Subgroups — C₁₉×#62054 #18068013

Order 4864.

1828 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3330	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3316	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3299	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3298	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3282	C₂	1	2	yes	maximal, complemented
13	C₁₉×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3266	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3258	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3225	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#3120	C₂	1	2	yes	maximal, complemented
20	C₁₉×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#3046	C₂	1	2	yes	maximal, complemented
22	C₂×C₁₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₉×#137	C₂²	1	2	yes	—
25	C₂×C₁₉×#135	C₂²	1	2	yes	—
26	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
27	C₁₉×#563	—	2	2	no	—
28	C₁₉×#557	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#556	C₂²	1	1	yes	characteristic
30	C₁₉×#556	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#554	—	2	1	no	—
32	C₁₉×#554	C₂²	1	2	yes	—
33	C₁₉×#553	—	2	1	no	—
34	C₁₉×#552	—	2	1	no	—
35	C₁₉×#551	—	2	2	no	—
36	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
37	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#548	—	2	1	no	—
40	C₁₉×#548	C₂²	1	2	yes	—
41	C₁₉×#547	C₂²	1	1	yes	characteristic
42	C₁₉×#547	C₂²	1	1	yes	characteristic
43	C₁₉×#547	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#546	C₂²	1	2	yes	—
45	C₁₉×#544	—	2	1	no	—
46	C₁₉×#542	—	2	1	no	—
47	C₁₉×#542	C₂²	1	2	yes	—
48	C₁₉×#541	C₂²	1	2	yes	complemented
49	C₁₉×#539	—	2	2	no	—
50	C₁₉×#539	—	2	2	no	—
51	C₁₉×#536	C₂²	1	2	yes	complemented
52	C₁₉×#533	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
54	C₁₉×#529	C₂²	1	1	yes	characteristic
55	C₁₉×#529	C₂²	1	1	yes	characteristic
56	C₁₉×#525	—	2	1	no	—
57	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
58	C₁₉×#520	C₂²	1	2	yes	—
59	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
60	C₁₉×#497	C₂²	1	2	yes	—
61	C₁₉×#495	C₂²	1	2	yes	—
62	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#489	C₂²	1	2	yes	complemented
65	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#487	C₂²	1	2	yes	complemented
68	C₁₉×#484	C₂²	1	1	yes	characteristic
69	C₁₉×#484	C₂²	1	2	yes	complemented
70	C₁₉×#483	C₂²	1	2	yes	complemented
71	C₁₉×#481	C₂²	1	1	yes	characteristic
72	C₁₉×#479	C₂²	1	2	yes	complemented
73	C₁₉×#478	C₂²	1	1	yes	characteristic
74	C₁₉×#478	C₂²	1	1	yes	characteristic
75	C₁₉×#477	C₂²	1	2	yes	complemented
76	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
77	C₁₉×#475	C₂²	1	2	yes	complemented
78	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
79	C₁₉×#470	C₂²	1	2	yes	complemented
80	C₁₉×#468	C₂²	1	2	yes	—
81	C₁₉×#467	C₂²	1	2	yes	—
82	C₁₉×#467	C₂²	1	2	yes	complemented
83	C₁₉×#465	C₂²	1	2	yes	—
84	C₁₉×#465	C₂²	1	2	yes	—
85	C₁₉×#464	C₂²	1	2	yes	—
86	C₁₉×#464	C₂²	1	2	yes	—
87	C₁₉×#464	C₂²	1	2	yes	complemented
88	C₁₉×#464	C₂²	1	2	yes	complemented
89	C₁₉×#463	C₂²	1	1	yes	characteristic
90	C₁₉×#463	C₂²	1	2	yes	—
91	C₁₉×#463	C₂²	1	1	yes	characteristic
92	C₁₉×#462	C₂²	1	2	yes	complemented
93	C₁₉×#462	C₂²	1	2	yes	complemented
94	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
95	C₁₉×#462	C₂²	1	2	yes	complemented
96	C₁₉×#461	C₂²	1	2	yes	—
97	C₁₉×#461	C₂²	1	2	yes	—
98	C₁₉×#461	C₂²	1	1	yes	characteristic
99	C₁₉×#461	C₂²	1	1	yes	characteristic
100	C₁₉×#461	C₂²	1	1	yes	characteristic
101	C₁₉×#461	C₂²	1	2	yes	—
102	C₁₉×#461	C₂²	1	1	yes	characteristic
103	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
104	C₁₉×#452	C₂²	1	2	yes	—
105	C₁₉×#452	C₂²	1	2	yes	—
106	C₁₉×#452	C₂²	1	2	yes	complemented
107	C₁₉×#451	C₂²	1	2	yes	—
108	C₁₉×#451	C₂²	1	2	yes	—
109	C₁₉×#451	C₂²	1	2	yes	complemented
110	C₁₉×#450	C₂²	1	1	yes	characteristic
111	C₁₉×#449	C₂²	1	2	yes	—
112	C₁₉×#448	C₂²	1	2	yes	—
113	C₁₉×#447	C₂²	1	1	yes	characteristic
114	C₁₉×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
116	C₁₉×#441	C₂²	1	2	yes	complemented
117	C₁₉×#440	C₂²	1	2	yes	—
118	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
119	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
121	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
122	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
123	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
124	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
125	C₁₉×#435	C₂²	1	2	yes	—
126	C₈×D₄×C₁₉	C₂²	1	2	yes	—
127	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
128	C₁₉×#433	C₂²	1	2	yes	complemented
129	C₁₉×#431	C₂²	1	1	yes	characteristic
130	C₁₉×#424	C₂²	1	2	yes	complemented
131	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
132	C₁₉×#417	C₂²	1	2	yes	complemented
133	C₂×C₁₉×#103	C₂²	1	2	yes	—
134	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
135	C₂×#41×C₁₉	—	2	1	no	—
136	C₂×#41×C₁₉	C₂³	1	2	yes	—
137	C₂×#41×C₁₉	C₂³	1	2	yes	—
138	C₂²×Q₈×C₁₉	—	2	1	no	—
139	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
140	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
141	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₁₉	—	2	1	no	—
143	C₁₉×#137	—	4	4	no	—
144	C₁₉×#135	—	4	4	no	—
145	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₁₉	—	4	4	no	—
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	1	yes	characteristic
155	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
158	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
160	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
161	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
162	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
163	C₁₉×C₄⋊Q₈	—	2	2	no	—
164	C₁₉×C₄⋊Q₈	—	2	1	no	—
165	C₁₉×C₄⋊Q₈	—	2	1	no	—
166	C₁₉×C₄⋊Q₈	—	2	1	no	—
167	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
168	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
173	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
174	C₁₉×#126	—	2	2	no	—
175	C₁₉×#126	—	2	2	no	—
176	C₁₉×#126	—	2	2	no	—
177	C₁₉×#126	—	2	2	no	—
178	C₁₉×#126	—	2	2	no	—
179	C₁₉×#126	—	2	1	no	—
180	C₁₉×#126	D₄	1	2	yes	—
181	C₁₉×#125	—	2	2	no	—
182	C₁₉×#125	—	2	2	no	—
183	C₁₉×#125	—	2	2	no	—
184	C₁₉×#125	—	2	2	no	—
185	C₁₉×#125	—	2	1	no	—
186	C₁₉×#125	—	2	1	no	—
187	C₁₉×#125	D₄	1	1	yes	characteristic
188	C₁₉×#125	C₂³	1	1	yes	characteristic
189	C₁₉×#124	—	2	2	no	—
190	C₁₉×#124	—	2	2	no	—
191	C₁₉×#124	D₄	1	1	yes	characteristic
192	C₁₉×#124	C₂³	1	1	yes	characteristic
193	C₁₉×#124	C₂³	1	2	yes	—
194	C₁₉×#124	C₂³	1	2	yes	—
195	C₁₉×#123	—	2	1	no	—
196	C₁₉×#123	—	2	2	no	—
197	C₁₉×#123	—	2	2	no	—
198	C₁₉×#123	—	2	2	no	—
199	C₁₉×#123	—	2	2	no	—
200	C₁₉×#123	—	2	2	no	—
201	C₁₉×#123	—	2	2	no	—
202	C₁₉×#123	—	2	2	no	—
203	C₁₉×#123	D₄	1	2	yes	—
204	C₁₉×C₂²⋊Q₈	—	2	1	no	—
205	C₁₉×C₂²⋊Q₈	—	2	1	no	—
206	C₁₉×C₂²⋊Q₈	—	2	1	no	—
207	C₁₉×C₂²⋊Q₈	—	2	2	no	—
208	C₁₉×C₂²⋊Q₈	—	2	1	no	—
209	C₁₉×C₂²⋊Q₈	—	2	1	no	—
210	C₁₉×C₂²⋊Q₈	—	2	2	no	—
211	C₁₉×C₂²⋊Q₈	—	2	2	no	—
212	C₁₉×C₂²⋊Q₈	—	2	2	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	—	2	2	no	—
218	C₁₉×C₂²⋊Q₈	—	2	2	no	—
219	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
220	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₁₉×#121	—	2	1	no	—
226	C₁₉×#121	—	2	2	no	—
227	C₁₉×#121	—	2	1	no	—
228	C₁₉×#121	—	2	2	no	—
229	C₁₉×#121	D₄	1	1	yes	characteristic
230	C₁₉×#121	C₂³	1	1	yes	characteristic
231	C₁₉×#121	C₂³	1	2	yes	—
232	C₁₉×#120	—	2	2	no	—
233	C₄×Q₈×C₁₉	—	2	1	no	—
234	C₄×Q₈×C₁₉	—	2	1	no	—
235	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
237	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
238	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
239	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
240	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₁₉	—	2	2	no	—
242	C₄×D₄×C₁₉	—	2	2	no	—
243	C₄×D₄×C₁₉	—	2	1	no	—
244	C₄×D₄×C₁₉	—	2	1	no	—
245	C₄×D₄×C₁₉	—	2	2	no	—
246	C₄×D₄×C₁₉	—	2	2	no	—
247	C₄×D₄×C₁₉	—	2	2	no	—
248	C₄×D₄×C₁₉	—	2	1	no	—
249	C₄×D₄×C₁₉	—	2	1	no	—
250	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₁₉	C₂³	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	1	yes	characteristic
256	C₄×D₄×C₁₉	C₂³	1	2	yes	—
257	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
258	C₁₉×#117	—	2	1	no	—
259	C₁₉×#117	—	2	2	no	—
260	C₁₉×#117	—	2	1	no	—
261	C₁₉×#117	—	2	1	no	—
262	C₁₉×#117	—	2	1	no	—
263	C₁₉×#117	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
265	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
266	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
267	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
268	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
269	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
272	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
273	C₂×C₄²×C₁₉	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×#106	C₂³	1	1	yes	characteristic
278	C₁₉×#106	C₂³	1	2	yes	—
279	C₁₉×#106	C₂³	1	1	yes	characteristic
280	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
285	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
286	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₉×#103	C₂³	1	2	yes	—
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	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	2	yes	—
298	C₁₉×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
303	C₁₉×#102	C₂³	1	1	yes	characteristic
304	C₁₉×#102	C₂³	1	1	yes	characteristic
305	C₁₉×#102	C₂³	1	1	yes	characteristic
306	C₁₉×#102	C₂³	1	1	yes	characteristic
307	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₁₉×#97	C₂³	1	2	yes	—
312	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₁₉	C₂³	1	2	yes	—
315	C₂⁴×C₁₉	—	2	1	no	—
316	#41×C₁₉	—	2	4	no	—
317	#41×C₁₉	—	4	2	no	—
318	#41×C₁₉	—	4	2	no	—
319	#41×C₁₉	—	4	2	no	—
320	#41×C₁₉	—	8	2	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	2	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	—	8	2	no	—
330	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
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	—	4	1	no	—
342	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₁₉	—	2	1	no	—
348	C₂²×C₄×C₁₉	—	2	2	no	—
349	C₂²×C₄×C₁₉	—	2	2	no	—
350	C₂²×C₄×C₁₉	—	2	2	no	—
351	C₂²×C₄×C₁₉	—	2	2	no	—
352	C₂²×C₄×C₁₉	—	2	1	no	—
353	C₂²×C₄×C₁₉	—	2	1	no	—
354	C₂²×C₄×C₁₉	—	2	1	no	—
355	C₂²×C₄×C₁₉	—	2	2	no	—
356	C₂²×C₄×C₁₉	—	2	1	no	—
357	C₂²×C₄×C₁₉	—	2	2	no	—
358	C₂²×C₄×C₁₉	—	2	1	no	—
359	C₂²×C₄×C₁₉	—	8	2	no	—
360	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
364	Q₁₆×C₁₉	—	4	2	no	—
365	Q₁₆×C₁₉	—	4	2	no	—
366	Q₁₆×C₁₉	—	4	2	no	—
367	Q₁₆×C₁₉	—	4	2	no	—
368	Q₁₆×C₁₉	—	4	2	no	—
369	SD₁₆×C₁₉	—	2	4	no	—
370	SD₁₆×C₁₉	—	2	4	no	—
371	SD₁₆×C₁₉	—	2	2	no	—
372	SD₁₆×C₁₉	—	4	2	no	—
373	SD₁₆×C₁₉	—	4	2	no	—
374	SD₁₆×C₁₉	—	4	1	no	—
375	SD₁₆×C₁₉	—	4	2	no	—
376	D₈×C₁₉	—	2	2	no	—
377	D₈×C₁₉	—	4	1	no	—
378	M₁₆×C₁₉	—	4	2	no	—
379	C₂×C₈×C₁₉	—	4	2	no	—
380	C₂×C₈×C₁₉	—	4	2	no	—
381	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
383	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
384	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
387	C₄⋊C₄×C₁₉	—	2	1	no	—
388	C₄⋊C₄×C₁₉	—	2	2	no	—
389	C₄⋊C₄×C₁₉	—	2	1	no	—
390	C₄⋊C₄×C₁₉	—	2	1	no	—
391	C₄⋊C₄×C₁₉	—	2	2	no	—
392	C₄⋊C₄×C₁₉	—	2	2	no	—
393	C₄⋊C₄×C₁₉	—	2	2	no	—
394	C₄⋊C₄×C₁₉	—	2	1	no	—
395	C₄⋊C₄×C₁₉	—	2	2	no	—
396	C₄⋊C₄×C₁₉	—	2	2	no	—
397	C₄⋊C₄×C₁₉	—	2	2	no	—
398	C₄⋊C₄×C₁₉	—	2	1	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	1	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	2	no	—
409	C₄⋊C₄×C₁₉	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
422	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
424	C₂²⋊C₄×C₁₉	—	2	2	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	1	no	—
431	C₂²⋊C₄×C₁₉	—	2	1	no	—
432	C₂²⋊C₄×C₁₉	—	2	1	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	2	no	—
437	C₂²⋊C₄×C₁₉	—	2	2	no	—
438	C₂²⋊C₄×C₁₉	—	2	1	no	—
439	C₂²⋊C₄×C₁₉	—	2	1	no	—
440	C₂²⋊C₄×C₁₉	—	2	1	no	—
441	C₂²⋊C₄×C₁₉	—	2	2	no	—
442	C₂²⋊C₄×C₁₉	—	2	1	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	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
448	C₄²×C₁₉	—	2	2	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	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
456	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
457	C₄²×C₁₉	C₂⁴	1	2	yes	—
458	#62054	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
459	C₂³×C₁₉	—	2	1	no	—
460	C₂³×C₁₉	—	2	1	no	—
461	C₂³×C₁₉	—	2	1	no	—
462	C₂³×C₁₉	—	4	2	no	—
463	C₂³×C₁₉	—	4	2	no	—
464	C₂³×C₁₉	—	8	1	no	—
465	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
466	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
467	Q₈×C₁₉	—	2	2	no	—
468	Q₈×C₁₉	—	2	2	no	—
469	Q₈×C₁₉	—	2	2	no	—
470	Q₈×C₁₉	—	2	1	no	—
471	Q₈×C₁₉	—	2	2	no	—
472	Q₈×C₁₉	—	2	1	no	—
473	Q₈×C₁₉	—	2	2	no	—
474	Q₈×C₁₉	—	2	2	no	—
475	Q₈×C₁₉	—	2	2	no	—
476	Q₈×C₁₉	—	4	2	no	—
477	Q₈×C₁₉	—	8	2	no	—
478	Q₈×C₁₉	—	8	2	no	—
479	Q₈×C₁₉	—	8	2	no	—
480	D₄×C₁₉	—	2	4	no	—
481	D₄×C₁₉	—	2	2	no	—
482	D₄×C₁₉	—	2	1	no	—
483	D₄×C₁₉	—	2	1	no	—
484	D₄×C₁₉	—	2	1	no	—
485	D₄×C₁₉	—	2	1	no	—
486	D₄×C₁₉	—	2	1	no	—
487	D₄×C₁₉	—	4	2	no	—
488	D₄×C₁₉	—	4	4	no	—
489	D₄×C₁₉	—	4	2	no	—
490	D₄×C₁₉	—	8	2	no	—
491	D₄×C₁₉	—	8	2	no	—
492	D₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
493	C₂×C₄×C₁₉	—	2	2	no	—
494	C₂×C₄×C₁₉	—	2	2	no	—
495	C₂×C₄×C₁₉	—	2	1	no	—
496	C₂×C₄×C₁₉	—	2	2	no	—
497	C₂×C₄×C₁₉	—	2	1	no	—
498	C₂×C₄×C₁₉	—	2	2	no	—
499	C₂×C₄×C₁₉	—	2	1	no	—
500	C₂×C₄×C₁₉	—	2	1	no	—
501	C₂×C₄×C₁₉	—	2	2	no	—
502	C₂×C₄×C₁₉	—	2	1	no	—
503	C₂×C₄×C₁₉	—	2	1	no	—
504	C₂×C₄×C₁₉	—	2	2	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	—	4	4	no	—
509	C₂×C₄×C₁₉	—	4	2	no	—
510	C₂×C₄×C₁₉	—	4	2	no	—
511	C₂×C₄×C₁₉	—	4	2	no	—
512	C₂×C₄×C₁₉	—	8	1	no	—
513	C₂×C₄×C₁₉	—	8	1	no	—
514	C₂×C₄×C₁₉	—	8	2	no	—
515	C₂×C₄×C₁₉	—	8	2	no	—
516	C₂×C₄×C₁₉	—	8	1	no	—
517	C₂×C₄×C₁₉	—	8	2	no	—
518	C₂×C₄×C₁₉	—	8	2	no	—
519	C₂×C₄×C₁₉	—	8	2	no	—
520	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
529	C₈×C₁₉	—	2	1	no	—
530	C₈×C₁₉	—	2	2	no	—
531	C₈×C₁₉	—	2	2	no	—
532	C₈×C₁₉	—	2	1	no	—
533	C₈×C₁₉	—	2	1	no	—
534	C₈×C₁₉	—	2	1	no	—
535	#3552	C₂×C₁₉	1	1	yes	characteristic, complemented
536	#3520	C₂×C₁₉	1	1	yes	characteristic, complemented
537	#3398	C₂×C₁₉	1	1	yes	characteristic, complemented
538	#3393	C₂×C₁₉	1	1	yes	characteristic, complemented
539	#3367	C₂×C₁₉	1	1	yes	characteristic, complemented
540	#3359	C₂×C₁₉	1	1	yes	characteristic, complemented
541	#3330	C₂×C₁₉	1	1	yes	characteristic, complemented
542	#3316	C₂×C₁₉	1	2	yes	complemented
543	#3299	C₂×C₁₉	1	2	yes	complemented
544	#3298	C₂×C₁₉	1	1	yes	characteristic, complemented
545	#3283	C₂×C₁₉	1	1	yes	characteristic, complemented
546	#3282	C₂×C₁₉	1	2	yes	complemented
547	#3276	C₂×C₁₉	1	1	yes	characteristic, complemented
548	#3266	C₂×C₁₉	1	2	yes	complemented
549	#3258	C₂×C₁₉	1	2	yes	complemented
550	#3248	C₂×C₁₉	1	1	yes	characteristic, complemented
551	#3225	C₂×C₁₉	1	2	yes	complemented
552	#3209	C₂×C₁₉	1	1	yes	characteristic, complemented
553	#3120	C₂×C₁₉	1	2	yes	complemented
554	#3105	C₂×C₁₉	1	1	yes	characteristic, complemented
555	#3046	C₂×C₁₉	1	2	yes	complemented
556	C₂×#461	C₂×C₁₉	1	1	yes	characteristic, complemented
557	#2994	C₂×C₁₉	1	1	yes	characteristic, complemented
558	C₂²×C₁₉	—	2	1	no	—
559	C₂²×C₁₉	—	2	1	no	—
560	C₂²×C₁₉	—	2	2	no	—
561	C₂²×C₁₉	—	2	2	no	—
562	C₂²×C₁₉	—	2	2	no	—
563	C₂²×C₁₉	—	2	2	no	—
564	C₂²×C₁₉	—	4	1	no	—
565	C₂²×C₁₉	—	4	1	no	—
566	C₂²×C₁₉	—	4	1	no	—
567	C₂²×C₁₉	—	4	1	no	—
568	C₂²×C₁₉	—	4	1	no	—
569	C₂²×C₁₉	—	4	1	no	—
570	C₂²×C₁₉	—	4	1	no	—
571	C₂²×C₁₉	—	4	1	no	—
572	C₂²×C₁₉	—	8	4	no	—
573	C₂²×C₁₉	#578	1	2	yes	—
574	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
575	C₄×C₁₉	—	2	2	no	—
576	C₄×C₁₉	—	2	1	no	—
577	C₄×C₁₉	—	2	1	no	—
578	C₄×C₁₉	—	2	2	no	—
579	C₄×C₁₉	—	2	1	no	—
580	C₄×C₁₉	—	2	1	no	—
581	C₄×C₁₉	—	2	2	no	—
582	C₄×C₁₉	—	4	2	no	—
583	C₄×C₁₉	—	4	2	no	—
584	C₄×C₁₉	—	4	2	no	—
585	C₄×C₁₉	—	4	1	no	—
586	C₄×C₁₉	—	4	1	no	—
587	C₄×C₁₉	—	4	1	no	—
588	C₄×C₁₉	—	4	1	no	—
589	C₄×C₁₉	—	4	2	no	—
590	C₄×C₁₉	—	4	1	no	—
591	C₄×C₁₉	#577	1	2	yes	—
592	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
593	C₄×C₁₉	#585	1	1	yes	characteristic
594	C₂×#137	C₂²×C₁₉	1	2	yes	—
595	C₂×#135	C₂²×C₁₉	1	2	yes	—
596	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
597	#563	—	2	2	no	—
598	#557	C₂²×C₁₉	1	1	yes	characteristic, complemented
599	#556	C₂²×C₁₉	1	1	yes	characteristic
600	#556	C₂²×C₁₉	1	1	yes	characteristic, complemented
601	#554	—	2	1	no	—
602	#554	C₂²×C₁₉	1	2	yes	—
603	#553	—	2	1	no	—
604	#552	—	2	1	no	—
605	#551	—	2	2	no	—
606	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
607	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
608	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
609	#548	—	2	1	no	—
610	#548	C₂²×C₁₉	1	2	yes	—
611	#547	C₂²×C₁₉	1	1	yes	characteristic
612	#547	C₂²×C₁₉	1	1	yes	characteristic
613	#547	C₂²×C₁₉	1	1	yes	characteristic, complemented
614	#546	C₂²×C₁₉	1	2	yes	—
615	#544	—	2	1	no	—
616	#542	—	2	1	no	—
617	#542	C₂²×C₁₉	1	2	yes	—
618	#541	C₂²×C₁₉	1	2	yes	complemented
619	#539	—	2	2	no	—
620	#539	—	2	2	no	—
621	#536	C₂²×C₁₉	1	2	yes	complemented
622	#533	C₂²×C₁₉	1	1	yes	characteristic
623	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
624	#529	C₂²×C₁₉	1	1	yes	characteristic
625	#529	C₂²×C₁₉	1	1	yes	characteristic
626	#525	—	2	1	no	—
627	C₂×C₂²⋊Q₈	—	2	1	no	—
628	#520	C₂²×C₁₉	1	2	yes	—
629	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
630	#497	C₂²×C₁₉	1	2	yes	—
631	#495	C₂²×C₁₉	1	2	yes	—
632	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
633	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
634	#489	C₂²×C₁₉	1	2	yes	complemented
635	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
636	#487	C₂²×C₁₉	1	2	yes	complemented
637	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
638	#484	C₂²×C₁₉	1	1	yes	characteristic
639	#484	C₂²×C₁₉	1	2	yes	complemented
640	#483	C₂²×C₁₉	1	2	yes	complemented
641	#481	C₂²×C₁₉	1	1	yes	characteristic
642	#479	C₂²×C₁₉	1	2	yes	complemented
643	#478	C₂²×C₁₉	1	1	yes	characteristic
644	#478	C₂²×C₁₉	1	1	yes	characteristic
645	#477	C₂²×C₁₉	1	2	yes	complemented
646	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
647	#475	C₂²×C₁₉	1	2	yes	complemented
648	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
649	#470	C₂²×C₁₉	1	2	yes	complemented
650	#468	C₂²×C₁₉	1	2	yes	—
651	#467	C₂²×C₁₉	1	2	yes	—
652	#467	C₂²×C₁₉	1	2	yes	complemented
653	#465	C₂²×C₁₉	1	2	yes	—
654	#465	C₂²×C₁₉	1	2	yes	—
655	#464	C₂²×C₁₉	1	2	yes	—
656	#464	C₂²×C₁₉	1	2	yes	—
657	#464	C₂²×C₁₉	1	2	yes	complemented
658	#464	C₂²×C₁₉	1	2	yes	complemented
659	#463	C₂²×C₁₉	1	1	yes	characteristic
660	#463	C₂²×C₁₉	1	1	yes	characteristic
661	#463	C₂²×C₁₉	1	2	yes	—
662	#462	C₂²×C₁₉	1	2	yes	complemented
663	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
664	#462	C₂²×C₁₉	1	2	yes	complemented
665	#462	C₂²×C₁₉	1	2	yes	complemented
666	#461	C₂²×C₁₉	1	1	yes	characteristic
667	#461	C₂²×C₁₉	1	2	yes	—
668	#461	C₂²×C₁₉	1	1	yes	characteristic
669	#461	C₂²×C₁₉	1	1	yes	characteristic
670	#461	C₂²×C₁₉	1	2	yes	—
671	#461	C₂²×C₁₉	1	1	yes	characteristic
672	#461	C₂²×C₁₉	1	2	yes	—
673	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
674	#452	C₂²×C₁₉	1	2	yes	—
675	#452	C₂²×C₁₉	1	2	yes	—
676	#452	C₂²×C₁₉	1	2	yes	complemented
677	#451	C₂²×C₁₉	1	2	yes	—
678	#451	C₂²×C₁₉	1	2	yes	—
679	#451	C₂²×C₁₉	1	2	yes	complemented
680	#450	C₂²×C₁₉	1	1	yes	characteristic
681	#449	C₂²×C₁₉	1	2	yes	—
682	#448	C₂²×C₁₉	1	2	yes	—
683	#447	C₂²×C₁₉	1	1	yes	characteristic
684	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
685	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
686	#441	C₂²×C₁₉	1	2	yes	complemented
687	#440	C₂²×C₁₉	1	2	yes	—
688	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
689	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
690	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
691	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
692	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
693	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
694	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
695	#435	C₂²×C₁₉	1	2	yes	—
696	C₈×D₄	C₂²×C₁₉	1	2	yes	—
697	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
698	#433	C₂²×C₁₉	1	2	yes	complemented
699	#431	C₂²×C₁₉	1	1	yes	characteristic
700	#424	C₂²×C₁₉	1	2	yes	complemented
701	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
702	#417	C₂²×C₁₉	1	2	yes	complemented
703	C₂×#103	C₂²×C₁₉	1	2	yes	—
704	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
705	C₂×C₁₉	—	2	2	no	—
706	C₂×C₁₉	—	4	2	no	—
707	C₂×C₁₉	—	4	2	no	—
708	C₂×C₁₉	—	8	1	no	—
709	C₂×C₁₉	—	8	1	no	—
710	C₂×C₁₉	#3488	1	1	yes	characteristic
711	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
712	C₂×C₁₉	C₂×#578	1	1	yes	characteristic
713	C₂×#41	—	2	1	no	—
714	C₂×#41	C₂³×C₁₉	1	2	yes	—
715	C₂×#41	C₂³×C₁₉	1	2	yes	—
716	C₂²×Q₈	—	2	1	no	—
717	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
718	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
719	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
720	C₂³×C₄	—	2	1	no	—
721	#137	—	4	4	no	—
722	#135	—	4	4	no	—
723	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
724	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
725	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
726	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
727	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
728	C₂×SD₁₆	—	4	4	no	—
729	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
730	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
732	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
736	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
737	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
738	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
739	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
740	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
741	C₄⋊Q₈	—	2	2	no	—
742	C₄⋊Q₈	—	2	1	no	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	—	2	1	no	—
745	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
746	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
750	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	1	no	—
758	#126	D₄×C₁₉	1	2	yes	—
759	#125	—	2	2	no	—
760	#125	—	2	2	no	—
761	#125	—	2	2	no	—
762	#125	—	2	2	no	—
763	#125	—	2	1	no	—
764	#125	—	2	1	no	—
765	#125	D₄×C₁₉	1	1	yes	characteristic
766	#125	C₂³×C₁₉	1	1	yes	characteristic
767	#124	—	2	2	no	—
768	#124	—	2	2	no	—
769	#124	D₄×C₁₉	1	1	yes	characteristic
770	#124	C₂³×C₁₉	1	1	yes	characteristic
771	#124	C₂³×C₁₉	1	2	yes	—
772	#124	C₂³×C₁₉	1	2	yes	—
773	#123	—	2	1	no	—
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	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	D₄×C₁₉	1	2	yes	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
798	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
799	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
800	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
801	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
802	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
803	#121	—	2	1	no	—
804	#121	—	2	2	no	—
805	#121	—	2	1	no	—
806	#121	—	2	2	no	—
807	#121	D₄×C₁₉	1	1	yes	characteristic
808	#121	C₂³×C₁₉	1	1	yes	characteristic
809	#121	C₂³×C₁₉	1	2	yes	—
810	#120	—	2	2	no	—
811	C₄×Q₈	—	2	1	no	—
812	C₄×Q₈	—	2	1	no	—
813	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
814	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
815	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
816	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
817	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
818	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₁₉	1	2	yes	—
833	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₁₉	1	2	yes	—
835	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
836	#117	—	2	1	no	—
837	#117	—	2	2	no	—
838	#117	—	2	1	no	—
839	#117	—	2	1	no	—
840	#117	—	2	1	no	—
841	#117	C₂³×C₁₉	1	2	yes	—
842	C₂×C₄⋊C₄	—	2	1	no	—
843	C₂×C₄⋊C₄	—	2	1	no	—
844	C₂×C₄⋊C₄	—	2	2	no	—
845	C₂×C₄⋊C₄	—	2	1	no	—
846	C₂×C₄⋊C₄	—	2	1	no	—
847	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
848	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
849	C₂×C₂²⋊C₄	—	2	1	no	—
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
852	#107	C₂³×C₁₉	1	1	yes	characteristic
853	#107	C₂³×C₁₉	1	1	yes	characteristic
854	#107	C₂³×C₁₉	1	2	yes	—
855	#106	C₂³×C₁₉	1	1	yes	characteristic
856	#106	C₂³×C₁₉	1	2	yes	—
857	#106	C₂³×C₁₉	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
859	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
863	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
864	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
865	#103	C₂³×C₁₉	1	2	yes	—
866	#103	C₂³×C₁₉	1	2	yes	—
867	#103	C₂³×C₁₉	1	2	yes	—
868	#103	C₂³×C₁₉	1	2	yes	—
869	#103	C₂³×C₁₉	1	1	yes	characteristic
870	#103	C₂³×C₁₉	1	2	yes	—
871	#103	C₂³×C₁₉	1	2	yes	—
872	#103	C₂³×C₁₉	1	2	yes	—
873	#103	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	#102	C₂³×C₁₉	1	1	yes	characteristic
879	#102	C₂³×C₁₉	1	2	yes	—
880	#102	C₂³×C₁₉	1	1	yes	characteristic
881	#102	C₂³×C₁₉	1	1	yes	characteristic
882	#102	C₂³×C₁₉	1	1	yes	characteristic
883	#102	C₂³×C₁₉	1	1	yes	characteristic
884	#102	C₂³×C₁₉	1	1	yes	characteristic
885	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
886	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
887	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
889	#97	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	2	yes	—
893	C₁₉	#62054	1	1	yes	characteristic, direct product factor, Sylow
894	C₂⁴	—	2	1	no	—
895	#41	—	2	4	no	—
896	#41	—	4	2	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	8	2	no	—
900	C₂×Q₈	—	2	1	no	—
901	C₂×Q₈	—	2	2	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	4	2	no	—
905	C₂×Q₈	—	4	2	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	—	8	2	no	—
909	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
910	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
911	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
913	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	4	1	no	—
921	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
922	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
923	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
924	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
925	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	8	2	no	—
939	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
940	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
943	Q₁₆	—	4	2	no	—
944	Q₁₆	—	4	2	no	—
945	Q₁₆	—	4	2	no	—
946	Q₁₆	—	4	2	no	—
947	Q₁₆	—	4	2	no	—
948	SD₁₆	—	2	4	no	—
949	SD₁₆	—	2	4	no	—
950	SD₁₆	—	2	2	no	—
951	SD₁₆	—	4	2	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	1	no	—
954	SD₁₆	—	4	2	no	—
955	D₈	—	2	2	no	—
956	D₈	—	4	1	no	—
957	M₁₆	—	4	2	no	—
958	C₂×C₈	—	4	2	no	—
959	C₂×C₈	—	4	2	no	—
960	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
965	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	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	C₂×D₄×C₁₉	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
995	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
996	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
997	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1033	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1034	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1035	C₄²	C₂⁴×C₁₉	1	2	yes	—
1036	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	4	2	no	—
1041	C₂³	—	4	2	no	—
1042	C₂³	—	8	1	no	—
1043	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1044	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	4	2	no	—
1055	Q₈	—	8	2	no	—
1056	Q₈	—	8	2	no	—
1057	Q₈	—	8	2	no	—
1058	D₄	—	2	4	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	4	4	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	8	1	no	—
1091	C₂×C₄	—	8	1	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	1	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1099	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1100	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1101	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1104	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1106	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1107	C₈	—	2	1	no	—
1108	C₈	—	2	2	no	—
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	1	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	8	4	no	—
1128	C₂²	C₁₉×#578	1	2	yes	—
1129	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1130	C₄	—	2	2	no	—
1131	C₄	—	2	1	no	—
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	2	no	—
1139	C₄	—	4	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	2	no	—
1145	C₄	—	4	1	no	—
1146	C₄	C₁₉×#577	1	2	yes	—
1147	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1148	C₄	C₁₉×#585	1	1	yes	characteristic
1149	C₂	—	2	2	no	—
1150	C₂	—	4	2	no	—
1151	C₂	—	4	2	no	—
1152	C₂	—	8	1	no	—
1153	C₂	—	8	1	no	—
1154	C₂	C₁₉×#3488	1	1	yes	characteristic
1155	C₂	C₂×C₁₉×#577	1	1	yes	characteristic
1156	C₂	C₂×C₁₉×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3552	C₂	semidirect
2. C₁₉×#3520	C₂	semidirect
3. C₁₉×#3398	C₂	semidirect
4. C₁₉×#3393	C₂	semidirect
5. C₁₉×#3367	C₂	semidirect
6. C₁₉×#3359	C₂	semidirect
7. C₁₉×#3330	C₂	semidirect
8. C₁₉×#3316	C₂	semidirect
9. C₁₉×#3299	C₂	semidirect
10. C₁₉×#3298	C₂	semidirect
11. C₁₉×#3283	C₂	semidirect
12. C₁₉×#3282	C₂	semidirect
13. C₁₉×#3276	C₂	semidirect
14. C₁₉×#3266	C₂	semidirect
15. C₁₉×#3258	C₂	semidirect
16. C₁₉×#3248	C₂	semidirect
17. C₁₉×#3225	C₂	semidirect
18. C₁₉×#3209	C₂	semidirect
19. C₁₉×#3120	C₂	semidirect
20. C₁₉×#3105	C₂	semidirect
21. C₁₉×#3046	C₂	semidirect
22. C₂×C₁₉×#461	C₂	semidirect
23. C₁₉×#2994	C₂	semidirect
28. C₁₉×#557	C₂²	semidirect
30. C₁₉×#556	C₂²	semidirect
38. D₄×Q₈×C₁₉	C₂²	semidirect
43. C₁₉×#547	C₂²	semidirect
48. C₁₉×#541	C₂²	semidirect
51. C₁₉×#536	C₂²	semidirect
62. C₁₉×#494	C₂²	semidirect
63. C₁₉×#494	C₂²	semidirect
64. C₁₉×#489	C₂²	semidirect
65. C₁₉×#487	C₂²	semidirect
66. C₁₉×#487	C₂²	semidirect
67. C₁₉×#487	C₂²	semidirect
69. C₁₉×#484	C₂²	semidirect
70. C₁₉×#483	C₂²	semidirect
72. C₁₉×#479	C₂²	semidirect
75. C₁₉×#477	C₂²	semidirect
76. C₁₉×#475	C₂²	semidirect
77. C₁₉×#475	C₂²	semidirect
78. C₁₉×#474	C₂²	semidirect
79. C₁₉×#470	C₂²	semidirect
82. C₁₉×#467	C₂²	semidirect
87. C₁₉×#464	C₂²	semidirect
88. C₁₉×#464	C₂²	semidirect
92. C₁₉×#462	C₂²	semidirect
93. C₁₉×#462	C₂²	semidirect
94. C₁₉×#462	C₂²	semidirect
95. C₁₉×#462	C₂²	semidirect
103. C₁₉×#461	C₂²	semidirect
106. C₁₉×#452	C₂²	semidirect
109. C₁₉×#451	C₂²	semidirect
114. C₁₉×#446	C₂²	semidirect
115. C₈×Q₈×C₁₉	C₂²	semidirect
116. C₁₉×#441	C₂²	semidirect
118. C₄×Q₁₆×C₁₉	C₂²	semidirect
124. C₁₉×#436	C₂²	semidirect
127. C₈×D₄×C₁₉	C₂²	semidirect
128. C₁₉×#433	C₂²	semidirect
130. C₁₉×#424	C₂²	semidirect
132. C₁₉×#417	C₂²	semidirect
134. C₂×C₁₉×#103	C₂²	semidirect
458. #62054	C₁₉	direct (N × H)
535. #3552	C₂×C₁₉	semidirect
536. #3520	C₂×C₁₉	semidirect
537. #3398	C₂×C₁₉	semidirect
538. #3393	C₂×C₁₉	semidirect
539. #3367	C₂×C₁₉	semidirect
540. #3359	C₂×C₁₉	semidirect
541. #3330	C₂×C₁₉	semidirect
542. #3316	C₂×C₁₉	semidirect
543. #3299	C₂×C₁₉	semidirect
544. #3298	C₂×C₁₉	semidirect
545. #3283	C₂×C₁₉	semidirect
546. #3282	C₂×C₁₉	semidirect
547. #3276	C₂×C₁₉	semidirect
548. #3266	C₂×C₁₉	semidirect
549. #3258	C₂×C₁₉	semidirect
550. #3248	C₂×C₁₉	semidirect
551. #3225	C₂×C₁₉	semidirect
552. #3209	C₂×C₁₉	semidirect
553. #3120	C₂×C₁₉	semidirect
554. #3105	C₂×C₁₉	semidirect
555. #3046	C₂×C₁₉	semidirect
556. C₂×#461	C₂×C₁₉	semidirect
557. #2994	C₂×C₁₉	semidirect
598. #557	C₂²×C₁₉	semidirect
600. #556	C₂²×C₁₉	semidirect
608. D₄×Q₈	C₂²×C₁₉	semidirect
613. #547	C₂²×C₁₉	semidirect
618. #541	C₂²×C₁₉	semidirect
621. #536	C₂²×C₁₉	semidirect
632. #494	C₂²×C₁₉	semidirect
633. #494	C₂²×C₁₉	semidirect
634. #489	C₂²×C₁₉	semidirect
635. #487	C₂²×C₁₉	semidirect
636. #487	C₂²×C₁₉	semidirect
637. #487	C₂²×C₁₉	semidirect
639. #484	C₂²×C₁₉	semidirect
640. #483	C₂²×C₁₉	semidirect
642. #479	C₂²×C₁₉	semidirect
645. #477	C₂²×C₁₉	semidirect
646. #475	C₂²×C₁₉	semidirect
647. #475	C₂²×C₁₉	semidirect
648. #474	C₂²×C₁₉	semidirect
649. #470	C₂²×C₁₉	semidirect
652. #467	C₂²×C₁₉	semidirect
657. #464	C₂²×C₁₉	semidirect
658. #464	C₂²×C₁₉	semidirect
662. #462	C₂²×C₁₉	semidirect
663. #462	C₂²×C₁₉	semidirect
664. #462	C₂²×C₁₉	semidirect
665. #462	C₂²×C₁₉	semidirect
673. #461	C₂²×C₁₉	semidirect
676. #452	C₂²×C₁₉	semidirect
679. #451	C₂²×C₁₉	semidirect
684. #446	C₂²×C₁₉	semidirect
685. C₈×Q₈	C₂²×C₁₉	semidirect
686. #441	C₂²×C₁₉	semidirect
688. C₄×Q₁₆	C₂²×C₁₉	semidirect
694. #436	C₂²×C₁₉	semidirect
697. C₈×D₄	C₂²×C₁₉	semidirect
698. #433	C₂²×C₁₉	semidirect
700. #424	C₂²×C₁₉	semidirect
702. #417	C₂²×C₁₉	semidirect
704. C₂×#103	C₂²×C₁₉	semidirect
893. C₁₉	#62054	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×#3552	2
C₁₉×#3520	2
C₁₉×#3398	2
C₁₉×#3393	2
C₁₉×#3367	2
C₁₉×#3359	2
C₁₉×#3330	2
C₁₉×#3316	2
C₁₉×#3299	2
C₁₉×#3298	2
C₁₉×#3283	2
C₁₉×#3282	2
C₁₉×#3276	2
C₁₉×#3266	2
C₁₉×#3258	2
C₁₉×#3248	2
C₁₉×#3225	2
C₁₉×#3209	2
C₁₉×#3120	2
C₁₉×#3105	2
C₁₉×#3046	2
C₂×C₁₉×#461	2
C₁₉×#2994	2
#62054	19

Subgroups — C19×#62054 #18068013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62054 #18068013