Subgroups — C₁₉×#61207 #18067166

Order 4864.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3500	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3327	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3323	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3316	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3314	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3313	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3311	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3300	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3296	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3140	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3076	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3059	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3057	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₉×#464	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#3011	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#3009	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₁₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#2935	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₉×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#2897	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
27	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
28	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#559	—	2	1	no	—
32	C₁₉×#557	—	2	1	no	—
33	C₁₉×#556	—	2	1	no	—
34	C₁₉×#556	—	2	1	no	—
35	C₁₉×#556	C₂²	1	2	yes	complemented
36	C₁₉×#554	C₂²	1	2	yes	complemented
37	C₁₉×#552	C₂²	1	2	yes	complemented
38	C₁₉×#552	C₂²	1	2	yes	complemented
39	C₁₉×#548	C₂²	1	2	yes	—
40	C₁₉×#548	C₂²	1	2	yes	—
41	C₁₉×#546	—	2	2	no	—
42	C₁₉×#546	—	2	2	no	—
43	C₁₉×#546	C₂²	1	2	yes	—
44	C₁₉×#546	C₂²	1	2	yes	—
45	C₁₉×#539	—	2	2	no	—
46	C₁₉×#536	—	2	1	no	—
47	C₁₉×#536	C₂²	1	1	yes	characteristic
48	C₁₉×#536	C₂²	1	1	yes	characteristic
49	C₁₉×#536	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#535	—	2	1	no	—
51	C₁₉×#535	C₂²	1	1	yes	characteristic
52	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#532	—	2	1	no	—
54	C₁₉×#532	C₂²	1	1	yes	characteristic
55	C₁₉×#529	—	2	2	no	—
56	C₂×C₁₉×#124	—	2	1	no	—
57	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
58	C₁₉×#520	C₂²	1	1	yes	characteristic
59	C₁₉×#520	C₂²	1	1	yes	characteristic, complemented
60	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
61	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#489	C₂²	1	2	yes	complemented
63	C₁₉×#489	C₂²	1	2	yes	complemented
64	C₁₉×#488	C₂²	1	2	yes	complemented
65	C₁₉×#488	C₂²	1	2	yes	complemented
66	C₁₉×#485	C₂²	1	2	yes	complemented
67	C₁₉×#485	C₂²	1	2	yes	complemented
68	C₁₉×#484	C₂²	1	2	yes	complemented
69	C₁₉×#483	C₂²	1	2	yes	complemented
70	C₁₉×#482	C₂²	1	2	yes	complemented
71	C₁₉×#482	C₂²	1	2	yes	complemented
72	C₁₉×#481	C₂²	1	2	yes	complemented
73	C₁₉×#480	C₂²	1	2	yes	complemented
74	C₁₉×#479	C₂²	1	1	yes	characteristic, complemented
75	C₁₉×#479	C₂²	1	1	yes	characteristic, complemented
76	C₁₉×#478	C₂²	1	1	yes	characteristic, complemented
77	C₁₉×#478	C₂²	1	1	yes	characteristic, complemented
78	C₁₉×#477	C₂²	1	1	yes	characteristic, complemented
79	C₁₉×#476	C₂²	1	1	yes	characteristic, complemented
80	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
81	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
82	C₁₉×#470	C₂²	1	2	yes	complemented
83	C₁₉×#470	C₂²	1	2	yes	complemented
84	C₁₉×#468	C₂²	1	2	yes	complemented
85	C₁₉×#468	C₂²	1	2	yes	complemented
86	C₁₉×#467	C₂²	1	2	yes	complemented
87	C₁₉×#467	C₂²	1	2	yes	complemented
88	C₁₉×#465	C₂²	1	2	yes	complemented
89	C₁₉×#465	C₂²	1	2	yes	complemented
90	C₁₉×#464	C₂²	1	2	yes	complemented
91	C₁₉×#464	C₂²	1	2	yes	complemented
92	C₁₉×#464	C₂²	1	2	yes	complemented
93	C₁₉×#464	C₂²	1	2	yes	complemented
94	C₁₉×#452	C₂²	1	2	yes	—
95	C₁₉×#452	C₂²	1	2	yes	—
96	C₁₉×#452	C₂²	1	2	yes	complemented
97	C₁₉×#452	C₂²	1	2	yes	complemented
98	C₁₉×#451	C₂²	1	2	yes	complemented
99	C₁₉×#451	C₂²	1	2	yes	complemented
100	C₁₉×#450	C₂²	1	2	yes	—
101	C₁₉×#450	C₂²	1	2	yes	—
102	C₁₉×#441	C₂²	1	2	yes	complemented
103	C₁₉×#440	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
106	C₁₉×#436	C₂²	1	2	yes	complemented
107	C₁₉×#435	C₂²	1	2	yes	complemented
108	C₁₉×#435	C₂²	1	2	yes	complemented
109	C₈×D₄×C₁₉	C₂²	1	2	yes	complemented
110	C₁₉×#428	C₂²	1	1	yes	characteristic, complemented
111	C₁₉×#427	C₂²	1	1	yes	characteristic, complemented
112	C₁₉×#427	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
114	C₁₉×#419	C₂²	1	1	yes	characteristic, complemented
115	C₁₉×#419	C₂²	1	1	yes	characteristic, complemented
116	C₁₉×#419	C₂²	1	2	yes	complemented
117	C₁₉×#419	C₂²	1	1	yes	characteristic, complemented
118	C₁₉×#418	C₂²	1	1	yes	characteristic
119	C₁₉×#418	C₂²	1	2	yes	—
120	C₁₉×#418	C₂²	1	1	yes	characteristic
121	C₁₉×#417	C₂²	1	1	yes	characteristic
122	C₁₉×#417	C₂²	1	2	yes	—
123	C₁₉×#417	C₂²	1	2	yes	complemented
124	C₁₉×#416	C₂²	1	1	yes	characteristic
125	C₁₉×#416	C₂²	1	1	yes	characteristic
126	C₁₉×#416	C₂²	1	2	yes	—
127	C₁₉×#416	C₂²	1	2	yes	complemented
128	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
130	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
131	C₂×C₁₉×#102	C₂²	1	2	yes	—
132	C₁₉×#408	C₂²	1	1	yes	characteristic
133	C₁₉×#408	C₂²	1	1	yes	characteristic, complemented
134	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
135	C₁₉×2₋¹⁺⁴	—	2	4	no	—
136	C₁₉×2₋¹⁺⁴	—	4	2	no	—
137	C₁₉×H(5,𝔽₂)	—	2	4	no	—
138	C₁₉×H(5,𝔽₂)	—	4	2	no	—
139	C₂×#41×C₁₉	—	2	1	no	—
140	C₂×#41×C₁₉	—	2	1	no	—
141	C₂×#41×C₁₉	—	2	2	no	—
142	C₂×#41×C₁₉	C₂³	1	2	yes	—
143	C₂×#41×C₁₉	C₂³	1	2	yes	—
144	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
145	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
146	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
147	C₂²×Q₈×C₁₉	—	2	1	no	—
148	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
151	C₂²×D₄×C₁₉	—	2	1	no	—
152	C₂²×D₄×C₁₉	—	2	2	no	—
153	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
154	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
155	C₁₉×#137	—	2	4	no	—
156	C₂×Q₁₆×C₁₉	—	4	2	no	—
157	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
158	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₁₉	—	4	2	no	—
161	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
164	C₁₉×#131	—	4	2	no	—
165	C₁₉×#131	—	4	2	no	—
166	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
167	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
168	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
169	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
170	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
171	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
172	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
173	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
174	C₁₉×C₄⋊Q₈	—	2	1	no	—
175	C₁₉×C₄⋊Q₈	—	2	1	no	—
176	C₁₉×C₄⋊Q₈	—	2	1	no	—
177	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
178	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₁₉×#127	—	2	1	no	—
181	C₁₉×#127	D₄	1	1	yes	characteristic
182	C₁₉×#126	—	2	2	no	—
183	C₁₉×#126	—	2	2	no	—
184	C₁₉×#126	—	2	2	no	—
185	C₁₉×#126	—	2	2	no	—
186	C₁₉×#125	—	2	2	no	—
187	C₁₉×#125	—	2	2	no	—
188	C₁₉×#125	—	2	2	no	—
189	C₁₉×#125	C₂³	1	1	yes	characteristic
190	C₁₉×#125	C₂³	1	1	yes	characteristic
191	C₁₉×#124	—	2	1	no	—
192	C₁₉×#124	—	2	1	no	—
193	C₁₉×#124	—	2	2	no	—
194	C₁₉×#124	—	2	1	no	—
195	C₁₉×#124	—	2	1	no	—
196	C₁₉×#124	—	2	2	no	—
197	C₁₉×#124	—	2	2	no	—
198	C₁₉×#124	—	2	1	no	—
199	C₁₉×#124	—	2	1	no	—
200	C₁₉×#124	D₄	1	1	yes	characteristic
201	C₁₉×#124	D₄	1	1	yes	characteristic
202	C₁₉×#124	C₂³	1	2	yes	—
203	C₁₉×#124	C₂³	1	2	yes	—
204	C₁₉×#123	—	2	2	no	—
205	C₁₉×#123	—	2	2	no	—
206	C₁₉×#123	—	2	2	no	—
207	C₁₉×#123	—	2	2	no	—
208	C₁₉×#123	—	2	2	no	—
209	C₁₉×#123	—	2	2	no	—
210	C₁₉×#123	—	2	2	no	—
211	C₁₉×C₂²⋊Q₈	—	2	1	no	—
212	C₁₉×C₂²⋊Q₈	—	2	1	no	—
213	C₁₉×C₂²⋊Q₈	—	2	2	no	—
214	C₁₉×C₂²⋊Q₈	—	2	2	no	—
215	C₁₉×C₂²⋊Q₈	—	2	2	no	—
216	C₁₉×C₂²⋊Q₈	—	2	2	no	—
217	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₁₉×#121	—	2	2	no	—
224	C₁₉×#121	—	2	2	no	—
225	C₁₉×#121	—	2	2	no	—
226	C₁₉×#121	—	2	2	no	—
227	C₁₉×#121	D₄	1	2	yes	—
228	C₁₉×#121	D₄	1	2	yes	—
229	C₁₉×#121	C₂³	1	2	yes	—
230	C₁₉×#121	C₂³	1	2	yes	—
231	C₁₉×#120	—	2	2	no	—
232	C₁₉×#120	—	2	2	no	—
233	C₁₉×#120	—	2	2	no	—
234	C₄×Q₈×C₁₉	—	2	1	no	—
235	C₄×Q₈×C₁₉	—	2	1	no	—
236	C₄×Q₈×C₁₉	—	2	2	no	—
237	C₄×Q₈×C₁₉	—	2	1	no	—
238	C₄×Q₈×C₁₉	—	2	1	no	—
239	C₄×Q₈×C₁₉	—	2	1	no	—
240	C₄×Q₈×C₁₉	—	2	1	no	—
241	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
242	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
244	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₁₉	—	2	2	no	—
246	C₄×D₄×C₁₉	—	2	1	no	—
247	C₄×D₄×C₁₉	—	2	2	no	—
248	C₄×D₄×C₁₉	—	2	1	no	—
249	C₄×D₄×C₁₉	—	2	2	no	—
250	C₄×D₄×C₁₉	—	2	1	no	—
251	C₄×D₄×C₁₉	—	2	1	no	—
252	C₄×D₄×C₁₉	—	2	2	no	—
253	C₄×D₄×C₁₉	—	2	2	no	—
254	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₁₉	C₂³	1	2	yes	—
257	C₄×D₄×C₁₉	C₂³	1	2	yes	—
258	C₁₉×#117	—	2	2	no	—
259	C₁₉×#117	—	2	2	no	—
260	C₁₉×#117	—	2	1	no	—
261	C₁₉×#117	C₂³	1	1	yes	characteristic
262	C₁₉×#117	C₂³	1	1	yes	characteristic
263	C₁₉×#117	C₂³	1	2	yes	—
264	C₁₉×#117	C₂³	1	2	yes	—
265	C₁₉×#117	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
267	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
270	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
272	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
273	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
274	C₂×C₄²×C₁₉	—	2	1	no	—
275	C₂×C₄²×C₁₉	—	2	1	no	—
276	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
277	C₁₉×#107	C₂³	1	1	yes	characteristic
278	C₁₉×#107	C₂³	1	1	yes	characteristic
279	C₁₉×#107	C₂³	1	1	yes	characteristic
280	C₁₉×#107	C₂³	1	1	yes	characteristic
281	C₁₉×#107	C₂³	1	2	yes	—
282	C₁₉×#106	C₂³	1	1	yes	characteristic
283	C₁₉×#106	C₂³	1	1	yes	characteristic
284	C₁₉×#106	C₂³	1	1	yes	characteristic
285	C₁₉×#106	C₂³	1	1	yes	characteristic
286	C₁₉×#106	C₂³	1	2	yes	—
287	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
289	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
290	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₁₉×#103	C₂³	1	1	yes	characteristic
292	C₁₉×#103	C₂³	1	2	yes	—
293	C₁₉×#103	C₂³	1	2	yes	—
294	C₁₉×#103	C₂³	1	2	yes	—
295	C₁₉×#103	C₂³	1	2	yes	—
296	C₁₉×#103	C₂³	1	1	yes	characteristic
297	C₁₉×#103	C₂³	1	1	yes	characteristic
298	C₁₉×#103	C₂³	1	1	yes	characteristic
299	C₁₉×#103	C₂³	1	2	yes	—
300	C₁₉×#103	C₂³	1	2	yes	—
301	C₁₉×#103	C₂³	1	2	yes	—
302	C₁₉×#103	C₂³	1	2	yes	—
303	C₁₉×#103	C₂³	1	2	yes	—
304	C₁₉×#102	C₂³	1	1	yes	characteristic
305	C₁₉×#102	C₂³	1	2	yes	—
306	C₁₉×#102	C₂³	1	2	yes	—
307	C₁₉×#102	C₂³	1	2	yes	—
308	C₁₉×#102	C₂³	1	2	yes	—
309	C₁₉×#102	C₂³	1	1	yes	characteristic
310	C₁₉×#102	C₂³	1	1	yes	characteristic
311	C₁₉×#102	C₂³	1	1	yes	characteristic
312	C₁₉×#102	C₂³	1	2	yes	—
313	C₁₉×#102	C₂³	1	2	yes	—
314	C₁₉×#102	C₂³	1	2	yes	—
315	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₁₉×#97	C₂³	1	2	yes	—
320	C₄×C₈×C₁₉	C₂³	1	2	yes	—
321	C₂⁴×C₁₉	—	2	2	no	—
322	C₂⁴×C₁₉	—	2	1	no	—
323	#41×C₁₉	—	2	2	no	—
324	#41×C₁₉	—	2	2	no	—
325	#41×C₁₉	—	2	2	no	—
326	#41×C₁₉	—	2	2	no	—
327	#41×C₁₉	—	2	2	no	—
328	#41×C₁₉	—	2	4	no	—
329	#41×C₁₉	—	2	4	no	—
330	#41×C₁₉	—	4	2	no	—
331	#41×C₁₉	—	4	2	no	—
332	#41×C₁₉	—	4	4	no	—
333	#41×C₁₉	—	4	4	no	—
334	#41×C₁₉	—	4	8	no	—
335	#41×C₁₉	#41	1	4	yes	—
336	C₂×Q₈×C₁₉	—	2	1	no	—
337	C₂×Q₈×C₁₉	—	2	1	no	—
338	C₂×Q₈×C₁₉	—	2	2	no	—
339	C₂×Q₈×C₁₉	—	2	1	no	—
340	C₂×Q₈×C₁₉	—	2	1	no	—
341	C₂×Q₈×C₁₉	—	2	4	no	—
342	C₂×Q₈×C₁₉	—	2	2	no	—
343	C₂×Q₈×C₁₉	—	2	2	no	—
344	C₂×Q₈×C₁₉	—	2	2	no	—
345	C₂×Q₈×C₁₉	—	2	2	no	—
346	C₂×Q₈×C₁₉	—	4	2	no	—
347	C₂×Q₈×C₁₉	—	4	4	no	—
348	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
349	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
350	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
351	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
352	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₁₉	—	2	1	no	—
354	C₂×D₄×C₁₉	—	2	4	no	—
355	C₂×D₄×C₁₉	—	2	2	no	—
356	C₂×D₄×C₁₉	—	2	2	no	—
357	C₂×D₄×C₁₉	—	2	2	no	—
358	C₂×D₄×C₁₉	—	2	2	no	—
359	C₂×D₄×C₁₉	—	2	2	no	—
360	C₂×D₄×C₁₉	—	2	1	no	—
361	C₂×D₄×C₁₉	—	2	2	no	—
362	C₂×D₄×C₁₉	—	2	2	no	—
363	C₂×D₄×C₁₉	—	4	2	no	—
364	C₂×D₄×C₁₉	—	4	4	no	—
365	C₂×D₄×C₁₉	—	4	8	no	—
366	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
367	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
369	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
370	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
371	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
373	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₁₉	—	2	1	no	—
375	C₂²×C₄×C₁₉	—	2	1	no	—
376	C₂²×C₄×C₁₉	—	2	1	no	—
377	C₂²×C₄×C₁₉	—	2	2	no	—
378	C₂²×C₄×C₁₉	—	2	1	no	—
379	C₂²×C₄×C₁₉	—	2	2	no	—
380	C₂²×C₄×C₁₉	—	2	2	no	—
381	C₂²×C₄×C₁₉	—	2	2	no	—
382	C₂²×C₄×C₁₉	—	2	2	no	—
383	C₂²×C₄×C₁₉	—	2	1	no	—
384	C₂²×C₄×C₁₉	—	2	1	no	—
385	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
388	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
389	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
390	Q₁₆×C₁₉	—	2	4	no	—
391	Q₁₆×C₁₉	—	4	2	no	—
392	Q₁₆×C₁₉	—	4	2	no	—
393	SD₁₆×C₁₉	—	2	4	no	—
394	SD₁₆×C₁₉	—	4	2	no	—
395	SD₁₆×C₁₉	—	4	2	no	—
396	M₁₆×C₁₉	—	2	2	no	—
397	M₁₆×C₁₉	—	2	2	no	—
398	M₁₆×C₁₉	—	4	2	no	—
399	M₁₆×C₁₉	—	4	2	no	—
400	C₂×C₈×C₁₉	—	2	2	no	—
401	C₂×C₈×C₁₉	—	2	2	no	—
402	C₂×C₈×C₁₉	—	4	2	no	—
403	C₂×C₈×C₁₉	—	4	2	no	—
404	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
407	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₁₉	—	2	2	no	—
411	C₄⋊C₄×C₁₉	—	2	2	no	—
412	C₄⋊C₄×C₁₉	—	2	1	no	—
413	C₄⋊C₄×C₁₉	—	2	2	no	—
414	C₄⋊C₄×C₁₉	—	2	2	no	—
415	C₄⋊C₄×C₁₉	—	2	1	no	—
416	C₄⋊C₄×C₁₉	—	2	1	no	—
417	C₄⋊C₄×C₁₉	—	2	1	no	—
418	C₄⋊C₄×C₁₉	—	2	1	no	—
419	C₄⋊C₄×C₁₉	—	2	2	no	—
420	C₄⋊C₄×C₁₉	—	2	2	no	—
421	C₄⋊C₄×C₁₉	—	2	1	no	—
422	C₄⋊C₄×C₁₉	—	2	2	no	—
423	C₄⋊C₄×C₁₉	—	2	2	no	—
424	C₄⋊C₄×C₁₉	—	2	1	no	—
425	C₄⋊C₄×C₁₉	—	2	1	no	—
426	C₄⋊C₄×C₁₉	—	2	1	no	—
427	C₄⋊C₄×C₁₉	—	2	2	no	—
428	C₄⋊C₄×C₁₉	—	2	2	no	—
429	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
430	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
431	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
432	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
433	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
434	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
438	C₂²⋊C₄×C₁₉	—	2	2	no	—
439	C₂²⋊C₄×C₁₉	—	2	2	no	—
440	C₂²⋊C₄×C₁₉	—	2	2	no	—
441	C₂²⋊C₄×C₁₉	—	2	2	no	—
442	C₂²⋊C₄×C₁₉	—	2	1	no	—
443	C₂²⋊C₄×C₁₉	—	2	1	no	—
444	C₂²⋊C₄×C₁₉	—	2	1	no	—
445	C₂²⋊C₄×C₁₉	—	2	2	no	—
446	C₂²⋊C₄×C₁₉	—	2	2	no	—
447	C₂²⋊C₄×C₁₉	—	2	2	no	—
448	C₂²⋊C₄×C₁₉	—	2	2	no	—
449	C₂²⋊C₄×C₁₉	—	2	2	no	—
450	C₂²⋊C₄×C₁₉	—	2	2	no	—
451	C₂²⋊C₄×C₁₉	—	2	2	no	—
452	C₂²⋊C₄×C₁₉	—	2	2	no	—
453	C₂²⋊C₄×C₁₉	—	2	2	no	—
454	C₂²⋊C₄×C₁₉	—	2	2	no	—
455	C₂²⋊C₄×C₁₉	—	2	1	no	—
456	C₂²⋊C₄×C₁₉	—	2	1	no	—
457	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
458	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
459	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
460	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
461	C₄²×C₁₉	—	2	2	no	—
462	C₄²×C₁₉	—	2	1	no	—
463	C₄²×C₁₉	—	2	1	no	—
464	C₄²×C₁₉	—	2	1	no	—
465	C₄²×C₁₉	—	2	2	no	—
466	C₄²×C₁₉	—	2	2	no	—
467	C₄²×C₁₉	—	2	2	no	—
468	C₄²×C₁₉	—	2	1	no	—
469	C₄²×C₁₉	—	2	1	no	—
470	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
473	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
474	#61207	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
475	C₂³×C₁₉	—	2	1	no	—
476	C₂³×C₁₉	—	2	2	no	—
477	C₂³×C₁₉	—	4	4	no	—
478	C₂³×C₁₉	—	4	2	no	—
479	C₂³×C₁₉	—	8	1	no	—
480	C₂³×C₁₉	—	8	1	no	—
481	C₂³×C₁₉	—	8	2	no	—
482	C₂³×C₁₉	—	8	2	no	—
483	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
484	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
485	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
486	Q₈×C₁₉	—	2	2	no	—
487	Q₈×C₁₉	—	2	2	no	—
488	Q₈×C₁₉	—	2	1	no	—
489	Q₈×C₁₉	—	2	2	no	—
490	Q₈×C₁₉	—	2	2	no	—
491	Q₈×C₁₉	—	2	2	no	—
492	Q₈×C₁₉	—	2	2	no	—
493	Q₈×C₁₉	—	4	4	no	—
494	Q₈×C₁₉	—	4	2	no	—
495	Q₈×C₁₉	—	4	2	no	—
496	Q₈×C₁₉	—	4	2	no	—
497	Q₈×C₁₉	—	8	1	no	—
498	Q₈×C₁₉	C₂×#41	1	2	yes	—
499	D₄×C₁₉	—	2	4	no	—
500	D₄×C₁₉	—	2	4	no	—
501	D₄×C₁₉	—	2	4	no	—
502	D₄×C₁₉	—	2	2	no	—
503	D₄×C₁₉	—	2	2	no	—
504	D₄×C₁₉	—	2	2	no	—
505	D₄×C₁₉	—	2	1	no	—
506	D₄×C₁₉	—	2	2	no	—
507	D₄×C₁₉	—	4	2	no	—
508	D₄×C₁₉	—	4	2	no	—
509	D₄×C₁₉	—	4	4	no	—
510	D₄×C₁₉	—	4	4	no	—
511	D₄×C₁₉	—	4	4	no	—
512	D₄×C₁₉	—	4	2	no	—
513	D₄×C₁₉	—	8	2	no	—
514	D₄×C₁₉	—	8	2	no	—
515	D₄×C₁₉	C₂×#41	1	2	yes	—
516	C₂×C₄×C₁₉	—	2	1	no	—
517	C₂×C₄×C₁₉	—	2	4	no	—
518	C₂×C₄×C₁₉	—	2	2	no	—
519	C₂×C₄×C₁₉	—	2	2	no	—
520	C₂×C₄×C₁₉	—	2	2	no	—
521	C₂×C₄×C₁₉	—	2	2	no	—
522	C₂×C₄×C₁₉	—	2	2	no	—
523	C₂×C₄×C₁₉	—	2	1	no	—
524	C₂×C₄×C₁₉	—	2	1	no	—
525	C₂×C₄×C₁₉	—	2	1	no	—
526	C₂×C₄×C₁₉	—	2	1	no	—
527	C₂×C₄×C₁₉	—	2	2	no	—
528	C₂×C₄×C₁₉	—	2	1	no	—
529	C₂×C₄×C₁₉	—	2	1	no	—
530	C₂×C₄×C₁₉	—	2	2	no	—
531	C₂×C₄×C₁₉	—	4	1	no	—
532	C₂×C₄×C₁₉	—	4	1	no	—
533	C₂×C₄×C₁₉	—	4	4	no	—
534	C₂×C₄×C₁₉	—	4	4	no	—
535	C₂×C₄×C₁₉	—	4	4	no	—
536	C₂×C₄×C₁₉	—	4	2	no	—
537	C₂×C₄×C₁₉	—	4	2	no	—
538	C₂×C₄×C₁₉	—	8	1	no	—
539	C₂×C₄×C₁₉	—	8	1	no	—
540	C₂×C₄×C₁₉	—	8	1	no	—
541	C₂×C₄×C₁₉	—	8	2	no	—
542	C₂×C₄×C₁₉	—	8	2	no	—
543	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
547	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
548	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
551	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
552	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
553	C₈×C₁₉	—	2	2	no	—
554	C₈×C₁₉	—	2	1	no	—
555	C₈×C₁₉	—	2	1	no	—
556	C₈×C₁₉	—	2	1	no	—
557	C₈×C₁₉	—	2	1	no	—
558	C₈×C₁₉	—	2	2	no	—
559	#3507	C₂×C₁₉	1	1	yes	characteristic, complemented
560	#3500	C₂×C₁₉	1	1	yes	characteristic
561	#3327	C₂×C₁₉	1	2	yes	complemented
562	#3323	C₂×C₁₉	1	2	yes	complemented
563	#3316	C₂×C₁₉	1	2	yes	complemented
564	#3314	C₂×C₁₉	1	2	yes	complemented
565	#3313	C₂×C₁₉	1	2	yes	complemented
566	#3311	C₂×C₁₉	1	2	yes	complemented
567	#3300	C₂×C₁₉	1	2	yes	complemented
568	#3296	C₂×C₁₉	1	2	yes	complemented
569	#3140	C₂×C₁₉	1	1	yes	characteristic, complemented
570	#3097	C₂×C₁₉	1	1	yes	characteristic, complemented
571	#3096	C₂×C₁₉	1	1	yes	characteristic, complemented
572	#3076	C₂×C₁₉	1	1	yes	characteristic, complemented
573	#3059	C₂×C₁₉	1	1	yes	characteristic, complemented
574	#3057	C₂×C₁₉	1	1	yes	characteristic, complemented
575	C₂×#464	C₂×C₁₉	1	1	yes	characteristic, complemented
576	#3011	C₂×C₁₉	1	1	yes	characteristic, complemented
577	#3009	C₂×C₁₉	1	1	yes	characteristic, complemented
578	C₄×#137	C₂×C₁₉	1	1	yes	characteristic, complemented
579	#2935	C₂×C₁₉	1	1	yes	characteristic, complemented
580	#2898	C₂×C₁₉	1	1	yes	characteristic, complemented
581	#2897	C₂×C₁₉	1	1	yes	characteristic, complemented
582	C₂²×C₁₉	—	2	1	no	—
583	C₂²×C₁₉	—	2	1	no	—
584	C₂²×C₁₉	—	2	2	no	—
585	C₂²×C₁₉	—	2	2	no	—
586	C₂²×C₁₉	—	2	2	no	—
587	C₂²×C₁₉	—	2	2	no	—
588	C₂²×C₁₉	—	2	2	no	—
589	C₂²×C₁₉	—	2	2	no	—
590	C₂²×C₁₉	—	2	2	no	—
591	C₂²×C₁₉	—	4	1	no	—
592	C₂²×C₁₉	—	4	1	no	—
593	C₂²×C₁₉	—	4	2	no	—
594	C₂²×C₁₉	—	4	2	no	—
595	C₂²×C₁₉	—	4	2	no	—
596	C₂²×C₁₉	—	16	2	no	—
597	C₂²×C₁₉	—	16	4	no	—
598	C₂²×C₁₉	#546	1	2	yes	—
599	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
600	C₄×C₁₉	—	2	1	no	—
601	C₄×C₁₉	—	2	1	no	—
602	C₄×C₁₉	—	2	1	no	—
603	C₄×C₁₉	—	2	1	no	—
604	C₄×C₁₉	—	2	2	no	—
605	C₄×C₁₉	—	2	2	no	—
606	C₄×C₁₉	—	2	2	no	—
607	C₄×C₁₉	—	4	2	no	—
608	C₄×C₁₉	—	4	1	no	—
609	C₄×C₁₉	—	4	1	no	—
610	C₄×C₁₉	—	4	1	no	—
611	C₄×C₁₉	—	4	1	no	—
612	C₄×C₁₉	—	4	1	no	—
613	C₄×C₁₉	—	4	1	no	—
614	C₄×C₁₉	—	4	2	no	—
615	C₄×C₁₉	—	4	2	no	—
616	C₄×C₁₉	#546	1	2	yes	—
617	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
618	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
619	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic
620	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
621	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
622	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
623	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
624	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
625	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic, complemented
626	#559	—	2	1	no	—
627	#557	—	2	1	no	—
628	#556	—	2	1	no	—
629	#556	—	2	1	no	—
630	#556	C₂²×C₁₉	1	2	yes	complemented
631	#554	C₂²×C₁₉	1	2	yes	complemented
632	#552	C₂²×C₁₉	1	2	yes	complemented
633	#552	C₂²×C₁₉	1	2	yes	complemented
634	#548	C₂²×C₁₉	1	2	yes	—
635	#548	C₂²×C₁₉	1	2	yes	—
636	#546	—	2	2	no	—
637	#546	—	2	2	no	—
638	#546	C₂²×C₁₉	1	2	yes	—
639	#546	C₂²×C₁₉	1	2	yes	—
640	#539	—	2	2	no	—
641	#536	—	2	1	no	—
642	#536	C₂²×C₁₉	1	1	yes	characteristic
643	#536	C₂²×C₁₉	1	1	yes	characteristic
644	#536	C₂²×C₁₉	1	1	yes	characteristic, complemented
645	#535	—	2	1	no	—
646	#535	C₂²×C₁₉	1	1	yes	characteristic
647	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
648	#532	—	2	1	no	—
649	#532	C₂²×C₁₉	1	1	yes	characteristic
650	#529	—	2	2	no	—
651	C₂×#124	—	2	1	no	—
652	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
653	#520	C₂²×C₁₉	1	1	yes	characteristic
654	#520	C₂²×C₁₉	1	1	yes	characteristic, complemented
655	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
656	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
657	#489	C₂²×C₁₉	1	2	yes	complemented
658	#489	C₂²×C₁₉	1	2	yes	complemented
659	#488	C₂²×C₁₉	1	2	yes	complemented
660	#488	C₂²×C₁₉	1	2	yes	complemented
661	#485	C₂²×C₁₉	1	2	yes	complemented
662	#485	C₂²×C₁₉	1	2	yes	complemented
663	#484	C₂²×C₁₉	1	2	yes	complemented
664	#483	C₂²×C₁₉	1	2	yes	complemented
665	#482	C₂²×C₁₉	1	2	yes	complemented
666	#482	C₂²×C₁₉	1	2	yes	complemented
667	#481	C₂²×C₁₉	1	2	yes	complemented
668	#480	C₂²×C₁₉	1	2	yes	complemented
669	#479	C₂²×C₁₉	1	1	yes	characteristic, complemented
670	#479	C₂²×C₁₉	1	1	yes	characteristic, complemented
671	#478	C₂²×C₁₉	1	1	yes	characteristic, complemented
672	#478	C₂²×C₁₉	1	1	yes	characteristic, complemented
673	#477	C₂²×C₁₉	1	1	yes	characteristic, complemented
674	#476	C₂²×C₁₉	1	1	yes	characteristic, complemented
675	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
676	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
677	#470	C₂²×C₁₉	1	2	yes	complemented
678	#470	C₂²×C₁₉	1	2	yes	complemented
679	#468	C₂²×C₁₉	1	2	yes	complemented
680	#468	C₂²×C₁₉	1	2	yes	complemented
681	#467	C₂²×C₁₉	1	2	yes	complemented
682	#467	C₂²×C₁₉	1	2	yes	complemented
683	#465	C₂²×C₁₉	1	2	yes	complemented
684	#465	C₂²×C₁₉	1	2	yes	complemented
685	#464	C₂²×C₁₉	1	2	yes	complemented
686	#464	C₂²×C₁₉	1	2	yes	complemented
687	#464	C₂²×C₁₉	1	2	yes	complemented
688	#464	C₂²×C₁₉	1	2	yes	complemented
689	#452	C₂²×C₁₉	1	2	yes	—
690	#452	C₂²×C₁₉	1	2	yes	—
691	#452	C₂²×C₁₉	1	2	yes	complemented
692	#452	C₂²×C₁₉	1	2	yes	complemented
693	#451	C₂²×C₁₉	1	2	yes	complemented
694	#451	C₂²×C₁₉	1	2	yes	complemented
695	#450	C₂²×C₁₉	1	2	yes	—
696	#450	C₂²×C₁₉	1	2	yes	—
697	#441	C₂²×C₁₉	1	2	yes	complemented
698	#440	C₂²×C₁₉	1	2	yes	complemented
699	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
700	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
701	#436	C₂²×C₁₉	1	2	yes	complemented
702	#435	C₂²×C₁₉	1	2	yes	complemented
703	#435	C₂²×C₁₉	1	2	yes	complemented
704	C₈×D₄	C₂²×C₁₉	1	2	yes	complemented
705	#428	C₂²×C₁₉	1	1	yes	characteristic, complemented
706	#427	C₂²×C₁₉	1	1	yes	characteristic, complemented
707	#427	C₂²×C₁₉	1	1	yes	characteristic, complemented
708	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
709	#419	C₂²×C₁₉	1	1	yes	characteristic, complemented
710	#419	C₂²×C₁₉	1	1	yes	characteristic, complemented
711	#419	C₂²×C₁₉	1	2	yes	complemented
712	#419	C₂²×C₁₉	1	1	yes	characteristic, complemented
713	#418	C₂²×C₁₉	1	1	yes	characteristic
714	#418	C₂²×C₁₉	1	1	yes	characteristic
715	#418	C₂²×C₁₉	1	2	yes	—
716	#417	C₂²×C₁₉	1	1	yes	characteristic
717	#417	C₂²×C₁₉	1	2	yes	—
718	#417	C₂²×C₁₉	1	2	yes	complemented
719	#416	C₂²×C₁₉	1	1	yes	characteristic
720	#416	C₂²×C₁₉	1	1	yes	characteristic
721	#416	C₂²×C₁₉	1	2	yes	—
722	#416	C₂²×C₁₉	1	2	yes	complemented
723	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
724	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
725	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
726	C₂×#102	C₂²×C₁₉	1	2	yes	—
727	#408	C₂²×C₁₉	1	1	yes	characteristic
728	#408	C₂²×C₁₉	1	1	yes	characteristic, complemented
729	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
730	C₂×C₁₉	—	2	2	no	—
731	C₂×C₁₉	—	4	2	no	—
732	C₂×C₁₉	—	4	2	no	—
733	C₂×C₁₉	—	4	2	no	—
734	C₂×C₁₉	—	8	2	no	—
735	C₂×C₁₉	C₂×#546	1	1	yes	characteristic
736	C₂×C₁₉	#3584	1	1	yes	characteristic
737	C₂×C₁₉	#3586	1	1	yes	characteristic
738	2₋¹⁺⁴	—	2	4	no	—
739	2₋¹⁺⁴	—	4	2	no	—
740	H(5,𝔽₂)	—	2	4	no	—
741	H(5,𝔽₂)	—	4	2	no	—
742	C₂×#41	—	2	1	no	—
743	C₂×#41	—	2	1	no	—
744	C₂×#41	—	2	2	no	—
745	C₂×#41	C₂³×C₁₉	1	2	yes	—
746	C₂×#41	C₂³×C₁₉	1	2	yes	—
747	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
748	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
749	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
750	C₂²×Q₈	—	2	1	no	—
751	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
752	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
753	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
754	C₂²×D₄	—	2	1	no	—
755	C₂²×D₄	—	2	2	no	—
756	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
757	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
758	#137	—	2	4	no	—
759	C₂×Q₁₆	—	4	2	no	—
760	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
761	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
762	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
763	C₂×SD₁₆	—	4	2	no	—
764	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
765	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
766	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
767	#131	—	4	2	no	—
768	#131	—	4	2	no	—
769	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
770	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
771	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
772	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
773	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
774	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
775	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
776	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
777	C₄⋊Q₈	—	2	1	no	—
778	C₄⋊Q₈	—	2	1	no	—
779	C₄⋊Q₈	—	2	1	no	—
780	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
781	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
782	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
783	#127	—	2	1	no	—
784	#127	D₄×C₁₉	1	1	yes	characteristic
785	#126	—	2	2	no	—
786	#126	—	2	2	no	—
787	#126	—	2	2	no	—
788	#126	—	2	2	no	—
789	#125	—	2	2	no	—
790	#125	—	2	2	no	—
791	#125	—	2	2	no	—
792	#125	C₂³×C₁₉	1	1	yes	characteristic
793	#125	C₂³×C₁₉	1	1	yes	characteristic
794	#124	—	2	1	no	—
795	#124	—	2	1	no	—
796	#124	—	2	2	no	—
797	#124	—	2	1	no	—
798	#124	—	2	1	no	—
799	#124	—	2	2	no	—
800	#124	—	2	2	no	—
801	#124	—	2	1	no	—
802	#124	—	2	1	no	—
803	#124	D₄×C₁₉	1	1	yes	characteristic
804	#124	D₄×C₁₉	1	1	yes	characteristic
805	#124	C₂³×C₁₉	1	2	yes	—
806	#124	C₂³×C₁₉	1	2	yes	—
807	#123	—	2	2	no	—
808	#123	—	2	2	no	—
809	#123	—	2	2	no	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	C₂²⋊Q₈	—	2	1	no	—
815	C₂²⋊Q₈	—	2	1	no	—
816	C₂²⋊Q₈	—	2	2	no	—
817	C₂²⋊Q₈	—	2	2	no	—
818	C₂²⋊Q₈	—	2	2	no	—
819	C₂²⋊Q₈	—	2	2	no	—
820	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
821	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
822	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
823	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
824	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
825	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
826	#121	—	2	2	no	—
827	#121	—	2	2	no	—
828	#121	—	2	2	no	—
829	#121	—	2	2	no	—
830	#121	D₄×C₁₉	1	2	yes	—
831	#121	D₄×C₁₉	1	2	yes	—
832	#121	C₂³×C₁₉	1	2	yes	—
833	#121	C₂³×C₁₉	1	2	yes	—
834	#120	—	2	2	no	—
835	#120	—	2	2	no	—
836	#120	—	2	2	no	—
837	C₄×Q₈	—	2	1	no	—
838	C₄×Q₈	—	2	1	no	—
839	C₄×Q₈	—	2	2	no	—
840	C₄×Q₈	—	2	1	no	—
841	C₄×Q₈	—	2	1	no	—
842	C₄×Q₈	—	2	1	no	—
843	C₄×Q₈	—	2	1	no	—
844	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
845	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
846	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
847	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
848	C₄×D₄	—	2	2	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	2	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	2	no	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	—	2	2	no	—
856	C₄×D₄	—	2	2	no	—
857	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
858	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
859	C₄×D₄	C₂³×C₁₉	1	2	yes	—
860	C₄×D₄	C₂³×C₁₉	1	2	yes	—
861	#117	—	2	2	no	—
862	#117	—	2	2	no	—
863	#117	—	2	1	no	—
864	#117	C₂³×C₁₉	1	1	yes	characteristic
865	#117	C₂³×C₁₉	1	1	yes	characteristic
866	#117	C₂³×C₁₉	1	2	yes	—
867	#117	C₂³×C₁₉	1	1	yes	characteristic
868	#117	C₂³×C₁₉	1	2	yes	—
869	C₂×C₄⋊C₄	—	2	1	no	—
870	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
871	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
872	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
873	C₂×C₂²⋊C₄	—	2	1	no	—
874	C₂×C₂²⋊C₄	—	2	1	no	—
875	C₂×C₂²⋊C₄	—	2	2	no	—
876	C₂×C₂²⋊C₄	—	2	2	no	—
877	C₂×C₄²	—	2	1	no	—
878	C₂×C₄²	—	2	1	no	—
879	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
880	#107	C₂³×C₁₉	1	1	yes	characteristic
881	#107	C₂³×C₁₉	1	1	yes	characteristic
882	#107	C₂³×C₁₉	1	1	yes	characteristic
883	#107	C₂³×C₁₉	1	1	yes	characteristic
884	#107	C₂³×C₁₉	1	2	yes	—
885	#106	C₂³×C₁₉	1	1	yes	characteristic
886	#106	C₂³×C₁₉	1	1	yes	characteristic
887	#106	C₂³×C₁₉	1	1	yes	characteristic
888	#106	C₂³×C₁₉	1	1	yes	characteristic
889	#106	C₂³×C₁₉	1	2	yes	—
890	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
891	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
892	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
893	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
894	#103	C₂³×C₁₉	1	1	yes	characteristic
895	#103	C₂³×C₁₉	1	2	yes	—
896	#103	C₂³×C₁₉	1	2	yes	—
897	#103	C₂³×C₁₉	1	2	yes	—
898	#103	C₂³×C₁₉	1	2	yes	—
899	#103	C₂³×C₁₉	1	1	yes	characteristic
900	#103	C₂³×C₁₉	1	1	yes	characteristic
901	#103	C₂³×C₁₉	1	1	yes	characteristic
902	#103	C₂³×C₁₉	1	2	yes	—
903	#103	C₂³×C₁₉	1	2	yes	—
904	#103	C₂³×C₁₉	1	2	yes	—
905	#103	C₂³×C₁₉	1	2	yes	—
906	#103	C₂³×C₁₉	1	2	yes	—
907	#102	C₂³×C₁₉	1	1	yes	characteristic
908	#102	C₂³×C₁₉	1	2	yes	—
909	#102	C₂³×C₁₉	1	2	yes	—
910	#102	C₂³×C₁₉	1	2	yes	—
911	#102	C₂³×C₁₉	1	2	yes	—
912	#102	C₂³×C₁₉	1	1	yes	characteristic
913	#102	C₂³×C₁₉	1	1	yes	characteristic
914	#102	C₂³×C₁₉	1	1	yes	characteristic
915	#102	C₂³×C₁₉	1	2	yes	—
916	#102	C₂³×C₁₉	1	2	yes	—
917	#102	C₂³×C₁₉	1	2	yes	—
918	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
919	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
920	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
921	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
922	#97	C₂³×C₁₉	1	2	yes	—
923	C₄×C₈	C₂³×C₁₉	1	2	yes	—
924	C₁₉	#61207	1	1	yes	characteristic, direct product factor, Sylow
925	C₂⁴	—	2	2	no	—
926	C₂⁴	—	2	1	no	—
927	#41	—	2	2	no	—
928	#41	—	2	2	no	—
929	#41	—	2	2	no	—
930	#41	—	2	2	no	—
931	#41	—	2	2	no	—
932	#41	—	2	4	no	—
933	#41	—	2	4	no	—
934	#41	—	4	2	no	—
935	#41	—	4	2	no	—
936	#41	—	4	4	no	—
937	#41	—	4	4	no	—
938	#41	—	4	8	no	—
939	#41	#41×C₁₉	1	4	yes	—
940	C₂×Q₈	—	2	1	no	—
941	C₂×Q₈	—	2	1	no	—
942	C₂×Q₈	—	2	2	no	—
943	C₂×Q₈	—	2	1	no	—
944	C₂×Q₈	—	2	1	no	—
945	C₂×Q₈	—	2	4	no	—
946	C₂×Q₈	—	2	2	no	—
947	C₂×Q₈	—	2	2	no	—
948	C₂×Q₈	—	2	2	no	—
949	C₂×Q₈	—	2	2	no	—
950	C₂×Q₈	—	4	2	no	—
951	C₂×Q₈	—	4	4	no	—
952	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
953	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
954	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
955	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
956	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	—	2	4	no	—
959	C₂×D₄	—	2	2	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	1	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	4	2	no	—
968	C₂×D₄	—	4	4	no	—
969	C₂×D₄	—	4	8	no	—
970	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
971	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
972	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
973	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
974	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
975	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
976	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
977	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	1	no	—
983	C₂²×C₄	—	2	2	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	1	no	—
989	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
990	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
991	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
992	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
993	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
994	Q₁₆	—	2	4	no	—
995	Q₁₆	—	4	2	no	—
996	Q₁₆	—	4	2	no	—
997	SD₁₆	—	2	4	no	—
998	SD₁₆	—	4	2	no	—
999	SD₁₆	—	4	2	no	—
1000	M₁₆	—	2	2	no	—
1001	M₁₆	—	2	2	no	—
1002	M₁₆	—	4	2	no	—
1003	M₁₆	—	4	2	no	—
1004	C₂×C₈	—	2	2	no	—
1005	C₂×C₈	—	2	2	no	—
1006	C₂×C₈	—	4	2	no	—
1007	C₂×C₈	—	4	2	no	—
1008	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
1009	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
1010	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1011	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1012	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1013	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	1	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1034	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1035	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1036	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1037	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1038	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1039	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1040	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1041	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1062	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1063	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1064	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1065	C₄²	—	2	2	no	—
1066	C₄²	—	2	1	no	—
1067	C₄²	—	2	1	no	—
1068	C₄²	—	2	1	no	—
1069	C₄²	—	2	2	no	—
1070	C₄²	—	2	2	no	—
1071	C₄²	—	2	2	no	—
1072	C₄²	—	2	1	no	—
1073	C₄²	—	2	1	no	—
1074	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1075	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1076	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1077	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1078	C₂³	—	2	1	no	—
1079	C₂³	—	2	2	no	—
1080	C₂³	—	4	4	no	—
1081	C₂³	—	4	2	no	—
1082	C₂³	—	8	1	no	—
1083	C₂³	—	8	1	no	—
1084	C₂³	—	8	2	no	—
1085	C₂³	—	8	2	no	—
1086	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1087	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1088	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1089	Q₈	—	2	2	no	—
1090	Q₈	—	2	2	no	—
1091	Q₈	—	2	1	no	—
1092	Q₈	—	2	2	no	—
1093	Q₈	—	2	2	no	—
1094	Q₈	—	2	2	no	—
1095	Q₈	—	2	2	no	—
1096	Q₈	—	4	4	no	—
1097	Q₈	—	4	2	no	—
1098	Q₈	—	4	2	no	—
1099	Q₈	—	4	2	no	—
1100	Q₈	—	8	1	no	—
1101	Q₈	C₂×#41×C₁₉	1	2	yes	—
1102	D₄	—	2	4	no	—
1103	D₄	—	2	4	no	—
1104	D₄	—	2	4	no	—
1105	D₄	—	2	2	no	—
1106	D₄	—	2	2	no	—
1107	D₄	—	2	2	no	—
1108	D₄	—	2	1	no	—
1109	D₄	—	2	2	no	—
1110	D₄	—	4	2	no	—
1111	D₄	—	4	2	no	—
1112	D₄	—	4	4	no	—
1113	D₄	—	4	4	no	—
1114	D₄	—	4	4	no	—
1115	D₄	—	4	2	no	—
1116	D₄	—	8	2	no	—
1117	D₄	—	8	2	no	—
1118	D₄	C₂×#41×C₁₉	1	2	yes	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	4	no	—
1121	C₂×C₄	—	2	2	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	4	1	no	—
1135	C₂×C₄	—	4	1	no	—
1136	C₂×C₄	—	4	4	no	—
1137	C₂×C₄	—	4	4	no	—
1138	C₂×C₄	—	4	4	no	—
1139	C₂×C₄	—	4	2	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	8	1	no	—
1142	C₂×C₄	—	8	1	no	—
1143	C₂×C₄	—	8	1	no	—
1144	C₂×C₄	—	8	2	no	—
1145	C₂×C₄	—	8	2	no	—
1146	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1147	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1148	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1149	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1150	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1151	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1152	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1153	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
1154	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
1155	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1156	C₈	—	2	2	no	—
1157	C₈	—	2	1	no	—
1158	C₈	—	2	1	no	—
1159	C₈	—	2	1	no	—
1160	C₈	—	2	1	no	—
1161	C₈	—	2	2	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	1	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	2	2	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	2	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	16	2	no	—
1177	C₂²	—	16	4	no	—
1178	C₂²	C₁₉×#546	1	2	yes	—
1179	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1180	C₄	—	2	2	no	—
1181	C₄	—	2	2	no	—
1182	C₄	—	2	2	no	—
1183	C₄	—	2	1	no	—
1184	C₄	—	2	1	no	—
1185	C₄	—	2	1	no	—
1186	C₄	—	2	1	no	—
1187	C₄	—	4	2	no	—
1188	C₄	—	4	2	no	—
1189	C₄	—	4	2	no	—
1190	C₄	—	4	1	no	—
1191	C₄	—	4	1	no	—
1192	C₄	—	4	1	no	—
1193	C₄	—	4	1	no	—
1194	C₄	—	4	1	no	—
1195	C₄	—	4	1	no	—
1196	C₄	C₁₉×#546	1	2	yes	—
1197	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
1198	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1199	C₂	—	2	2	no	—
1200	C₂	—	4	2	no	—
1201	C₂	—	4	2	no	—
1202	C₂	—	4	2	no	—
1203	C₂	—	8	2	no	—
1204	C₂	C₂×C₁₉×#546	1	1	yes	characteristic
1205	C₂	C₁₉×#3584	1	1	yes	characteristic
1206	C₂	C₁₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3500	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3507	C₂	semidirect
3. C₁₉×#3327	C₂	semidirect
4. C₁₉×#3323	C₂	semidirect
5. C₁₉×#3316	C₂	semidirect
6. C₁₉×#3314	C₂	semidirect
7. C₁₉×#3313	C₂	semidirect
8. C₁₉×#3311	C₂	semidirect
9. C₁₉×#3300	C₂	semidirect
10. C₁₉×#3296	C₂	semidirect
11. C₁₉×#3140	C₂	semidirect
12. C₁₉×#3097	C₂	semidirect
13. C₁₉×#3096	C₂	semidirect
14. C₁₉×#3076	C₂	semidirect
15. C₁₉×#3059	C₂	semidirect
16. C₁₉×#3057	C₂	semidirect
17. C₂×C₁₉×#464	C₂	semidirect
18. C₁₉×#3011	C₂	semidirect
19. C₁₉×#3009	C₂	semidirect
20. C₄×C₁₉×#137	C₂	semidirect
21. C₁₉×#2935	C₂	semidirect
22. C₁₉×#2898	C₂	semidirect
23. C₁₉×#2897	C₂	semidirect
27. C₂²×Q₁₆×C₁₉	C₂²	semidirect
30. C₂×C₁₉×#131	C₂²	semidirect
35. C₁₉×#556	C₂²	semidirect
36. C₁₉×#554	C₂²	semidirect
37. C₁₉×#552	C₂²	semidirect
38. C₁₉×#552	C₂²	semidirect
49. C₁₉×#536	C₂²	semidirect
52. C₁₉×#533	C₂²	semidirect
59. C₁₉×#520	C₂²	semidirect
61. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
62. C₁₉×#489	C₂²	semidirect
63. C₁₉×#489	C₂²	semidirect
64. C₁₉×#488	C₂²	semidirect
65. C₁₉×#488	C₂²	semidirect
66. C₁₉×#485	C₂²	semidirect
67. C₁₉×#485	C₂²	semidirect
68. C₁₉×#484	C₂²	semidirect
69. C₁₉×#483	C₂²	semidirect
70. C₁₉×#482	C₂²	semidirect
71. C₁₉×#482	C₂²	semidirect
72. C₁₉×#481	C₂²	semidirect
73. C₁₉×#480	C₂²	semidirect
74. C₁₉×#479	C₂²	semidirect
75. C₁₉×#479	C₂²	semidirect
76. C₁₉×#478	C₂²	semidirect
77. C₁₉×#478	C₂²	semidirect
78. C₁₉×#477	C₂²	semidirect
79. C₁₉×#476	C₂²	semidirect
80. C₁₉×#475	C₂²	semidirect
81. C₁₉×#474	C₂²	semidirect
82. C₁₉×#470	C₂²	semidirect
83. C₁₉×#470	C₂²	semidirect
84. C₁₉×#468	C₂²	semidirect
85. C₁₉×#468	C₂²	semidirect
86. C₁₉×#467	C₂²	semidirect
87. C₁₉×#467	C₂²	semidirect
88. C₁₉×#465	C₂²	semidirect
89. C₁₉×#465	C₂²	semidirect
90. C₁₉×#464	C₂²	semidirect
91. C₁₉×#464	C₂²	semidirect
92. C₁₉×#464	C₂²	semidirect
93. C₁₉×#464	C₂²	semidirect
96. C₁₉×#452	C₂²	semidirect
97. C₁₉×#452	C₂²	semidirect
98. C₁₉×#451	C₂²	semidirect
99. C₁₉×#451	C₂²	semidirect
102. C₁₉×#441	C₂²	semidirect
103. C₁₉×#440	C₂²	semidirect
104. C₄×Q₁₆×C₁₉	C₂²	semidirect
105. C₄×SD₁₆×C₁₉	C₂²	semidirect
106. C₁₉×#436	C₂²	semidirect
107. C₁₉×#435	C₂²	semidirect
108. C₁₉×#435	C₂²	semidirect
109. C₈×D₄×C₁₉	C₂²	semidirect
110. C₁₉×#428	C₂²	semidirect
111. C₁₉×#427	C₂²	semidirect
112. C₁₉×#427	C₂²	semidirect
113. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
114. C₁₉×#419	C₂²	semidirect
115. C₁₉×#419	C₂²	semidirect
116. C₁₉×#419	C₂²	semidirect
117. C₁₉×#419	C₂²	semidirect
123. C₁₉×#417	C₂²	semidirect
127. C₁₉×#416	C₂²	semidirect
128. C₂×C₁₉×#103	C₂²	semidirect
129. C₂×C₁₉×#103	C₂²	semidirect
133. C₁₉×#408	C₂²	semidirect
134. C₄×M₁₆×C₁₉	C₂²	semidirect
474. #61207	C₁₉	direct (N × H)
559. #3507	C₂×C₁₉	semidirect
561. #3327	C₂×C₁₉	semidirect
562. #3323	C₂×C₁₉	semidirect
563. #3316	C₂×C₁₉	semidirect
564. #3314	C₂×C₁₉	semidirect
565. #3313	C₂×C₁₉	semidirect
566. #3311	C₂×C₁₉	semidirect
567. #3300	C₂×C₁₉	semidirect
568. #3296	C₂×C₁₉	semidirect
569. #3140	C₂×C₁₉	semidirect
570. #3097	C₂×C₁₉	semidirect
571. #3096	C₂×C₁₉	semidirect
572. #3076	C₂×C₁₉	semidirect
573. #3059	C₂×C₁₉	semidirect
574. #3057	C₂×C₁₉	semidirect
575. C₂×#464	C₂×C₁₉	semidirect
576. #3011	C₂×C₁₉	semidirect
577. #3009	C₂×C₁₉	semidirect
578. C₄×#137	C₂×C₁₉	semidirect
579. #2935	C₂×C₁₉	semidirect
580. #2898	C₂×C₁₉	semidirect
581. #2897	C₂×C₁₉	semidirect
622. C₂²×Q₁₆	C₂²×C₁₉	semidirect
625. C₂×#131	C₂²×C₁₉	semidirect
630. #556	C₂²×C₁₉	semidirect
631. #554	C₂²×C₁₉	semidirect
632. #552	C₂²×C₁₉	semidirect
633. #552	C₂²×C₁₉	semidirect
644. #536	C₂²×C₁₉	semidirect
647. #533	C₂²×C₁₉	semidirect
654. #520	C₂²×C₁₉	semidirect
656. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
657. #489	C₂²×C₁₉	semidirect
658. #489	C₂²×C₁₉	semidirect
659. #488	C₂²×C₁₉	semidirect
660. #488	C₂²×C₁₉	semidirect
661. #485	C₂²×C₁₉	semidirect
662. #485	C₂²×C₁₉	semidirect
663. #484	C₂²×C₁₉	semidirect
664. #483	C₂²×C₁₉	semidirect
665. #482	C₂²×C₁₉	semidirect
666. #482	C₂²×C₁₉	semidirect
667. #481	C₂²×C₁₉	semidirect
668. #480	C₂²×C₁₉	semidirect
669. #479	C₂²×C₁₉	semidirect
670. #479	C₂²×C₁₉	semidirect
671. #478	C₂²×C₁₉	semidirect
672. #478	C₂²×C₁₉	semidirect
673. #477	C₂²×C₁₉	semidirect
674. #476	C₂²×C₁₉	semidirect
675. #475	C₂²×C₁₉	semidirect
676. #474	C₂²×C₁₉	semidirect
677. #470	C₂²×C₁₉	semidirect
678. #470	C₂²×C₁₉	semidirect
679. #468	C₂²×C₁₉	semidirect
680. #468	C₂²×C₁₉	semidirect
681. #467	C₂²×C₁₉	semidirect
682. #467	C₂²×C₁₉	semidirect
683. #465	C₂²×C₁₉	semidirect
684. #465	C₂²×C₁₉	semidirect
685. #464	C₂²×C₁₉	semidirect
686. #464	C₂²×C₁₉	semidirect
687. #464	C₂²×C₁₉	semidirect
688. #464	C₂²×C₁₉	semidirect
691. #452	C₂²×C₁₉	semidirect
692. #452	C₂²×C₁₉	semidirect
693. #451	C₂²×C₁₉	semidirect
694. #451	C₂²×C₁₉	semidirect
697. #441	C₂²×C₁₉	semidirect
698. #440	C₂²×C₁₉	semidirect
699. C₄×Q₁₆	C₂²×C₁₉	semidirect
700. C₄×SD₁₆	C₂²×C₁₉	semidirect
701. #436	C₂²×C₁₉	semidirect
702. #435	C₂²×C₁₉	semidirect
703. #435	C₂²×C₁₉	semidirect
704. C₈×D₄	C₂²×C₁₉	semidirect
705. #428	C₂²×C₁₉	semidirect
706. #427	C₂²×C₁₉	semidirect
707. #427	C₂²×C₁₉	semidirect
708. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
709. #419	C₂²×C₁₉	semidirect
710. #419	C₂²×C₁₉	semidirect
711. #419	C₂²×C₁₉	semidirect
712. #419	C₂²×C₁₉	semidirect
718. #417	C₂²×C₁₉	semidirect
722. #416	C₂²×C₁₉	semidirect
723. C₂×#103	C₂²×C₁₉	semidirect
724. C₂×#103	C₂²×C₁₉	semidirect
728. #408	C₂²×C₁₉	semidirect
729. C₄×M₁₆	C₂²×C₁₉	semidirect
924. C₁₉	#61207	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×#3507	2
C₁₉×#3500	2
C₁₉×#3327	2
C₁₉×#3323	2
C₁₉×#3316	2
C₁₉×#3314	2
C₁₉×#3313	2
C₁₉×#3311	2
C₁₉×#3300	2
C₁₉×#3296	2
C₁₉×#3140	2
C₁₉×#3097	2
C₁₉×#3096	2
C₁₉×#3076	2
C₁₉×#3059	2
C₁₉×#3057	2
C₂×C₁₉×#464	2
C₁₉×#3011	2
C₁₉×#3009	2
C₄×C₁₉×#137	2
C₁₉×#2935	2
C₁₉×#2898	2
C₁₉×#2897	2
#61207	19

Subgroups — C19×#61207 #18067166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61207 #18067166