Subgroups — C₁₉×#18923 #18024882

Order 4864.

1122 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3497	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3227	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1651	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1642	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1540	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×2₋¹⁺⁴	—	2	1	no	—
11	C₁₉×#550	—	2	1	no	—
12	C₁₉×#550	C₂²	1	2	yes	—
13	D₄×Q₈×C₁₉	—	2	1	no	—
14	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
15	C₁₉×#548	—	2	2	no	—
16	C₁₉×#548	—	2	2	no	—
17	C₁₉×#537	—	2	2	no	—
18	C₁₉×#537	—	2	1	no	—
19	C₁₉×#532	—	2	2	no	—
20	C₁₉×#532	C₂²	1	1	yes	characteristic
21	C₁₉×#532	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#498	C₂²	1	2	yes	—
25	C₁₉×#492	—	2	1	no	—
26	C₁₉×#487	—	2	1	no	—
27	C₁₉×#486	C₂²	1	2	yes	—
28	C₁₉×#481	—	2	2	no	—
29	C₁₉×#476	—	2	2	no	—
30	C₁₉×#475	—	2	2	no	—
31	C₁₉×#475	C₂²	1	4	yes	—
32	C₁₉×#461	C₂²	1	4	yes	—
33	C₁₉×#448	—	2	2	no	—
34	C₁₉×#431	C₂²	1	1	yes	characteristic
35	C₁₉×#431	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#106	—	2	1	no	—
37	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#103	—	2	1	no	—
39	C₁₉×#332	C₂²	1	2	yes	—
40	C₁₉×#331	C₂²	1	2	yes	—
41	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	—
42	C₁₉×D₄⋊C₈	C₂²	1	4	yes	—
43	C₁₉×2₋¹⁺⁴	—	4	4	no	—
44	C₁₉×2₋¹⁺⁴	—	4	4	no	—
45	C₂×#41×C₁₉	—	2	4	no	—
46	C₂×#41×C₁₉	—	2	2	no	—
47	C₂×#41×C₁₉	—	2	2	no	—
48	C₂×#41×C₁₉	—	2	1	no	—
49	C₂×#41×C₁₉	—	2	1	no	—
50	C₂²×Q₈×C₁₉	—	2	2	no	—
51	C₂²×Q₈×C₁₉	—	2	2	no	—
52	C₂²×Q₈×C₁₉	—	2	1	no	—
53	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
54	C₂×SD₁₆×C₁₉	—	2	4	no	—
55	C₂²×C₈×C₁₉	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	2	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₁₉×#127	—	2	2	no	—
64	C₁₉×#127	D₄	1	1	yes	characteristic
65	C₁₉×#127	C₂³	1	1	yes	characteristic
66	C₁₉×#124	—	2	4	no	—
67	C₁₉×#124	—	2	1	no	—
68	C₁₉×#124	—	2	1	no	—
69	C₁₉×C₂²⋊Q₈	—	2	2	no	—
70	C₁₉×C₂²⋊Q₈	—	2	4	no	—
71	C₁₉×C₂²⋊Q₈	—	2	2	no	—
72	C₁₉×C₂²⋊Q₈	—	2	4	no	—
73	C₁₉×#121	—	2	4	no	—
74	C₁₉×#121	—	2	2	no	—
75	C₁₉×#121	—	2	4	no	—
76	C₁₉×#121	—	2	4	no	—
77	C₁₉×#121	—	2	1	no	—
78	C₁₉×#121	—	2	1	no	—
79	C₁₉×#121	—	2	2	no	—
80	C₁₉×#121	D₄	1	2	yes	—
81	C₁₉×#121	D₄	1	2	yes	—
82	C₄×Q₈×C₁₉	—	2	1	no	—
83	C₄×Q₈×C₁₉	—	2	1	no	—
84	C₄×Q₈×C₁₉	D₄	1	2	yes	—
85	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
86	C₄×D₄×C₁₉	—	2	4	no	—
87	C₄×D₄×C₁₉	—	2	2	no	—
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₄×D₄×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	—	2	1	no	—
91	C₄×D₄×C₁₉	D₄	1	2	yes	—
92	C₄×D₄×C₁₉	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₁₉	—	2	1	no	—
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₁₉×#106	—	2	4	no	—
100	C₁₉×#106	—	2	4	no	—
101	C₁₉×C₄⋊C₈	—	2	1	no	—
102	C₁₉×C₄⋊C₈	—	2	1	no	—
103	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
104	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
105	C₁₉×#103	—	2	4	no	—
106	C₁₉×#103	—	2	4	no	—
107	C₁₉×#102	—	2	4	no	—
108	C₁₉×C₂²⋊C₈	—	2	1	no	—
109	C₁₉×C₂²⋊C₈	—	2	1	no	—
110	C₄×C₈×C₁₉	—	2	1	no	—
111	C₄×C₈×C₁₉	C₂³	1	2	yes	—
112	#41×C₁₉	—	4	16	no	—
113	#41×C₁₉	—	4	4	no	—
114	#41×C₁₉	—	4	8	no	—
115	#41×C₁₉	—	4	4	no	—
116	#41×C₁₉	—	4	2	no	—
117	#41×C₁₉	—	4	2	no	—
118	#41×C₁₉	—	4	2	no	—
119	#41×C₁₉	—	4	2	no	—
120	C₂×Q₈×C₁₉	—	2	4	no	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	2	2	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	2	no	—
126	C₂×Q₈×C₁₉	—	4	4	no	—
127	C₂×Q₈×C₁₉	—	4	8	no	—
128	C₂×Q₈×C₁₉	—	4	4	no	—
129	C₂×Q₈×C₁₉	—	4	1	no	—
130	C₂×Q₈×C₁₉	—	8	2	no	—
131	C₂×Q₈×C₁₉	SD₁₆	1	4	yes	complemented
132	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
133	C₂×D₄×C₁₉	—	2	4	no	—
134	C₂×D₄×C₁₉	—	2	2	no	—
135	C₂×D₄×C₁₉	—	2	2	no	—
136	C₂×D₄×C₁₉	—	2	4	no	—
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	—	2	1	no	—
139	C₂×D₄×C₁₉	—	2	1	no	—
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
142	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	4	no	—
145	C₂²×C₄×C₁₉	—	2	4	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	4	1	no	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	SD₁₆×C₁₉	—	8	4	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₂×C₈×C₁₉	—	2	2	no	—
156	C₂×C₈×C₁₉	—	2	2	no	—
157	C₂×C₈×C₁₉	—	4	2	no	—
158	C₄⋊C₄×C₁₉	—	2	4	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	4	1	no	—
167	C₄⋊C₄×C₁₉	—	4	1	no	—
168	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
170	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₂²⋊C₄×C₁₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₉	—	2	4	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₄²×C₁₉	—	2	2	no	—
178	C₄²×C₁₉	—	2	2	no	—
179	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
183	#18923	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂³×C₁₉	—	2	2	no	—
185	C₂³×C₁₉	—	2	2	no	—
186	C₂³×C₁₉	#120	1	1	yes	characteristic
187	Q₈×C₁₉	—	2	2	no	—
188	Q₈×C₁₉	—	2	4	no	—
189	Q₈×C₁₉	—	4	8	no	—
190	Q₈×C₁₉	—	4	1	no	—
191	Q₈×C₁₉	—	4	1	no	—
192	Q₈×C₁₉	—	4	2	no	—
193	Q₈×C₁₉	—	4	4	no	—
194	Q₈×C₁₉	—	8	2	no	—
195	Q₈×C₁₉	C₂×SD₁₆	1	4	yes	—
196	D₄×C₁₉	—	2	4	no	—
197	D₄×C₁₉	—	4	2	no	—
198	D₄×C₁₉	—	4	8	no	—
199	D₄×C₁₉	—	4	4	no	—
200	D₄×C₁₉	—	4	4	no	—
201	D₄×C₁₉	—	4	1	no	—
202	D₄×C₁₉	—	4	1	no	—
203	D₄×C₁₉	—	4	2	no	—
204	D₄×C₁₉	—	4	2	no	—
205	D₄×C₁₉	—	8	1	no	—
206	D₄×C₁₉	—	8	4	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	4	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	8	no	—
215	C₂×C₄×C₁₉	—	4	8	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	4	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	8	1	no	—
221	C₂×C₄×C₁₉	—	8	2	no	—
222	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
224	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
226	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
227	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
230	C₈×C₁₉	—	4	2	no	—
231	C₈×C₁₉	—	4	2	no	—
232	C₈×C₁₉	—	4	2	no	—
233	#3497	C₂×C₁₉	1	1	yes	characteristic
234	#3227	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#3206	C₂×C₁₉	1	1	yes	characteristic, complemented
236	C₂×#475	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#1651	C₂×C₁₉	1	4	yes	complemented
238	#1642	C₂×C₁₉	1	4	yes	complemented
239	#1540	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#1480	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#1479	C₂×C₁₉	1	1	yes	characteristic, complemented
242	C₂²×C₁₉	—	2	1	no	—
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	4	2	no	—
245	C₂²×C₁₉	—	4	2	no	—
246	C₂²×C₁₉	—	4	2	no	—
247	C₂²×C₁₉	—	4	2	no	—
248	C₂²×C₁₉	—	4	2	no	—
249	C₂²×C₁₉	—	4	2	no	—
250	C₂²×C₁₉	#450	1	2	yes	—
251	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
252	C₄×C₁₉	—	2	4	no	—
253	C₄×C₁₉	—	2	1	no	—
254	C₄×C₁₉	—	2	1	no	—
255	C₄×C₁₉	—	2	1	no	—
256	C₄×C₁₉	—	4	2	no	—
257	C₄×C₁₉	—	4	2	no	—
258	C₄×C₁₉	—	4	2	no	—
259	C₄×C₁₉	—	8	2	no	—
260	C₄×C₁₉	#450	1	2	yes	—
261	C₄×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
262	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
263	C₄×C₁₉	#577	1	2	yes	—
264	C₂×2₋¹⁺⁴	—	2	1	no	—
265	#550	—	2	1	no	—
266	#550	C₂²×C₁₉	1	2	yes	—
267	D₄×Q₈	—	2	1	no	—
268	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
269	#548	—	2	2	no	—
270	#548	—	2	2	no	—
271	#537	—	2	2	no	—
272	#537	—	2	1	no	—
273	#532	—	2	2	no	—
274	#532	C₂²×C₁₉	1	1	yes	characteristic
275	#532	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
277	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
278	#498	C₂²×C₁₉	1	2	yes	—
279	#492	—	2	1	no	—
280	#487	—	2	1	no	—
281	#486	C₂²×C₁₉	1	2	yes	—
282	#481	—	2	2	no	—
283	#476	—	2	2	no	—
284	#475	—	2	2	no	—
285	#475	C₂²×C₁₉	1	4	yes	—
286	#461	C₂²×C₁₉	1	4	yes	—
287	#448	—	2	2	no	—
288	#431	C₂²×C₁₉	1	1	yes	characteristic
289	#431	C₂²×C₁₉	1	1	yes	characteristic
290	C₂×#106	—	2	1	no	—
291	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
292	C₂×#103	—	2	1	no	—
293	#332	C₂²×C₁₉	1	2	yes	—
294	#331	C₂²×C₁₉	1	2	yes	—
295	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	—
296	D₄⋊C₈	C₂²×C₁₉	1	4	yes	—
297	C₂×C₁₉	—	2	2	no	—
298	C₂×C₁₉	—	8	2	no	—
299	C₂×C₁₉	—	8	2	no	—
300	C₂×C₁₉	C₂×#450	1	1	yes	characteristic
301	C₂×C₁₉	#3010	1	1	yes	characteristic
302	C₂×C₁₉	#3022	1	1	yes	characteristic
303	2₋¹⁺⁴	—	4	4	no	—
304	2₋¹⁺⁴	—	4	4	no	—
305	C₂×#41	—	2	4	no	—
306	C₂×#41	—	2	2	no	—
307	C₂×#41	—	2	2	no	—
308	C₂×#41	—	2	1	no	—
309	C₂×#41	—	2	1	no	—
310	C₂²×Q₈	—	2	2	no	—
311	C₂²×Q₈	—	2	2	no	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
314	C₂×SD₁₆	—	2	4	no	—
315	C₂²×C₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	—	2	1	no	—
318	C₄⋊Q₈	—	2	1	no	—
319	C₄⋊Q₈	—	2	1	no	—
320	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
321	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
322	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
323	#127	—	2	2	no	—
324	#127	D₄×C₁₉	1	1	yes	characteristic
325	#127	C₂³×C₁₉	1	1	yes	characteristic
326	#124	—	2	4	no	—
327	#124	—	2	1	no	—
328	#124	—	2	1	no	—
329	C₂²⋊Q₈	—	2	2	no	—
330	C₂²⋊Q₈	—	2	4	no	—
331	C₂²⋊Q₈	—	2	2	no	—
332	C₂²⋊Q₈	—	2	4	no	—
333	#121	—	2	4	no	—
334	#121	—	2	2	no	—
335	#121	—	2	4	no	—
336	#121	—	2	4	no	—
337	#121	—	2	1	no	—
338	#121	—	2	1	no	—
339	#121	—	2	2	no	—
340	#121	D₄×C₁₉	1	2	yes	—
341	#121	D₄×C₁₉	1	2	yes	—
342	C₄×Q₈	—	2	1	no	—
343	C₄×Q₈	—	2	1	no	—
344	C₄×Q₈	D₄×C₁₉	1	2	yes	—
345	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	2	1	no	—
350	C₄×D₄	—	2	1	no	—
351	C₄×D₄	D₄×C₁₉	1	2	yes	—
352	C₄×D₄	C₂³×C₁₉	1	2	yes	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
359	#106	—	2	4	no	—
360	#106	—	2	4	no	—
361	C₄⋊C₈	—	2	1	no	—
362	C₄⋊C₈	—	2	1	no	—
363	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
364	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
365	#103	—	2	4	no	—
366	#103	—	2	4	no	—
367	#102	—	2	4	no	—
368	C₂²⋊C₈	—	2	1	no	—
369	C₂²⋊C₈	—	2	1	no	—
370	C₄×C₈	—	2	1	no	—
371	C₄×C₈	C₂³×C₁₉	1	2	yes	—
372	C₁₉	#18923	1	1	yes	characteristic, direct product factor, Sylow
373	#41	—	4	16	no	—
374	#41	—	4	8	no	—
375	#41	—	4	4	no	—
376	#41	—	4	4	no	—
377	#41	—	4	2	no	—
378	#41	—	4	2	no	—
379	#41	—	4	2	no	—
380	#41	—	4	2	no	—
381	C₂×Q₈	—	2	4	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	4	8	no	—
388	C₂×Q₈	—	4	4	no	—
389	C₂×Q₈	—	4	4	no	—
390	C₂×Q₈	—	4	1	no	—
391	C₂×Q₈	—	8	2	no	—
392	C₂×Q₈	SD₁₆×C₁₉	1	4	yes	complemented
393	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
403	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	4	1	no	—
411	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
414	SD₁₆	—	8	4	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	4	2	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	4	1	no	—
428	C₄⋊C₄	—	4	1	no	—
429	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
430	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
431	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
432	C₂²⋊C₄	—	2	4	no	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	2	no	—
440	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	C₁₉×#120	1	1	yes	characteristic
447	Q₈	—	2	4	no	—
448	Q₈	—	2	2	no	—
449	Q₈	—	4	8	no	—
450	Q₈	—	4	2	no	—
451	Q₈	—	4	1	no	—
452	Q₈	—	4	1	no	—
453	Q₈	—	4	4	no	—
454	Q₈	—	8	2	no	—
455	Q₈	C₂×SD₁₆×C₁₉	1	4	yes	—
456	D₄	—	2	4	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	8	no	—
459	D₄	—	4	4	no	—
460	D₄	—	4	4	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	1	no	—
463	D₄	—	4	1	no	—
464	D₄	—	4	2	no	—
465	D₄	—	8	1	no	—
466	D₄	—	8	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	8	no	—
475	C₂×C₄	—	4	8	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	8	1	no	—
481	C₂×C₄	—	8	2	no	—
482	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
483	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
484	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
485	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
486	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
487	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
489	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
490	C₈	—	4	2	no	—
491	C₈	—	4	2	no	—
492	C₈	—	4	2	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	C₁₉×#450	1	2	yes	—
502	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
503	C₄	—	2	4	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	2	no	—
510	C₄	—	8	2	no	—
511	C₄	C₁₉×#450	1	2	yes	—
512	C₄	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
513	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
514	C₄	C₁₉×#577	1	2	yes	—
515	C₂	—	2	2	no	—
516	C₂	—	8	2	no	—
517	C₂	—	8	2	no	—
518	C₂	C₂×C₁₉×#450	1	1	yes	characteristic
519	C₂	C₁₉×#3010	1	1	yes	characteristic
520	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3497	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×#3206	C₂	semidirect
4. C₂×C₁₉×#475	C₂	semidirect
5. C₁₉×#1651	C₂	semidirect
6. C₁₉×#1642	C₂	semidirect
7. C₁₉×#1540	C₂	semidirect
8. C₁₉×#1480	C₂	semidirect
9. C₁₉×#1479	C₂	semidirect
131. C₂×Q₈×C₁₉	SD₁₆	semidirect
183. #18923	C₁₉	direct (N × H)
234. #3227	C₂×C₁₉	semidirect
235. #3206	C₂×C₁₉	semidirect
236. C₂×#475	C₂×C₁₉	semidirect
237. #1651	C₂×C₁₉	semidirect
238. #1642	C₂×C₁₉	semidirect
239. #1540	C₂×C₁₉	semidirect
240. #1480	C₂×C₁₉	semidirect
241. #1479	C₂×C₁₉	semidirect
372. C₁₉	#18923	direct (N × H)
392. C₂×Q₈	SD₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3497	2
C₁₉×#3227	2
C₁₉×#3206	2
C₂×C₁₉×#475	2
C₁₉×#1651	2
C₁₉×#1642	2
C₁₉×#1540	2
C₁₉×#1480	2
C₁₉×#1479	2
#18923	19

Subgroups — C19×#18923 #18024882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18923 #18024882