Subgroups — C₁₉×#18540 #18024499

Order 4864.

1146 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3113	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3110	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1651	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1649	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1491	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1490	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₉	—	2	1	no	—
11	D₄×Q₈×C₁₉	—	2	2	no	—
12	D₄×Q₈×C₁₉	—	2	2	no	—
13	D₄×Q₈×C₁₉	—	2	2	no	—
14	D₄×Q₈×C₁₉	C₂²	1	4	yes	—
15	C₁₉×#533	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	—	2	1	no	—
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#501	—	2	2	no	—
24	C₁₉×#500	C₂²	1	2	yes	complemented
25	C₁₉×#498	C₂²	1	2	yes	complemented
26	C₁₉×#484	—	2	1	no	—
27	C₁₉×#483	—	2	1	no	—
28	C₁₉×#475	C₂²	1	2	yes	complemented
29	C₁₉×#474	C₂²	1	2	yes	—
30	C₁₉×#462	C₂²	1	2	yes	complemented
31	C₁₉×#461	C₂²	1	2	yes	—
32	C₁₉×#451	—	2	1	no	—
33	C₁₉×#450	—	2	1	no	—
34	C₁₉×#441	—	2	2	no	—
35	C₁₉×#440	—	2	2	no	—
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#428	—	2	2	no	—
39	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
40	C₁₉×#332	C₂²	1	4	yes	complemented
41	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	complemented
42	C₁₉×D₄⋊C₈	C₂²	1	4	yes	—
43	C₂²×Q₈×C₁₉	—	2	2	no	—
44	C₂²×Q₈×C₁₉	—	2	4	no	—
45	C₂²×Q₈×C₁₉	—	2	4	no	—
46	C₂²×Q₈×C₁₉	—	2	1	no	—
47	C₂²×Q₈×C₁₉	—	4	8	no	—
48	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	—	2	2	no	—
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂×Q₁₆×C₁₉	—	2	2	no	—
53	C₂×SD₁₆×C₁₉	—	2	2	no	—
54	C₂×M₁₆×C₁₉	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	—	2	4	no	—
56	C₁₉×C₄⋊Q₈	—	2	4	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
60	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₁₉×#125	—	2	1	no	—
64	C₁₉×C₂²⋊Q₈	—	2	4	no	—
65	C₁₉×C₂²⋊Q₈	—	2	8	no	—
66	C₁₉×C₂²⋊Q₈	—	2	4	no	—
67	C₁₉×C₂²⋊Q₈	—	2	8	no	—
68	C₁₉×C₂²⋊Q₈	—	2	1	no	—
69	C₁₉×C₂²⋊Q₈	—	2	1	no	—
70	C₄×Q₈×C₁₉	—	2	1	no	—
71	C₄×Q₈×C₁₉	—	2	1	no	—
72	C₄×Q₈×C₁₉	—	2	1	no	—
73	C₄×Q₈×C₁₉	—	2	1	no	—
74	C₄×Q₈×C₁₉	D₄	1	2	yes	—
75	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
76	C₄×D₄×C₁₉	—	2	4	no	—
77	C₄×D₄×C₁₉	—	2	4	no	—
78	C₄×D₄×C₁₉	—	2	1	no	—
79	C₄×D₄×C₁₉	—	2	1	no	—
80	C₄×D₄×C₁₉	D₄	1	2	yes	—
81	C₄×D₄×C₁₉	C₂³	1	2	yes	—
82	C₁₉×#117	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄²×C₁₉	—	2	1	no	—
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₁₉×#107	—	2	4	no	—
94	C₁₉×#107	—	2	2	no	—
95	C₁₉×#106	—	2	4	no	—
96	C₁₉×#106	—	2	2	no	—
97	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
98	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
99	C₁₉×#103	—	2	2	no	—
100	C₁₉×#103	—	2	2	no	—
101	C₁₉×#103	—	2	2	no	—
102	C₁₉×#102	—	2	2	no	—
103	C₁₉×C₂²⋊C₈	—	2	1	no	—
104	C₁₉×C₂²⋊C₈	—	2	1	no	—
105	C₁₉×#97	—	2	1	no	—
106	C₁₉×#97	—	2	1	no	—
107	C₁₉×#97	—	2	1	no	—
108	C₄×C₈×C₁₉	C₂³	1	2	yes	—
109	C₂⁴×C₁₉	—	2	1	no	—
110	C₂×Q₈×C₁₉	—	2	4	no	—
111	C₂×Q₈×C₁₉	—	2	8	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	4	8	no	—
118	C₂×Q₈×C₁₉	—	4	4	no	—
119	C₂×Q₈×C₁₉	—	4	16	no	—
120	C₂×Q₈×C₁₉	—	4	8	no	—
121	C₂×Q₈×C₁₉	—	4	8	no	—
122	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₁₉	—	2	4	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	8	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	4	8	no	—
134	C₂²×C₄×C₁₉	—	4	4	no	—
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	Q₁₆×C₁₉	—	4	4	no	—
139	SD₁₆×C₁₉	—	4	4	no	—
140	M₁₆×C₁₉	—	2	4	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₂×C₈×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	8	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	4	1	no	—
157	C₄⋊C₄×C₁₉	—	4	1	no	—
158	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
161	C₂²⋊C₄×C₁₉	—	2	8	no	—
162	C₂²⋊C₄×C₁₉	—	2	2	no	—
163	C₂²⋊C₄×C₁₉	—	2	2	no	—
164	C₂²⋊C₄×C₁₉	—	4	1	no	—
165	C₄²×C₁₉	—	2	2	no	—
166	C₄²×C₁₉	—	2	2	no	—
167	C₄²×C₁₉	—	4	1	no	—
168	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
172	#18540	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂³×C₁₉	—	2	4	no	—
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	4	2	no	—
176	C₂³×C₁₉	—	4	2	no	—
177	C₂³×C₁₉	#120	1	1	yes	characteristic
178	Q₈×C₁₉	—	2	4	no	—
179	Q₈×C₁₉	—	2	2	no	—
180	Q₈×C₁₉	—	4	16	no	—
181	Q₈×C₁₉	—	4	4	no	—
182	Q₈×C₁₉	—	4	4	no	—
183	Q₈×C₁₉	—	4	2	no	—
184	Q₈×C₁₉	—	4	2	no	—
185	Q₈×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
186	D₄×C₁₉	—	2	4	no	—
187	D₄×C₁₉	—	2	2	no	—
188	D₄×C₁₉	#137	1	4	yes	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	4	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	4	16	no	—
198	C₂×C₄×C₁₉	—	4	4	no	—
199	C₂×C₄×C₁₉	—	4	4	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	4	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
206	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
208	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
211	C₈×C₁₉	—	2	4	no	—
212	C₈×C₁₉	—	4	2	no	—
213	C₈×C₁₉	—	4	2	no	—
214	C₂×D₄×Q₈	C₂×C₁₉	1	1	yes	characteristic
215	#3165	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#3113	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#3110	C₂×C₁₉	1	1	yes	characteristic
218	#1651	C₂×C₁₉	1	4	yes	complemented
219	#1649	C₂×C₁₉	1	4	yes	complemented
220	#1556	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#1491	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#1490	C₂×C₁₉	1	1	yes	characteristic
223	C₂²×C₁₉	—	2	1	no	—
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	2	4	no	—
226	C₂²×C₁₉	—	4	8	no	—
227	C₂²×C₁₉	—	4	2	no	—
228	C₂²×C₁₉	—	4	2	no	—
229	C₂²×C₁₉	#456	1	2	yes	—
230	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
231	C₄×C₁₉	—	2	4	no	—
232	C₄×C₁₉	—	2	1	no	—
233	C₄×C₁₉	—	2	1	no	—
234	C₄×C₁₉	—	2	1	no	—
235	C₄×C₁₉	—	2	1	no	—
236	C₄×C₁₉	—	4	4	no	—
237	C₄×C₁₉	—	4	2	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	8	1	no	—
240	C₄×C₁₉	—	8	1	no	—
241	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
242	C₄×C₁₉	C₂×#137	1	2	yes	—
243	C₂³×Q₈	—	2	1	no	—
244	D₄×Q₈	—	2	2	no	—
245	D₄×Q₈	—	2	2	no	—
246	D₄×Q₈	—	2	2	no	—
247	D₄×Q₈	C₂²×C₁₉	1	4	yes	—
248	#533	C₂²×C₁₉	1	1	yes	characteristic
249	C₂×C₄⋊Q₈	—	2	1	no	—
250	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×C₂²⋊Q₈	—	2	1	no	—
252	C₂×C₂²⋊Q₈	—	2	2	no	—
253	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
254	C₂×C₄×D₄	—	2	1	no	—
255	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
256	#501	—	2	2	no	—
257	#500	C₂²×C₁₉	1	2	yes	complemented
258	#498	C₂²×C₁₉	1	2	yes	complemented
259	#484	—	2	1	no	—
260	#483	—	2	1	no	—
261	#475	C₂²×C₁₉	1	2	yes	complemented
262	#474	C₂²×C₁₉	1	2	yes	—
263	#462	C₂²×C₁₉	1	2	yes	complemented
264	#461	C₂²×C₁₉	1	2	yes	—
265	#451	—	2	1	no	—
266	#450	—	2	1	no	—
267	#441	—	2	2	no	—
268	#440	—	2	2	no	—
269	#432	C₂²×C₁₉	1	1	yes	characteristic
270	#432	C₂²×C₁₉	1	1	yes	characteristic
271	#428	—	2	2	no	—
272	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
273	#332	C₂²×C₁₉	1	4	yes	complemented
274	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	complemented
275	D₄⋊C₈	C₂²×C₁₉	1	4	yes	—
276	C₂×C₁₉	—	2	2	no	—
277	C₂×C₁₉	—	4	4	no	—
278	C₂×C₁₉	#3003	1	1	yes	characteristic
279	C₂×C₁₉	#3004	1	1	yes	characteristic
280	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
281	C₂²×Q₈	—	2	2	no	—
282	C₂²×Q₈	—	2	4	no	—
283	C₂²×Q₈	—	2	4	no	—
284	C₂²×Q₈	—	2	1	no	—
285	C₂²×Q₈	—	4	8	no	—
286	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
287	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
288	C₂³×C₄	—	2	2	no	—
289	C₂³×C₄	—	2	1	no	—
290	C₂×Q₁₆	—	2	2	no	—
291	C₂×SD₁₆	—	2	2	no	—
292	C₂×M₁₆	—	2	1	no	—
293	C₄⋊Q₈	—	2	4	no	—
294	C₄⋊Q₈	—	2	4	no	—
295	C₄⋊Q₈	—	2	1	no	—
296	C₄⋊Q₈	—	2	1	no	—
297	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
298	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
299	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
300	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
301	#125	—	2	1	no	—
302	C₂²⋊Q₈	—	2	4	no	—
303	C₂²⋊Q₈	—	2	8	no	—
304	C₂²⋊Q₈	—	2	4	no	—
305	C₂²⋊Q₈	—	2	8	no	—
306	C₂²⋊Q₈	—	2	1	no	—
307	C₂²⋊Q₈	—	2	1	no	—
308	C₄×Q₈	—	2	1	no	—
309	C₄×Q₈	—	2	1	no	—
310	C₄×Q₈	—	2	1	no	—
311	C₄×Q₈	—	2	1	no	—
312	C₄×Q₈	D₄×C₁₉	1	2	yes	—
313	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
314	C₄×D₄	—	2	4	no	—
315	C₄×D₄	—	2	4	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	D₄×C₁₉	1	2	yes	—
319	C₄×D₄	C₂³×C₁₉	1	2	yes	—
320	#117	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
325	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
326	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
331	#107	—	2	4	no	—
332	#107	—	2	2	no	—
333	#106	—	2	4	no	—
334	#106	—	2	2	no	—
335	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
336	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
337	#103	—	2	2	no	—
338	#103	—	2	2	no	—
339	#103	—	2	2	no	—
340	#102	—	2	2	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	2	1	no	—
343	#97	—	2	1	no	—
344	#97	—	2	1	no	—
345	#97	—	2	1	no	—
346	C₄×C₈	C₂³×C₁₉	1	2	yes	—
347	C₁₉	#18540	1	1	yes	characteristic, direct product factor, Sylow
348	C₂⁴	—	2	1	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	2	8	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	4	8	no	—
357	C₂×Q₈	—	4	4	no	—
358	C₂×Q₈	—	4	16	no	—
359	C₂×Q₈	—	4	8	no	—
360	C₂×Q₈	—	4	8	no	—
361	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	8	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	4	8	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
377	Q₁₆	—	4	4	no	—
378	SD₁₆	—	4	4	no	—
379	M₁₆	—	2	4	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	4	1	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
398	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
399	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
400	C₂²⋊C₄	—	2	8	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	4	1	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	4	1	no	—
407	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
408	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
409	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
410	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
411	C₂³	—	2	4	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	C₁₉×#120	1	1	yes	characteristic
416	Q₈	—	2	4	no	—
417	Q₈	—	2	2	no	—
418	Q₈	—	4	16	no	—
419	Q₈	—	4	4	no	—
420	Q₈	—	4	4	no	—
421	Q₈	—	4	2	no	—
422	Q₈	—	4	2	no	—
423	Q₈	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
424	D₄	—	2	4	no	—
425	D₄	—	2	2	no	—
426	D₄	C₁₉×#137	1	4	yes	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	16	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
444	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
445	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
449	C₈	—	2	4	no	—
450	C₈	—	4	2	no	—
451	C₈	—	4	2	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	4	8	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	C₁₉×#456	1	2	yes	—
459	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
460	C₄	—	2	4	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	4	4	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	8	1	no	—
469	C₄	—	8	1	no	—
470	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
471	C₄	C₂×C₁₉×#137	1	2	yes	—
472	C₂	—	2	2	no	—
473	C₂	—	4	4	no	—
474	C₂	C₁₉×#3003	1	1	yes	characteristic
475	C₂	C₁₉×#3004	1	1	yes	characteristic
476	C₂	C₂×C₁₉×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
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×#3165	C₂	semidirect
3. C₁₉×#3113	C₂	semidirect
5. C₁₉×#1651	C₂	semidirect
6. C₁₉×#1649	C₂	semidirect
7. C₁₉×#1556	C₂	semidirect
8. C₁₉×#1491	C₂	semidirect
24. C₁₉×#500	C₂²	semidirect
25. C₁₉×#498	C₂²	semidirect
28. C₁₉×#475	C₂²	semidirect
30. C₁₉×#462	C₂²	semidirect
40. C₁₉×#332	C₂²	semidirect
41. C₁₉×Q₈⋊C₈	C₂²	semidirect
172. #18540	C₁₉	direct (N × H)
215. #3165	C₂×C₁₉	semidirect
216. #3113	C₂×C₁₉	semidirect
218. #1651	C₂×C₁₉	semidirect
219. #1649	C₂×C₁₉	semidirect
220. #1556	C₂×C₁₉	semidirect
221. #1491	C₂×C₁₉	semidirect
257. #500	C₂²×C₁₉	semidirect
258. #498	C₂²×C₁₉	semidirect
261. #475	C₂²×C₁₉	semidirect
263. #462	C₂²×C₁₉	semidirect
273. #332	C₂²×C₁₉	semidirect
274. Q₈⋊C₈	C₂²×C₁₉	semidirect
347. C₁₉	#18540	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₁₉	2
C₁₉×#3165	2
C₁₉×#3113	2
C₁₉×#3110	2
C₁₉×#1651	2
C₁₉×#1649	2
C₁₉×#1556	2
C₁₉×#1491	2
C₁₉×#1490	2
#18540	19

Subgroups — C19×#18540 #18024499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18540 #18024499