Subgroups — C₁₉×#19788 #18025747

Order 4864.

704 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×#3366	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3294	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3284	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1717	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1702	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1644	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1635	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1621	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1619	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1582	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1580	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#135	—	2	1	no	—
17	C₁₉×#554	C₂²	1	1	yes	characteristic
18	C₁₉×#550	C₂²	1	1	yes	characteristic, complemented
19	C₁₉×#547	C₂²	1	1	yes	characteristic
20	D₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#493	C₂²	1	1	yes	characteristic
22	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#490	—	2	1	no	—
24	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#486	C₂²	1	1	yes	characteristic
26	C₁₉×#486	C₂²	1	1	yes	characteristic
27	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#481	—	2	1	no	—
29	C₁₉×#480	—	2	1	no	—
30	C₁₉×#478	—	2	1	no	—
31	C₁₉×#476	C₂²	1	1	yes	characteristic
32	C₁₉×#476	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#474	C₂²	1	1	yes	characteristic
34	C₁₉×#466	—	2	1	no	—
35	C₁₉×#465	—	2	1	no	—
36	C₁₉×#465	—	2	1	no	—
37	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#460	C₂²	1	1	yes	characteristic
39	C₁₉×#459	—	2	1	no	—
40	C₁₉×#459	C₂²	1	1	yes	characteristic
41	C₁₉×#459	C₂²	1	1	yes	characteristic
42	C₁₉×#459	C₂²	1	1	yes	characteristic
43	C₁₉×#452	—	2	1	no	—
44	C₁₉×#450	—	2	1	no	—
45	C₁₉×#449	—	2	1	no	—
46	C₁₉×#447	—	2	1	no	—
47	C₁₉×#446	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#442	—	2	1	no	—
49	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
50	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
51	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₁₉×#102	—	2	1	no	—
55	C₂×C₁₉×#102	—	2	1	no	—
56	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#333	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#331	C₂²	1	1	yes	characteristic
61	C₁₉×#331	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#322	C₂²	1	1	yes	characteristic, complemented
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂×#41×C₁₉	—	2	1	no	—
69	C₂²×D₄×C₁₉	—	2	1	no	—
70	C₂²×D₄×C₁₉	—	2	1	no	—
71	C₁₉×#135	—	4	4	no	—
72	C₂×Q₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×SD₁₆×C₁₉	—	2	1	no	—
75	C₂×SD₁₆×C₁₉	—	2	1	no	—
76	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
77	C₂×D₈×C₁₉	—	2	1	no	—
78	C₂×D₈×C₁₉	—	2	1	no	—
79	C₂×D₈×C₁₉	—	2	1	no	—
80	C₂×D₈×C₁₉	—	4	1	no	—
81	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
82	C₂²×C₈×C₁₉	—	2	1	no	—
83	C₂²×C₈×C₁₉	—	2	1	no	—
84	C₂²×C₈×C₁₉	—	2	1	no	—
85	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₁₉×#127	—	2	1	no	—
88	C₁₉×#127	C₂³	1	1	yes	characteristic
89	C₁₉×#127	C₂³	1	1	yes	characteristic
90	C₁₉×#125	—	2	1	no	—
91	C₁₉×#123	—	4	1	no	—
92	C₁₉×C₂²⋊Q₈	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	—	2	1	no	—
94	C₁₉×C₂²⋊Q₈	—	4	1	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	2	1	no	—
98	C₁₉×#121	—	2	1	no	—
99	C₁₉×#121	—	4	1	no	—
100	C₁₉×#120	—	4	1	no	—
101	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	—	2	1	no	—
104	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₁₉×#107	—	2	1	no	—
110	C₁₉×#107	D₄	1	1	yes	characteristic
111	C₁₉×#106	—	2	1	no	—
112	C₁₉×#106	—	2	1	no	—
113	C₁₉×#106	D₄	1	1	yes	characteristic
114	C₁₉×C₄⋊C₈	—	2	1	no	—
115	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₉×#103	—	2	1	no	—
120	C₁₉×#103	—	4	1	no	—
121	C₁₉×#103	D₄	1	1	yes	characteristic
122	C₁₉×#102	—	2	1	no	—
123	C₁₉×#102	—	2	1	no	—
124	C₁₉×#102	—	2	1	no	—
125	C₁₉×#102	—	2	1	no	—
126	C₁₉×#102	—	2	1	no	—
127	C₁₉×#102	—	2	1	no	—
128	C₁₉×#102	—	2	1	no	—
129	C₁₉×#102	—	2	1	no	—
130	C₁₉×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	2	1	no	—
134	C₁₉×#102	—	2	1	no	—
135	C₁₉×#102	D₄	1	1	yes	characteristic
136	C₁₉×#102	D₄	1	1	yes	characteristic
137	C₁₉×#102	D₄	1	1	yes	characteristic
138	C₁₉×C₂²⋊C₈	—	2	1	no	—
139	C₁₉×C₂²⋊C₈	—	2	1	no	—
140	C₁₉×C₂²⋊C₈	—	2	1	no	—
141	C₁₉×#97	—	2	1	no	—
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
145	C₂⁴×C₁₉	—	4	1	no	—
146	#41×C₁₉	—	4	2	no	—
147	#41×C₁₉	—	4	2	no	—
148	#41×C₁₉	—	8	1	no	—
149	#41×C₁₉	—	8	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	4	1	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	—	4	2	no	—
164	C₂×D₄×C₁₉	—	4	2	no	—
165	C₂×D₄×C₁₉	—	4	1	no	—
166	C₂×D₄×C₁₉	—	8	1	no	—
167	C₂×D₄×C₁₉	—	8	1	no	—
168	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	4	1	no	—
175	C₂²×C₄×C₁₉	—	4	1	no	—
176	C₂²×C₄×C₁₉	—	4	1	no	—
177	Q₁₆×C₁₉	—	4	2	no	—
178	SD₁₆×C₁₉	—	2	2	no	—
179	SD₁₆×C₁₉	—	4	2	no	—
180	SD₁₆×C₁₉	—	8	1	no	—
181	SD₁₆×C₁₉	—	8	1	no	—
182	D₈×C₁₉	—	2	2	no	—
183	D₈×C₁₉	—	4	2	no	—
184	D₈×C₁₉	—	4	2	no	—
185	D₈×C₁₉	—	8	1	no	—
186	D₈×C₁₉	—	8	2	no	—
187	C₂×C₈×C₁₉	—	2	1	no	—
188	C₂×C₈×C₁₉	—	2	1	no	—
189	C₂×C₈×C₁₉	—	2	1	no	—
190	C₂×C₈×C₁₉	—	2	1	no	—
191	C₂×C₈×C₁₉	—	2	1	no	—
192	C₂×C₈×C₁₉	—	4	2	no	—
193	C₂×C₈×C₁₉	—	8	1	no	—
194	C₂×C₈×C₁₉	—	8	1	no	—
195	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	1	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	4	1	no	—
205	C₄⋊C₄×C₁₉	—	4	1	no	—
206	C₄⋊C₄×C₁₉	—	4	1	no	—
207	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₂²⋊C₄×C₁₉	—	2	1	no	—
212	C₂²⋊C₄×C₁₉	—	2	1	no	—
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₂²⋊C₄×C₁₉	—	4	1	no	—
215	C₂²⋊C₄×C₁₉	—	4	1	no	—
216	C₂²⋊C₄×C₁₉	—	4	1	no	—
217	C₂²⋊C₄×C₁₉	—	4	1	no	—
218	C₄²×C₁₉	—	2	1	no	—
219	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
220	#19788	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	2	1	no	—
223	C₂³×C₁₉	—	2	1	no	—
224	C₂³×C₁₉	—	4	1	no	—
225	C₂³×C₁₉	—	4	1	no	—
226	C₂³×C₁₉	—	8	2	no	—
227	C₂³×C₁₉	—	8	2	no	—
228	C₂³×C₁₉	—	16	1	no	—
229	Q₈×C₁₉	—	2	1	no	—
230	Q₈×C₁₉	—	2	1	no	—
231	Q₈×C₁₉	—	4	1	no	—
232	Q₈×C₁₉	—	4	1	no	—
233	Q₈×C₁₉	—	8	1	no	—
234	D₄×C₁₉	—	2	1	no	—
235	D₄×C₁₉	—	2	1	no	—
236	D₄×C₁₉	—	2	1	no	—
237	D₄×C₁₉	—	2	1	no	—
238	D₄×C₁₉	—	4	1	no	—
239	D₄×C₁₉	—	4	1	no	—
240	D₄×C₁₉	—	4	1	no	—
241	D₄×C₁₉	—	4	1	no	—
242	D₄×C₁₉	—	4	1	no	—
243	D₄×C₁₉	—	4	1	no	—
244	D₄×C₁₉	—	4	1	no	—
245	D₄×C₁₉	—	4	1	no	—
246	D₄×C₁₉	—	8	1	no	—
247	D₄×C₁₉	—	8	1	no	—
248	D₄×C₁₉	—	8	2	no	—
249	D₄×C₁₉	—	8	2	no	—
250	D₄×C₁₉	—	8	2	no	—
251	D₄×C₁₉	—	8	2	no	—
252	D₄×C₁₉	—	16	1	no	—
253	D₄×C₁₉	#135	1	2	yes	complemented
254	D₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	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	—	8	2	no	—
269	C₂×C₄×C₁₉	—	8	2	no	—
270	C₂×C₄×C₁₉	—	16	1	no	—
271	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
274	C₈×C₁₉	—	2	1	no	—
275	C₈×C₁₉	—	2	1	no	—
276	C₈×C₁₉	—	2	1	no	—
277	C₈×C₁₉	—	2	1	no	—
278	C₈×C₁₉	—	4	1	no	—
279	C₈×C₁₉	—	4	1	no	—
280	C₈×C₁₉	—	4	1	no	—
281	C₈×C₁₉	—	4	1	no	—
282	C₈×C₁₉	—	4	1	no	—
283	#3366	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#3295	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#3294	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#3284	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1717	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1702	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1677	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1677	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1665	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1644	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1635	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1621	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#1619	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1582	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#1580	C₂×C₁₉	1	1	yes	characteristic, complemented
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	—	2	2	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	1	no	—
303	C₂²×C₁₉	—	4	1	no	—
304	C₂²×C₁₉	—	4	1	no	—
305	C₂²×C₁₉	—	4	1	no	—
306	C₂²×C₁₉	—	4	1	no	—
307	C₂²×C₁₉	—	8	1	no	—
308	C₂²×C₁₉	—	8	1	no	—
309	C₂²×C₁₉	—	8	1	no	—
310	C₂²×C₁₉	—	8	1	no	—
311	C₂²×C₁₉	—	8	1	no	—
312	C₂²×C₁₉	—	8	1	no	—
313	C₂²×C₁₉	—	16	4	no	—
314	C₂²×C₁₉	D₄²	1	1	yes	characteristic
315	C₄×C₁₉	—	2	1	no	—
316	C₄×C₁₉	—	4	1	no	—
317	C₄×C₁₉	—	4	1	no	—
318	C₄×C₁₉	—	4	1	no	—
319	C₄×C₁₉	—	4	1	no	—
320	C₄×C₁₉	—	4	1	no	—
321	C₄×C₁₉	—	8	1	no	—
322	C₄×C₁₉	—	8	1	no	—
323	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
324	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
325	C₄×C₁₉	#576	1	1	yes	characteristic
326	C₄×C₁₉	#577	1	1	yes	characteristic
327	C₂×#135	—	2	1	no	—
328	#554	C₂²×C₁₉	1	1	yes	characteristic
329	#550	C₂²×C₁₉	1	1	yes	characteristic, complemented
330	#547	C₂²×C₁₉	1	1	yes	characteristic
331	D₄²	C₂²×C₁₉	1	1	yes	characteristic
332	#493	C₂²×C₁₉	1	1	yes	characteristic
333	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
334	#490	—	2	1	no	—
335	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
336	#486	C₂²×C₁₉	1	1	yes	characteristic
337	#486	C₂²×C₁₉	1	1	yes	characteristic
338	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	#481	—	2	1	no	—
340	#480	—	2	1	no	—
341	#478	—	2	1	no	—
342	#476	C₂²×C₁₉	1	1	yes	characteristic
343	#476	C₂²×C₁₉	1	1	yes	characteristic, complemented
344	#474	C₂²×C₁₉	1	1	yes	characteristic
345	#466	—	2	1	no	—
346	#465	—	2	1	no	—
347	#465	—	2	1	no	—
348	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
349	#460	C₂²×C₁₉	1	1	yes	characteristic
350	#459	—	2	1	no	—
351	#459	C₂²×C₁₉	1	1	yes	characteristic
352	#459	C₂²×C₁₉	1	1	yes	characteristic
353	#459	C₂²×C₁₉	1	1	yes	characteristic
354	#452	—	2	1	no	—
355	#450	—	2	1	no	—
356	#449	—	2	1	no	—
357	#447	—	2	1	no	—
358	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
359	#442	—	2	1	no	—
360	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
361	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
362	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
363	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
364	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
365	C₂×#102	—	2	1	no	—
366	C₂×#102	—	2	1	no	—
367	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
368	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
369	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
370	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
371	#331	C₂²×C₁₉	1	1	yes	characteristic
372	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
373	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
374	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
375	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
376	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
377	#322	C₂²×C₁₉	1	1	yes	characteristic, complemented
378	C₂×C₁₉	—	4	2	no	—
379	C₂×C₁₉	—	4	2	no	—
380	C₂×C₁₉	—	8	1	no	—
381	C₂×C₁₉	—	16	1	no	—
382	C₂×C₁₉	—	16	1	no	—
383	C₂×C₁₉	#3264	1	1	yes	characteristic
384	C₂×C₁₉	#3282	1	1	yes	characteristic
385	C₂×C₁₉	#3288	1	1	yes	characteristic
386	C₂×#41	—	2	1	no	—
387	C₂×#41	—	2	1	no	—
388	C₂²×D₄	—	2	1	no	—
389	C₂²×D₄	—	2	1	no	—
390	#135	—	4	4	no	—
391	C₂×Q₁₆	—	2	1	no	—
392	C₂×SD₁₆	—	2	1	no	—
393	C₂×SD₁₆	—	2	1	no	—
394	C₂×SD₁₆	—	2	1	no	—
395	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
396	C₂×D₈	—	2	1	no	—
397	C₂×D₈	—	2	1	no	—
398	C₂×D₈	—	2	1	no	—
399	C₂×D₈	—	4	1	no	—
400	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
401	C₂²×C₈	—	2	1	no	—
402	C₂²×C₈	—	2	1	no	—
403	C₂²×C₈	—	2	1	no	—
404	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
405	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
406	#127	—	2	1	no	—
407	#127	C₂³×C₁₉	1	1	yes	characteristic
408	#127	C₂³×C₁₉	1	1	yes	characteristic
409	#125	—	2	1	no	—
410	#123	—	4	1	no	—
411	C₂²⋊Q₈	—	2	1	no	—
412	C₂²⋊Q₈	—	2	1	no	—
413	C₂²⋊Q₈	—	4	1	no	—
414	#121	—	2	1	no	—
415	#121	—	2	1	no	—
416	#121	—	2	1	no	—
417	#121	—	2	1	no	—
418	#121	—	4	1	no	—
419	#120	—	4	1	no	—
420	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	—	2	1	no	—
423	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
424	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
425	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	#107	—	2	1	no	—
429	#107	D₄×C₁₉	1	1	yes	characteristic
430	#106	—	2	1	no	—
431	#106	—	2	1	no	—
432	#106	D₄×C₁₉	1	1	yes	characteristic
433	C₄⋊C₈	—	2	1	no	—
434	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
435	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
436	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
437	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
438	#103	—	2	1	no	—
439	#103	—	4	1	no	—
440	#103	D₄×C₁₉	1	1	yes	characteristic
441	#102	—	2	1	no	—
442	#102	—	2	1	no	—
443	#102	—	2	1	no	—
444	#102	—	2	1	no	—
445	#102	—	2	1	no	—
446	#102	—	2	1	no	—
447	#102	—	2	1	no	—
448	#102	—	2	1	no	—
449	#102	—	2	1	no	—
450	#102	—	2	1	no	—
451	#102	—	2	1	no	—
452	#102	—	2	1	no	—
453	#102	—	2	1	no	—
454	#102	D₄×C₁₉	1	1	yes	characteristic
455	#102	D₄×C₁₉	1	1	yes	characteristic
456	#102	D₄×C₁₉	1	1	yes	characteristic
457	C₂²⋊C₈	—	2	1	no	—
458	C₂²⋊C₈	—	2	1	no	—
459	C₂²⋊C₈	—	2	1	no	—
460	#97	—	2	1	no	—
461	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
462	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
463	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
464	C₁₉	#19788	1	1	yes	characteristic, direct product factor, Sylow
465	C₂⁴	—	4	1	no	—
466	#41	—	4	2	no	—
467	#41	—	4	2	no	—
468	#41	—	8	1	no	—
469	#41	—	8	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	4	1	no	—
480	C₂×D₄	—	4	1	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂×D₄	—	4	1	no	—
483	C₂×D₄	—	4	2	no	—
484	C₂×D₄	—	4	2	no	—
485	C₂×D₄	—	4	1	no	—
486	C₂×D₄	—	8	1	no	—
487	C₂×D₄	—	8	1	no	—
488	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	4	1	no	—
495	C₂²×C₄	—	4	1	no	—
496	C₂²×C₄	—	4	1	no	—
497	Q₁₆	—	4	2	no	—
498	SD₁₆	—	2	2	no	—
499	SD₁₆	—	4	2	no	—
500	SD₁₆	—	8	1	no	—
501	SD₁₆	—	8	1	no	—
502	D₈	—	2	2	no	—
503	D₈	—	4	2	no	—
504	D₈	—	4	2	no	—
505	D₈	—	8	1	no	—
506	D₈	—	8	2	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	4	2	no	—
513	C₂×C₈	—	8	1	no	—
514	C₂×C₈	—	8	1	no	—
515	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	4	1	no	—
525	C₄⋊C₄	—	4	1	no	—
526	C₄⋊C₄	—	4	1	no	—
527	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
530	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	2	1	no	—
533	C₂²⋊C₄	—	2	1	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₂²⋊C₄	—	4	1	no	—
536	C₂²⋊C₄	—	4	1	no	—
537	C₂²⋊C₄	—	4	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
540	C₂³	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	8	2	no	—
546	C₂³	—	8	2	no	—
547	C₂³	—	16	1	no	—
548	Q₈	—	2	1	no	—
549	Q₈	—	2	1	no	—
550	Q₈	—	4	1	no	—
551	Q₈	—	4	1	no	—
552	Q₈	—	8	1	no	—
553	D₄	—	2	1	no	—
554	D₄	—	2	1	no	—
555	D₄	—	2	1	no	—
556	D₄	—	2	1	no	—
557	D₄	—	4	1	no	—
558	D₄	—	4	1	no	—
559	D₄	—	4	1	no	—
560	D₄	—	4	1	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	1	no	—
565	D₄	—	8	1	no	—
566	D₄	—	8	1	no	—
567	D₄	—	8	2	no	—
568	D₄	—	8	2	no	—
569	D₄	—	8	2	no	—
570	D₄	—	8	2	no	—
571	D₄	—	16	1	no	—
572	D₄	C₁₉×#135	1	2	yes	complemented
573	D₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	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	—	8	2	no	—
588	C₂×C₄	—	8	2	no	—
589	C₂×C₄	—	16	1	no	—
590	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
591	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
592	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
593	C₈	—	2	1	no	—
594	C₈	—	2	1	no	—
595	C₈	—	2	1	no	—
596	C₈	—	2	1	no	—
597	C₈	—	4	1	no	—
598	C₈	—	4	1	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₈	—	4	1	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	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	—	16	4	no	—
618	C₂²	D₄²×C₁₉	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	8	1	no	—
626	C₄	—	8	1	no	—
627	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
628	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
629	C₄	C₁₉×#576	1	1	yes	characteristic
630	C₄	C₁₉×#577	1	1	yes	characteristic
631	C₂	—	4	2	no	—
632	C₂	—	4	2	no	—
633	C₂	—	8	1	no	—
634	C₂	—	16	1	no	—
635	C₂	—	16	1	no	—
636	C₂	C₁₉×#3264	1	1	yes	characteristic
637	C₂	C₁₉×#3282	1	1	yes	characteristic
638	C₂	C₁₉×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3366	C₂	semidirect
2. C₁₉×#3295	C₂	semidirect
3. C₁₉×#3294	C₂	semidirect
4. C₁₉×#3284	C₂	semidirect
5. C₁₉×#1717	C₂	semidirect
6. C₁₉×#1702	C₂	semidirect
7. C₁₉×#1677	C₂	semidirect
8. C₁₉×#1677	C₂	semidirect
9. C₁₉×#1665	C₂	semidirect
10. C₁₉×#1644	C₂	semidirect
11. C₁₉×#1635	C₂	semidirect
12. C₁₉×#1621	C₂	semidirect
13. C₁₉×#1619	C₂	semidirect
14. C₁₉×#1582	C₂	semidirect
15. C₁₉×#1580	C₂	semidirect
18. C₁₉×#550	C₂²	semidirect
22. C₁₉×#492	C₂²	semidirect
24. C₁₉×#487	C₂²	semidirect
27. C₁₉×#486	C₂²	semidirect
32. C₁₉×#476	C₂²	semidirect
37. C₁₉×#462	C₂²	semidirect
47. C₁₉×#446	C₂²	semidirect
53. C₈×D₄×C₁₉	C₂²	semidirect
56. C₁₉×#334	C₂²	semidirect
57. C₁₉×#334	C₂²	semidirect
58. C₁₉×#333	C₂²	semidirect
59. C₁₉×#332	C₂²	semidirect
61. C₁₉×#331	C₂²	semidirect
62. C₁₉×Q₈⋊C₈	C₂²	semidirect
65. C₁₉×D₄⋊C₈	C₂²	semidirect
66. C₁₉×#322	C₂²	semidirect
220. #19788	C₁₉	direct (N × H)
253. D₄×C₁₉	#135	semidirect
283. #3366	C₂×C₁₉	semidirect
284. #3295	C₂×C₁₉	semidirect
285. #3294	C₂×C₁₉	semidirect
286. #3284	C₂×C₁₉	semidirect
287. #1717	C₂×C₁₉	semidirect
288. #1702	C₂×C₁₉	semidirect
289. #1677	C₂×C₁₉	semidirect
290. #1677	C₂×C₁₉	semidirect
291. #1665	C₂×C₁₉	semidirect
292. #1644	C₂×C₁₉	semidirect
293. #1635	C₂×C₁₉	semidirect
294. #1621	C₂×C₁₉	semidirect
295. #1619	C₂×C₁₉	semidirect
296. #1582	C₂×C₁₉	semidirect
297. #1580	C₂×C₁₉	semidirect
329. #550	C₂²×C₁₉	semidirect
333. #492	C₂²×C₁₉	semidirect
335. #487	C₂²×C₁₉	semidirect
338. #486	C₂²×C₁₉	semidirect
343. #476	C₂²×C₁₉	semidirect
348. #462	C₂²×C₁₉	semidirect
358. #446	C₂²×C₁₉	semidirect
364. C₈×D₄	C₂²×C₁₉	semidirect
367. #334	C₂²×C₁₉	semidirect
368. #334	C₂²×C₁₉	semidirect
369. #333	C₂²×C₁₉	semidirect
370. #332	C₂²×C₁₉	semidirect
372. #331	C₂²×C₁₉	semidirect
373. Q₈⋊C₈	C₂²×C₁₉	semidirect
376. D₄⋊C₈	C₂²×C₁₉	semidirect
377. #322	C₂²×C₁₉	semidirect
464. C₁₉	#19788	direct (N × H)
572. D₄	C₁₉×#135	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3366	2
C₁₉×#3295	2
C₁₉×#3294	2
C₁₉×#3284	2
C₁₉×#1717	2
C₁₉×#1702	2
C₁₉×#1677	2
C₁₉×#1665	2
C₁₉×#1644	2
C₁₉×#1635	2
C₁₉×#1621	2
C₁₉×#1619	2
C₁₉×#1582	2
C₁₉×#1580	2
#19788	19

Subgroups — C19×#19788 #18025747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19788 #18025747