Subgroups — C₁₉×#62300 #18068259

Order 4864.

1838 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3520	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3344	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3335	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3331	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3328	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3316	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3312	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3299	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3298	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3270	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3255	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×#3195	C₂	1	2	yes	maximal, complemented
19	C₁₉×#3185	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×#470	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×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
26	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
27	C₁₉×#556	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	—	2	1	no	—
32	C₁₉×#554	C₂²	1	1	yes	characteristic
33	C₁₉×#554	C₂²	1	2	yes	—
34	C₁₉×#554	C₂²	1	1	yes	characteristic
35	C₁₉×#552	C₂²	1	2	yes	—
36	C₁₉×#551	—	2	2	no	—
37	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
38	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#548	C₂²	1	2	yes	—
42	C₁₉×#547	C₂²	1	1	yes	characteristic
43	C₁₉×#547	C₂²	1	1	yes	characteristic
44	C₁₉×#546	—	2	1	no	—
45	C₁₉×#544	—	2	1	no	—
46	C₁₉×#543	—	2	2	no	—
47	C₁₉×#542	—	2	1	no	—
48	C₁₉×#539	—	2	2	no	—
49	C₁₉×#533	C₂²	1	1	yes	characteristic
50	C₁₉×#533	C₂²	1	1	yes	characteristic
51	C₁₉×#533	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	—
55	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
56	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
57	C₁₉×#520	—	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×#498	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#497	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#494	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×#487	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×#483	C₂²	1	2	yes	complemented
72	C₁₉×#483	C₂²	1	2	yes	complemented
73	C₁₉×#483	C₂²	1	2	yes	complemented
74	C₁₉×#483	C₂²	1	2	yes	complemented
75	C₁₉×#481	C₂²	1	2	yes	complemented
76	C₁₉×#479	C₂²	1	2	yes	complemented
77	C₁₉×#477	C₂²	1	1	yes	characteristic, complemented
78	C₁₉×#476	C₂²	1	1	yes	characteristic, complemented
79	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
80	C₁₉×#475	C₂²	1	2	yes	complemented
81	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
82	C₁₉×#470	C₂²	1	1	yes	characteristic
83	C₁₉×#470	C₂²	1	1	yes	characteristic
84	C₁₉×#470	C₂²	1	2	yes	—
85	C₁₉×#470	C₂²	1	2	yes	—
86	C₁₉×#470	C₂²	1	2	yes	—
87	C₁₉×#470	C₂²	1	2	yes	—
88	C₁₉×#470	C₂²	1	2	yes	—
89	C₁₉×#470	C₂²	1	2	yes	complemented
90	C₁₉×#470	C₂²	1	2	yes	complemented
91	C₁₉×#470	C₂²	1	2	yes	complemented
92	C₁₉×#470	C₂²	1	2	yes	complemented
93	C₁₉×#468	C₂²	1	1	yes	characteristic
94	C₁₉×#468	C₂²	1	1	yes	characteristic
95	C₁₉×#468	C₂²	1	2	yes	—
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×#462	C₂²	1	2	yes	complemented
103	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
104	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
105	C₁₉×#461	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×#451	C₂²	1	2	yes	complemented
110	C₁₉×#451	C₂²	1	2	yes	complemented
111	C₁₉×#451	C₂²	1	2	yes	complemented
112	C₁₉×#451	C₂²	1	2	yes	complemented
113	C₁₉×#448	C₂²	1	2	yes	complemented
114	C₁₉×#441	C₂²	1	2	yes	complemented
115	C₁₉×#441	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
121	C₁₉×#436	C₂²	1	1	yes	characteristic
122	C₁₉×#435	C₂²	1	2	yes	—
123	C₁₉×#435	C₂²	1	2	yes	—
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×#106	C₂²	1	2	yes	complemented
128	C₁₉×#423	C₂²	1	1	yes	characteristic
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×#103	C₂²	1	2	yes	complemented
133	C₁₉×#407	C₂²	1	2	yes	—
134	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
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×Q₈×C₁₉	C₂³	1	2	yes	—
140	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
141	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
142	C₁₉×#137	—	4	4	no	—
143	C₂×Q₁₆×C₁₉	—	4	4	no	—
144	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
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×Q₁₆×C₁₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
154	C₂×M₁₆×C₁₉	—	4	4	no	—
155	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
157	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
158	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
159	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
160	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
161	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
162	C₁₉×C₄⋊Q₈	—	2	1	no	—
163	C₁₉×C₄⋊Q₈	—	2	1	no	—
164	C₁₉×C₄⋊Q₈	—	2	2	no	—
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×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×#126	—	2	2	no	—
173	C₁₉×#126	—	2	2	no	—
174	C₁₉×#126	—	2	1	no	—
175	C₁₉×#125	—	2	2	no	—
176	C₁₉×#125	—	2	1	no	—
177	C₁₉×#125	—	2	2	no	—
178	C₁₉×#125	—	2	1	no	—
179	C₁₉×#125	—	2	1	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	1	no	—
184	C₁₉×#124	—	2	2	no	—
185	C₁₉×#124	C₂³	1	1	yes	characteristic
186	C₁₉×#123	—	2	2	no	—
187	C₁₉×#123	—	2	2	no	—
188	C₁₉×#123	—	2	1	no	—
189	C₁₉×#123	—	2	2	no	—
190	C₁₉×#123	—	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	2	no	—
195	C₁₉×C₂²⋊Q₈	—	2	2	no	—
196	C₁₉×C₂²⋊Q₈	—	2	2	no	—
197	C₁₉×C₂²⋊Q₈	—	2	1	no	—
198	C₁₉×C₂²⋊Q₈	—	2	1	no	—
199	C₁₉×C₂²⋊Q₈	—	2	1	no	—
200	C₁₉×C₂²⋊Q₈	—	2	2	no	—
201	C₁₉×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
206	C₁₉×C₂²⋊Q₈	—	2	2	no	—
207	C₁₉×C₂²⋊Q₈	—	2	2	no	—
208	C₁₉×C₂²⋊Q₈	—	2	2	no	—
209	C₁₉×C₂²⋊Q₈	—	2	2	no	—
210	C₁₉×C₂²⋊Q₈	—	2	2	no	—
211	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
220	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₁₉×#121	—	2	2	no	—
224	C₁₉×#121	—	2	1	no	—
225	C₁₉×#121	C₂³	1	2	yes	—
226	C₁₉×#121	C₂³	1	1	yes	characteristic
227	C₁₉×#120	—	2	2	no	—
228	C₄×Q₈×C₁₉	—	2	1	no	—
229	C₄×Q₈×C₁₉	—	2	1	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×Q₈×C₁₉	C₂³	1	2	yes	—
237	C₄×D₄×C₁₉	—	2	2	no	—
238	C₄×D₄×C₁₉	—	2	1	no	—
239	C₄×D₄×C₁₉	—	2	1	no	—
240	C₄×D₄×C₁₉	—	2	2	no	—
241	C₄×D₄×C₁₉	—	2	1	no	—
242	C₄×D₄×C₁₉	—	2	1	no	—
243	C₄×D₄×C₁₉	—	2	1	no	—
244	C₄×D₄×C₁₉	—	2	2	no	—
245	C₄×D₄×C₁₉	—	2	2	no	—
246	C₄×D₄×C₁₉	—	2	1	no	—
247	C₄×D₄×C₁₉	—	2	2	no	—
248	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
249	C₄×D₄×C₁₉	D₄	1	2	yes	—
250	C₄×D₄×C₁₉	D₄	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	C₁₉×#117	—	2	1	no	—
256	C₁₉×#117	—	2	1	no	—
257	C₁₉×#117	—	2	1	no	—
258	C₁₉×#117	—	2	2	no	—
259	C₁₉×#117	—	2	1	no	—
260	C₁₉×#117	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
262	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
263	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
264	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
265	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
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	1	yes	characteristic
277	C₁₉×#106	C₂³	1	1	yes	characteristic
278	C₁₉×#106	C₂³	1	2	yes	—
279	C₁₉×#106	C₂³	1	2	yes	—
280	C₁₉×#106	C₂³	1	2	yes	—
281	C₁₉×#106	C₂³	1	2	yes	—
282	C₁₉×#106	C₂³	1	1	yes	characteristic
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	2	yes	—
287	C₁₉×#103	C₂³	1	1	yes	characteristic
288	C₁₉×#103	C₂³	1	1	yes	characteristic
289	C₁₉×#103	C₂³	1	2	yes	—
290	C₁₉×#103	C₂³	1	2	yes	—
291	C₁₉×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
300	C₁₉×#103	C₂³	1	1	yes	characteristic
301	C₁₉×#103	C₂³	1	1	yes	characteristic
302	C₁₉×#103	C₂³	1	2	yes	—
303	C₁₉×#103	C₂³	1	2	yes	—
304	C₁₉×#102	C₂³	1	1	yes	characteristic
305	C₁₉×#102	C₂³	1	2	yes	—
306	C₁₉×#102	C₂³	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
316	#41×C₁₉	—	4	2	no	—
317	#41×C₁₉	—	4	2	no	—
318	#41×C₁₉	—	4	4	no	—
319	C₂×Q₈×C₁₉	—	2	1	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	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	—	4	2	no	—
330	C₂×Q₈×C₁₉	—	4	2	no	—
331	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
335	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
336	C₂×D₄×C₁₉	—	2	4	no	—
337	C₂×D₄×C₁₉	—	2	1	no	—
338	C₂×D₄×C₁₉	—	2	2	no	—
339	C₂×D₄×C₁₉	—	2	2	no	—
340	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
342	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
343	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₁₉	—	2	2	no	—
345	C₂²×C₄×C₁₉	—	2	2	no	—
346	C₂²×C₄×C₁₉	—	2	2	no	—
347	C₂²×C₄×C₁₉	—	2	2	no	—
348	C₂²×C₄×C₁₉	—	2	2	no	—
349	C₂²×C₄×C₁₉	—	2	2	no	—
350	C₂²×C₄×C₁₉	—	2	1	no	—
351	C₂²×C₄×C₁₉	—	2	2	no	—
352	C₂²×C₄×C₁₉	—	4	2	no	—
353	C₂²×C₄×C₁₉	—	4	2	no	—
354	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
357	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
358	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
359	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
362	Q₁₆×C₁₉	—	2	2	no	—
363	Q₁₆×C₁₉	—	2	4	no	—
364	Q₁₆×C₁₉	—	4	2	no	—
365	Q₁₆×C₁₉	—	4	2	no	—
366	Q₁₆×C₁₉	—	4	1	no	—
367	Q₁₆×C₁₉	—	4	2	no	—
368	Q₁₆×C₁₉	—	4	2	no	—
369	SD₁₆×C₁₉	—	2	2	no	—
370	SD₁₆×C₁₉	—	4	1	no	—
371	SD₁₆×C₁₉	—	4	2	no	—
372	M₁₆×C₁₉	—	2	2	no	—
373	M₁₆×C₁₉	—	2	4	no	—
374	M₁₆×C₁₉	—	4	2	no	—
375	M₁₆×C₁₉	—	4	2	no	—
376	M₁₆×C₁₉	—	4	1	no	—
377	C₂×C₈×C₁₉	—	2	4	no	—
378	C₂×C₈×C₁₉	—	4	2	no	—
379	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
381	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
382	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
385	C₄⋊C₄×C₁₉	—	2	1	no	—
386	C₄⋊C₄×C₁₉	—	2	2	no	—
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	2	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	2	no	—
399	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
405	C₄⋊C₄×C₁₉	—	2	1	no	—
406	C₄⋊C₄×C₁₉	—	2	1	no	—
407	C₄⋊C₄×C₁₉	—	2	2	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	2	no	—
413	C₄⋊C₄×C₁₉	—	2	1	no	—
414	C₄⋊C₄×C₁₉	—	2	1	no	—
415	C₄⋊C₄×C₁₉	—	2	1	no	—
416	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₁₉	C₂×D₄	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	2	yes	—
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	C₂²⋊C₄×C₁₉	—	2	1	no	—
426	C₂²⋊C₄×C₁₉	—	2	2	no	—
427	C₂²⋊C₄×C₁₉	—	2	1	no	—
428	C₂²⋊C₄×C₁₉	—	2	1	no	—
429	C₂²⋊C₄×C₁₉	—	2	2	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	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	C₄²×C₁₉	—	2	2	no	—
448	C₄²×C₁₉	—	2	2	no	—
449	C₄²×C₁₉	—	2	1	no	—
450	C₄²×C₁₉	—	2	2	no	—
451	C₄²×C₁₉	—	2	1	no	—
452	C₄²×C₁₉	—	2	1	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	#62300	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
458	C₂³×C₁₉	—	2	4	no	—
459	C₂³×C₁₉	—	2	1	no	—
460	C₂³×C₁₉	—	4	2	no	—
461	C₂³×C₁₉	—	4	2	no	—
462	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
463	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
464	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
465	Q₈×C₁₉	—	2	1	no	—
466	Q₈×C₁₉	—	2	2	no	—
467	Q₈×C₁₉	—	2	1	no	—
468	Q₈×C₁₉	—	2	1	no	—
469	Q₈×C₁₉	—	2	2	no	—
470	Q₈×C₁₉	—	2	1	no	—
471	Q₈×C₁₉	—	2	1	no	—
472	Q₈×C₁₉	—	2	1	no	—
473	Q₈×C₁₉	—	2	2	no	—
474	Q₈×C₁₉	—	2	2	no	—
475	Q₈×C₁₉	—	4	2	no	—
476	Q₈×C₁₉	—	8	1	no	—
477	Q₈×C₁₉	—	8	1	no	—
478	Q₈×C₁₉	—	8	2	no	—
479	Q₈×C₁₉	—	8	2	no	—
480	Q₈×C₁₉	—	8	2	no	—
481	D₄×C₁₉	—	2	4	no	—
482	D₄×C₁₉	—	2	2	no	—
483	D₄×C₁₉	—	2	1	no	—
484	D₄×C₁₉	—	2	1	no	—
485	D₄×C₁₉	—	4	2	no	—
486	D₄×C₁₉	—	4	4	no	—
487	D₄×C₁₉	—	8	2	no	—
488	D₄×C₁₉	#137	1	4	yes	complemented
489	C₂×C₄×C₁₉	—	2	2	no	—
490	C₂×C₄×C₁₉	—	2	2	no	—
491	C₂×C₄×C₁₉	—	2	1	no	—
492	C₂×C₄×C₁₉	—	2	2	no	—
493	C₂×C₄×C₁₉	—	2	1	no	—
494	C₂×C₄×C₁₉	—	2	2	no	—
495	C₂×C₄×C₁₉	—	2	2	no	—
496	C₂×C₄×C₁₉	—	2	1	no	—
497	C₂×C₄×C₁₉	—	2	2	no	—
498	C₂×C₄×C₁₉	—	2	1	no	—
499	C₂×C₄×C₁₉	—	2	2	no	—
500	C₂×C₄×C₁₉	—	2	1	no	—
501	C₂×C₄×C₁₉	—	2	1	no	—
502	C₂×C₄×C₁₉	—	2	2	no	—
503	C₂×C₄×C₁₉	—	2	1	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	—	4	2	no	—
508	C₂×C₄×C₁₉	—	4	2	no	—
509	C₂×C₄×C₁₉	—	4	2	no	—
510	C₂×C₄×C₁₉	—	4	1	no	—
511	C₂×C₄×C₁₉	—	4	4	no	—
512	C₂×C₄×C₁₉	—	4	2	no	—
513	C₂×C₄×C₁₉	—	8	2	no	—
514	C₂×C₄×C₁₉	—	8	2	no	—
515	C₂×C₄×C₁₉	—	8	2	no	—
516	C₂×C₄×C₁₉	—	8	2	no	—
517	C₂×C₄×C₁₉	—	8	2	no	—
518	C₂×C₄×C₁₉	—	8	2	no	—
519	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
523	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
527	C₈×C₁₉	—	2	2	no	—
528	C₈×C₁₉	—	2	1	no	—
529	C₈×C₁₉	—	2	2	no	—
530	C₈×C₁₉	—	2	1	no	—
531	C₈×C₁₉	—	2	1	no	—
532	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
533	#3520	C₂×C₁₉	1	1	yes	characteristic
534	#3501	C₂×C₁₉	1	1	yes	characteristic, complemented
535	#3356	C₂×C₁₉	1	1	yes	characteristic, complemented
536	#3344	C₂×C₁₉	1	2	yes	complemented
537	#3335	C₂×C₁₉	1	1	yes	characteristic, complemented
538	#3331	C₂×C₁₉	1	1	yes	characteristic, complemented
539	#3328	C₂×C₁₉	1	1	yes	characteristic, complemented
540	#3316	C₂×C₁₉	1	2	yes	complemented
541	#3312	C₂×C₁₉	1	2	yes	complemented
542	#3299	C₂×C₁₉	1	1	yes	characteristic, complemented
543	#3298	C₂×C₁₉	1	1	yes	characteristic, complemented
544	D₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
545	#3276	C₂×C₁₉	1	1	yes	characteristic, complemented
546	#3270	C₂×C₁₉	1	2	yes	complemented
547	#3255	C₂×C₁₉	1	1	yes	characteristic, complemented
548	#3252	C₂×C₁₉	1	1	yes	characteristic, complemented
549	#3196	C₂×C₁₉	1	2	yes	complemented
550	#3195	C₂×C₁₉	1	2	yes	complemented
551	#3185	C₂×C₁₉	1	1	yes	characteristic, complemented
552	#3172	C₂×C₁₉	1	1	yes	characteristic, complemented
553	#3056	C₂×C₁₉	1	2	yes	complemented
554	C₂×#470	C₂×C₁₉	1	2	yes	complemented
555	D₄×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
556	C₂²×C₁₉	—	2	2	no	—
557	C₂²×C₁₉	—	2	2	no	—
558	C₂²×C₁₉	—	2	1	no	—
559	C₂²×C₁₉	—	2	2	no	—
560	C₂²×C₁₉	—	2	1	no	—
561	C₂²×C₁₉	—	2	2	no	—
562	C₂²×C₁₉	—	2	1	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	—	8	4	no	—
568	C₂²×C₁₉	C₂×#137	1	4	yes	—
569	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
570	C₄×C₁₉	—	2	1	no	—
571	C₄×C₁₉	—	2	1	no	—
572	C₄×C₁₉	—	2	1	no	—
573	C₄×C₁₉	—	2	2	no	—
574	C₄×C₁₉	—	2	2	no	—
575	C₄×C₁₉	—	2	1	no	—
576	C₄×C₁₉	—	4	1	no	—
577	C₄×C₁₉	—	4	2	no	—
578	C₄×C₁₉	—	4	1	no	—
579	C₄×C₁₉	—	4	1	no	—
580	C₄×C₁₉	—	4	2	no	—
581	C₄×C₁₉	—	4	1	no	—
582	C₄×C₁₉	—	4	1	no	—
583	C₄×C₁₉	—	4	2	no	—
584	C₄×C₁₉	—	4	1	no	—
585	C₄×C₁₉	—	4	1	no	—
586	C₄×C₁₉	—	4	2	no	—
587	C₄×C₁₉	C₂×#137	1	2	yes	—
588	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
589	C₄×C₁₉	#585	1	1	yes	characteristic
590	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
591	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
592	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
593	#556	C₂²×C₁₉	1	1	yes	characteristic
594	#554	—	2	1	no	—
595	#554	—	2	2	no	—
596	#554	—	2	1	no	—
597	#554	—	2	1	no	—
598	#554	C₂²×C₁₉	1	1	yes	characteristic
599	#554	C₂²×C₁₉	1	1	yes	characteristic
600	#554	C₂²×C₁₉	1	2	yes	—
601	#552	C₂²×C₁₉	1	2	yes	—
602	#551	—	2	2	no	—
603	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
604	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
605	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
606	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
607	#548	C₂²×C₁₉	1	2	yes	—
608	#547	C₂²×C₁₉	1	1	yes	characteristic
609	#547	C₂²×C₁₉	1	1	yes	characteristic
610	#546	—	2	1	no	—
611	#544	—	2	1	no	—
612	#543	—	2	2	no	—
613	#542	—	2	1	no	—
614	#539	—	2	2	no	—
615	#533	C₂²×C₁₉	1	1	yes	characteristic
616	#533	C₂²×C₁₉	1	1	yes	characteristic
617	#533	C₂²×C₁₉	1	1	yes	characteristic
618	#529	C₂²×C₁₉	1	1	yes	characteristic
619	#525	C₂²×C₁₉	1	2	yes	—
620	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
621	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
622	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
623	#520	—	2	1	no	—
624	#518	—	2	1	no	—
625	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
626	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
627	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
628	#497	C₂²×C₁₉	1	1	yes	characteristic, complemented
629	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
630	#491	C₂²×C₁₉	1	1	yes	characteristic, complemented
631	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
632	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
633	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
634	#485	C₂²×C₁₉	1	2	yes	complemented
635	#485	C₂²×C₁₉	1	2	yes	complemented
636	#484	C₂²×C₁₉	1	2	yes	complemented
637	#483	C₂²×C₁₉	1	2	yes	complemented
638	#483	C₂²×C₁₉	1	2	yes	complemented
639	#483	C₂²×C₁₉	1	2	yes	complemented
640	#483	C₂²×C₁₉	1	2	yes	complemented
641	#481	C₂²×C₁₉	1	2	yes	complemented
642	#479	C₂²×C₁₉	1	2	yes	complemented
643	#477	C₂²×C₁₉	1	1	yes	characteristic, complemented
644	#476	C₂²×C₁₉	1	1	yes	characteristic, complemented
645	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
646	#475	C₂²×C₁₉	1	2	yes	complemented
647	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
648	#470	C₂²×C₁₉	1	1	yes	characteristic
649	#470	C₂²×C₁₉	1	1	yes	characteristic
650	#470	C₂²×C₁₉	1	2	yes	—
651	#470	C₂²×C₁₉	1	2	yes	—
652	#470	C₂²×C₁₉	1	2	yes	—
653	#470	C₂²×C₁₉	1	2	yes	—
654	#470	C₂²×C₁₉	1	2	yes	—
655	#470	C₂²×C₁₉	1	2	yes	complemented
656	#470	C₂²×C₁₉	1	2	yes	complemented
657	#470	C₂²×C₁₉	1	2	yes	complemented
658	#470	C₂²×C₁₉	1	2	yes	complemented
659	#468	C₂²×C₁₉	1	1	yes	characteristic
660	#468	C₂²×C₁₉	1	1	yes	characteristic
661	#468	C₂²×C₁₉	1	2	yes	—
662	#467	C₂²×C₁₉	1	2	yes	complemented
663	#467	C₂²×C₁₉	1	2	yes	complemented
664	#465	C₂²×C₁₉	1	2	yes	complemented
665	#465	C₂²×C₁₉	1	2	yes	complemented
666	#464	C₂²×C₁₉	1	2	yes	complemented
667	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
668	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
669	#462	C₂²×C₁₉	1	2	yes	complemented
670	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
671	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
672	#452	C₂²×C₁₉	1	2	yes	complemented
673	#452	C₂²×C₁₉	1	2	yes	complemented
674	#451	C₂²×C₁₉	1	2	yes	complemented
675	#451	C₂²×C₁₉	1	2	yes	complemented
676	#451	C₂²×C₁₉	1	2	yes	complemented
677	#451	C₂²×C₁₉	1	2	yes	complemented
678	#451	C₂²×C₁₉	1	2	yes	complemented
679	#448	C₂²×C₁₉	1	2	yes	complemented
680	#441	C₂²×C₁₉	1	2	yes	complemented
681	#441	C₂²×C₁₉	1	2	yes	complemented
682	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
683	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
684	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
685	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
686	#436	C₂²×C₁₉	1	1	yes	characteristic
687	#436	C₂²×C₁₉	1	1	yes	characteristic
688	#435	C₂²×C₁₉	1	2	yes	—
689	#435	C₂²×C₁₉	1	2	yes	—
690	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
691	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
692	#428	C₂²×C₁₉	1	2	yes	complemented
693	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
694	#423	C₂²×C₁₉	1	1	yes	characteristic
695	#419	C₂²×C₁₉	1	2	yes	complemented
696	#417	C₂²×C₁₉	1	2	yes	complemented
697	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
698	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
699	#407	C₂²×C₁₉	1	2	yes	—
700	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
701	C₂×C₁₉	—	2	4	no	—
702	C₂×C₁₉	—	4	2	no	—
703	C₂×C₁₉	—	4	1	no	—
704	C₂×C₁₉	—	8	1	no	—
705	C₂×C₁₉	#3496	1	1	yes	characteristic
706	C₂×C₁₉	C₂²×#137	1	1	yes	characteristic
707	C₂×C₁₉	#3586	1	1	yes	characteristic
708	C₂×#41	—	2	1	no	—
709	C₂×#41	C₂³×C₁₉	1	2	yes	—
710	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
711	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
712	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
713	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
714	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
715	#137	—	4	4	no	—
716	C₂×Q₁₆	—	4	4	no	—
717	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
718	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
719	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
720	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
721	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
722	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
723	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
724	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
725	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
726	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
727	C₂×M₁₆	—	4	4	no	—
728	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
729	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
730	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
731	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
732	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
733	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
734	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
735	C₄⋊Q₈	—	2	1	no	—
736	C₄⋊Q₈	—	2	1	no	—
737	C₄⋊Q₈	—	2	2	no	—
738	C₄⋊Q₈	—	2	1	no	—
739	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
742	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
743	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
744	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	1	no	—
748	#125	—	2	2	no	—
749	#125	—	2	1	no	—
750	#125	—	2	2	no	—
751	#125	—	2	1	no	—
752	#125	—	2	1	no	—
753	#125	—	2	1	no	—
754	#125	—	2	1	no	—
755	#125	C₂³×C₁₉	1	1	yes	characteristic
756	#124	—	2	1	no	—
757	#124	—	2	2	no	—
758	#124	C₂³×C₁₉	1	1	yes	characteristic
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	1	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	1	no	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	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	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
786	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
788	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
789	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
790	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
791	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
792	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
795	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
796	#121	—	2	2	no	—
797	#121	—	2	1	no	—
798	#121	C₂³×C₁₉	1	1	yes	characteristic
799	#121	C₂³×C₁₉	1	2	yes	—
800	#120	—	2	2	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	2	1	no	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
807	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	2	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	1	yes	characteristic
822	C₄×D₄	D₄×C₁₉	1	2	yes	—
823	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₁₉	1	2	yes	—
828	#117	—	2	1	no	—
829	#117	—	2	1	no	—
830	#117	—	2	1	no	—
831	#117	—	2	2	no	—
832	#117	—	2	1	no	—
833	#117	C₂³×C₁₉	1	2	yes	—
834	C₂×C₄⋊C₄	—	2	2	no	—
835	C₂×C₄⋊C₄	—	2	2	no	—
836	C₂×C₄⋊C₄	—	2	2	no	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
839	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
840	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
841	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
842	C₂×C₂²⋊C₄	—	2	2	no	—
843	C₂×C₂²⋊C₄	—	2	2	no	—
844	C₂×C₂²⋊C₄	—	2	2	no	—
845	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
846	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
847	#107	C₂³×C₁₉	1	1	yes	characteristic
848	#107	C₂³×C₁₉	1	2	yes	—
849	#107	C₂³×C₁₉	1	1	yes	characteristic
850	#106	C₂³×C₁₉	1	1	yes	characteristic
851	#106	C₂³×C₁₉	1	2	yes	—
852	#106	C₂³×C₁₉	1	2	yes	—
853	#106	C₂³×C₁₉	1	2	yes	—
854	#106	C₂³×C₁₉	1	2	yes	—
855	#106	C₂³×C₁₉	1	1	yes	characteristic
856	#106	C₂³×C₁₉	1	2	yes	—
857	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
860	#103	C₂³×C₁₉	1	1	yes	characteristic
861	#103	C₂³×C₁₉	1	1	yes	characteristic
862	#103	C₂³×C₁₉	1	2	yes	—
863	#103	C₂³×C₁₉	1	2	yes	—
864	#103	C₂³×C₁₉	1	2	yes	—
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	1	yes	characteristic
873	#103	C₂³×C₁₉	1	1	yes	characteristic
874	#103	C₂³×C₁₉	1	1	yes	characteristic
875	#103	C₂³×C₁₉	1	2	yes	—
876	#103	C₂³×C₁₉	1	2	yes	—
877	#102	C₂³×C₁₉	1	1	yes	characteristic
878	#102	C₂³×C₁₉	1	2	yes	—
879	#102	C₂³×C₁₉	1	1	yes	characteristic
880	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
884	#97	C₂³×C₁₉	1	1	yes	characteristic
885	#97	C₂³×C₁₉	1	1	yes	characteristic
886	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
887	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
888	C₁₉	#62300	1	1	yes	characteristic, direct product factor, Sylow
889	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
890	#41	—	4	2	no	—
891	#41	—	4	2	no	—
892	#41	—	4	4	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	2	no	—
897	C₂×Q₈	—	2	2	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	4	2	no	—
900	C₂×Q₈	—	4	2	no	—
901	C₂×Q₈	—	4	2	no	—
902	C₂×Q₈	—	4	2	no	—
903	C₂×Q₈	—	4	2	no	—
904	C₂×Q₈	—	4	2	no	—
905	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
906	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
907	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
908	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
909	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
910	C₂×D₄	—	2	4	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
915	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
916	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
917	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	4	2	no	—
927	C₂²×C₄	—	4	2	no	—
928	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
929	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
930	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
931	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
932	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
933	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
934	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
935	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
936	Q₁₆	—	2	2	no	—
937	Q₁₆	—	2	4	no	—
938	Q₁₆	—	4	2	no	—
939	Q₁₆	—	4	2	no	—
940	Q₁₆	—	4	1	no	—
941	Q₁₆	—	4	2	no	—
942	Q₁₆	—	4	2	no	—
943	SD₁₆	—	2	2	no	—
944	SD₁₆	—	4	1	no	—
945	SD₁₆	—	4	2	no	—
946	M₁₆	—	2	2	no	—
947	M₁₆	—	2	4	no	—
948	M₁₆	—	4	2	no	—
949	M₁₆	—	4	2	no	—
950	M₁₆	—	4	1	no	—
951	C₂×C₈	—	2	4	no	—
952	C₂×C₈	—	4	2	no	—
953	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
954	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
955	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
956	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
957	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
958	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	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	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
991	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
992	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
993	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1018	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1019	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1020	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1028	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1029	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1030	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1031	C₂³	—	2	4	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	4	2	no	—
1034	C₂³	—	4	2	no	—
1035	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1036	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1037	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	2	2	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	1	no	—
1045	Q₈	—	2	1	no	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	4	2	no	—
1049	Q₈	—	8	2	no	—
1050	Q₈	—	8	2	no	—
1051	Q₈	—	8	2	no	—
1052	Q₈	—	8	1	no	—
1053	Q₈	—	8	1	no	—
1054	D₄	—	2	4	no	—
1055	D₄	—	2	2	no	—
1056	D₄	—	2	1	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	4	2	no	—
1059	D₄	—	4	4	no	—
1060	D₄	—	8	2	no	—
1061	D₄	C₁₉×#137	1	4	yes	complemented
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	4	2	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	4	1	no	—
1084	C₂×C₄	—	4	4	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	8	2	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	—	8	2	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	—	8	2	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1093	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1094	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1095	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1096	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1097	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1098	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1099	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1100	C₈	—	2	2	no	—
1101	C₈	—	2	1	no	—
1102	C₈	—	2	2	no	—
1103	C₈	—	2	1	no	—
1104	C₈	—	2	1	no	—
1105	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	1	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	2	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	2	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	8	4	no	—
1118	C₂²	C₂×C₁₉×#137	1	4	yes	—
1119	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1120	C₄	—	2	1	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	2	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	1	no	—
1137	C₄	C₂×C₁₉×#137	1	2	yes	—
1138	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1139	C₄	C₁₉×#585	1	1	yes	characteristic
1140	C₂	—	2	4	no	—
1141	C₂	—	4	1	no	—
1142	C₂	—	4	2	no	—
1143	C₂	—	8	1	no	—
1144	C₂	C₁₉×#3496	1	1	yes	characteristic
1145	C₂	C₂²×C₁₉×#137	1	1	yes	characteristic
1146	C₂	C₁₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3520	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×#3356	C₂	semidirect
4. C₁₉×#3344	C₂	semidirect
5. C₁₉×#3335	C₂	semidirect
6. C₁₉×#3331	C₂	semidirect
7. C₁₉×#3328	C₂	semidirect
8. C₁₉×#3316	C₂	semidirect
9. C₁₉×#3312	C₂	semidirect
10. C₁₉×#3299	C₂	semidirect
11. C₁₉×#3298	C₂	semidirect
12. D₄×Q₁₆×C₁₉	C₂	semidirect
13. C₁₉×#3276	C₂	semidirect
14. C₁₉×#3270	C₂	semidirect
15. C₁₉×#3255	C₂	semidirect
16. C₁₉×#3252	C₂	semidirect
17. C₁₉×#3196	C₂	semidirect
18. C₁₉×#3195	C₂	semidirect
19. C₁₉×#3185	C₂	semidirect
20. C₁₉×#3172	C₂	semidirect
21. C₁₉×#3056	C₂	semidirect
22. C₂×C₁₉×#470	C₂	semidirect
23. D₄×M₁₆×C₁₉	C₂	semidirect
24. C₂×C₁₉×#137	C₂²	semidirect
25. C₂²×Q₁₆×C₁₉	C₂²	semidirect
60. C₁₉×#501	C₂²	semidirect
61. C₁₉×#498	C₂²	semidirect
62. C₁₉×#497	C₂²	semidirect
63. C₁₉×#494	C₂²	semidirect
64. C₁₉×#491	C₂²	semidirect
65. C₁₉×#489	C₂²	semidirect
66. C₁₉×#487	C₂²	semidirect
67. C₁₉×#487	C₂²	semidirect
68. C₁₉×#485	C₂²	semidirect
69. C₁₉×#485	C₂²	semidirect
70. C₁₉×#484	C₂²	semidirect
71. C₁₉×#483	C₂²	semidirect
72. C₁₉×#483	C₂²	semidirect
73. C₁₉×#483	C₂²	semidirect
74. C₁₉×#483	C₂²	semidirect
75. C₁₉×#481	C₂²	semidirect
76. C₁₉×#479	C₂²	semidirect
77. C₁₉×#477	C₂²	semidirect
78. C₁₉×#476	C₂²	semidirect
79. C₁₉×#475	C₂²	semidirect
80. C₁₉×#475	C₂²	semidirect
81. C₁₉×#475	C₂²	semidirect
89. C₁₉×#470	C₂²	semidirect
90. C₁₉×#470	C₂²	semidirect
91. C₁₉×#470	C₂²	semidirect
92. C₁₉×#470	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×#462	C₂²	semidirect
103. C₁₉×#462	C₂²	semidirect
104. C₁₉×#462	C₂²	semidirect
105. C₁₉×#461	C₂²	semidirect
106. C₁₉×#452	C₂²	semidirect
107. C₁₉×#452	C₂²	semidirect
108. C₁₉×#451	C₂²	semidirect
109. C₁₉×#451	C₂²	semidirect
110. C₁₉×#451	C₂²	semidirect
111. C₁₉×#451	C₂²	semidirect
112. C₁₉×#451	C₂²	semidirect
113. C₁₉×#448	C₂²	semidirect
114. C₁₉×#441	C₂²	semidirect
115. C₁₉×#441	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
126. C₁₉×#428	C₂²	semidirect
127. C₂×C₁₉×#106	C₂²	semidirect
129. C₁₉×#419	C₂²	semidirect
130. C₁₉×#417	C₂²	semidirect
131. C₂×C₁₉×#103	C₂²	semidirect
132. C₂×C₁₉×#103	C₂²	semidirect
457. #62300	C₁₉	direct (N × H)
488. D₄×C₁₉	#137	semidirect
534. #3501	C₂×C₁₉	semidirect
535. #3356	C₂×C₁₉	semidirect
536. #3344	C₂×C₁₉	semidirect
537. #3335	C₂×C₁₉	semidirect
538. #3331	C₂×C₁₉	semidirect
539. #3328	C₂×C₁₉	semidirect
540. #3316	C₂×C₁₉	semidirect
541. #3312	C₂×C₁₉	semidirect
542. #3299	C₂×C₁₉	semidirect
543. #3298	C₂×C₁₉	semidirect
544. D₄×Q₁₆	C₂×C₁₉	semidirect
545. #3276	C₂×C₁₉	semidirect
546. #3270	C₂×C₁₉	semidirect
547. #3255	C₂×C₁₉	semidirect
548. #3252	C₂×C₁₉	semidirect
549. #3196	C₂×C₁₉	semidirect
550. #3195	C₂×C₁₉	semidirect
551. #3185	C₂×C₁₉	semidirect
552. #3172	C₂×C₁₉	semidirect
553. #3056	C₂×C₁₉	semidirect
554. C₂×#470	C₂×C₁₉	semidirect
555. D₄×M₁₆	C₂×C₁₉	semidirect
590. C₂×#137	C₂²×C₁₉	semidirect
591. C₂²×Q₁₆	C₂²×C₁₉	semidirect
626. #501	C₂²×C₁₉	semidirect
627. #498	C₂²×C₁₉	semidirect
628. #497	C₂²×C₁₉	semidirect
629. #494	C₂²×C₁₉	semidirect
630. #491	C₂²×C₁₉	semidirect
631. #489	C₂²×C₁₉	semidirect
632. #487	C₂²×C₁₉	semidirect
633. #487	C₂²×C₁₉	semidirect
634. #485	C₂²×C₁₉	semidirect
635. #485	C₂²×C₁₉	semidirect
636. #484	C₂²×C₁₉	semidirect
637. #483	C₂²×C₁₉	semidirect
638. #483	C₂²×C₁₉	semidirect
639. #483	C₂²×C₁₉	semidirect
640. #483	C₂²×C₁₉	semidirect
641. #481	C₂²×C₁₉	semidirect
642. #479	C₂²×C₁₉	semidirect
643. #477	C₂²×C₁₉	semidirect
644. #476	C₂²×C₁₉	semidirect
645. #475	C₂²×C₁₉	semidirect
646. #475	C₂²×C₁₉	semidirect
647. #475	C₂²×C₁₉	semidirect
655. #470	C₂²×C₁₉	semidirect
656. #470	C₂²×C₁₉	semidirect
657. #470	C₂²×C₁₉	semidirect
658. #470	C₂²×C₁₉	semidirect
662. #467	C₂²×C₁₉	semidirect
663. #467	C₂²×C₁₉	semidirect
664. #465	C₂²×C₁₉	semidirect
665. #465	C₂²×C₁₉	semidirect
666. #464	C₂²×C₁₉	semidirect
667. #462	C₂²×C₁₉	semidirect
668. #462	C₂²×C₁₉	semidirect
669. #462	C₂²×C₁₉	semidirect
670. #462	C₂²×C₁₉	semidirect
671. #461	C₂²×C₁₉	semidirect
672. #452	C₂²×C₁₉	semidirect
673. #452	C₂²×C₁₉	semidirect
674. #451	C₂²×C₁₉	semidirect
675. #451	C₂²×C₁₉	semidirect
676. #451	C₂²×C₁₉	semidirect
677. #451	C₂²×C₁₉	semidirect
678. #451	C₂²×C₁₉	semidirect
679. #448	C₂²×C₁₉	semidirect
680. #441	C₂²×C₁₉	semidirect
681. #441	C₂²×C₁₉	semidirect
682. C₄×Q₁₆	C₂²×C₁₉	semidirect
683. C₄×Q₁₆	C₂²×C₁₉	semidirect
684. C₄×SD₁₆	C₂²×C₁₉	semidirect
685. C₄×SD₁₆	C₂²×C₁₉	semidirect
692. #428	C₂²×C₁₉	semidirect
693. C₂×#106	C₂²×C₁₉	semidirect
695. #419	C₂²×C₁₉	semidirect
696. #417	C₂²×C₁₉	semidirect
697. C₂×#103	C₂²×C₁₉	semidirect
698. C₂×#103	C₂²×C₁₉	semidirect
888. C₁₉	#62300	direct (N × H)
1061. 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×#3520	2
C₁₉×#3501	2
C₁₉×#3356	2
C₁₉×#3344	2
C₁₉×#3335	2
C₁₉×#3331	2
C₁₉×#3328	2
C₁₉×#3316	2
C₁₉×#3312	2
C₁₉×#3299	2
C₁₉×#3298	2
D₄×Q₁₆×C₁₉	2
C₁₉×#3276	2
C₁₉×#3270	2
C₁₉×#3255	2
C₁₉×#3252	2
C₁₉×#3196	2
C₁₉×#3195	2
C₁₉×#3185	2
C₁₉×#3172	2
C₁₉×#3056	2
C₂×C₁₉×#470	2
D₄×M₁₆×C₁₉	2
#62300	19

Subgroups — C19×#62300 #18068259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62300 #18068259