Subgroups — C₂×C₁₉×#2051 #18029487

Order 4864.

1490 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#108	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#417	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#408	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2051	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
12	C₂×C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
13	C₂×C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
14	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	—
15	C₂²×SD₁₆×C₁₉	—	2	1	no	—
16	C₂²×D₈×C₁₉	—	2	1	no	—
17	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#108	—	2	4	no	—
23	C₂×C₁₉×#108	C₂²	1	4	yes	complemented
24	C₁₉×#417	—	2	2	no	—
25	C₁₉×#417	C₂²	1	4	yes	complemented
26	C₂×C₁₉×#103	—	2	1	no	—
27	C₂×C₁₉×#102	—	2	1	no	—
28	C₂×C₁₉×#102	—	2	2	no	—
29	C₂×C₁₉×#102	—	2	2	no	—
30	C₂×C₁₉×#102	C₂²	1	4	yes	complemented
31	C₂×C₁₉×#100	—	2	4	no	—
32	C₂×C₁₉×#100	C₂²	1	4	yes	complemented
33	C₁₉×#408	—	2	2	no	—
34	C₁₉×#408	C₂²	1	4	yes	complemented
35	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
36	C₁₉×#343	C₂²	1	4	yes	complemented
37	C₂⁵×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	—	2	2	no	—
41	C₂×#41×C₁₉	—	2	2	no	—
42	C₂×#41×C₁₉	—	2	2	no	—
43	C₂×#41×C₁₉	—	2	2	no	—
44	C₂×#41×C₁₉	D₄	1	2	yes	—
45	C₂×#41×C₁₉	C₂³	1	2	yes	—
46	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂²×D₄×C₁₉	—	2	2	no	—
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	—	2	2	no	—
54	C₂²×D₄×C₁₉	—	2	2	no	—
55	C₂²×D₄×C₁₉	—	2	1	no	—
56	C₂²×D₄×C₁₉	D₄	1	4	yes	—
57	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
58	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₉	—	2	1	no	—
60	C₂³×C₄×C₁₉	—	2	1	no	—
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₁₉×AGL(1,ℤ/8)	—	2	16	no	—
63	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
64	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
65	C₂×SD₁₆×C₁₉	—	2	8	no	—
66	C₂×SD₁₆×C₁₉	—	2	4	no	—
67	C₂×D₈×C₁₉	—	2	8	no	—
68	C₂×D₈×C₁₉	—	2	4	no	—
69	C₂×M₁₆×C₁₉	—	2	2	no	—
70	C₂×M₁₆×C₁₉	—	2	1	no	—
71	C₂×M₁₆×C₁₉	—	2	1	no	—
72	C₂×M₁₆×C₁₉	—	2	1	no	—
73	C₂×M₁₆×C₁₉	—	2	2	no	—
74	C₂×M₁₆×C₁₉	—	2	2	no	—
75	C₂×M₁₆×C₁₉	—	2	2	no	—
76	C₂×M₁₆×C₁₉	—	2	2	no	—
77	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
78	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
79	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
80	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
81	C₂²×C₈×C₁₉	—	2	2	no	—
82	C₂²×C₈×C₁₉	—	2	1	no	—
83	C₂²×C₈×C₁₉	—	2	2	no	—
84	C₂²×C₈×C₁₉	—	2	1	no	—
85	C₂²×C₈×C₁₉	—	2	1	no	—
86	C₂²×C₈×C₁₉	D₄	1	2	yes	—
87	C₂²×C₈×C₁₉	D₄	1	2	yes	—
88	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
95	C₁₉×#108	—	2	8	no	—
96	C₁₉×#103	—	2	4	no	—
97	C₁₉×#102	—	2	4	no	—
98	C₁₉×#102	—	2	8	no	—
99	C₁₉×#100	—	2	8	no	—
100	C₁₉×C₂²⋊C₈	—	2	8	no	—
101	C₂⁴×C₁₉	—	2	1	no	—
102	C₂⁴×C₁₉	—	2	4	no	—
103	C₂⁴×C₁₉	—	2	2	no	—
104	C₂⁴×C₁₉	—	4	1	no	—
105	C₂⁴×C₁₉	—	4	1	no	—
106	C₂⁴×C₁₉	—	4	2	no	—
107	C₂⁴×C₁₉	—	8	2	no	—
108	C₂⁴×C₁₉	—	8	2	no	—
109	C₂⁴×C₁₉	#41	1	1	yes	characteristic
110	#41×C₁₉	—	2	4	no	—
111	#41×C₁₉	—	2	4	no	—
112	#41×C₁₉	—	2	2	no	—
113	#41×C₁₉	—	2	2	no	—
114	#41×C₁₉	—	2	2	no	—
115	#41×C₁₉	—	2	2	no	—
116	#41×C₁₉	—	4	2	no	—
117	#41×C₁₉	—	4	2	no	—
118	#41×C₁₉	—	4	2	no	—
119	#41×C₁₉	—	4	2	no	—
120	C₂×Q₈×C₁₉	—	2	1	no	—
121	C₂×Q₈×C₁₉	—	2	2	no	—
122	C₂×Q₈×C₁₉	—	2	2	no	—
123	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	4	no	—
128	C₂×D₄×C₁₉	—	2	4	no	—
129	C₂×D₄×C₁₉	—	2	4	no	—
130	C₂×D₄×C₁₉	—	2	4	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	4	no	—
134	C₂×D₄×C₁₉	—	2	2	no	—
135	C₂×D₄×C₁₉	—	2	2	no	—
136	C₂×D₄×C₁₉	—	2	2	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	—	4	2	no	—
140	C₂×D₄×C₁₉	—	4	2	no	—
141	C₂×D₄×C₁₉	—	4	2	no	—
142	C₂×D₄×C₁₉	—	4	2	no	—
143	C₂×D₄×C₁₉	—	4	1	no	—
144	C₂×D₄×C₁₉	—	4	1	no	—
145	C₂×D₄×C₁₉	—	4	2	no	—
146	C₂×D₄×C₁₉	—	4	2	no	—
147	C₂×D₄×C₁₉	—	4	2	no	—
148	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
149	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	2	no	—
154	C₂²×C₄×C₁₉	—	4	2	no	—
155	C₂²×C₄×C₁₉	—	4	2	no	—
156	C₂²×C₄×C₁₉	—	4	1	no	—
157	C₂²×C₄×C₁₉	—	4	1	no	—
158	C₂²×C₄×C₁₉	—	8	2	no	—
159	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	#41	1	2	yes	—
166	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	#41	1	2	yes	—
168	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
169	SD₁₆×C₁₉	—	2	16	no	—
170	D₈×C₁₉	—	2	16	no	—
171	M₁₆×C₁₉	—	2	4	no	—
172	M₁₆×C₁₉	—	2	2	no	—
173	M₁₆×C₁₉	—	2	2	no	—
174	M₁₆×C₁₉	—	2	2	no	—
175	M₁₆×C₁₉	—	2	2	no	—
176	M₁₆×C₁₉	—	2	2	no	—
177	M₁₆×C₁₉	—	4	2	no	—
178	M₁₆×C₁₉	—	4	2	no	—
179	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
180	C₂×C₈×C₁₉	—	2	4	no	—
181	C₂×C₈×C₁₉	—	2	4	no	—
182	C₂×C₈×C₁₉	—	2	4	no	—
183	C₂×C₈×C₁₉	—	2	2	no	—
184	C₂×C₈×C₁₉	—	2	2	no	—
185	C₂×C₈×C₁₉	—	2	2	no	—
186	C₂×C₈×C₁₉	—	2	2	no	—
187	C₂×C₈×C₁₉	—	2	2	no	—
188	C₂×C₈×C₁₉	—	4	2	no	—
189	C₂×C₈×C₁₉	—	4	2	no	—
190	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	4	1	no	—
194	C₄⋊C₄×C₁₉	—	4	1	no	—
195	C₂×#2051	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂³×C₁₉	—	2	2	no	—
197	C₂³×C₁₉	—	2	2	no	—
198	C₂³×C₁₉	—	2	2	no	—
199	C₂³×C₁₉	—	2	4	no	—
200	C₂³×C₁₉	—	4	2	no	—
201	C₂³×C₁₉	—	4	2	no	—
202	C₂³×C₁₉	—	4	2	no	—
203	C₂³×C₁₉	—	4	4	no	—
204	C₂³×C₁₉	—	4	4	no	—
205	C₂³×C₁₉	—	4	2	no	—
206	C₂³×C₁₉	—	4	2	no	—
207	C₂³×C₁₉	—	8	8	no	—
208	C₂³×C₁₉	—	8	2	no	—
209	C₂³×C₁₉	—	8	2	no	—
210	C₂³×C₁₉	—	8	8	no	—
211	C₂³×C₁₉	—	8	2	no	—
212	C₂³×C₁₉	—	8	2	no	—
213	C₂³×C₁₉	—	8	2	no	—
214	C₂³×C₁₉	—	8	2	no	—
215	C₂³×C₁₉	#121	1	1	yes	characteristic
216	C₂³×C₁₉	#121	1	1	yes	characteristic
217	C₂³×C₁₉	#123	1	2	yes	—
218	C₂³×C₁₉	#124	1	2	yes	—
219	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
220	Q₈×C₁₉	—	2	2	no	—
221	Q₈×C₁₉	—	2	2	no	—
222	Q₈×C₁₉	—	4	2	no	—
223	D₄×C₁₉	—	2	2	no	—
224	D₄×C₁₉	—	2	4	no	—
225	D₄×C₁₉	—	2	4	no	—
226	D₄×C₁₉	—	2	2	no	—
227	D₄×C₁₉	—	4	2	no	—
228	D₄×C₁₉	—	4	2	no	—
229	D₄×C₁₉	—	4	4	no	—
230	D₄×C₁₉	—	4	2	no	—
231	D₄×C₁₉	—	4	2	no	—
232	D₄×C₁₉	—	4	4	no	—
233	D₄×C₁₉	—	4	4	no	—
234	D₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	4	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	8	2	no	—
242	C₂×C₄×C₁₉	—	8	2	no	—
243	C₂×C₄×C₁₉	—	8	2	no	—
244	C₂×C₄×C₁₉	#120	1	2	yes	—
245	C₂×C₄×C₁₉	#120	1	2	yes	—
246	C₂×C₄×C₁₉	#121	1	2	yes	—
247	C₂×C₄×C₁₉	#121	1	2	yes	—
248	C₂×C₄×C₁₉	#121	1	2	yes	—
249	C₂×C₄×C₁₉	#121	1	2	yes	—
250	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
251	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
252	C₂×C₄×C₁₉	#123	1	2	yes	—
253	C₂×C₄×C₁₉	#123	1	2	yes	—
254	C₂×C₄×C₁₉	#123	1	2	yes	—
255	C₂×C₄×C₁₉	#124	1	2	yes	—
256	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
262	C₈×C₁₉	—	2	4	no	—
263	C₈×C₁₉	—	2	4	no	—
264	C₈×C₁₉	—	4	2	no	—
265	C₈×C₁₉	—	4	2	no	—
266	C₂²×AGL(1,ℤ/8)	C₂×C₁₉	1	1	yes	characteristic
267	C₂²×#108	C₂×C₁₉	1	1	yes	characteristic, complemented
268	C₂×#417	C₂×C₁₉	1	1	yes	characteristic, complemented
269	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
270	C₂²×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
271	C₂×#408	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#2051	C₂×C₁₉	1	8	yes	direct product factor
273	C₂×#343	C₂×C₁₉	1	1	yes	characteristic, complemented
274	C₂²×C₁₉	—	2	4	no	—
275	C₂²×C₁₉	—	2	4	no	—
276	C₂²×C₁₉	—	2	1	no	—
277	C₂²×C₁₉	—	2	1	no	—
278	C₂²×C₁₉	—	2	1	no	—
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	4	2	no	—
281	C₂²×C₁₉	—	4	4	no	—
282	C₂²×C₁₉	—	4	2	no	—
283	C₂²×C₁₉	—	4	2	no	—
284	C₂²×C₁₉	—	8	4	no	—
285	C₂²×C₁₉	—	8	4	no	—
286	C₂²×C₁₉	—	8	8	no	—
287	C₂²×C₁₉	—	8	4	no	—
288	C₂²×C₁₉	—	8	8	no	—
289	C₂²×C₁₉	—	8	2	no	—
290	C₂²×C₁₉	—	8	2	no	—
291	C₂²×C₁₉	#394	1	2	yes	—
292	C₂²×C₁₉	#394	1	2	yes	—
293	C₂²×C₁₉	#471	1	2	yes	—
294	C₂²×C₁₉	#472	1	2	yes	—
295	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
296	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
297	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
298	C₄×C₁₉	—	4	2	no	—
299	C₄×C₁₉	—	8	2	no	—
300	C₄×C₁₉	#394	1	2	yes	—
301	C₄×C₁₉	#394	1	2	yes	—
302	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
303	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
304	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
305	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
306	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
307	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
308	C₂×AGL(1,ℤ/8)	—	2	2	no	—
309	C₂×AGL(1,ℤ/8)	—	2	4	no	—
310	C₂×AGL(1,ℤ/8)	—	2	4	no	—
311	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	—
312	C₂²×SD₁₆	—	2	1	no	—
313	C₂²×D₈	—	2	1	no	—
314	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
315	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
316	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
317	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
318	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×#108	—	2	4	no	—
320	C₂×#108	C₂²×C₁₉	1	4	yes	complemented
321	#417	—	2	2	no	—
322	#417	C₂²×C₁₉	1	4	yes	complemented
323	C₂×#103	—	2	1	no	—
324	C₂×#102	—	2	1	no	—
325	C₂×#102	—	2	2	no	—
326	C₂×#102	—	2	2	no	—
327	C₂×#102	C₂²×C₁₉	1	4	yes	complemented
328	C₂×#100	—	2	4	no	—
329	C₂×#100	C₂²×C₁₉	1	4	yes	complemented
330	#408	—	2	2	no	—
331	#408	C₂²×C₁₉	1	4	yes	complemented
332	C₂×C₂²⋊C₈	—	2	2	no	—
333	#343	C₂²×C₁₉	1	4	yes	complemented
334	C₂×C₁₉	—	2	1	no	—
335	C₂×C₁₉	—	2	1	no	—
336	C₂×C₁₉	—	2	2	no	—
337	C₂×C₁₉	—	8	2	no	—
338	C₂×C₁₉	—	8	4	no	—
339	C₂×C₁₉	#2051	1	4	yes	direct product factor
340	C₂×C₁₉	C₂×#394	1	1	yes	characteristic
341	C₂×C₁₉	C₂×#471	1	1	yes	characteristic
342	C₂×C₁₉	C₂×#472	1	1	yes	characteristic
343	C₂⁵	—	2	1	no	—
344	C₂×#41	—	2	1	no	—
345	C₂×#41	—	2	1	no	—
346	C₂×#41	—	2	2	no	—
347	C₂×#41	—	2	2	no	—
348	C₂×#41	—	2	2	no	—
349	C₂×#41	—	2	2	no	—
350	C₂×#41	D₄×C₁₉	1	2	yes	—
351	C₂×#41	C₂³×C₁₉	1	2	yes	—
352	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
353	C₂²×D₄	—	2	1	no	—
354	C₂²×D₄	—	2	1	no	—
355	C₂²×D₄	—	2	2	no	—
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	—	2	1	no	—
358	C₂²×D₄	—	2	1	no	—
359	C₂²×D₄	—	2	2	no	—
360	C₂²×D₄	—	2	2	no	—
361	C₂²×D₄	—	2	1	no	—
362	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
363	C₂²×D₄	D₄×C₁₉	1	4	yes	—
364	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
365	C₂³×C₄	—	2	1	no	—
366	C₂³×C₄	—	2	1	no	—
367	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
368	AGL(1,ℤ/8)	—	2	16	no	—
369	AGL(1,ℤ/8)	—	2	8	no	—
370	AGL(1,ℤ/8)	—	2	8	no	—
371	C₂×SD₁₆	—	2	8	no	—
372	C₂×SD₁₆	—	2	4	no	—
373	C₂×D₈	—	2	8	no	—
374	C₂×D₈	—	2	4	no	—
375	C₂×M₁₆	—	2	2	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	2	no	—
380	C₂×M₁₆	—	2	2	no	—
381	C₂×M₁₆	—	2	2	no	—
382	C₂×M₁₆	—	2	2	no	—
383	C₂×M₁₆	D₄×C₁₉	1	4	yes	—
384	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
385	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
386	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
387	C₂²×C₈	—	2	2	no	—
388	C₂²×C₈	—	2	1	no	—
389	C₂²×C₈	—	2	2	no	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	D₄×C₁₉	1	2	yes	—
393	C₂²×C₈	D₄×C₁₉	1	2	yes	—
394	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
401	#108	—	2	8	no	—
402	#103	—	2	4	no	—
403	#102	—	2	4	no	—
404	#102	—	2	8	no	—
405	#100	—	2	8	no	—
406	C₂²⋊C₈	—	2	8	no	—
407	C₁₉	C₂×#2051	1	1	yes	characteristic, direct product factor, Sylow
408	C₂⁴	—	2	1	no	—
409	C₂⁴	—	2	4	no	—
410	C₂⁴	—	2	2	no	—
411	C₂⁴	—	4	1	no	—
412	C₂⁴	—	4	1	no	—
413	C₂⁴	—	4	2	no	—
414	C₂⁴	—	8	2	no	—
415	C₂⁴	—	8	2	no	—
416	C₂⁴	#41×C₁₉	1	1	yes	characteristic
417	#41	—	2	4	no	—
418	#41	—	2	4	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	—	4	2	no	—
424	#41	—	4	2	no	—
425	#41	—	4	2	no	—
426	#41	—	4	2	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	4	2	no	—
447	C₂×D₄	—	4	2	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	—	4	1	no	—
450	C₂×D₄	—	4	2	no	—
451	C₂×D₄	—	4	2	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	—	4	2	no	—
455	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
456	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	4	2	no	—
462	C₂²×C₄	—	4	2	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	8	2	no	—
466	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
467	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
468	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
472	C₂²×C₄	#41×C₁₉	1	2	yes	—
473	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
474	C₂²×C₄	#41×C₁₉	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
476	SD₁₆	—	2	16	no	—
477	D₈	—	2	16	no	—
478	M₁₆	—	2	4	no	—
479	M₁₆	—	2	2	no	—
480	M₁₆	—	2	2	no	—
481	M₁₆	—	2	2	no	—
482	M₁₆	—	2	2	no	—
483	M₁₆	—	2	2	no	—
484	M₁₆	—	4	2	no	—
485	M₁₆	—	4	2	no	—
486	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
487	C₂×C₈	—	2	4	no	—
488	C₂×C₈	—	2	4	no	—
489	C₂×C₈	—	2	4	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	4	2	no	—
496	C₂×C₈	—	4	2	no	—
497	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	—	4	1	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	2	4	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	4	no	—
508	C₂³	—	4	4	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	8	2	no	—
514	C₂³	—	8	2	no	—
515	C₂³	—	8	8	no	—
516	C₂³	—	8	2	no	—
517	C₂³	—	8	2	no	—
518	C₂³	—	8	8	no	—
519	C₂³	—	8	2	no	—
520	C₂³	—	8	2	no	—
521	C₂³	C₁₉×#121	1	1	yes	characteristic
522	C₂³	C₁₉×#121	1	1	yes	characteristic
523	C₂³	C₁₉×#123	1	2	yes	—
524	C₂³	C₁₉×#124	1	2	yes	—
525	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
526	Q₈	—	2	2	no	—
527	Q₈	—	2	2	no	—
528	Q₈	—	4	2	no	—
529	D₄	—	2	2	no	—
530	D₄	—	2	4	no	—
531	D₄	—	2	4	no	—
532	D₄	—	2	2	no	—
533	D₄	—	4	4	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	4	no	—
537	D₄	—	4	4	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	8	2	no	—
548	C₂×C₄	—	8	2	no	—
549	C₂×C₄	—	8	2	no	—
550	C₂×C₄	C₁₉×#120	1	2	yes	—
551	C₂×C₄	C₁₉×#120	1	2	yes	—
552	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
553	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
554	C₂×C₄	C₁₉×#121	1	2	yes	—
555	C₂×C₄	C₁₉×#121	1	2	yes	—
556	C₂×C₄	C₁₉×#121	1	2	yes	—
557	C₂×C₄	C₁₉×#121	1	2	yes	—
558	C₂×C₄	C₁₉×#123	1	2	yes	—
559	C₂×C₄	C₁₉×#123	1	2	yes	—
560	C₂×C₄	C₁₉×#123	1	2	yes	—
561	C₂×C₄	C₁₉×#124	1	2	yes	—
562	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
563	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
564	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
565	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
566	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
567	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
568	C₈	—	2	4	no	—
569	C₈	—	2	4	no	—
570	C₈	—	4	2	no	—
571	C₈	—	4	2	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	4	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	8	4	no	—
583	C₂²	—	8	8	no	—
584	C₂²	—	8	4	no	—
585	C₂²	—	8	2	no	—
586	C₂²	—	8	2	no	—
587	C₂²	—	8	4	no	—
588	C₂²	—	8	8	no	—
589	C₂²	C₁₉×#394	1	2	yes	—
590	C₂²	C₁₉×#394	1	2	yes	—
591	C₂²	C₁₉×#471	1	2	yes	—
592	C₂²	C₁₉×#472	1	2	yes	—
593	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
594	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
595	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
596	C₄	—	4	2	no	—
597	C₄	—	8	2	no	—
598	C₄	C₁₉×#394	1	2	yes	—
599	C₄	C₁₉×#394	1	2	yes	—
600	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
601	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
602	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
603	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
604	C₂	—	2	2	no	—
605	C₂	—	2	1	no	—
606	C₂	—	2	1	no	—
607	C₂	—	8	2	no	—
608	C₂	—	8	4	no	—
609	C₂	C₁₉×#2051	1	4	yes	direct product factor
610	C₂	C₂×C₁₉×#394	1	1	yes	characteristic
611	C₂	C₂×C₁₉×#471	1	1	yes	characteristic
612	C₂	C₂×C₁₉×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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. C₂²×C₁₉×#108	C₂	semidirect
3. C₂×C₁₉×#417	C₂	semidirect
4. C₂²×C₁₉×#102	C₂	semidirect
5. C₂²×C₁₉×#100	C₂	semidirect
6. C₂×C₁₉×#408	C₂	semidirect
7. C₁₉×#2051	C₂	direct (N × H)
8. C₂×C₁₉×#343	C₂	semidirect
23. C₂×C₁₉×#108	C₂²	semidirect
25. C₁₉×#417	C₂²	semidirect
30. C₂×C₁₉×#102	C₂²	semidirect
32. C₂×C₁₉×#100	C₂²	semidirect
34. C₁₉×#408	C₂²	semidirect
36. C₁₉×#343	C₂²	semidirect
195. C₂×#2051	C₁₉	direct (N × H)
267. C₂²×#108	C₂×C₁₉	semidirect
268. C₂×#417	C₂×C₁₉	semidirect
269. C₂²×#102	C₂×C₁₉	semidirect
270. C₂²×#100	C₂×C₁₉	semidirect
271. C₂×#408	C₂×C₁₉	semidirect
272. #2051	C₂×C₁₉	direct (N × H)
273. C₂×#343	C₂×C₁₉	semidirect
320. C₂×#108	C₂²×C₁₉	semidirect
322. #417	C₂²×C₁₉	semidirect
327. C₂×#102	C₂²×C₁₉	semidirect
329. C₂×#100	C₂²×C₁₉	semidirect
331. #408	C₂²×C₁₉	semidirect
333. #343	C₂²×C₁₉	semidirect
339. C₂×C₁₉	#2051	direct (N × H)
407. C₁₉	C₂×#2051	direct (N × H)
609. C₂	C₁₉×#2051	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×AGL(1,ℤ/8)	2
C₂²×C₁₉×#108	2
C₂×C₁₉×#417	2
C₂²×C₁₉×#102	2
C₂²×C₁₉×#100	2
C₂×C₁₉×#408	2
C₁₉×#2051	2
C₂×C₁₉×#343	2
C₂×#2051	19

Subgroups — C2×C19×#2051 #18029487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2051 #18029487