Subgroups — C₁₉×#19589 #18025548

Order 4864.

602 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3247	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3227	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3218	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1702	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1701	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1692	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1691	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1682	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1681	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1672	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1671	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1573	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1551	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#332	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#532	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₉×#529	C₂²	1	1	yes	characteristic
19	C₁₉×#498	C₂²	1	1	yes	characteristic
20	C₁₉×#498	C₂²	1	1	yes	characteristic
21	C₁₉×#497	—	2	1	no	—
22	C₁₉×#491	—	2	1	no	—
23	C₁₉×#486	C₂²	1	1	yes	characteristic
24	C₁₉×#486	C₂²	1	1	yes	characteristic
25	C₁₉×#481	—	2	1	no	—
26	C₁₉×#481	—	2	1	no	—
27	C₁₉×#478	—	2	1	no	—
28	C₁₉×#477	C₂²	1	1	yes	characteristic
29	C₁₉×#476	—	2	1	no	—
30	C₁₉×#476	—	2	1	no	—
31	C₁₉×#476	C₂²	1	1	yes	characteristic
32	C₁₉×#466	—	2	1	no	—
33	C₁₉×#465	—	2	1	no	—
34	C₁₉×#463	—	2	1	no	—
35	C₁₉×#462	C₂²	1	1	yes	characteristic
36	C₁₉×#462	C₂²	1	1	yes	characteristic
37	C₁₉×#461	C₂²	1	1	yes	characteristic
38	C₁₉×#461	C₂²	1	1	yes	characteristic
39	C₁₉×#460	C₂²	1	1	yes	characteristic
40	C₁₉×#459	C₂²	1	1	yes	characteristic
41	C₁₉×#451	—	2	1	no	—
42	C₁₉×#448	—	2	1	no	—
43	C₁₉×#446	C₂²	1	1	yes	characteristic
44	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#436	C₂²	1	1	yes	characteristic
46	C₁₉×#435	—	2	1	no	—
47	C₈×D₄×C₁₉	—	2	1	no	—
48	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#433	—	2	1	no	—
50	C₁₉×#432	C₂²	1	1	yes	characteristic
51	C₁₉×#431	C₂²	1	1	yes	characteristic
52	C₁₉×#424	—	2	1	no	—
53	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
55	C₁₉×#335	C₂²	1	1	yes	characteristic
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#334	C₂²	1	1	yes	characteristic
59	C₁₉×#333	C₂²	1	1	yes	characteristic
60	C₁₉×#333	C₂²	1	1	yes	characteristic
61	C₁₉×#332	C₂²	1	1	yes	characteristic
62	C₁₉×#332	C₂²	1	1	yes	characteristic
63	C₁₉×#332	C₂²	1	1	yes	characteristic
64	C₁₉×#332	C₂²	1	1	yes	characteristic
65	C₁₉×#331	C₂²	1	1	yes	characteristic
66	C₁₉×#331	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂²×Q₈×C₁₉	—	2	1	no	—
69	C₂×Q₁₆×C₁₉	—	2	1	no	—
70	C₂×Q₁₆×C₁₉	—	2	1	no	—
71	C₂×SD₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×D₈×C₁₉	—	2	1	no	—
75	C₂×M₁₆×C₁₉	—	2	1	no	—
76	C₂²×C₈×C₁₉	—	2	1	no	—
77	C₂²×C₈×C₁₉	—	2	1	no	—
78	C₂²×C₈×C₁₉	—	2	1	no	—
79	C₁₉×C₄⋊Q₈	—	2	1	no	—
80	C₁₉×C₄⋊Q₈	—	2	1	no	—
81	C₁₉×C₄⋊Q₈	—	2	1	no	—
82	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₉×#127	C₂³	1	1	yes	characteristic
86	C₁₉×#126	—	2	1	no	—
87	C₁₉×#125	D₄	1	1	yes	characteristic
88	C₁₉×#124	—	2	1	no	—
89	C₁₉×#124	D₄	1	1	yes	characteristic
90	C₁₉×#123	—	2	1	no	—
91	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
92	C₁₉×#121	—	2	1	no	—
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#121	D₄	1	1	yes	characteristic
95	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	—	2	1	no	—
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₁₉×#117	—	2	1	no	—
101	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₁₉×#107	—	2	1	no	—
105	C₁₉×#106	—	2	1	no	—
106	C₁₉×#106	—	2	1	no	—
107	C₁₉×#106	—	2	1	no	—
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×#106	—	2	1	no	—
110	C₁₉×C₄⋊C₈	—	2	1	no	—
111	C₁₉×C₄⋊C₈	—	2	1	no	—
112	C₁₉×C₄⋊C₈	—	2	1	no	—
113	C₁₉×C₄⋊C₈	—	2	1	no	—
114	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
115	C₁₉×C₄⋊C₈	D₄	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×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₉×#103	—	2	1	no	—
123	C₁₉×#103	—	2	1	no	—
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	—	2	1	no	—
126	C₁₉×#103	—	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×C₂²⋊C₈	—	2	1	no	—
135	C₁₉×C₂²⋊C₈	—	2	1	no	—
136	C₁₉×C₂²⋊C₈	—	2	1	no	—
137	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
138	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
139	C₁₉×#97	—	2	1	no	—
140	C₁₉×#97	—	2	1	no	—
141	C₄×C₈×C₁₉	—	2	1	no	—
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	#41×C₁₉	—	8	2	no	—
145	C₂×Q₈×C₁₉	—	2	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	4	1	no	—
149	C₂×Q₈×C₁₉	—	8	1	no	—
150	C₂×Q₈×C₁₉	—	8	1	no	—
151	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
157	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	4	1	no	—
160	C₂²×C₄×C₁₉	—	4	1	no	—
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
164	Q₁₆×C₁₉	—	8	1	no	—
165	Q₁₆×C₁₉	—	8	1	no	—
166	SD₁₆×C₁₉	—	8	1	no	—
167	SD₁₆×C₁₉	—	8	1	no	—
168	SD₁₆×C₁₉	—	8	1	no	—
169	D₈×C₁₉	—	8	1	no	—
170	M₁₆×C₁₉	—	8	1	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	8	1	no	—
178	C₂×C₈×C₁₉	—	8	1	no	—
179	C₂×C₈×C₁₉	—	8	1	no	—
180	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	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	—	4	1	no	—
195	C₄⋊C₄×C₁₉	—	4	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	1	no	—
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂²⋊C₄×C₁₉	—	2	1	no	—
201	C₂²⋊C₄×C₁₉	—	2	1	no	—
202	C₂²⋊C₄×C₁₉	—	2	1	no	—
203	C₂²⋊C₄×C₁₉	—	4	1	no	—
204	C₂²⋊C₄×C₁₉	—	4	1	no	—
205	C₄²×C₁₉	—	2	1	no	—
206	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₉	#41	1	1	yes	characteristic
209	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
210	#19589	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂³×C₁₉	—	2	1	no	—
212	C₂³×C₁₉	—	4	1	no	—
213	C₂³×C₁₉	#121	1	1	yes	characteristic
214	Q₈×C₁₉	—	2	1	no	—
215	Q₈×C₁₉	—	2	1	no	—
216	Q₈×C₁₉	—	4	1	no	—
217	Q₈×C₁₉	—	4	1	no	—
218	Q₈×C₁₉	—	4	1	no	—
219	Q₈×C₁₉	—	4	1	no	—
220	Q₈×C₁₉	—	8	1	no	—
221	Q₈×C₁₉	—	8	2	no	—
222	D₄×C₁₉	—	2	1	no	—
223	D₄×C₁₉	—	2	1	no	—
224	D₄×C₁₉	—	4	2	no	—
225	D₄×C₁₉	—	4	1	no	—
226	D₄×C₁₉	—	4	1	no	—
227	D₄×C₁₉	—	4	1	no	—
228	D₄×C₁₉	—	4	1	no	—
229	D₄×C₁₉	—	8	1	no	—
230	D₄×C₁₉	—	8	2	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	4	1	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	—	8	2	no	—
245	C₂×C₄×C₁₉	—	8	2	no	—
246	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
252	C₈×C₁₉	—	2	1	no	—
253	C₈×C₁₉	—	2	1	no	—
254	C₈×C₁₉	—	2	1	no	—
255	C₈×C₁₉	—	2	1	no	—
256	C₈×C₁₉	—	4	1	no	—
257	C₈×C₁₉	—	4	1	no	—
258	C₈×C₁₉	—	4	1	no	—
259	C₈×C₁₉	—	4	1	no	—
260	C₈×C₁₉	—	4	1	no	—
261	C₈×C₁₉	—	4	1	no	—
262	#3247	C₂×C₁₉	1	1	yes	characteristic
263	#3227	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#3218	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#2994	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1702	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1701	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#1692	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1691	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#1682	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#1681	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1672	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1671	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1573	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1551	C₂×C₁₉	1	1	yes	characteristic, complemented
276	C₂×#332	C₂×C₁₉	1	1	yes	characteristic, complemented
277	C₂²×C₁₉	—	2	1	no	—
278	C₂²×C₁₉	—	2	1	no	—
279	C₂²×C₁₉	—	4	1	no	—
280	C₂²×C₁₉	—	4	1	no	—
281	C₂²×C₁₉	—	4	1	no	—
282	C₂²×C₁₉	—	8	1	no	—
283	C₂²×C₁₉	—	8	1	no	—
284	C₂²×C₁₉	—	8	1	no	—
285	C₂²×C₁₉	#471	1	2	yes	—
286	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
287	C₄×C₁₉	—	2	1	no	—
288	C₄×C₁₉	—	2	1	no	—
289	C₄×C₁₉	—	2	1	no	—
290	C₄×C₁₉	—	2	1	no	—
291	C₄×C₁₉	—	4	1	no	—
292	C₄×C₁₉	—	4	1	no	—
293	C₄×C₁₉	—	4	1	no	—
294	C₄×C₁₉	—	8	1	no	—
295	C₄×C₁₉	—	8	1	no	—
296	C₄×C₁₉	—	8	1	no	—
297	C₄×C₁₉	#576	1	1	yes	characteristic
298	C₄×C₁₉	#577	1	1	yes	characteristic
299	C₄×C₁₉	#577	1	1	yes	characteristic
300	C₄×C₁₉	#578	1	1	yes	characteristic
301	#532	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
303	#529	C₂²×C₁₉	1	1	yes	characteristic
304	#498	C₂²×C₁₉	1	1	yes	characteristic
305	#498	C₂²×C₁₉	1	1	yes	characteristic
306	#497	—	2	1	no	—
307	#491	—	2	1	no	—
308	#486	C₂²×C₁₉	1	1	yes	characteristic
309	#486	C₂²×C₁₉	1	1	yes	characteristic
310	#481	—	2	1	no	—
311	#481	—	2	1	no	—
312	#478	—	2	1	no	—
313	#477	C₂²×C₁₉	1	1	yes	characteristic
314	#476	—	2	1	no	—
315	#476	—	2	1	no	—
316	#476	C₂²×C₁₉	1	1	yes	characteristic
317	#466	—	2	1	no	—
318	#465	—	2	1	no	—
319	#463	—	2	1	no	—
320	#462	C₂²×C₁₉	1	1	yes	characteristic
321	#462	C₂²×C₁₉	1	1	yes	characteristic
322	#461	C₂²×C₁₉	1	1	yes	characteristic
323	#461	C₂²×C₁₉	1	1	yes	characteristic
324	#460	C₂²×C₁₉	1	1	yes	characteristic
325	#459	C₂²×C₁₉	1	1	yes	characteristic
326	#451	—	2	1	no	—
327	#448	—	2	1	no	—
328	#446	C₂²×C₁₉	1	1	yes	characteristic
329	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
330	#436	C₂²×C₁₉	1	1	yes	characteristic
331	#435	—	2	1	no	—
332	C₈×D₄	—	2	1	no	—
333	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
334	#433	—	2	1	no	—
335	#432	C₂²×C₁₉	1	1	yes	characteristic
336	#431	C₂²×C₁₉	1	1	yes	characteristic
337	#424	—	2	1	no	—
338	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
339	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
340	#335	C₂²×C₁₉	1	1	yes	characteristic
341	#335	C₂²×C₁₉	1	1	yes	characteristic
342	#334	C₂²×C₁₉	1	1	yes	characteristic
343	#334	C₂²×C₁₉	1	1	yes	characteristic
344	#333	C₂²×C₁₉	1	1	yes	characteristic
345	#333	C₂²×C₁₉	1	1	yes	characteristic
346	#332	C₂²×C₁₉	1	1	yes	characteristic
347	#332	C₂²×C₁₉	1	1	yes	characteristic
348	#332	C₂²×C₁₉	1	1	yes	characteristic
349	#332	C₂²×C₁₉	1	1	yes	characteristic
350	#331	C₂²×C₁₉	1	1	yes	characteristic
351	#331	C₂²×C₁₉	1	1	yes	characteristic
352	C₂×C₁₉	—	2	2	no	—
353	C₂×C₁₉	—	8	1	no	—
354	C₂×C₁₉	—	16	1	no	—
355	C₂×C₁₉	#3046	1	1	yes	characteristic
356	C₂×C₁₉	#3062	1	1	yes	characteristic
357	C₂×C₁₉	C₂×#471	1	1	yes	characteristic
358	C₂×#41	—	2	1	no	—
359	C₂²×Q₈	—	2	1	no	—
360	C₂×Q₁₆	—	2	1	no	—
361	C₂×Q₁₆	—	2	1	no	—
362	C₂×SD₁₆	—	2	1	no	—
363	C₂×SD₁₆	—	2	1	no	—
364	C₂×SD₁₆	—	2	1	no	—
365	C₂×D₈	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂²×C₈	—	2	1	no	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	C₄⋊Q₈	—	2	1	no	—
371	C₄⋊Q₈	—	2	1	no	—
372	C₄⋊Q₈	—	2	1	no	—
373	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
374	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
375	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
376	#127	C₂³×C₁₉	1	1	yes	characteristic
377	#126	—	2	1	no	—
378	#125	D₄×C₁₉	1	1	yes	characteristic
379	#124	—	2	1	no	—
380	#124	D₄×C₁₉	1	1	yes	characteristic
381	#123	—	2	1	no	—
382	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
383	#121	—	2	1	no	—
384	#121	—	2	1	no	—
385	#121	D₄×C₁₉	1	1	yes	characteristic
386	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
391	#117	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
395	#107	—	2	1	no	—
396	#106	—	2	1	no	—
397	#106	—	2	1	no	—
398	#106	—	2	1	no	—
399	#106	—	2	1	no	—
400	#106	—	2	1	no	—
401	C₄⋊C₈	—	2	1	no	—
402	C₄⋊C₈	—	2	1	no	—
403	C₄⋊C₈	—	2	1	no	—
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
406	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
407	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
408	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
409	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
410	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
411	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
412	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
413	#103	—	2	1	no	—
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	2	1	no	—
418	#102	—	2	1	no	—
419	#102	—	2	1	no	—
420	#102	—	2	1	no	—
421	#102	—	2	1	no	—
422	#102	—	2	1	no	—
423	#102	—	2	1	no	—
424	#102	—	2	1	no	—
425	C₂²⋊C₈	—	2	1	no	—
426	C₂²⋊C₈	—	2	1	no	—
427	C₂²⋊C₈	—	2	1	no	—
428	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
429	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
430	#97	—	2	1	no	—
431	#97	—	2	1	no	—
432	C₄×C₈	—	2	1	no	—
433	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
434	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
435	C₁₉	#19589	1	1	yes	characteristic, direct product factor, Sylow
436	#41	—	8	2	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	4	1	no	—
441	C₂×Q₈	—	8	1	no	—
442	C₂×Q₈	—	8	1	no	—
443	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	4	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	#41×C₁₉	1	1	yes	characteristic
456	Q₁₆	—	8	1	no	—
457	Q₁₆	—	8	1	no	—
458	SD₁₆	—	8	1	no	—
459	SD₁₆	—	8	1	no	—
460	SD₁₆	—	8	1	no	—
461	D₈	—	8	1	no	—
462	M₁₆	—	8	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	8	1	no	—
470	C₂×C₈	—	8	1	no	—
471	C₂×C₈	—	8	1	no	—
472	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
473	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
499	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₄²	#41×C₁₉	1	1	yes	characteristic
501	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
502	C₂³	—	2	1	no	—
503	C₂³	—	4	1	no	—
504	C₂³	C₁₉×#121	1	1	yes	characteristic
505	Q₈	—	2	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	4	1	no	—
511	Q₈	—	8	1	no	—
512	Q₈	—	8	2	no	—
513	D₄	—	2	1	no	—
514	D₄	—	2	1	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	1	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	1	no	—
519	D₄	—	4	1	no	—
520	D₄	—	8	1	no	—
521	D₄	—	8	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	8	2	no	—
536	C₂×C₄	—	8	2	no	—
537	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
538	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
539	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
542	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
543	C₈	—	2	1	no	—
544	C₈	—	2	1	no	—
545	C₈	—	2	1	no	—
546	C₈	—	2	1	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	1	no	—
551	C₈	—	4	1	no	—
552	C₈	—	4	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	8	1	no	—
559	C₂²	—	8	1	no	—
560	C₂²	—	8	1	no	—
561	C₂²	C₁₉×#471	1	2	yes	—
562	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	8	1	no	—
571	C₄	—	8	1	no	—
572	C₄	—	8	1	no	—
573	C₄	C₁₉×#576	1	1	yes	characteristic
574	C₄	C₁₉×#577	1	1	yes	characteristic
575	C₄	C₁₉×#577	1	1	yes	characteristic
576	C₄	C₁₉×#578	1	1	yes	characteristic
577	C₂	—	2	2	no	—
578	C₂	—	8	1	no	—
579	C₂	—	16	1	no	—
580	C₂	C₁₉×#3046	1	1	yes	characteristic
581	C₂	C₁₉×#3062	1	1	yes	characteristic
582	C₂	C₂×C₁₉×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3247	C₂
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
2. C₁₉×#3227	C₂	semidirect
3. C₁₉×#3218	C₂	semidirect
4. C₁₉×#2994	C₂	semidirect
5. C₁₉×#1702	C₂	semidirect
6. C₁₉×#1701	C₂	semidirect
7. C₁₉×#1692	C₂	semidirect
8. C₁₉×#1691	C₂	semidirect
9. C₁₉×#1682	C₂	semidirect
10. C₁₉×#1681	C₂	semidirect
11. C₁₉×#1672	C₂	semidirect
12. C₁₉×#1671	C₂	semidirect
13. C₁₉×#1573	C₂	semidirect
14. C₁₉×#1551	C₂	semidirect
15. C₂×C₁₉×#332	C₂	semidirect
210. #19589	C₁₉	direct (N × H)
263. #3227	C₂×C₁₉	semidirect
264. #3218	C₂×C₁₉	semidirect
265. #2994	C₂×C₁₉	semidirect
266. #1702	C₂×C₁₉	semidirect
267. #1701	C₂×C₁₉	semidirect
268. #1692	C₂×C₁₉	semidirect
269. #1691	C₂×C₁₉	semidirect
270. #1682	C₂×C₁₉	semidirect
271. #1681	C₂×C₁₉	semidirect
272. #1672	C₂×C₁₉	semidirect
273. #1671	C₂×C₁₉	semidirect
274. #1573	C₂×C₁₉	semidirect
275. #1551	C₂×C₁₉	semidirect
276. C₂×#332	C₂×C₁₉	semidirect
435. C₁₉	#19589	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×#3247	2
C₁₉×#3227	2
C₁₉×#3218	2
C₁₉×#2994	2
C₁₉×#1702	2
C₁₉×#1701	2
C₁₉×#1692	2
C₁₉×#1691	2
C₁₉×#1682	2
C₁₉×#1681	2
C₁₉×#1672	2
C₁₉×#1671	2
C₁₉×#1573	2
C₁₉×#1551	2
C₂×C₁₉×#332	2
#19589	19

Subgroups — C19×#19589 #18025548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19589 #18025548