Subgroups — C₁₉×#19014 #18024973

Order 4864.

1140 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3217	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3151	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1656	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1655	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1530	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1527	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1524	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
11	C₂²×SD₁₆×C₁₉	—	2	1	no	—
12	C₂²×D₈×C₁₉	—	2	1	no	—
13	C₁₉×#562	C₂²	1	2	yes	complemented
14	C₁₉×H(3,𝔽₄)	C₂²	1	2	yes	complemented
15	C₁₉×#559	—	2	1	no	—
16	C₁₉×#548	—	2	1	no	—
17	C₁₉×#546	—	2	2	no	—
18	C₁₉×#546	—	2	1	no	—
19	D₄²×C₁₉	—	2	1	no	—
20	C₁₉×#542	—	2	1	no	—
21	C₁₉×#538	—	2	2	no	—
22	C₁₉×#538	—	2	1	no	—
23	C₁₉×#535	—	2	1	no	—
24	C₁₉×#534	—	2	1	no	—
25	C₁₉×#532	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
27	C₁₉×#529	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
29	C₁₉×#496	—	2	2	no	—
30	C₁₉×#496	C₂²	1	2	yes	complemented
31	C₁₉×#496	C₂²	1	4	yes	complemented
32	C₁₉×#496	C₂²	1	4	yes	complemented
33	C₁₉×#493	—	2	1	no	—
34	C₁₉×#492	—	2	1	no	—
35	C₁₉×#490	C₂²	1	2	yes	complemented
36	C₁₉×#460	—	2	1	no	—
37	C₁₉×#459	—	2	1	no	—
38	C₁₉×#450	—	2	1	no	—
39	C₁₉×#447	—	2	1	no	—
40	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
41	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#330	C₂²	1	2	yes	complemented
44	C₁₉×#329	C₂²	1	2	yes	complemented
45	C₁₉×#329	C₂²	1	4	yes	complemented
46	C₁₉×#329	C₂²	1	4	yes	complemented
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂×#41×C₁₉	D₄	1	2	yes	—
49	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₉	—	2	2	no	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	—	2	1	no	—
54	C₂²×D₄×C₁₉	—	2	1	no	—
55	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
56	C₁₉×AGL(1,ℤ/8)	—	4	8	no	—
57	C₂×SD₁₆×C₁₉	—	2	4	no	—
58	C₂×SD₁₆×C₁₉	—	2	4	no	—
59	C₂×SD₁₆×C₁₉	—	2	2	no	—
60	C₂×SD₁₆×C₁₉	—	4	4	no	—
61	C₂×D₈×C₁₉	—	2	4	no	—
62	C₂×D₈×C₁₉	—	2	4	no	—
63	C₂×D₈×C₁₉	—	2	2	no	—
64	C₂×D₈×C₁₉	—	4	4	no	—
65	C₂×M₁₆×C₁₉	—	2	1	no	—
66	C₂²×C₈×C₁₉	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
68	C₁₉×#127	—	2	1	no	—
69	C₁₉×#127	—	2	1	no	—
70	C₁₉×#127	—	2	1	no	—
71	C₁₉×#127	—	2	1	no	—
72	C₁₉×#127	D₄	1	1	yes	characteristic
73	C₁₉×#127	C₂³	1	2	yes	—
74	C₁₉×#126	—	2	2	no	—
75	C₁₉×#126	—	2	1	no	—
76	C₁₉×#125	C₂³	1	1	yes	characteristic
77	C₁₉×#124	—	2	1	no	—
78	C₁₉×#124	—	2	2	no	—
79	C₁₉×#124	—	2	2	no	—
80	C₁₉×#124	—	2	2	no	—
81	C₁₉×#124	—	2	1	no	—
82	C₁₉×#124	—	2	1	no	—
83	C₁₉×#124	D₄	1	2	yes	—
84	C₁₉×#124	C₂³	1	2	yes	—
85	C₁₉×#124	C₂³	1	1	yes	characteristic
86	C₁₉×#124	C₂³	1	2	yes	—
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×#123	—	2	1	no	—
90	C₁₉×#123	—	2	2	no	—
91	C₁₉×#123	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
96	C₁₉×#121	—	2	2	no	—
97	C₁₉×#121	—	2	2	no	—
98	C₁₉×#121	—	2	2	no	—
99	C₁₉×#121	—	2	1	no	—
100	C₁₉×#121	—	2	2	no	—
101	C₁₉×#121	—	2	2	no	—
102	C₁₉×#121	—	2	1	no	—
103	C₁₉×#121	—	2	1	no	—
104	C₁₉×#121	D₄	1	1	yes	characteristic
105	C₁₉×#120	—	2	2	no	—
106	C₁₉×#120	—	2	2	no	—
107	C₁₉×#120	—	2	2	no	—
108	C₁₉×#120	—	2	2	no	—
109	C₁₉×#120	—	2	2	no	—
110	C₄×Q₈×C₁₉	—	2	1	no	—
111	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
112	C₄×D₄×C₁₉	—	2	2	no	—
113	C₄×D₄×C₁₉	—	2	2	no	—
114	C₄×D₄×C₁₉	—	2	1	no	—
115	C₄×D₄×C₁₉	—	2	1	no	—
116	C₄×D₄×C₁₉	—	2	1	no	—
117	C₄×D₄×C₁₉	—	2	1	no	—
118	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
119	C₁₉×#117	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
121	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
123	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
124	C₁₉×C₄⋊C₈	—	2	1	no	—
125	C₁₉×#102	—	2	2	no	—
126	C₁₉×#102	—	2	2	no	—
127	C₁₉×C₂²⋊C₈	—	2	1	no	—
128	C₁₉×#97	—	2	1	no	—
129	C₁₉×#97	C₂³	1	2	yes	—
130	C₁₉×#97	C₂³	1	2	yes	—
131	C₁₉×#97	C₂³	1	2	yes	—
132	C₄×C₈×C₁₉	—	2	1	no	—
133	C₂⁴×C₁₉	—	2	2	no	—
134	C₂⁴×C₁₉	—	2	1	no	—
135	C₂⁴×C₁₉	—	4	1	no	—
136	#41×C₁₉	—	4	4	no	—
137	#41×C₁₉	—	8	2	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	4	2	no	—
140	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
142	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	2	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	2	2	no	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	2	no	—
154	C₂×D₄×C₁₉	—	2	2	no	—
155	C₂×D₄×C₁₉	—	2	2	no	—
156	C₂×D₄×C₁₉	—	4	2	no	—
157	C₂×D₄×C₁₉	—	4	2	no	—
158	C₂×D₄×C₁₉	—	4	2	no	—
159	C₂×D₄×C₁₉	—	4	4	no	—
160	C₂×D₄×C₁₉	—	4	1	no	—
161	C₂×D₄×C₁₉	—	4	1	no	—
162	C₂×D₄×C₁₉	—	4	1	no	—
163	C₂×D₄×C₁₉	—	8	2	no	—
164	C₂×D₄×C₁₉	—	8	2	no	—
165	C₂×D₄×C₁₉	—	8	4	no	—
166	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
168	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
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	1	no	—
173	C₂²×C₄×C₁₉	—	2	2	no	—
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	SD₁₆×C₁₉	—	4	8	no	—
178	SD₁₆×C₁₉	—	4	8	no	—
179	SD₁₆×C₁₉	—	8	2	no	—
180	D₈×C₁₉	—	4	8	no	—
181	D₈×C₁₉	—	4	8	no	—
182	D₈×C₁₉	—	8	2	no	—
183	M₁₆×C₁₉	—	2	4	no	—
184	C₂×C₈×C₁₉	—	2	4	no	—
185	C₂×C₈×C₁₉	—	2	2	no	—
186	C₂×C₈×C₁₉	—	2	2	no	—
187	C₂×C₈×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	2	1	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	1	no	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	1	no	—
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	1	no	—
211	C₂²⋊C₄×C₁₉	—	2	1	no	—
212	C₂²⋊C₄×C₁₉	—	2	2	no	—
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₄²×C₁₉	—	2	2	no	—
215	C₄²×C₁₉	—	2	1	no	—
216	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
220	#19014	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	2	2	no	—
223	C₂³×C₁₉	—	2	2	no	—
224	C₂³×C₁₉	—	4	2	no	—
225	C₂³×C₁₉	—	4	2	no	—
226	C₂³×C₁₉	—	8	1	no	—
227	C₂³×C₁₉	—	8	1	no	—
228	C₂³×C₁₉	—	8	2	no	—
229	C₂³×C₁₉	—	8	2	no	—
230	C₂³×C₁₉	—	8	2	no	—
231	C₂³×C₁₉	—	8	2	no	—
232	C₂³×C₁₉	—	8	2	no	—
233	C₂³×C₁₉	—	8	2	no	—
234	C₂³×C₁₉	#120	1	1	yes	characteristic
235	Q₈×C₁₉	—	4	2	no	—
236	Q₈×C₁₉	—	4	2	no	—
237	Q₈×C₁₉	—	4	1	no	—
238	Q₈×C₁₉	—	4	2	no	—
239	D₄×C₁₉	—	4	2	no	—
240	D₄×C₁₉	—	4	2	no	—
241	D₄×C₁₉	—	4	1	no	—
242	D₄×C₁₉	—	4	2	no	—
243	D₄×C₁₉	—	4	4	no	—
244	D₄×C₁₉	—	4	2	no	—
245	D₄×C₁₉	—	4	2	no	—
246	D₄×C₁₉	—	4	2	no	—
247	D₄×C₁₉	—	4	2	no	—
248	D₄×C₁₉	—	4	4	no	—
249	D₄×C₁₉	—	4	2	no	—
250	D₄×C₁₉	—	4	2	no	—
251	D₄×C₁₉	—	8	1	no	—
252	D₄×C₁₉	—	8	2	no	—
253	D₄×C₁₉	—	8	2	no	—
254	D₄×C₁₉	—	8	2	no	—
255	D₄×C₁₉	—	8	2	no	—
256	D₄×C₁₉	—	8	2	no	—
257	D₄×C₁₉	—	8	2	no	—
258	D₄×C₁₉	—	8	2	no	—
259	D₄×C₁₉	—	8	2	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	2	no	—
264	C₂×C₄×C₁₉	—	2	2	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	2	no	—
269	C₂×C₄×C₁₉	—	8	2	no	—
270	C₂×C₄×C₁₉	—	8	1	no	—
271	C₂×C₄×C₁₉	—	8	2	no	—
272	C₂×C₄×C₁₉	—	8	2	no	—
273	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
274	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
275	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
276	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
279	C₈×C₁₉	—	2	4	no	—
280	C₈×C₁₉	—	2	4	no	—
281	C₈×C₁₉	—	4	2	no	—
282	#3558	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#3217	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#3151	C₂×C₁₉	1	1	yes	characteristic, complemented
285	C₂×#496	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1656	C₂×C₁₉	1	4	yes	complemented
287	#1655	C₂×C₁₉	1	4	yes	complemented
288	#1530	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1527	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1524	C₂×C₁₉	1	1	yes	characteristic, complemented
291	C₂²×C₁₉	—	2	1	no	—
292	C₂²×C₁₉	—	2	1	no	—
293	C₂²×C₁₉	—	4	1	no	—
294	C₂²×C₁₉	—	4	2	no	—
295	C₂²×C₁₉	—	4	2	no	—
296	C₂²×C₁₉	—	4	2	no	—
297	C₂²×C₁₉	—	4	2	no	—
298	C₂²×C₁₉	—	4	1	no	—
299	C₂²×C₁₉	—	4	1	no	—
300	C₂²×C₁₉	—	4	2	no	—
301	C₂²×C₁₉	—	4	2	no	—
302	C₂²×C₁₉	—	8	2	no	—
303	C₂²×C₁₉	—	8	2	no	—
304	C₂²×C₁₉	—	8	2	no	—
305	C₂²×C₁₉	—	16	2	no	—
306	C₂²×C₁₉	—	16	4	no	—
307	C₂²×C₁₉	—	16	4	no	—
308	C₂²×C₁₉	#453	1	2	yes	—
309	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
310	C₄×C₁₉	—	2	1	no	—
311	C₄×C₁₉	—	2	1	no	—
312	C₄×C₁₉	—	2	1	no	—
313	C₄×C₁₉	—	2	1	no	—
314	C₄×C₁₉	—	2	1	no	—
315	C₄×C₁₉	—	4	1	no	—
316	C₄×C₁₉	—	4	1	no	—
317	C₄×C₁₉	—	4	2	no	—
318	C₄×C₁₉	—	4	2	no	—
319	C₄×C₁₉	—	4	1	no	—
320	C₄×C₁₉	#453	1	2	yes	—
321	C₂×AGL(1,ℤ/8)	—	2	2	no	—
322	C₂²×SD₁₆	—	2	1	no	—
323	C₂²×D₈	—	2	1	no	—
324	#562	C₂²×C₁₉	1	2	yes	complemented
325	H(3,𝔽₄)	C₂²×C₁₉	1	2	yes	complemented
326	#559	—	2	1	no	—
327	#548	—	2	1	no	—
328	#546	—	2	2	no	—
329	#546	—	2	1	no	—
330	D₄²	—	2	1	no	—
331	#542	—	2	1	no	—
332	#538	—	2	2	no	—
333	#538	—	2	1	no	—
334	#535	—	2	1	no	—
335	#534	—	2	1	no	—
336	#532	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic, complemented
338	#529	C₂²×C₁₉	1	1	yes	characteristic
339	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
340	#496	—	2	2	no	—
341	#496	C₂²×C₁₉	1	4	yes	complemented
342	#496	C₂²×C₁₉	1	4	yes	complemented
343	#496	C₂²×C₁₉	1	2	yes	complemented
344	#493	—	2	1	no	—
345	#492	—	2	1	no	—
346	#490	C₂²×C₁₉	1	2	yes	complemented
347	#460	—	2	1	no	—
348	#459	—	2	1	no	—
349	#450	—	2	1	no	—
350	#447	—	2	1	no	—
351	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
352	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
353	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic, complemented
354	#330	C₂²×C₁₉	1	2	yes	complemented
355	#329	C₂²×C₁₉	1	2	yes	complemented
356	#329	C₂²×C₁₉	1	4	yes	complemented
357	#329	C₂²×C₁₉	1	4	yes	complemented
358	C₂×C₁₉	—	2	2	no	—
359	C₂×C₁₉	—	8	2	no	—
360	C₂×C₁₉	—	8	1	no	—
361	C₂×C₁₉	—	8	2	no	—
362	C₂×C₁₉	—	16	2	no	—
363	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
364	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
365	C₂×C₁₉	#3021	1	1	yes	characteristic
366	C₂×#41	—	2	1	no	—
367	C₂×#41	D₄×C₁₉	1	2	yes	—
368	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
369	C₂²×D₄	—	2	2	no	—
370	C₂²×D₄	—	2	1	no	—
371	C₂²×D₄	—	2	1	no	—
372	C₂²×D₄	—	2	1	no	—
373	C₂²×D₄	—	2	1	no	—
374	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
375	AGL(1,ℤ/8)	—	4	8	no	—
376	C₂×SD₁₆	—	2	4	no	—
377	C₂×SD₁₆	—	2	4	no	—
378	C₂×SD₁₆	—	2	2	no	—
379	C₂×SD₁₆	—	4	4	no	—
380	C₂×D₈	—	2	4	no	—
381	C₂×D₈	—	2	4	no	—
382	C₂×D₈	—	2	2	no	—
383	C₂×D₈	—	4	4	no	—
384	C₂×M₁₆	—	2	1	no	—
385	C₂²×C₈	—	2	1	no	—
386	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
387	#127	—	2	1	no	—
388	#127	—	2	1	no	—
389	#127	—	2	1	no	—
390	#127	—	2	1	no	—
391	#127	D₄×C₁₉	1	1	yes	characteristic
392	#127	C₂³×C₁₉	1	2	yes	—
393	#126	—	2	2	no	—
394	#126	—	2	1	no	—
395	#125	C₂³×C₁₉	1	1	yes	characteristic
396	#124	—	2	1	no	—
397	#124	—	2	2	no	—
398	#124	—	2	2	no	—
399	#124	—	2	2	no	—
400	#124	—	2	1	no	—
401	#124	—	2	1	no	—
402	#124	D₄×C₁₉	1	2	yes	—
403	#124	C₂³×C₁₉	1	2	yes	—
404	#124	C₂³×C₁₉	1	1	yes	characteristic
405	#124	C₂³×C₁₉	1	2	yes	—
406	#123	—	2	2	no	—
407	#123	—	2	2	no	—
408	#123	—	2	1	no	—
409	#123	—	2	2	no	—
410	#123	—	2	2	no	—
411	C₂²⋊Q₈	—	2	1	no	—
412	C₂²⋊Q₈	—	2	2	no	—
413	C₂²⋊Q₈	—	2	2	no	—
414	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
415	#121	—	2	2	no	—
416	#121	—	2	2	no	—
417	#121	—	2	2	no	—
418	#121	—	2	1	no	—
419	#121	—	2	2	no	—
420	#121	—	2	2	no	—
421	#121	—	2	1	no	—
422	#121	—	2	1	no	—
423	#121	D₄×C₁₉	1	1	yes	characteristic
424	#120	—	2	2	no	—
425	#120	—	2	2	no	—
426	#120	—	2	2	no	—
427	#120	—	2	2	no	—
428	#120	—	2	2	no	—
429	C₄×Q₈	—	2	1	no	—
430	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
431	C₄×D₄	—	2	2	no	—
432	C₄×D₄	—	2	2	no	—
433	C₄×D₄	—	2	1	no	—
434	C₄×D₄	—	2	1	no	—
435	C₄×D₄	—	2	1	no	—
436	C₄×D₄	—	2	1	no	—
437	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
438	#117	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	2	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
443	C₄⋊C₈	—	2	1	no	—
444	#102	—	2	2	no	—
445	#102	—	2	2	no	—
446	C₂²⋊C₈	—	2	1	no	—
447	#97	—	2	1	no	—
448	#97	C₂³×C₁₉	1	2	yes	—
449	#97	C₂³×C₁₉	1	2	yes	—
450	#97	C₂³×C₁₉	1	2	yes	—
451	C₄×C₈	—	2	1	no	—
452	C₁₉	#19014	1	1	yes	characteristic, direct product factor, Sylow
453	C₂⁴	—	2	2	no	—
454	C₂⁴	—	2	1	no	—
455	C₂⁴	—	4	1	no	—
456	#41	—	4	4	no	—
457	#41	—	8	2	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	4	2	no	—
460	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
462	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	4	2	no	—
477	C₂×D₄	—	4	2	no	—
478	C₂×D₄	—	4	2	no	—
479	C₂×D₄	—	4	4	no	—
480	C₂×D₄	—	4	1	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂×D₄	—	4	1	no	—
483	C₂×D₄	—	8	2	no	—
484	C₂×D₄	—	8	2	no	—
485	C₂×D₄	—	8	4	no	—
486	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
488	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
497	SD₁₆	—	4	8	no	—
498	SD₁₆	—	4	8	no	—
499	SD₁₆	—	8	2	no	—
500	D₈	—	4	8	no	—
501	D₈	—	4	8	no	—
502	D₈	—	8	2	no	—
503	M₁₆	—	2	4	no	—
504	C₂×C₈	—	2	4	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₂×C₈	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	1	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	1	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	1	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₄²	—	2	2	no	—
535	C₄²	—	2	1	no	—
536	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
537	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
538	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
539	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
540	C₂³	—	2	1	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	4	2	no	—
544	C₂³	—	4	2	no	—
545	C₂³	—	8	1	no	—
546	C₂³	—	8	1	no	—
547	C₂³	—	8	2	no	—
548	C₂³	—	8	2	no	—
549	C₂³	—	8	2	no	—
550	C₂³	—	8	2	no	—
551	C₂³	—	8	2	no	—
552	C₂³	—	8	2	no	—
553	C₂³	C₁₉×#120	1	1	yes	characteristic
554	Q₈	—	4	2	no	—
555	Q₈	—	4	2	no	—
556	Q₈	—	4	1	no	—
557	Q₈	—	4	2	no	—
558	D₄	—	4	2	no	—
559	D₄	—	4	2	no	—
560	D₄	—	4	1	no	—
561	D₄	—	4	2	no	—
562	D₄	—	4	4	no	—
563	D₄	—	4	2	no	—
564	D₄	—	4	2	no	—
565	D₄	—	4	2	no	—
566	D₄	—	4	2	no	—
567	D₄	—	4	4	no	—
568	D₄	—	4	2	no	—
569	D₄	—	4	2	no	—
570	D₄	—	8	1	no	—
571	D₄	—	8	2	no	—
572	D₄	—	8	2	no	—
573	D₄	—	8	2	no	—
574	D₄	—	8	2	no	—
575	D₄	—	8	2	no	—
576	D₄	—	8	2	no	—
577	D₄	—	8	2	no	—
578	D₄	—	8	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	8	2	no	—
589	C₂×C₄	—	8	1	no	—
590	C₂×C₄	—	8	2	no	—
591	C₂×C₄	—	8	2	no	—
592	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
593	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
594	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
595	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
596	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
597	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
598	C₈	—	2	4	no	—
599	C₈	—	2	4	no	—
600	C₈	—	4	2	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	8	2	no	—
613	C₂²	—	8	2	no	—
614	C₂²	—	8	2	no	—
615	C₂²	—	16	2	no	—
616	C₂²	—	16	4	no	—
617	C₂²	—	16	4	no	—
618	C₂²	C₁₉×#453	1	2	yes	—
619	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	1	no	—
630	C₄	C₁₉×#453	1	2	yes	—
631	C₂	—	2	2	no	—
632	C₂	—	8	1	no	—
633	C₂	—	8	2	no	—
634	C₂	—	8	2	no	—
635	C₂	—	16	2	no	—
636	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
637	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
638	C₂	C₁₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ 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×#3558	C₂	semidirect
2. C₁₉×#3217	C₂	semidirect
3. C₁₉×#3151	C₂	semidirect
4. C₂×C₁₉×#496	C₂	semidirect
5. C₁₉×#1656	C₂	semidirect
6. C₁₉×#1655	C₂	semidirect
7. C₁₉×#1530	C₂	semidirect
8. C₁₉×#1527	C₂	semidirect
9. C₁₉×#1524	C₂	semidirect
13. C₁₉×#562	C₂²	semidirect
14. C₁₉×H(3,𝔽₄)	C₂²	semidirect
26. C₂×C₁₉×#127	C₂²	semidirect
30. C₁₉×#496	C₂²	semidirect
31. C₁₉×#496	C₂²	semidirect
32. C₁₉×#496	C₂²	semidirect
35. C₁₉×#490	C₂²	semidirect
40. C₁₉×#432	C₂²	semidirect
41. C₄×M₁₆×C₁₉	C₂²	semidirect
42. C₂×C₁₉×#97	C₂²	semidirect
43. C₁₉×#330	C₂²	semidirect
44. C₁₉×#329	C₂²	semidirect
45. C₁₉×#329	C₂²	semidirect
46. C₁₉×#329	C₂²	semidirect
220. #19014	C₁₉	direct (N × H)
282. #3558	C₂×C₁₉	semidirect
283. #3217	C₂×C₁₉	semidirect
284. #3151	C₂×C₁₉	semidirect
285. C₂×#496	C₂×C₁₉	semidirect
286. #1656	C₂×C₁₉	semidirect
287. #1655	C₂×C₁₉	semidirect
288. #1530	C₂×C₁₉	semidirect
289. #1527	C₂×C₁₉	semidirect
290. #1524	C₂×C₁₉	semidirect
324. #562	C₂²×C₁₉	semidirect
325. H(3,𝔽₄)	C₂²×C₁₉	semidirect
337. C₂×#127	C₂²×C₁₉	semidirect
341. #496	C₂²×C₁₉	semidirect
342. #496	C₂²×C₁₉	semidirect
343. #496	C₂²×C₁₉	semidirect
346. #490	C₂²×C₁₉	semidirect
351. #432	C₂²×C₁₉	semidirect
352. C₄×M₁₆	C₂²×C₁₉	semidirect
353. C₂×#97	C₂²×C₁₉	semidirect
354. #330	C₂²×C₁₉	semidirect
355. #329	C₂²×C₁₉	semidirect
356. #329	C₂²×C₁₉	semidirect
357. #329	C₂²×C₁₉	semidirect
452. C₁₉	#19014	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×#3558	2
C₁₉×#3217	2
C₁₉×#3151	2
C₂×C₁₉×#496	2
C₁₉×#1656	2
C₁₉×#1655	2
C₁₉×#1530	2
C₁₉×#1527	2
C₁₉×#1524	2
#19014	19

Subgroups — C19×#19014 #18024973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19014 #18024973