Subgroups — C₁₉×#24458 #18030417

Order 4864.

1328 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#577	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#473	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3046	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#455	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3011	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2897	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2051	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2046	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2015	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2003	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1908	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1882	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1876	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1866	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1793	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
18	C₁₉×#577	—	2	4	no	—
19	C₁₉×#577	—	2	4	no	—
20	C₂×C₁₉×#137	—	2	1	no	—
21	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
25	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#135	—	2	1	no	—
27	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
28	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
29	C₂²×SD₁₆×C₁₉	—	2	1	no	—
30	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
33	C₁₉×#536	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
35	C₁₉×#520	C₂²	1	1	yes	characteristic
36	C₁₉×#473	—	2	4	no	—
37	C₁₉×#464	—	2	1	no	—
38	C₁₉×#463	—	2	1	no	—
39	C₁₉×#462	—	2	1	no	—
40	C₁₉×#461	—	2	1	no	—
41	C₁₉×#455	—	2	4	no	—
42	C₁₉×#452	—	2	1	no	—
43	C₁₉×#452	—	2	1	no	—
44	C₁₉×#451	—	2	1	no	—
45	C₁₉×#451	—	2	1	no	—
46	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#424	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
49	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×#419	C₂²	1	1	yes	characteristic, complemented
52	C₁₉×#418	—	2	1	no	—
53	C₁₉×#418	C₂²	1	1	yes	characteristic
54	C₁₉×#417	—	2	1	no	—
55	C₁₉×#417	C₂²	1	1	yes	characteristic
56	C₁₉×#417	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#416	—	2	1	no	—
58	C₁₉×#416	C₂²	1	1	yes	characteristic
59	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₁₉×#102	—	2	1	no	—
61	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
62	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
65	C₁₉×#408	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#391	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#343	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#341	C₂²	1	1	yes	characteristic, complemented
69	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
70	C₁₉×#336	C₂²	1	1	yes	characteristic, complemented
71	C₁₉×2₋¹⁺⁴	—	2	2	no	—
72	C₁₉×2₋¹⁺⁴	—	2	2	no	—
73	C₁₉×2₋¹⁺⁴	—	2	2	no	—
74	C₁₉×2₋¹⁺⁴	—	4	1	no	—
75	C₁₉×H(5,𝔽₂)	—	2	2	no	—
76	C₁₉×H(5,𝔽₂)	—	2	2	no	—
77	C₁₉×H(5,𝔽₂)	—	4	1	no	—
78	C₁₉×H(5,𝔽₂)	D₄	1	4	yes	—
79	C₂×#41×C₁₉	—	2	1	no	—
80	C₂×#41×C₁₉	—	2	1	no	—
81	C₂×#41×C₁₉	—	2	1	no	—
82	C₂×#41×C₁₉	—	2	1	no	—
83	C₂×#41×C₁₉	—	4	1	no	—
84	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₁₉	—	2	1	no	—
88	C₂²×Q₈×C₁₉	—	2	1	no	—
89	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₉	—	2	1	no	—
92	C₂²×D₄×C₁₉	—	2	1	no	—
93	C₂²×D₄×C₁₉	—	4	1	no	—
94	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₁₉×#137	—	2	8	no	—
96	C₁₉×#137	—	2	2	no	—
97	C₁₉×#137	—	2	2	no	—
98	C₁₉×#137	—	2	2	no	—
99	C₁₉×#137	—	2	2	no	—
100	C₁₉×#137	—	2	2	no	—
101	C₁₉×#137	D₄	1	4	yes	—
102	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
103	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
104	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
105	C₁₉×#135	—	2	8	no	—
106	C₁₉×#135	—	2	2	no	—
107	C₁₉×#135	—	2	2	no	—
108	C₂×Q₁₆×C₁₉	—	2	1	no	—
109	C₂×Q₁₆×C₁₉	—	2	1	no	—
110	C₂×Q₁₆×C₁₉	—	2	1	no	—
111	C₂×Q₁₆×C₁₉	—	2	2	no	—
112	C₂×Q₁₆×C₁₉	—	2	1	no	—
113	C₂×Q₁₆×C₁₉	—	2	1	no	—
114	C₂×Q₁₆×C₁₉	—	4	1	no	—
115	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
116	C₂×SD₁₆×C₁₉	—	2	8	no	—
117	C₂×SD₁₆×C₁₉	—	2	1	no	—
118	C₂×SD₁₆×C₁₉	—	2	2	no	—
119	C₂×SD₁₆×C₁₉	—	2	1	no	—
120	C₂×SD₁₆×C₁₉	—	2	2	no	—
121	C₂×SD₁₆×C₁₉	—	2	1	no	—
122	C₂×SD₁₆×C₁₉	—	2	1	no	—
123	C₂×SD₁₆×C₁₉	—	2	1	no	—
124	C₂×SD₁₆×C₁₉	—	2	1	no	—
125	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
126	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
127	C₂×D₈×C₁₉	—	2	1	no	—
128	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
129	C₁₉×#131	—	2	2	no	—
130	C₁₉×#131	—	2	2	no	—
131	C₁₉×#131	—	2	2	no	—
132	C₁₉×#131	—	4	1	no	—
133	C₂×M₁₆×C₁₉	—	2	1	no	—
134	C₂×M₁₆×C₁₉	—	2	1	no	—
135	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
136	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₁₉	—	2	1	no	—
140	C₂²×C₈×C₁₉	—	2	1	no	—
141	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₁₉×C₄⋊Q₈	—	2	1	no	—
144	C₁₉×#124	—	2	2	no	—
145	C₁₉×#124	—	2	1	no	—
146	C₁₉×#124	—	4	1	no	—
147	C₁₉×#123	—	4	1	no	—
148	C₁₉×C₂²⋊Q₈	—	2	1	no	—
149	C₁₉×C₂²⋊Q₈	—	2	1	no	—
150	C₄×Q₈×C₁₉	—	2	1	no	—
151	C₄×D₄×C₁₉	—	2	1	no	—
152	C₄×D₄×C₁₉	—	4	1	no	—
153	C₁₉×#117	—	2	1	no	—
154	C₁₉×#117	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
158	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
159	C₁₉×#108	—	2	2	no	—
160	C₁₉×C₄⋊C₈	—	2	1	no	—
161	C₁₉×C₄⋊C₈	—	2	1	no	—
162	C₁₉×#104	—	2	2	no	—
163	C₁₉×#104	—	2	2	no	—
164	C₁₉×#104	—	4	1	no	—
165	C₁₉×#103	—	2	1	no	—
166	C₁₉×#103	—	2	1	no	—
167	C₁₉×#103	—	2	1	no	—
168	C₁₉×#103	—	2	1	no	—
169	C₁₉×#103	—	2	1	no	—
170	C₁₉×#103	—	2	1	no	—
171	C₁₉×#103	D₄	1	1	yes	characteristic
172	C₁₉×#103	D₄	1	1	yes	characteristic
173	C₁₉×#102	—	2	1	no	—
174	C₁₉×#102	—	2	1	no	—
175	C₁₉×#102	—	2	1	no	—
176	C₁₉×#102	—	2	1	no	—
177	C₁₉×#102	—	2	1	no	—
178	C₁₉×#102	—	2	1	no	—
179	C₁₉×#102	D₄	1	1	yes	characteristic
180	C₁₉×#102	D₄	1	1	yes	characteristic
181	C₁₉×#101	—	2	2	no	—
182	C₁₉×#101	—	2	2	no	—
183	C₁₉×#100	—	2	2	no	—
184	C₁₉×C₂²⋊C₈	—	2	1	no	—
185	C₁₉×C₂²⋊C₈	—	2	1	no	—
186	C₁₉×#95	—	4	1	no	—
187	C₂⁴×C₁₉	—	2	1	no	—
188	C₂⁴×C₁₉	—	4	1	no	—
189	#41×C₁₉	—	2	1	no	—
190	#41×C₁₉	—	2	1	no	—
191	#41×C₁₉	—	2	1	no	—
192	#41×C₁₉	—	2	1	no	—
193	#41×C₁₉	—	2	4	no	—
194	#41×C₁₉	—	2	4	no	—
195	#41×C₁₉	—	2	4	no	—
196	#41×C₁₉	—	2	1	no	—
197	#41×C₁₉	—	2	1	no	—
198	#41×C₁₉	—	2	1	no	—
199	#41×C₁₉	—	2	1	no	—
200	#41×C₁₉	—	4	2	no	—
201	#41×C₁₉	—	4	4	no	—
202	#41×C₁₉	—	4	2	no	—
203	#41×C₁₉	—	4	2	no	—
204	#41×C₁₉	—	4	2	no	—
205	#41×C₁₉	—	4	4	no	—
206	#41×C₁₉	—	4	2	no	—
207	#41×C₁₉	C₂×D₄	1	2	yes	—
208	#41×C₁₉	C₂×D₄	1	2	yes	—
209	#41×C₁₉	C₂×D₄	1	2	yes	—
210	#41×C₁₉	#41	1	2	yes	—
211	C₂×Q₈×C₁₉	—	2	1	no	—
212	C₂×Q₈×C₁₉	—	2	4	no	—
213	C₂×Q₈×C₁₉	—	2	1	no	—
214	C₂×Q₈×C₁₉	—	2	1	no	—
215	C₂×Q₈×C₁₉	—	2	1	no	—
216	C₂×Q₈×C₁₉	—	2	1	no	—
217	C₂×Q₈×C₁₉	—	2	1	no	—
218	C₂×Q₈×C₁₉	—	2	1	no	—
219	C₂×Q₈×C₁₉	—	2	1	no	—
220	C₂×Q₈×C₁₉	—	2	1	no	—
221	C₂×Q₈×C₁₉	—	2	1	no	—
222	C₂×Q₈×C₁₉	—	2	1	no	—
223	C₂×Q₈×C₁₉	—	4	1	no	—
224	C₂×Q₈×C₁₉	—	4	2	no	—
225	C₂×Q₈×C₁₉	—	4	2	no	—
226	C₂×Q₈×C₁₉	—	4	2	no	—
227	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
228	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
230	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
231	C₂×D₄×C₁₉	—	2	1	no	—
232	C₂×D₄×C₁₉	—	2	1	no	—
233	C₂×D₄×C₁₉	—	2	4	no	—
234	C₂×D₄×C₁₉	—	2	4	no	—
235	C₂×D₄×C₁₉	—	2	1	no	—
236	C₂×D₄×C₁₉	—	2	1	no	—
237	C₂×D₄×C₁₉	—	2	1	no	—
238	C₂×D₄×C₁₉	—	2	1	no	—
239	C₂×D₄×C₁₉	—	2	1	no	—
240	C₂×D₄×C₁₉	—	2	1	no	—
241	C₂×D₄×C₁₉	—	4	2	no	—
242	C₂×D₄×C₁₉	—	4	2	no	—
243	C₂×D₄×C₁₉	—	4	1	no	—
244	C₂×D₄×C₁₉	—	4	1	no	—
245	C₂×D₄×C₁₉	—	4	4	no	—
246	C₂×D₄×C₁₉	—	4	4	no	—
247	C₂×D₄×C₁₉	—	4	1	no	—
248	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
249	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
250	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
251	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₁₉	—	2	1	no	—
253	C₂²×C₄×C₁₉	—	2	1	no	—
254	C₂²×C₄×C₁₉	—	2	1	no	—
255	C₂²×C₄×C₁₉	—	2	1	no	—
256	C₂²×C₄×C₁₉	—	2	1	no	—
257	C₂²×C₄×C₁₉	—	2	1	no	—
258	C₂²×C₄×C₁₉	—	2	1	no	—
259	C₂²×C₄×C₁₉	—	4	1	no	—
260	C₂²×C₄×C₁₉	—	4	1	no	—
261	C₂²×C₄×C₁₉	—	4	1	no	—
262	C₂²×C₄×C₁₉	—	4	1	no	—
263	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
264	Q₁₆×C₁₉	—	2	4	no	—
265	Q₁₆×C₁₉	—	2	2	no	—
266	Q₁₆×C₁₉	—	4	2	no	—
267	Q₁₆×C₁₉	—	4	2	no	—
268	Q₁₆×C₁₉	—	4	2	no	—
269	Q₁₆×C₁₉	—	4	2	no	—
270	SD₁₆×C₁₉	—	2	4	no	—
271	SD₁₆×C₁₉	—	2	4	no	—
272	SD₁₆×C₁₉	—	2	4	no	—
273	SD₁₆×C₁₉	—	2	2	no	—
274	SD₁₆×C₁₉	—	2	2	no	—
275	SD₁₆×C₁₉	—	2	4	no	—
276	SD₁₆×C₁₉	—	4	2	no	—
277	SD₁₆×C₁₉	—	4	2	no	—
278	D₈×C₁₉	—	2	4	no	—
279	D₈×C₁₉	—	2	2	no	—
280	M₁₆×C₁₉	—	2	4	no	—
281	M₁₆×C₁₉	—	2	1	no	—
282	M₁₆×C₁₉	—	2	1	no	—
283	M₁₆×C₁₉	—	2	1	no	—
284	M₁₆×C₁₉	—	2	1	no	—
285	M₁₆×C₁₉	—	2	1	no	—
286	M₁₆×C₁₉	—	2	1	no	—
287	M₁₆×C₁₉	—	2	1	no	—
288	M₁₆×C₁₉	—	4	2	no	—
289	M₁₆×C₁₉	C₂×D₄	1	2	yes	—
290	C₂×C₈×C₁₉	—	2	4	no	—
291	C₂×C₈×C₁₉	—	2	1	no	—
292	C₂×C₈×C₁₉	—	2	1	no	—
293	C₂×C₈×C₁₉	—	2	1	no	—
294	C₂×C₈×C₁₉	—	2	1	no	—
295	C₂×C₈×C₁₉	—	2	1	no	—
296	C₂×C₈×C₁₉	—	2	1	no	—
297	C₂×C₈×C₁₉	—	2	1	no	—
298	C₂×C₈×C₁₉	—	2	1	no	—
299	C₂×C₈×C₁₉	—	4	2	no	—
300	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
301	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
302	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
303	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
304	C₄⋊C₄×C₁₉	—	2	1	no	—
305	C₄⋊C₄×C₁₉	—	2	1	no	—
306	C₄⋊C₄×C₁₉	—	4	1	no	—
307	C₄⋊C₄×C₁₉	—	4	1	no	—
308	C₄⋊C₄×C₁₉	—	4	1	no	—
309	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
311	C₂²⋊C₄×C₁₉	—	2	1	no	—
312	C₂²⋊C₄×C₁₉	—	4	1	no	—
313	C₂²⋊C₄×C₁₉	—	4	1	no	—
314	C₂²⋊C₄×C₁₉	—	4	1	no	—
315	C₂²⋊C₄×C₁₉	—	4	4	no	—
316	C₄²×C₁₉	—	2	1	no	—
317	C₄²×C₁₉	—	2	1	no	—
318	C₄²×C₁₉	—	2	1	no	—
319	C₄²×C₁₉	—	4	1	no	—
320	#24458	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
321	C₂³×C₁₉	—	2	1	no	—
322	C₂³×C₁₉	—	2	1	no	—
323	C₂³×C₁₉	—	2	1	no	—
324	C₂³×C₁₉	—	2	2	no	—
325	C₂³×C₁₉	—	4	4	no	—
326	C₂³×C₁₉	—	4	1	no	—
327	C₂³×C₁₉	—	4	1	no	—
328	C₂³×C₁₉	—	8	1	no	—
329	C₂³×C₁₉	—	8	1	no	—
330	C₂³×C₁₉	—	16	1	no	—
331	C₂³×C₁₉	—	16	1	no	—
332	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
333	Q₈×C₁₉	—	2	1	no	—
334	Q₈×C₁₉	—	2	1	no	—
335	Q₈×C₁₉	—	2	2	no	—
336	Q₈×C₁₉	—	2	1	no	—
337	Q₈×C₁₉	—	2	2	no	—
338	Q₈×C₁₉	—	2	1	no	—
339	Q₈×C₁₉	—	4	4	no	—
340	Q₈×C₁₉	—	4	1	no	—
341	Q₈×C₁₉	—	4	1	no	—
342	Q₈×C₁₉	—	4	1	no	—
343	Q₈×C₁₉	—	4	1	no	—
344	Q₈×C₁₉	—	4	1	no	—
345	Q₈×C₁₉	—	4	1	no	—
346	Q₈×C₁₉	#120	1	2	yes	—
347	Q₈×C₁₉	#121	1	2	yes	—
348	D₄×C₁₉	—	2	2	no	—
349	D₄×C₁₉	—	2	2	no	—
350	D₄×C₁₉	—	2	2	no	—
351	D₄×C₁₉	—	2	2	no	—
352	D₄×C₁₉	—	2	1	no	—
353	D₄×C₁₉	—	2	2	no	—
354	D₄×C₁₉	—	2	2	no	—
355	D₄×C₁₉	—	2	1	no	—
356	D₄×C₁₉	—	2	1	no	—
357	D₄×C₁₉	—	2	1	no	—
358	D₄×C₁₉	—	4	4	no	—
359	D₄×C₁₉	—	4	4	no	—
360	D₄×C₁₉	—	4	4	no	—
361	D₄×C₁₉	—	4	1	no	—
362	D₄×C₁₉	—	4	1	no	—
363	D₄×C₁₉	—	4	1	no	—
364	D₄×C₁₉	—	4	1	no	—
365	D₄×C₁₉	#120	1	2	yes	—
366	D₄×C₁₉	#121	1	2	yes	—
367	C₂×C₄×C₁₉	—	2	1	no	—
368	C₂×C₄×C₁₉	—	2	1	no	—
369	C₂×C₄×C₁₉	—	2	2	no	—
370	C₂×C₄×C₁₉	—	2	2	no	—
371	C₂×C₄×C₁₉	—	2	2	no	—
372	C₂×C₄×C₁₉	—	2	2	no	—
373	C₂×C₄×C₁₉	—	2	1	no	—
374	C₂×C₄×C₁₉	—	2	1	no	—
375	C₂×C₄×C₁₉	—	2	1	no	—
376	C₂×C₄×C₁₉	—	2	2	no	—
377	C₂×C₄×C₁₉	—	4	4	no	—
378	C₂×C₄×C₁₉	—	4	4	no	—
379	C₂×C₄×C₁₉	—	4	4	no	—
380	C₂×C₄×C₁₉	—	4	1	no	—
381	C₂×C₄×C₁₉	—	4	1	no	—
382	C₂×C₄×C₁₉	—	4	1	no	—
383	C₂×C₄×C₁₉	—	4	1	no	—
384	C₂×C₄×C₁₉	—	4	1	no	—
385	C₂×C₄×C₁₉	—	4	1	no	—
386	C₂×C₄×C₁₉	—	4	1	no	—
387	C₂×C₄×C₁₉	—	4	1	no	—
388	C₂×C₄×C₁₉	—	4	1	no	—
389	C₂×C₄×C₁₉	—	4	1	no	—
390	C₂×C₄×C₁₉	—	4	1	no	—
391	C₂×C₄×C₁₉	—	8	1	no	—
392	C₂×C₄×C₁₉	—	16	1	no	—
393	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
398	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
399	C₈×C₁₉	—	2	1	no	—
400	C₈×C₁₉	—	2	2	no	—
401	C₈×C₁₉	—	2	1	no	—
402	C₈×C₁₉	—	2	1	no	—
403	C₈×C₁₉	—	2	1	no	—
404	C₈×C₁₉	—	4	1	no	—
405	C₈×C₁₉	—	4	1	no	—
406	C₈×C₁₉	—	4	1	no	—
407	C₂×#577	C₂×C₁₉	1	1	yes	characteristic
408	C₂×#473	C₂×C₁₉	1	1	yes	characteristic, complemented
409	#3046	C₂×C₁₉	1	1	yes	characteristic, complemented
410	C₂×#455	C₂×C₁₉	1	1	yes	characteristic, complemented
411	#3011	C₂×C₁₉	1	1	yes	characteristic, complemented
412	#2897	C₂×C₁₉	1	1	yes	characteristic, complemented
413	#2051	C₂×C₁₉	1	1	yes	characteristic, complemented
414	#2046	C₂×C₁₉	1	1	yes	characteristic, complemented
415	#2015	C₂×C₁₉	1	1	yes	characteristic, complemented
416	#2003	C₂×C₁₉	1	1	yes	characteristic, complemented
417	#1908	C₂×C₁₉	1	1	yes	characteristic, complemented
418	#1882	C₂×C₁₉	1	1	yes	characteristic, complemented
419	#1876	C₂×C₁₉	1	1	yes	characteristic, complemented
420	#1866	C₂×C₁₉	1	1	yes	characteristic, complemented
421	#1793	C₂×C₁₉	1	1	yes	characteristic, complemented
422	C₂²×C₁₉	—	2	1	no	—
423	C₂²×C₁₉	—	2	1	no	—
424	C₂²×C₁₉	—	2	2	no	—
425	C₂²×C₁₉	—	2	2	no	—
426	C₂²×C₁₉	—	4	1	no	—
427	C₂²×C₁₉	—	4	1	no	—
428	C₂²×C₁₉	—	4	1	no	—
429	C₂²×C₁₉	—	4	1	no	—
430	C₂²×C₁₉	—	4	1	no	—
431	C₂²×C₁₉	—	4	2	no	—
432	C₂²×C₁₉	—	4	1	no	—
433	C₂²×C₁₉	—	4	1	no	—
434	C₂²×C₁₉	—	8	2	no	—
435	C₂²×C₁₉	—	8	1	no	—
436	C₂²×C₁₉	—	8	1	no	—
437	C₂²×C₁₉	—	16	1	no	—
438	C₂²×C₁₉	—	16	4	no	—
439	C₂²×C₁₉	#534	1	1	yes	characteristic
440	C₂²×C₁₉	D₄²	1	1	yes	characteristic
441	C₂²×C₁₉	#546	1	1	yes	characteristic
442	C₄×C₁₉	—	2	2	no	—
443	C₄×C₁₉	—	2	2	no	—
444	C₄×C₁₉	—	4	1	no	—
445	C₄×C₁₉	—	4	2	no	—
446	C₄×C₁₉	—	4	1	no	—
447	C₄×C₁₉	—	4	1	no	—
448	C₄×C₁₉	—	8	1	no	—
449	C₄×C₁₉	—	8	1	no	—
450	C₄×C₁₉	—	8	1	no	—
451	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
452	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
453	C₄×C₁₉	D₄²	1	1	yes	characteristic
454	C₄×C₁₉	#546	1	1	yes	characteristic
455	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic
456	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
457	#577	—	2	4	no	—
458	#577	—	2	4	no	—
459	C₂×#137	—	2	1	no	—
460	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
461	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
462	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
463	C₂×AGL(1,ℤ/8)	—	2	1	no	—
464	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
465	C₂×#135	—	2	1	no	—
466	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
467	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
468	C₂²×SD₁₆	—	2	1	no	—
469	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
470	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
471	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
472	#536	C₂²×C₁₉	1	1	yes	characteristic, complemented
473	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
474	#520	C₂²×C₁₉	1	1	yes	characteristic
475	#473	—	2	4	no	—
476	#464	—	2	1	no	—
477	#463	—	2	1	no	—
478	#462	—	2	1	no	—
479	#461	—	2	1	no	—
480	#455	—	2	4	no	—
481	#452	—	2	1	no	—
482	#452	—	2	1	no	—
483	#451	—	2	1	no	—
484	#451	—	2	1	no	—
485	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic, complemented
486	#424	C₂²×C₁₉	1	1	yes	characteristic, complemented
487	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
488	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
489	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
490	#419	C₂²×C₁₉	1	1	yes	characteristic, complemented
491	#418	—	2	1	no	—
492	#418	C₂²×C₁₉	1	1	yes	characteristic
493	#417	—	2	1	no	—
494	#417	C₂²×C₁₉	1	1	yes	characteristic
495	#417	C₂²×C₁₉	1	1	yes	characteristic, complemented
496	#416	—	2	1	no	—
497	#416	C₂²×C₁₉	1	1	yes	characteristic
498	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
499	C₂×#102	—	2	1	no	—
500	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
501	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic, complemented
502	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic, complemented
503	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
504	#408	C₂²×C₁₉	1	1	yes	characteristic, complemented
505	#391	C₂²×C₁₉	1	1	yes	characteristic, complemented
506	#343	C₂²×C₁₉	1	1	yes	characteristic, complemented
507	#341	C₂²×C₁₉	1	1	yes	characteristic, complemented
508	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
509	#336	C₂²×C₁₉	1	1	yes	characteristic, complemented
510	C₂×C₁₉	—	2	1	no	—
511	C₂×C₁₉	—	2	1	no	—
512	C₂×C₁₉	—	4	2	no	—
513	C₂×C₁₉	—	4	2	no	—
514	C₂×C₁₉	—	8	1	no	—
515	C₂×C₁₉	—	8	2	no	—
516	C₂×C₁₉	#2410	1	1	yes	characteristic
517	C₂×C₁₉	#3289	1	1	yes	characteristic
518	C₂×C₁₉	#3290	1	1	yes	characteristic
519	2₋¹⁺⁴	—	2	2	no	—
520	2₋¹⁺⁴	—	2	2	no	—
521	2₋¹⁺⁴	—	2	2	no	—
522	2₋¹⁺⁴	—	4	1	no	—
523	H(5,𝔽₂)	—	2	2	no	—
524	H(5,𝔽₂)	—	2	2	no	—
525	H(5,𝔽₂)	—	4	1	no	—
526	H(5,𝔽₂)	D₄×C₁₉	1	4	yes	—
527	C₂×#41	—	2	1	no	—
528	C₂×#41	—	2	1	no	—
529	C₂×#41	—	2	1	no	—
530	C₂×#41	—	2	1	no	—
531	C₂×#41	—	4	1	no	—
532	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
533	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
534	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
535	C₂²×Q₈	—	2	1	no	—
536	C₂²×Q₈	—	2	1	no	—
537	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
538	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	—	2	1	no	—
541	C₂²×D₄	—	4	1	no	—
542	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
543	#137	—	2	8	no	—
544	#137	—	2	2	no	—
545	#137	—	2	2	no	—
546	#137	—	2	2	no	—
547	#137	—	2	2	no	—
548	#137	—	2	2	no	—
549	#137	D₄×C₁₉	1	4	yes	—
550	AGL(1,ℤ/8)	—	2	8	no	—
551	AGL(1,ℤ/8)	—	2	2	no	—
552	AGL(1,ℤ/8)	—	2	2	no	—
553	#135	—	2	8	no	—
554	#135	—	2	2	no	—
555	#135	—	2	2	no	—
556	C₂×Q₁₆	—	2	1	no	—
557	C₂×Q₁₆	—	2	2	no	—
558	C₂×Q₁₆	—	2	1	no	—
559	C₂×Q₁₆	—	2	1	no	—
560	C₂×Q₁₆	—	2	1	no	—
561	C₂×Q₁₆	—	2	1	no	—
562	C₂×Q₁₆	—	4	1	no	—
563	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
564	C₂×SD₁₆	—	2	8	no	—
565	C₂×SD₁₆	—	2	1	no	—
566	C₂×SD₁₆	—	2	2	no	—
567	C₂×SD₁₆	—	2	1	no	—
568	C₂×SD₁₆	—	2	2	no	—
569	C₂×SD₁₆	—	2	1	no	—
570	C₂×SD₁₆	—	2	1	no	—
571	C₂×SD₁₆	—	2	1	no	—
572	C₂×SD₁₆	—	2	1	no	—
573	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
574	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
575	C₂×D₈	—	2	1	no	—
576	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
577	#131	—	2	2	no	—
578	#131	—	2	2	no	—
579	#131	—	2	2	no	—
580	#131	—	4	1	no	—
581	C₂×M₁₆	—	2	1	no	—
582	C₂×M₁₆	—	2	1	no	—
583	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
584	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
585	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
586	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
587	C₂²×C₈	—	2	1	no	—
588	C₂²×C₈	—	2	1	no	—
589	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
590	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
591	C₄⋊Q₈	—	2	1	no	—
592	#124	—	2	2	no	—
593	#124	—	2	1	no	—
594	#124	—	4	1	no	—
595	#123	—	4	1	no	—
596	C₂²⋊Q₈	—	2	1	no	—
597	C₂²⋊Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	—	4	1	no	—
601	#117	—	2	1	no	—
602	#117	C₂³×C₁₉	1	1	yes	characteristic
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	—	4	1	no	—
606	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
607	#108	—	2	2	no	—
608	C₄⋊C₈	—	2	1	no	—
609	C₄⋊C₈	—	2	1	no	—
610	#104	—	2	2	no	—
611	#104	—	2	2	no	—
612	#104	—	4	1	no	—
613	#103	—	2	1	no	—
614	#103	—	2	1	no	—
615	#103	—	2	1	no	—
616	#103	—	2	1	no	—
617	#103	—	2	1	no	—
618	#103	—	2	1	no	—
619	#103	D₄×C₁₉	1	1	yes	characteristic
620	#103	D₄×C₁₉	1	1	yes	characteristic
621	#102	—	2	1	no	—
622	#102	—	2	1	no	—
623	#102	—	2	1	no	—
624	#102	—	2	1	no	—
625	#102	—	2	1	no	—
626	#102	—	2	1	no	—
627	#102	D₄×C₁₉	1	1	yes	characteristic
628	#102	D₄×C₁₉	1	1	yes	characteristic
629	#101	—	2	2	no	—
630	#101	—	2	2	no	—
631	#100	—	2	2	no	—
632	C₂²⋊C₈	—	2	1	no	—
633	C₂²⋊C₈	—	2	1	no	—
634	#95	—	4	1	no	—
635	C₁₉	#24458	1	1	yes	characteristic, direct product factor, Sylow
636	C₂⁴	—	2	1	no	—
637	C₂⁴	—	4	1	no	—
638	#41	—	2	1	no	—
639	#41	—	2	1	no	—
640	#41	—	2	1	no	—
641	#41	—	2	1	no	—
642	#41	—	2	4	no	—
643	#41	—	2	4	no	—
644	#41	—	2	4	no	—
645	#41	—	2	1	no	—
646	#41	—	2	1	no	—
647	#41	—	2	1	no	—
648	#41	—	2	1	no	—
649	#41	—	4	2	no	—
650	#41	—	4	4	no	—
651	#41	—	4	2	no	—
652	#41	—	4	2	no	—
653	#41	—	4	2	no	—
654	#41	—	4	4	no	—
655	#41	—	4	2	no	—
656	#41	C₂×D₄×C₁₉	1	2	yes	—
657	#41	C₂×D₄×C₁₉	1	2	yes	—
658	#41	C₂×D₄×C₁₉	1	2	yes	—
659	#41	#41×C₁₉	1	2	yes	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	4	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	4	1	no	—
673	C₂×Q₈	—	4	2	no	—
674	C₂×Q₈	—	4	2	no	—
675	C₂×Q₈	—	4	2	no	—
676	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
677	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
678	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
679	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	1	no	—
693	C₂×D₄	—	4	1	no	—
694	C₂×D₄	—	4	4	no	—
695	C₂×D₄	—	4	4	no	—
696	C₂×D₄	—	4	1	no	—
697	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
698	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
699	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
700	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	4	1	no	—
709	C₂²×C₄	—	4	1	no	—
710	C₂²×C₄	—	4	1	no	—
711	C₂²×C₄	—	4	1	no	—
712	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
713	Q₁₆	—	2	4	no	—
714	Q₁₆	—	2	2	no	—
715	Q₁₆	—	4	2	no	—
716	Q₁₆	—	4	2	no	—
717	Q₁₆	—	4	2	no	—
718	Q₁₆	—	4	2	no	—
719	SD₁₆	—	2	4	no	—
720	SD₁₆	—	2	4	no	—
721	SD₁₆	—	2	4	no	—
722	SD₁₆	—	2	2	no	—
723	SD₁₆	—	2	2	no	—
724	SD₁₆	—	2	4	no	—
725	SD₁₆	—	4	2	no	—
726	SD₁₆	—	4	2	no	—
727	D₈	—	2	4	no	—
728	D₈	—	2	2	no	—
729	M₁₆	—	2	4	no	—
730	M₁₆	—	2	1	no	—
731	M₁₆	—	2	1	no	—
732	M₁₆	—	2	1	no	—
733	M₁₆	—	2	1	no	—
734	M₁₆	—	2	1	no	—
735	M₁₆	—	2	1	no	—
736	M₁₆	—	2	1	no	—
737	M₁₆	—	4	2	no	—
738	M₁₆	C₂×D₄×C₁₉	1	2	yes	—
739	C₂×C₈	—	2	4	no	—
740	C₂×C₈	—	2	1	no	—
741	C₂×C₈	—	2	1	no	—
742	C₂×C₈	—	2	1	no	—
743	C₂×C₈	—	2	1	no	—
744	C₂×C₈	—	2	1	no	—
745	C₂×C₈	—	2	1	no	—
746	C₂×C₈	—	2	1	no	—
747	C₂×C₈	—	2	1	no	—
748	C₂×C₈	—	4	2	no	—
749	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
750	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
751	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
752	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
753	C₄⋊C₄	—	2	1	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	4	1	no	—
756	C₄⋊C₄	—	4	1	no	—
757	C₄⋊C₄	—	4	1	no	—
758	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
759	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
760	C₂²⋊C₄	—	2	1	no	—
761	C₂²⋊C₄	—	4	1	no	—
762	C₂²⋊C₄	—	4	1	no	—
763	C₂²⋊C₄	—	4	1	no	—
764	C₂²⋊C₄	—	4	4	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	1	no	—
768	C₄²	—	4	1	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	4	4	no	—
774	C₂³	—	4	1	no	—
775	C₂³	—	4	1	no	—
776	C₂³	—	8	1	no	—
777	C₂³	—	8	1	no	—
778	C₂³	—	16	1	no	—
779	C₂³	—	16	1	no	—
780	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
781	Q₈	—	2	1	no	—
782	Q₈	—	2	1	no	—
783	Q₈	—	2	2	no	—
784	Q₈	—	2	1	no	—
785	Q₈	—	2	2	no	—
786	Q₈	—	2	1	no	—
787	Q₈	—	4	4	no	—
788	Q₈	—	4	1	no	—
789	Q₈	—	4	1	no	—
790	Q₈	—	4	1	no	—
791	Q₈	—	4	1	no	—
792	Q₈	—	4	1	no	—
793	Q₈	—	4	1	no	—
794	Q₈	C₁₉×#120	1	2	yes	—
795	Q₈	C₁₉×#121	1	2	yes	—
796	D₄	—	2	2	no	—
797	D₄	—	2	2	no	—
798	D₄	—	2	2	no	—
799	D₄	—	2	2	no	—
800	D₄	—	2	1	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	1	no	—
804	D₄	—	2	1	no	—
805	D₄	—	2	1	no	—
806	D₄	—	4	4	no	—
807	D₄	—	4	4	no	—
808	D₄	—	4	4	no	—
809	D₄	—	4	1	no	—
810	D₄	—	4	1	no	—
811	D₄	—	4	1	no	—
812	D₄	—	4	1	no	—
813	D₄	C₁₉×#120	1	2	yes	—
814	D₄	C₁₉×#121	1	2	yes	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	4	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	1	no	—
836	C₂×C₄	—	4	1	no	—
837	C₂×C₄	—	4	1	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	8	1	no	—
840	C₂×C₄	—	16	1	no	—
841	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
845	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
846	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
847	C₈	—	2	1	no	—
848	C₈	—	2	2	no	—
849	C₈	—	2	1	no	—
850	C₈	—	2	1	no	—
851	C₈	—	2	1	no	—
852	C₈	—	4	1	no	—
853	C₈	—	4	1	no	—
854	C₈	—	4	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	8	2	no	—
868	C₂²	—	8	1	no	—
869	C₂²	—	8	1	no	—
870	C₂²	—	16	1	no	—
871	C₂²	—	16	4	no	—
872	C₂²	C₁₉×#534	1	1	yes	characteristic
873	C₂²	D₄²×C₁₉	1	1	yes	characteristic
874	C₂²	C₁₉×#546	1	1	yes	characteristic
875	C₄	—	2	2	no	—
876	C₄	—	2	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	1	no	—
881	C₄	—	8	1	no	—
882	C₄	—	8	1	no	—
883	C₄	—	8	1	no	—
884	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
885	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
886	C₄	D₄²×C₁₉	1	1	yes	characteristic
887	C₄	C₁₉×#546	1	1	yes	characteristic
888	C₂	—	2	1	no	—
889	C₂	—	2	1	no	—
890	C₂	—	4	2	no	—
891	C₂	—	4	2	no	—
892	C₂	—	8	1	no	—
893	C₂	—	8	2	no	—
894	C₂	C₁₉×#2410	1	1	yes	characteristic
895	C₂	C₁₉×#3289	1	1	yes	characteristic
896	C₂	C₁₉×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#577	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#473	C₂	semidirect
3. C₁₉×#3046	C₂	semidirect
4. C₂×C₁₉×#455	C₂	semidirect
5. C₁₉×#3011	C₂	semidirect
6. C₁₉×#2897	C₂	semidirect
7. C₁₉×#2051	C₂	semidirect
8. C₁₉×#2046	C₂	semidirect
9. C₁₉×#2015	C₂	semidirect
10. C₁₉×#2003	C₂	semidirect
11. C₁₉×#1908	C₂	semidirect
12. C₁₉×#1882	C₂	semidirect
13. C₁₉×#1876	C₂	semidirect
14. C₁₉×#1866	C₂	semidirect
15. C₁₉×#1793	C₂	semidirect
28. C₂²×Q₁₆×C₁₉	C₂²	semidirect
33. C₁₉×#536	C₂²	semidirect
46. C₂×C₁₉×#108	C₂²	semidirect
47. C₁₉×#424	C₂²	semidirect
50. C₂×C₁₉×#104	C₂²	semidirect
51. C₁₉×#419	C₂²	semidirect
56. C₁₉×#417	C₂²	semidirect
59. C₂×C₁₉×#103	C₂²	semidirect
62. C₂×C₁₉×#101	C₂²	semidirect
63. C₂×C₁₉×#101	C₂²	semidirect
65. C₁₉×#408	C₂²	semidirect
66. C₁₉×#391	C₂²	semidirect
67. C₁₉×#343	C₂²	semidirect
68. C₁₉×#341	C₂²	semidirect
69. C₁₉×#339	C₂²	semidirect
70. C₁₉×#336	C₂²	semidirect
320. #24458	C₁₉	direct (N × H)
408. C₂×#473	C₂×C₁₉	semidirect
409. #3046	C₂×C₁₉	semidirect
410. C₂×#455	C₂×C₁₉	semidirect
411. #3011	C₂×C₁₉	semidirect
412. #2897	C₂×C₁₉	semidirect
413. #2051	C₂×C₁₉	semidirect
414. #2046	C₂×C₁₉	semidirect
415. #2015	C₂×C₁₉	semidirect
416. #2003	C₂×C₁₉	semidirect
417. #1908	C₂×C₁₉	semidirect
418. #1882	C₂×C₁₉	semidirect
419. #1876	C₂×C₁₉	semidirect
420. #1866	C₂×C₁₉	semidirect
421. #1793	C₂×C₁₉	semidirect
467. C₂²×Q₁₆	C₂²×C₁₉	semidirect
472. #536	C₂²×C₁₉	semidirect
485. C₂×#108	C₂²×C₁₉	semidirect
486. #424	C₂²×C₁₉	semidirect
489. C₂×#104	C₂²×C₁₉	semidirect
490. #419	C₂²×C₁₉	semidirect
495. #417	C₂²×C₁₉	semidirect
498. C₂×#103	C₂²×C₁₉	semidirect
501. C₂×#101	C₂²×C₁₉	semidirect
502. C₂×#101	C₂²×C₁₉	semidirect
504. #408	C₂²×C₁₉	semidirect
505. #391	C₂²×C₁₉	semidirect
506. #343	C₂²×C₁₉	semidirect
507. #341	C₂²×C₁₉	semidirect
508. #339	C₂²×C₁₉	semidirect
509. #336	C₂²×C₁₉	semidirect
635. C₁₉	#24458	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×#577	2
C₂×C₁₉×#473	2
C₁₉×#3046	2
C₂×C₁₉×#455	2
C₁₉×#3011	2
C₁₉×#2897	2
C₁₉×#2051	2
C₁₉×#2046	2
C₁₉×#2015	2
C₁₉×#2003	2
C₁₉×#1908	2
C₁₉×#1882	2
C₁₉×#1876	2
C₁₉×#1866	2
C₁₉×#1793	2
#24458	19

Subgroups — C19×#24458 #18030417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24458 #18030417