Subgroups — C₁₉×#32941 #18038900

Order 4864.

1342 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#471	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#465	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3007	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3006	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1908	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1907	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1901	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1900	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1815	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1810	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#137	C₂²	1	2	yes	—
14	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₁₉×#131	—	2	8	no	—
17	C₂×C₁₉×#131	—	2	1	no	—
18	C₂×C₁₉×#131	—	2	1	no	—
19	C₂×C₁₉×#131	C₂²	1	2	yes	—
20	C₂×C₁₉×#131	C₂²	1	2	yes	—
21	C₂²×M₁₆×C₁₉	—	2	1	no	—
22	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₁₉	—	2	1	no	—
24	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
27	C₁₉×#471	—	2	8	no	—
28	C₁₉×#465	—	2	1	no	—
29	C₁₉×#465	—	2	1	no	—
30	C₁₉×#465	—	2	1	no	—
31	C₁₉×#465	—	2	1	no	—
32	C₁₉×#452	—	2	2	no	—
33	C₁₉×#451	—	2	1	no	—
34	C₁₉×#450	—	2	1	no	—
35	C₁₉×#449	—	2	2	no	—
36	C₁₉×#448	—	2	1	no	—
37	C₁₉×#447	—	2	1	no	—
38	C₂×C₁₉×#108	C₂²	1	2	yes	complemented
39	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#417	C₂²	1	2	yes	—
41	C₁₉×#417	C₂²	1	2	yes	—
42	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₉×#101	C₂²	1	2	yes	complemented
45	C₂×C₁₉×#100	C₂²	1	2	yes	complemented
46	C₁₉×#407	C₂²	1	1	yes	characteristic
47	C₁₉×#407	C₂²	1	1	yes	characteristic
48	C₁₉×#343	C₂²	1	2	yes	complemented
49	C₁₉×#343	C₂²	1	2	yes	complemented
50	C₁₉×#341	C₂²	1	2	yes	complemented
51	C₂×#41×C₁₉	—	2	4	no	—
52	C₂×#41×C₁₉	—	2	4	no	—
53	C₂×#41×C₁₉	—	2	1	no	—
54	C₂×#41×C₁₉	—	2	1	no	—
55	C₂×#41×C₁₉	D₄	1	2	yes	—
56	C₂×#41×C₁₉	C₂³	1	2	yes	—
57	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	—	2	1	no	—
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₁₉×#137	—	2	4	no	—
66	C₁₉×#137	—	2	4	no	—
67	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
68	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
69	C₂×Q₁₆×C₁₉	—	2	2	no	—
70	C₂×SD₁₆×C₁₉	—	2	2	no	—
71	C₂×SD₁₆×C₁₉	—	2	2	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×SD₁₆×C₁₉	—	2	4	no	—
75	C₂×D₈×C₁₉	—	2	2	no	—
76	C₁₉×#131	—	2	8	no	—
77	C₁₉×#131	—	2	8	no	—
78	C₁₉×#131	—	2	4	no	—
79	C₁₉×#131	—	2	4	no	—
80	C₁₉×#131	—	2	4	no	—
81	C₁₉×#131	D₄	1	8	yes	complemented
82	C₂×M₁₆×C₁₉	—	2	8	no	—
83	C₂×M₁₆×C₁₉	—	2	1	no	—
84	C₂×M₁₆×C₁₉	—	2	4	no	—
85	C₂×M₁₆×C₁₉	—	2	2	no	—
86	C₂×M₁₆×C₁₉	—	2	2	no	—
87	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
88	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
89	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
90	C₂²×C₈×C₁₉	—	2	8	no	—
91	C₂²×C₈×C₁₉	—	2	1	no	—
92	C₂²×C₈×C₁₉	—	2	2	no	—
93	C₂²×C₈×C₁₉	—	2	2	no	—
94	C₂²×C₈×C₁₉	—	2	4	no	—
95	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
96	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
98	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
99	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×C₂²⋊Q₈	—	2	1	no	—
102	C₁₉×C₂²⋊Q₈	—	2	1	no	—
103	C₁₉×C₂²⋊Q₈	—	2	1	no	—
104	C₁₉×C₂²⋊Q₈	—	2	1	no	—
105	C₁₉×#121	—	2	1	no	—
106	C₁₉×#121	—	2	1	no	—
107	C₁₉×#121	—	2	1	no	—
108	C₁₉×#121	—	2	1	no	—
109	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₁₉×#108	—	2	4	no	—
115	C₁₉×#106	—	2	1	no	—
116	C₁₉×#106	—	2	1	no	—
117	C₁₉×#103	—	2	2	no	—
118	C₁₉×#103	—	2	2	no	—
119	C₁₉×#103	—	2	1	no	—
120	C₁₉×#103	—	2	1	no	—
121	C₁₉×#102	—	2	2	no	—
122	C₁₉×#102	—	2	2	no	—
123	C₁₉×#102	—	2	1	no	—
124	C₁₉×#102	—	2	1	no	—
125	C₁₉×#101	—	2	4	no	—
126	C₁₉×#100	—	2	4	no	—
127	C₁₉×C₂²⋊C₈	—	2	1	no	—
128	C₁₉×C₂²⋊C₈	—	2	1	no	—
129	C₁₉×C₂²⋊C₈	—	2	1	no	—
130	C₁₉×C₂²⋊C₈	—	2	1	no	—
131	C₂⁴×C₁₉	—	2	1	no	—
132	C₂⁴×C₁₉	—	2	1	no	—
133	C₂⁴×C₁₉	#41	1	1	yes	characteristic
134	#41×C₁₉	—	2	4	no	—
135	#41×C₁₉	—	2	8	no	—
136	#41×C₁₉	—	2	4	no	—
137	#41×C₁₉	—	2	4	no	—
138	#41×C₁₉	—	2	4	no	—
139	#41×C₁₉	—	2	2	no	—
140	#41×C₁₉	—	2	2	no	—
141	#41×C₁₉	C₂×D₄	1	4	yes	—
142	#41×C₁₉	#41	1	4	yes	—
143	C₂×Q₈×C₁₉	—	2	4	no	—
144	C₂×Q₈×C₁₉	—	2	1	no	—
145	C₂×Q₈×C₁₉	—	2	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	2	no	—
148	C₂×Q₈×C₁₉	—	2	2	no	—
149	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
150	C₂×D₄×C₁₉	—	2	8	no	—
151	C₂×D₄×C₁₉	—	2	2	no	—
152	C₂×D₄×C₁₉	—	2	2	no	—
153	C₂×D₄×C₁₉	—	2	4	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	2	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	4	1	no	—
160	C₂×D₄×C₁₉	—	4	1	no	—
161	C₂×D₄×C₁₉	—	8	2	no	—
162	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₁₉	—	2	4	no	—
164	C₂²×C₄×C₁₉	—	2	4	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	2	no	—
167	C₂²×C₄×C₁₉	—	2	2	no	—
168	C₂²×C₄×C₁₉	—	2	2	no	—
169	C₂²×C₄×C₁₉	—	2	2	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
179	Q₁₆×C₁₉	—	4	4	no	—
180	SD₁₆×C₁₉	—	4	4	no	—
181	SD₁₆×C₁₉	—	4	4	no	—
182	SD₁₆×C₁₉	—	4	2	no	—
183	SD₁₆×C₁₉	—	4	2	no	—
184	D₈×C₁₉	—	4	4	no	—
185	M₁₆×C₁₉	—	2	4	no	—
186	M₁₆×C₁₉	—	2	8	no	—
187	M₁₆×C₁₉	—	2	2	no	—
188	M₁₆×C₁₉	—	2	8	no	—
189	M₁₆×C₁₉	—	2	2	no	—
190	M₁₆×C₁₉	—	2	2	no	—
191	M₁₆×C₁₉	—	2	2	no	—
192	M₁₆×C₁₉	—	2	2	no	—
193	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
194	C₂×C₈×C₁₉	—	2	4	no	—
195	C₂×C₈×C₁₉	—	2	8	no	—
196	C₂×C₈×C₁₉	—	2	2	no	—
197	C₂×C₈×C₁₉	—	2	2	no	—
198	C₂×C₈×C₁₉	—	2	2	no	—
199	C₂×C₈×C₁₉	—	2	8	no	—
200	C₂×C₈×C₁₉	—	2	2	no	—
201	C₂×C₈×C₁₉	—	2	2	no	—
202	C₂×C₈×C₁₉	—	2	2	no	—
203	C₂×C₈×C₁₉	—	2	2	no	—
204	C₂×C₈×C₁₉	—	2	2	no	—
205	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
209	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₄⋊C₄×C₁₉	—	2	1	no	—
211	C₄⋊C₄×C₁₉	—	2	1	no	—
212	C₄⋊C₄×C₁₉	—	2	1	no	—
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	—	4	1	no	—
215	C₄⋊C₄×C₁₉	—	4	1	no	—
216	C₂²⋊C₄×C₁₉	—	4	1	no	—
217	C₂²⋊C₄×C₁₉	—	4	1	no	—
218	C₂²⋊C₄×C₁₉	—	4	1	no	—
219	C₂²⋊C₄×C₁₉	—	4	1	no	—
220	#32941	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂³×C₁₉	—	2	4	no	—
222	C₂³×C₁₉	—	2	2	no	—
223	C₂³×C₁₉	—	2	2	no	—
224	C₂³×C₁₉	—	2	2	no	—
225	C₂³×C₁₉	—	4	1	no	—
226	C₂³×C₁₉	—	4	2	no	—
227	C₂³×C₁₉	—	4	2	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	4	2	no	—
230	C₂³×C₁₉	—	8	1	no	—
231	C₂³×C₁₉	—	8	1	no	—
232	C₂³×C₁₉	#121	1	1	yes	characteristic
233	C₂³×C₁₉	#121	1	1	yes	characteristic
234	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
235	Q₈×C₁₉	—	2	4	no	—
236	Q₈×C₁₉	—	2	2	no	—
237	Q₈×C₁₉	—	4	1	no	—
238	Q₈×C₁₉	—	4	2	no	—
239	Q₈×C₁₉	—	4	1	no	—
240	Q₈×C₁₉	#121	1	4	yes	—
241	D₄×C₁₉	—	2	8	no	—
242	D₄×C₁₉	—	2	4	no	—
243	D₄×C₁₉	—	2	4	no	—
244	D₄×C₁₉	—	2	4	no	—
245	D₄×C₁₉	—	2	2	no	—
246	D₄×C₁₉	—	4	1	no	—
247	D₄×C₁₉	—	4	2	no	—
248	D₄×C₁₉	—	4	1	no	—
249	D₄×C₁₉	—	8	2	no	—
250	D₄×C₁₉	—	8	2	no	—
251	D₄×C₁₉	#121	1	4	yes	—
252	C₂×C₄×C₁₉	—	2	4	no	—
253	C₂×C₄×C₁₉	—	2	8	no	—
254	C₂×C₄×C₁₉	—	2	2	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	4	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	4	no	—
263	C₂×C₄×C₁₉	—	2	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	2	no	—
268	C₂×C₄×C₁₉	—	8	1	no	—
269	C₂×C₄×C₁₉	—	8	1	no	—
270	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
271	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
272	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
276	C₈×C₁₉	—	2	1	no	—
277	C₈×C₁₉	—	2	4	no	—
278	C₈×C₁₉	—	2	1	no	—
279	C₈×C₁₉	—	4	2	no	—
280	C₈×C₁₉	—	4	2	no	—
281	C₈×C₁₉	#120	1	2	yes	—
282	C₈×C₁₉	#120	1	2	yes	—
283	C₂²×#131	C₂×C₁₉	1	1	yes	characteristic, complemented
284	C₂×#471	C₂×C₁₉	1	2	yes	complemented
285	C₂×#465	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#3007	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#3006	C₂×C₁₉	1	1	yes	characteristic
288	#1908	C₂×C₁₉	1	2	yes	complemented
289	#1907	C₂×C₁₉	1	2	yes	complemented
290	#1901	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1900	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1815	C₂×C₁₉	1	2	yes	complemented
293	#1810	C₂×C₁₉	1	1	yes	characteristic, complemented
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	2	1	no	—
297	C₂²×C₁₉	—	2	1	no	—
298	C₂²×C₁₉	—	2	1	no	—
299	C₂²×C₁₉	—	2	4	no	—
300	C₂²×C₁₉	—	2	1	no	—
301	C₂²×C₁₉	—	2	1	no	—
302	C₂²×C₁₉	—	4	4	no	—
303	C₂²×C₁₉	—	4	8	no	—
304	C₂²×C₁₉	—	4	2	no	—
305	C₂²×C₁₉	—	4	2	no	—
306	C₂²×C₁₉	—	8	1	no	—
307	C₂²×C₁₉	—	8	1	no	—
308	C₂²×C₁₉	—	8	1	no	—
309	C₂²×C₁₉	—	16	2	no	—
310	C₂²×C₁₉	#471	1	2	yes	complemented
311	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
312	C₂²×C₁₉	#525	1	2	yes	—
313	C₄×C₁₉	—	2	1	no	—
314	C₄×C₁₉	—	2	4	no	—
315	C₄×C₁₉	—	2	1	no	—
316	C₄×C₁₉	—	8	1	no	—
317	C₄×C₁₉	—	8	1	no	—
318	C₄×C₁₉	—	8	1	no	—
319	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
320	C₄×C₁₉	C₂×#121	1	2	yes	—
321	C₄×C₁₉	#525	1	1	yes	characteristic
322	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×#137	C₂²×C₁₉	1	2	yes	—
324	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	—
325	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
326	C₂×#131	—	2	8	no	—
327	C₂×#131	—	2	1	no	—
328	C₂×#131	—	2	1	no	—
329	C₂×#131	C₂²×C₁₉	1	2	yes	—
330	C₂×#131	C₂²×C₁₉	1	2	yes	—
331	C₂²×M₁₆	—	2	1	no	—
332	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
333	C₂³×C₈	—	2	1	no	—
334	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
337	#471	—	2	8	no	—
338	#465	—	2	1	no	—
339	#465	—	2	1	no	—
340	#465	—	2	1	no	—
341	#465	—	2	1	no	—
342	#452	—	2	2	no	—
343	#451	—	2	1	no	—
344	#450	—	2	1	no	—
345	#449	—	2	2	no	—
346	#448	—	2	1	no	—
347	#447	—	2	1	no	—
348	C₂×#108	C₂²×C₁₉	1	2	yes	complemented
349	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic, complemented
350	#417	C₂²×C₁₉	1	2	yes	—
351	#417	C₂²×C₁₉	1	2	yes	—
352	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
353	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
354	C₂×#101	C₂²×C₁₉	1	2	yes	complemented
355	C₂×#100	C₂²×C₁₉	1	2	yes	complemented
356	#407	C₂²×C₁₉	1	1	yes	characteristic
357	#407	C₂²×C₁₉	1	1	yes	characteristic
358	#343	C₂²×C₁₉	1	2	yes	complemented
359	#343	C₂²×C₁₉	1	2	yes	complemented
360	#341	C₂²×C₁₉	1	2	yes	complemented
361	C₂×C₁₉	—	2	2	no	—
362	C₂×C₁₉	—	2	2	no	—
363	C₂×C₁₉	—	4	1	no	—
364	C₂×C₁₉	—	4	4	no	—
365	C₂×C₁₉	—	16	1	no	—
366	C₂×C₁₉	#2847	1	1	yes	characteristic
367	C₂×C₁₉	C₂×#471	1	1	yes	characteristic
368	C₂×C₁₉	#3067	1	1	yes	characteristic
369	C₂×#41	—	2	4	no	—
370	C₂×#41	—	2	4	no	—
371	C₂×#41	—	2	1	no	—
372	C₂×#41	—	2	1	no	—
373	C₂×#41	D₄×C₁₉	1	2	yes	—
374	C₂×#41	C₂³×C₁₉	1	2	yes	—
375	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
376	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	—	2	1	no	—
379	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
380	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
383	#137	—	2	4	no	—
384	#137	—	2	4	no	—
385	AGL(1,ℤ/8)	—	2	4	no	—
386	AGL(1,ℤ/8)	—	2	4	no	—
387	C₂×Q₁₆	—	2	2	no	—
388	C₂×SD₁₆	—	2	2	no	—
389	C₂×SD₁₆	—	2	2	no	—
390	C₂×SD₁₆	—	2	1	no	—
391	C₂×SD₁₆	—	2	1	no	—
392	C₂×SD₁₆	—	2	4	no	—
393	C₂×D₈	—	2	2	no	—
394	#131	—	2	8	no	—
395	#131	—	2	8	no	—
396	#131	—	2	4	no	—
397	#131	—	2	4	no	—
398	#131	—	2	4	no	—
399	#131	D₄×C₁₉	1	8	yes	complemented
400	C₂×M₁₆	—	2	8	no	—
401	C₂×M₁₆	—	2	1	no	—
402	C₂×M₁₆	—	2	4	no	—
403	C₂×M₁₆	—	2	2	no	—
404	C₂×M₁₆	—	2	2	no	—
405	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
406	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
407	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
408	C₂²×C₈	—	2	8	no	—
409	C₂²×C₈	—	2	1	no	—
410	C₂²×C₈	—	2	2	no	—
411	C₂²×C₈	—	2	2	no	—
412	C₂²×C₈	—	2	4	no	—
413	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
414	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
415	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
416	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
417	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
418	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
419	C₂²⋊Q₈	—	2	1	no	—
420	C₂²⋊Q₈	—	2	1	no	—
421	C₂²⋊Q₈	—	2	1	no	—
422	C₂²⋊Q₈	—	2	1	no	—
423	#121	—	2	1	no	—
424	#121	—	2	1	no	—
425	#121	—	2	1	no	—
426	#121	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	#108	—	2	4	no	—
433	#106	—	2	1	no	—
434	#106	—	2	1	no	—
435	#103	—	2	2	no	—
436	#103	—	2	2	no	—
437	#103	—	2	1	no	—
438	#103	—	2	1	no	—
439	#102	—	2	2	no	—
440	#102	—	2	2	no	—
441	#102	—	2	1	no	—
442	#102	—	2	1	no	—
443	#101	—	2	4	no	—
444	#100	—	2	4	no	—
445	C₂²⋊C₈	—	2	1	no	—
446	C₂²⋊C₈	—	2	1	no	—
447	C₂²⋊C₈	—	2	1	no	—
448	C₂²⋊C₈	—	2	1	no	—
449	C₁₉	#32941	1	1	yes	characteristic, direct product factor, Sylow
450	C₂⁴	—	2	1	no	—
451	C₂⁴	—	2	1	no	—
452	C₂⁴	#41×C₁₉	1	1	yes	characteristic
453	#41	—	2	4	no	—
454	#41	—	2	8	no	—
455	#41	—	2	4	no	—
456	#41	—	2	4	no	—
457	#41	—	2	4	no	—
458	#41	—	2	2	no	—
459	#41	—	2	2	no	—
460	#41	C₂×D₄×C₁₉	1	4	yes	—
461	#41	#41×C₁₉	1	4	yes	—
462	C₂×Q₈	—	2	4	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	2	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
469	C₂×D₄	—	2	8	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	4	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	4	1	no	—
479	C₂×D₄	—	4	1	no	—
480	C₂×D₄	—	8	2	no	—
481	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
497	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
498	Q₁₆	—	4	4	no	—
499	SD₁₆	—	4	4	no	—
500	SD₁₆	—	4	4	no	—
501	SD₁₆	—	4	2	no	—
502	SD₁₆	—	4	2	no	—
503	D₈	—	4	4	no	—
504	M₁₆	—	2	4	no	—
505	M₁₆	—	2	8	no	—
506	M₁₆	—	2	2	no	—
507	M₁₆	—	2	8	no	—
508	M₁₆	—	2	2	no	—
509	M₁₆	—	2	2	no	—
510	M₁₆	—	2	2	no	—
511	M₁₆	—	2	2	no	—
512	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
513	C₂×C₈	—	2	4	no	—
514	C₂×C₈	—	2	8	no	—
515	C₂×C₈	—	2	2	no	—
516	C₂×C₈	—	2	2	no	—
517	C₂×C₈	—	2	2	no	—
518	C₂×C₈	—	2	8	no	—
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	—	2	2	no	—
522	C₂×C₈	—	2	2	no	—
523	C₂×C₈	—	2	2	no	—
524	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
526	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
527	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	4	1	no	—
534	C₄⋊C₄	—	4	1	no	—
535	C₂²⋊C₄	—	4	1	no	—
536	C₂²⋊C₄	—	4	1	no	—
537	C₂²⋊C₄	—	4	1	no	—
538	C₂²⋊C₄	—	4	1	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	2	no	—
545	C₂³	—	4	2	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	2	no	—
548	C₂³	—	8	1	no	—
549	C₂³	—	8	1	no	—
550	C₂³	C₁₉×#121	1	1	yes	characteristic
551	C₂³	C₁₉×#121	1	1	yes	characteristic
552	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
553	Q₈	—	2	4	no	—
554	Q₈	—	2	2	no	—
555	Q₈	—	4	1	no	—
556	Q₈	—	4	2	no	—
557	Q₈	—	4	1	no	—
558	Q₈	C₁₉×#121	1	4	yes	—
559	D₄	—	2	8	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	2	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	2	no	—
566	D₄	—	4	1	no	—
567	D₄	—	8	2	no	—
568	D₄	—	8	2	no	—
569	D₄	C₁₉×#121	1	4	yes	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	8	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	8	1	no	—
587	C₂×C₄	—	8	1	no	—
588	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
589	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
590	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
591	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
592	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
593	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
594	C₈	—	2	1	no	—
595	C₈	—	2	4	no	—
596	C₈	—	2	1	no	—
597	C₈	—	4	2	no	—
598	C₈	—	4	2	no	—
599	C₈	C₁₉×#120	1	2	yes	—
600	C₈	C₁₉×#120	1	2	yes	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	4	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	4	8	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	—	8	1	no	—
616	C₂²	—	16	2	no	—
617	C₂²	C₁₉×#471	1	2	yes	complemented
618	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
619	C₂²	C₁₉×#525	1	2	yes	—
620	C₄	—	2	1	no	—
621	C₄	—	2	4	no	—
622	C₄	—	2	1	no	—
623	C₄	—	8	1	no	—
624	C₄	—	8	1	no	—
625	C₄	—	8	1	no	—
626	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
627	C₄	C₂×C₁₉×#121	1	2	yes	—
628	C₄	C₁₉×#525	1	1	yes	characteristic
629	C₂	—	2	2	no	—
630	C₂	—	2	2	no	—
631	C₂	—	4	1	no	—
632	C₂	—	4	4	no	—
633	C₂	—	16	1	no	—
634	C₂	C₁₉×#2847	1	1	yes	characteristic
635	C₂	C₂×C₁₉×#471	1	1	yes	characteristic
636	C₂	C₁₉×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3006	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×#131	C₂	semidirect
2. C₂×C₁₉×#471	C₂	semidirect
3. C₂×C₁₉×#465	C₂	semidirect
4. C₁₉×#3007	C₂	semidirect
6. C₁₉×#1908	C₂	semidirect
7. C₁₉×#1907	C₂	semidirect
8. C₁₉×#1901	C₂	semidirect
9. C₁₉×#1900	C₂	semidirect
10. C₁₉×#1815	C₂	semidirect
11. C₁₉×#1810	C₂	semidirect
15. C₂²×SD₁₆×C₁₉	C₂²	semidirect
38. C₂×C₁₉×#108	C₂²	semidirect
39. C₂×C₁₉×#106	C₂²	semidirect
42. C₂×C₁₉×#103	C₂²	semidirect
43. C₂×C₁₉×#102	C₂²	semidirect
44. C₂×C₁₉×#101	C₂²	semidirect
45. C₂×C₁₉×#100	C₂²	semidirect
48. C₁₉×#343	C₂²	semidirect
49. C₁₉×#343	C₂²	semidirect
50. C₁₉×#341	C₂²	semidirect
81. C₁₉×#131	D₄	semidirect
220. #32941	C₁₉	direct (N × H)
283. C₂²×#131	C₂×C₁₉	semidirect
284. C₂×#471	C₂×C₁₉	semidirect
285. C₂×#465	C₂×C₁₉	semidirect
286. #3007	C₂×C₁₉	semidirect
288. #1908	C₂×C₁₉	semidirect
289. #1907	C₂×C₁₉	semidirect
290. #1901	C₂×C₁₉	semidirect
291. #1900	C₂×C₁₉	semidirect
292. #1815	C₂×C₁₉	semidirect
293. #1810	C₂×C₁₉	semidirect
310. C₂²×C₁₉	#471	semidirect
325. C₂²×SD₁₆	C₂²×C₁₉	semidirect
348. C₂×#108	C₂²×C₁₉	semidirect
349. C₂×#106	C₂²×C₁₉	semidirect
352. C₂×#103	C₂²×C₁₉	semidirect
353. C₂×#102	C₂²×C₁₉	semidirect
354. C₂×#101	C₂²×C₁₉	semidirect
355. C₂×#100	C₂²×C₁₉	semidirect
358. #343	C₂²×C₁₉	semidirect
359. #343	C₂²×C₁₉	semidirect
360. #341	C₂²×C₁₉	semidirect
399. #131	D₄×C₁₉	semidirect
449. C₁₉	#32941	direct (N × H)
617. C₂²	C₁₉×#471	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#131	2
C₂×C₁₉×#471	2
C₂×C₁₉×#465	2
C₁₉×#3007	2
C₁₉×#3006	2
C₁₉×#1908	2
C₁₉×#1907	2
C₁₉×#1901	2
C₁₉×#1900	2
C₁₉×#1815	2
C₁₉×#1810	2
#32941	19

Subgroups — C19×#32941 #18038900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32941 #18038900