄×D₄	—	2	1	no	—
456	C₄×D₄	—	2	1	no	—
457	C₄×D₄	—	2	1	no	—
458	C₄×D₄	—	2	1	no	—
459	C₄×D₄	—	2	1	no	—
460	C₄×D₄	—	4	4	no	—
461	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
462	#117	—	2	2	no	—
463	#117	—	2	1	no	—
464	#117	—	2	1	no	—
465	#117	—	2	1	no	—
466	#117	—	2	1	no	—
467	#117	—	2	1	no	—
468	C₂×C₄⋊C₄	—	2	1	no	—
469	C₂×C₄⋊C₄	—	2	1	no	—
470	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	2	1	no	—
477	C₂×C₂²⋊C₄	—	2	1	no	—
478	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
480	C₂×C₄²	—	2	2	no	—
481	C₂×C₄²	—	2	1	no	—
482	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
483	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
484	#107	—	2	2	no	—
485	#106	—	2	2	no	—
486	C₄⋊C₈	—	2	1	no	—
487	C₄⋊C₈	—	2	1	no	—
488	#103	—	2	2	no	—
489	#102	—	2	2	no	—
490	#102	—	2	2	no	—
491	#102	—	2	2	no	—
492	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
493	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
494	C₄×C₈	—	2	1	no	—
495	C₄×C₈	—	2	1	no	—
496	#95	—	2	1	no	—
497	#95	—	2	1	no	—
498	#95	C₂³×C₁₉	1	1	yes	characteristic
499	#95	C₂³×C₁₉	1	1	yes	characteristic
500	C₁₉	#18126	1	1	yes	characteristic, direct product factor, Sylow
501	C₂⁴	—	2	1	no	—
502	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
503	#41	—	4	2	no	—
504	#41	—	4	2	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	4	2	no	—
516	C₂×D₄	—	4	2	no	—
517	C₂×D₄	—	4	2	no	—
518	C₂×D₄	—	4	2	no	—
519	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	4	1	no	—
531	C₂²×C₄	—	4	1	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	—	4	2	no	—
534	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
535	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
538	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
539	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
540	SD₁₆	—	4	4	no	—
541	D₈	—	4	4	no	—
542	C₂×C₈	—	2	2	no	—
543	C₂×C₈	—	2	2	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	4	2	no	—
561	C₄⋊C₄	—	4	2	no	—
562	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
563	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
564	C₂²⋊C₄	—	2	2	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	2	no	—
568	C₂²⋊C₄	—	2	2	no	—
569	C₂²⋊C₄	—	2	2	no	—
570	C₂²⋊C₄	—	2	2	no	—
571	C₂²⋊C₄	—	2	1	no	—
572	C₂²⋊C₄	—	2	1	no	—
573	C₂²⋊C₄	—	2	2	no	—
574	C₂²⋊C₄	—	2	1	no	—
575	C₂²⋊C₄	—	2	1	no	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	4	2	no	—
578	C₂²⋊C₄	—	4	2	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	4	2	no	—
581	C₂²⋊C₄	—	4	1	no	—
582	C₂²⋊C₄	—	4	1	no	—
583	C₄²	—	2	2	no	—
584	C₄²	—	2	2	no	—
585	C₄²	—	2	1	no	—
586	C₄²	—	2	2	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	4	2	no	—
589	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
590	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
591	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
592	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
593	C₂³	—	2	2	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
607	Q₈	—	4	2	no	—
608	Q₈	—	4	2	no	—
609	Q₈	—	8	1	no	—
610	D₄	—	2	2	no	—
611	D₄	—	2	2	no	—
612	D₄	—	4	2	no	—
613	D₄	—	4	1	no	—
614	D₄	—	4	1	no	—
615	D₄	—	4	8	no	—
616	D₄	—	4	2	no	—
617	D₄	—	4	2	no	—
618	D₄	—	4	2	no	—
619	D₄	—	8	1	no	—
620	D₄	—	8	2	no	—
621	D₄	—	8	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	8	2	no	—
647	C₂×C₄	—	8	2	no	—
648	C₂×C₄	—	8	2	no	—
649	C₂×C₄	—	8	2	no	—
650	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
651	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
652	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
653	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
654	C₂×C₄	C₁₉×#135	1	2	yes	—
655	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
656	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
657	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
658	C₈	—	4	2	no	—
659	C₈	—	4	2	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	4	2	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	1	no	—
672	C₂²	—	8	1	no	—
673	C₂²	—	8	1	no	—
674	C₂²	—	8	1	no	—
675	C₂²	—	8	1	no	—
676	C₂²	—	8	1	no	—
677	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
678	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
679	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	1	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	1	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	2	no	—
691	C₄	—	8	1	no	—
692	C₄	—	8	1	no	—
693	C₄	C₁₉×#449	1	2	yes	—
694	C₄	C₁₉×#449	1	2	yes	—
695	C₂	—	2	1	no	—
696	C₂	—	2	1	no	—
697	C₂	—	8	1	no	—
698	C₂	—	8	2	no	—
699	C₂	—	8	2	no	—
700	C₂	C₂×C₁₉×#449	1	1	yes	characteristic
701	C₂	C₁₉×#3018	1	1	yes	characteristic
702	C₂	C₁₉×#3025	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×#120
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₉×#3455	C₂	semidirect
2. C₁₉×#3101	C₂	semidirect
3. C₁₉×#3100	C₂	semidirect
4. C₁₉×#2392	C₂	semidirect
5. C₁₉×#1612	C₂	semidirect
6. C₁₉×#1609	C₂	semidirect
7. C₁₉×#1600	C₂	semidirect
8. C₁₉×#1597	C₂	semidirect
9. C₁₉×#1503	C₂	semidirect
10. C₁₉×#1502	C₂	semidirect
11. C₁₉×#1458	C₂	semidirect
62. C₁₉×C₄⋊Q₈	D₄	semidirect
63. C₁₉×C₄⋊Q₈	D₄	semidirect
64. C₁₉×C₄⋊Q₈	D₄	semidirect
65. C₁₉×#127	D₄	semidirect
97. C₄×Q₈×C₁₉	D₄	semidirect
110. C₄×D₄×C₁₉	D₄	semidirect
241. #18126	C₁₉	direct (N × H)
309. #3455	C₂×C₁₉	semidirect
310. #3101	C₂×C₁₉	semidirect
311. #3100	C₂×C₁₉	semidirect
312. #2392	C₂×C₁₉	semidirect
313. #1612	C₂×C₁₉	semidirect
314. #1609	C₂×C₁₉	semidirect
315. #1600	C₂×C₁₉	semidirect
316. #1597	C₂×C₁₉	semidirect
317. #1503	C₂×C₁₉	semidirect
318. #1502	C₂×C₁₉	semidirect
319. #1458	C₂×C₁₉	semidirect
413. C₄⋊Q₈	D₄×C₁₉	semidirect
414. C₄⋊Q₈	D₄×C₁₉	semidirect
415. C₄⋊Q₈	D₄×C₁₉	semidirect
416. #127	D₄×C₁₉	semidirect
448. C₄×Q₈	D₄×C₁₉	semidirect
461. C₄×D₄	D₄×C₁₉	semidirect
500. C₁₉	#18126	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×#3455	2
C₁₉×#3101	2
C₁₉×#3100	2
C₁₉×#2392	2
C₁₉×#1612	2
C₁₉×#1609	2
C₁₉×#1600	2
C₁₉×#1597	2
C₁₉×#1503	2
C₁₉×#1502	2
C₁₉×#1458	2
#18126	19

Subgroups — C19×#18126 #18024085

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18126 #18024085