Subgroups — C₁₉×#23545 #18029504

Order 4864.

1410 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#137	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#416	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2311	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2310	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2056	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2055	C₂	1	4	yes	maximal, complemented
9	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#137	—	2	4	no	—
13	C₂×C₁₉×#137	—	2	4	no	—
14	C₂×C₁₉×#137	—	2	4	no	—
15	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
17	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#424	—	2	4	no	—
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	4	yes	—
24	C₁₉×#416	—	2	4	no	—
25	C₂×C₁₉×#103	—	2	4	no	—
26	C₂×C₁₉×#103	C₂²	1	4	yes	—
27	C₂×C₁₉×#103	C₂²	1	2	yes	—
28	C₂×C₁₉×#102	C₂²	1	2	yes	—
29	C₁₉×#391	—	2	2	no	—
30	C₁₉×#391	C₂²	1	4	yes	—
31	C₁₉×#391	C₂²	1	2	yes	—
32	C₁₉×#390	C₂²	1	2	yes	—
33	C₁₉×#386	—	2	2	no	—
34	C₁₉×#381	—	2	2	no	—
35	C₁₉×#380	—	2	2	no	—
36	C₁₉×#340	C₂²	1	4	yes	—
37	C₂×#41×C₁₉	—	2	2	no	—
38	C₂×#41×C₁₉	—	2	2	no	—
39	C₂×#41×C₁₉	—	2	2	no	—
40	C₂×#41×C₁₉	—	2	2	no	—
41	C₂×#41×C₁₉	—	2	2	no	—
42	C₂×#41×C₁₉	D₄	1	4	yes	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	—	2	2	no	—
45	C₂²×Q₈×C₁₉	—	2	2	no	—
46	C₂²×Q₈×C₁₉	—	2	2	no	—
47	C₂²×Q₈×C₁₉	—	2	2	no	—
48	C₂²×Q₈×C₁₉	—	2	2	no	—
49	C₂²×Q₈×C₁₉	D₄	1	4	yes	—
50	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
51	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	—	2	1	no	—
55	C₂³×C₄×C₁₉	—	2	1	no	—
56	C₂³×C₄×C₁₉	—	2	1	no	—
57	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×#137	—	2	32	no	—
59	C₂×Q₁₆×C₁₉	—	2	4	no	—
60	C₂×Q₁₆×C₁₉	—	2	4	no	—
61	C₂×Q₁₆×C₁₉	—	2	4	no	—
62	C₂×SD₁₆×C₁₉	—	2	4	no	—
63	C₂×SD₁₆×C₁₉	—	2	4	no	—
64	C₂×SD₁₆×C₁₉	—	2	4	no	—
65	C₂×M₁₆×C₁₉	—	2	2	no	—
66	C₂×M₁₆×C₁₉	—	2	2	no	—
67	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
68	C₂²×C₈×C₁₉	—	2	2	no	—
69	C₂²×C₈×C₁₉	—	2	2	no	—
70	C₂²×C₈×C₁₉	—	2	2	no	—
71	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
72	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
73	C₁₉×#117	—	2	2	no	—
74	C₁₉×#117	—	2	2	no	—
75	C₁₉×#117	—	2	2	no	—
76	C₁₉×#117	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
86	C₂×C₄²×C₁₉	—	2	1	no	—
87	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
88	C₁₉×C₄⋊C₈	—	2	8	no	—
89	C₁₉×#103	—	2	8	no	—
90	C₁₉×#103	—	2	4	no	—
91	C₁₉×#102	—	2	4	no	—
92	C₁₉×#95	—	2	4	no	—
93	C₁₉×#95	—	2	8	no	—
94	C₂⁴×C₁₉	—	2	1	no	—
95	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
96	#41×C₁₉	—	2	8	no	—
97	#41×C₁₉	—	2	8	no	—
98	#41×C₁₉	—	4	4	no	—
99	#41×C₁₉	—	4	4	no	—
100	C₂×Q₈×C₁₉	—	2	4	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	1	no	—
103	C₂×Q₈×C₁₉	—	2	8	no	—
104	C₂×Q₈×C₁₉	—	2	8	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	—	2	1	no	—
108	C₂×Q₈×C₁₉	—	2	1	no	—
109	C₂×Q₈×C₁₉	—	2	2	no	—
110	C₂×Q₈×C₁₉	—	2	2	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	4	2	no	—
114	C₂×Q₈×C₁₉	—	4	2	no	—
115	C₂×Q₈×C₁₉	—	4	4	no	—
116	C₂×Q₈×C₁₉	—	4	4	no	—
117	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
118	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₁₉	—	2	4	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	—	4	2	no	—
126	C₂×D₄×C₁₉	—	4	2	no	—
127	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₉	—	2	4	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	4	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	4	2	no	—
135	C₂²×C₄×C₁₉	—	4	2	no	—
136	C₂²×C₄×C₁₉	—	4	2	no	—
137	C₂²×C₄×C₁₉	—	4	2	no	—
138	C₂²×C₄×C₁₉	—	4	2	no	—
139	C₂²×C₄×C₁₉	—	8	2	no	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	#41	1	2	yes	—
146	C₂²×C₄×C₁₉	#41	1	2	yes	—
147	C₂²×C₄×C₁₉	#41	1	2	yes	—
148	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
149	Q₁₆×C₁₉	—	2	16	no	—
150	SD₁₆×C₁₉	—	2	16	no	—
151	M₁₆×C₁₉	—	2	8	no	—
152	C₂×C₈×C₁₉	—	2	2	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₂×C₈×C₁₉	—	2	2	no	—
156	C₂×C₈×C₁₉	—	2	2	no	—
157	C₂×C₈×C₁₉	—	4	4	no	—
158	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
159	C₄⋊C₄×C₁₉	—	2	4	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	4	2	no	—
165	C₂²⋊C₄×C₁₉	—	2	4	no	—
166	C₂²⋊C₄×C₁₉	—	4	2	no	—
167	C₂²⋊C₄×C₁₉	—	8	4	no	—
168	C₄²×C₁₉	—	2	2	no	—
169	C₄²×C₁₉	—	2	2	no	—
170	C₄²×C₁₉	—	4	2	no	—
171	#23545	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	4	1	no	—
176	C₂³×C₁₉	—	4	1	no	—
177	C₂³×C₁₉	—	4	2	no	—
178	C₂³×C₁₉	—	4	2	no	—
179	C₂³×C₁₉	#121	1	2	yes	—
180	C₂³×C₁₉	#121	1	2	yes	—
181	C₂³×C₁₉	#121	1	2	yes	—
182	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₁₉	—	2	4	no	—
184	Q₈×C₁₉	—	2	2	no	—
185	Q₈×C₁₉	—	2	4	no	—
186	Q₈×C₁₉	—	2	2	no	—
187	Q₈×C₁₉	—	4	2	no	—
188	Q₈×C₁₉	—	4	1	no	—
189	Q₈×C₁₉	—	4	2	no	—
190	Q₈×C₁₉	—	4	1	no	—
191	Q₈×C₁₉	—	4	8	no	—
192	D₄×C₁₉	—	2	2	no	—
193	D₄×C₁₉	—	2	2	no	—
194	D₄×C₁₉	—	4	8	no	—
195	D₄×C₁₉	—	4	1	no	—
196	D₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	2	4	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	8	no	—
207	C₂×C₄×C₁₉	—	4	8	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	4	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	8	4	no	—
214	C₂×C₄×C₁₉	#120	1	4	yes	—
215	C₂×C₄×C₁₉	#121	1	2	yes	—
216	C₂×C₄×C₁₉	#121	1	2	yes	—
217	C₂×C₄×C₁₉	#121	1	2	yes	—
218	C₂×C₄×C₁₉	#123	1	4	yes	—
219	C₂×C₄×C₁₉	#123	1	4	yes	—
220	C₂×C₄×C₁₉	#124	1	4	yes	—
221	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
227	C₈×C₁₉	—	2	4	no	—
228	C₈×C₁₉	—	4	2	no	—
229	C₂²×#137	C₂×C₁₉	1	1	yes	characteristic
230	C₂×#424	C₂×C₁₉	1	1	yes	characteristic, complemented
231	C₂×#416	C₂×C₁₉	1	1	yes	characteristic
232	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#2311	C₂×C₁₉	1	1	yes	characteristic
234	#2310	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#2056	C₂×C₁₉	1	4	yes	complemented
236	#2055	C₂×C₁₉	1	4	yes	complemented
237	#1736	C₂×C₁₉	1	1	yes	characteristic, complemented
238	C₂²×C₁₉	—	2	2	no	—
239	C₂²×C₁₉	—	2	2	no	—
240	C₂²×C₁₉	—	2	4	no	—
241	C₂²×C₁₉	—	2	4	no	—
242	C₂²×C₁₉	—	4	2	no	—
243	C₂²×C₁₉	—	4	4	no	—
244	C₂²×C₁₉	—	8	1	no	—
245	C₂²×C₁₉	—	8	1	no	—
246	C₂²×C₁₉	—	8	2	no	—
247	C₂²×C₁₉	#394	1	4	yes	—
248	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
249	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
250	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
251	C₂²×C₁₉	#577	1	2	yes	—
252	C₂²×C₁₉	#578	1	2	yes	—
253	C₄×C₁₉	—	4	2	no	—
254	C₄×C₁₉	—	4	4	no	—
255	C₄×C₁₉	—	4	4	no	—
256	C₄×C₁₉	—	8	2	no	—
257	C₄×C₁₉	—	8	2	no	—
258	C₄×C₁₉	#394	1	4	yes	—
259	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
260	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
261	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
262	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
263	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
264	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×#137	—	2	4	no	—
266	C₂×#137	—	2	4	no	—
267	C₂×#137	—	2	4	no	—
268	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	—
269	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
270	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
271	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
272	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
273	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
275	#424	—	2	4	no	—
276	C₂×C₄⋊C₈	C₂²×C₁₉	1	4	yes	—
277	#416	—	2	4	no	—
278	C₂×#103	—	2	4	no	—
279	C₂×#103	C₂²×C₁₉	1	4	yes	—
280	C₂×#103	C₂²×C₁₉	1	2	yes	—
281	C₂×#102	C₂²×C₁₉	1	2	yes	—
282	#391	—	2	2	no	—
283	#391	C₂²×C₁₉	1	4	yes	—
284	#391	C₂²×C₁₉	1	2	yes	—
285	#390	C₂²×C₁₉	1	2	yes	—
286	#386	—	2	2	no	—
287	#381	—	2	2	no	—
288	#380	—	2	2	no	—
289	#340	C₂²×C₁₉	1	4	yes	—
290	C₂×C₁₉	—	2	4	no	—
291	C₂×C₁₉	—	8	2	no	—
292	C₂×C₁₉	C₂×#394	1	1	yes	characteristic
293	C₂×C₁₉	#3043	1	1	yes	characteristic
294	C₂×C₁₉	#3044	1	1	yes	characteristic
295	C₂×C₁₉	#3046	1	2	yes	—
296	C₂×C₁₉	#3063	1	2	yes	—
297	C₂×#41	—	2	2	no	—
298	C₂×#41	—	2	2	no	—
299	C₂×#41	—	2	2	no	—
300	C₂×#41	—	2	2	no	—
301	C₂×#41	—	2	2	no	—
302	C₂×#41	D₄×C₁₉	1	4	yes	—
303	C₂²×Q₈	—	2	1	no	—
304	C₂²×Q₈	—	2	2	no	—
305	C₂²×Q₈	—	2	2	no	—
306	C₂²×Q₈	—	2	2	no	—
307	C₂²×Q₈	—	2	2	no	—
308	C₂²×Q₈	—	2	2	no	—
309	C₂²×Q₈	D₄×C₁₉	1	4	yes	—
310	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
311	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	—	2	1	no	—
316	C₂³×C₄	—	2	1	no	—
317	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
318	#137	—	2	32	no	—
319	C₂×Q₁₆	—	2	4	no	—
320	C₂×Q₁₆	—	2	4	no	—
321	C₂×Q₁₆	—	2	4	no	—
322	C₂×SD₁₆	—	2	4	no	—
323	C₂×SD₁₆	—	2	4	no	—
324	C₂×SD₁₆	—	2	4	no	—
325	C₂×M₁₆	—	2	2	no	—
326	C₂×M₁₆	—	2	2	no	—
327	C₂×M₁₆	D₄×C₁₉	1	4	yes	—
328	C₂²×C₈	—	2	2	no	—
329	C₂²×C₈	—	2	2	no	—
330	C₂²×C₈	—	2	2	no	—
331	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
332	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
333	#117	—	2	2	no	—
334	#117	—	2	2	no	—
335	#117	—	2	2	no	—
336	#117	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	—	2	4	no	—
345	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
348	C₄⋊C₈	—	2	8	no	—
349	#103	—	2	8	no	—
350	#103	—	2	4	no	—
351	#102	—	2	4	no	—
352	#95	—	2	4	no	—
353	#95	—	2	8	no	—
354	C₁₉	#23545	1	1	yes	characteristic, direct product factor, Sylow
355	C₂⁴	—	2	1	no	—
356	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
357	#41	—	2	8	no	—
358	#41	—	2	8	no	—
359	#41	—	4	4	no	—
360	#41	—	4	4	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	8	no	—
365	C₂×Q₈	—	2	8	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	4	2	no	—
375	C₂×Q₈	—	4	2	no	—
376	C₂×Q₈	—	4	4	no	—
377	C₂×Q₈	—	4	4	no	—
378	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
379	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	4	2	no	—
388	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	8	2	no	—
401	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
402	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
403	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
404	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	#41×C₁₉	1	2	yes	—
407	C₂²×C₄	#41×C₁₉	1	2	yes	—
408	C₂²×C₄	#41×C₁₉	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
410	Q₁₆	—	2	16	no	—
411	SD₁₆	—	2	16	no	—
412	M₁₆	—	2	8	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	4	4	no	—
419	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	4	2	no	—
428	C₂²⋊C₄	—	8	4	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	4	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	C₁₉×#121	1	2	yes	—
440	C₂³	C₁₉×#121	1	2	yes	—
441	C₂³	C₁₉×#121	1	2	yes	—
442	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
443	Q₈	—	2	4	no	—
444	Q₈	—	2	2	no	—
445	Q₈	—	2	4	no	—
446	Q₈	—	2	2	no	—
447	Q₈	—	4	8	no	—
448	Q₈	—	4	2	no	—
449	Q₈	—	4	1	no	—
450	Q₈	—	4	2	no	—
451	Q₈	—	4	1	no	—
452	D₄	—	2	2	no	—
453	D₄	—	2	2	no	—
454	D₄	—	4	8	no	—
455	D₄	—	4	1	no	—
456	D₄	—	4	1	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	8	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	8	4	no	—
474	C₂×C₄	C₁₉×#120	1	4	yes	—
475	C₂×C₄	C₁₉×#121	1	2	yes	—
476	C₂×C₄	C₁₉×#121	1	2	yes	—
477	C₂×C₄	C₁₉×#121	1	2	yes	—
478	C₂×C₄	C₁₉×#123	1	4	yes	—
479	C₂×C₄	C₁₉×#123	1	4	yes	—
480	C₂×C₄	C₁₉×#124	1	4	yes	—
481	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
484	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
485	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
486	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
487	C₈	—	2	4	no	—
488	C₈	—	4	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	8	1	no	—
496	C₂²	—	8	1	no	—
497	C₂²	—	8	2	no	—
498	C₂²	C₁₉×#394	1	4	yes	—
499	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
500	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
501	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
502	C₂²	C₁₉×#577	1	2	yes	—
503	C₂²	C₁₉×#578	1	2	yes	—
504	C₄	—	4	4	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	4	no	—
507	C₄	—	8	2	no	—
508	C₄	—	8	2	no	—
509	C₄	C₁₉×#394	1	4	yes	—
510	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
511	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
512	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
513	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
514	C₂	—	2	4	no	—
515	C₂	—	8	2	no	—
516	C₂	C₂×C₁₉×#394	1	1	yes	characteristic
517	C₂	C₁₉×#3043	1	1	yes	characteristic
518	C₂	C₁₉×#3044	1	1	yes	characteristic
519	C₂	C₁₉×#3046	1	2	yes	—
520	C₂	C₁₉×#3063	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#424	C₂	semidirect
4. C₂²×C₁₉×#103	C₂	semidirect
6. C₁₉×#2310	C₂	semidirect
7. C₁₉×#2056	C₂	semidirect
8. C₁₉×#2055	C₂	semidirect
9. C₁₉×#1736	C₂	semidirect
171. #23545	C₁₉	direct (N × H)
230. C₂×#424	C₂×C₁₉	semidirect
232. C₂²×#103	C₂×C₁₉	semidirect
234. #2310	C₂×C₁₉	semidirect
235. #2056	C₂×C₁₉	semidirect
236. #2055	C₂×C₁₉	semidirect
237. #1736	C₂×C₁₉	semidirect
354. C₁₉	#23545	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#137	2
C₂×C₁₉×#424	2
C₂×C₁₉×#416	2
C₂²×C₁₉×#103	2
C₁₉×#2311	2
C₁₉×#2310	2
C₁₉×#2056	2
C₁₉×#2055	2
C₁₉×#1736	2
#23545	19

Subgroups — C19×#23545 #18029504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23545 #18029504