Subgroups — C₂×C₁₉×#1609 #18024064

Order 4864.

1060 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#539	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#483	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#480	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1609	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#328	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#327	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×#324	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#539	—	2	2	no	—
10	C₁₉×#539	—	2	2	no	—
11	C₁₉×#539	—	2	2	no	—
12	C₁₉×#539	C₂²	1	4	yes	—
13	C₂×C₁₉×#126	—	2	1	no	—
14	C₂×C₁₉×#125	—	2	1	no	—
15	C₂×C₁₉×#123	—	2	1	no	—
16	C₂×C₁₉×#123	—	2	1	no	—
17	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₉	—	2	1	no	—
21	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#483	—	2	2	no	—
25	C₁₉×#483	C₂²	1	4	yes	complemented
26	C₁₉×#480	—	2	2	no	—
27	C₁₉×#480	C₂²	1	4	yes	—
28	C₂×C₁₉×#107	—	2	1	no	—
29	C₂×C₁₉×#106	—	2	1	no	—
30	C₂×C₁₉×#103	—	2	1	no	—
31	C₂×C₁₉×#102	—	2	1	no	—
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₁₉×#398	—	2	2	no	—
35	C₁₉×#398	C₂²	1	4	yes	complemented
36	C₂×C₁₉×#95	—	2	1	no	—
37	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
38	C₁₉×#328	C₂²	1	4	yes	complemented
39	C₁₉×#327	C₂²	1	4	yes	—
40	C₁₉×#324	C₂²	1	4	yes	complemented
41	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	—	2	1	no	—
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₉	—	2	1	no	—
51	C₂²×C₈×C₁₉	—	2	1	no	—
52	C₁₉×#126	—	2	4	no	—
53	C₁₉×#126	—	2	4	no	—
54	C₁₉×#125	—	2	4	no	—
55	C₁₉×#125	—	2	4	no	—
56	C₁₉×#123	—	2	4	no	—
57	C₁₉×#123	—	2	4	no	—
58	C₁₉×#123	—	2	4	no	—
59	C₁₉×#123	—	2	4	no	—
60	C₁₉×C₂²⋊Q₈	—	2	4	no	—
61	C₁₉×C₂²⋊Q₈	—	2	4	no	—
62	C₁₉×C₂²⋊Q₈	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
65	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
66	C₁₉×#121	—	2	1	no	—
67	C₁₉×#121	—	2	1	no	—
68	C₁₉×#121	D₄	1	2	yes	—
69	C₁₉×#121	C₂³	1	2	yes	—
70	C₄×D₄×C₁₉	—	2	4	no	—
71	C₄×D₄×C₁₉	—	2	4	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
86	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
87	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₄²×C₁₉	—	2	1	no	—
98	C₁₉×#107	—	2	4	no	—
99	C₁₉×#106	—	2	4	no	—
100	C₁₉×#103	—	2	4	no	—
101	C₁₉×#102	—	2	4	no	—
102	C₁₉×C₂²⋊C₈	—	2	1	no	—
103	C₁₉×C₂²⋊C₈	—	2	1	no	—
104	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
105	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
106	C₁₉×#95	—	2	4	no	—
107	C₁₉×#95	—	2	1	no	—
108	C₁₉×#95	C₂³	1	2	yes	—
109	C₂⁴×C₁₉	—	2	1	no	—
110	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	4	2	no	—
113	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	1	no	—
117	C₂×D₄×C₁₉	—	4	2	no	—
118	C₂×D₄×C₁₉	—	4	2	no	—
119	C₂×D₄×C₁₉	—	4	2	no	—
120	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	4	no	—
132	C₂²×C₄×C₁₉	—	2	1	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	1	no	—
139	C₂²×C₄×C₁₉	—	4	1	no	—
140	C₂²×C₄×C₁₉	—	4	2	no	—
141	C₂²×C₄×C₁₉	—	4	2	no	—
142	C₂²×C₄×C₁₉	—	8	2	no	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	—	2	2	no	—
153	C₂×C₈×C₁₉	—	4	2	no	—
154	C₂×C₈×C₁₉	—	4	2	no	—
155	C₄⋊C₄×C₁₉	—	2	4	no	—
156	C₄⋊C₄×C₁₉	—	2	4	no	—
157	C₄⋊C₄×C₁₉	—	2	4	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	4	8	no	—
169	C₄⋊C₄×C₁₉	—	4	1	no	—
170	C₄⋊C₄×C₁₉	—	4	1	no	—
171	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
172	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
173	C₂²⋊C₄×C₁₉	—	2	4	no	—
174	C₂²⋊C₄×C₁₉	—	2	4	no	—
175	C₂²⋊C₄×C₁₉	—	2	4	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂²⋊C₄×C₁₉	—	2	2	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₄²×C₁₉	—	2	4	no	—
181	C₂×#1609	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂³×C₁₉	—	2	2	no	—
183	C₂³×C₁₉	—	2	2	no	—
184	C₂³×C₁₉	—	2	2	no	—
185	C₂³×C₁₉	—	4	2	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	4	2	no	—
188	C₂³×C₁₉	#120	1	1	yes	characteristic
189	C₂³×C₁₉	#120	1	1	yes	characteristic
190	C₂³×C₁₉	#135	1	2	yes	—
191	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
192	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₁₉	—	4	2	no	—
194	Q₈×C₁₉	—	8	1	no	—
195	D₄×C₁₉	—	4	2	no	—
196	D₄×C₁₉	—	4	2	no	—
197	D₄×C₁₉	—	4	2	no	—
198	D₄×C₁₉	—	4	4	no	—
199	D₄×C₁₉	—	8	1	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	8	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	2	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	8	1	no	—
228	C₂×C₄×C₁₉	—	8	4	no	—
229	C₂×C₄×C₁₉	—	8	2	no	—
230	C₂×C₄×C₁₉	—	8	2	no	—
231	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
235	C₈×C₁₉	—	4	2	no	—
236	C₈×C₁₉	—	4	2	no	—
237	C₂×#539	C₂×C₁₉	1	1	yes	characteristic
238	C₂×#483	C₂×C₁₉	1	1	yes	characteristic, complemented
239	C₂×#480	C₂×C₁₉	1	1	yes	characteristic
240	C₂×#398	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#1609	C₂×C₁₉	1	8	yes	direct product factor
242	C₂×#328	C₂×C₁₉	1	1	yes	characteristic, complemented
243	C₂×#327	C₂×C₁₉	1	1	yes	characteristic
244	C₂×#324	C₂×C₁₉	1	1	yes	characteristic, complemented
245	C₂²×C₁₉	—	2	4	no	—
246	C₂²×C₁₉	—	2	4	no	—
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	1	no	—
249	C₂²×C₁₉	—	2	1	no	—
250	C₂²×C₁₉	—	2	1	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	4	2	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	—	8	4	no	—
255	C₂²×C₁₉	#449	1	2	yes	—
256	C₂²×C₁₉	#449	1	2	yes	—
257	C₂²×C₁₉	#456	1	2	yes	—
258	C₂²×C₁₉	#458	1	2	yes	—
259	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
260	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
261	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
262	C₄×C₁₉	—	2	1	no	—
263	C₄×C₁₉	—	2	1	no	—
264	C₄×C₁₉	—	2	1	no	—
265	C₄×C₁₉	—	2	1	no	—
266	C₄×C₁₉	—	4	4	no	—
267	C₄×C₁₉	—	4	2	no	—
268	C₄×C₁₉	—	4	2	no	—
269	C₄×C₁₉	—	4	2	no	—
270	C₄×C₁₉	—	4	2	no	—
271	C₄×C₁₉	—	4	2	no	—
272	C₄×C₁₉	—	8	2	no	—
273	#539	—	2	2	no	—
274	#539	—	2	2	no	—
275	#539	—	2	2	no	—
276	#539	C₂²×C₁₉	1	4	yes	—
277	C₂×#126	—	2	1	no	—
278	C₂×#125	—	2	1	no	—
279	C₂×#123	—	2	1	no	—
280	C₂×#123	—	2	1	no	—
281	C₂×C₂²⋊Q₈	—	2	1	no	—
282	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
283	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
284	C₂×C₄×D₄	—	2	1	no	—
285	C₂²×C₄⋊C₄	—	2	1	no	—
286	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
287	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
288	#483	—	2	2	no	—
289	#483	C₂²×C₁₉	1	4	yes	complemented
290	#480	—	2	2	no	—
291	#480	C₂²×C₁₉	1	4	yes	—
292	C₂×#107	—	2	1	no	—
293	C₂×#106	—	2	1	no	—
294	C₂×#103	—	2	1	no	—
295	C₂×#102	—	2	1	no	—
296	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
298	#398	—	2	2	no	—
299	#398	C₂²×C₁₉	1	4	yes	complemented
300	C₂×#95	—	2	1	no	—
301	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
302	#328	C₂²×C₁₉	1	4	yes	complemented
303	#327	C₂²×C₁₉	1	4	yes	—
304	#324	C₂²×C₁₉	1	4	yes	complemented
305	C₂×C₁₉	—	2	1	no	—
306	C₂×C₁₉	—	2	1	no	—
307	C₂×C₁₉	—	2	2	no	—
308	C₂×C₁₉	—	8	2	no	—
309	C₂×C₁₉	#1609	1	4	yes	direct product factor
310	C₂×C₁₉	C₂×#449	1	1	yes	characteristic
311	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
312	C₂×C₁₉	C₂×#458	1	1	yes	characteristic
313	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
316	C₂³×C₄	—	2	1	no	—
317	C₂³×C₄	—	2	1	no	—
318	C₂³×C₄	—	2	1	no	—
319	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
320	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
322	C₂²×C₈	—	2	1	no	—
323	C₂²×C₈	—	2	1	no	—
324	#126	—	2	4	no	—
325	#126	—	2	4	no	—
326	#125	—	2	4	no	—
327	#125	—	2	4	no	—
328	#123	—	2	4	no	—
329	#123	—	2	4	no	—
330	#123	—	2	4	no	—
331	#123	—	2	4	no	—
332	C₂²⋊Q₈	—	2	4	no	—
333	C₂²⋊Q₈	—	2	4	no	—
334	C₂²⋊Q₈	—	2	1	no	—
335	C₂²⋊Q₈	—	2	1	no	—
336	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
337	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
338	#121	—	2	1	no	—
339	#121	—	2	1	no	—
340	#121	D₄×C₁₉	1	2	yes	—
341	#121	C₂³×C₁₉	1	2	yes	—
342	C₄×D₄	—	2	4	no	—
343	C₄×D₄	—	2	4	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	4	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	4	4	no	—
359	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
360	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
361	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₄²	—	2	1	no	—
370	#107	—	2	4	no	—
371	#106	—	2	4	no	—
372	#103	—	2	4	no	—
373	#102	—	2	4	no	—
374	C₂²⋊C₈	—	2	1	no	—
375	C₂²⋊C₈	—	2	1	no	—
376	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
377	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
378	#95	—	2	4	no	—
379	#95	—	2	1	no	—
380	#95	C₂³×C₁₉	1	2	yes	—
381	C₁₉	C₂×#1609	1	1	yes	characteristic, direct product factor, Sylow
382	C₂⁴	—	2	1	no	—
383	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	4	2	no	—
386	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	4	2	no	—
393	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	4	2	no	—
408	C₂²×C₄	—	4	2	no	—
409	C₂²×C₄	—	4	2	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	—	4	1	no	—
412	C₂²×C₄	—	4	1	no	—
413	C₂²×C₄	—	4	2	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	—	8	2	no	—
416	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
417	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
420	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	4	2	no	—
427	C₂×C₈	—	4	2	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	4	8	no	—
442	C₄⋊C₄	—	4	1	no	—
443	C₄⋊C₄	—	4	1	no	—
444	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
445	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₄²	—	2	4	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	C₁₉×#120	1	1	yes	characteristic
461	C₂³	C₁₉×#120	1	1	yes	characteristic
462	C₂³	C₁₉×#135	1	2	yes	—
463	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
464	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
465	Q₈	—	4	2	no	—
466	Q₈	—	8	1	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	4	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	8	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	8	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	8	1	no	—
500	C₂×C₄	—	8	4	no	—
501	C₂×C₄	—	8	2	no	—
502	C₂×C₄	—	8	2	no	—
503	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
504	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
507	C₈	—	4	2	no	—
508	C₈	—	4	2	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	4	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	8	4	no	—
519	C₂²	C₁₉×#449	1	2	yes	—
520	C₂²	C₁₉×#449	1	2	yes	—
521	C₂²	C₁₉×#456	1	2	yes	—
522	C₂²	C₁₉×#458	1	2	yes	—
523	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
524	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
525	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	2	1	no	—
529	C₄	—	2	1	no	—
530	C₄	—	4	4	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	8	2	no	—
537	C₂	—	2	1	no	—
538	C₂	—	2	2	no	—
539	C₂	—	2	1	no	—
540	C₂	—	8	2	no	—
541	C₂	C₁₉×#1609	1	4	yes	direct product factor
542	C₂	C₂×C₁₉×#449	1	1	yes	characteristic
543	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
544	C₂	C₂×C₁₉×#458	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#483	C₂	semidirect
4. C₂×C₁₉×#398	C₂	semidirect
5. C₁₉×#1609	C₂	direct (N × H)
6. C₂×C₁₉×#328	C₂	semidirect
8. C₂×C₁₉×#324	C₂	semidirect
25. C₁₉×#483	C₂²	semidirect
35. C₁₉×#398	C₂²	semidirect
38. C₁₉×#328	C₂²	semidirect
40. C₁₉×#324	C₂²	semidirect
181. C₂×#1609	C₁₉	direct (N × H)
238. C₂×#483	C₂×C₁₉	semidirect
240. C₂×#398	C₂×C₁₉	semidirect
241. #1609	C₂×C₁₉	direct (N × H)
242. C₂×#328	C₂×C₁₉	semidirect
244. C₂×#324	C₂×C₁₉	semidirect
289. #483	C₂²×C₁₉	semidirect
299. #398	C₂²×C₁₉	semidirect
302. #328	C₂²×C₁₉	semidirect
304. #324	C₂²×C₁₉	semidirect
309. C₂×C₁₉	#1609	direct (N × H)
381. C₁₉	C₂×#1609	direct (N × H)
541. C₂	C₁₉×#1609	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×#539	2
C₂×C₁₉×#483	2
C₂×C₁₉×#480	2
C₂×C₁₉×#398	2
C₁₉×#1609	2
C₂×C₁₉×#328	2
C₂×C₁₉×#327	2
C₂×C₁₉×#324	2
C₂×#1609	19

Subgroups — C2×C19×#1609 #18024064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1609 #18024064