Subgroups — C₁₉×#18747 #18024706

Order 4864.

1634 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3077	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1639	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1629	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1486	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₉	—	2	1	no	—
11	C₂³×D₄×C₁₉	—	2	1	no	—
12	D₄²×C₁₉	—	2	2	no	—
13	D₄²×C₁₉	—	2	2	no	—
14	D₄²×C₁₉	—	2	2	no	—
15	D₄²×C₁₉	C₂²	1	4	yes	—
16	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#121	—	2	1	no	—
19	C₂×C₁₉×#121	—	2	1	no	—
20	C₂×C₁₉×#120	—	2	2	no	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#492	C₂²	1	2	yes	complemented
24	C₁₉×#486	C₂²	1	2	yes	complemented
25	C₁₉×#483	—	2	1	no	—
26	C₁₉×#478	—	2	2	no	—
27	C₁₉×#476	C₂²	1	2	yes	complemented
28	C₁₉×#476	C₂²	1	2	yes	complemented
29	C₁₉×#474	C₂²	1	2	yes	complemented
30	C₁₉×#461	C₂²	1	2	yes	complemented
31	C₁₉×#460	—	2	2	no	—
32	C₁₉×#450	—	2	2	no	—
33	C₁₉×#450	—	2	1	no	—
34	C₄×SD₁₆×C₁₉	—	2	2	no	—
35	C₁₉×#431	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#431	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#428	—	2	1	no	—
38	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#418	—	2	1	no	—
40	C₁₉×#331	C₂²	1	4	yes	complemented
41	C₁₉×D₄⋊C₈	C₂²	1	4	yes	complemented
42	C₁₉×D₄⋊C₈	C₂²	1	4	yes	complemented
43	C₂⁵×C₁₉	—	2	2	no	—
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	—	2	2	no	—
46	C₂²×D₄×C₁₉	—	2	4	no	—
47	C₂²×D₄×C₁₉	—	2	4	no	—
48	C₂²×D₄×C₁₉	—	2	4	no	—
49	C₂²×D₄×C₁₉	—	2	4	no	—
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	—	4	8	no	—
53	C₂²×D₄×C₁₉	—	4	4	no	—
54	C₂²×D₄×C₁₉	—	4	4	no	—
55	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
56	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₁₉	D₄	1	2	yes	—
58	C₂³×C₄×C₁₉	—	2	1	no	—
59	C₂³×C₄×C₁₉	—	2	1	no	—
60	C₂×SD₁₆×C₁₉	—	2	2	no	—
61	C₂×SD₁₆×C₁₉	—	2	4	no	—
62	C₂×M₁₆×C₁₉	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
64	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
65	C₁₉×#127	—	2	1	no	—
66	C₁₉×#127	—	2	1	no	—
67	C₁₉×#127	D₄	1	2	yes	—
68	C₁₉×#127	C₂³	1	2	yes	—
69	C₁₉×#125	—	2	1	no	—
70	C₁₉×C₂²⋊Q₈	—	2	1	no	—
71	C₁₉×C₂²⋊Q₈	—	2	1	no	—
72	C₁₉×#121	—	2	4	no	—
73	C₁₉×#121	—	2	4	no	—
74	C₁₉×#121	—	2	4	no	—
75	C₁₉×#121	—	2	4	no	—
76	C₁₉×#120	—	2	8	no	—
77	C₁₉×#120	—	2	8	no	—
78	C₄×Q₈×C₁₉	—	2	1	no	—
79	C₄×Q₈×C₁₉	—	2	1	no	—
80	C₄×D₄×C₁₉	—	2	1	no	—
81	C₄×D₄×C₁₉	—	2	1	no	—
82	C₄×D₄×C₁₉	—	2	1	no	—
83	C₄×D₄×C₁₉	—	2	1	no	—
84	C₄×D₄×C₁₉	D₄	1	2	yes	—
85	C₄×D₄×C₁₉	D₄	1	2	yes	—
86	C₄×D₄×C₁₉	C₂³	1	2	yes	—
87	C₄×D₄×C₁₉	C₂³	1	2	yes	—
88	C₁₉×#117	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
95	C₁₉×#107	—	2	2	no	—
96	C₁₉×#106	—	2	2	no	—
97	C₁₉×#106	—	2	2	no	—
98	C₁₉×C₄⋊C₈	—	2	1	no	—
99	C₁₉×C₄⋊C₈	—	2	1	no	—
100	C₁₉×C₄⋊C₈	C₂³	1	2	yes	complemented
101	C₁₉×C₄⋊C₈	C₂³	1	2	yes	complemented
102	C₁₉×#103	—	2	2	no	—
103	C₁₉×#102	—	2	2	no	—
104	C₁₉×#102	—	2	2	no	—
105	C₁₉×#102	—	2	2	no	—
106	C₁₉×#102	—	2	4	no	—
107	C₁₉×C₂²⋊C₈	—	2	1	no	—
108	C₁₉×C₂²⋊C₈	—	2	1	no	—
109	C₄×C₈×C₁₉	—	2	1	no	—
110	C₄×C₈×C₁₉	C₂³	1	2	yes	complemented
111	C₂⁴×C₁₉	—	2	1	no	—
112	C₂⁴×C₁₉	—	2	1	no	—
113	C₂⁴×C₁₉	—	2	8	no	—
114	C₂⁴×C₁₉	—	2	2	no	—
115	C₂⁴×C₁₉	—	4	8	no	—
116	C₂⁴×C₁₉	—	4	8	no	—
117	C₂⁴×C₁₉	—	8	4	no	—
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×D₄×C₁₉	—	2	4	no	—
121	C₂×D₄×C₁₉	—	2	8	no	—
122	C₂×D₄×C₁₉	—	2	8	no	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	4	4	no	—
132	C₂×D₄×C₁₉	—	4	16	no	—
133	C₂×D₄×C₁₉	—	4	8	no	—
134	C₂×D₄×C₁₉	—	4	8	no	—
135	C₂×D₄×C₁₉	—	4	16	no	—
136	C₂×D₄×C₁₉	—	4	8	no	—
137	C₂×D₄×C₁₉	—	4	8	no	—
138	C₂×D₄×C₁₉	—	4	8	no	—
139	C₂×D₄×C₁₉	—	4	8	no	—
140	C₂×D₄×C₁₉	—	4	2	no	—
141	C₂×D₄×C₁₉	—	4	2	no	—
142	C₂×D₄×C₁₉	—	8	2	no	—
143	C₂×D₄×C₁₉	SD₁₆	1	4	yes	complemented
144	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	4	4	no	—
154	C₂²×C₄×C₁₉	—	4	2	no	—
155	C₂²×C₄×C₁₉	—	4	2	no	—
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	SD₁₆×C₁₉	—	4	4	no	—
160	SD₁₆×C₁₉	—	8	4	no	—
161	M₁₆×C₁₉	—	4	2	no	—
162	C₂×C₈×C₁₉	—	2	2	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	4	1	no	—
172	C₄⋊C₄×C₁₉	—	4	1	no	—
173	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
174	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
175	C₂²⋊C₄×C₁₉	—	2	8	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂²⋊C₄×C₁₉	—	2	2	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₉	—	4	1	no	—
181	C₄²×C₁₉	—	4	1	no	—
182	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
186	#18747	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂³×C₁₉	—	2	4	no	—
188	C₂³×C₁₉	—	2	2	no	—
189	C₂³×C₁₉	—	2	2	no	—
190	C₂³×C₁₉	—	2	4	no	—
191	C₂³×C₁₉	—	2	4	no	—
192	C₂³×C₁₉	—	4	2	no	—
193	C₂³×C₁₉	—	4	2	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	4	4	no	—
196	C₂³×C₁₉	—	4	16	no	—
197	C₂³×C₁₉	—	4	16	no	—
198	C₂³×C₁₉	—	4	4	no	—
199	C₂³×C₁₉	—	4	2	no	—
200	C₂³×C₁₉	—	4	4	no	—
201	C₂³×C₁₉	—	8	8	no	—
202	C₂³×C₁₉	—	8	32	no	—
203	C₂³×C₁₉	#120	1	1	yes	characteristic
204	Q₈×C₁₉	—	4	2	no	—
205	Q₈×C₁₉	—	4	2	no	—
206	D₄×C₁₉	—	2	4	no	—
207	D₄×C₁₉	—	2	2	no	—
208	D₄×C₁₉	—	2	2	no	—
209	D₄×C₁₉	—	2	4	no	—
210	D₄×C₁₉	—	4	4	no	—
211	D₄×C₁₉	—	4	4	no	—
212	D₄×C₁₉	—	4	16	no	—
213	D₄×C₁₉	—	4	16	no	—
214	D₄×C₁₉	—	4	2	no	—
215	D₄×C₁₉	—	4	2	no	—
216	D₄×C₁₉	—	4	4	no	—
217	D₄×C₁₉	—	4	4	no	—
218	D₄×C₁₉	—	8	2	no	—
219	D₄×C₁₉	C₂×SD₁₆	1	4	yes	—
220	D₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	4	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	4	no	—
231	C₂×C₄×C₁₉	—	4	4	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
236	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
238	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
239	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
242	C₈×C₁₉	—	4	2	no	—
243	C₈×C₁₉	—	4	2	no	—
244	C₈×C₁₉	—	4	2	no	—
245	C₂×D₄²	C₂×C₁₉	1	1	yes	characteristic
246	#3208	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#3101	C₂×C₁₉	1	1	yes	characteristic, complemented
248	#3077	C₂×C₁₉	1	1	yes	characteristic, complemented
249	#1639	C₂×C₁₉	1	4	yes	complemented
250	#1629	C₂×C₁₉	1	4	yes	complemented
251	#1545	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#1486	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#1478	C₂×C₁₉	1	1	yes	characteristic, complemented
254	C₂²×C₁₉	—	2	1	no	—
255	C₂²×C₁₉	—	2	1	no	—
256	C₂²×C₁₉	—	2	4	no	—
257	C₂²×C₁₉	—	2	4	no	—
258	C₂²×C₁₉	—	4	8	no	—
259	C₂²×C₁₉	—	4	8	no	—
260	C₂²×C₁₉	—	4	2	no	—
261	C₂²×C₁₉	—	4	2	no	—
262	C₂²×C₁₉	—	4	2	no	—
263	C₂²×C₁₉	—	4	2	no	—
264	C₂²×C₁₉	—	4	4	no	—
265	C₂²×C₁₉	—	4	4	no	—
266	C₂²×C₁₉	—	4	4	no	—
267	C₂²×C₁₉	—	8	8	no	—
268	C₂²×C₁₉	—	8	32	no	—
269	C₂²×C₁₉	#450	1	2	yes	—
270	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
271	C₄×C₁₉	—	2	1	no	—
272	C₄×C₁₉	—	2	1	no	—
273	C₄×C₁₉	—	2	1	no	—
274	C₄×C₁₉	—	4	2	no	—
275	C₄×C₁₉	—	4	2	no	—
276	C₄×C₁₉	—	8	1	no	—
277	C₄×C₁₉	—	8	1	no	—
278	C₄×C₁₉	#450	1	2	yes	—
279	C₄×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
280	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
281	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
282	C₂³×D₄	—	2	1	no	—
283	C₂³×D₄	—	2	1	no	—
284	D₄²	—	2	2	no	—
285	D₄²	—	2	2	no	—
286	D₄²	—	2	2	no	—
287	D₄²	C₂²×C₁₉	1	4	yes	—
288	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
289	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
290	C₂×#121	—	2	1	no	—
291	C₂×#121	—	2	1	no	—
292	C₂×#120	—	2	2	no	—
293	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
295	#492	C₂²×C₁₉	1	2	yes	complemented
296	#486	C₂²×C₁₉	1	2	yes	complemented
297	#483	—	2	1	no	—
298	#478	—	2	2	no	—
299	#476	C₂²×C₁₉	1	2	yes	complemented
300	#476	C₂²×C₁₉	1	2	yes	complemented
301	#474	C₂²×C₁₉	1	2	yes	complemented
302	#461	C₂²×C₁₉	1	2	yes	complemented
303	#460	—	2	2	no	—
304	#450	—	2	1	no	—
305	#450	—	2	2	no	—
306	C₄×SD₁₆	—	2	2	no	—
307	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
308	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
309	#428	—	2	1	no	—
310	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
311	#418	—	2	1	no	—
312	#331	C₂²×C₁₉	1	4	yes	complemented
313	D₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
314	D₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
315	C₂×C₁₉	—	2	2	no	—
316	C₂×C₁₉	—	4	4	no	—
317	C₂×C₁₉	—	4	4	no	—
318	C₂×C₁₉	—	8	4	no	—
319	C₂×C₁₉	C₂×#450	1	1	yes	characteristic
320	C₂×C₁₉	#3003	1	1	yes	characteristic
321	C₂×C₁₉	#3019	1	1	yes	characteristic
322	C₂⁵	—	2	2	no	—
323	C₂²×D₄	—	2	2	no	—
324	C₂²×D₄	—	2	2	no	—
325	C₂²×D₄	—	2	4	no	—
326	C₂²×D₄	—	2	4	no	—
327	C₂²×D₄	—	2	4	no	—
328	C₂²×D₄	—	2	4	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	—	4	8	no	—
332	C₂²×D₄	—	4	4	no	—
333	C₂²×D₄	—	4	4	no	—
334	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
335	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
336	C₂²×D₄	D₄×C₁₉	1	2	yes	—
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	—	2	1	no	—
339	C₂×SD₁₆	—	2	2	no	—
340	C₂×SD₁₆	—	2	4	no	—
341	C₂×M₁₆	—	2	1	no	—
342	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic, complemented
343	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic, complemented
344	#127	—	2	1	no	—
345	#127	—	2	1	no	—
346	#127	D₄×C₁₉	1	2	yes	—
347	#127	C₂³×C₁₉	1	2	yes	—
348	#125	—	2	1	no	—
349	C₂²⋊Q₈	—	2	1	no	—
350	C₂²⋊Q₈	—	2	1	no	—
351	#121	—	2	4	no	—
352	#121	—	2	4	no	—
353	#121	—	2	4	no	—
354	#121	—	2	4	no	—
355	#120	—	2	8	no	—
356	#120	—	2	8	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×Q₈	—	2	1	no	—
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	D₄×C₁₉	1	2	yes	—
364	C₄×D₄	D₄×C₁₉	1	2	yes	—
365	C₄×D₄	C₂³×C₁₉	1	2	yes	—
366	C₄×D₄	C₂³×C₁₉	1	2	yes	—
367	#117	—	2	1	no	—
368	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
369	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
374	#107	—	2	2	no	—
375	#106	—	2	2	no	—
376	#106	—	2	2	no	—
377	C₄⋊C₈	—	2	1	no	—
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	C₂³×C₁₉	1	2	yes	complemented
380	C₄⋊C₈	C₂³×C₁₉	1	2	yes	complemented
381	#103	—	2	2	no	—
382	#102	—	2	2	no	—
383	#102	—	2	2	no	—
384	#102	—	2	2	no	—
385	#102	—	2	4	no	—
386	C₂²⋊C₈	—	2	1	no	—
387	C₂²⋊C₈	—	2	1	no	—
388	C₄×C₈	—	2	1	no	—
389	C₄×C₈	C₂³×C₁₉	1	2	yes	complemented
390	C₁₉	#18747	1	1	yes	characteristic, direct product factor, Sylow
391	C₂⁴	—	2	1	no	—
392	C₂⁴	—	2	1	no	—
393	C₂⁴	—	2	8	no	—
394	C₂⁴	—	2	2	no	—
395	C₂⁴	—	4	8	no	—
396	C₂⁴	—	4	8	no	—
397	C₂⁴	—	8	4	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	8	no	—
402	C₂×D₄	—	2	8	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	4	16	no	—
413	C₂×D₄	—	4	16	no	—
414	C₂×D₄	—	4	8	no	—
415	C₂×D₄	—	4	8	no	—
416	C₂×D₄	—	4	8	no	—
417	C₂×D₄	—	4	8	no	—
418	C₂×D₄	—	4	8	no	—
419	C₂×D₄	—	4	8	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	4	2	no	—
422	C₂×D₄	—	8	2	no	—
423	C₂×D₄	SD₁₆×C₁₉	1	4	yes	complemented
424	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
425	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
426	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	2	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
439	SD₁₆	—	4	4	no	—
440	SD₁₆	—	8	4	no	—
441	M₁₆	—	4	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	4	1	no	—
452	C₄⋊C₄	—	4	1	no	—
453	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
454	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	4	1	no	—
461	C₄²	—	4	1	no	—
462	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
466	C₂³	—	2	4	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	4	no	—
475	C₂³	—	4	16	no	—
476	C₂³	—	4	16	no	—
477	C₂³	—	4	4	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	4	no	—
480	C₂³	—	8	8	no	—
481	C₂³	—	8	32	no	—
482	C₂³	C₁₉×#120	1	1	yes	characteristic
483	Q₈	—	4	2	no	—
484	Q₈	—	4	2	no	—
485	D₄	—	2	4	no	—
486	D₄	—	2	4	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	2	no	—
489	D₄	—	4	4	no	—
490	D₄	—	4	4	no	—
491	D₄	—	4	16	no	—
492	D₄	—	4	16	no	—
493	D₄	—	4	4	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	2	no	—
496	D₄	—	4	4	no	—
497	D₄	—	8	2	no	—
498	D₄	C₂×SD₁₆×C₁₉	1	4	yes	—
499	D₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	4	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	4	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
514	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
515	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
516	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
517	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
518	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
521	C₈	—	4	2	no	—
522	C₈	—	4	2	no	—
523	C₈	—	4	2	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	4	8	no	—
529	C₂²	—	4	8	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	4	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	8	8	no	—
538	C₂²	—	8	32	no	—
539	C₂²	C₁₉×#450	1	2	yes	—
540	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	8	1	no	—
547	C₄	—	8	1	no	—
548	C₄	C₁₉×#450	1	2	yes	—
549	C₄	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
550	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
551	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
552	C₂	—	2	2	no	—
553	C₂	—	4	4	no	—
554	C₂	—	4	4	no	—
555	C₂	—	8	4	no	—
556	C₂	C₂×C₁₉×#450	1	1	yes	characteristic
557	C₂	C₁₉×#3003	1	1	yes	characteristic
558	C₂	C₁₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×D₄²×C₁₉	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×#3208	C₂	semidirect
3. C₁₉×#3101	C₂	semidirect
4. C₁₉×#3077	C₂	semidirect
5. C₁₉×#1639	C₂	semidirect
6. C₁₉×#1629	C₂	semidirect
7. C₁₉×#1545	C₂	semidirect
8. C₁₉×#1486	C₂	semidirect
9. C₁₉×#1478	C₂	semidirect
16. C₁₉×#533	C₂²	semidirect
23. C₁₉×#492	C₂²	semidirect
24. C₁₉×#486	C₂²	semidirect
27. C₁₉×#476	C₂²	semidirect
28. C₁₉×#476	C₂²	semidirect
29. C₁₉×#474	C₂²	semidirect
30. C₁₉×#461	C₂²	semidirect
35. C₁₉×#431	C₂²	semidirect
36. C₁₉×#431	C₂²	semidirect
38. C₁₉×#423	C₂²	semidirect
40. C₁₉×#331	C₂²	semidirect
41. C₁₉×D₄⋊C₈	C₂²	semidirect
42. C₁₉×D₄⋊C₈	C₂²	semidirect
63. C₁₉×C₄⋊Q₈	C₂³	semidirect
64. C₁₉×C₄⋊Q₈	C₂³	semidirect
100. C₁₉×C₄⋊C₈	C₂³	semidirect
101. C₁₉×C₄⋊C₈	C₂³	semidirect
110. C₄×C₈×C₁₉	C₂³	semidirect
143. C₂×D₄×C₁₉	SD₁₆	semidirect
186. #18747	C₁₉	direct (N × H)
246. #3208	C₂×C₁₉	semidirect
247. #3101	C₂×C₁₉	semidirect
248. #3077	C₂×C₁₉	semidirect
249. #1639	C₂×C₁₉	semidirect
250. #1629	C₂×C₁₉	semidirect
251. #1545	C₂×C₁₉	semidirect
252. #1486	C₂×C₁₉	semidirect
253. #1478	C₂×C₁₉	semidirect
288. #533	C₂²×C₁₉	semidirect
295. #492	C₂²×C₁₉	semidirect
296. #486	C₂²×C₁₉	semidirect
299. #476	C₂²×C₁₉	semidirect
300. #476	C₂²×C₁₉	semidirect
301. #474	C₂²×C₁₉	semidirect
302. #461	C₂²×C₁₉	semidirect
307. #431	C₂²×C₁₉	semidirect
308. #431	C₂²×C₁₉	semidirect
310. #423	C₂²×C₁₉	semidirect
312. #331	C₂²×C₁₉	semidirect
313. D₄⋊C₈	C₂²×C₁₉	semidirect
314. D₄⋊C₈	C₂²×C₁₉	semidirect
342. C₄⋊Q₈	C₂³×C₁₉	semidirect
343. C₄⋊Q₈	C₂³×C₁₉	semidirect
379. C₄⋊C₈	C₂³×C₁₉	semidirect
380. C₄⋊C₈	C₂³×C₁₉	semidirect
389. C₄×C₈	C₂³×C₁₉	semidirect
390. C₁₉	#18747	direct (N × H)
423. C₂×D₄	SD₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₁₉	2
C₁₉×#3208	2
C₁₉×#3101	2
C₁₉×#3077	2
C₁₉×#1639	2
C₁₉×#1629	2
C₁₉×#1545	2
C₁₉×#1486	2
C₁₉×#1478	2
#18747	19

Subgroups — C19×#18747 #18024706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18747 #18024706