Subgroups — C₁₉×#23876 #18029835

Order 4864.

2012 conjugacy classes of subgroups.

The subgroup lattice has 938 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, complemented
2	C₁₉×#3488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#453	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3003	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2433	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2006	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2002	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1900	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1883	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1871	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1789	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
13	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
16	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
17	C₂×C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
18	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
20	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
21	C₂²×SD₁₆×C₁₉	—	2	1	no	—
22	C₂²×D₈×C₁₉	—	2	1	no	—
23	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#550	—	2	1	no	—
25	C₁₉×#548	—	2	1	no	—
26	C₁₉×#546	—	2	1	no	—
27	C₁₉×#546	—	2	2	no	—
28	D₄²×C₁₉	—	2	2	no	—
29	D₄²×C₁₉	—	2	1	no	—
30	C₁₉×#537	—	2	1	no	—
31	C₁₉×#537	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#535	—	2	1	no	—
33	C₁₉×#535	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₉×#127	C₂²	1	2	yes	complemented
35	C₁₉×#525	—	2	1	no	—
36	C₁₉×#525	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#121	—	2	1	no	—
38	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#120	—	2	2	no	—
40	C₁₉×#520	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#453	—	2	8	no	—
42	C₁₉×#450	—	2	1	no	—
43	C₁₉×#450	—	2	1	no	—
44	C₁₉×#447	—	2	1	no	—
45	C₁₉×#447	—	2	1	no	—
46	C₂×C₁₉×#104	C₂²	1	2	yes	complemented
47	C₂×C₁₉×#104	C₂²	1	2	yes	complemented
48	C₂×C₁₉×#104	C₂²	1	2	yes	complemented
49	C₁₉×#418	C₂²	1	2	yes	complemented
50	C₂×C₁₉×#100	C₂²	1	2	yes	complemented
51	C₁₉×#407	C₂²	1	1	yes	characteristic, complemented
52	C₁₉×#392	—	2	2	no	—
53	C₁₉×#390	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×#343	C₂²	1	2	yes	complemented
56	C₁₉×#339	C₂²	1	2	yes	complemented
57	C₂⁵×C₁₉	—	2	1	no	—
58	C₁₉×H(5,𝔽₂)	—	2	4	no	—
59	C₁₉×H(5,𝔽₂)	—	4	2	no	—
60	C₂×#41×C₁₉	—	2	1	no	—
61	C₂×#41×C₁₉	—	2	1	no	—
62	C₂×#41×C₁₉	—	2	1	no	—
63	C₂×#41×C₁₉	—	2	1	no	—
64	C₂×#41×C₁₉	—	2	4	no	—
65	C₂×#41×C₁₉	—	4	2	no	—
66	C₂×#41×C₁₉	D₄	1	1	yes	characteristic, complemented
67	C₂×#41×C₁₉	D₄	1	1	yes	characteristic, complemented
68	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic, complemented
72	C₂²×D₄×C₁₉	—	2	4	no	—
73	C₂²×D₄×C₁₉	—	2	1	no	—
74	C₂²×D₄×C₁₉	—	2	2	no	—
75	C₂²×D₄×C₁₉	—	2	2	no	—
76	C₂²×D₄×C₁₉	—	2	1	no	—
77	C₂²×D₄×C₁₉	—	2	1	no	—
78	C₂²×D₄×C₁₉	—	2	4	no	—
79	C₂²×D₄×C₁₉	—	2	1	no	—
80	C₂²×D₄×C₁₉	—	2	1	no	—
81	C₂²×D₄×C₁₉	—	2	1	no	—
82	C₂²×D₄×C₁₉	—	2	1	no	—
83	C₂²×D₄×C₁₉	—	2	1	no	—
84	C₂²×D₄×C₁₉	—	4	2	no	—
85	C₂²×D₄×C₁₉	D₄	1	2	yes	—
86	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic, complemented
87	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₉	—	2	1	no	—
90	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
92	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
93	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
94	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
95	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
96	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
97	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
98	C₁₉×AGL(1,ℤ/8)	D₄	1	8	yes	complemented
99	C₂×SD₁₆×C₁₉	—	2	8	no	—
100	C₂×SD₁₆×C₁₉	—	2	2	no	—
101	C₂×SD₁₆×C₁₉	—	2	2	no	—
102	C₂×SD₁₆×C₁₉	—	2	2	no	—
103	C₂×D₈×C₁₉	—	2	8	no	—
104	C₂×D₈×C₁₉	—	2	2	no	—
105	C₂×D₈×C₁₉	—	2	2	no	—
106	C₂×D₈×C₁₉	—	2	2	no	—
107	C₂×M₁₆×C₁₉	—	2	1	no	—
108	C₂×M₁₆×C₁₉	—	2	4	no	—
109	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
110	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
111	C₂²×C₈×C₁₉	—	2	1	no	—
112	C₁₉×#127	—	2	2	no	—
113	C₁₉×#127	—	2	1	no	—
114	C₁₉×#127	—	2	4	no	—
115	C₁₉×#127	—	4	2	no	—
116	C₁₉×#124	—	2	2	no	—
117	C₁₉×#124	—	2	1	no	—
118	C₁₉×#123	—	2	2	no	—
119	C₁₉×#123	—	2	1	no	—
120	C₁₉×C₂²⋊Q₈	—	2	2	no	—
121	C₁₉×C₂²⋊Q₈	—	2	1	no	—
122	C₁₉×C₂²⋊Q₈	—	2	1	no	—
123	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
124	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
125	C₁₉×#121	—	2	2	no	—
126	C₁₉×#121	—	2	2	no	—
127	C₁₉×#121	—	2	2	no	—
128	C₁₉×#121	—	2	2	no	—
129	C₁₉×#121	—	2	2	no	—
130	C₁₉×#121	—	2	1	no	—
131	C₁₉×#121	—	2	1	no	—
132	C₁₉×#121	—	2	1	no	—
133	C₁₉×#121	—	2	1	no	—
134	C₁₉×#121	—	2	1	no	—
135	C₁₉×#121	—	2	1	no	—
136	C₁₉×#121	—	2	2	no	—
137	C₁₉×#121	—	2	1	no	—
138	C₁₉×#121	—	2	1	no	—
139	C₁₉×#121	D₄	1	1	yes	characteristic, complemented
140	C₁₉×#121	D₄	1	1	yes	characteristic, complemented
141	C₁₉×#120	—	2	2	no	—
142	C₁₉×#120	—	2	2	no	—
143	C₁₉×#120	—	2	2	no	—
144	C₁₉×#120	—	2	1	no	—
145	C₁₉×#120	—	2	2	no	—
146	C₁₉×#120	—	4	8	no	—
147	C₄×Q₈×C₁₉	—	2	1	no	—
148	C₄×D₄×C₁₉	—	2	2	no	—
149	C₄×D₄×C₁₉	—	2	2	no	—
150	C₄×D₄×C₁₉	—	2	1	no	—
151	C₄×D₄×C₁₉	—	2	2	no	—
152	C₄×D₄×C₁₉	—	2	1	no	—
153	C₄×D₄×C₁₉	—	2	1	no	—
154	C₁₉×#117	—	2	1	no	—
155	C₁₉×#117	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
159	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
161	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
162	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
163	C₁₉×#104	—	2	4	no	—
164	C₁₉×#104	—	2	4	no	—
165	C₁₉×#104	—	4	2	no	—
166	C₁₉×#102	—	2	2	no	—
167	C₁₉×#102	—	2	2	no	—
168	C₁₉×#100	—	2	4	no	—
169	C₁₉×C₂²⋊C₈	—	2	1	no	—
170	C₁₉×C₂²⋊C₈	—	2	1	no	—
171	C₁₉×#95	—	2	1	no	—
172	C₂⁴×C₁₉	—	2	2	no	—
173	C₂⁴×C₁₉	—	2	2	no	—
174	C₂⁴×C₁₉	—	2	1	no	—
175	C₂⁴×C₁₉	—	4	4	no	—
176	C₂⁴×C₁₉	—	4	4	no	—
177	C₂⁴×C₁₉	—	4	1	no	—
178	C₂⁴×C₁₉	—	4	1	no	—
179	C₂⁴×C₁₉	—	8	2	no	—
180	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
182	#41×C₁₉	—	2	2	no	—
183	#41×C₁₉	—	2	2	no	—
184	#41×C₁₉	—	2	2	no	—
185	#41×C₁₉	—	2	2	no	—
186	#41×C₁₉	—	2	2	no	—
187	#41×C₁₉	—	2	2	no	—
188	#41×C₁₉	—	2	2	no	—
189	#41×C₁₉	—	4	4	no	—
190	#41×C₁₉	—	4	1	no	—
191	#41×C₁₉	—	4	1	no	—
192	#41×C₁₉	—	4	4	no	—
193	#41×C₁₉	—	4	4	no	—
194	#41×C₁₉	—	4	2	no	—
195	#41×C₁₉	—	4	2	no	—
196	#41×C₁₉	C₂×D₄	1	4	yes	—
197	C₂×Q₈×C₁₉	—	2	1	no	—
198	C₂×Q₈×C₁₉	—	2	2	no	—
199	C₂×Q₈×C₁₉	—	4	1	no	—
200	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₂×D₄×C₁₉	—	2	1	no	—
204	C₂×D₄×C₁₉	—	2	4	no	—
205	C₂×D₄×C₁₉	—	2	4	no	—
206	C₂×D₄×C₁₉	—	2	2	no	—
207	C₂×D₄×C₁₉	—	2	2	no	—
208	C₂×D₄×C₁₉	—	2	2	no	—
209	C₂×D₄×C₁₉	—	2	2	no	—
210	C₂×D₄×C₁₉	—	2	1	no	—
211	C₂×D₄×C₁₉	—	2	1	no	—
212	C₂×D₄×C₁₉	—	2	1	no	—
213	C₂×D₄×C₁₉	—	2	1	no	—
214	C₂×D₄×C₁₉	—	2	1	no	—
215	C₂×D₄×C₁₉	—	2	2	no	—
216	C₂×D₄×C₁₉	—	2	2	no	—
217	C₂×D₄×C₁₉	—	2	2	no	—
218	C₂×D₄×C₁₉	—	2	1	no	—
219	C₂×D₄×C₁₉	—	2	2	no	—
220	C₂×D₄×C₁₉	—	2	1	no	—
221	C₂×D₄×C₁₉	—	2	2	no	—
222	C₂×D₄×C₁₉	—	2	2	no	—
223	C₂×D₄×C₁₉	—	2	2	no	—
224	C₂×D₄×C₁₉	—	2	1	no	—
225	C₂×D₄×C₁₉	—	2	1	no	—
226	C₂×D₄×C₁₉	—	2	2	no	—
227	C₂×D₄×C₁₉	—	2	2	no	—
228	C₂×D₄×C₁₉	—	2	2	no	—
229	C₂×D₄×C₁₉	—	2	2	no	—
230	C₂×D₄×C₁₉	—	4	1	no	—
231	C₂×D₄×C₁₉	—	4	4	no	—
232	C₂×D₄×C₁₉	—	4	4	no	—
233	C₂×D₄×C₁₉	—	4	4	no	—
234	C₂×D₄×C₁₉	—	4	4	no	—
235	C₂×D₄×C₁₉	—	4	2	no	—
236	C₂×D₄×C₁₉	—	4	2	no	—
237	C₂×D₄×C₁₉	—	4	8	no	—
238	C₂×D₄×C₁₉	—	4	4	no	—
239	C₂×D₄×C₁₉	—	4	8	no	—
240	C₂×D₄×C₁₉	—	4	2	no	—
241	C₂×D₄×C₁₉	—	4	2	no	—
242	C₂×D₄×C₁₉	—	4	4	no	—
243	C₂×D₄×C₁₉	—	4	8	no	—
244	C₂×D₄×C₁₉	—	4	1	no	—
245	C₂×D₄×C₁₉	—	4	1	no	—
246	C₂×D₄×C₁₉	—	8	4	no	—
247	C₂×D₄×C₁₉	—	8	4	no	—
248	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
249	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
250	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
251	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	complemented
252	C₂²×C₄×C₁₉	—	2	1	no	—
253	C₂²×C₄×C₁₉	—	2	2	no	—
254	C₂²×C₄×C₁₉	—	2	2	no	—
255	C₂²×C₄×C₁₉	—	2	2	no	—
256	C₂²×C₄×C₁₉	—	2	1	no	—
257	C₂²×C₄×C₁₉	—	2	2	no	—
258	C₂²×C₄×C₁₉	—	2	2	no	—
259	C₂²×C₄×C₁₉	—	2	1	no	—
260	C₂²×C₄×C₁₉	—	2	1	no	—
261	C₂²×C₄×C₁₉	—	2	1	no	—
262	C₂²×C₄×C₁₉	—	2	1	no	—
263	C₂²×C₄×C₁₉	—	4	4	no	—
264	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
271	SD₁₆×C₁₉	—	2	8	no	—
272	SD₁₆×C₁₉	—	2	8	no	—
273	SD₁₆×C₁₉	—	4	4	no	—
274	D₈×C₁₉	—	2	8	no	—
275	D₈×C₁₉	—	2	8	no	—
276	D₈×C₁₉	—	4	4	no	—
277	M₁₆×C₁₉	—	2	4	no	—
278	M₁₆×C₁₉	—	2	2	no	—
279	M₁₆×C₁₉	—	2	2	no	—
280	M₁₆×C₁₉	—	2	2	no	—
281	M₁₆×C₁₉	C₂×D₄	1	4	yes	complemented
282	C₂×C₈×C₁₉	—	2	4	no	—
283	C₂×C₈×C₁₉	—	2	2	no	—
284	C₂×C₈×C₁₉	—	2	2	no	—
285	C₄⋊C₄×C₁₉	—	2	2	no	—
286	C₄⋊C₄×C₁₉	—	2	2	no	—
287	C₄⋊C₄×C₁₉	—	2	1	no	—
288	C₄⋊C₄×C₁₉	—	2	1	no	—
289	C₄⋊C₄×C₁₉	—	2	1	no	—
290	C₄⋊C₄×C₁₉	—	2	1	no	—
291	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
292	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
293	C₂²⋊C₄×C₁₉	—	2	2	no	—
294	C₂²⋊C₄×C₁₉	—	2	2	no	—
295	C₂²⋊C₄×C₁₉	—	2	4	no	—
296	C₂²⋊C₄×C₁₉	—	2	2	no	—
297	C₂²⋊C₄×C₁₉	—	2	2	no	—
298	C₂²⋊C₄×C₁₉	—	2	2	no	—
299	C₂²⋊C₄×C₁₉	—	2	1	no	—
300	C₂²⋊C₄×C₁₉	—	2	1	no	—
301	C₂²⋊C₄×C₁₉	—	2	1	no	—
302	C₂²⋊C₄×C₁₉	—	2	1	no	—
303	C₂²⋊C₄×C₁₉	—	2	2	no	—
304	C₂²⋊C₄×C₁₉	—	2	2	no	—
305	C₂²⋊C₄×C₁₉	—	2	1	no	—
306	C₂²⋊C₄×C₁₉	—	4	8	no	—
307	C₄²×C₁₉	—	2	2	no	—
308	C₄²×C₁₉	—	2	1	no	—
309	C₄²×C₁₉	—	2	2	no	—
310	C₄²×C₁₉	—	2	2	no	—
311	#23876	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
312	C₂³×C₁₉	—	2	1	no	—
313	C₂³×C₁₉	—	2	2	no	—
314	C₂³×C₁₉	—	2	2	no	—
315	C₂³×C₁₉	—	2	2	no	—
316	C₂³×C₁₉	—	2	1	no	—
317	C₂³×C₁₉	—	2	1	no	—
318	C₂³×C₁₉	—	2	4	no	—
319	C₂³×C₁₉	—	2	4	no	—
320	C₂³×C₁₉	—	4	1	no	—
321	C₂³×C₁₉	—	4	2	no	—
322	C₂³×C₁₉	—	4	4	no	—
323	C₂³×C₁₉	—	4	4	no	—
324	C₂³×C₁₉	—	4	4	no	—
325	C₂³×C₁₉	—	4	4	no	—
326	C₂³×C₁₉	—	4	4	no	—
327	C₂³×C₁₉	—	4	2	no	—
328	C₂³×C₁₉	—	4	2	no	—
329	C₂³×C₁₉	—	4	2	no	—
330	C₂³×C₁₉	—	4	2	no	—
331	C₂³×C₁₉	—	4	2	no	—
332	C₂³×C₁₉	—	8	1	no	—
333	C₂³×C₁₉	—	8	2	no	—
334	C₂³×C₁₉	—	8	2	no	—
335	C₂³×C₁₉	—	8	2	no	—
336	C₂³×C₁₉	—	8	2	no	—
337	C₂³×C₁₉	—	8	2	no	—
338	C₂³×C₁₉	—	8	16	no	—
339	C₂³×C₁₉	—	8	2	no	—
340	C₂³×C₁₉	#120	1	1	yes	characteristic
341	C₂³×C₁₉	#120	1	1	yes	characteristic
342	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₁₉	—	2	1	no	—
344	Q₈×C₁₉	—	2	1	no	—
345	Q₈×C₁₉	—	2	1	no	—
346	Q₈×C₁₉	—	2	2	no	—
347	Q₈×C₁₉	—	4	2	no	—
348	Q₈×C₁₉	#120	1	2	yes	complemented
349	D₄×C₁₉	—	2	4	no	—
350	D₄×C₁₉	—	2	1	no	—
351	D₄×C₁₉	—	2	4	no	—
352	D₄×C₁₉	—	2	1	no	—
353	D₄×C₁₉	—	2	1	no	—
354	D₄×C₁₉	—	2	2	no	—
355	D₄×C₁₉	—	2	4	no	—
356	D₄×C₁₉	—	4	2	no	—
357	D₄×C₁₉	—	4	2	no	—
358	D₄×C₁₉	—	4	4	no	—
359	D₄×C₁₉	—	4	4	no	—
360	D₄×C₁₉	—	4	4	no	—
361	D₄×C₁₉	—	4	2	no	—
362	D₄×C₁₉	—	4	4	no	—
363	D₄×C₁₉	—	4	2	no	—
364	D₄×C₁₉	—	4	2	no	—
365	D₄×C₁₉	—	4	4	no	—
366	D₄×C₁₉	—	4	2	no	—
367	D₄×C₁₉	—	4	1	no	—
368	D₄×C₁₉	—	4	2	no	—
369	D₄×C₁₉	—	4	1	no	—
370	D₄×C₁₉	—	4	2	no	—
371	D₄×C₁₉	—	4	2	no	—
372	D₄×C₁₉	—	8	1	no	—
373	D₄×C₁₉	—	8	2	no	—
374	D₄×C₁₉	—	8	2	no	—
375	D₄×C₁₉	—	8	2	no	—
376	D₄×C₁₉	—	8	2	no	—
377	D₄×C₁₉	—	8	16	no	—
378	D₄×C₁₉	#120	1	2	yes	complemented
379	C₂×C₄×C₁₉	—	2	1	no	—
380	C₂×C₄×C₁₉	—	2	2	no	—
381	C₂×C₄×C₁₉	—	2	1	no	—
382	C₂×C₄×C₁₉	—	2	1	no	—
383	C₂×C₄×C₁₉	—	2	1	no	—
384	C₂×C₄×C₁₉	—	2	1	no	—
385	C₂×C₄×C₁₉	—	2	2	no	—
386	C₂×C₄×C₁₉	—	2	2	no	—
387	C₂×C₄×C₁₉	—	2	4	no	—
388	C₂×C₄×C₁₉	—	2	4	no	—
389	C₂×C₄×C₁₉	—	2	1	no	—
390	C₂×C₄×C₁₉	—	2	2	no	—
391	C₂×C₄×C₁₉	—	2	1	no	—
392	C₂×C₄×C₁₉	—	2	1	no	—
393	C₂×C₄×C₁₉	—	2	1	no	—
394	C₂×C₄×C₁₉	—	4	2	no	—
395	C₂×C₄×C₁₉	—	4	2	no	—
396	C₂×C₄×C₁₉	—	4	2	no	—
397	C₂×C₄×C₁₉	—	4	4	no	—
398	C₂×C₄×C₁₉	—	4	2	no	—
399	C₂×C₄×C₁₉	—	4	2	no	—
400	C₂×C₄×C₁₉	—	4	1	no	—
401	C₂×C₄×C₁₉	—	4	1	no	—
402	C₂×C₄×C₁₉	—	4	2	no	—
403	C₂×C₄×C₁₉	—	4	2	no	—
404	C₂×C₄×C₁₉	—	8	2	no	—
405	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
406	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
407	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
411	C₈×C₁₉	—	2	4	no	—
412	C₈×C₁₉	—	4	2	no	—
413	C₂²×AGL(1,ℤ/8)	C₂×C₁₉	1	1	yes	characteristic, complemented
414	#3488	C₂×C₁₉	1	1	yes	characteristic, complemented
415	C₂×#453	C₂×C₁₉	1	2	yes	complemented
416	#3003	C₂×C₁₉	1	1	yes	characteristic, complemented
417	#2433	C₂×C₁₉	1	1	yes	characteristic, complemented
418	#2006	C₂×C₁₉	1	2	yes	complemented
419	#2002	C₂×C₁₉	1	2	yes	complemented
420	#1900	C₂×C₁₉	1	1	yes	characteristic, complemented
421	#1883	C₂×C₁₉	1	2	yes	complemented
422	#1871	C₂×C₁₉	1	1	yes	characteristic, complemented
423	#1789	C₂×C₁₉	1	1	yes	characteristic, complemented
424	C₂²×C₁₉	—	2	1	no	—
425	C₂²×C₁₉	—	2	1	no	—
426	C₂²×C₁₉	—	2	1	no	—
427	C₂²×C₁₉	—	2	1	no	—
428	C₂²×C₁₉	—	2	1	no	—
429	C₂²×C₁₉	—	2	2	no	—
430	C₂²×C₁₉	—	2	1	no	—
431	C₂²×C₁₉	—	2	1	no	—
432	C₂²×C₁₉	—	4	4	no	—
433	C₂²×C₁₉	—	4	8	no	—
434	C₂²×C₁₉	—	4	1	no	—
435	C₂²×C₁₉	—	4	1	no	—
436	C₂²×C₁₉	—	4	1	no	—
437	C₂²×C₁₉	—	4	1	no	—
438	C₂²×C₁₉	—	4	2	no	—
439	C₂²×C₁₉	—	4	4	no	—
440	C₂²×C₁₉	—	4	2	no	—
441	C₂²×C₁₉	—	4	1	no	—
442	C₂²×C₁₉	—	4	1	no	—
443	C₂²×C₁₉	—	4	1	no	—
444	C₂²×C₁₉	—	4	2	no	—
445	C₂²×C₁₉	—	4	1	no	—
446	C₂²×C₁₉	—	8	4	no	—
447	C₂²×C₁₉	—	8	4	no	—
448	C₂²×C₁₉	—	8	4	no	—
449	C₂²×C₁₉	—	8	8	no	—
450	C₂²×C₁₉	—	8	8	no	—
451	C₂²×C₁₉	—	8	2	no	—
452	C₂²×C₁₉	—	8	2	no	—
453	C₂²×C₁₉	—	16	4	no	—
454	C₂²×C₁₉	#453	1	2	yes	complemented
455	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
456	C₂²×C₁₉	D₄²	1	2	yes	—
457	C₄×C₁₉	—	2	1	no	—
458	C₄×C₁₉	—	2	1	no	—
459	C₄×C₁₉	—	2	2	no	—
460	C₄×C₁₉	—	4	4	no	—
461	C₄×C₁₉	—	4	1	no	—
462	C₄×C₁₉	—	4	1	no	—
463	C₄×C₁₉	—	4	2	no	—
464	C₄×C₁₉	—	4	1	no	—
465	C₄×C₁₉	—	4	1	no	—
466	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
467	C₄×C₁₉	#534	1	1	yes	characteristic
468	C₄×C₁₉	D₄²	1	2	yes	—
469	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic, complemented
470	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
471	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
472	C₂×AGL(1,ℤ/8)	—	2	1	no	—
473	C₂×AGL(1,ℤ/8)	—	2	1	no	—
474	C₂×AGL(1,ℤ/8)	—	2	8	no	—
475	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	—
476	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	complemented
477	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	complemented
478	C₂²×SD₁₆	—	2	1	no	—
479	C₂²×D₈	—	2	1	no	—
480	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
481	#550	—	2	1	no	—
482	#548	—	2	1	no	—
483	#546	—	2	1	no	—
484	#546	—	2	2	no	—
485	D₄²	—	2	2	no	—
486	D₄²	—	2	1	no	—
487	#537	—	2	1	no	—
488	#537	C₂²×C₁₉	1	1	yes	characteristic, complemented
489	#535	—	2	1	no	—
490	#535	C₂²×C₁₉	1	1	yes	characteristic, complemented
491	C₂×#127	C₂²×C₁₉	1	2	yes	complemented
492	#525	—	2	1	no	—
493	#525	C₂²×C₁₉	1	1	yes	characteristic
494	C₂×#121	—	2	1	no	—
495	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
496	C₂×#120	—	2	2	no	—
497	#520	C₂²×C₁₉	1	1	yes	characteristic, complemented
498	#453	—	2	8	no	—
499	#450	—	2	1	no	—
500	#450	—	2	1	no	—
501	#447	—	2	1	no	—
502	#447	—	2	1	no	—
503	C₂×#104	C₂²×C₁₉	1	2	yes	complemented
504	C₂×#104	C₂²×C₁₉	1	2	yes	complemented
505	C₂×#104	C₂²×C₁₉	1	2	yes	complemented
506	#418	C₂²×C₁₉	1	2	yes	complemented
507	C₂×#100	C₂²×C₁₉	1	2	yes	complemented
508	#407	C₂²×C₁₉	1	1	yes	characteristic, complemented
509	#392	—	2	2	no	—
510	#390	C₂²×C₁₉	1	2	yes	complemented
511	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
512	#343	C₂²×C₁₉	1	2	yes	complemented
513	#339	C₂²×C₁₉	1	2	yes	complemented
514	C₂×C₁₉	—	2	2	no	—
515	C₂×C₁₉	—	2	2	no	—
516	C₂×C₁₉	—	4	1	no	—
517	C₂×C₁₉	—	4	2	no	—
518	C₂×C₁₉	—	8	1	no	—
519	C₂×C₁₉	—	8	4	no	—
520	C₂×C₁₉	—	8	2	no	—
521	C₂×C₁₉	—	8	1	no	—
522	C₂×C₁₉	#2403	1	1	yes	characteristic
523	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
524	C₂×C₁₉	#3021	1	1	yes	characteristic
525	C₂⁵	—	2	1	no	—
526	H(5,𝔽₂)	—	2	4	no	—
527	H(5,𝔽₂)	—	4	2	no	—
528	C₂×#41	—	2	1	no	—
529	C₂×#41	—	2	1	no	—
530	C₂×#41	—	2	1	no	—
531	C₂×#41	—	2	1	no	—
532	C₂×#41	—	2	4	no	—
533	C₂×#41	—	4	2	no	—
534	C₂×#41	D₄×C₁₉	1	1	yes	characteristic, complemented
535	C₂×#41	D₄×C₁₉	1	1	yes	characteristic, complemented
536	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
537	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
538	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
539	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
540	C₂²×D₄	—	2	4	no	—
541	C₂²×D₄	—	2	1	no	—
542	C₂²×D₄	—	2	2	no	—
543	C₂²×D₄	—	2	2	no	—
544	C₂²×D₄	—	2	1	no	—
545	C₂²×D₄	—	2	1	no	—
546	C₂²×D₄	—	2	4	no	—
547	C₂²×D₄	—	2	1	no	—
548	C₂²×D₄	—	2	1	no	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	—	2	1	no	—
551	C₂²×D₄	—	2	1	no	—
552	C₂²×D₄	—	4	2	no	—
553	C₂²×D₄	D₄×C₁₉	1	2	yes	—
554	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic, complemented
555	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
556	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
557	C₂³×C₄	—	2	1	no	—
558	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
559	AGL(1,ℤ/8)	—	2	8	no	—
560	AGL(1,ℤ/8)	—	2	8	no	—
561	AGL(1,ℤ/8)	—	2	4	no	—
562	AGL(1,ℤ/8)	—	2	4	no	—
563	AGL(1,ℤ/8)	—	2	4	no	—
564	AGL(1,ℤ/8)	—	2	4	no	—
565	AGL(1,ℤ/8)	—	4	2	no	—
566	AGL(1,ℤ/8)	D₄×C₁₉	1	8	yes	complemented
567	C₂×SD₁₆	—	2	8	no	—
568	C₂×SD₁₆	—	2	2	no	—
569	C₂×SD₁₆	—	2	2	no	—
570	C₂×SD₁₆	—	2	2	no	—
571	C₂×D₈	—	2	8	no	—
572	C₂×D₈	—	2	2	no	—
573	C₂×D₈	—	2	2	no	—
574	C₂×D₈	—	2	2	no	—
575	C₂×M₁₆	—	2	1	no	—
576	C₂×M₁₆	—	2	4	no	—
577	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
578	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
579	C₂²×C₈	—	2	1	no	—
580	#127	—	2	2	no	—
581	#127	—	2	1	no	—
582	#127	—	2	4	no	—
583	#127	—	4	2	no	—
584	#124	—	2	2	no	—
585	#124	—	2	1	no	—
586	#123	—	2	2	no	—
587	#123	—	2	1	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	—	2	1	no	—
590	C₂²⋊Q₈	—	2	1	no	—
591	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
592	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	—	2	2	no	—
596	#121	—	2	2	no	—
597	#121	—	2	2	no	—
598	#121	—	2	1	no	—
599	#121	—	2	1	no	—
600	#121	—	2	1	no	—
601	#121	—	2	1	no	—
602	#121	—	2	1	no	—
603	#121	—	2	1	no	—
604	#121	—	2	2	no	—
605	#121	—	2	1	no	—
606	#121	—	2	1	no	—
607	#121	D₄×C₁₉	1	1	yes	characteristic, complemented
608	#121	D₄×C₁₉	1	1	yes	characteristic, complemented
609	#120	—	2	2	no	—
610	#120	—	2	2	no	—
611	#120	—	2	2	no	—
612	#120	—	2	1	no	—
613	#120	—	2	2	no	—
614	#120	—	4	8	no	—
615	C₄×Q₈	—	2	1	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	1	no	—
622	#117	—	2	1	no	—
623	#117	C₂³×C₁₉	1	1	yes	characteristic
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	—	2	2	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	4	no	—
629	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
630	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
631	#104	—	2	4	no	—
632	#104	—	2	4	no	—
633	#104	—	4	2	no	—
634	#102	—	2	2	no	—
635	#102	—	2	2	no	—
636	#100	—	2	4	no	—
637	C₂²⋊C₈	—	2	1	no	—
638	C₂²⋊C₈	—	2	1	no	—
639	#95	—	2	1	no	—
640	C₁₉	#23876	1	1	yes	characteristic, direct product factor, Sylow
641	C₂⁴	—	2	2	no	—
642	C₂⁴	—	2	2	no	—
643	C₂⁴	—	2	1	no	—
644	C₂⁴	—	4	4	no	—
645	C₂⁴	—	4	4	no	—
646	C₂⁴	—	4	1	no	—
647	C₂⁴	—	4	1	no	—
648	C₂⁴	—	8	2	no	—
649	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
650	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
651	#41	—	2	2	no	—
652	#41	—	2	2	no	—
653	#41	—	2	2	no	—
654	#41	—	2	2	no	—
655	#41	—	2	2	no	—
656	#41	—	2	2	no	—
657	#41	—	2	2	no	—
658	#41	—	4	4	no	—
659	#41	—	4	1	no	—
660	#41	—	4	1	no	—
661	#41	—	4	4	no	—
662	#41	—	4	4	no	—
663	#41	—	4	2	no	—
664	#41	—	4	2	no	—
665	#41	C₂×D₄×C₁₉	1	4	yes	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	4	1	no	—
669	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
670	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
671	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	4	1	no	—
700	C₂×D₄	—	4	4	no	—
701	C₂×D₄	—	4	4	no	—
702	C₂×D₄	—	4	4	no	—
703	C₂×D₄	—	4	4	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	—	4	8	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	—	4	8	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	4	4	no	—
712	C₂×D₄	—	4	8	no	—
713	C₂×D₄	—	4	1	no	—
714	C₂×D₄	—	4	1	no	—
715	C₂×D₄	—	8	4	no	—
716	C₂×D₄	—	8	4	no	—
717	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
718	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
719	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
720	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	complemented
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	4	4	no	—
733	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
734	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
735	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
736	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
737	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
738	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
740	SD₁₆	—	2	8	no	—
741	SD₁₆	—	2	8	no	—
742	SD₁₆	—	4	4	no	—
743	D₈	—	2	8	no	—
744	D₈	—	2	8	no	—
745	D₈	—	4	4	no	—
746	M₁₆	—	2	4	no	—
747	M₁₆	—	2	2	no	—
748	M₁₆	—	2	2	no	—
749	M₁₆	—	2	2	no	—
750	M₁₆	C₂×D₄×C₁₉	1	4	yes	complemented
751	C₂×C₈	—	2	4	no	—
752	C₂×C₈	—	2	2	no	—
753	C₂×C₈	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
761	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	1	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	1	no	—
771	C₂²⋊C₄	—	2	1	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	1	no	—
775	C₂²⋊C₄	—	4	8	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	1	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	2	4	no	—
787	C₂³	—	2	4	no	—
788	C₂³	—	4	1	no	—
789	C₂³	—	4	2	no	—
790	C₂³	—	4	4	no	—
791	C₂³	—	4	4	no	—
792	C₂³	—	4	4	no	—
793	C₂³	—	4	4	no	—
794	C₂³	—	4	4	no	—
795	C₂³	—	4	2	no	—
796	C₂³	—	4	2	no	—
797	C₂³	—	4	2	no	—
798	C₂³	—	4	2	no	—
799	C₂³	—	4	2	no	—
800	C₂³	—	8	1	no	—
801	C₂³	—	8	2	no	—
802	C₂³	—	8	2	no	—
803	C₂³	—	8	2	no	—
804	C₂³	—	8	2	no	—
805	C₂³	—	8	2	no	—
806	C₂³	—	8	16	no	—
807	C₂³	—	8	2	no	—
808	C₂³	C₁₉×#120	1	1	yes	characteristic
809	C₂³	C₁₉×#120	1	1	yes	characteristic
810	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
811	Q₈	—	2	1	no	—
812	Q₈	—	2	1	no	—
813	Q₈	—	2	1	no	—
814	Q₈	—	2	2	no	—
815	Q₈	—	4	2	no	—
816	Q₈	C₁₉×#120	1	2	yes	complemented
817	D₄	—	2	4	no	—
818	D₄	—	2	1	no	—
819	D₄	—	2	4	no	—
820	D₄	—	2	1	no	—
821	D₄	—	2	1	no	—
822	D₄	—	2	2	no	—
823	D₄	—	2	4	no	—
824	D₄	—	4	2	no	—
825	D₄	—	4	2	no	—
826	D₄	—	4	4	no	—
827	D₄	—	4	4	no	—
828	D₄	—	4	4	no	—
829	D₄	—	4	2	no	—
830	D₄	—	4	4	no	—
831	D₄	—	4	4	no	—
832	D₄	—	4	2	no	—
833	D₄	—	4	2	no	—
834	D₄	—	4	2	no	—
835	D₄	—	4	1	no	—
836	D₄	—	4	2	no	—
837	D₄	—	4	1	no	—
838	D₄	—	4	2	no	—
839	D₄	—	4	2	no	—
840	D₄	—	8	2	no	—
841	D₄	—	8	1	no	—
842	D₄	—	8	2	no	—
843	D₄	—	8	2	no	—
844	D₄	—	8	2	no	—
845	D₄	—	8	16	no	—
846	D₄	C₁₉×#120	1	2	yes	complemented
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	4	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	4	4	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	4	2	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	—	4	1	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	8	2	no	—
873	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
874	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
875	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
876	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
877	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
878	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
879	C₈	—	2	4	no	—
880	C₈	—	4	2	no	—
881	C₂²	—	2	1	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	2	1	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	1	no	—
888	C₂²	—	2	1	no	—
889	C₂²	—	4	4	no	—
890	C₂²	—	4	8	no	—
891	C₂²	—	4	1	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	4	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	1	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	8	4	no	—
904	C₂²	—	8	4	no	—
905	C₂²	—	8	4	no	—
906	C₂²	—	8	8	no	—
907	C₂²	—	8	8	no	—
908	C₂²	—	8	2	no	—
909	C₂²	—	8	2	no	—
910	C₂²	—	16	4	no	—
911	C₂²	C₁₉×#453	1	2	yes	complemented
912	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
913	C₂²	D₄²×C₁₉	1	2	yes	—
914	C₄	—	2	1	no	—
915	C₄	—	2	1	no	—
916	C₄	—	2	2	no	—
917	C₄	—	4	4	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	1	no	—
923	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
924	C₄	C₁₉×#534	1	1	yes	characteristic
925	C₄	D₄²×C₁₉	1	2	yes	—
926	C₂	—	2	2	no	—
927	C₂	—	2	2	no	—
928	C₂	—	4	1	no	—
929	C₂	—	4	2	no	—
930	C₂	—	8	4	no	—
931	C₂	—	8	1	no	—
932	C₂	—	8	2	no	—
933	C₂	—	8	1	no	—
934	C₂	C₁₉×#2403	1	1	yes	characteristic
935	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
936	C₂	C₁₉×#3021	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
2. C₁₉×#3488	C₂	semidirect
3. C₂×C₁₉×#453	C₂	semidirect
4. C₁₉×#3003	C₂	semidirect
5. C₁₉×#2433	C₂	semidirect
6. C₁₉×#2006	C₂	semidirect
7. C₁₉×#2002	C₂	semidirect
8. C₁₉×#1900	C₂	semidirect
9. C₁₉×#1883	C₂	semidirect
10. C₁₉×#1871	C₂	semidirect
11. C₁₉×#1789	C₂	semidirect
12. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
14. C₂³×D₄×C₁₉	C₂²	semidirect
19. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂²×M₁₆×C₁₉	C₂²	semidirect
31. C₁₉×#537	C₂²	semidirect
33. C₁₉×#535	C₂²	semidirect
34. C₂×C₁₉×#127	C₂²	semidirect
40. C₁₉×#520	C₂²	semidirect
46. C₂×C₁₉×#104	C₂²	semidirect
47. C₂×C₁₉×#104	C₂²	semidirect
48. C₂×C₁₉×#104	C₂²	semidirect
49. C₁₉×#418	C₂²	semidirect
50. C₂×C₁₉×#100	C₂²	semidirect
51. C₁₉×#407	C₂²	semidirect
53. C₁₉×#390	C₂²	semidirect
54. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
55. C₁₉×#343	C₂²	semidirect
56. C₁₉×#339	C₂²	semidirect
66. C₂×#41×C₁₉	D₄	semidirect
67. C₂×#41×C₁₉	D₄	semidirect
71. C₂²×Q₈×C₁₉	D₄	semidirect
86. C₂²×D₄×C₁₉	D₄	semidirect
98. C₁₉×AGL(1,ℤ/8)	D₄	semidirect
123. C₁₉×C₂²⋊Q₈	D₄	semidirect
124. C₁₉×C₂²⋊Q₈	D₄	semidirect
139. C₁₉×#121	D₄	semidirect
140. C₁₉×#121	D₄	semidirect
251. C₂×D₄×C₁₉	C₂×D₄	semidirect
281. M₁₆×C₁₉	C₂×D₄	semidirect
311. #23876	C₁₉	direct (N × H)
348. Q₈×C₁₉	#120	semidirect
378. D₄×C₁₉	#120	semidirect
413. C₂²×AGL(1,ℤ/8)	C₂×C₁₉	semidirect
414. #3488	C₂×C₁₉	semidirect
415. C₂×#453	C₂×C₁₉	semidirect
416. #3003	C₂×C₁₉	semidirect
417. #2433	C₂×C₁₉	semidirect
418. #2006	C₂×C₁₉	semidirect
419. #2002	C₂×C₁₉	semidirect
420. #1900	C₂×C₁₉	semidirect
421. #1883	C₂×C₁₉	semidirect
422. #1871	C₂×C₁₉	semidirect
423. #1789	C₂×C₁₉	semidirect
454. C₂²×C₁₉	#453	semidirect
469. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
471. C₂³×D₄	C₂²×C₁₉	semidirect
476. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
477. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
480. C₂²×M₁₆	C₂²×C₁₉	semidirect
488. #537	C₂²×C₁₉	semidirect
490. #535	C₂²×C₁₉	semidirect
491. C₂×#127	C₂²×C₁₉	semidirect
497. #520	C₂²×C₁₉	semidirect
503. C₂×#104	C₂²×C₁₉	semidirect
504. C₂×#104	C₂²×C₁₉	semidirect
505. C₂×#104	C₂²×C₁₉	semidirect
506. #418	C₂²×C₁₉	semidirect
507. C₂×#100	C₂²×C₁₉	semidirect
508. #407	C₂²×C₁₉	semidirect
510. #390	C₂²×C₁₉	semidirect
511. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
512. #343	C₂²×C₁₉	semidirect
513. #339	C₂²×C₁₉	semidirect
534. C₂×#41	D₄×C₁₉	semidirect
535. C₂×#41	D₄×C₁₉	semidirect
539. C₂²×Q₈	D₄×C₁₉	semidirect
554. C₂²×D₄	D₄×C₁₉	semidirect
566. AGL(1,ℤ/8)	D₄×C₁₉	semidirect
591. C₂²⋊Q₈	D₄×C₁₉	semidirect
592. C₂²⋊Q₈	D₄×C₁₉	semidirect
607. #121	D₄×C₁₉	semidirect
608. #121	D₄×C₁₉	semidirect
640. C₁₉	#23876	direct (N × H)
720. C₂×D₄	C₂×D₄×C₁₉	semidirect
750. M₁₆	C₂×D₄×C₁₉	semidirect
816. Q₈	C₁₉×#120	semidirect
846. D₄	C₁₉×#120	semidirect
911. C₂²	C₁₉×#453	semidirect

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
C₁₉×#3488	2
C₂×C₁₉×#453	2
C₁₉×#3003	2
C₁₉×#2433	2
C₁₉×#2006	2
C₁₉×#2002	2
C₁₉×#1900	2
C₁₉×#1883	2
C₁₉×#1871	2
C₁₉×#1789	2
#23876	19

Subgroups — C19×#23876 #18029835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23876 #18029835