Subgroups — C₁₉×#32935 #18038894

Order 4864.

1580 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	C₂³×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#468	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#465	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2848	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2847	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1895	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1894	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1809	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1808	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
14	C₂²×M₁₆×C₁₉	—	2	8	no	—
15	C₂²×M₁₆×C₁₉	—	2	4	no	—
16	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
17	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
18	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#121	C₂²	1	2	yes	—
24	C₂×C₁₉×#120	—	2	1	no	—
25	C₁₉×#468	—	2	8	no	—
26	C₁₉×#465	—	2	4	no	—
27	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
28	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
30	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
32	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#386	—	2	2	no	—
34	C₁₉×#386	—	2	1	no	—
35	C₁₉×#385	—	2	2	no	—
36	C₁₉×#385	—	2	1	no	—
37	C₁₉×#380	C₂²	1	1	yes	characteristic
38	C₁₉×#380	C₂²	1	1	yes	characteristic
39	C₁₉×#380	C₂²	1	2	yes	—
40	C₁₉×#380	C₂²	1	2	yes	—
41	C₁₉×#379	—	2	1	no	—
42	C₁₉×#340	C₂²	1	2	yes	complemented
43	C₁₉×#340	C₂²	1	2	yes	complemented
44	C₁₉×#340	C₂²	1	2	yes	complemented
45	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	—	2	2	no	—
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	—	2	4	no	—
51	C₂³×C₄×C₁₉	—	2	2	no	—
52	C₂³×C₄×C₁₉	—	2	4	no	—
53	C₂³×C₄×C₁₉	—	2	2	no	—
54	C₂³×C₄×C₁₉	D₄	1	2	yes	—
55	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
58	C₂×SD₁₆×C₁₉	—	2	2	no	—
59	C₂×SD₁₆×C₁₉	—	2	4	no	—
60	C₂×M₁₆×C₁₉	—	2	32	no	—
61	C₂×M₁₆×C₁₉	—	2	4	no	—
62	C₂×M₁₆×C₁₉	—	2	4	no	—
63	C₂×M₁₆×C₁₉	—	2	4	no	—
64	C₂×M₁₆×C₁₉	—	2	4	no	—
65	C₂×M₁₆×C₁₉	—	2	4	no	—
66	C₂×M₁₆×C₁₉	D₄	1	8	yes	complemented
67	C₂²×C₈×C₁₉	—	2	2	no	—
68	C₂²×C₈×C₁₉	—	2	4	no	—
69	C₂²×C₈×C₁₉	—	2	4	no	—
70	C₂²×C₈×C₁₉	D₄	1	4	yes	complemented
71	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×C₂²⋊Q₈	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	4	no	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	2	4	no	—
78	C₁₉×#121	—	2	2	no	—
79	C₁₉×#121	—	2	4	no	—
80	C₁₉×#121	—	2	2	no	—
81	C₁₉×#121	—	2	4	no	—
82	C₁₉×#120	—	4	4	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
97	C₁₉×#107	—	2	4	no	—
98	C₁₉×#106	—	2	2	no	—
99	C₁₉×#103	—	2	2	no	—
100	C₁₉×#103	—	2	4	no	—
101	C₁₉×#102	—	2	2	no	—
102	C₁₉×#102	—	2	4	no	—
103	C₁₉×#95	—	2	1	no	—
104	C₁₉×#95	—	2	2	no	—
105	C₁₉×#95	—	2	1	no	—
106	C₁₉×#95	—	2	2	no	—
107	C₂⁴×C₁₉	—	2	4	no	—
108	C₂⁴×C₁₉	—	2	2	no	—
109	C₂⁴×C₁₉	—	2	2	no	—
110	C₂⁴×C₁₉	—	2	2	no	—
111	C₂⁴×C₁₉	—	2	1	no	—
112	C₂⁴×C₁₉	—	4	2	no	—
113	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
114	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	2	2	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	1	no	—
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	4	4	no	—
124	C₂×D₄×C₁₉	—	4	4	no	—
125	C₂×D₄×C₁₉	—	4	4	no	—
126	C₂×D₄×C₁₉	—	4	2	no	—
127	C₂×D₄×C₁₉	—	4	2	no	—
128	C₂×D₄×C₁₉	—	4	2	no	—
129	C₂²×C₄×C₁₉	—	2	8	no	—
130	C₂²×C₄×C₁₉	—	2	8	no	—
131	C₂²×C₄×C₁₉	—	2	16	no	—
132	C₂²×C₄×C₁₉	—	2	4	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	4	no	—
135	C₂²×C₄×C₁₉	—	2	4	no	—
136	C₂²×C₄×C₁₉	—	2	4	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₁₉	#41	1	4	yes	—
153	C₂²×C₄×C₁₉	#41	1	2	yes	—
154	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
155	SD₁₆×C₁₉	—	4	4	no	—
156	M₁₆×C₁₉	—	2	16	no	—
157	M₁₆×C₁₉	—	2	16	no	—
158	C₂×C₈×C₁₉	—	2	8	no	—
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₂×C₈×C₁₉	—	2	8	no	—
163	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
164	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
165	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
166	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	4	2	no	—
176	C₄⋊C₄×C₁₉	—	4	4	no	—
177	C₂²⋊C₄×C₁₉	—	4	4	no	—
178	C₂²⋊C₄×C₁₉	—	4	4	no	—
179	C₂²⋊C₄×C₁₉	—	4	4	no	—
180	C₂²⋊C₄×C₁₉	—	4	2	no	—
181	C₂²⋊C₄×C₁₉	—	4	2	no	—
182	C₂²⋊C₄×C₁₉	—	4	2	no	—
183	C₂²⋊C₄×C₁₉	—	4	2	no	—
184	C₂²⋊C₄×C₁₉	—	4	4	no	—
185	#32935	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂³×C₁₉	—	2	2	no	—
187	C₂³×C₁₉	—	2	2	no	—
188	C₂³×C₁₉	—	2	8	no	—
189	C₂³×C₁₉	—	2	2	no	—
190	C₂³×C₁₉	—	2	2	no	—
191	C₂³×C₁₉	—	2	2	no	—
192	C₂³×C₁₉	—	2	2	no	—
193	C₂³×C₁₉	—	2	2	no	—
194	C₂³×C₁₉	—	2	2	no	—
195	C₂³×C₁₉	—	4	8	no	—
196	C₂³×C₁₉	—	4	8	no	—
197	C₂³×C₁₉	—	4	4	no	—
198	C₂³×C₁₉	—	4	4	no	—
199	C₂³×C₁₉	—	4	1	no	—
200	C₂³×C₁₉	—	4	2	no	—
201	C₂³×C₁₉	—	4	1	no	—
202	C₂³×C₁₉	—	4	1	no	—
203	C₂³×C₁₉	—	4	2	no	—
204	C₂³×C₁₉	#121	1	4	yes	—
205	C₂³×C₁₉	#121	1	2	yes	—
206	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
207	C₂³×C₁₉	#137	1	2	yes	—
208	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
209	Q₈×C₁₉	—	4	1	no	—
210	Q₈×C₁₉	—	4	1	no	—
211	Q₈×C₁₉	—	4	2	no	—
212	D₄×C₁₉	—	4	1	no	—
213	D₄×C₁₉	—	4	1	no	—
214	D₄×C₁₉	—	4	2	no	—
215	D₄×C₁₉	—	8	8	no	—
216	D₄×C₁₉	—	8	4	no	—
217	C₂×C₄×C₁₉	—	2	8	no	—
218	C₂×C₄×C₁₉	—	2	16	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	4	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	4	no	—
226	C₂×C₄×C₁₉	—	2	4	no	—
227	C₂×C₄×C₁₉	—	2	4	no	—
228	C₂×C₄×C₁₉	—	2	4	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	#121	1	2	yes	—
243	C₂×C₄×C₁₉	#121	1	4	yes	—
244	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
248	C₈×C₁₉	—	2	4	no	—
249	C₈×C₁₉	—	2	2	no	—
250	C₈×C₁₉	#120	1	4	yes	complemented
251	C₂³×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
252	C₂×#468	C₂×C₁₉	1	2	yes	complemented
253	C₂×#465	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#2848	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#2847	C₂×C₁₉	1	1	yes	characteristic
256	#1895	C₂×C₁₉	1	2	yes	complemented
257	#1894	C₂×C₁₉	1	2	yes	complemented
258	#1893	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1892	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1809	C₂×C₁₉	1	2	yes	complemented
261	#1808	C₂×C₁₉	1	1	yes	characteristic, complemented
262	C₂²×C₁₉	—	2	2	no	—
263	C₂²×C₁₉	—	2	2	no	—
264	C₂²×C₁₉	—	2	4	no	—
265	C₂²×C₁₉	—	2	4	no	—
266	C₂²×C₁₉	—	2	4	no	—
267	C₂²×C₁₉	—	2	4	no	—
268	C₂²×C₁₉	—	2	4	no	—
269	C₂²×C₁₉	—	4	16	no	—
270	C₂²×C₁₉	—	4	2	no	—
271	C₂²×C₁₉	—	4	2	no	—
272	C₂²×C₁₉	—	4	2	no	—
273	C₂²×C₁₉	—	4	2	no	—
274	C₂²×C₁₉	—	8	1	no	—
275	C₂²×C₁₉	—	8	1	no	—
276	C₂²×C₁₉	—	8	1	no	—
277	C₂²×C₁₉	—	8	2	no	—
278	C₂²×C₁₉	—	8	2	no	—
279	C₂²×C₁₉	#468	1	4	yes	complemented
280	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
281	C₂²×C₁₉	C₂×#121	1	2	yes	—
282	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
283	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
284	C₂²×C₁₉	#575	1	2	yes	—
285	C₄×C₁₉	—	2	2	no	—
286	C₄×C₁₉	—	2	4	no	—
287	C₄×C₁₉	—	8	1	no	—
288	C₄×C₁₉	—	8	1	no	—
289	C₄×C₁₉	—	8	1	no	—
290	C₄×C₁₉	—	8	2	no	—
291	C₄×C₁₉	—	8	2	no	—
292	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
293	C₄×C₁₉	#525	1	1	yes	characteristic
294	C₄×C₁₉	#525	1	2	yes	—
295	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
296	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
297	C₂²×M₁₆	—	2	8	no	—
298	C₂²×M₁₆	—	2	4	no	—
299	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
300	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
301	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
302	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
303	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
304	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
305	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
306	C₂×#121	C₂²×C₁₉	1	2	yes	—
307	C₂×#120	—	2	1	no	—
308	#468	—	2	8	no	—
309	#465	—	2	4	no	—
310	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
311	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic, complemented
312	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
313	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
314	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
315	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
316	#386	—	2	2	no	—
317	#386	—	2	1	no	—
318	#385	—	2	2	no	—
319	#385	—	2	1	no	—
320	#380	C₂²×C₁₉	1	1	yes	characteristic
321	#380	C₂²×C₁₉	1	1	yes	characteristic
322	#380	C₂²×C₁₉	1	2	yes	—
323	#380	C₂²×C₁₉	1	2	yes	—
324	#379	—	2	1	no	—
325	#340	C₂²×C₁₉	1	2	yes	complemented
326	#340	C₂²×C₁₉	1	2	yes	complemented
327	#340	C₂²×C₁₉	1	2	yes	complemented
328	C₂×C₁₉	—	2	4	no	—
329	C₂×C₁₉	—	4	4	no	—
330	C₂×C₁₉	—	16	1	no	—
331	C₂×C₁₉	#2847	1	1	yes	characteristic
332	C₂×C₁₉	C₂×#468	1	1	yes	characteristic
333	C₂×C₁₉	#3054	1	1	yes	characteristic
334	C₂×C₁₉	#3055	1	2	yes	—
335	C₂×C₁₉	#3056	1	2	yes	—
336	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
337	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
338	C₂²×D₄	—	2	2	no	—
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
341	C₂³×C₄	—	2	4	no	—
342	C₂³×C₄	—	2	2	no	—
343	C₂³×C₄	—	2	4	no	—
344	C₂³×C₄	—	2	2	no	—
345	C₂³×C₄	D₄×C₁₉	1	2	yes	—
346	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
348	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
349	C₂×SD₁₆	—	2	2	no	—
350	C₂×SD₁₆	—	2	4	no	—
351	C₂×M₁₆	—	2	32	no	—
352	C₂×M₁₆	—	2	4	no	—
353	C₂×M₁₆	—	2	4	no	—
354	C₂×M₁₆	—	2	4	no	—
355	C₂×M₁₆	—	2	4	no	—
356	C₂×M₁₆	—	2	4	no	—
357	C₂×M₁₆	D₄×C₁₉	1	8	yes	complemented
358	C₂²×C₈	—	2	2	no	—
359	C₂²×C₈	—	2	4	no	—
360	C₂²×C₈	—	2	4	no	—
361	C₂²×C₈	D₄×C₁₉	1	4	yes	complemented
362	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
363	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
365	C₂²⋊Q₈	—	2	2	no	—
366	C₂²⋊Q₈	—	2	4	no	—
367	C₂²⋊Q₈	—	2	2	no	—
368	C₂²⋊Q₈	—	2	4	no	—
369	#121	—	2	2	no	—
370	#121	—	2	4	no	—
371	#121	—	2	2	no	—
372	#121	—	2	4	no	—
373	#120	—	4	4	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	2	no	—
376	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	2	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	#107	—	2	4	no	—
389	#106	—	2	2	no	—
390	#103	—	2	2	no	—
391	#103	—	2	4	no	—
392	#102	—	2	2	no	—
393	#102	—	2	4	no	—
394	#95	—	2	1	no	—
395	#95	—	2	2	no	—
396	#95	—	2	1	no	—
397	#95	—	2	2	no	—
398	C₁₉	#32935	1	1	yes	characteristic, direct product factor, Sylow
399	C₂⁴	—	2	4	no	—
400	C₂⁴	—	2	2	no	—
401	C₂⁴	—	2	2	no	—
402	C₂⁴	—	2	2	no	—
403	C₂⁴	—	2	1	no	—
404	C₂⁴	—	4	2	no	—
405	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
406	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	4	4	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	2	no	—
419	C₂×D₄	—	4	2	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂²×C₄	—	2	8	no	—
422	C₂²×C₄	—	2	8	no	—
423	C₂²×C₄	—	2	16	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	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	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
442	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
444	C₂²×C₄	#41×C₁₉	1	4	yes	—
445	C₂²×C₄	#41×C₁₉	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
447	SD₁₆	—	4	4	no	—
448	M₁₆	—	2	16	no	—
449	M₁₆	—	2	16	no	—
450	C₂×C₈	—	2	8	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	8	no	—
455	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
456	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
457	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
458	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	4	2	no	—
468	C₄⋊C₄	—	4	4	no	—
469	C₂²⋊C₄	—	4	4	no	—
470	C₂²⋊C₄	—	4	4	no	—
471	C₂²⋊C₄	—	4	4	no	—
472	C₂²⋊C₄	—	4	2	no	—
473	C₂²⋊C₄	—	4	2	no	—
474	C₂²⋊C₄	—	4	2	no	—
475	C₂²⋊C₄	—	4	2	no	—
476	C₂²⋊C₄	—	4	4	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	8	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	4	8	no	—
487	C₂³	—	4	8	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	4	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	2	no	—
495	C₂³	C₁₉×#121	1	4	yes	—
496	C₂³	C₁₉×#121	1	2	yes	—
497	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
498	C₂³	C₁₉×#137	1	2	yes	—
499	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
500	Q₈	—	4	1	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	4	2	no	—
503	D₄	—	4	1	no	—
504	D₄	—	4	1	no	—
505	D₄	—	4	2	no	—
506	D₄	—	8	8	no	—
507	D₄	—	8	4	no	—
508	C₂×C₄	—	2	8	no	—
509	C₂×C₄	—	2	16	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	C₁₉×#121	1	2	yes	—
534	C₂×C₄	C₁₉×#121	1	4	yes	—
535	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
536	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
537	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
538	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
539	C₈	—	2	4	no	—
540	C₈	—	2	2	no	—
541	C₈	C₁₉×#120	1	4	yes	complemented
542	C₂²	—	2	2	no	—
543	C₂²	—	2	4	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	4	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	2	4	no	—
549	C₂²	—	4	16	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	2	no	—
557	C₂²	—	8	2	no	—
558	C₂²	—	8	1	no	—
559	C₂²	C₁₉×#468	1	4	yes	complemented
560	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
561	C₂²	C₂×C₁₉×#121	1	2	yes	—
562	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
563	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
564	C₂²	C₁₉×#575	1	2	yes	—
565	C₄	—	2	2	no	—
566	C₄	—	2	4	no	—
567	C₄	—	8	1	no	—
568	C₄	—	8	1	no	—
569	C₄	—	8	2	no	—
570	C₄	—	8	2	no	—
571	C₄	—	8	1	no	—
572	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
573	C₄	C₁₉×#525	1	1	yes	characteristic
574	C₄	C₁₉×#525	1	2	yes	—
575	C₂	—	2	4	no	—
576	C₂	—	4	4	no	—
577	C₂	—	16	1	no	—
578	C₂	C₁₉×#2847	1	1	yes	characteristic
579	C₂	C₂×C₁₉×#468	1	1	yes	characteristic
580	C₂	C₁₉×#3054	1	1	yes	characteristic
581	C₂	C₁₉×#3055	1	2	yes	—
582	C₂	C₁₉×#3056	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2847	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×M₁₆×C₁₉	C₂	semidirect
2. C₂×C₁₉×#468	C₂	semidirect
3. C₂×C₁₉×#465	C₂	semidirect
4. C₁₉×#2848	C₂	semidirect
6. C₁₉×#1895	C₂	semidirect
7. C₁₉×#1894	C₂	semidirect
8. C₁₉×#1893	C₂	semidirect
9. C₁₉×#1892	C₂	semidirect
10. C₁₉×#1809	C₂	semidirect
11. C₁₉×#1808	C₂	semidirect
13. C₂²×SD₁₆×C₁₉	C₂²	semidirect
27. C₂×C₁₉×#107	C₂²	semidirect
28. C₂×C₁₉×#106	C₂²	semidirect
29. C₂×C₁₉×#103	C₂²	semidirect
30. C₂×C₁₉×#103	C₂²	semidirect
31. C₂×C₁₉×#102	C₂²	semidirect
32. C₂×C₁₉×#102	C₂²	semidirect
42. C₁₉×#340	C₂²	semidirect
43. C₁₉×#340	C₂²	semidirect
44. C₁₉×#340	C₂²	semidirect
66. C₂×M₁₆×C₁₉	D₄	semidirect
70. C₂²×C₈×C₁₉	D₄	semidirect
185. #32935	C₁₉	direct (N × H)
250. C₈×C₁₉	#120	semidirect
251. C₂³×M₁₆	C₂×C₁₉	semidirect
252. C₂×#468	C₂×C₁₉	semidirect
253. C₂×#465	C₂×C₁₉	semidirect
254. #2848	C₂×C₁₉	semidirect
256. #1895	C₂×C₁₉	semidirect
257. #1894	C₂×C₁₉	semidirect
258. #1893	C₂×C₁₉	semidirect
259. #1892	C₂×C₁₉	semidirect
260. #1809	C₂×C₁₉	semidirect
261. #1808	C₂×C₁₉	semidirect
279. C₂²×C₁₉	#468	semidirect
296. C₂²×SD₁₆	C₂²×C₁₉	semidirect
310. C₂×#107	C₂²×C₁₉	semidirect
311. C₂×#106	C₂²×C₁₉	semidirect
312. C₂×#103	C₂²×C₁₉	semidirect
313. C₂×#103	C₂²×C₁₉	semidirect
314. C₂×#102	C₂²×C₁₉	semidirect
315. C₂×#102	C₂²×C₁₉	semidirect
325. #340	C₂²×C₁₉	semidirect
326. #340	C₂²×C₁₉	semidirect
327. #340	C₂²×C₁₉	semidirect
357. C₂×M₁₆	D₄×C₁₉	semidirect
361. C₂²×C₈	D₄×C₁₉	semidirect
398. C₁₉	#32935	direct (N × H)
541. C₈	C₁₉×#120	semidirect
559. C₂²	C₁₉×#468	semidirect

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₁₉	2
C₂×C₁₉×#468	2
C₂×C₁₉×#465	2
C₁₉×#2848	2
C₁₉×#2847	2
C₁₉×#1895	2
C₁₉×#1894	2
C₁₉×#1893	2
C₁₉×#1892	2
C₁₉×#1809	2
C₁₉×#1808	2
#32935	19

Subgroups — C19×#32935 #18038894

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32935 #18038894