Subgroups — C₁₉×#23671 #18029630

Order 4864.

874 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#424	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2317	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2316	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2088	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2088	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2087	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2086	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1735	C₂	1	1	yes	maximal, characteristic
11	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#428	—	2	4	no	—
20	C₂×C₁₉×#107	C₂²	1	2	yes	—
21	C₂×C₁₉×#106	C₂²	1	2	yes	—
22	C₁₉×#424	—	2	4	no	—
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
25	C₁₉×#389	—	2	1	no	—
26	C₁₉×#389	—	2	1	no	—
27	C₁₉×#389	C₂²	1	2	yes	—
28	C₁₉×#389	C₂²	1	2	yes	—
29	C₁₉×#389	C₂²	1	2	yes	—
30	C₁₉×#389	C₂²	1	2	yes	—
31	C₁₉×#385	—	2	2	no	—
32	C₁₉×#384	—	2	1	no	—
33	C₁₉×#382	—	2	1	no	—
34	C₁₉×#380	—	2	2	no	—
35	C₁₉×#340	C₂²	1	2	yes	—
36	C₁₉×#340	C₂²	1	2	yes	—
37	C₁₉×#340	C₂²	1	1	yes	characteristic
38	C₁₉×#340	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	1	yes	characteristic
40	C₁₉×#340	C₂²	1	1	yes	characteristic
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#340	C₂²	1	2	yes	—
43	C₂³×C₄×C₁₉	—	2	1	no	—
44	C₂³×C₄×C₁₉	—	2	1	no	—
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
49	C₂²×C₈×C₁₉	—	2	2	no	—
50	C₂²×C₈×C₁₉	—	2	2	no	—
51	C₂²×C₈×C₁₉	—	2	2	no	—
52	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
55	C₁₉×#117	—	2	2	no	—
56	C₁₉×#117	—	2	2	no	—
57	C₁₉×#117	—	2	2	no	—
58	C₁₉×#117	—	2	2	no	—
59	C₁₉×#117	—	2	2	no	—
60	C₁₉×#117	Q₈	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₉	Q₈	1	4	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
82	C₂×C₄²×C₁₉	—	2	1	no	—
83	C₂×C₄²×C₁₉	—	2	1	no	—
84	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
85	C₁₉×#107	—	2	4	no	—
86	C₁₉×#106	—	2	4	no	—
87	C₁₉×C₄⋊C₈	—	2	4	no	—
88	C₁₉×C₄⋊C₈	—	2	4	no	—
89	C₁₉×#95	—	2	2	no	—
90	C₁₉×#95	—	2	2	no	—
91	C₁₉×#95	—	2	2	no	—
92	C₁₉×#95	—	2	2	no	—
93	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	4	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	4	2	no	—
102	C₂²×C₄×C₁₉	—	8	1	no	—
103	C₂²×C₄×C₁₉	—	8	1	no	—
104	C₂²×C₄×C₁₉	—	8	1	no	—
105	C₂²×C₄×C₁₉	—	8	1	no	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
112	C₂²×C₄×C₁₉	#41	1	2	yes	—
113	C₂²×C₄×C₁₉	#41	1	2	yes	—
114	C₂²×C₄×C₁₉	#41	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
116	M₁₆×C₁₉	—	2	8	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	1	no	—
120	C₂×C₈×C₁₉	—	2	1	no	—
121	C₂×C₈×C₁₉	—	2	1	no	—
122	C₂×C₈×C₁₉	—	2	1	no	—
123	C₂×C₈×C₁₉	—	2	1	no	—
124	C₂×C₈×C₁₉	—	2	1	no	—
125	C₂×C₈×C₁₉	—	4	4	no	—
126	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	4	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	4	2	no	—
140	C₄⋊C₄×C₁₉	—	8	2	no	—
141	C₄⋊C₄×C₁₉	—	8	2	no	—
142	C₄⋊C₄×C₁₉	—	8	2	no	—
143	C₄⋊C₄×C₁₉	—	8	2	no	—
144	C₄⋊C₄×C₁₉	C₂×Q₈	1	4	yes	—
145	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
146	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
147	C₂²⋊C₄×C₁₉	—	2	4	no	—
148	C₂²⋊C₄×C₁₉	—	2	4	no	—
149	C₂²⋊C₄×C₁₉	—	4	2	no	—
150	C₄²×C₁₉	—	2	4	no	—
151	C₄²×C₁₉	—	2	2	no	—
152	C₄²×C₁₉	—	2	2	no	—
153	C₄²×C₁₉	—	4	2	no	—
154	#23671	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂³×C₁₉	—	2	1	no	—
156	C₂³×C₁₉	—	2	1	no	—
157	C₂³×C₁₉	—	2	1	no	—
158	C₂³×C₁₉	—	2	1	no	—
159	C₂³×C₁₉	#121	1	2	yes	—
160	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
161	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
162	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	8	4	no	—
188	C₂×C₄×C₁₉	—	8	4	no	—
189	C₂×C₄×C₁₉	#121	1	2	yes	—
190	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
191	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
192	C₂×C₄×C₁₉	#123	1	4	yes	—
193	C₂×C₄×C₁₉	#125	1	4	yes	—
194	C₂×C₄×C₁₉	#125	1	4	yes	—
195	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
196	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
202	C₈×C₁₉	—	2	4	no	—
203	C₈×C₁₉	—	4	1	no	—
204	C₈×C₁₉	—	4	1	no	—
205	C₂×#428	C₂×C₁₉	1	1	yes	characteristic
206	C₂×#424	C₂×C₁₉	1	1	yes	characteristic
207	#2317	C₂×C₁₉	1	1	yes	characteristic
208	#2316	C₂×C₁₉	1	1	yes	characteristic
209	#2088	C₂×C₁₉	1	2	yes	complemented
210	#2088	C₂×C₁₉	1	2	yes	complemented
211	#2087	C₂×C₁₉	1	2	yes	complemented
212	#2086	C₂×C₁₉	1	2	yes	complemented
213	#1736	C₂×C₁₉	1	1	yes	characteristic
214	#1735	C₂×C₁₉	1	1	yes	characteristic
215	C₂×#340	C₂×C₁₉	1	1	yes	characteristic
216	C₂²×C₁₉	—	2	2	no	—
217	C₂²×C₁₉	—	2	2	no	—
218	C₂²×C₁₉	—	2	2	no	—
219	C₂²×C₁₉	—	2	2	no	—
220	C₂²×C₁₉	—	2	2	no	—
221	C₂²×C₁₉	—	2	2	no	—
222	C₂²×C₁₉	#398	1	4	yes	—
223	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
224	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
225	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
226	C₂²×C₁₉	#576	1	1	yes	characteristic
227	C₂²×C₁₉	#577	1	1	yes	characteristic
228	C₂²×C₁₉	#577	1	1	yes	characteristic
229	C₂²×C₁₉	#578	1	1	yes	characteristic
230	C₄×C₁₉	—	4	4	no	—
231	C₄×C₁₉	—	4	2	no	—
232	C₄×C₁₉	—	4	2	no	—
233	C₄×C₁₉	—	4	2	no	—
234	C₄×C₁₉	—	4	2	no	—
235	C₄×C₁₉	—	8	1	no	—
236	C₄×C₁₉	—	8	2	no	—
237	C₄×C₁₉	—	8	1	no	—
238	C₄×C₁₉	#398	1	4	yes	—
239	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
240	C₄×C₁₉	C₂×#125	1	1	yes	characteristic
241	C₄×C₁₉	C₂×#125	1	1	yes	characteristic
242	C₄×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
243	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
244	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
245	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
246	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
248	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
249	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
250	#428	—	2	4	no	—
251	C₂×#107	C₂²×C₁₉	1	2	yes	—
252	C₂×#106	C₂²×C₁₉	1	2	yes	—
253	#424	—	2	4	no	—
254	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
255	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
256	#389	—	2	1	no	—
257	#389	—	2	1	no	—
258	#389	C₂²×C₁₉	1	2	yes	—
259	#389	C₂²×C₁₉	1	2	yes	—
260	#389	C₂²×C₁₉	1	2	yes	—
261	#389	C₂²×C₁₉	1	2	yes	—
262	#385	—	2	2	no	—
263	#384	—	2	1	no	—
264	#382	—	2	1	no	—
265	#380	—	2	2	no	—
266	#340	C₂²×C₁₉	1	1	yes	characteristic
267	#340	C₂²×C₁₉	1	2	yes	—
268	#340	C₂²×C₁₉	1	2	yes	—
269	#340	C₂²×C₁₉	1	1	yes	characteristic
270	#340	C₂²×C₁₉	1	2	yes	—
271	#340	C₂²×C₁₉	1	2	yes	—
272	#340	C₂²×C₁₉	1	1	yes	characteristic
273	#340	C₂²×C₁₉	1	1	yes	characteristic
274	C₂×C₁₉	—	2	4	no	—
275	C₂×C₁₉	C₂×#398	1	1	yes	characteristic
276	C₂×C₁₉	#3062	1	1	yes	characteristic
277	C₂×C₁₉	#3063	1	1	yes	characteristic
278	C₂×C₁₉	#3081	1	1	yes	characteristic
279	C₂×C₁₉	#3082	1	1	yes	characteristic
280	C₂×C₁₉	#3083	1	1	yes	characteristic
281	C₂×C₁₉	#3084	1	1	yes	characteristic
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	D₄×C₁₉	1	4	yes	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
294	#117	—	2	2	no	—
295	#117	—	2	2	no	—
296	#117	—	2	2	no	—
297	#117	—	2	2	no	—
298	#117	—	2	2	no	—
299	#117	Q₈×C₁₉	1	4	yes	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
310	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
311	C₂×C₄⋊C₄	Q₈×C₁₉	1	4	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
324	#107	—	2	4	no	—
325	#106	—	2	4	no	—
326	C₄⋊C₈	—	2	4	no	—
327	C₄⋊C₈	—	2	4	no	—
328	#95	—	2	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	#95	—	2	2	no	—
332	C₁₉	#23671	1	1	yes	characteristic, direct product factor, Sylow
333	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	8	1	no	—
343	C₂²×C₄	—	8	1	no	—
344	C₂²×C₄	—	8	1	no	—
345	C₂²×C₄	—	8	1	no	—
346	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
350	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
351	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
352	C₂²×C₄	#41×C₁₉	1	2	yes	—
353	C₂²×C₄	#41×C₁₉	1	2	yes	—
354	C₂²×C₄	#41×C₁₉	1	2	yes	—
355	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
356	M₁₆	—	2	8	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	4	4	no	—
366	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	—	8	2	no	—
381	C₄⋊C₄	—	8	2	no	—
382	C₄⋊C₄	—	8	2	no	—
383	C₄⋊C₄	—	8	2	no	—
384	C₄⋊C₄	C₂×Q₈×C₁₉	1	4	yes	—
385	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
386	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₄²	—	2	4	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	4	2	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	C₁₉×#121	1	2	yes	—
399	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
400	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
401	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	8	4	no	—
427	C₂×C₄	—	8	4	no	—
428	C₂×C₄	C₁₉×#121	1	2	yes	—
429	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
430	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
431	C₂×C₄	C₁₉×#123	1	4	yes	—
432	C₂×C₄	C₁₉×#125	1	4	yes	—
433	C₂×C₄	C₁₉×#125	1	4	yes	—
434	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
435	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
436	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
437	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
438	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
439	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
440	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
441	C₈	—	2	4	no	—
442	C₈	—	4	1	no	—
443	C₈	—	4	1	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	C₁₉×#398	1	4	yes	—
451	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
452	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
453	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
454	C₂²	C₁₉×#576	1	1	yes	characteristic
455	C₂²	C₁₉×#577	1	1	yes	characteristic
456	C₂²	C₁₉×#577	1	1	yes	characteristic
457	C₂²	C₁₉×#578	1	1	yes	characteristic
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	4	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	8	2	no	—
464	C₄	—	8	1	no	—
465	C₄	—	8	1	no	—
466	C₄	C₁₉×#398	1	4	yes	—
467	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
468	C₄	C₂×C₁₉×#125	1	1	yes	characteristic
469	C₄	C₂×C₁₉×#125	1	1	yes	characteristic
470	C₄	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
471	C₂	—	2	4	no	—
472	C₂	C₂×C₁₉×#398	1	1	yes	characteristic
473	C₂	C₁₉×#3062	1	1	yes	characteristic
474	C₂	C₁₉×#3063	1	1	yes	characteristic
475	C₂	C₁₉×#3081	1	1	yes	characteristic
476	C₂	C₁₉×#3082	1	1	yes	characteristic
477	C₂	C₁₉×#3083	1	1	yes	characteristic
478	C₂	C₁₉×#3084	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
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
5. C₁₉×#2088	C₂	semidirect
6. C₁₉×#2088	C₂	semidirect
7. C₁₉×#2087	C₂	semidirect
8. C₁₉×#2086	C₂	semidirect
154. #23671	C₁₉	direct (N × H)
209. #2088	C₂×C₁₉	semidirect
210. #2088	C₂×C₁₉	semidirect
211. #2087	C₂×C₁₉	semidirect
212. #2086	C₂×C₁₉	semidirect
332. C₁₉	#23671	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#428	2
C₂×C₁₉×#424	2
C₁₉×#2317	2
C₁₉×#2316	2
C₁₉×#2088	2
C₁₉×#2087	2
C₁₉×#2086	2
C₁₉×#1736	2
C₁₉×#1735	2
C₂×C₁₉×#340	2
#23671	19

Subgroups — C19×#23671 #18029630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23671 #18029630