Subgroups — C₂×C₁₉×#2077 #18029595

Order 4864.

1270 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2077	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
17	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
18	C₂×C₁₉×#106	—	2	4	no	—
19	C₂×C₁₉×#106	C₂²	1	4	yes	complemented
20	C₂×C₁₉×C₂²⋊C₈	—	2	4	no	—
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
22	C₁₉×#380	—	2	2	no	—
23	C₁₉×#380	—	2	2	no	—
24	C₁₉×#380	C₂²	1	4	yes	—
25	C₁₉×#380	C₂²	1	4	yes	—
26	C₂×C₁₉×#95	—	2	1	no	—
27	C₂×C₁₉×#95	—	2	1	no	—
28	C₁₉×#340	C₂²	1	4	yes	complemented
29	C₁₉×#340	C₂²	1	4	yes	complemented
30	C₁₉×#340	C₂²	1	4	yes	complemented
31	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	—	2	2	no	—
33	C₂³×C₄×C₁₉	—	2	2	no	—
34	C₂³×C₄×C₁₉	—	2	2	no	—
35	C₂³×C₄×C₁₉	—	2	2	no	—
36	C₂³×C₄×C₁₉	—	2	2	no	—
37	C₂³×C₄×C₁₉	—	2	2	no	—
38	C₂³×C₄×C₁₉	—	2	1	no	—
39	C₂³×C₄×C₁₉	—	2	1	no	—
40	C₂³×C₄×C₁₉	—	2	1	no	—
41	C₂³×C₄×C₁₉	—	2	1	no	—
42	C₂³×C₄×C₁₉	D₄	1	2	yes	—
43	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₉	—	2	2	no	—
47	C₂²×C₈×C₁₉	—	2	2	no	—
48	C₂²×C₈×C₁₉	—	2	2	no	—
49	C₂²×C₈×C₁₉	—	2	2	no	—
50	C₂²×C₈×C₁₉	—	2	2	no	—
51	C₂²×C₈×C₁₉	D₄	1	4	yes	—
52	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
74	C₁₉×#106	—	2	8	no	—
75	C₁₉×C₂²⋊C₈	—	2	8	no	—
76	C₁₉×#95	—	2	4	no	—
77	C₁₉×#95	—	2	4	no	—
78	C₂⁴×C₁₉	—	2	2	no	—
79	C₂⁴×C₁₉	—	2	2	no	—
80	C₂⁴×C₁₉	—	2	2	no	—
81	C₂⁴×C₁₉	—	2	2	no	—
82	C₂⁴×C₁₉	—	2	2	no	—
83	C₂⁴×C₁₉	—	2	2	no	—
84	C₂⁴×C₁₉	SD₁₆	1	4	yes	—
85	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
86	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
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	4	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	4	4	no	—
104	C₂²×C₄×C₁₉	—	4	4	no	—
105	C₂²×C₄×C₁₉	—	4	4	no	—
106	C₂²×C₄×C₁₉	—	4	4	no	—
107	C₂²×C₄×C₁₉	—	4	2	no	—
108	C₂²×C₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	—	4	2	no	—
110	C₂²×C₄×C₁₉	—	4	2	no	—
111	C₂²×C₄×C₁₉	—	4	2	no	—
112	C₂²×C₄×C₁₉	—	4	2	no	—
113	C₂²×C₄×C₁₉	—	4	2	no	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	—	4	2	no	—
116	C₂²×C₄×C₁₉	—	4	2	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	—	4	2	no	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₉	#41	1	2	yes	—
123	C₂²×C₄×C₁₉	#41	1	2	yes	—
124	C₂²×C₄×C₁₉	#41	1	2	yes	—
125	C₂²×C₄×C₁₉	#41	1	2	yes	—
126	C₂²×C₄×C₁₉	#41	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₁₉	—	2	8	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	4	4	no	—
135	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	4	2	no	—
145	C₄⋊C₄×C₁₉	—	4	2	no	—
146	C₄⋊C₄×C₁₉	—	4	2	no	—
147	C₄⋊C₄×C₁₉	—	4	2	no	—
148	C₂²⋊C₄×C₁₉	—	4	8	no	—
149	C₂²⋊C₄×C₁₉	—	4	8	no	—
150	C₂×#2077	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	2	2	no	—
153	C₂³×C₁₉	—	2	2	no	—
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	2	8	no	—
158	C₂³×C₁₉	—	2	8	no	—
159	C₂³×C₁₉	—	2	8	no	—
160	C₂³×C₁₉	—	4	4	no	—
161	C₂³×C₁₉	—	4	4	no	—
162	C₂³×C₁₉	—	4	4	no	—
163	C₂³×C₁₉	—	4	4	no	—
164	C₂³×C₁₉	#121	1	2	yes	—
165	C₂³×C₁₉	#123	1	2	yes	—
166	C₂³×C₁₉	#123	1	2	yes	—
167	C₂³×C₁₉	C₂×SD₁₆	1	4	yes	—
168	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
169	C₂³×C₁₉	#135	1	2	yes	—
170	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
171	C₂³×C₁₉	#137	1	2	yes	—
172	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	4	4	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	8	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	8	4	no	—
195	C₂×C₄×C₁₉	—	8	4	no	—
196	C₂×C₄×C₁₉	—	8	4	no	—
197	C₂×C₄×C₁₉	—	8	4	no	—
198	C₂×C₄×C₁₉	#121	1	2	yes	—
199	C₂×C₄×C₁₉	#123	1	4	yes	—
200	C₂×C₄×C₁₉	#123	1	2	yes	—
201	C₂×C₄×C₁₉	#123	1	2	yes	—
202	C₂×C₄×C₁₉	#124	1	4	yes	—
203	C₂×C₄×C₁₉	#126	1	4	yes	—
204	C₂×C₄×C₁₉	#126	1	4	yes	—
205	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
211	C₈×C₁₉	—	2	4	no	—
212	C₈×C₁₉	—	4	2	no	—
213	C₂²×#106	C₂×C₁₉	1	1	yes	characteristic, complemented
214	C₂²×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic
215	C₂×#380	C₂×C₁₉	1	1	yes	characteristic
216	C₂×#380	C₂×C₁₉	1	1	yes	characteristic
217	#2077	C₂×C₁₉	1	8	yes	direct product factor
218	C₂×#340	C₂×C₁₉	1	1	yes	characteristic, complemented
219	C₂×#340	C₂×C₁₉	1	1	yes	characteristic, complemented
220	C₂×#340	C₂×C₁₉	1	1	yes	characteristic, complemented
221	C₂²×C₁₉	—	2	4	no	—
222	C₂²×C₁₉	—	2	4	no	—
223	C₂²×C₁₉	—	2	4	no	—
224	C₂²×C₁₉	—	4	2	no	—
225	C₂²×C₁₉	—	4	2	no	—
226	C₂²×C₁₉	—	4	16	no	—
227	C₂²×C₁₉	—	4	2	no	—
228	C₂²×C₁₉	—	4	2	no	—
229	C₂²×C₁₉	#397	1	4	yes	—
230	C₂²×C₁₉	#465	1	4	yes	—
231	C₂²×C₁₉	#468	1	4	yes	—
232	C₂²×C₁₉	#481	1	4	yes	—
233	C₂²×C₁₉	#482	1	4	yes	—
234	C₂²×C₁₉	#483	1	4	yes	—
235	C₂²×C₁₉	#485	1	4	yes	—
236	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
237	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
238	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
239	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
240	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
241	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
242	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
243	C₄×C₁₉	—	4	2	no	—
244	C₄×C₁₉	—	8	2	no	—
245	C₄×C₁₉	—	8	2	no	—
246	C₄×C₁₉	—	8	2	no	—
247	C₄×C₁₉	—	8	2	no	—
248	C₄×C₁₉	#397	1	4	yes	—
249	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
250	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
251	C₄×C₁₉	C₂×#126	1	1	yes	characteristic
252	C₄×C₁₉	C₂×#126	1	1	yes	characteristic
253	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
254	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
255	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
256	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
257	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
258	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
259	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
260	C₂²×C₂²⋊C₄	—	2	1	no	—
261	C₂²×C₂²⋊C₄	—	2	1	no	—
262	C₂×#106	—	2	4	no	—
263	C₂×#106	C₂²×C₁₉	1	4	yes	complemented
264	C₂×C₂²⋊C₈	—	2	4	no	—
265	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
266	#380	—	2	2	no	—
267	#380	—	2	2	no	—
268	#380	C₂²×C₁₉	1	4	yes	—
269	#380	C₂²×C₁₉	1	4	yes	—
270	C₂×#95	—	2	1	no	—
271	C₂×#95	—	2	1	no	—
272	#340	C₂²×C₁₉	1	4	yes	complemented
273	#340	C₂²×C₁₉	1	4	yes	complemented
274	#340	C₂²×C₁₉	1	4	yes	complemented
275	C₂×C₁₉	—	4	4	no	—
276	C₂×C₁₉	#2077	1	8	yes	direct product factor
277	C₂×C₁₉	C₂×#397	1	1	yes	characteristic
278	C₂×C₁₉	C₂×#465	1	1	yes	characteristic
279	C₂×C₁₉	C₂×#468	1	1	yes	characteristic
280	C₂×C₁₉	C₂×#483	1	1	yes	characteristic
281	C₂×C₁₉	C₂×#482	1	1	yes	characteristic
282	C₂×C₁₉	C₂×#485	1	1	yes	characteristic
283	C₂×C₁₉	C₂×#481	1	1	yes	characteristic
284	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
285	C₂³×C₄	—	2	2	no	—
286	C₂³×C₄	—	2	2	no	—
287	C₂³×C₄	—	2	2	no	—
288	C₂³×C₄	—	2	2	no	—
289	C₂³×C₄	—	2	2	no	—
290	C₂³×C₄	—	2	2	no	—
291	C₂³×C₄	—	2	1	no	—
292	C₂³×C₄	—	2	1	no	—
293	C₂³×C₄	—	2	1	no	—
294	C₂³×C₄	—	2	1	no	—
295	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
296	C₂³×C₄	D₄×C₁₉	1	2	yes	—
297	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
298	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
299	C₂²×C₈	—	2	2	no	—
300	C₂²×C₈	—	2	2	no	—
301	C₂²×C₈	—	2	2	no	—
302	C₂²×C₈	—	2	2	no	—
303	C₂²×C₈	—	2	2	no	—
304	C₂²×C₈	D₄×C₁₉	1	4	yes	—
305	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
306	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
323	C₂×C₂²⋊C₄	—	2	4	no	—
324	C₂×C₂²⋊C₄	—	2	4	no	—
325	C₂×C₂²⋊C₄	—	4	4	no	—
326	C₂×C₂²⋊C₄	—	4	4	no	—
327	#106	—	2	8	no	—
328	C₂²⋊C₈	—	2	8	no	—
329	#95	—	2	4	no	—
330	#95	—	2	4	no	—
331	C₁₉	C₂×#2077	1	1	yes	characteristic, direct product factor, Sylow
332	C₂⁴	—	2	2	no	—
333	C₂⁴	—	2	2	no	—
334	C₂⁴	—	2	2	no	—
335	C₂⁴	—	2	2	no	—
336	C₂⁴	—	2	2	no	—
337	C₂⁴	—	2	2	no	—
338	C₂⁴	SD₁₆×C₁₉	1	4	yes	—
339	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
340	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	4	4	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	—	4	4	no	—
360	C₂²×C₄	—	4	4	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
376	C₂²×C₄	#41×C₁₉	1	2	yes	—
377	C₂²×C₄	#41×C₁₉	1	2	yes	—
378	C₂²×C₄	#41×C₁₉	1	2	yes	—
379	C₂²×C₄	#41×C₁₉	1	2	yes	—
380	C₂²×C₄	#41×C₁₉	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
382	C₂×C₈	—	2	8	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	4	4	no	—
389	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	4	2	no	—
399	C₄⋊C₄	—	4	2	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₂²⋊C₄	—	4	8	no	—
403	C₂²⋊C₄	—	4	8	no	—
404	C₂³	—	2	8	no	—
405	C₂³	—	2	8	no	—
406	C₂³	—	2	8	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	4	4	no	—
414	C₂³	—	4	4	no	—
415	C₂³	—	4	4	no	—
416	C₂³	—	4	4	no	—
417	C₂³	C₁₉×#121	1	2	yes	—
418	C₂³	C₁₉×#123	1	2	yes	—
419	C₂³	C₁₉×#123	1	2	yes	—
420	C₂³	C₂×SD₁₆×C₁₉	1	4	yes	—
421	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
422	C₂³	C₁₉×#135	1	2	yes	—
423	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
424	C₂³	C₁₉×#137	1	2	yes	—
425	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	8	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	8	4	no	—
448	C₂×C₄	—	8	4	no	—
449	C₂×C₄	—	8	4	no	—
450	C₂×C₄	—	8	4	no	—
451	C₂×C₄	C₁₉×#121	1	2	yes	—
452	C₂×C₄	C₁₉×#123	1	2	yes	—
453	C₂×C₄	C₁₉×#123	1	2	yes	—
454	C₂×C₄	C₁₉×#123	1	4	yes	—
455	C₂×C₄	C₁₉×#124	1	4	yes	—
456	C₂×C₄	C₁₉×#126	1	4	yes	—
457	C₂×C₄	C₁₉×#126	1	4	yes	—
458	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
459	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
460	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
461	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
462	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
463	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
464	C₈	—	2	4	no	—
465	C₈	—	4	2	no	—
466	C₂²	—	2	4	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	16	no	—
473	C₂²	—	4	2	no	—
474	C₂²	C₁₉×#397	1	4	yes	—
475	C₂²	C₁₉×#465	1	4	yes	—
476	C₂²	C₁₉×#468	1	4	yes	—
477	C₂²	C₁₉×#481	1	4	yes	—
478	C₂²	C₁₉×#482	1	4	yes	—
479	C₂²	C₁₉×#483	1	4	yes	—
480	C₂²	C₁₉×#485	1	4	yes	—
481	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
482	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
483	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
484	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
485	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
486	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
487	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
488	C₄	—	4	2	no	—
489	C₄	—	8	2	no	—
490	C₄	—	8	2	no	—
491	C₄	—	8	2	no	—
492	C₄	—	8	2	no	—
493	C₄	C₁₉×#397	1	4	yes	—
494	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
495	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
496	C₄	C₂×C₁₉×#126	1	1	yes	characteristic
497	C₄	C₂×C₁₉×#126	1	1	yes	characteristic
498	C₂	—	4	4	no	—
499	C₂	C₁₉×#2077	1	8	yes	direct product factor
500	C₂	C₂×C₁₉×#397	1	1	yes	characteristic
501	C₂	C₂×C₁₉×#465	1	1	yes	characteristic
502	C₂	C₂×C₁₉×#468	1	1	yes	characteristic
503	C₂	C₂×C₁₉×#483	1	1	yes	characteristic
504	C₂	C₂×C₁₉×#482	1	1	yes	characteristic
505	C₂	C₂×C₁₉×#485	1	1	yes	characteristic
506	C₂	C₂×C₁₉×#481	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×#106	C₂	semidirect
5. C₁₉×#2077	C₂	direct (N × H)
6. C₂×C₁₉×#340	C₂	semidirect
7. C₂×C₁₉×#340	C₂	semidirect
8. C₂×C₁₉×#340	C₂	semidirect
19. C₂×C₁₉×#106	C₂²	semidirect
28. C₁₉×#340	C₂²	semidirect
29. C₁₉×#340	C₂²	semidirect
30. C₁₉×#340	C₂²	semidirect
150. C₂×#2077	C₁₉	direct (N × H)
213. C₂²×#106	C₂×C₁₉	semidirect
217. #2077	C₂×C₁₉	direct (N × H)
218. C₂×#340	C₂×C₁₉	semidirect
219. C₂×#340	C₂×C₁₉	semidirect
220. C₂×#340	C₂×C₁₉	semidirect
263. C₂×#106	C₂²×C₁₉	semidirect
272. #340	C₂²×C₁₉	semidirect
273. #340	C₂²×C₁₉	semidirect
274. #340	C₂²×C₁₉	semidirect
276. C₂×C₁₉	#2077	direct (N × H)
331. C₁₉	C₂×#2077	direct (N × H)
499. C₂	C₁₉×#2077	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×#106	2
C₂²×C₁₉×C₂²⋊C₈	2
C₂×C₁₉×#380	2
C₁₉×#2077	2
C₂×C₁₉×#340	2
C₂×#2077	19

Subgroups — C2×C19×#2077 #18029595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2077 #18029595