Subgroups — C₁₉×#24031 #18029990

Order 4864.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3488	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3093	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2896	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2500	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2040	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2039	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2037	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2037	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1900	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1871	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1860	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1859	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1792	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1792	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1789	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
19	C₁₉×#550	—	2	1	no	—
20	C₁₉×#548	—	2	1	no	—
21	C₁₉×#546	—	2	1	no	—
22	C₁₉×#546	—	2	2	no	—
23	D₄²×C₁₉	—	2	2	no	—
24	D₄²×C₁₉	—	2	1	no	—
25	C₁₉×#537	—	2	1	no	—
26	C₁₉×#537	C₂²	1	1	yes	characteristic
27	C₁₉×#535	—	2	1	no	—
28	C₁₉×#535	C₂²	1	1	yes	characteristic
29	C₁₉×#525	—	2	1	no	—
30	C₁₉×#525	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#121	—	2	1	no	—
32	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
33	C₁₉×#520	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#485	—	2	1	no	—
36	C₁₉×#485	—	2	1	no	—
37	C₁₉×#482	—	2	1	no	—
38	C₁₉×#482	—	2	1	no	—
39	C₁₉×#428	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#428	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
43	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#419	—	2	1	no	—
48	C₁₉×#418	—	2	1	no	—
49	C₁₉×#417	C₂²	1	1	yes	characteristic
50	C₁₉×#417	C₂²	1	1	yes	characteristic
51	C₁₉×#417	C₂²	1	1	yes	characteristic, complemented
52	C₁₉×#417	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#417	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#417	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×#416	—	2	1	no	—
56	C₁₉×#416	—	2	1	no	—
57	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#407	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#394	—	2	2	no	—
61	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#388	—	2	2	no	—
64	C₁₉×#384	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#382	C₂²	1	1	yes	characteristic, complemented
66	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#343	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#343	C₂²	1	1	yes	characteristic, complemented
69	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
70	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
71	C₁₉×H(5,𝔽₂)	—	2	2	no	—
72	C₁₉×H(5,𝔽₂)	—	2	2	no	—
73	C₁₉×H(5,𝔽₂)	—	4	1	no	—
74	C₁₉×H(5,𝔽₂)	—	4	1	no	—
75	C₂×#41×C₁₉	—	2	1	no	—
76	C₂×#41×C₁₉	—	2	1	no	—
77	C₂×#41×C₁₉	—	2	1	no	—
78	C₂×#41×C₁₉	—	2	1	no	—
79	C₂×#41×C₁₉	—	2	2	no	—
80	C₂×#41×C₁₉	—	2	2	no	—
81	C₂×#41×C₁₉	—	4	1	no	—
82	C₂×#41×C₁₉	—	4	1	no	—
83	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
84	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
85	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
89	C₂²×D₄×C₁₉	—	2	1	no	—
90	C₂²×D₄×C₁₉	—	2	2	no	—
91	C₂²×D₄×C₁₉	—	2	2	no	—
92	C₂²×D₄×C₁₉	—	2	1	no	—
93	C₂²×D₄×C₁₉	—	2	1	no	—
94	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
95	C₂²×D₄×C₁₉	D₄	1	2	yes	—
96	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₉	—	2	1	no	—
98	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×M₁₆×C₁₉	—	2	1	no	—
100	C₂×M₁₆×C₁₉	—	4	1	no	—
101	C₂×M₁₆×C₁₉	—	4	1	no	—
102	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₁₉	—	2	1	no	—
107	C₁₉×#127	—	2	2	no	—
108	C₁₉×#127	—	2	1	no	—
109	C₁₉×#124	—	2	2	no	—
110	C₁₉×#124	—	2	1	no	—
111	C₁₉×#123	—	2	2	no	—
112	C₁₉×#123	—	2	1	no	—
113	C₁₉×C₂²⋊Q₈	—	2	2	no	—
114	C₁₉×C₂²⋊Q₈	—	2	1	no	—
115	C₁₉×C₂²⋊Q₈	—	2	1	no	—
116	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
117	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
118	C₁₉×#121	—	2	2	no	—
119	C₁₉×#121	—	2	2	no	—
120	C₁₉×#121	—	2	2	no	—
121	C₁₉×#121	—	2	2	no	—
122	C₁₉×#121	—	2	2	no	—
123	C₁₉×#121	—	2	1	no	—
124	C₁₉×#121	—	2	1	no	—
125	C₁₉×#121	—	2	1	no	—
126	C₁₉×#121	—	2	1	no	—
127	C₁₉×#121	—	2	1	no	—
128	C₁₉×#121	—	2	1	no	—
129	C₁₉×#121	—	2	2	no	—
130	C₁₉×#121	—	2	1	no	—
131	C₁₉×#121	—	2	1	no	—
132	C₁₉×#121	D₄	1	1	yes	characteristic
133	C₁₉×#121	D₄	1	1	yes	characteristic
134	C₁₉×#120	—	2	2	no	—
135	C₁₉×#120	—	2	2	no	—
136	C₁₉×#120	—	2	2	no	—
137	C₁₉×#120	—	2	1	no	—
138	C₁₉×#120	—	2	2	no	—
139	C₄×Q₈×C₁₉	—	2	1	no	—
140	C₄×D₄×C₁₉	—	2	2	no	—
141	C₄×D₄×C₁₉	—	2	2	no	—
142	C₄×D₄×C₁₉	—	2	1	no	—
143	C₄×D₄×C₁₉	—	2	2	no	—
144	C₄×D₄×C₁₉	—	2	1	no	—
145	C₄×D₄×C₁₉	—	2	1	no	—
146	C₁₉×#117	—	2	1	no	—
147	C₁₉×#117	—	2	1	no	—
148	C₁₉×#117	—	2	1	no	—
149	C₁₉×#117	—	2	1	no	—
150	C₁₉×#117	—	2	1	no	—
151	C₁₉×#117	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
158	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
160	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
162	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
163	C₂×C₄²×C₁₉	—	2	1	no	—
164	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
166	C₁₉×#107	—	2	1	no	—
167	C₁₉×#107	—	2	1	no	—
168	C₁₉×#106	—	2	1	no	—
169	C₁₉×#106	—	2	1	no	—
170	C₁₉×#104	—	2	2	no	—
171	C₁₉×#104	—	2	2	no	—
172	C₁₉×#104	—	4	1	no	—
173	C₁₉×#104	—	4	1	no	—
174	C₁₉×#104	—	4	1	no	—
175	C₁₉×#104	—	4	1	no	—
176	C₁₉×#103	—	2	1	no	—
177	C₁₉×#103	—	2	1	no	—
178	C₁₉×#103	—	2	1	no	—
179	C₁₉×#103	—	2	1	no	—
180	C₁₉×#103	—	2	1	no	—
181	C₁₉×#103	—	2	1	no	—
182	C₁₉×#102	—	2	1	no	—
183	C₁₉×#102	—	2	1	no	—
184	C₁₉×#102	—	2	1	no	—
185	C₁₉×#102	—	2	1	no	—
186	C₁₉×#102	—	2	1	no	—
187	C₁₉×#102	—	2	1	no	—
188	C₁₉×#100	—	4	1	no	—
189	C₁₉×#100	—	4	1	no	—
190	C₁₉×C₂²⋊C₈	—	2	1	no	—
191	C₁₉×C₂²⋊C₈	—	2	1	no	—
192	C₁₉×#95	—	2	1	no	—
193	C₁₉×#95	—	2	2	no	—
194	C₂⁴×C₁₉	—	2	2	no	—
195	C₂⁴×C₁₉	—	2	1	no	—
196	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
197	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
198	#41×C₁₉	—	2	1	no	—
199	#41×C₁₉	—	2	1	no	—
200	#41×C₁₉	—	2	2	no	—
201	#41×C₁₉	—	2	2	no	—
202	#41×C₁₉	—	2	1	no	—
203	#41×C₁₉	—	2	1	no	—
204	#41×C₁₉	—	2	1	no	—
205	#41×C₁₉	—	2	1	no	—
206	#41×C₁₉	—	2	1	no	—
207	#41×C₁₉	—	2	1	no	—
208	#41×C₁₉	—	2	1	no	—
209	#41×C₁₉	—	2	1	no	—
210	#41×C₁₉	—	4	2	no	—
211	#41×C₁₉	—	4	2	no	—
212	#41×C₁₉	—	4	1	no	—
213	#41×C₁₉	—	4	1	no	—
214	#41×C₁₉	—	4	2	no	—
215	#41×C₁₉	—	4	2	no	—
216	#41×C₁₉	—	4	2	no	—
217	#41×C₁₉	—	4	2	no	—
218	#41×C₁₉	—	4	2	no	—
219	#41×C₁₉	—	4	2	no	—
220	#41×C₁₉	#41	1	2	yes	—
221	#41×C₁₉	#41	1	2	yes	—
222	C₂×Q₈×C₁₉	—	2	1	no	—
223	C₂×Q₈×C₁₉	—	2	2	no	—
224	C₂×Q₈×C₁₉	—	4	1	no	—
225	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
226	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
227	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
228	C₂×D₄×C₁₉	—	2	1	no	—
229	C₂×D₄×C₁₉	—	2	2	no	—
230	C₂×D₄×C₁₉	—	2	2	no	—
231	C₂×D₄×C₁₉	—	2	2	no	—
232	C₂×D₄×C₁₉	—	2	2	no	—
233	C₂×D₄×C₁₉	—	2	1	no	—
234	C₂×D₄×C₁₉	—	2	1	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	2	no	—
239	C₂×D₄×C₁₉	—	2	2	no	—
240	C₂×D₄×C₁₉	—	2	2	no	—
241	C₂×D₄×C₁₉	—	2	1	no	—
242	C₂×D₄×C₁₉	—	2	2	no	—
243	C₂×D₄×C₁₉	—	2	1	no	—
244	C₂×D₄×C₁₉	—	2	1	no	—
245	C₂×D₄×C₁₉	—	2	1	no	—
246	C₂×D₄×C₁₉	—	2	1	no	—
247	C₂×D₄×C₁₉	—	2	1	no	—
248	C₂×D₄×C₁₉	—	2	1	no	—
249	C₂×D₄×C₁₉	—	2	1	no	—
250	C₂×D₄×C₁₉	—	4	1	no	—
251	C₂×D₄×C₁₉	—	4	2	no	—
252	C₂×D₄×C₁₉	—	4	2	no	—
253	C₂×D₄×C₁₉	—	4	2	no	—
254	C₂×D₄×C₁₉	—	4	2	no	—
255	C₂×D₄×C₁₉	—	4	4	no	—
256	C₂×D₄×C₁₉	—	4	4	no	—
257	C₂×D₄×C₁₉	—	4	2	no	—
258	C₂×D₄×C₁₉	—	4	2	no	—
259	C₂×D₄×C₁₉	—	8	2	no	—
260	C₂×D₄×C₁₉	—	8	4	no	—
261	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
262	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
263	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₁₉	—	2	1	no	—
265	C₂²×C₄×C₁₉	—	2	1	no	—
266	C₂²×C₄×C₁₉	—	2	1	no	—
267	C₂²×C₄×C₁₉	—	2	1	no	—
268	C₂²×C₄×C₁₉	—	2	1	no	—
269	C₂²×C₄×C₁₉	—	2	2	no	—
270	C₂²×C₄×C₁₉	—	2	1	no	—
271	C₂²×C₄×C₁₉	—	2	1	no	—
272	C₂²×C₄×C₁₉	—	2	2	no	—
273	C₂²×C₄×C₁₉	—	2	1	no	—
274	C₂²×C₄×C₁₉	—	2	1	no	—
275	C₂²×C₄×C₁₉	—	2	1	no	—
276	C₂²×C₄×C₁₉	—	2	1	no	—
277	C₂²×C₄×C₁₉	—	2	1	no	—
278	C₂²×C₄×C₁₉	—	2	1	no	—
279	C₂²×C₄×C₁₉	—	2	1	no	—
280	C₂²×C₄×C₁₉	—	4	2	no	—
281	C₂²×C₄×C₁₉	—	4	2	no	—
282	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
288	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
289	M₁₆×C₁₉	—	2	1	no	—
290	M₁₆×C₁₉	—	2	1	no	—
291	M₁₆×C₁₉	—	2	1	no	—
292	M₁₆×C₁₉	—	2	1	no	—
293	M₁₆×C₁₉	—	2	1	no	—
294	M₁₆×C₁₉	—	2	1	no	—
295	M₁₆×C₁₉	—	2	1	no	—
296	M₁₆×C₁₉	—	2	1	no	—
297	M₁₆×C₁₉	—	4	2	no	—
298	C₂×C₈×C₁₉	—	2	1	no	—
299	C₂×C₈×C₁₉	—	2	1	no	—
300	C₂×C₈×C₁₉	—	2	1	no	—
301	C₂×C₈×C₁₉	—	2	1	no	—
302	C₂×C₈×C₁₉	—	4	2	no	—
303	C₄⋊C₄×C₁₉	—	2	2	no	—
304	C₄⋊C₄×C₁₉	—	2	2	no	—
305	C₄⋊C₄×C₁₉	—	2	1	no	—
306	C₄⋊C₄×C₁₉	—	2	1	no	—
307	C₄⋊C₄×C₁₉	—	2	1	no	—
308	C₄⋊C₄×C₁₉	—	2	1	no	—
309	C₄⋊C₄×C₁₉	—	2	1	no	—
310	C₄⋊C₄×C₁₉	—	2	1	no	—
311	C₄⋊C₄×C₁₉	—	2	1	no	—
312	C₄⋊C₄×C₁₉	—	2	1	no	—
313	C₄⋊C₄×C₁₉	—	8	2	no	—
314	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
315	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
316	C₂²⋊C₄×C₁₉	—	2	2	no	—
317	C₂²⋊C₄×C₁₉	—	2	2	no	—
318	C₂²⋊C₄×C₁₉	—	2	2	no	—
319	C₂²⋊C₄×C₁₉	—	2	2	no	—
320	C₂²⋊C₄×C₁₉	—	2	2	no	—
321	C₂²⋊C₄×C₁₉	—	2	1	no	—
322	C₂²⋊C₄×C₁₉	—	2	1	no	—
323	C₂²⋊C₄×C₁₉	—	2	1	no	—
324	C₂²⋊C₄×C₁₉	—	2	1	no	—
325	C₂²⋊C₄×C₁₉	—	2	2	no	—
326	C₂²⋊C₄×C₁₉	—	2	2	no	—
327	C₂²⋊C₄×C₁₉	—	2	1	no	—
328	C₂²⋊C₄×C₁₉	—	4	2	no	—
329	C₂²⋊C₄×C₁₉	—	4	4	no	—
330	C₂²⋊C₄×C₁₉	—	4	1	no	—
331	C₂²⋊C₄×C₁₉	—	4	1	no	—
332	C₂²⋊C₄×C₁₉	—	8	2	no	—
333	C₄²×C₁₉	—	2	2	no	—
334	C₄²×C₁₉	—	2	1	no	—
335	C₄²×C₁₉	—	2	1	no	—
336	C₄²×C₁₉	—	2	1	no	—
337	C₄²×C₁₉	—	2	1	no	—
338	C₄²×C₁₉	—	2	1	no	—
339	C₄²×C₁₉	—	4	1	no	—
340	C₄²×C₁₉	—	4	1	no	—
341	#24031	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
342	C₂³×C₁₉	—	2	1	no	—
343	C₂³×C₁₉	—	2	1	no	—
344	C₂³×C₁₉	—	2	1	no	—
345	C₂³×C₁₉	—	2	2	no	—
346	C₂³×C₁₉	—	2	1	no	—
347	C₂³×C₁₉	—	2	1	no	—
348	C₂³×C₁₉	—	2	2	no	—
349	C₂³×C₁₉	—	2	2	no	—
350	C₂³×C₁₉	—	4	1	no	—
351	C₂³×C₁₉	—	4	1	no	—
352	C₂³×C₁₉	—	4	2	no	—
353	C₂³×C₁₉	—	4	2	no	—
354	C₂³×C₁₉	—	4	4	no	—
355	C₂³×C₁₉	—	4	2	no	—
356	C₂³×C₁₉	—	4	2	no	—
357	C₂³×C₁₉	—	8	1	no	—
358	C₂³×C₁₉	—	8	2	no	—
359	C₂³×C₁₉	—	8	2	no	—
360	C₂³×C₁₉	#120	1	1	yes	characteristic
361	C₂³×C₁₉	#120	1	1	yes	characteristic
362	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
363	Q₈×C₁₉	—	2	1	no	—
364	Q₈×C₁₉	—	2	1	no	—
365	Q₈×C₁₉	—	2	1	no	—
366	Q₈×C₁₉	—	2	1	no	—
367	Q₈×C₁₉	—	2	1	no	—
368	Q₈×C₁₉	—	4	2	no	—
369	Q₈×C₁₉	#123	1	2	yes	—
370	D₄×C₁₉	—	2	2	no	—
371	D₄×C₁₉	—	2	2	no	—
372	D₄×C₁₉	—	2	1	no	—
373	D₄×C₁₉	—	2	1	no	—
374	D₄×C₁₉	—	2	1	no	—
375	D₄×C₁₉	—	2	1	no	—
376	D₄×C₁₉	—	2	1	no	—
377	D₄×C₁₉	—	4	2	no	—
378	D₄×C₁₉	—	4	2	no	—
379	D₄×C₁₉	—	4	4	no	—
380	D₄×C₁₉	—	4	2	no	—
381	D₄×C₁₉	—	4	4	no	—
382	D₄×C₁₉	—	4	4	no	—
383	D₄×C₁₉	—	4	2	no	—
384	D₄×C₁₉	—	4	1	no	—
385	D₄×C₁₉	—	4	1	no	—
386	D₄×C₁₉	—	4	1	no	—
387	D₄×C₁₉	—	4	1	no	—
388	D₄×C₁₉	—	4	1	no	—
389	D₄×C₁₉	—	4	1	no	—
390	D₄×C₁₉	—	4	1	no	—
391	D₄×C₁₉	—	4	1	no	—
392	D₄×C₁₉	—	8	1	no	—
393	D₄×C₁₉	—	8	2	no	—
394	D₄×C₁₉	—	8	2	no	—
395	D₄×C₁₉	—	8	2	no	—
396	D₄×C₁₉	—	8	2	no	—
397	D₄×C₁₉	#123	1	2	yes	—
398	C₂×C₄×C₁₉	—	2	1	no	—
399	C₂×C₄×C₁₉	—	2	1	no	—
400	C₂×C₄×C₁₉	—	2	1	no	—
401	C₂×C₄×C₁₉	—	2	1	no	—
402	C₂×C₄×C₁₉	—	2	1	no	—
403	C₂×C₄×C₁₉	—	2	1	no	—
404	C₂×C₄×C₁₉	—	2	1	no	—
405	C₂×C₄×C₁₉	—	2	1	no	—
406	C₂×C₄×C₁₉	—	2	1	no	—
407	C₂×C₄×C₁₉	—	2	1	no	—
408	C₂×C₄×C₁₉	—	2	1	no	—
409	C₂×C₄×C₁₉	—	2	2	no	—
410	C₂×C₄×C₁₉	—	2	2	no	—
411	C₂×C₄×C₁₉	—	2	2	no	—
412	C₂×C₄×C₁₉	—	2	1	no	—
413	C₂×C₄×C₁₉	—	2	2	no	—
414	C₂×C₄×C₁₉	—	2	1	no	—
415	C₂×C₄×C₁₉	—	2	1	no	—
416	C₂×C₄×C₁₉	—	2	1	no	—
417	C₂×C₄×C₁₉	—	4	2	no	—
418	C₂×C₄×C₁₉	—	4	2	no	—
419	C₂×C₄×C₁₉	—	4	2	no	—
420	C₂×C₄×C₁₉	—	4	4	no	—
421	C₂×C₄×C₁₉	—	4	1	no	—
422	C₂×C₄×C₁₉	—	4	1	no	—
423	C₂×C₄×C₁₉	—	4	1	no	—
424	C₂×C₄×C₁₉	—	4	1	no	—
425	C₂×C₄×C₁₉	—	4	1	no	—
426	C₂×C₄×C₁₉	—	4	1	no	—
427	C₂×C₄×C₁₉	—	4	2	no	—
428	C₂×C₄×C₁₉	—	4	1	no	—
429	C₂×C₄×C₁₉	—	4	2	no	—
430	C₂×C₄×C₁₉	—	4	1	no	—
431	C₂×C₄×C₁₉	—	4	2	no	—
432	C₂×C₄×C₁₉	—	4	1	no	—
433	C₂×C₄×C₁₉	—	4	1	no	—
434	C₂×C₄×C₁₉	—	4	1	no	—
435	C₂×C₄×C₁₉	—	8	2	no	—
436	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
437	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
438	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
441	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
442	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
443	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
444	C₈×C₁₉	—	4	1	no	—
445	C₈×C₁₉	—	4	1	no	—
446	C₈×C₁₉	—	4	1	no	—
447	C₈×C₁₉	—	4	1	no	—
448	#3488	C₂×C₁₉	1	1	yes	characteristic
449	#3093	C₂×C₁₉	1	1	yes	characteristic, complemented
450	#2896	C₂×C₁₉	1	1	yes	characteristic, complemented
451	#2500	C₂×C₁₉	1	1	yes	characteristic, complemented
452	#2040	C₂×C₁₉	1	1	yes	characteristic, complemented
453	#2039	C₂×C₁₉	1	1	yes	characteristic, complemented
454	#2037	C₂×C₁₉	1	1	yes	characteristic, complemented
455	#2037	C₂×C₁₉	1	1	yes	characteristic, complemented
456	#1900	C₂×C₁₉	1	1	yes	characteristic, complemented
457	#1871	C₂×C₁₉	1	1	yes	characteristic, complemented
458	#1860	C₂×C₁₉	1	1	yes	characteristic, complemented
459	#1859	C₂×C₁₉	1	1	yes	characteristic, complemented
460	#1792	C₂×C₁₉	1	1	yes	characteristic, complemented
461	#1792	C₂×C₁₉	1	1	yes	characteristic, complemented
462	#1789	C₂×C₁₉	1	1	yes	characteristic, complemented
463	C₂²×C₁₉	—	2	1	no	—
464	C₂²×C₁₉	—	2	1	no	—
465	C₂²×C₁₉	—	2	1	no	—
466	C₂²×C₁₉	—	2	1	no	—
467	C₂²×C₁₉	—	2	2	no	—
468	C₂²×C₁₉	—	2	1	no	—
469	C₂²×C₁₉	—	2	1	no	—
470	C₂²×C₁₉	—	2	1	no	—
471	C₂²×C₁₉	—	2	1	no	—
472	C₂²×C₁₉	—	4	1	no	—
473	C₂²×C₁₉	—	4	1	no	—
474	C₂²×C₁₉	—	4	1	no	—
475	C₂²×C₁₉	—	4	1	no	—
476	C₂²×C₁₉	—	4	2	no	—
477	C₂²×C₁₉	—	4	1	no	—
478	C₂²×C₁₉	—	4	2	no	—
479	C₂²×C₁₉	—	4	1	no	—
480	C₂²×C₁₉	—	4	2	no	—
481	C₂²×C₁₉	—	4	1	no	—
482	C₂²×C₁₉	—	4	1	no	—
483	C₂²×C₁₉	—	8	1	no	—
484	C₂²×C₁₉	—	8	1	no	—
485	C₂²×C₁₉	—	8	2	no	—
486	C₂²×C₁₉	—	8	2	no	—
487	C₂²×C₁₉	—	8	4	no	—
488	C₂²×C₁₉	—	16	4	no	—
489	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
490	C₂²×C₁₉	#546	1	1	yes	characteristic
491	C₂²×C₁₉	#546	1	1	yes	characteristic
492	C₄×C₁₉	—	2	1	no	—
493	C₄×C₁₉	—	2	1	no	—
494	C₄×C₁₉	—	2	2	no	—
495	C₄×C₁₉	—	4	2	no	—
496	C₄×C₁₉	—	4	1	no	—
497	C₄×C₁₉	—	4	1	no	—
498	C₄×C₁₉	—	4	1	no	—
499	C₄×C₁₉	—	4	2	no	—
500	C₄×C₁₉	—	4	1	no	—
501	C₄×C₁₉	—	8	1	no	—
502	C₄×C₁₉	—	8	1	no	—
503	C₄×C₁₉	—	8	1	no	—
504	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
505	C₄×C₁₉	#534	1	1	yes	characteristic
506	C₄×C₁₉	#546	1	1	yes	characteristic
507	C₄×C₁₉	#546	1	1	yes	characteristic
508	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
509	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
510	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
511	#550	—	2	1	no	—
512	#548	—	2	1	no	—
513	#546	—	2	1	no	—
514	#546	—	2	2	no	—
515	D₄²	—	2	2	no	—
516	D₄²	—	2	1	no	—
517	#537	—	2	1	no	—
518	#537	C₂²×C₁₉	1	1	yes	characteristic
519	#535	—	2	1	no	—
520	#535	C₂²×C₁₉	1	1	yes	characteristic
521	#525	—	2	1	no	—
522	#525	C₂²×C₁₉	1	1	yes	characteristic
523	C₂×#121	—	2	1	no	—
524	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
525	#520	C₂²×C₁₉	1	1	yes	characteristic
526	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
527	#485	—	2	1	no	—
528	#485	—	2	1	no	—
529	#482	—	2	1	no	—
530	#482	—	2	1	no	—
531	#428	C₂²×C₁₉	1	1	yes	characteristic, complemented
532	#428	C₂²×C₁₉	1	1	yes	characteristic, complemented
533	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
534	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
535	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
536	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
537	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
538	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
539	#419	—	2	1	no	—
540	#418	—	2	1	no	—
541	#417	C₂²×C₁₉	1	1	yes	characteristic
542	#417	C₂²×C₁₉	1	1	yes	characteristic
543	#417	C₂²×C₁₉	1	1	yes	characteristic, complemented
544	#417	C₂²×C₁₉	1	1	yes	characteristic, complemented
545	#417	C₂²×C₁₉	1	1	yes	characteristic, complemented
546	#417	C₂²×C₁₉	1	1	yes	characteristic, complemented
547	#416	—	2	1	no	—
548	#416	—	2	1	no	—
549	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic, complemented
550	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic, complemented
551	#407	C₂²×C₁₉	1	1	yes	characteristic, complemented
552	#394	—	2	2	no	—
553	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
554	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
555	#388	—	2	2	no	—
556	#384	C₂²×C₁₉	1	1	yes	characteristic, complemented
557	#382	C₂²×C₁₉	1	1	yes	characteristic, complemented
558	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
559	#343	C₂²×C₁₉	1	1	yes	characteristic, complemented
560	#343	C₂²×C₁₉	1	1	yes	characteristic, complemented
561	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
562	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
563	C₂×C₁₉	—	2	1	no	—
564	C₂×C₁₉	—	2	1	no	—
565	C₂×C₁₉	—	4	1	no	—
566	C₂×C₁₉	—	4	1	no	—
567	C₂×C₁₉	—	4	2	no	—
568	C₂×C₁₉	—	8	1	no	—
569	C₂×C₁₉	—	8	2	no	—
570	C₂×C₁₉	—	8	1	no	—
571	C₂×C₁₉	#2405	1	1	yes	characteristic
572	C₂×C₁₉	#3018	1	1	yes	characteristic
573	C₂×C₁₉	#3019	1	1	yes	characteristic
574	H(5,𝔽₂)	—	2	2	no	—
575	H(5,𝔽₂)	—	2	2	no	—
576	H(5,𝔽₂)	—	4	1	no	—
577	H(5,𝔽₂)	—	4	1	no	—
578	C₂×#41	—	2	1	no	—
579	C₂×#41	—	2	1	no	—
580	C₂×#41	—	2	1	no	—
581	C₂×#41	—	2	1	no	—
582	C₂×#41	—	2	2	no	—
583	C₂×#41	—	2	2	no	—
584	C₂×#41	—	4	1	no	—
585	C₂×#41	—	4	1	no	—
586	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
587	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
588	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
589	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
590	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
591	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
592	C₂²×D₄	—	2	1	no	—
593	C₂²×D₄	—	2	2	no	—
594	C₂²×D₄	—	2	2	no	—
595	C₂²×D₄	—	2	1	no	—
596	C₂²×D₄	—	2	1	no	—
597	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
598	C₂²×D₄	D₄×C₁₉	1	2	yes	—
599	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
600	C₂³×C₄	—	2	1	no	—
601	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
602	C₂×M₁₆	—	2	1	no	—
603	C₂×M₁₆	—	4	1	no	—
604	C₂×M₁₆	—	4	1	no	—
605	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
606	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
607	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
608	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
609	C₂²×C₈	—	2	1	no	—
610	#127	—	2	2	no	—
611	#127	—	2	1	no	—
612	#124	—	2	2	no	—
613	#124	—	2	1	no	—
614	#123	—	2	2	no	—
615	#123	—	2	1	no	—
616	C₂²⋊Q₈	—	2	2	no	—
617	C₂²⋊Q₈	—	2	1	no	—
618	C₂²⋊Q₈	—	2	1	no	—
619	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
620	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
621	#121	—	2	2	no	—
622	#121	—	2	2	no	—
623	#121	—	2	2	no	—
624	#121	—	2	2	no	—
625	#121	—	2	2	no	—
626	#121	—	2	1	no	—
627	#121	—	2	1	no	—
628	#121	—	2	1	no	—
629	#121	—	2	1	no	—
630	#121	—	2	1	no	—
631	#121	—	2	1	no	—
632	#121	—	2	2	no	—
633	#121	—	2	1	no	—
634	#121	—	2	1	no	—
635	#121	D₄×C₁₉	1	1	yes	characteristic
636	#121	D₄×C₁₉	1	1	yes	characteristic
637	#120	—	2	2	no	—
638	#120	—	2	2	no	—
639	#120	—	2	2	no	—
640	#120	—	2	1	no	—
641	#120	—	2	2	no	—
642	C₄×Q₈	—	2	1	no	—
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	1	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	1	no	—
648	C₄×D₄	—	2	1	no	—
649	#117	—	2	1	no	—
650	#117	—	2	1	no	—
651	#117	—	2	1	no	—
652	#117	—	2	1	no	—
653	#117	—	2	1	no	—
654	#117	C₂³×C₁₉	1	1	yes	characteristic
655	C₂×C₄⋊C₄	—	2	1	no	—
656	C₂×C₄⋊C₄	—	2	2	no	—
657	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
660	C₂×C₂²⋊C₄	—	2	2	no	—
661	C₂×C₂²⋊C₄	—	2	1	no	—
662	C₂×C₂²⋊C₄	—	2	1	no	—
663	C₂×C₂²⋊C₄	—	2	2	no	—
664	C₂×C₂²⋊C₄	—	2	2	no	—
665	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
666	C₂×C₄²	—	2	1	no	—
667	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
669	#107	—	2	1	no	—
670	#107	—	2	1	no	—
671	#106	—	2	1	no	—
672	#106	—	2	1	no	—
673	#104	—	2	2	no	—
674	#104	—	2	2	no	—
675	#104	—	4	1	no	—
676	#104	—	4	1	no	—
677	#104	—	4	1	no	—
678	#104	—	4	1	no	—
679	#103	—	2	1	no	—
680	#103	—	2	1	no	—
681	#103	—	2	1	no	—
682	#103	—	2	1	no	—
683	#103	—	2	1	no	—
684	#103	—	2	1	no	—
685	#102	—	2	1	no	—
686	#102	—	2	1	no	—
687	#102	—	2	1	no	—
688	#102	—	2	1	no	—
689	#102	—	2	1	no	—
690	#102	—	2	1	no	—
691	#100	—	4	1	no	—
692	#100	—	4	1	no	—
693	C₂²⋊C₈	—	2	1	no	—
694	C₂²⋊C₈	—	2	1	no	—
695	#95	—	2	1	no	—
696	#95	—	2	2	no	—
697	C₁₉	#24031	1	1	yes	characteristic, direct product factor, Sylow
698	C₂⁴	—	2	2	no	—
699	C₂⁴	—	2	1	no	—
700	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
701	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
702	#41	—	2	1	no	—
703	#41	—	2	1	no	—
704	#41	—	2	2	no	—
705	#41	—	2	2	no	—
706	#41	—	2	1	no	—
707	#41	—	2	1	no	—
708	#41	—	2	1	no	—
709	#41	—	2	1	no	—
710	#41	—	2	1	no	—
711	#41	—	2	1	no	—
712	#41	—	2	1	no	—
713	#41	—	2	1	no	—
714	#41	—	4	2	no	—
715	#41	—	4	2	no	—
716	#41	—	4	1	no	—
717	#41	—	4	1	no	—
718	#41	—	4	2	no	—
719	#41	—	4	2	no	—
720	#41	—	4	2	no	—
721	#41	—	4	2	no	—
722	#41	—	4	2	no	—
723	#41	—	4	2	no	—
724	#41	#41×C₁₉	1	2	yes	—
725	#41	#41×C₁₉	1	2	yes	—
726	C₂×Q₈	—	2	1	no	—
727	C₂×Q₈	—	2	2	no	—
728	C₂×Q₈	—	4	1	no	—
729	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
730	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
731	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
732	C₂×D₄	—	2	1	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	1	no	—
738	C₂×D₄	—	2	1	no	—
739	C₂×D₄	—	2	1	no	—
740	C₂×D₄	—	2	1	no	—
741	C₂×D₄	—	2	1	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	1	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	1	no	—
748	C₂×D₄	—	2	1	no	—
749	C₂×D₄	—	2	1	no	—
750	C₂×D₄	—	2	1	no	—
751	C₂×D₄	—	2	1	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	1	no	—
754	C₂×D₄	—	4	1	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	2	no	—
759	C₂×D₄	—	4	4	no	—
760	C₂×D₄	—	4	4	no	—
761	C₂×D₄	—	4	2	no	—
762	C₂×D₄	—	4	2	no	—
763	C₂×D₄	—	8	2	no	—
764	C₂×D₄	—	8	4	no	—
765	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
766	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
767	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	1	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	1	no	—
775	C₂²×C₄	—	2	1	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	1	no	—
778	C₂²×C₄	—	2	1	no	—
779	C₂²×C₄	—	2	1	no	—
780	C₂²×C₄	—	2	1	no	—
781	C₂²×C₄	—	2	1	no	—
782	C₂²×C₄	—	2	1	no	—
783	C₂²×C₄	—	2	1	no	—
784	C₂²×C₄	—	4	2	no	—
785	C₂²×C₄	—	4	2	no	—
786	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
787	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
788	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
789	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
790	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
791	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
793	M₁₆	—	2	1	no	—
794	M₁₆	—	2	1	no	—
795	M₁₆	—	2	1	no	—
796	M₁₆	—	2	1	no	—
797	M₁₆	—	2	1	no	—
798	M₁₆	—	2	1	no	—
799	M₁₆	—	2	1	no	—
800	M₁₆	—	2	1	no	—
801	M₁₆	—	4	2	no	—
802	C₂×C₈	—	2	1	no	—
803	C₂×C₈	—	2	1	no	—
804	C₂×C₈	—	2	1	no	—
805	C₂×C₈	—	2	1	no	—
806	C₂×C₈	—	4	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	1	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	1	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	8	2	no	—
818	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
819	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	1	no	—
826	C₂²⋊C₄	—	2	1	no	—
827	C₂²⋊C₄	—	2	1	no	—
828	C₂²⋊C₄	—	2	1	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	1	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	4	no	—
834	C₂²⋊C₄	—	4	1	no	—
835	C₂²⋊C₄	—	4	1	no	—
836	C₂²⋊C₄	—	8	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	1	no	—
839	C₄²	—	2	1	no	—
840	C₄²	—	2	1	no	—
841	C₄²	—	2	1	no	—
842	C₄²	—	2	1	no	—
843	C₄²	—	4	1	no	—
844	C₄²	—	4	1	no	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	4	1	no	—
854	C₂³	—	4	1	no	—
855	C₂³	—	4	2	no	—
856	C₂³	—	4	2	no	—
857	C₂³	—	4	4	no	—
858	C₂³	—	4	2	no	—
859	C₂³	—	4	2	no	—
860	C₂³	—	8	1	no	—
861	C₂³	—	8	2	no	—
862	C₂³	—	8	2	no	—
863	C₂³	C₁₉×#120	1	1	yes	characteristic
864	C₂³	C₁₉×#120	1	1	yes	characteristic
865	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
866	Q₈	—	2	1	no	—
867	Q₈	—	2	1	no	—
868	Q₈	—	2	1	no	—
869	Q₈	—	2	1	no	—
870	Q₈	—	2	1	no	—
871	Q₈	—	4	2	no	—
872	Q₈	C₁₉×#123	1	2	yes	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	2	1	no	—
876	D₄	—	2	1	no	—
877	D₄	—	2	1	no	—
878	D₄	—	2	1	no	—
879	D₄	—	2	1	no	—
880	D₄	—	4	2	no	—
881	D₄	—	4	2	no	—
882	D₄	—	4	4	no	—
883	D₄	—	4	2	no	—
884	D₄	—	4	4	no	—
885	D₄	—	4	4	no	—
886	D₄	—	4	2	no	—
887	D₄	—	4	1	no	—
888	D₄	—	4	1	no	—
889	D₄	—	4	1	no	—
890	D₄	—	4	1	no	—
891	D₄	—	4	1	no	—
892	D₄	—	4	1	no	—
893	D₄	—	4	1	no	—
894	D₄	—	4	1	no	—
895	D₄	—	8	2	no	—
896	D₄	—	8	1	no	—
897	D₄	—	8	2	no	—
898	D₄	—	8	2	no	—
899	D₄	—	8	2	no	—
900	D₄	C₁₉×#123	1	2	yes	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	4	2	no	—
921	C₂×C₄	—	4	2	no	—
922	C₂×C₄	—	4	2	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	1	no	—
925	C₂×C₄	—	4	1	no	—
926	C₂×C₄	—	4	1	no	—
927	C₂×C₄	—	4	1	no	—
928	C₂×C₄	—	4	1	no	—
929	C₂×C₄	—	4	1	no	—
930	C₂×C₄	—	4	2	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	2	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	4	2	no	—
935	C₂×C₄	—	4	1	no	—
936	C₂×C₄	—	4	1	no	—
937	C₂×C₄	—	4	1	no	—
938	C₂×C₄	—	8	2	no	—
939	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
940	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
941	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
942	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
943	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
944	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
945	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
946	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
947	C₈	—	4	1	no	—
948	C₈	—	4	1	no	—
949	C₈	—	4	1	no	—
950	C₈	—	4	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	2	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	4	1	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	1	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	1	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	1	no	—
971	C₂²	—	8	1	no	—
972	C₂²	—	8	1	no	—
973	C₂²	—	8	2	no	—
974	C₂²	—	8	2	no	—
975	C₂²	—	8	4	no	—
976	C₂²	—	16	4	no	—
977	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
978	C₂²	C₁₉×#546	1	1	yes	characteristic
979	C₂²	C₁₉×#546	1	1	yes	characteristic
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	2	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	1	no	—
985	C₄	—	4	1	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	1	no	—
989	C₄	—	8	1	no	—
990	C₄	—	8	1	no	—
991	C₄	—	8	1	no	—
992	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
993	C₄	C₁₉×#534	1	1	yes	characteristic
994	C₄	C₁₉×#546	1	1	yes	characteristic
995	C₄	C₁₉×#546	1	1	yes	characteristic
996	C₂	—	2	1	no	—
997	C₂	—	2	1	no	—
998	C₂	—	4	1	no	—
999	C₂	—	4	1	no	—
1000	C₂	—	4	2	no	—
1001	C₂	—	8	1	no	—
1002	C₂	—	8	2	no	—
1003	C₂	—	8	1	no	—
1004	C₂	C₁₉×#2405	1	1	yes	characteristic
1005	C₂	C₁₉×#3018	1	1	yes	characteristic
1006	C₂	C₁₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3488	C₂
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
2. C₁₉×#3093	C₂	semidirect
3. C₁₉×#2896	C₂	semidirect
4. C₁₉×#2500	C₂	semidirect
5. C₁₉×#2040	C₂	semidirect
6. C₁₉×#2039	C₂	semidirect
7. C₁₉×#2037	C₂	semidirect
8. C₁₉×#2037	C₂	semidirect
9. C₁₉×#1900	C₂	semidirect
10. C₁₉×#1871	C₂	semidirect
11. C₁₉×#1860	C₂	semidirect
12. C₁₉×#1859	C₂	semidirect
13. C₁₉×#1792	C₂	semidirect
14. C₁₉×#1792	C₂	semidirect
15. C₁₉×#1789	C₂	semidirect
18. C₂²×M₁₆×C₁₉	C₂²	semidirect
34. C₂×C₁₉×#117	C₂²	semidirect
39. C₁₉×#428	C₂²	semidirect
40. C₁₉×#428	C₂²	semidirect
43. C₂×C₁₉×#104	C₂²	semidirect
44. C₂×C₁₉×#104	C₂²	semidirect
45. C₂×C₁₉×#104	C₂²	semidirect
46. C₂×C₁₉×#104	C₂²	semidirect
51. C₁₉×#417	C₂²	semidirect
52. C₁₉×#417	C₂²	semidirect
53. C₁₉×#417	C₂²	semidirect
54. C₁₉×#417	C₂²	semidirect
57. C₂×C₁₉×#100	C₂²	semidirect
58. C₂×C₁₉×#100	C₂²	semidirect
59. C₁₉×#407	C₂²	semidirect
61. C₁₉×#390	C₂²	semidirect
62. C₁₉×#390	C₂²	semidirect
64. C₁₉×#384	C₂²	semidirect
65. C₁₉×#382	C₂²	semidirect
66. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
67. C₁₉×#343	C₂²	semidirect
68. C₁₉×#343	C₂²	semidirect
69. C₁₉×#339	C₂²	semidirect
70. C₁₉×#339	C₂²	semidirect
341. #24031	C₁₉	direct (N × H)
449. #3093	C₂×C₁₉	semidirect
450. #2896	C₂×C₁₉	semidirect
451. #2500	C₂×C₁₉	semidirect
452. #2040	C₂×C₁₉	semidirect
453. #2039	C₂×C₁₉	semidirect
454. #2037	C₂×C₁₉	semidirect
455. #2037	C₂×C₁₉	semidirect
456. #1900	C₂×C₁₉	semidirect
457. #1871	C₂×C₁₉	semidirect
458. #1860	C₂×C₁₉	semidirect
459. #1859	C₂×C₁₉	semidirect
460. #1792	C₂×C₁₉	semidirect
461. #1792	C₂×C₁₉	semidirect
462. #1789	C₂×C₁₉	semidirect
510. C₂²×M₁₆	C₂²×C₁₉	semidirect
526. C₂×#117	C₂²×C₁₉	semidirect
531. #428	C₂²×C₁₉	semidirect
532. #428	C₂²×C₁₉	semidirect
535. C₂×#104	C₂²×C₁₉	semidirect
536. C₂×#104	C₂²×C₁₉	semidirect
537. C₂×#104	C₂²×C₁₉	semidirect
538. C₂×#104	C₂²×C₁₉	semidirect
543. #417	C₂²×C₁₉	semidirect
544. #417	C₂²×C₁₉	semidirect
545. #417	C₂²×C₁₉	semidirect
546. #417	C₂²×C₁₉	semidirect
549. C₂×#100	C₂²×C₁₉	semidirect
550. C₂×#100	C₂²×C₁₉	semidirect
551. #407	C₂²×C₁₉	semidirect
553. #390	C₂²×C₁₉	semidirect
554. #390	C₂²×C₁₉	semidirect
556. #384	C₂²×C₁₉	semidirect
557. #382	C₂²×C₁₉	semidirect
558. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
559. #343	C₂²×C₁₉	semidirect
560. #343	C₂²×C₁₉	semidirect
561. #339	C₂²×C₁₉	semidirect
562. #339	C₂²×C₁₉	semidirect
697. C₁₉	#24031	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3488	2
C₁₉×#3093	2
C₁₉×#2896	2
C₁₉×#2500	2
C₁₉×#2040	2
C₁₉×#2039	2
C₁₉×#2037	2
C₁₉×#1900	2
C₁₉×#1871	2
C₁₉×#1860	2
C₁₉×#1859	2
C₁₉×#1792	2
C₁₉×#1789	2
#24031	19

Subgroups — C19×#24031 #18029990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24031 #18029990