Subgroups — C₁₉×#62296 #18068255

Order 4864.

1902 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3519	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3346	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3338	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3333	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3329	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3320	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3314	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3299	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3266	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3252	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3196	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3193	C₂	1	2	yes	maximal, complemented
19	C₁₉×#3182	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#3172	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#3056	C₂	1	2	yes	maximal, complemented
22	C₂×C₁₉×#468	C₂	1	2	yes	maximal, complemented
23	D₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
25	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
26	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	complemented
27	C₁₉×#555	C₂²	1	1	yes	characteristic
28	C₁₉×#554	—	2	1	no	—
29	C₁₉×#554	—	2	2	no	—
30	C₁₉×#554	—	2	1	no	—
31	C₁₉×#554	C₂²	1	1	yes	characteristic
32	C₁₉×#554	C₂²	1	1	yes	characteristic
33	C₁₉×#554	C₂²	1	2	yes	complemented
34	C₁₉×#554	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#553	—	2	1	no	—
36	C₁₉×#553	C₂²	1	2	yes	—
37	C₁₉×#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
40	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#546	—	2	2	no	—
42	C₁₉×#546	C₂²	1	2	yes	—
43	D₄²×C₁₉	—	2	1	no	—
44	D₄²×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#544	—	2	1	no	—
46	C₁₉×#543	—	2	2	no	—
47	C₁₉×#540	—	2	1	no	—
48	C₁₉×#538	—	2	2	no	—
49	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×#532	C₂²	1	1	yes	characteristic
52	C₁₉×#529	C₂²	1	1	yes	characteristic
53	C₁₉×#525	C₂²	1	2	yes	—
54	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
55	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
56	C₂×C₁₉×#121	C₂²	1	2	yes	—
57	C₁₉×#518	—	2	1	no	—
58	C₁₉×#518	—	2	1	no	—
59	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
60	C₁₉×#501	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#497	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#491	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#489	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#485	C₂²	1	2	yes	complemented
69	C₁₉×#485	C₂²	1	2	yes	complemented
70	C₁₉×#484	C₂²	1	2	yes	complemented
71	C₁₉×#484	C₂²	1	2	yes	complemented
72	C₁₉×#484	C₂²	1	2	yes	complemented
73	C₁₉×#481	C₂²	1	2	yes	complemented
74	C₁₉×#480	C₂²	1	2	yes	complemented
75	C₁₉×#480	C₂²	1	2	yes	complemented
76	C₁₉×#479	C₂²	1	2	yes	complemented
77	C₁₉×#477	C₂²	1	1	yes	characteristic, complemented
78	C₁₉×#477	C₂²	1	1	yes	characteristic, complemented
79	C₁₉×#477	C₂²	1	1	yes	characteristic, complemented
80	C₁₉×#476	C₂²	1	1	yes	characteristic, complemented
81	C₁₉×#474	C₂²	1	2	yes	complemented
82	C₁₉×#470	C₂²	1	1	yes	characteristic, complemented
83	C₁₉×#470	C₂²	1	1	yes	characteristic, complemented
84	C₁₉×#470	C₂²	1	2	yes	complemented
85	C₁₉×#468	C₂²	1	1	yes	characteristic
86	C₁₉×#468	C₂²	1	1	yes	characteristic
87	C₁₉×#468	C₂²	1	2	yes	—
88	C₁₉×#468	C₂²	1	2	yes	complemented
89	C₁₉×#468	C₂²	1	2	yes	complemented
90	C₁₉×#468	C₂²	1	2	yes	complemented
91	C₁₉×#468	C₂²	1	2	yes	complemented
92	C₁₉×#468	C₂²	1	2	yes	complemented
93	C₁₉×#468	C₂²	1	2	yes	complemented
94	C₁₉×#468	C₂²	1	2	yes	complemented
95	C₁₉×#468	C₂²	1	2	yes	complemented
96	C₁₉×#467	C₂²	1	2	yes	complemented
97	C₁₉×#467	C₂²	1	2	yes	complemented
98	C₁₉×#465	C₂²	1	2	yes	complemented
99	C₁₉×#465	C₂²	1	2	yes	complemented
100	C₁₉×#464	C₂²	1	2	yes	complemented
101	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
102	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
103	C₁₉×#461	C₂²	1	2	yes	complemented
104	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
105	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
106	C₁₉×#452	C₂²	1	2	yes	complemented
107	C₁₉×#452	C₂²	1	2	yes	complemented
108	C₁₉×#451	C₂²	1	2	yes	complemented
109	C₁₉×#450	C₂²	1	2	yes	complemented
110	C₁₉×#450	C₂²	1	2	yes	complemented
111	C₁₉×#448	C₂²	1	2	yes	complemented
112	C₁₉×#448	C₂²	1	2	yes	complemented
113	C₁₉×#448	C₂²	1	2	yes	complemented
114	C₁₉×#440	C₂²	1	2	yes	complemented
115	C₁₉×#440	C₂²	1	2	yes	complemented
116	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
117	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
120	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
121	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
122	C₁₉×#435	C₂²	1	2	yes	complemented
123	C₁₉×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
125	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
126	C₁₉×#428	C₂²	1	2	yes	complemented
127	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
128	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
129	C₁₉×#419	C₂²	1	2	yes	complemented
130	C₁₉×#417	C₂²	1	2	yes	complemented
131	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
132	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
133	C₁₉×#407	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₁₉	—	2	1	no	—
136	C₂×#41×C₁₉	C₂³	1	2	yes	—
137	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
138	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
139	C₂²×D₄×C₁₉	—	2	2	no	—
140	C₂²×D₄×C₁₉	—	2	1	no	—
141	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
142	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
143	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
144	C₁₉×#137	—	4	4	no	—
145	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₁₉	—	4	4	no	—
149	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
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×M₁₆×C₁₉	—	4	4	no	—
157	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
158	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
159	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
160	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
161	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
162	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
163	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
164	C₁₉×C₄⋊Q₈	—	2	1	no	—
165	C₁₉×C₄⋊Q₈	—	2	1	no	—
166	C₁₉×C₄⋊Q₈	—	2	2	no	—
167	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₁₉×#127	—	2	1	no	—
173	C₁₉×#127	C₂³	1	1	yes	characteristic
174	C₁₉×#126	—	2	2	no	—
175	C₁₉×#126	—	2	1	no	—
176	C₁₉×#125	—	2	1	no	—
177	C₁₉×#125	—	2	1	no	—
178	C₁₉×#125	—	2	1	no	—
179	C₁₉×#125	—	2	2	no	—
180	C₁₉×#125	—	2	1	no	—
181	C₁₉×#125	—	2	1	no	—
182	C₁₉×#125	C₂³	1	1	yes	characteristic
183	C₁₉×#124	—	2	2	no	—
184	C₁₉×#124	—	2	1	no	—
185	C₁₉×#124	C₂³	1	1	yes	characteristic
186	C₁₉×#123	—	2	2	no	—
187	C₁₉×#123	—	2	1	no	—
188	C₁₉×#123	—	2	2	no	—
189	C₁₉×#123	—	2	2	no	—
190	C₁₉×C₂²⋊Q₈	—	2	2	no	—
191	C₁₉×C₂²⋊Q₈	—	2	2	no	—
192	C₁₉×C₂²⋊Q₈	—	2	2	no	—
193	C₁₉×C₂²⋊Q₈	—	2	2	no	—
194	C₁₉×C₂²⋊Q₈	—	2	1	no	—
195	C₁₉×C₂²⋊Q₈	—	2	1	no	—
196	C₁₉×C₂²⋊Q₈	—	2	2	no	—
197	C₁₉×C₂²⋊Q₈	—	2	2	no	—
198	C₁₉×C₂²⋊Q₈	—	2	2	no	—
199	C₁₉×C₂²⋊Q₈	—	2	2	no	—
200	C₁₉×C₂²⋊Q₈	—	2	2	no	—
201	C₁₉×C₂²⋊Q₈	—	2	2	no	—
202	C₁₉×C₂²⋊Q₈	—	2	2	no	—
203	C₁₉×C₂²⋊Q₈	—	2	2	no	—
204	C₁₉×C₂²⋊Q₈	—	2	2	no	—
205	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₁₉×#121	—	2	2	no	—
215	C₁₉×#121	—	2	1	no	—
216	C₁₉×#121	—	2	2	no	—
217	C₁₉×#121	—	2	2	no	—
218	C₁₉×#121	—	2	1	no	—
219	C₁₉×#121	—	2	1	no	—
220	C₁₉×#121	—	2	2	no	—
221	C₁₉×#121	—	2	2	no	—
222	C₁₉×#121	C₂³	1	2	yes	—
223	C₁₉×#121	C₂³	1	2	yes	—
224	C₁₉×#121	C₂³	1	2	yes	—
225	C₁₉×#121	C₂³	1	1	yes	characteristic
226	C₁₉×#121	C₂³	1	2	yes	—
227	C₁₉×#120	—	2	2	no	—
228	C₁₉×#120	—	2	2	no	—
229	C₁₉×#120	—	2	2	no	—
230	C₄×Q₈×C₁₉	—	2	1	no	—
231	C₄×Q₈×C₁₉	—	2	1	no	—
232	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
236	C₄×D₄×C₁₉	—	2	1	no	—
237	C₄×D₄×C₁₉	—	2	1	no	—
238	C₄×D₄×C₁₉	—	2	2	no	—
239	C₄×D₄×C₁₉	—	2	1	no	—
240	C₄×D₄×C₁₉	—	2	1	no	—
241	C₄×D₄×C₁₉	—	2	2	no	—
242	C₄×D₄×C₁₉	—	2	1	no	—
243	C₄×D₄×C₁₉	—	2	2	no	—
244	C₄×D₄×C₁₉	—	2	2	no	—
245	C₄×D₄×C₁₉	—	2	1	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	D₄	1	1	yes	characteristic
250	C₄×D₄×C₁₉	D₄	1	2	yes	—
251	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
252	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₁₉	C₂³	1	2	yes	—
254	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₁₉	C₂³	1	2	yes	—
256	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
257	C₁₉×#117	—	2	1	no	—
258	C₁₉×#117	—	2	1	no	—
259	C₁₉×#117	—	2	1	no	—
260	C₁₉×#117	—	2	1	no	—
261	C₁₉×#117	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
263	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
264	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
268	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
272	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
273	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
274	C₁₉×#107	C₂³	1	1	yes	characteristic
275	C₁₉×#107	C₂³	1	2	yes	—
276	C₁₉×#107	C₂³	1	2	yes	—
277	C₁₉×#107	C₂³	1	2	yes	—
278	C₁₉×#107	C₂³	1	2	yes	—
279	C₁₉×#107	C₂³	1	1	yes	characteristic
280	C₁₉×#107	C₂³	1	2	yes	—
281	C₁₉×#106	C₂³	1	1	yes	characteristic
282	C₁₉×#106	C₂³	1	2	yes	—
283	C₁₉×#106	C₂³	1	1	yes	characteristic
284	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
287	C₁₉×#103	C₂³	1	1	yes	characteristic
288	C₁₉×#103	C₂³	1	2	yes	—
289	C₁₉×#103	C₂³	1	2	yes	—
290	C₁₉×#103	C₂³	1	2	yes	—
291	C₁₉×#103	C₂³	1	1	yes	characteristic
292	C₁₉×#103	C₂³	1	2	yes	—
293	C₁₉×#103	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	1	yes	characteristic
301	C₁₉×#102	C₂³	1	2	yes	—
302	C₁₉×#102	C₂³	1	2	yes	—
303	C₁₉×#102	C₂³	1	2	yes	—
304	C₁₉×#102	C₂³	1	2	yes	—
305	C₁₉×#102	C₂³	1	1	yes	characteristic
306	C₁₉×#102	C₂³	1	2	yes	—
307	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₁₉×#97	C₂³	1	1	yes	characteristic
312	C₁₉×#97	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
315	C₂⁴×C₁₉	—	2	2	no	—
316	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
317	#41×C₁₉	—	4	2	no	—
318	#41×C₁₉	—	4	2	no	—
319	#41×C₁₉	—	8	2	no	—
320	C₂×Q₈×C₁₉	—	2	1	no	—
321	C₂×Q₈×C₁₉	—	2	1	no	—
322	C₂×Q₈×C₁₉	—	2	2	no	—
323	C₂×Q₈×C₁₉	—	2	2	no	—
324	C₂×Q₈×C₁₉	—	2	1	no	—
325	C₂×Q₈×C₁₉	—	4	2	no	—
326	C₂×Q₈×C₁₉	—	4	2	no	—
327	C₂×Q₈×C₁₉	—	4	2	no	—
328	C₂×Q₈×C₁₉	—	4	2	no	—
329	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₁₉	—	2	4	no	—
334	C₂×D₄×C₁₉	—	2	2	no	—
335	C₂×D₄×C₁₉	—	2	2	no	—
336	C₂×D₄×C₁₉	—	2	1	no	—
337	C₂×D₄×C₁₉	—	2	2	no	—
338	C₂×D₄×C₁₉	—	2	2	no	—
339	C₂×D₄×C₁₉	—	2	2	no	—
340	C₂×D₄×C₁₉	—	2	1	no	—
341	C₂×D₄×C₁₉	—	2	1	no	—
342	C₂×D₄×C₁₉	—	2	2	no	—
343	C₂×D₄×C₁₉	—	4	2	no	—
344	C₂×D₄×C₁₉	—	4	2	no	—
345	C₂×D₄×C₁₉	—	4	4	no	—
346	C₂×D₄×C₁₉	—	8	4	no	—
347	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
349	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₁₉	—	2	2	no	—
353	C₂²×C₄×C₁₉	—	2	2	no	—
354	C₂²×C₄×C₁₉	—	2	2	no	—
355	C₂²×C₄×C₁₉	—	2	2	no	—
356	C₂²×C₄×C₁₉	—	2	2	no	—
357	C₂²×C₄×C₁₉	—	2	1	no	—
358	C₂²×C₄×C₁₉	—	2	2	no	—
359	C₂²×C₄×C₁₉	—	2	2	no	—
360	C₂²×C₄×C₁₉	—	4	2	no	—
361	C₂²×C₄×C₁₉	—	4	2	no	—
362	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
365	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
366	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
367	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
370	Q₁₆×C₁₉	—	2	2	no	—
371	Q₁₆×C₁₉	—	4	1	no	—
372	Q₁₆×C₁₉	—	4	2	no	—
373	SD₁₆×C₁₉	—	2	2	no	—
374	SD₁₆×C₁₉	—	2	4	no	—
375	SD₁₆×C₁₉	—	4	2	no	—
376	SD₁₆×C₁₉	—	4	2	no	—
377	SD₁₆×C₁₉	—	4	2	no	—
378	SD₁₆×C₁₉	—	4	1	no	—
379	SD₁₆×C₁₉	—	4	2	no	—
380	M₁₆×C₁₉	—	2	2	no	—
381	M₁₆×C₁₉	—	2	4	no	—
382	M₁₆×C₁₉	—	4	2	no	—
383	M₁₆×C₁₉	—	4	2	no	—
384	M₁₆×C₁₉	—	4	1	no	—
385	C₂×C₈×C₁₉	—	2	4	no	—
386	C₂×C₈×C₁₉	—	4	2	no	—
387	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
389	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₁₉	—	2	1	no	—
394	C₄⋊C₄×C₁₉	—	2	2	no	—
395	C₄⋊C₄×C₁₉	—	2	1	no	—
396	C₄⋊C₄×C₁₉	—	2	2	no	—
397	C₄⋊C₄×C₁₉	—	2	2	no	—
398	C₄⋊C₄×C₁₉	—	2	2	no	—
399	C₄⋊C₄×C₁₉	—	2	2	no	—
400	C₄⋊C₄×C₁₉	—	2	2	no	—
401	C₄⋊C₄×C₁₉	—	2	2	no	—
402	C₄⋊C₄×C₁₉	—	2	2	no	—
403	C₄⋊C₄×C₁₉	—	2	1	no	—
404	C₄⋊C₄×C₁₉	—	2	1	no	—
405	C₄⋊C₄×C₁₉	—	2	1	no	—
406	C₄⋊C₄×C₁₉	—	2	1	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	—	2	2	no	—
412	C₄⋊C₄×C₁₉	—	2	1	no	—
413	C₄⋊C₄×C₁₉	—	2	1	no	—
414	C₄⋊C₄×C₁₉	—	2	1	no	—
415	C₄⋊C₄×C₁₉	—	2	2	no	—
416	C₄⋊C₄×C₁₉	—	2	1	no	—
417	C₄⋊C₄×C₁₉	—	2	1	no	—
418	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
424	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
426	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
427	C₂²⋊C₄×C₁₉	—	2	1	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	2	no	—
435	C₂²⋊C₄×C₁₉	—	2	2	no	—
436	C₂²⋊C₄×C₁₉	—	2	1	no	—
437	C₂²⋊C₄×C₁₉	—	2	1	no	—
438	C₂²⋊C₄×C₁₉	—	2	1	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	2	no	—
444	C₂²⋊C₄×C₁₉	—	2	1	no	—
445	C₂²⋊C₄×C₁₉	—	2	2	no	—
446	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
450	C₄²×C₁₉	—	2	2	no	—
451	C₄²×C₁₉	—	2	1	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	1	yes	characteristic
456	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
458	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
459	#62296	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
460	C₂³×C₁₉	—	2	4	no	—
461	C₂³×C₁₉	—	2	1	no	—
462	C₂³×C₁₉	—	2	2	no	—
463	C₂³×C₁₉	—	4	2	no	—
464	C₂³×C₁₉	—	4	2	no	—
465	C₂³×C₁₉	—	4	4	no	—
466	C₂³×C₁₉	—	8	2	no	—
467	C₂³×C₁₉	—	8	2	no	—
468	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
469	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
470	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
471	Q₈×C₁₉	—	2	1	no	—
472	Q₈×C₁₉	—	2	2	no	—
473	Q₈×C₁₉	—	2	1	no	—
474	Q₈×C₁₉	—	2	1	no	—
475	Q₈×C₁₉	—	2	2	no	—
476	Q₈×C₁₉	—	2	1	no	—
477	Q₈×C₁₉	—	2	1	no	—
478	Q₈×C₁₉	—	2	1	no	—
479	Q₈×C₁₉	—	8	1	no	—
480	Q₈×C₁₉	—	8	1	no	—
481	Q₈×C₁₉	—	8	2	no	—
482	Q₈×C₁₉	—	8	2	no	—
483	Q₈×C₁₉	—	8	1	no	—
484	D₄×C₁₉	—	2	4	no	—
485	D₄×C₁₉	—	2	2	no	—
486	D₄×C₁₉	—	2	1	no	—
487	D₄×C₁₉	—	2	2	no	—
488	D₄×C₁₉	—	2	1	no	—
489	D₄×C₁₉	—	2	2	no	—
490	D₄×C₁₉	—	4	2	no	—
491	D₄×C₁₉	—	4	4	no	—
492	D₄×C₁₉	—	4	4	no	—
493	D₄×C₁₉	—	4	2	no	—
494	D₄×C₁₉	—	8	2	no	—
495	D₄×C₁₉	—	8	1	no	—
496	D₄×C₁₉	—	8	2	no	—
497	D₄×C₁₉	—	8	2	no	—
498	D₄×C₁₉	—	8	2	no	—
499	D₄×C₁₉	#137	1	4	yes	complemented
500	C₂×C₄×C₁₉	—	2	2	no	—
501	C₂×C₄×C₁₉	—	2	2	no	—
502	C₂×C₄×C₁₉	—	2	1	no	—
503	C₂×C₄×C₁₉	—	2	2	no	—
504	C₂×C₄×C₁₉	—	2	1	no	—
505	C₂×C₄×C₁₉	—	2	2	no	—
506	C₂×C₄×C₁₉	—	2	2	no	—
507	C₂×C₄×C₁₉	—	2	1	no	—
508	C₂×C₄×C₁₉	—	2	1	no	—
509	C₂×C₄×C₁₉	—	2	2	no	—
510	C₂×C₄×C₁₉	—	2	2	no	—
511	C₂×C₄×C₁₉	—	2	1	no	—
512	C₂×C₄×C₁₉	—	2	1	no	—
513	C₂×C₄×C₁₉	—	2	1	no	—
514	C₂×C₄×C₁₉	—	2	2	no	—
515	C₂×C₄×C₁₉	—	2	1	no	—
516	C₂×C₄×C₁₉	—	2	1	no	—
517	C₂×C₄×C₁₉	—	4	2	no	—
518	C₂×C₄×C₁₉	—	4	2	no	—
519	C₂×C₄×C₁₉	—	4	2	no	—
520	C₂×C₄×C₁₉	—	4	1	no	—
521	C₂×C₄×C₁₉	—	4	2	no	—
522	C₂×C₄×C₁₉	—	8	2	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	2	no	—
528	C₂×C₄×C₁₉	—	8	2	no	—
529	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
537	C₈×C₁₉	—	2	2	no	—
538	C₈×C₁₉	—	2	1	no	—
539	C₈×C₁₉	—	2	2	no	—
540	C₈×C₁₉	—	2	1	no	—
541	C₈×C₁₉	—	2	1	no	—
542	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
543	#3519	C₂×C₁₉	1	1	yes	characteristic
544	#3501	C₂×C₁₉	1	1	yes	characteristic, complemented
545	#3357	C₂×C₁₉	1	1	yes	characteristic, complemented
546	#3346	C₂×C₁₉	1	2	yes	complemented
547	#3338	C₂×C₁₉	1	1	yes	characteristic, complemented
548	#3333	C₂×C₁₉	1	1	yes	characteristic, complemented
549	#3329	C₂×C₁₉	1	1	yes	characteristic, complemented
550	#3320	C₂×C₁₉	1	2	yes	complemented
551	#3314	C₂×C₁₉	1	2	yes	complemented
552	#3299	C₂×C₁₉	1	1	yes	characteristic, complemented
553	#3295	C₂×C₁₉	1	1	yes	characteristic, complemented
554	D₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
555	#3278	C₂×C₁₉	1	1	yes	characteristic, complemented
556	#3266	C₂×C₁₉	1	2	yes	complemented
557	#3254	C₂×C₁₉	1	1	yes	characteristic, complemented
558	#3252	C₂×C₁₉	1	1	yes	characteristic, complemented
559	#3196	C₂×C₁₉	1	2	yes	complemented
560	#3193	C₂×C₁₉	1	2	yes	complemented
561	#3182	C₂×C₁₉	1	1	yes	characteristic, complemented
562	#3172	C₂×C₁₉	1	1	yes	characteristic, complemented
563	#3056	C₂×C₁₉	1	2	yes	complemented
564	C₂×#468	C₂×C₁₉	1	2	yes	complemented
565	D₄×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
566	C₂²×C₁₉	—	2	2	no	—
567	C₂²×C₁₉	—	2	2	no	—
568	C₂²×C₁₉	—	2	1	no	—
569	C₂²×C₁₉	—	2	2	no	—
570	C₂²×C₁₉	—	2	1	no	—
571	C₂²×C₁₉	—	2	2	no	—
572	C₂²×C₁₉	—	2	1	no	—
573	C₂²×C₁₉	—	2	2	no	—
574	C₂²×C₁₉	—	4	2	no	—
575	C₂²×C₁₉	—	4	1	no	—
576	C₂²×C₁₉	—	4	2	no	—
577	C₂²×C₁₉	—	4	1	no	—
578	C₂²×C₁₉	—	4	1	no	—
579	C₂²×C₁₉	—	4	2	no	—
580	C₂²×C₁₉	—	8	4	no	—
581	C₂²×C₁₉	—	16	4	no	—
582	C₂²×C₁₉	C₂×#137	1	4	yes	—
583	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
584	C₄×C₁₉	—	2	1	no	—
585	C₄×C₁₉	—	2	1	no	—
586	C₄×C₁₉	—	2	1	no	—
587	C₄×C₁₉	—	2	2	no	—
588	C₄×C₁₉	—	2	2	no	—
589	C₄×C₁₉	—	2	1	no	—
590	C₄×C₁₉	—	4	1	no	—
591	C₄×C₁₉	—	4	2	no	—
592	C₄×C₁₉	—	4	1	no	—
593	C₄×C₁₉	—	4	2	no	—
594	C₄×C₁₉	—	4	1	no	—
595	C₄×C₁₉	—	4	1	no	—
596	C₄×C₁₉	—	4	1	no	—
597	C₄×C₁₉	—	4	2	no	—
598	C₄×C₁₉	—	4	1	no	—
599	C₄×C₁₉	—	4	1	no	—
600	C₄×C₁₉	C₂×#137	1	2	yes	—
601	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
602	C₄×C₁₉	#585	1	1	yes	characteristic
603	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
604	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
605	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	complemented
606	#555	C₂²×C₁₉	1	1	yes	characteristic
607	#554	—	2	1	no	—
608	#554	—	2	2	no	—
609	#554	—	2	1	no	—
610	#554	C₂²×C₁₉	1	1	yes	characteristic
611	#554	C₂²×C₁₉	1	1	yes	characteristic
612	#554	C₂²×C₁₉	1	1	yes	characteristic, complemented
613	#554	C₂²×C₁₉	1	2	yes	complemented
614	#553	—	2	1	no	—
615	#553	C₂²×C₁₉	1	2	yes	—
616	#550	C₂²×C₁₉	1	1	yes	characteristic
617	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
618	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
619	D₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
620	#546	—	2	2	no	—
621	#546	C₂²×C₁₉	1	2	yes	—
622	D₄²	—	2	1	no	—
623	D₄²	C₂²×C₁₉	1	1	yes	characteristic
624	#544	—	2	1	no	—
625	#543	—	2	2	no	—
626	#540	—	2	1	no	—
627	#538	—	2	2	no	—
628	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
629	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
630	#532	C₂²×C₁₉	1	1	yes	characteristic
631	#529	C₂²×C₁₉	1	1	yes	characteristic
632	#525	C₂²×C₁₉	1	2	yes	—
633	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	complemented
634	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	complemented
635	C₂×#121	C₂²×C₁₉	1	2	yes	—
636	#518	—	2	1	no	—
637	#518	—	2	1	no	—
638	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
639	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
640	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
641	#497	C₂²×C₁₉	1	1	yes	characteristic, complemented
642	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
643	#491	C₂²×C₁₉	1	1	yes	characteristic, complemented
644	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
645	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
646	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
647	#485	C₂²×C₁₉	1	2	yes	complemented
648	#485	C₂²×C₁₉	1	2	yes	complemented
649	#484	C₂²×C₁₉	1	2	yes	complemented
650	#484	C₂²×C₁₉	1	2	yes	complemented
651	#484	C₂²×C₁₉	1	2	yes	complemented
652	#481	C₂²×C₁₉	1	2	yes	complemented
653	#480	C₂²×C₁₉	1	2	yes	complemented
654	#480	C₂²×C₁₉	1	2	yes	complemented
655	#479	C₂²×C₁₉	1	2	yes	complemented
656	#477	C₂²×C₁₉	1	1	yes	characteristic, complemented
657	#477	C₂²×C₁₉	1	1	yes	characteristic, complemented
658	#477	C₂²×C₁₉	1	1	yes	characteristic, complemented
659	#476	C₂²×C₁₉	1	1	yes	characteristic, complemented
660	#474	C₂²×C₁₉	1	2	yes	complemented
661	#470	C₂²×C₁₉	1	1	yes	characteristic, complemented
662	#470	C₂²×C₁₉	1	1	yes	characteristic, complemented
663	#470	C₂²×C₁₉	1	2	yes	complemented
664	#468	C₂²×C₁₉	1	1	yes	characteristic
665	#468	C₂²×C₁₉	1	1	yes	characteristic
666	#468	C₂²×C₁₉	1	2	yes	—
667	#468	C₂²×C₁₉	1	2	yes	complemented
668	#468	C₂²×C₁₉	1	2	yes	complemented
669	#468	C₂²×C₁₉	1	2	yes	complemented
670	#468	C₂²×C₁₉	1	2	yes	complemented
671	#468	C₂²×C₁₉	1	2	yes	complemented
672	#468	C₂²×C₁₉	1	2	yes	complemented
673	#468	C₂²×C₁₉	1	2	yes	complemented
674	#468	C₂²×C₁₉	1	2	yes	complemented
675	#467	C₂²×C₁₉	1	2	yes	complemented
676	#467	C₂²×C₁₉	1	2	yes	complemented
677	#465	C₂²×C₁₉	1	2	yes	complemented
678	#465	C₂²×C₁₉	1	2	yes	complemented
679	#464	C₂²×C₁₉	1	2	yes	complemented
680	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
681	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
682	#461	C₂²×C₁₉	1	2	yes	complemented
683	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
684	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
685	#452	C₂²×C₁₉	1	2	yes	complemented
686	#452	C₂²×C₁₉	1	2	yes	complemented
687	#451	C₂²×C₁₉	1	2	yes	complemented
688	#450	C₂²×C₁₉	1	2	yes	complemented
689	#450	C₂²×C₁₉	1	2	yes	complemented
690	#448	C₂²×C₁₉	1	2	yes	complemented
691	#448	C₂²×C₁₉	1	2	yes	complemented
692	#448	C₂²×C₁₉	1	2	yes	complemented
693	#440	C₂²×C₁₉	1	2	yes	complemented
694	#440	C₂²×C₁₉	1	2	yes	complemented
695	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
696	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
697	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
698	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
699	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
700	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
701	#435	C₂²×C₁₉	1	2	yes	complemented
702	#435	C₂²×C₁₉	1	2	yes	complemented
703	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
704	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
705	#428	C₂²×C₁₉	1	2	yes	complemented
706	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
707	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
708	#419	C₂²×C₁₉	1	2	yes	complemented
709	#417	C₂²×C₁₉	1	2	yes	complemented
710	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
711	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
712	#407	C₂²×C₁₉	1	2	yes	complemented
713	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
714	C₂×C₁₉	—	2	4	no	—
715	C₂×C₁₉	—	4	2	no	—
716	C₂×C₁₉	—	4	1	no	—
717	C₂×C₁₉	—	8	2	no	—
718	C₂×C₁₉	—	8	1	no	—
719	C₂×C₁₉	#3496	1	1	yes	characteristic
720	C₂×C₁₉	C₂²×#137	1	1	yes	characteristic
721	C₂×C₁₉	#3585	1	1	yes	characteristic
722	C₂×#41	—	2	1	no	—
723	C₂×#41	C₂³×C₁₉	1	2	yes	—
724	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
725	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
726	C₂²×D₄	—	2	2	no	—
727	C₂²×D₄	—	2	1	no	—
728	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
729	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
730	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
731	#137	—	4	4	no	—
732	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
733	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
734	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
735	C₂×SD₁₆	—	4	4	no	—
736	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
737	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
739	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
740	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
742	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
743	C₂×M₁₆	—	4	4	no	—
744	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
745	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
746	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
747	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
748	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
749	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
750	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
751	C₄⋊Q₈	—	2	1	no	—
752	C₄⋊Q₈	—	2	1	no	—
753	C₄⋊Q₈	—	2	2	no	—
754	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
755	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
756	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
757	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
758	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
759	#127	—	2	1	no	—
760	#127	C₂³×C₁₉	1	1	yes	characteristic
761	#126	—	2	2	no	—
762	#126	—	2	1	no	—
763	#125	—	2	1	no	—
764	#125	—	2	1	no	—
765	#125	—	2	1	no	—
766	#125	—	2	2	no	—
767	#125	—	2	1	no	—
768	#125	—	2	1	no	—
769	#125	C₂³×C₁₉	1	1	yes	characteristic
770	#124	—	2	2	no	—
771	#124	—	2	1	no	—
772	#124	C₂³×C₁₉	1	1	yes	characteristic
773	#123	—	2	2	no	—
774	#123	—	2	1	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
793	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
795	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
796	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
797	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
798	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
799	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
800	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
801	#121	—	2	2	no	—
802	#121	—	2	1	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	C₂³×C₁₉	1	1	yes	characteristic
810	#121	C₂³×C₁₉	1	2	yes	—
811	#121	C₂³×C₁₉	1	2	yes	—
812	#121	C₂³×C₁₉	1	2	yes	—
813	#121	C₂³×C₁₉	1	2	yes	—
814	#120	—	2	2	no	—
815	#120	—	2	2	no	—
816	#120	—	2	2	no	—
817	C₄×Q₈	—	2	1	no	—
818	C₄×Q₈	—	2	1	no	—
819	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
820	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
821	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
822	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
837	C₄×D₄	D₄×C₁₉	1	2	yes	—
838	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₁₉	1	2	yes	—
841	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₁₉	1	2	yes	—
843	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
844	#117	—	2	1	no	—
845	#117	—	2	1	no	—
846	#117	—	2	1	no	—
847	#117	—	2	1	no	—
848	#117	C₂³×C₁₉	1	2	yes	—
849	C₂×C₄⋊C₄	—	2	2	no	—
850	C₂×C₄⋊C₄	—	2	2	no	—
851	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
852	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
853	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
854	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
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×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
860	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
861	#107	C₂³×C₁₉	1	1	yes	characteristic
862	#107	C₂³×C₁₉	1	2	yes	—
863	#107	C₂³×C₁₉	1	2	yes	—
864	#107	C₂³×C₁₉	1	2	yes	—
865	#107	C₂³×C₁₉	1	2	yes	—
866	#107	C₂³×C₁₉	1	1	yes	characteristic
867	#107	C₂³×C₁₉	1	2	yes	—
868	#106	C₂³×C₁₉	1	1	yes	characteristic
869	#106	C₂³×C₁₉	1	2	yes	—
870	#106	C₂³×C₁₉	1	1	yes	characteristic
871	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
872	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
873	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
874	#103	C₂³×C₁₉	1	1	yes	characteristic
875	#103	C₂³×C₁₉	1	2	yes	—
876	#103	C₂³×C₁₉	1	2	yes	—
877	#103	C₂³×C₁₉	1	2	yes	—
878	#103	C₂³×C₁₉	1	1	yes	characteristic
879	#103	C₂³×C₁₉	1	2	yes	—
880	#103	C₂³×C₁₉	1	1	yes	characteristic
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	2	yes	—
887	#102	C₂³×C₁₉	1	1	yes	characteristic
888	#102	C₂³×C₁₉	1	2	yes	—
889	#102	C₂³×C₁₉	1	2	yes	—
890	#102	C₂³×C₁₉	1	2	yes	—
891	#102	C₂³×C₁₉	1	2	yes	—
892	#102	C₂³×C₁₉	1	1	yes	characteristic
893	#102	C₂³×C₁₉	1	2	yes	—
894	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
895	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
896	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
897	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
898	#97	C₂³×C₁₉	1	1	yes	characteristic
899	#97	C₂³×C₁₉	1	1	yes	characteristic
900	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
901	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
902	C₁₉	#62296	1	1	yes	characteristic, direct product factor, Sylow
903	C₂⁴	—	2	2	no	—
904	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	8	2	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	2	no	—
911	C₂×Q₈	—	2	2	no	—
912	C₂×Q₈	—	2	1	no	—
913	C₂×Q₈	—	4	2	no	—
914	C₂×Q₈	—	4	2	no	—
915	C₂×Q₈	—	4	2	no	—
916	C₂×Q₈	—	4	2	no	—
917	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
918	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
919	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
920	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
921	C₂×D₄	—	2	4	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	4	2	no	—
932	C₂×D₄	—	4	2	no	—
933	C₂×D₄	—	4	4	no	—
934	C₂×D₄	—	8	4	no	—
935	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
936	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
937	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
938	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
939	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	4	2	no	—
949	C₂²×C₄	—	4	2	no	—
950	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
951	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
952	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
953	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
954	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
955	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
956	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
957	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
958	Q₁₆	—	2	2	no	—
959	Q₁₆	—	4	1	no	—
960	Q₁₆	—	4	2	no	—
961	SD₁₆	—	2	2	no	—
962	SD₁₆	—	2	4	no	—
963	SD₁₆	—	4	2	no	—
964	SD₁₆	—	4	2	no	—
965	SD₁₆	—	4	2	no	—
966	SD₁₆	—	4	1	no	—
967	SD₁₆	—	4	2	no	—
968	M₁₆	—	2	2	no	—
969	M₁₆	—	2	4	no	—
970	M₁₆	—	4	2	no	—
971	M₁₆	—	4	2	no	—
972	M₁₆	—	4	1	no	—
973	C₂×C₈	—	2	4	no	—
974	C₂×C₈	—	4	2	no	—
975	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
978	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
979	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
980	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	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	1	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1007	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1008	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1009	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1010	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1011	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1012	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1013	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1014	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	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	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	1	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	1	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
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	2	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	2	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1044	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1045	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1046	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1047	C₂³	—	2	4	no	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	4	2	no	—
1051	C₂³	—	4	2	no	—
1052	C₂³	—	4	4	no	—
1053	C₂³	—	8	2	no	—
1054	C₂³	—	8	2	no	—
1055	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1056	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1057	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1058	Q₈	—	2	1	no	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	1	no	—
1061	Q₈	—	2	1	no	—
1062	Q₈	—	2	2	no	—
1063	Q₈	—	2	1	no	—
1064	Q₈	—	2	1	no	—
1065	Q₈	—	2	1	no	—
1066	Q₈	—	8	2	no	—
1067	Q₈	—	8	2	no	—
1068	Q₈	—	8	1	no	—
1069	Q₈	—	8	1	no	—
1070	Q₈	—	8	1	no	—
1071	D₄	—	2	4	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	1	no	—
1074	D₄	—	2	2	no	—
1075	D₄	—	2	1	no	—
1076	D₄	—	2	2	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	4	4	no	—
1079	D₄	—	4	4	no	—
1080	D₄	—	4	2	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	1	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	2	no	—
1085	D₄	—	8	2	no	—
1086	D₄	C₁₉×#137	1	4	yes	complemented
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	2	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	8	2	no	—
1110	C₂×C₄	—	8	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	C₂²×D₄×C₁₉	1	1	yes	characteristic
1117	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1118	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1119	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1120	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1121	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1122	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1123	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1124	C₈	—	2	2	no	—
1125	C₈	—	2	1	no	—
1126	C₈	—	2	2	no	—
1127	C₈	—	2	1	no	—
1128	C₈	—	2	1	no	—
1129	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	2	1	no	—
1137	C₂²	—	2	2	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	2	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	8	4	no	—
1145	C₂²	—	16	4	no	—
1146	C₂²	C₂×C₁₉×#137	1	4	yes	—
1147	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	2	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	2	no	—
1163	C₄	—	4	1	no	—
1164	C₄	C₂×C₁₉×#137	1	2	yes	—
1165	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1166	C₄	C₁₉×#585	1	1	yes	characteristic
1167	C₂	—	2	4	no	—
1168	C₂	—	4	1	no	—
1169	C₂	—	4	2	no	—
1170	C₂	—	8	1	no	—
1171	C₂	—	8	2	no	—
1172	C₂	C₁₉×#3496	1	1	yes	characteristic
1173	C₂	C₂²×C₁₉×#137	1	1	yes	characteristic
1174	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×#3519	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3501	C₂	semidirect
3. C₁₉×#3357	C₂	semidirect
4. C₁₉×#3346	C₂	semidirect
5. C₁₉×#3338	C₂	semidirect
6. C₁₉×#3333	C₂	semidirect
7. C₁₉×#3329	C₂	semidirect
8. C₁₉×#3320	C₂	semidirect
9. C₁₉×#3314	C₂	semidirect
10. C₁₉×#3299	C₂	semidirect
11. C₁₉×#3295	C₂	semidirect
12. D₄×SD₁₆×C₁₉	C₂	semidirect
13. C₁₉×#3278	C₂	semidirect
14. C₁₉×#3266	C₂	semidirect
15. C₁₉×#3254	C₂	semidirect
16. C₁₉×#3252	C₂	semidirect
17. C₁₉×#3196	C₂	semidirect
18. C₁₉×#3193	C₂	semidirect
19. C₁₉×#3182	C₂	semidirect
20. C₁₉×#3172	C₂	semidirect
21. C₁₉×#3056	C₂	semidirect
22. C₂×C₁₉×#468	C₂	semidirect
23. D₄×M₁₆×C₁₉	C₂	semidirect
24. C₂×C₁₉×#137	C₂²	semidirect
25. C₂²×SD₁₆×C₁₉	C₂²	semidirect
26. C₂²×M₁₆×C₁₉	C₂²	semidirect
33. C₁₉×#554	C₂²	semidirect
34. C₁₉×#554	C₂²	semidirect
39. D₄×Q₈×C₁₉	C₂²	semidirect
40. D₄×Q₈×C₁₉	C₂²	semidirect
49. C₁₉×#533	C₂²	semidirect
50. C₁₉×#533	C₂²	semidirect
54. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
55. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
60. C₁₉×#501	C₂²	semidirect
61. C₁₉×#500	C₂²	semidirect
62. C₁₉×#497	C₂²	semidirect
63. C₁₉×#492	C₂²	semidirect
64. C₁₉×#491	C₂²	semidirect
65. C₁₉×#489	C₂²	semidirect
66. C₁₉×#487	C₂²	semidirect
67. C₁₉×#486	C₂²	semidirect
68. C₁₉×#485	C₂²	semidirect
69. C₁₉×#485	C₂²	semidirect
70. C₁₉×#484	C₂²	semidirect
71. C₁₉×#484	C₂²	semidirect
72. C₁₉×#484	C₂²	semidirect
73. C₁₉×#481	C₂²	semidirect
74. C₁₉×#480	C₂²	semidirect
75. C₁₉×#480	C₂²	semidirect
76. C₁₉×#479	C₂²	semidirect
77. C₁₉×#477	C₂²	semidirect
78. C₁₉×#477	C₂²	semidirect
79. C₁₉×#477	C₂²	semidirect
80. C₁₉×#476	C₂²	semidirect
81. C₁₉×#474	C₂²	semidirect
82. C₁₉×#470	C₂²	semidirect
83. C₁₉×#470	C₂²	semidirect
84. C₁₉×#470	C₂²	semidirect
88. C₁₉×#468	C₂²	semidirect
89. C₁₉×#468	C₂²	semidirect
90. C₁₉×#468	C₂²	semidirect
91. C₁₉×#468	C₂²	semidirect
92. C₁₉×#468	C₂²	semidirect
93. C₁₉×#468	C₂²	semidirect
94. C₁₉×#468	C₂²	semidirect
95. C₁₉×#468	C₂²	semidirect
96. C₁₉×#467	C₂²	semidirect
97. C₁₉×#467	C₂²	semidirect
98. C₁₉×#465	C₂²	semidirect
99. C₁₉×#465	C₂²	semidirect
100. C₁₉×#464	C₂²	semidirect
101. C₁₉×#462	C₂²	semidirect
102. C₁₉×#461	C₂²	semidirect
103. C₁₉×#461	C₂²	semidirect
104. C₁₉×#460	C₂²	semidirect
105. C₁₉×#460	C₂²	semidirect
106. C₁₉×#452	C₂²	semidirect
107. C₁₉×#452	C₂²	semidirect
108. C₁₉×#451	C₂²	semidirect
109. C₁₉×#450	C₂²	semidirect
110. C₁₉×#450	C₂²	semidirect
111. C₁₉×#448	C₂²	semidirect
112. C₁₉×#448	C₂²	semidirect
113. C₁₉×#448	C₂²	semidirect
114. C₁₉×#440	C₂²	semidirect
115. C₁₉×#440	C₂²	semidirect
116. C₄×Q₁₆×C₁₉	C₂²	semidirect
117. C₄×Q₁₆×C₁₉	C₂²	semidirect
118. C₄×SD₁₆×C₁₉	C₂²	semidirect
119. C₄×SD₁₆×C₁₉	C₂²	semidirect
120. C₁₉×#436	C₂²	semidirect
121. C₁₉×#436	C₂²	semidirect
122. C₁₉×#435	C₂²	semidirect
123. C₁₉×#435	C₂²	semidirect
126. C₁₉×#428	C₂²	semidirect
127. C₂×C₁₉×#107	C₂²	semidirect
128. C₁₉×#423	C₂²	semidirect
129. C₁₉×#419	C₂²	semidirect
130. C₁₉×#417	C₂²	semidirect
131. C₂×C₁₉×#103	C₂²	semidirect
132. C₂×C₁₉×#102	C₂²	semidirect
133. C₁₉×#407	C₂²	semidirect
134. C₄×M₁₆×C₁₉	C₂²	semidirect
459. #62296	C₁₉	direct (N × H)
499. D₄×C₁₉	#137	semidirect
544. #3501	C₂×C₁₉	semidirect
545. #3357	C₂×C₁₉	semidirect
546. #3346	C₂×C₁₉	semidirect
547. #3338	C₂×C₁₉	semidirect
548. #3333	C₂×C₁₉	semidirect
549. #3329	C₂×C₁₉	semidirect
550. #3320	C₂×C₁₉	semidirect
551. #3314	C₂×C₁₉	semidirect
552. #3299	C₂×C₁₉	semidirect
553. #3295	C₂×C₁₉	semidirect
554. D₄×SD₁₆	C₂×C₁₉	semidirect
555. #3278	C₂×C₁₉	semidirect
556. #3266	C₂×C₁₉	semidirect
557. #3254	C₂×C₁₉	semidirect
558. #3252	C₂×C₁₉	semidirect
559. #3196	C₂×C₁₉	semidirect
560. #3193	C₂×C₁₉	semidirect
561. #3182	C₂×C₁₉	semidirect
562. #3172	C₂×C₁₉	semidirect
563. #3056	C₂×C₁₉	semidirect
564. C₂×#468	C₂×C₁₉	semidirect
565. D₄×M₁₆	C₂×C₁₉	semidirect
603. C₂×#137	C₂²×C₁₉	semidirect
604. C₂²×SD₁₆	C₂²×C₁₉	semidirect
605. C₂²×M₁₆	C₂²×C₁₉	semidirect
612. #554	C₂²×C₁₉	semidirect
613. #554	C₂²×C₁₉	semidirect
618. D₄×Q₈	C₂²×C₁₉	semidirect
619. D₄×Q₈	C₂²×C₁₉	semidirect
628. #533	C₂²×C₁₉	semidirect
629. #533	C₂²×C₁₉	semidirect
633. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
634. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
639. #501	C₂²×C₁₉	semidirect
640. #500	C₂²×C₁₉	semidirect
641. #497	C₂²×C₁₉	semidirect
642. #492	C₂²×C₁₉	semidirect
643. #491	C₂²×C₁₉	semidirect
644. #489	C₂²×C₁₉	semidirect
645. #487	C₂²×C₁₉	semidirect
646. #486	C₂²×C₁₉	semidirect
647. #485	C₂²×C₁₉	semidirect
648. #485	C₂²×C₁₉	semidirect
649. #484	C₂²×C₁₉	semidirect
650. #484	C₂²×C₁₉	semidirect
651. #484	C₂²×C₁₉	semidirect
652. #481	C₂²×C₁₉	semidirect
653. #480	C₂²×C₁₉	semidirect
654. #480	C₂²×C₁₉	semidirect
655. #479	C₂²×C₁₉	semidirect
656. #477	C₂²×C₁₉	semidirect
657. #477	C₂²×C₁₉	semidirect
658. #477	C₂²×C₁₉	semidirect
659. #476	C₂²×C₁₉	semidirect
660. #474	C₂²×C₁₉	semidirect
661. #470	C₂²×C₁₉	semidirect
662. #470	C₂²×C₁₉	semidirect
663. #470	C₂²×C₁₉	semidirect
667. #468	C₂²×C₁₉	semidirect
668. #468	C₂²×C₁₉	semidirect
669. #468	C₂²×C₁₉	semidirect
670. #468	C₂²×C₁₉	semidirect
671. #468	C₂²×C₁₉	semidirect
672. #468	C₂²×C₁₉	semidirect
673. #468	C₂²×C₁₉	semidirect
674. #468	C₂²×C₁₉	semidirect
675. #467	C₂²×C₁₉	semidirect
676. #467	C₂²×C₁₉	semidirect
677. #465	C₂²×C₁₉	semidirect
678. #465	C₂²×C₁₉	semidirect
679. #464	C₂²×C₁₉	semidirect
680. #462	C₂²×C₁₉	semidirect
681. #461	C₂²×C₁₉	semidirect
682. #461	C₂²×C₁₉	semidirect
683. #460	C₂²×C₁₉	semidirect
684. #460	C₂²×C₁₉	semidirect
685. #452	C₂²×C₁₉	semidirect
686. #452	C₂²×C₁₉	semidirect
687. #451	C₂²×C₁₉	semidirect
688. #450	C₂²×C₁₉	semidirect
689. #450	C₂²×C₁₉	semidirect
690. #448	C₂²×C₁₉	semidirect
691. #448	C₂²×C₁₉	semidirect
692. #448	C₂²×C₁₉	semidirect
693. #440	C₂²×C₁₉	semidirect
694. #440	C₂²×C₁₉	semidirect
695. C₄×Q₁₆	C₂²×C₁₉	semidirect
696. C₄×Q₁₆	C₂²×C₁₉	semidirect
697. C₄×SD₁₆	C₂²×C₁₉	semidirect
698. C₄×SD₁₆	C₂²×C₁₉	semidirect
699. #436	C₂²×C₁₉	semidirect
700. #436	C₂²×C₁₉	semidirect
701. #435	C₂²×C₁₉	semidirect
702. #435	C₂²×C₁₉	semidirect
705. #428	C₂²×C₁₉	semidirect
706. C₂×#107	C₂²×C₁₉	semidirect
707. #423	C₂²×C₁₉	semidirect
708. #419	C₂²×C₁₉	semidirect
709. #417	C₂²×C₁₉	semidirect
710. C₂×#103	C₂²×C₁₉	semidirect
711. C₂×#102	C₂²×C₁₉	semidirect
712. #407	C₂²×C₁₉	semidirect
713. C₄×M₁₆	C₂²×C₁₉	semidirect
902. C₁₉	#62296	direct (N × H)
1086. D₄	C₁₉×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3519	2
C₁₉×#3501	2
C₁₉×#3357	2
C₁₉×#3346	2
C₁₉×#3338	2
C₁₉×#3333	2
C₁₉×#3329	2
C₁₉×#3320	2
C₁₉×#3314	2
C₁₉×#3299	2
C₁₉×#3295	2
D₄×SD₁₆×C₁₉	2
C₁₉×#3278	2
C₁₉×#3266	2
C₁₉×#3254	2
C₁₉×#3252	2
C₁₉×#3196	2
C₁₉×#3193	2
C₁₉×#3182	2
C₁₉×#3172	2
C₁₉×#3056	2
C₂×C₁₉×#468	2
D₄×M₁₆×C₁₉	2
#62296	19

Subgroups — C19×#62296 #18068255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62296 #18068255