Subgroups — C₁₉×#60592 #18066551

Order 4864.

2098 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3125	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3124	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3118	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3118	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3114	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3111	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3105	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3102	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3097	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3077	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3076	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3040	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#463	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3009	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#3008	C₂	1	1	yes	maximal, characteristic
19	C₁₉×#2949	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#2948	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₉×#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#559	—	2	1	no	—
30	C₁₉×#559	—	2	1	no	—
31	C₁₉×#556	—	2	1	no	—
32	C₁₉×#556	—	2	1	no	—
33	C₁₉×#551	—	2	2	no	—
34	C₁₉×#551	—	2	2	no	—
35	C₁₉×#542	C₂²	1	2	yes	complemented
36	C₁₉×#542	C₂²	1	2	yes	complemented
37	C₁₉×#536	C₂²	1	1	yes	characteristic
38	C₁₉×#535	C₂²	1	1	yes	characteristic
39	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#529	C₂²	1	2	yes	complemented
41	C₁₉×#529	C₂²	1	2	yes	complemented
42	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#520	—	2	1	no	—
44	C₁₉×#520	C₂²	1	1	yes	characteristic
45	C₁₉×#520	C₂²	1	1	yes	characteristic
46	C₁₉×#520	C₂²	1	2	yes	complemented
47	C₁₉×#519	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#518	—	2	2	no	—
49	C₁₉×#518	—	2	1	no	—
50	C₁₉×#518	C₂²	1	1	yes	characteristic
51	C₁₉×#518	C₂²	1	2	yes	complemented
52	C₁₉×#518	C₂²	1	1	yes	characteristic, complemented
53	C₄×#41×C₁₉	—	2	1	no	—
54	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
55	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
56	C₄×#41×C₁₉	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₁₉	—	2	1	no	—
58	C₂×C₄×D₄×C₁₉	—	2	2	no	—
59	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
60	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
61	C₁₉×#485	C₂²	1	2	yes	complemented
62	C₁₉×#485	C₂²	1	2	yes	complemented
63	C₁₉×#484	C₂²	1	2	yes	complemented
64	C₁₉×#483	C₂²	1	2	yes	complemented
65	C₁₉×#482	C₂²	1	2	yes	complemented
66	C₁₉×#482	C₂²	1	2	yes	complemented
67	C₁₉×#481	C₂²	1	2	yes	complemented
68	C₁₉×#480	C₂²	1	2	yes	complemented
69	C₁₉×#479	C₂²	1	1	yes	characteristic, complemented
70	C₁₉×#479	C₂²	1	1	yes	characteristic, complemented
71	C₁₉×#478	C₂²	1	1	yes	characteristic, complemented
72	C₁₉×#478	C₂²	1	1	yes	characteristic, complemented
73	C₁₉×#478	C₂²	1	2	yes	complemented
74	C₁₉×#478	C₂²	1	2	yes	complemented
75	C₁₉×#477	C₂²	1	1	yes	characteristic, complemented
76	C₁₉×#476	C₂²	1	1	yes	characteristic, complemented
77	C₁₉×#476	C₂²	1	2	yes	complemented
78	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
79	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
80	C₁₉×#474	C₂²	1	2	yes	complemented
81	C₁₉×#464	C₂²	1	2	yes	complemented
82	C₁₉×#464	C₂²	1	2	yes	complemented
83	C₁₉×#463	C₂²	1	2	yes	complemented
84	C₁₉×#463	C₂²	1	2	yes	complemented
85	C₁₉×#463	C₂²	1	2	yes	complemented
86	C₁₉×#463	C₂²	1	2	yes	complemented
87	C₁₉×#463	C₂²	1	2	yes	complemented
88	C₁₉×#463	C₂²	1	2	yes	complemented
89	C₁₉×#452	C₂²	1	2	yes	complemented
90	C₁₉×#452	C₂²	1	2	yes	complemented
91	C₁₉×#450	C₂²	1	2	yes	complemented
92	C₁₉×#450	C₂²	1	2	yes	complemented
93	C₁₉×#449	C₂²	1	2	yes	—
94	C₁₉×#449	C₂²	1	2	yes	—
95	C₁₉×#447	C₂²	1	2	yes	—
96	C₁₉×#447	C₂²	1	2	yes	—
97	C₁₉×#442	C₂²	1	2	yes	complemented
98	C₁₉×#442	C₂²	1	2	yes	complemented
99	C₁₉×#442	C₂²	1	2	yes	complemented
100	C₁₉×#441	C₂²	1	2	yes	complemented
101	C₁₉×#440	C₂²	1	2	yes	complemented
102	C₁₉×#440	C₂²	1	2	yes	complemented
103	C₁₉×#440	C₂²	1	2	yes	complemented
104	C₁₉×#440	C₂²	1	2	yes	complemented
105	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
108	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
110	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
111	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
112	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
113	C₁₉×#433	C₂²	1	2	yes	complemented
114	C₁₉×#433	C₂²	1	2	yes	complemented
115	C₁₉×#432	C₂²	1	2	yes	complemented
116	C₁₉×#431	C₂²	1	2	yes	complemented
117	C₁₉×#428	C₂²	1	1	yes	characteristic, complemented
118	C₁₉×#428	C₂²	1	1	yes	characteristic, complemented
119	C₁₉×#427	C₂²	1	1	yes	characteristic, complemented
120	C₁₉×#427	C₂²	1	1	yes	characteristic, complemented
121	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
123	C₁₉×#419	C₂²	1	1	yes	characteristic, complemented
124	C₁₉×#418	C₂²	1	1	yes	characteristic
125	C₁₉×#418	C₂²	1	1	yes	characteristic
126	C₁₉×#418	C₂²	1	1	yes	characteristic, complemented
127	C₁₉×#416	C₂²	1	1	yes	characteristic
128	C₁₉×#416	C₂²	1	1	yes	characteristic
129	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
131	C₁₉×#408	C₂²	1	1	yes	characteristic
132	C₁₉×#408	C₂²	1	1	yes	characteristic
133	C₁₉×#405	C₂²	1	1	yes	characteristic, complemented
134	C₁₉×#405	C₂²	1	1	yes	characteristic, complemented
135	C₁₉×H(5,𝔽₂)	—	2	4	no	—
136	C₁₉×H(5,𝔽₂)	—	2	4	no	—
137	C₂×#41×C₁₉	—	2	1	no	—
138	C₂×#41×C₁₉	C₂³	1	2	yes	—
139	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
140	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
141	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₁₉	—	2	2	no	—
143	C₂²×D₄×C₁₉	—	2	1	no	—
144	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
146	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₁₉	—	2	1	no	—
148	C₂³×C₄×C₁₉	—	2	2	no	—
149	C₁₉×#137	—	2	4	no	—
150	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
151	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₁₉	—	2	4	no	—
153	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
157	C₂×D₈×C₁₉	—	2	4	no	—
158	C₂×D₈×C₁₉	C₂³	1	2	yes	—
159	C₂×D₈×C₁₉	C₂³	1	2	yes	—
160	C₂×D₈×C₁₉	C₂³	1	2	yes	—
161	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
162	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
163	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
164	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
165	C₁₉×C₄⋊Q₈	—	2	1	no	—
166	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₁₉×#127	—	2	1	no	—
169	C₁₉×#126	—	2	2	no	—
170	C₁₉×#126	—	2	2	no	—
171	C₁₉×#126	—	2	2	no	—
172	C₁₉×#126	—	2	2	no	—
173	C₁₉×#125	C₂³	1	1	yes	characteristic
174	C₁₉×#125	C₂³	1	1	yes	characteristic
175	C₁₉×#124	—	2	1	no	—
176	C₁₉×#124	—	2	1	no	—
177	C₁₉×#124	—	2	2	no	—
178	C₁₉×#124	—	2	2	no	—
179	C₁₉×#124	—	2	1	no	—
180	C₁₉×#124	—	2	1	no	—
181	C₁₉×#124	C₂³	1	2	yes	—
182	C₁₉×#124	C₂³	1	2	yes	—
183	C₁₉×#123	—	2	2	no	—
184	C₁₉×#123	—	2	2	no	—
185	C₁₉×#123	—	2	2	no	—
186	C₁₉×#123	—	2	2	no	—
187	C₁₉×#123	—	2	2	no	—
188	C₁₉×C₂²⋊Q₈	—	2	1	no	—
189	C₁₉×C₂²⋊Q₈	—	2	1	no	—
190	C₁₉×C₂²⋊Q₈	—	2	2	no	—
191	C₁₉×C₂²⋊Q₈	—	2	2	no	—
192	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₁₉×#121	C₂³	1	2	yes	—
195	C₁₉×#121	C₂³	1	2	yes	—
196	C₁₉×#120	—	2	2	no	—
197	C₄×Q₈×C₁₉	—	2	1	no	—
198	C₄×Q₈×C₁₉	—	2	1	no	—
199	C₄×Q₈×C₁₉	—	2	1	no	—
200	C₄×Q₈×C₁₉	—	2	1	no	—
201	C₄×Q₈×C₁₉	—	2	1	no	—
202	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
203	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
204	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
205	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
206	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
207	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
208	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
209	C₄×D₄×C₁₉	—	2	2	no	—
210	C₄×D₄×C₁₉	—	2	1	no	—
211	C₄×D₄×C₁₉	—	2	1	no	—
212	C₄×D₄×C₁₉	—	2	2	no	—
213	C₄×D₄×C₁₉	—	2	1	no	—
214	C₄×D₄×C₁₉	—	2	2	no	—
215	C₄×D₄×C₁₉	—	2	2	no	—
216	C₄×D₄×C₁₉	—	2	2	no	—
217	C₄×D₄×C₁₉	—	2	1	no	—
218	C₄×D₄×C₁₉	—	2	2	no	—
219	C₄×D₄×C₁₉	—	2	1	no	—
220	C₄×D₄×C₁₉	—	2	2	no	—
221	C₄×D₄×C₁₉	—	2	1	no	—
222	C₄×D₄×C₁₉	—	2	1	no	—
223	C₄×D₄×C₁₉	—	2	2	no	—
224	C₄×D₄×C₁₉	—	2	2	no	—
225	C₄×D₄×C₁₉	—	2	2	no	—
226	C₄×D₄×C₁₉	—	2	1	no	—
227	C₄×D₄×C₁₉	—	2	2	no	—
228	C₄×D₄×C₁₉	—	2	1	no	—
229	C₄×D₄×C₁₉	—	2	2	no	—
230	C₄×D₄×C₁₉	D₄	1	2	yes	—
231	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
232	C₄×D₄×C₁₉	D₄	1	2	yes	—
233	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
234	C₄×D₄×C₁₉	C₂³	1	2	yes	—
235	C₄×D₄×C₁₉	C₂³	1	2	yes	—
236	C₄×D₄×C₁₉	C₂³	1	2	yes	—
237	C₄×D₄×C₁₉	C₂³	1	2	yes	—
238	C₄×D₄×C₁₉	C₂³	1	2	yes	—
239	C₄×D₄×C₁₉	C₂³	1	2	yes	—
240	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₁₉	C₂³	1	2	yes	—
242	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
243	C₁₉×#117	—	2	1	no	—
244	C₁₉×#117	—	2	2	no	—
245	C₁₉×#117	—	2	2	no	—
246	C₁₉×#117	—	2	1	no	—
247	C₁₉×#117	—	2	2	no	—
248	C₁₉×#117	—	2	2	no	—
249	C₁₉×#117	—	2	2	no	—
250	C₁₉×#117	C₂³	1	1	yes	characteristic
251	C₁₉×#117	C₂³	1	1	yes	characteristic
252	C₁₉×#117	C₂³	1	1	yes	characteristic
253	C₁₉×#117	C₂³	1	2	yes	—
254	C₁₉×#117	C₂³	1	1	yes	characteristic
255	C₁₉×#117	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
257	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
258	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
260	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
261	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
262	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
263	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
268	C₂×C₄²×C₁₉	—	2	1	no	—
269	C₂×C₄²×C₁₉	—	2	2	no	—
270	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
271	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
272	C₁₉×#107	C₂³	1	1	yes	characteristic
273	C₁₉×#107	C₂³	1	1	yes	characteristic
274	C₁₉×#107	C₂³	1	1	yes	characteristic
275	C₁₉×#107	C₂³	1	1	yes	characteristic
276	C₁₉×#107	C₂³	1	2	yes	—
277	C₁₉×#107	C₂³	1	2	yes	—
278	C₁₉×#106	C₂³	1	1	yes	characteristic
279	C₁₉×#106	C₂³	1	1	yes	characteristic
280	C₁₉×#106	C₂³	1	1	yes	characteristic
281	C₁₉×#106	C₂³	1	1	yes	characteristic
282	C₁₉×#106	C₂³	1	2	yes	—
283	C₁₉×#106	C₂³	1	2	yes	—
284	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
289	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
290	C₁₉×#103	C₂³	1	2	yes	—
291	C₁₉×#103	C₂³	1	2	yes	—
292	C₁₉×#103	C₂³	1	1	yes	characteristic
293	C₁₉×#103	C₂³	1	1	yes	characteristic
294	C₁₉×#103	C₂³	1	1	yes	characteristic
295	C₁₉×#103	C₂³	1	1	yes	characteristic
296	C₁₉×#103	C₂³	1	2	yes	—
297	C₁₉×#103	C₂³	1	2	yes	—
298	C₁₉×#102	C₂³	1	2	yes	—
299	C₁₉×#102	C₂³	1	2	yes	—
300	C₁₉×#102	C₂³	1	1	yes	characteristic
301	C₁₉×#102	C₂³	1	1	yes	characteristic
302	C₁₉×#102	C₂³	1	1	yes	characteristic
303	C₁₉×#102	C₂³	1	1	yes	characteristic
304	C₁₉×#102	C₂³	1	2	yes	—
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	2	yes	—
310	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₁₉×#97	C₂³	1	2	yes	—
315	C₁₉×#97	C₂³	1	2	yes	—
316	C₄×C₈×C₁₉	C₂³	1	2	yes	—
317	C₄×C₈×C₁₉	C₂³	1	2	yes	—
318	C₂⁴×C₁₉	—	2	2	no	—
319	C₂⁴×C₁₉	—	2	1	no	—
320	C₂⁴×C₁₉	—	2	1	no	—
321	#41×C₁₉	—	2	8	no	—
322	#41×C₁₉	—	2	4	no	—
323	#41×C₁₉	—	2	4	no	—
324	#41×C₁₉	—	2	2	no	—
325	#41×C₁₉	—	2	2	no	—
326	#41×C₁₉	—	2	2	no	—
327	#41×C₁₉	#41	1	4	yes	—
328	C₂×Q₈×C₁₉	—	2	1	no	—
329	C₂×Q₈×C₁₉	—	2	1	no	—
330	C₂×Q₈×C₁₉	—	2	1	no	—
331	C₂×Q₈×C₁₉	—	2	2	no	—
332	C₂×Q₈×C₁₉	—	2	2	no	—
333	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
334	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₁₉	—	2	16	no	—
337	C₂×D₄×C₁₉	—	2	8	no	—
338	C₂×D₄×C₁₉	—	2	2	no	—
339	C₂×D₄×C₁₉	—	2	1	no	—
340	C₂×D₄×C₁₉	—	2	4	no	—
341	C₂×D₄×C₁₉	—	2	4	no	—
342	C₂×D₄×C₁₉	—	2	2	no	—
343	C₂×D₄×C₁₉	—	2	2	no	—
344	C₂×D₄×C₁₉	—	2	2	no	—
345	C₂×D₄×C₁₉	—	2	1	no	—
346	C₂×D₄×C₁₉	—	2	1	no	—
347	C₂×D₄×C₁₉	—	2	2	no	—
348	C₂×D₄×C₁₉	—	2	2	no	—
349	C₂×D₄×C₁₉	—	2	2	no	—
350	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
352	C₂×D₄×C₁₉	#41	1	4	yes	—
353	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
354	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₁₉	—	2	2	no	—
357	C₂²×C₄×C₁₉	—	2	1	no	—
358	C₂²×C₄×C₁₉	—	2	1	no	—
359	C₂²×C₄×C₁₉	—	2	2	no	—
360	C₂²×C₄×C₁₉	—	2	1	no	—
361	C₂²×C₄×C₁₉	—	2	1	no	—
362	C₂²×C₄×C₁₉	—	2	2	no	—
363	C₂²×C₄×C₁₉	—	2	2	no	—
364	C₂²×C₄×C₁₉	—	2	1	no	—
365	C₂²×C₄×C₁₉	—	2	2	no	—
366	C₂²×C₄×C₁₉	—	2	2	no	—
367	C₂²×C₄×C₁₉	—	2	2	no	—
368	C₂²×C₄×C₁₉	—	2	2	no	—
369	C₂²×C₄×C₁₉	—	2	2	no	—
370	C₂²×C₄×C₁₉	—	8	2	no	—
371	C₂²×C₄×C₁₉	—	8	4	no	—
372	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
374	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
376	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
377	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
378	Q₁₆×C₁₉	—	2	4	no	—
379	SD₁₆×C₁₉	—	2	4	no	—
380	SD₁₆×C₁₉	—	2	4	no	—
381	SD₁₆×C₁₉	—	2	4	no	—
382	SD₁₆×C₁₉	—	2	4	no	—
383	D₈×C₁₉	—	2	4	no	—
384	D₈×C₁₉	—	2	4	no	—
385	D₈×C₁₉	—	2	4	no	—
386	M₁₆×C₁₉	—	2	2	no	—
387	M₁₆×C₁₉	—	2	2	no	—
388	C₂×C₈×C₁₉	—	2	2	no	—
389	C₂×C₈×C₁₉	—	2	2	no	—
390	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
395	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
396	C₄⋊C₄×C₁₉	—	2	2	no	—
397	C₄⋊C₄×C₁₉	—	2	1	no	—
398	C₄⋊C₄×C₁₉	—	2	2	no	—
399	C₄⋊C₄×C₁₉	—	2	1	no	—
400	C₄⋊C₄×C₁₉	—	2	1	no	—
401	C₄⋊C₄×C₁₉	—	2	1	no	—
402	C₄⋊C₄×C₁₉	—	2	1	no	—
403	C₄⋊C₄×C₁₉	—	2	2	no	—
404	C₄⋊C₄×C₁₉	—	2	2	no	—
405	C₄⋊C₄×C₁₉	—	2	2	no	—
406	C₄⋊C₄×C₁₉	—	2	2	no	—
407	C₄⋊C₄×C₁₉	—	2	1	no	—
408	C₄⋊C₄×C₁₉	—	2	1	no	—
409	C₄⋊C₄×C₁₉	—	2	1	no	—
410	C₄⋊C₄×C₁₉	—	2	1	no	—
411	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
422	C₂²⋊C₄×C₁₉	—	2	2	no	—
423	C₂²⋊C₄×C₁₉	—	2	1	no	—
424	C₂²⋊C₄×C₁₉	—	2	1	no	—
425	C₂²⋊C₄×C₁₉	—	2	1	no	—
426	C₂²⋊C₄×C₁₉	—	2	2	no	—
427	C₂²⋊C₄×C₁₉	—	2	2	no	—
428	C₂²⋊C₄×C₁₉	—	2	2	no	—
429	C₂²⋊C₄×C₁₉	—	2	1	no	—
430	C₂²⋊C₄×C₁₉	—	2	2	no	—
431	C₂²⋊C₄×C₁₉	—	2	2	no	—
432	C₂²⋊C₄×C₁₉	—	2	2	no	—
433	C₂²⋊C₄×C₁₉	—	2	2	no	—
434	C₂²⋊C₄×C₁₉	—	2	1	no	—
435	C₂²⋊C₄×C₁₉	—	2	2	no	—
436	C₂²⋊C₄×C₁₉	—	2	2	no	—
437	C₂²⋊C₄×C₁₉	—	2	2	no	—
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	2	no	—
443	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
446	C₄²×C₁₉	—	2	1	no	—
447	C₄²×C₁₉	—	2	2	no	—
448	C₄²×C₁₉	—	2	1	no	—
449	C₄²×C₁₉	—	2	2	no	—
450	C₄²×C₁₉	—	2	1	no	—
451	C₄²×C₁₉	—	2	2	no	—
452	C₄²×C₁₉	—	2	2	no	—
453	C₄²×C₁₉	—	2	1	no	—
454	C₄²×C₁₉	—	2	1	no	—
455	C₄²×C₁₉	C₂×D₄	1	2	yes	—
456	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₁₉	C₂×D₄	1	2	yes	—
458	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
460	C₄²×C₁₉	C₂⁴	1	2	yes	—
461	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
462	#60592	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
463	C₂³×C₁₉	—	2	8	no	—
464	C₂³×C₁₉	—	2	2	no	—
465	C₂³×C₁₉	—	2	1	no	—
466	C₂³×C₁₉	—	2	4	no	—
467	C₂³×C₁₉	—	2	2	no	—
468	C₂³×C₁₉	—	4	2	no	—
469	C₂³×C₁₉	—	8	1	no	—
470	C₂³×C₁₉	—	8	2	no	—
471	C₂³×C₁₉	—	8	1	no	—
472	C₂³×C₁₉	—	8	2	no	—
473	C₂³×C₁₉	—	8	1	no	—
474	C₂³×C₁₉	—	8	1	no	—
475	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
476	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
477	Q₈×C₁₉	—	2	2	no	—
478	Q₈×C₁₉	—	2	1	no	—
479	Q₈×C₁₉	—	2	2	no	—
480	Q₈×C₁₉	—	2	2	no	—
481	Q₈×C₁₉	—	4	2	no	—
482	Q₈×C₁₉	—	8	1	no	—
483	Q₈×C₁₉	—	8	1	no	—
484	Q₈×C₁₉	C₂×#41	1	2	yes	—
485	D₄×C₁₉	—	2	8	no	—
486	D₄×C₁₉	—	2	8	no	—
487	D₄×C₁₉	—	2	4	no	—
488	D₄×C₁₉	—	2	4	no	—
489	D₄×C₁₉	—	2	2	no	—
490	D₄×C₁₉	—	2	4	no	—
491	D₄×C₁₉	—	2	2	no	—
492	D₄×C₁₉	—	2	1	no	—
493	D₄×C₁₉	—	2	2	no	—
494	D₄×C₁₉	—	2	2	no	—
495	D₄×C₁₉	—	4	2	no	—
496	D₄×C₁₉	—	8	2	no	—
497	D₄×C₁₉	—	8	2	no	—
498	D₄×C₁₉	C₂×#41	1	2	yes	—
499	D₄×C₁₉	C₂×#41	1	4	yes	—
500	C₂×C₄×C₁₉	—	2	8	no	—
501	C₂×C₄×C₁₉	—	2	1	no	—
502	C₂×C₄×C₁₉	—	2	4	no	—
503	C₂×C₄×C₁₉	—	2	2	no	—
504	C₂×C₄×C₁₉	—	2	2	no	—
505	C₂×C₄×C₁₉	—	2	1	no	—
506	C₂×C₄×C₁₉	—	2	1	no	—
507	C₂×C₄×C₁₉	—	2	1	no	—
508	C₂×C₄×C₁₉	—	2	2	no	—
509	C₂×C₄×C₁₉	—	2	2	no	—
510	C₂×C₄×C₁₉	—	2	1	no	—
511	C₂×C₄×C₁₉	—	2	1	no	—
512	C₂×C₄×C₁₉	—	2	1	no	—
513	C₂×C₄×C₁₉	—	4	2	no	—
514	C₂×C₄×C₁₉	—	4	1	no	—
515	C₂×C₄×C₁₉	—	4	2	no	—
516	C₂×C₄×C₁₉	—	4	1	no	—
517	C₂×C₄×C₁₉	—	4	2	no	—
518	C₂×C₄×C₁₉	—	4	4	no	—
519	C₂×C₄×C₁₉	—	4	2	no	—
520	C₂×C₄×C₁₉	—	8	2	no	—
521	C₂×C₄×C₁₉	—	8	2	no	—
522	C₂×C₄×C₁₉	—	8	1	no	—
523	C₂×C₄×C₁₉	—	8	2	no	—
524	C₂×C₄×C₁₉	—	8	2	no	—
525	C₂×C₄×C₁₉	—	8	2	no	—
526	C₂×C₄×C₁₉	—	8	2	no	—
527	C₂×C₄×C₁₉	—	8	1	no	—
528	C₂×C₄×C₁₉	—	8	2	no	—
529	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
538	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
539	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
540	C₈×C₁₉	—	2	1	no	—
541	C₈×C₁₉	—	2	1	no	—
542	C₈×C₁₉	—	2	1	no	—
543	C₈×C₁₉	—	2	1	no	—
544	C₈×C₁₉	—	2	2	no	—
545	C₈×C₁₉	—	2	2	no	—
546	#3510	C₂×C₁₉	1	1	yes	characteristic, complemented
547	C₄×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic, complemented
548	#3125	C₂×C₁₉	1	2	yes	complemented
549	#3124	C₂×C₁₉	1	2	yes	complemented
550	#3118	C₂×C₁₉	1	2	yes	complemented
551	#3118	C₂×C₁₉	1	2	yes	complemented
552	#3114	C₂×C₁₉	1	2	yes	complemented
553	#3111	C₂×C₁₉	1	2	yes	complemented
554	#3105	C₂×C₁₉	1	2	yes	complemented
555	#3102	C₂×C₁₉	1	2	yes	complemented
556	#3097	C₂×C₁₉	1	1	yes	characteristic, complemented
557	#3096	C₂×C₁₉	1	1	yes	characteristic, complemented
558	#3077	C₂×C₁₉	1	1	yes	characteristic, complemented
559	#3076	C₂×C₁₉	1	1	yes	characteristic, complemented
560	#3040	C₂×C₁₉	1	1	yes	characteristic, complemented
561	C₂×#463	C₂×C₁₉	1	1	yes	characteristic, complemented
562	#3009	C₂×C₁₉	1	1	yes	characteristic, complemented
563	#3008	C₂×C₁₉	1	1	yes	characteristic
564	#2949	C₂×C₁₉	1	1	yes	characteristic, complemented
565	#2948	C₂×C₁₉	1	1	yes	characteristic, complemented
566	#2947	C₂×C₁₉	1	1	yes	characteristic, complemented
567	#2946	C₂×C₁₉	1	1	yes	characteristic, complemented
568	#2925	C₂×C₁₉	1	1	yes	characteristic, complemented
569	C₂²×C₁₉	—	2	1	no	—
570	C₂²×C₁₉	—	2	1	no	—
571	C₂²×C₁₉	—	2	2	no	—
572	C₂²×C₁₉	—	2	2	no	—
573	C₂²×C₁₉	—	2	2	no	—
574	C₂²×C₁₉	—	2	4	no	—
575	C₂²×C₁₉	—	2	2	no	—
576	C₂²×C₁₉	—	4	2	no	—
577	C₂²×C₁₉	—	4	1	no	—
578	C₂²×C₁₉	—	4	2	no	—
579	C₂²×C₁₉	—	4	1	no	—
580	C₂²×C₁₉	—	4	2	no	—
581	C₂²×C₁₉	—	4	2	no	—
582	C₂²×C₁₉	—	4	2	no	—
583	C₂²×C₁₉	—	8	4	no	—
584	C₂²×C₁₉	—	8	8	no	—
585	C₂²×C₁₉	—	16	2	no	—
586	C₂²×C₁₉	#525	1	2	yes	—
587	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
588	C₄×C₁₉	—	2	1	no	—
589	C₄×C₁₉	—	2	2	no	—
590	C₄×C₁₉	—	2	1	no	—
591	C₄×C₁₉	—	2	1	no	—
592	C₄×C₁₉	—	2	2	no	—
593	C₄×C₁₉	—	2	1	no	—
594	C₄×C₁₉	—	2	2	no	—
595	C₄×C₁₉	—	2	2	no	—
596	C₄×C₁₉	—	4	1	no	—
597	C₄×C₁₉	—	4	1	no	—
598	C₄×C₁₉	—	4	1	no	—
599	C₄×C₁₉	—	4	1	no	—
600	C₄×C₁₉	—	4	2	no	—
601	C₄×C₁₉	—	4	1	no	—
602	C₄×C₁₉	—	4	1	no	—
603	C₄×C₁₉	—	4	2	no	—
604	C₄×C₁₉	#525	1	2	yes	—
605	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
606	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
607	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
608	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
609	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
610	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
611	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
612	#559	—	2	1	no	—
613	#559	—	2	1	no	—
614	#556	—	2	1	no	—
615	#556	—	2	1	no	—
616	#551	—	2	2	no	—
617	#551	—	2	2	no	—
618	#542	C₂²×C₁₉	1	2	yes	complemented
619	#542	C₂²×C₁₉	1	2	yes	complemented
620	#536	C₂²×C₁₉	1	1	yes	characteristic
621	#535	C₂²×C₁₉	1	1	yes	characteristic
622	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
623	#529	C₂²×C₁₉	1	2	yes	complemented
624	#529	C₂²×C₁₉	1	2	yes	complemented
625	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic, complemented
626	#520	—	2	1	no	—
627	#520	C₂²×C₁₉	1	1	yes	characteristic
628	#520	C₂²×C₁₉	1	1	yes	characteristic
629	#520	C₂²×C₁₉	1	2	yes	complemented
630	#519	C₂²×C₁₉	1	1	yes	characteristic, complemented
631	#518	—	2	2	no	—
632	#518	—	2	1	no	—
633	#518	C₂²×C₁₉	1	1	yes	characteristic
634	#518	C₂²×C₁₉	1	2	yes	complemented
635	#518	C₂²×C₁₉	1	1	yes	characteristic, complemented
636	C₄×#41	—	2	1	no	—
637	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
638	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
639	C₄×#41	C₂²×C₁₉	1	2	yes	complemented
640	C₂×C₄×D₄	—	2	1	no	—
641	C₂×C₄×D₄	—	2	2	no	—
642	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
643	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	complemented
644	#485	C₂²×C₁₉	1	2	yes	complemented
645	#485	C₂²×C₁₉	1	2	yes	complemented
646	#484	C₂²×C₁₉	1	2	yes	complemented
647	#483	C₂²×C₁₉	1	2	yes	complemented
648	#482	C₂²×C₁₉	1	2	yes	complemented
649	#482	C₂²×C₁₉	1	2	yes	complemented
650	#481	C₂²×C₁₉	1	2	yes	complemented
651	#480	C₂²×C₁₉	1	2	yes	complemented
652	#479	C₂²×C₁₉	1	1	yes	characteristic, complemented
653	#479	C₂²×C₁₉	1	1	yes	characteristic, complemented
654	#478	C₂²×C₁₉	1	1	yes	characteristic, complemented
655	#478	C₂²×C₁₉	1	1	yes	characteristic, complemented
656	#478	C₂²×C₁₉	1	2	yes	complemented
657	#478	C₂²×C₁₉	1	2	yes	complemented
658	#477	C₂²×C₁₉	1	1	yes	characteristic, complemented
659	#476	C₂²×C₁₉	1	1	yes	characteristic, complemented
660	#476	C₂²×C₁₉	1	2	yes	complemented
661	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
662	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
663	#474	C₂²×C₁₉	1	2	yes	complemented
664	#464	C₂²×C₁₉	1	2	yes	complemented
665	#464	C₂²×C₁₉	1	2	yes	complemented
666	#463	C₂²×C₁₉	1	2	yes	complemented
667	#463	C₂²×C₁₉	1	2	yes	complemented
668	#463	C₂²×C₁₉	1	2	yes	complemented
669	#463	C₂²×C₁₉	1	2	yes	complemented
670	#463	C₂²×C₁₉	1	2	yes	complemented
671	#463	C₂²×C₁₉	1	2	yes	complemented
672	#452	C₂²×C₁₉	1	2	yes	complemented
673	#452	C₂²×C₁₉	1	2	yes	complemented
674	#450	C₂²×C₁₉	1	2	yes	complemented
675	#450	C₂²×C₁₉	1	2	yes	complemented
676	#449	C₂²×C₁₉	1	2	yes	—
677	#449	C₂²×C₁₉	1	2	yes	—
678	#447	C₂²×C₁₉	1	2	yes	—
679	#447	C₂²×C₁₉	1	2	yes	—
680	#442	C₂²×C₁₉	1	2	yes	complemented
681	#442	C₂²×C₁₉	1	2	yes	complemented
682	#442	C₂²×C₁₉	1	2	yes	complemented
683	#441	C₂²×C₁₉	1	2	yes	complemented
684	#440	C₂²×C₁₉	1	2	yes	complemented
685	#440	C₂²×C₁₉	1	2	yes	complemented
686	#440	C₂²×C₁₉	1	2	yes	complemented
687	#440	C₂²×C₁₉	1	2	yes	complemented
688	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
689	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
690	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
691	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
692	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
693	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
694	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
695	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
696	#433	C₂²×C₁₉	1	2	yes	complemented
697	#433	C₂²×C₁₉	1	2	yes	complemented
698	#432	C₂²×C₁₉	1	2	yes	complemented
699	#431	C₂²×C₁₉	1	2	yes	complemented
700	#428	C₂²×C₁₉	1	1	yes	characteristic, complemented
701	#428	C₂²×C₁₉	1	1	yes	characteristic, complemented
702	#427	C₂²×C₁₉	1	1	yes	characteristic, complemented
703	#427	C₂²×C₁₉	1	1	yes	characteristic, complemented
704	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
705	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
706	#419	C₂²×C₁₉	1	1	yes	characteristic, complemented
707	#418	C₂²×C₁₉	1	1	yes	characteristic
708	#418	C₂²×C₁₉	1	1	yes	characteristic
709	#418	C₂²×C₁₉	1	1	yes	characteristic, complemented
710	#416	C₂²×C₁₉	1	1	yes	characteristic
711	#416	C₂²×C₁₉	1	1	yes	characteristic
712	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
713	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
714	#408	C₂²×C₁₉	1	1	yes	characteristic
715	#408	C₂²×C₁₉	1	1	yes	characteristic
716	#405	C₂²×C₁₉	1	1	yes	characteristic, complemented
717	#405	C₂²×C₁₉	1	1	yes	characteristic, complemented
718	C₂×C₁₉	—	2	2	no	—
719	C₂×C₁₉	—	4	2	no	—
720	C₂×C₁₉	—	4	4	no	—
721	C₂×C₁₉	—	4	2	no	—
722	C₂×C₁₉	—	8	2	no	—
723	C₂×C₁₉	C₂×#525	1	1	yes	characteristic
724	C₂×C₁₉	#3584	1	1	yes	characteristic
725	C₂×C₁₉	#3585	1	1	yes	characteristic
726	H(5,𝔽₂)	—	2	4	no	—
727	H(5,𝔽₂)	—	2	4	no	—
728	C₂×#41	—	2	1	no	—
729	C₂×#41	C₂³×C₁₉	1	2	yes	—
730	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
731	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
732	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
733	C₂²×D₄	—	2	2	no	—
734	C₂²×D₄	—	2	1	no	—
735	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
736	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
737	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
738	C₂³×C₄	—	2	1	no	—
739	C₂³×C₄	—	2	2	no	—
740	#137	—	2	4	no	—
741	AGL(1,ℤ/8)	—	2	4	no	—
742	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
743	C₂×SD₁₆	—	2	4	no	—
744	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
748	C₂×D₈	—	2	4	no	—
749	C₂×D₈	C₂³×C₁₉	1	2	yes	—
750	C₂×D₈	C₂³×C₁₉	1	2	yes	—
751	C₂×D₈	C₂³×C₁₉	1	2	yes	—
752	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
753	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
754	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
755	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
756	C₄⋊Q₈	—	2	1	no	—
757	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
758	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
759	#127	—	2	1	no	—
760	#126	—	2	2	no	—
761	#126	—	2	2	no	—
762	#126	—	2	2	no	—
763	#126	—	2	2	no	—
764	#125	C₂³×C₁₉	1	1	yes	characteristic
765	#125	C₂³×C₁₉	1	1	yes	characteristic
766	#124	—	2	1	no	—
767	#124	—	2	1	no	—
768	#124	—	2	2	no	—
769	#124	—	2	2	no	—
770	#124	—	2	1	no	—
771	#124	—	2	1	no	—
772	#124	C₂³×C₁₉	1	2	yes	—
773	#124	C₂³×C₁₉	1	2	yes	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
784	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
785	#121	C₂³×C₁₉	1	2	yes	—
786	#121	C₂³×C₁₉	1	2	yes	—
787	#120	—	2	2	no	—
788	C₄×Q₈	—	2	1	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
794	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
798	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
799	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	D₄×C₁₉	1	2	yes	—
822	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
823	C₄×D₄	D₄×C₁₉	1	2	yes	—
824	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₁₉	1	2	yes	—
826	C₄×D₄	C₂³×C₁₉	1	2	yes	—
827	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₁₉	1	2	yes	—
829	C₄×D₄	C₂³×C₁₉	1	2	yes	—
830	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₁₉	1	2	yes	—
832	C₄×D₄	C₂³×C₁₉	1	2	yes	—
833	C₄×D₄	C₂³×C₁₉	1	2	yes	—
834	#117	—	2	1	no	—
835	#117	—	2	2	no	—
836	#117	—	2	2	no	—
837	#117	—	2	1	no	—
838	#117	—	2	2	no	—
839	#117	—	2	2	no	—
840	#117	—	2	2	no	—
841	#117	C₂³×C₁₉	1	1	yes	characteristic
842	#117	C₂³×C₁₉	1	2	yes	—
843	#117	C₂³×C₁₉	1	1	yes	characteristic
844	#117	C₂³×C₁₉	1	1	yes	characteristic
845	#117	C₂³×C₁₉	1	1	yes	characteristic
846	#117	C₂³×C₁₉	1	2	yes	—
847	C₂×C₄⋊C₄	—	2	1	no	—
848	C₂×C₄⋊C₄	—	2	2	no	—
849	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
850	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
851	C₂×C₂²⋊C₄	—	2	1	no	—
852	C₂×C₂²⋊C₄	—	2	2	no	—
853	C₂×C₂²⋊C₄	—	2	1	no	—
854	C₂×C₂²⋊C₄	—	2	1	no	—
855	C₂×C₂²⋊C₄	—	2	2	no	—
856	C₂×C₂²⋊C₄	—	2	2	no	—
857	C₂×C₂²⋊C₄	—	2	2	no	—
858	C₂×C₂²⋊C₄	—	2	2	no	—
859	C₂×C₄²	—	2	1	no	—
860	C₂×C₄²	—	2	2	no	—
861	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
862	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
863	#107	C₂³×C₁₉	1	1	yes	characteristic
864	#107	C₂³×C₁₉	1	1	yes	characteristic
865	#107	C₂³×C₁₉	1	1	yes	characteristic
866	#107	C₂³×C₁₉	1	1	yes	characteristic
867	#107	C₂³×C₁₉	1	2	yes	—
868	#107	C₂³×C₁₉	1	2	yes	—
869	#106	C₂³×C₁₉	1	1	yes	characteristic
870	#106	C₂³×C₁₉	1	1	yes	characteristic
871	#106	C₂³×C₁₉	1	1	yes	characteristic
872	#106	C₂³×C₁₉	1	1	yes	characteristic
873	#106	C₂³×C₁₉	1	2	yes	—
874	#106	C₂³×C₁₉	1	2	yes	—
875	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
876	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
877	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
878	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
879	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
880	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
881	#103	C₂³×C₁₉	1	2	yes	—
882	#103	C₂³×C₁₉	1	2	yes	—
883	#103	C₂³×C₁₉	1	1	yes	characteristic
884	#103	C₂³×C₁₉	1	1	yes	characteristic
885	#103	C₂³×C₁₉	1	1	yes	characteristic
886	#103	C₂³×C₁₉	1	1	yes	characteristic
887	#103	C₂³×C₁₉	1	2	yes	—
888	#103	C₂³×C₁₉	1	2	yes	—
889	#102	C₂³×C₁₉	1	2	yes	—
890	#102	C₂³×C₁₉	1	2	yes	—
891	#102	C₂³×C₁₉	1	1	yes	characteristic
892	#102	C₂³×C₁₉	1	1	yes	characteristic
893	#102	C₂³×C₁₉	1	1	yes	characteristic
894	#102	C₂³×C₁₉	1	1	yes	characteristic
895	#102	C₂³×C₁₉	1	2	yes	—
896	#102	C₂³×C₁₉	1	2	yes	—
897	#102	C₂³×C₁₉	1	2	yes	—
898	#102	C₂³×C₁₉	1	2	yes	—
899	#102	C₂³×C₁₉	1	2	yes	—
900	#102	C₂³×C₁₉	1	2	yes	—
901	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
902	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
904	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
905	#97	C₂³×C₁₉	1	2	yes	—
906	#97	C₂³×C₁₉	1	2	yes	—
907	C₄×C₈	C₂³×C₁₉	1	2	yes	—
908	C₄×C₈	C₂³×C₁₉	1	2	yes	—
909	C₁₉	#60592	1	1	yes	characteristic, direct product factor, Sylow
910	C₂⁴	—	2	2	no	—
911	C₂⁴	—	2	1	no	—
912	C₂⁴	—	2	1	no	—
913	#41	—	2	8	no	—
914	#41	—	2	4	no	—
915	#41	—	2	4	no	—
916	#41	—	2	2	no	—
917	#41	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	#41×C₁₉	1	4	yes	—
920	C₂×Q₈	—	2	1	no	—
921	C₂×Q₈	—	2	1	no	—
922	C₂×Q₈	—	2	1	no	—
923	C₂×Q₈	—	2	2	no	—
924	C₂×Q₈	—	2	2	no	—
925	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
926	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
927	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
928	C₂×D₄	—	2	16	no	—
929	C₂×D₄	—	2	8	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	4	no	—
933	C₂×D₄	—	2	4	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
943	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
944	C₂×D₄	#41×C₁₉	1	4	yes	—
945	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
946	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
947	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	1	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	8	2	no	—
963	C₂²×C₄	—	8	4	no	—
964	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
965	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
966	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
967	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
968	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
969	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
970	Q₁₆	—	2	4	no	—
971	SD₁₆	—	2	4	no	—
972	SD₁₆	—	2	4	no	—
973	SD₁₆	—	2	4	no	—
974	SD₁₆	—	2	4	no	—
975	D₈	—	2	4	no	—
976	D₈	—	2	4	no	—
977	D₈	—	2	4	no	—
978	M₁₆	—	2	2	no	—
979	M₁₆	—	2	2	no	—
980	C₂×C₈	—	2	2	no	—
981	C₂×C₈	—	2	2	no	—
982	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
983	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
984	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
985	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
986	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1004	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1005	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1006	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1007	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1008	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1009	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1010	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1011	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1012	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1013	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1036	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1037	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	2	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	2	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	2	no	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	1	no	—
1047	C₄²	C₂×D₄×C₁₉	1	2	yes	—
1048	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1049	C₄²	C₂×D₄×C₁₉	1	2	yes	—
1050	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1051	C₄²	C₂⁴×C₁₉	1	2	yes	—
1052	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1053	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1054	C₂³	—	2	8	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	2	1	no	—
1057	C₂³	—	2	4	no	—
1058	C₂³	—	2	2	no	—
1059	C₂³	—	4	2	no	—
1060	C₂³	—	8	1	no	—
1061	C₂³	—	8	2	no	—
1062	C₂³	—	8	1	no	—
1063	C₂³	—	8	2	no	—
1064	C₂³	—	8	1	no	—
1065	C₂³	—	8	1	no	—
1066	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1067	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1068	Q₈	—	2	2	no	—
1069	Q₈	—	2	1	no	—
1070	Q₈	—	2	2	no	—
1071	Q₈	—	2	2	no	—
1072	Q₈	—	4	2	no	—
1073	Q₈	—	8	1	no	—
1074	Q₈	—	8	1	no	—
1075	Q₈	C₂×#41×C₁₉	1	2	yes	—
1076	D₄	—	2	8	no	—
1077	D₄	—	2	8	no	—
1078	D₄	—	2	4	no	—
1079	D₄	—	2	4	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	4	no	—
1082	D₄	—	2	2	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	2	no	—
1085	D₄	—	2	2	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	8	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	C₂×#41×C₁₉	1	2	yes	—
1090	D₄	C₂×#41×C₁₉	1	4	yes	—
1091	C₂×C₄	—	2	8	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	4	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	4	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	—	8	2	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	1	no	—
1117	C₂×C₄	—	8	2	no	—
1118	C₂×C₄	—	8	1	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1121	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1123	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1125	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1126	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1127	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1128	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
1129	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
1130	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1131	C₈	—	2	1	no	—
1132	C₈	—	2	1	no	—
1133	C₈	—	2	1	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	2	no	—
1136	C₈	—	2	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	4	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	8	4	no	—
1152	C₂²	—	8	8	no	—
1153	C₂²	—	16	2	no	—
1154	C₂²	C₁₉×#525	1	2	yes	—
1155	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1156	C₄	—	2	2	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	4	2	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	2	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	1	no	—
1172	C₄	C₁₉×#525	1	2	yes	—
1173	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
1174	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
1175	C₂	—	2	2	no	—
1176	C₂	—	4	2	no	—
1177	C₂	—	4	4	no	—
1178	C₂	—	4	2	no	—
1179	C₂	—	8	2	no	—
1180	C₂	C₂×C₁₉×#525	1	1	yes	characteristic
1181	C₂	C₁₉×#3584	1	1	yes	characteristic
1182	C₂	C₁₉×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3008	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3510	C₂	semidirect
2. C₄×C₁₉×H(5,𝔽₂)	C₂	semidirect
3. C₁₉×#3125	C₂	semidirect
4. C₁₉×#3124	C₂	semidirect
5. C₁₉×#3118	C₂	semidirect
6. C₁₉×#3118	C₂	semidirect
7. C₁₉×#3114	C₂	semidirect
8. C₁₉×#3111	C₂	semidirect
9. C₁₉×#3105	C₂	semidirect
10. C₁₉×#3102	C₂	semidirect
11. C₁₉×#3097	C₂	semidirect
12. C₁₉×#3096	C₂	semidirect
13. C₁₉×#3077	C₂	semidirect
14. C₁₉×#3076	C₂	semidirect
15. C₁₉×#3040	C₂	semidirect
16. C₂×C₁₉×#463	C₂	semidirect
17. C₁₉×#3009	C₂	semidirect
19. C₁₉×#2949	C₂	semidirect
20. C₁₉×#2948	C₂	semidirect
21. C₁₉×#2947	C₂	semidirect
22. C₁₉×#2946	C₂	semidirect
23. C₁₉×#2925	C₂	semidirect
35. C₁₉×#542	C₂²	semidirect
36. C₁₉×#542	C₂²	semidirect
39. C₁₉×#533	C₂²	semidirect
40. C₁₉×#529	C₂²	semidirect
41. C₁₉×#529	C₂²	semidirect
42. C₂×C₁₉×#124	C₂²	semidirect
46. C₁₉×#520	C₂²	semidirect
47. C₁₉×#519	C₂²	semidirect
51. C₁₉×#518	C₂²	semidirect
52. C₁₉×#518	C₂²	semidirect
56. C₄×#41×C₁₉	C₂²	semidirect
60. C₂×C₄×D₄×C₁₉	C₂²	semidirect
61. C₁₉×#485	C₂²	semidirect
62. C₁₉×#485	C₂²	semidirect
63. C₁₉×#484	C₂²	semidirect
64. C₁₉×#483	C₂²	semidirect
65. C₁₉×#482	C₂²	semidirect
66. C₁₉×#482	C₂²	semidirect
67. C₁₉×#481	C₂²	semidirect
68. C₁₉×#480	C₂²	semidirect
69. C₁₉×#479	C₂²	semidirect
70. C₁₉×#479	C₂²	semidirect
71. C₁₉×#478	C₂²	semidirect
72. C₁₉×#478	C₂²	semidirect
73. C₁₉×#478	C₂²	semidirect
74. C₁₉×#478	C₂²	semidirect
75. C₁₉×#477	C₂²	semidirect
76. C₁₉×#476	C₂²	semidirect
77. C₁₉×#476	C₂²	semidirect
78. C₁₉×#475	C₂²	semidirect
79. C₁₉×#474	C₂²	semidirect
80. C₁₉×#474	C₂²	semidirect
81. C₁₉×#464	C₂²	semidirect
82. C₁₉×#464	C₂²	semidirect
83. C₁₉×#463	C₂²	semidirect
84. C₁₉×#463	C₂²	semidirect
85. C₁₉×#463	C₂²	semidirect
86. C₁₉×#463	C₂²	semidirect
87. C₁₉×#463	C₂²	semidirect
88. C₁₉×#463	C₂²	semidirect
89. C₁₉×#452	C₂²	semidirect
90. C₁₉×#452	C₂²	semidirect
91. C₁₉×#450	C₂²	semidirect
92. C₁₉×#450	C₂²	semidirect
97. C₁₉×#442	C₂²	semidirect
98. C₁₉×#442	C₂²	semidirect
99. C₁₉×#442	C₂²	semidirect
100. C₁₉×#441	C₂²	semidirect
101. C₁₉×#440	C₂²	semidirect
102. C₁₉×#440	C₂²	semidirect
103. C₁₉×#440	C₂²	semidirect
104. C₁₉×#440	C₂²	semidirect
105. C₄×Q₁₆×C₁₉	C₂²	semidirect
106. C₄×SD₁₆×C₁₉	C₂²	semidirect
107. C₄×SD₁₆×C₁₉	C₂²	semidirect
108. C₄×SD₁₆×C₁₉	C₂²	semidirect
109. C₄×SD₁₆×C₁₉	C₂²	semidirect
110. C₄×D₈×C₁₉	C₂²	semidirect
111. C₄×D₈×C₁₉	C₂²	semidirect
112. C₄×D₈×C₁₉	C₂²	semidirect
113. C₁₉×#433	C₂²	semidirect
114. C₁₉×#433	C₂²	semidirect
115. C₁₉×#432	C₂²	semidirect
116. C₁₉×#431	C₂²	semidirect
117. C₁₉×#428	C₂²	semidirect
118. C₁₉×#428	C₂²	semidirect
119. C₁₉×#427	C₂²	semidirect
120. C₁₉×#427	C₂²	semidirect
121. C₁₉×#423	C₂²	semidirect
122. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
123. C₁₉×#419	C₂²	semidirect
126. C₁₉×#418	C₂²	semidirect
129. C₂×C₁₉×#103	C₂²	semidirect
130. C₂×C₁₉×#102	C₂²	semidirect
133. C₁₉×#405	C₂²	semidirect
134. C₁₉×#405	C₂²	semidirect
462. #60592	C₁₉	direct (N × H)
546. #3510	C₂×C₁₉	semidirect
547. C₄×H(5,𝔽₂)	C₂×C₁₉	semidirect
548. #3125	C₂×C₁₉	semidirect
549. #3124	C₂×C₁₉	semidirect
550. #3118	C₂×C₁₉	semidirect
551. #3118	C₂×C₁₉	semidirect
552. #3114	C₂×C₁₉	semidirect
553. #3111	C₂×C₁₉	semidirect
554. #3105	C₂×C₁₉	semidirect
555. #3102	C₂×C₁₉	semidirect
556. #3097	C₂×C₁₉	semidirect
557. #3096	C₂×C₁₉	semidirect
558. #3077	C₂×C₁₉	semidirect
559. #3076	C₂×C₁₉	semidirect
560. #3040	C₂×C₁₉	semidirect
561. C₂×#463	C₂×C₁₉	semidirect
562. #3009	C₂×C₁₉	semidirect
564. #2949	C₂×C₁₉	semidirect
565. #2948	C₂×C₁₉	semidirect
566. #2947	C₂×C₁₉	semidirect
567. #2946	C₂×C₁₉	semidirect
568. #2925	C₂×C₁₉	semidirect
618. #542	C₂²×C₁₉	semidirect
619. #542	C₂²×C₁₉	semidirect
622. #533	C₂²×C₁₉	semidirect
623. #529	C₂²×C₁₉	semidirect
624. #529	C₂²×C₁₉	semidirect
625. C₂×#124	C₂²×C₁₉	semidirect
629. #520	C₂²×C₁₉	semidirect
630. #519	C₂²×C₁₉	semidirect
634. #518	C₂²×C₁₉	semidirect
635. #518	C₂²×C₁₉	semidirect
639. C₄×#41	C₂²×C₁₉	semidirect
643. C₂×C₄×D₄	C₂²×C₁₉	semidirect
644. #485	C₂²×C₁₉	semidirect
645. #485	C₂²×C₁₉	semidirect
646. #484	C₂²×C₁₉	semidirect
647. #483	C₂²×C₁₉	semidirect
648. #482	C₂²×C₁₉	semidirect
649. #482	C₂²×C₁₉	semidirect
650. #481	C₂²×C₁₉	semidirect
651. #480	C₂²×C₁₉	semidirect
652. #479	C₂²×C₁₉	semidirect
653. #479	C₂²×C₁₉	semidirect
654. #478	C₂²×C₁₉	semidirect
655. #478	C₂²×C₁₉	semidirect
656. #478	C₂²×C₁₉	semidirect
657. #478	C₂²×C₁₉	semidirect
658. #477	C₂²×C₁₉	semidirect
659. #476	C₂²×C₁₉	semidirect
660. #476	C₂²×C₁₉	semidirect
661. #475	C₂²×C₁₉	semidirect
662. #474	C₂²×C₁₉	semidirect
663. #474	C₂²×C₁₉	semidirect
664. #464	C₂²×C₁₉	semidirect
665. #464	C₂²×C₁₉	semidirect
666. #463	C₂²×C₁₉	semidirect
667. #463	C₂²×C₁₉	semidirect
668. #463	C₂²×C₁₉	semidirect
669. #463	C₂²×C₁₉	semidirect
670. #463	C₂²×C₁₉	semidirect
671. #463	C₂²×C₁₉	semidirect
672. #452	C₂²×C₁₉	semidirect
673. #452	C₂²×C₁₉	semidirect
674. #450	C₂²×C₁₉	semidirect
675. #450	C₂²×C₁₉	semidirect
680. #442	C₂²×C₁₉	semidirect
681. #442	C₂²×C₁₉	semidirect
682. #442	C₂²×C₁₉	semidirect
683. #441	C₂²×C₁₉	semidirect
684. #440	C₂²×C₁₉	semidirect
685. #440	C₂²×C₁₉	semidirect
686. #440	C₂²×C₁₉	semidirect
687. #440	C₂²×C₁₉	semidirect
688. C₄×Q₁₆	C₂²×C₁₉	semidirect
689. C₄×SD₁₆	C₂²×C₁₉	semidirect
690. C₄×SD₁₆	C₂²×C₁₉	semidirect
691. C₄×SD₁₆	C₂²×C₁₉	semidirect
692. C₄×SD₁₆	C₂²×C₁₉	semidirect
693. C₄×D₈	C₂²×C₁₉	semidirect
694. C₄×D₈	C₂²×C₁₉	semidirect
695. C₄×D₈	C₂²×C₁₉	semidirect
696. #433	C₂²×C₁₉	semidirect
697. #433	C₂²×C₁₉	semidirect
698. #432	C₂²×C₁₉	semidirect
699. #431	C₂²×C₁₉	semidirect
700. #428	C₂²×C₁₉	semidirect
701. #428	C₂²×C₁₉	semidirect
702. #427	C₂²×C₁₉	semidirect
703. #427	C₂²×C₁₉	semidirect
704. #423	C₂²×C₁₉	semidirect
705. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
706. #419	C₂²×C₁₉	semidirect
709. #418	C₂²×C₁₉	semidirect
712. C₂×#103	C₂²×C₁₉	semidirect
713. C₂×#102	C₂²×C₁₉	semidirect
716. #405	C₂²×C₁₉	semidirect
717. #405	C₂²×C₁₉	semidirect
909. C₁₉	#60592	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×#3510	2
C₄×C₁₉×H(5,𝔽₂)	2
C₁₉×#3125	2
C₁₉×#3124	2
C₁₉×#3118	2
C₁₉×#3114	2
C₁₉×#3111	2
C₁₉×#3105	2
C₁₉×#3102	2
C₁₉×#3097	2
C₁₉×#3096	2
C₁₉×#3077	2
C₁₉×#3076	2
C₁₉×#3040	2
C₂×C₁₉×#463	2
C₁₉×#3009	2
C₁₉×#3008	2
C₁₉×#2949	2
C₁₉×#2948	2
C₁₉×#2947	2
C₁₉×#2946	2
C₁₉×#2925	2
#60592	19

Subgroups — C19×#60592 #18066551

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60592 #18066551