Subgroups — C₁₉×#23570 #18029529

Order 4864.

1436 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₁₉	C₂	1	2	yes	maximal, complemented
3	C₄×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2034	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2024	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2014	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2000	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₉×#102	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₉	—	2	1	no	—
13	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
14	C₁₉×#532	—	2	8	no	—
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#124	—	2	1	no	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#121	—	2	1	no	—
20	C₂×C₁₉×#121	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₉	—	2	1	no	—
23	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₄×SD₁₆×C₁₉	—	2	8	no	—
26	C₂×C₁₉×#106	C₂²	1	2	yes	—
27	C₂×C₁₉×#103	C₂²	1	2	yes	—
28	C₂×C₁₉×#102	C₂²	1	2	yes	—
29	C₂×C₁₉×#102	C₂²	1	2	yes	—
30	C₂×C₁₉×#102	C₂²	1	2	yes	—
31	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
33	C₁₉×#391	C₂²	1	1	yes	characteristic
34	C₁₉×#389	C₂²	1	1	yes	characteristic
35	C₁₉×#387	—	2	1	no	—
36	C₁₉×#385	—	2	1	no	—
37	C₁₉×#380	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#340	C₂²	1	2	yes	—
43	C₁₉×#336	C₂²	1	1	yes	characteristic
44	C₁₉×#336	C₂²	1	1	yes	characteristic
45	C₂×#41×C₁₉	—	2	8	no	—
46	C₂×#41×C₁₉	—	4	4	no	—
47	C₂×#41×C₁₉	—	4	4	no	—
48	C₂²×Q₈×C₁₉	—	2	1	no	—
49	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₁₉	—	2	2	no	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₉	—	2	2	no	—
55	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×SD₁₆×C₁₉	—	2	4	no	—
59	C₂×SD₁₆×C₁₉	—	2	4	no	—
60	C₂×SD₁₆×C₁₉	—	2	4	no	—
61	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
63	C₁₉×C₄⋊Q₈	—	2	4	no	—
64	C₁₉×#127	—	2	4	no	—
65	C₁₉×#124	—	2	8	no	—
66	C₁₉×C₂²⋊Q₈	—	2	2	no	—
67	C₁₉×C₂²⋊Q₈	—	2	2	no	—
68	C₁₉×#121	—	2	8	no	—
69	C₁₉×#121	—	2	4	no	—
70	C₁₉×#121	—	2	4	no	—
71	C₄×Q₈×C₁₉	—	2	4	no	—
72	C₄×D₄×C₁₉	—	2	8	no	—
73	C₄×D₄×C₁₉	—	2	4	no	—
74	C₄×D₄×C₁₉	D₄	1	8	yes	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄²×C₁₉	—	2	4	no	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	—	2	1	no	—
90	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
94	C₁₉×#106	—	2	4	no	—
95	C₁₉×#103	—	2	4	no	—
96	C₁₉×#102	—	2	4	no	—
97	C₁₉×#102	—	2	4	no	—
98	C₁₉×#102	—	2	4	no	—
99	C₁₉×C₂²⋊C₈	—	2	4	no	—
100	C₄×C₈×C₁₉	—	2	4	no	—
101	C₁₉×#95	—	2	1	no	—
102	C₁₉×#95	—	2	1	no	—
103	C₁₉×#95	—	2	1	no	—
104	C₁₉×#95	—	2	1	no	—
105	C₁₉×#95	—	2	1	no	—
106	C₂⁴×C₁₉	—	2	2	no	—
107	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
108	#41×C₁₉	—	4	32	no	—
109	C₂×Q₈×C₁₉	—	2	4	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	4	2	no	—
114	C₂×Q₈×C₁₉	—	4	2	no	—
115	C₂×Q₈×C₁₉	#41	1	2	yes	complemented
116	C₂×D₄×C₁₉	—	2	4	no	—
117	C₂×D₄×C₁₉	—	2	8	no	—
118	C₂×D₄×C₁₉	—	2	4	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	4	2	no	—
125	C₂×D₄×C₁₉	—	4	2	no	—
126	C₂×D₄×C₁₉	—	4	4	no	—
127	C₂×D₄×C₁₉	—	4	4	no	—
128	C₂×D₄×C₁₉	—	4	2	no	—
129	C₂×D₄×C₁₉	—	4	2	no	—
130	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	8	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	4	1	no	—
146	C₂²×C₄×C₁₉	—	4	4	no	—
147	C₂²×C₄×C₁₉	—	4	4	no	—
148	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	complemented
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
155	SD₁₆×C₁₉	—	2	16	no	—
156	C₂×C₈×C₁₉	—	2	2	no	—
157	C₂×C₈×C₁₉	—	2	2	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	#41	1	4	yes	complemented
162	C₄⋊C₄×C₁₉	—	2	4	no	—
163	C₄⋊C₄×C₁₉	—	2	4	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	4	2	no	—
169	C₄⋊C₄×C₁₉	—	4	2	no	—
170	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
171	C₄⋊C₄×C₁₉	#41	1	2	yes	complemented
172	C₂²⋊C₄×C₁₉	—	2	8	no	—
173	C₂²⋊C₄×C₁₉	—	2	4	no	—
174	C₂²⋊C₄×C₁₉	—	2	8	no	—
175	C₂²⋊C₄×C₁₉	—	4	2	no	—
176	C₄²×C₁₉	—	2	2	no	—
177	C₄²×C₁₉	—	2	2	no	—
178	C₄²×C₁₉	—	2	2	no	—
179	C₄²×C₁₉	—	4	2	no	—
180	C₄²×C₁₉	—	4	2	no	—
181	C₄²×C₁₉	C₂×D₄	1	4	yes	—
182	#23570	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂³×C₁₉	—	2	1	no	—
184	C₂³×C₁₉	—	2	1	no	—
185	C₂³×C₁₉	—	2	1	no	—
186	C₂³×C₁₉	—	2	1	no	—
187	C₂³×C₁₉	—	2	1	no	—
188	C₂³×C₁₉	—	2	1	no	—
189	C₂³×C₁₉	—	2	4	no	—
190	C₂³×C₁₉	—	4	2	no	—
191	C₂³×C₁₉	—	4	2	no	—
192	C₂³×C₁₉	—	4	2	no	—
193	C₂³×C₁₉	—	4	2	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	4	2	no	—
196	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
197	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₁₉	—	2	4	no	—
199	Q₈×C₁₉	—	4	8	no	—
200	Q₈×C₁₉	—	4	2	no	—
201	D₄×C₁₉	—	2	4	no	—
202	D₄×C₁₉	—	2	4	no	—
203	D₄×C₁₉	—	4	8	no	—
204	D₄×C₁₉	—	4	8	no	—
205	D₄×C₁₉	—	4	16	no	—
206	D₄×C₁₉	—	4	2	no	—
207	D₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	8	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	4	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	4	4	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	1	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	16	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	#120	1	2	yes	—
238	C₂×C₄×C₁₉	#120	1	2	yes	—
239	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
240	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
241	C₂×C₄×C₁₉	#135	1	2	yes	—
242	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
243	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
246	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
247	C₈×C₁₉	—	2	4	no	—
248	C₈×C₁₉	—	4	2	no	—
249	C₂×#532	C₂×C₁₉	1	1	yes	characteristic
250	C₂×C₄×SD₁₆	C₂×C₁₉	1	2	yes	complemented
251	C₄×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#2058	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#2041	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#2034	C₂×C₁₉	1	2	yes	complemented
255	#2024	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#2014	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#2000	C₂×C₁₉	1	2	yes	complemented
258	C₄×#102	C₂×C₁₉	1	2	yes	complemented
259	C₄×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
260	C₂²×C₁₉	—	2	2	no	—
261	C₂²×C₁₉	—	2	2	no	—
262	C₂²×C₁₉	—	2	2	no	—
263	C₂²×C₁₉	—	4	1	no	—
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	—	4	1	no	—
266	C₂²×C₁₉	—	4	1	no	—
267	C₂²×C₁₉	—	4	4	no	—
268	C₂²×C₁₉	—	4	4	no	—
269	C₂²×C₁₉	—	4	4	no	—
270	C₂²×C₁₉	—	8	2	no	—
271	C₂²×C₁₉	—	8	2	no	—
272	C₂²×C₁₉	—	8	2	no	—
273	C₂²×C₁₉	—	8	2	no	—
274	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
275	C₂²×C₁₉	#525	1	1	yes	characteristic
276	C₂²×C₁₉	#532	1	1	yes	characteristic
277	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
278	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
279	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
280	C₂²×C₁₉	#575	1	1	yes	characteristic
281	C₄×C₁₉	—	2	2	no	—
282	C₄×C₁₉	—	2	2	no	—
283	C₄×C₁₉	—	2	2	no	—
284	C₄×C₁₉	—	4	2	no	—
285	C₄×C₁₉	—	4	1	no	—
286	C₄×C₁₉	—	4	2	no	—
287	C₄×C₁₉	—	4	4	no	—
288	C₄×C₁₉	—	8	1	no	—
289	C₄×C₁₉	—	8	1	no	—
290	C₄×C₁₉	#450	1	4	yes	—
291	C₄×C₁₉	#525	1	2	yes	—
292	C₄×C₁₉	#532	1	2	yes	—
293	C₂²×#41	—	2	1	no	—
294	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
295	#532	—	2	8	no	—
296	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
298	C₂×#124	—	2	1	no	—
299	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
300	C₂×#121	—	2	1	no	—
301	C₂×#121	C₂²×C₁₉	1	2	yes	—
302	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
303	C₂×C₄×D₄	—	2	1	no	—
304	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
305	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
306	C₄×SD₁₆	—	2	8	no	—
307	C₂×#106	C₂²×C₁₉	1	2	yes	—
308	C₂×#103	C₂²×C₁₉	1	2	yes	—
309	C₂×#102	C₂²×C₁₉	1	2	yes	—
310	C₂×#102	C₂²×C₁₉	1	2	yes	—
311	C₂×#102	C₂²×C₁₉	1	2	yes	—
312	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
313	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
314	#391	C₂²×C₁₉	1	1	yes	characteristic
315	#389	C₂²×C₁₉	1	1	yes	characteristic
316	#387	—	2	1	no	—
317	#385	—	2	1	no	—
318	#380	C₂²×C₁₉	1	1	yes	characteristic
319	C₄×C₄⋊C₄	—	2	1	no	—
320	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
321	C₄×C₂²⋊C₄	—	2	1	no	—
322	#340	C₂²×C₁₉	1	2	yes	—
323	#340	C₂²×C₁₉	1	2	yes	—
324	#336	C₂²×C₁₉	1	1	yes	characteristic
325	#336	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×C₁₉	—	4	2	no	—
327	C₂×C₁₉	—	8	4	no	—
328	C₂×C₁₉	#2388	1	1	yes	characteristic
329	C₂×C₁₉	C₂×#450	1	1	yes	characteristic
330	C₂×C₁₉	#3002	1	1	yes	characteristic
331	C₂×C₁₉	#3103	1	1	yes	characteristic
332	C₂×C₁₉	#3106	1	1	yes	characteristic
333	C₂×C₁₉	#3167	1	1	yes	characteristic
334	C₂×C₁₉	#3171	1	1	yes	characteristic
335	C₂×#41	—	2	8	no	—
336	C₂×#41	—	4	4	no	—
337	C₂×#41	—	4	4	no	—
338	C₂²×Q₈	—	2	1	no	—
339	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
340	C₂²×D₄	—	2	2	no	—
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
344	C₂³×C₄	—	2	2	no	—
345	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
346	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
348	C₂×SD₁₆	—	2	4	no	—
349	C₂×SD₁₆	—	2	4	no	—
350	C₂×SD₁₆	—	2	4	no	—
351	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
352	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
353	C₄⋊Q₈	—	2	4	no	—
354	#127	—	2	4	no	—
355	#124	—	2	8	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	#121	—	2	8	no	—
359	#121	—	2	4	no	—
360	#121	—	2	4	no	—
361	C₄×Q₈	—	2	4	no	—
362	C₄×D₄	—	2	8	no	—
363	C₄×D₄	—	2	4	no	—
364	C₄×D₄	D₄×C₁₉	1	8	yes	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₄²	—	2	4	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	—	2	1	no	—
380	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
381	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
384	#106	—	2	4	no	—
385	#103	—	2	4	no	—
386	#102	—	2	4	no	—
387	#102	—	2	4	no	—
388	#102	—	2	4	no	—
389	C₂²⋊C₈	—	2	4	no	—
390	C₄×C₈	—	2	4	no	—
391	#95	—	2	1	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	C₁₉	#23570	1	1	yes	characteristic, direct product factor, Sylow
397	C₂⁴	—	2	2	no	—
398	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
399	#41	—	4	32	no	—
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	4	2	no	—
405	C₂×Q₈	—	4	2	no	—
406	C₂×Q₈	#41×C₁₉	1	2	yes	complemented
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	2	8	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	4	2	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	—	4	2	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	8	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	4	1	no	—
437	C₂²×C₄	—	4	4	no	—
438	C₂²×C₄	—	4	4	no	—
439	C₂²×C₄	SD₁₆×C₁₉	1	4	yes	complemented
440	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
445	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
446	SD₁₆	—	2	16	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	#41×C₁₉	1	4	yes	complemented
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	4	2	no	—
460	C₄⋊C₄	—	4	2	no	—
461	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
462	C₄⋊C₄	#41×C₁₉	1	2	yes	complemented
463	C₂²⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	8	no	—
466	C₂²⋊C₄	—	4	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	4	2	no	—
471	C₄²	—	4	2	no	—
472	C₄²	C₂×D₄×C₁₉	1	4	yes	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	1	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
487	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
488	Q₈	—	2	4	no	—
489	Q₈	—	4	8	no	—
490	Q₈	—	4	2	no	—
491	D₄	—	2	4	no	—
492	D₄	—	2	4	no	—
493	D₄	—	4	8	no	—
494	D₄	—	4	8	no	—
495	D₄	—	4	16	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	8	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	16	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	C₁₉×#120	1	2	yes	—
528	C₂×C₄	C₁₉×#120	1	2	yes	—
529	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
530	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
531	C₂×C₄	C₁₉×#135	1	2	yes	—
532	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
533	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
534	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
535	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
536	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
537	C₈	—	2	4	no	—
538	C₈	—	4	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	4	4	no	—
548	C₂²	—	4	4	no	—
549	C₂²	—	8	2	no	—
550	C₂²	—	8	2	no	—
551	C₂²	—	8	2	no	—
552	C₂²	—	8	2	no	—
553	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
554	C₂²	C₁₉×#525	1	1	yes	characteristic
555	C₂²	C₁₉×#532	1	1	yes	characteristic
556	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
557	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
558	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
559	C₂²	C₁₉×#575	1	1	yes	characteristic
560	C₄	—	2	2	no	—
561	C₄	—	2	2	no	—
562	C₄	—	2	2	no	—
563	C₄	—	4	4	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	2	no	—
567	C₄	—	8	1	no	—
568	C₄	—	8	1	no	—
569	C₄	C₁₉×#450	1	4	yes	—
570	C₄	C₁₉×#525	1	2	yes	—
571	C₄	C₁₉×#532	1	2	yes	—
572	C₂	—	4	2	no	—
573	C₂	—	8	4	no	—
574	C₂	C₁₉×#2388	1	1	yes	characteristic
575	C₂	C₂×C₁₉×#450	1	1	yes	characteristic
576	C₂	C₁₉×#3002	1	1	yes	characteristic
577	C₂	C₁₉×#3103	1	1	yes	characteristic
578	C₂	C₁₉×#3106	1	1	yes	characteristic
579	C₂	C₁₉×#3167	1	1	yes	characteristic
580	C₂	C₁₉×#3171	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂²×D₄
prime radical	C₂×C₁₉×#532	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×SD₁₆×C₁₉	C₂	semidirect
3. C₄×C₁₉×C₂²⋊Q₈	C₂	semidirect
4. C₁₉×#2058	C₂	semidirect
5. C₁₉×#2041	C₂	semidirect
6. C₁₉×#2034	C₂	semidirect
7. C₁₉×#2024	C₂	semidirect
8. C₁₉×#2014	C₂	semidirect
9. C₁₉×#2000	C₂	semidirect
10. C₄×C₁₉×#102	C₂	semidirect
11. C₄×C₁₉×C₂²⋊C₈	C₂	semidirect
115. C₂×Q₈×C₁₉	#41	semidirect
148. C₂²×C₄×C₁₉	SD₁₆	semidirect
161. C₂×C₈×C₁₉	#41	semidirect
171. C₄⋊C₄×C₁₉	#41	semidirect
182. #23570	C₁₉	direct (N × H)
250. C₂×C₄×SD₁₆	C₂×C₁₉	semidirect
251. C₄×C₂²⋊Q₈	C₂×C₁₉	semidirect
252. #2058	C₂×C₁₉	semidirect
253. #2041	C₂×C₁₉	semidirect
254. #2034	C₂×C₁₉	semidirect
255. #2024	C₂×C₁₉	semidirect
256. #2014	C₂×C₁₉	semidirect
257. #2000	C₂×C₁₉	semidirect
258. C₄×#102	C₂×C₁₉	semidirect
259. C₄×C₂²⋊C₈	C₂×C₁₉	semidirect
396. C₁₉	#23570	direct (N × H)
406. C₂×Q₈	#41×C₁₉	semidirect
439. C₂²×C₄	SD₁₆×C₁₉	semidirect
452. C₂×C₈	#41×C₁₉	semidirect
462. C₄⋊C₄	#41×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#532	2
C₂×C₄×SD₁₆×C₁₉	2
C₄×C₁₉×C₂²⋊Q₈	2
C₁₉×#2058	2
C₁₉×#2041	2
C₁₉×#2034	2
C₁₉×#2024	2
C₁₉×#2014	2
C₁₉×#2000	2
C₄×C₁₉×#102	2
C₄×C₁₉×C₂²⋊C₈	2
#23570	19

Subgroups — C19×#23570 #18029529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23570 #18029529