Subgroups — C₂×C₁₉×#2059 #18029509

Order 4864.

1238 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#389	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2059	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#125	—	2	4	no	—
12	C₂×C₁₉×#125	—	2	4	no	—
13	C₂×C₁₉×#125	—	2	2	no	—
14	C₂×C₁₉×#125	C₂²	1	4	yes	—
15	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#107	—	2	4	no	—
24	C₂×C₁₉×#107	C₂²	1	4	yes	—
25	C₂×C₁₉×#106	—	2	4	no	—
26	C₂×C₁₉×#106	C₂²	1	4	yes	—
27	C₁₉×#389	—	2	2	no	—
28	C₁₉×#389	C₂²	1	4	yes	—
29	C₂×C₁₉×#95	—	2	1	no	—
30	C₁₉×#340	C₂²	1	4	yes	—
31	C₁₉×#340	C₂²	1	4	yes	—
32	C₁₉×#336	C₂²	1	4	yes	—
33	C₂³×C₄×C₁₉	—	2	1	no	—
34	C₂³×C₄×C₁₉	—	2	1	no	—
35	C₂³×C₄×C₁₉	—	2	1	no	—
36	C₂³×C₄×C₁₉	—	2	1	no	—
37	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₉	—	2	2	no	—
41	C₂²×C₈×C₁₉	—	2	2	no	—
42	C₂²×C₈×C₁₉	—	2	2	no	—
43	C₂²×C₈×C₁₉	—	2	2	no	—
44	C₂²×C₈×C₁₉	Q₈	1	4	yes	—
45	C₂²×C₈×C₁₉	Q₈	1	4	yes	—
46	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
48	C₁₉×#125	—	2	16	no	—
49	C₁₉×#125	—	2	8	no	—
50	C₁₉×#125	—	2	8	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
65	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
66	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
67	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
68	C₂×C₄⋊C₄×C₁₉	Q₈	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₄²×C₁₉	—	2	2	no	—
74	C₂×C₄²×C₁₉	—	2	2	no	—
75	C₂×C₄²×C₁₉	D₄	1	2	yes	—
76	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
77	C₁₉×#107	—	2	8	no	—
78	C₁₉×#106	—	2	8	no	—
79	C₁₉×#95	—	2	4	no	—
80	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	4	no	—
84	C₂²×C₄×C₁₉	—	2	4	no	—
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	4	2	no	—
95	C₂²×C₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	—	4	2	no	—
97	C₂²×C₄×C₁₉	—	4	2	no	—
98	C₂²×C₄×C₁₉	—	4	2	no	—
99	C₂²×C₄×C₁₉	—	4	2	no	—
100	C₂²×C₄×C₁₉	—	4	2	no	—
101	C₂²×C₄×C₁₉	—	4	2	no	—
102	C₂²×C₄×C₁₉	—	4	2	no	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
111	C₂²×C₄×C₁₉	#41	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₁₉	—	2	8	no	—
114	C₂×C₈×C₁₉	—	2	8	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	C₂×Q₈	1	4	yes	—
120	C₂×C₈×C₁₉	C₂×Q₈	1	4	yes	—
121	C₄⋊C₄×C₁₉	—	2	16	no	—
122	C₄⋊C₄×C₁₉	—	2	16	no	—
123	C₄⋊C₄×C₁₉	—	2	4	no	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	—	2	4	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	4	8	no	—
132	C₄⋊C₄×C₁₉	—	4	2	no	—
133	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
134	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
135	C₄⋊C₄×C₁₉	C₂×Q₈	1	4	yes	—
136	C₄²×C₁₉	—	2	4	no	—
137	C₄²×C₁₉	—	2	2	no	—
138	C₄²×C₁₉	—	2	2	no	—
139	C₂×#2059	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₁₉	#120	1	2	yes	—
141	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
142	C₂³×C₁₉	C₄⋊Q₈	1	2	yes	—
143	C₂³×C₁₉	#135	1	2	yes	—
144	C₂³×C₁₉	#135	1	2	yes	—
145	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
146	C₂³×C₁₉	#137	1	2	yes	—
147	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	4	no	—
164	C₂×C₄×C₁₉	—	4	8	no	—
165	C₂×C₄×C₁₉	—	4	4	no	—
166	C₂×C₄×C₁₉	—	4	8	no	—
167	C₂×C₄×C₁₉	—	4	8	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	8	4	no	—
172	C₂×C₄×C₁₉	#120	1	2	yes	—
173	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
174	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
175	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
176	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
177	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
178	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
179	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
185	C₈×C₁₉	—	2	4	no	—
186	C₈×C₁₉	—	2	4	no	—
187	C₂²×#125	C₂×C₁₉	1	1	yes	characteristic
188	C₂²×#107	C₂×C₁₉	1	1	yes	characteristic
189	C₂²×#106	C₂×C₁₉	1	1	yes	characteristic
190	C₂×#389	C₂×C₁₉	1	1	yes	characteristic
191	#2059	C₂×C₁₉	1	8	yes	direct product factor
192	C₂×#340	C₂×C₁₉	1	1	yes	characteristic
193	C₂×#340	C₂×C₁₉	1	1	yes	characteristic
194	C₂×#336	C₂×C₁₉	1	1	yes	characteristic
195	C₂²×C₁₉	#395	1	4	yes	—
196	C₂²×C₁₉	#449	1	4	yes	—
197	C₂²×C₁₉	#452	1	4	yes	—
198	C₂²×C₁₉	#478	1	4	yes	—
199	C₂²×C₁₉	#479	1	4	yes	—
200	C₂²×C₁₉	#499	1	4	yes	—
201	C₂²×C₁₉	#501	1	4	yes	—
202	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
203	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
204	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
205	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
206	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
207	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
208	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
209	C₄×C₁₉	—	4	4	no	—
210	C₄×C₁₉	—	4	2	no	—
211	C₄×C₁₉	—	4	4	no	—
212	C₄×C₁₉	—	4	2	no	—
213	C₄×C₁₉	—	4	4	no	—
214	C₄×C₁₉	—	8	2	no	—
215	C₄×C₁₉	#395	1	4	yes	—
216	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
217	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
218	C₄×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
219	C₄×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
220	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
221	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
222	C₂×#125	—	2	4	no	—
223	C₂×#125	—	2	4	no	—
224	C₂×#125	—	2	2	no	—
225	C₂×#125	C₂²×C₁₉	1	4	yes	—
226	C₂²×C₄⋊C₄	—	2	1	no	—
227	C₂²×C₄⋊C₄	—	2	1	no	—
228	C₂²×C₄⋊C₄	—	2	1	no	—
229	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
230	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
231	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
232	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
233	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×#107	—	2	4	no	—
235	C₂×#107	C₂²×C₁₉	1	4	yes	—
236	C₂×#106	—	2	4	no	—
237	C₂×#106	C₂²×C₁₉	1	4	yes	—
238	#389	—	2	2	no	—
239	#389	C₂²×C₁₉	1	4	yes	—
240	C₂×#95	—	2	1	no	—
241	#340	C₂²×C₁₉	1	4	yes	—
242	#340	C₂²×C₁₉	1	4	yes	—
243	#336	C₂²×C₁₉	1	4	yes	—
244	C₂×C₁₉	#2059	1	8	yes	direct product factor
245	C₂×C₁₉	C₂×#395	1	1	yes	characteristic
246	C₂×C₁₉	C₂×#449	1	1	yes	characteristic
247	C₂×C₁₉	C₂×#452	1	1	yes	characteristic
248	C₂×C₁₉	C₂×#478	1	1	yes	characteristic
249	C₂×C₁₉	C₂×#479	1	1	yes	characteristic
250	C₂×C₁₉	C₂×#499	1	1	yes	characteristic
251	C₂×C₁₉	C₂×#501	1	1	yes	characteristic
252	C₂³×C₄	—	2	1	no	—
253	C₂³×C₄	—	2	1	no	—
254	C₂³×C₄	—	2	1	no	—
255	C₂³×C₄	—	2	1	no	—
256	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
257	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
259	C₂²×C₈	—	2	2	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	Q₈×C₁₉	1	4	yes	—
264	C₂²×C₈	Q₈×C₁₉	1	4	yes	—
265	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
266	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
267	#125	—	2	16	no	—
268	#125	—	2	8	no	—
269	#125	—	2	8	no	—
270	C₂×C₄⋊C₄	—	2	8	no	—
271	C₂×C₄⋊C₄	—	2	8	no	—
272	C₂×C₄⋊C₄	—	2	4	no	—
273	C₂×C₄⋊C₄	—	2	4	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	4	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	4	4	no	—
285	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
286	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
287	C₂×C₄⋊C₄	Q₈×C₁₉	1	4	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	D₄×C₁₉	1	2	yes	—
295	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
296	#107	—	2	8	no	—
297	#106	—	2	8	no	—
298	#95	—	2	4	no	—
299	C₁₉	C₂×#2059	1	1	yes	characteristic, direct product factor, Sylow
300	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
328	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
329	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
330	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
331	C₂²×C₄	#41×C₁₉	1	2	yes	—
332	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
333	C₂×C₈	—	2	8	no	—
334	C₂×C₈	—	2	8	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	C₂×Q₈×C₁₉	1	4	yes	—
340	C₂×C₈	C₂×Q₈×C₁₉	1	4	yes	—
341	C₄⋊C₄	—	2	16	no	—
342	C₄⋊C₄	—	2	16	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	8	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
354	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
355	C₄⋊C₄	C₂×Q₈×C₁₉	1	4	yes	—
356	C₄²	—	2	4	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₂³	C₁₉×#120	1	2	yes	—
360	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
361	C₂³	C₁₉×C₄⋊Q₈	1	2	yes	—
362	C₂³	C₁₉×#135	1	2	yes	—
363	C₂³	C₁₉×#135	1	2	yes	—
364	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
365	C₂³	C₁₉×#137	1	2	yes	—
366	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	8	no	—
380	C₂×C₄	—	4	8	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	8	4	no	—
391	C₂×C₄	C₁₉×#120	1	2	yes	—
392	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
393	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
394	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
395	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
396	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
397	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
398	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
400	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
401	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
402	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
403	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
404	C₈	—	2	4	no	—
405	C₈	—	2	4	no	—
406	C₂²	C₁₉×#395	1	4	yes	—
407	C₂²	C₁₉×#449	1	4	yes	—
408	C₂²	C₁₉×#452	1	4	yes	—
409	C₂²	C₁₉×#478	1	4	yes	—
410	C₂²	C₁₉×#479	1	4	yes	—
411	C₂²	C₁₉×#499	1	4	yes	—
412	C₂²	C₁₉×#501	1	4	yes	—
413	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
414	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
415	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
416	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
417	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
418	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
419	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
420	C₄	—	4	2	no	—
421	C₄	—	4	4	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	4	no	—
425	C₄	—	8	2	no	—
426	C₄	C₁₉×#395	1	4	yes	—
427	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
428	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
429	C₄	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
430	C₄	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
431	C₂	C₁₉×#2059	1	8	yes	direct product factor
432	C₂	C₂×C₁₉×#395	1	1	yes	characteristic
433	C₂	C₂×C₁₉×#449	1	1	yes	characteristic
434	C₂	C₂×C₁₉×#452	1	1	yes	characteristic
435	C₂	C₂×C₁₉×#478	1	1	yes	characteristic
436	C₂	C₂×C₁₉×#479	1	1	yes	characteristic
437	C₂	C₂×C₁₉×#499	1	1	yes	characteristic
438	C₂	C₂×C₁₉×#501	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
5. C₁₉×#2059	C₂	direct (N × H)
139. C₂×#2059	C₁₉	direct (N × H)
191. #2059	C₂×C₁₉	direct (N × H)
244. C₂×C₁₉	#2059	direct (N × H)
299. C₁₉	C₂×#2059	direct (N × H)
431. C₂	C₁₉×#2059	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×#125	2
C₂²×C₁₉×#107	2
C₂²×C₁₉×#106	2
C₂×C₁₉×#389	2
C₁₉×#2059	2
C₂×C₁₉×#340	2
C₂×C₁₉×#336	2
C₂×#2059	19

Subgroups — C2×C19×#2059 #18029509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2059 #18029509