Subgroups — C₁₉×#62293 #18068252

Order 4864.

1780 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3539	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3538	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3352	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3351	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3320	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3317	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3315	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3312	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3278	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3276	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3261	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3260	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3201	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3196	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3177	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3174	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3063	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3056	C₂	1	2	yes	maximal, complemented
19	C₁₉×#2930	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₉×#137	C₂²	1	2	yes	—
21	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
22	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#563	—	2	2	no	—
25	C₁₉×#560	—	2	2	no	—
26	C₁₉×#553	—	2	2	no	—
27	C₁₉×#553	C₂²	1	2	yes	—
28	C₁₉×#552	C₂²	1	2	yes	—
29	C₁₉×#552	C₂²	1	2	yes	—
30	C₁₉×#552	C₂²	1	2	yes	—
31	C₁₉×#551	—	2	2	no	—
32	C₁₉×#550	C₂²	1	2	yes	—
33	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
34	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
35	C₁₉×#547	C₂²	1	2	yes	—
36	C₁₉×#544	—	2	2	no	—
37	C₁₉×#541	C₂²	1	1	yes	characteristic
38	C₁₉×#541	C₂²	1	1	yes	characteristic
39	C₁₉×#541	C₂²	1	1	yes	characteristic
40	C₁₉×#540	—	2	2	no	—
41	C₁₉×#540	C₂²	1	1	yes	characteristic
42	C₁₉×#539	—	2	2	no	—
43	C₁₉×#539	—	2	2	no	—
44	C₁₉×#537	C₂²	1	2	yes	—
45	C₁₉×#536	C₂²	1	2	yes	—
46	C₁₉×#525	C₂²	1	2	yes	—
47	C₁₉×#525	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
49	C₁₉×#499	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#499	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
52	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#491	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#491	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×#491	C₂²	1	1	yes	characteristic, complemented
56	C₁₉×#490	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#485	C₂²	1	2	yes	—
58	C₁₉×#485	C₂²	1	2	yes	—
59	C₁₉×#485	C₂²	1	2	yes	complemented
60	C₁₉×#484	C₂²	1	2	yes	—
61	C₁₉×#484	C₂²	1	2	yes	complemented
62	C₁₉×#483	C₂²	1	2	yes	complemented
63	C₁₉×#482	C₂²	1	2	yes	complemented
64	C₁₉×#481	C₂²	1	2	yes	—
65	C₁₉×#479	C₂²	1	2	yes	complemented
66	C₁₉×#479	C₂²	1	2	yes	complemented
67	C₁₉×#479	C₂²	1	2	yes	complemented
68	C₁₉×#478	C₂²	1	2	yes	complemented
69	C₁₉×#470	C₂²	1	2	yes	—
70	C₁₉×#470	C₂²	1	2	yes	—
71	C₁₉×#470	C₂²	1	2	yes	—
72	C₁₉×#470	C₂²	1	2	yes	—
73	C₁₉×#470	C₂²	1	2	yes	complemented
74	C₁₉×#468	C₂²	1	2	yes	—
75	C₁₉×#468	C₂²	1	2	yes	—
76	C₁₉×#468	C₂²	1	2	yes	—
77	C₁₉×#468	C₂²	1	2	yes	—
78	C₁₉×#468	C₂²	1	2	yes	complemented
79	C₁₉×#467	C₂²	1	2	yes	—
80	C₁₉×#467	C₂²	1	2	yes	—
81	C₁₉×#467	C₂²	1	2	yes	complemented
82	C₁₉×#465	C₂²	1	2	yes	—
83	C₁₉×#465	C₂²	1	2	yes	—
84	C₁₉×#465	C₂²	1	2	yes	complemented
85	C₁₉×#462	C₂²	1	2	yes	complemented
86	C₁₉×#462	C₂²	1	2	yes	complemented
87	C₁₉×#461	C₂²	1	2	yes	complemented
88	C₁₉×#460	C₂²	1	2	yes	complemented
89	C₁₉×#452	C₂²	1	2	yes	—
90	C₁₉×#452	C₂²	1	2	yes	—
91	C₁₉×#452	C₂²	1	2	yes	complemented
92	C₁₉×#452	C₂²	1	2	yes	complemented
93	C₁₉×#451	C₂²	1	2	yes	—
94	C₁₉×#451	C₂²	1	2	yes	complemented
95	C₁₉×#448	C₂²	1	2	yes	—
96	C₁₉×#448	C₂²	1	2	yes	complemented
97	C₁₉×#441	C₂²	1	2	yes	complemented
98	C₁₉×#440	C₂²	1	2	yes	complemented
99	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
100	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
101	C₁₉×#436	C₂²	1	2	yes	—
102	C₁₉×#436	C₂²	1	2	yes	—
103	C₁₉×#435	C₂²	1	2	yes	—
104	C₁₉×#435	C₂²	1	2	yes	—
105	C₁₉×#428	C₂²	1	2	yes	—
106	C₁₉×#428	C₂²	1	2	yes	complemented
107	C₁₉×#424	C₂²	1	1	yes	characteristic
108	C₁₉×#419	C₂²	1	2	yes	—
109	C₁₉×#417	C₂²	1	2	yes	—
110	C₁₉×#416	C₂²	1	2	yes	complemented
111	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
112	C₁₉×#408	C₂²	1	1	yes	characteristic
113	C₁₉×#407	C₂²	1	1	yes	characteristic
114	C₁₉×#405	C₂²	1	1	yes	characteristic
115	C₂×#41×C₁₉	C₂³	1	2	yes	—
116	C₂×#41×C₁₉	C₂³	1	2	yes	—
117	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
118	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
119	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
121	C₁₉×#137	—	4	4	no	—
122	C₁₉×#137	—	4	4	no	—
123	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
124	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
126	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
131	C₁₉×#131	—	4	2	no	—
132	C₂×M₁₆×C₁₉	—	4	2	no	—
133	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
134	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
135	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
136	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
138	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
141	C₁₉×C₄⋊Q₈	—	2	2	no	—
142	C₁₉×C₄⋊Q₈	—	2	2	no	—
143	C₁₉×C₄⋊Q₈	—	2	2	no	—
144	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
145	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
146	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
147	C₁₉×#127	—	2	2	no	—
148	C₁₉×#127	C₂³	1	1	yes	characteristic
149	C₁₉×#126	—	2	2	no	—
150	C₁₉×#126	—	2	2	no	—
151	C₁₉×#126	—	2	2	no	—
152	C₁₉×#126	—	2	2	no	—
153	C₁₉×#126	—	2	2	no	—
154	C₁₉×#126	—	2	2	no	—
155	C₁₉×#126	—	2	2	no	—
156	C₁₉×#125	—	2	2	no	—
157	C₁₉×#125	—	2	2	no	—
158	C₁₉×#125	—	2	2	no	—
159	C₁₉×#125	—	2	2	no	—
160	C₁₉×#125	—	2	2	no	—
161	C₁₉×#125	—	2	2	no	—
162	C₁₉×#125	C₂³	1	1	yes	characteristic
163	C₁₉×#125	C₂³	1	1	yes	characteristic
164	C₁₉×#125	C₂³	1	1	yes	characteristic
165	C₁₉×#125	C₂³	1	1	yes	characteristic
166	C₁₉×#124	—	2	2	no	—
167	C₁₉×#123	—	2	2	no	—
168	C₁₉×#123	—	2	2	no	—
169	C₁₉×#123	—	2	2	no	—
170	C₁₉×#123	—	2	2	no	—
171	C₁₉×#123	—	2	2	no	—
172	C₁₉×#123	—	2	2	no	—
173	C₁₉×#123	—	2	2	no	—
174	C₁₉×#123	—	2	2	no	—
175	C₁₉×#123	—	2	2	no	—
176	C₁₉×#123	—	2	2	no	—
177	C₁₉×#123	D₄	1	2	yes	—
178	C₁₉×C₂²⋊Q₈	—	2	2	no	—
179	C₁₉×C₂²⋊Q₈	—	2	2	no	—
180	C₁₉×C₂²⋊Q₈	—	2	2	no	—
181	C₁₉×C₂²⋊Q₈	—	2	2	no	—
182	C₁₉×C₂²⋊Q₈	—	2	2	no	—
183	C₁₉×C₂²⋊Q₈	—	2	2	no	—
184	C₁₉×C₂²⋊Q₈	—	2	2	no	—
185	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
186	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
187	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
188	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₁₉×#121	—	2	2	no	—
196	C₁₉×#121	—	2	2	no	—
197	C₁₉×#121	—	2	2	no	—
198	C₁₉×#121	—	2	2	no	—
199	C₁₉×#121	—	2	2	no	—
200	C₁₉×#121	—	2	2	no	—
201	C₁₉×#121	—	2	2	no	—
202	C₁₉×#121	—	2	2	no	—
203	C₁₉×#121	D₄	1	2	yes	—
204	C₁₉×#121	C₂³	1	2	yes	—
205	C₁₉×#121	C₂³	1	2	yes	—
206	C₁₉×#121	C₂³	1	2	yes	—
207	C₁₉×#120	—	2	2	no	—
208	C₁₉×#120	D₄	1	2	yes	—
209	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
210	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
211	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
212	C₄×D₄×C₁₉	—	2	2	no	—
213	C₄×D₄×C₁₉	—	2	2	no	—
214	C₄×D₄×C₁₉	—	2	2	no	—
215	C₄×D₄×C₁₉	—	2	2	no	—
216	C₄×D₄×C₁₉	—	2	2	no	—
217	C₄×D₄×C₁₉	—	2	2	no	—
218	C₄×D₄×C₁₉	C₂³	1	2	yes	—
219	C₄×D₄×C₁₉	C₂³	1	2	yes	—
220	C₄×D₄×C₁₉	C₂³	1	2	yes	—
221	C₁₉×#117	—	2	2	no	—
222	C₁₉×#117	—	2	2	no	—
223	C₁₉×#117	—	2	2	no	—
224	C₁₉×#117	C₂³	1	2	yes	—
225	C₁₉×#117	C₂³	1	2	yes	—
226	C₁₉×#117	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
228	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
229	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
232	C₁₉×#107	C₂³	1	2	yes	—
233	C₁₉×#107	C₂³	1	2	yes	—
234	C₁₉×#107	C₂³	1	2	yes	—
235	C₁₉×#107	C₂³	1	2	yes	—
236	C₁₉×#106	C₂³	1	2	yes	—
237	C₁₉×#106	C₂³	1	2	yes	—
238	C₁₉×#106	C₂³	1	2	yes	—
239	C₁₉×#106	C₂³	1	2	yes	—
240	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
241	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
242	C₁₉×#103	C₂³	1	2	yes	—
243	C₁₉×#103	C₂³	1	2	yes	—
244	C₁₉×#103	C₂³	1	2	yes	—
245	C₁₉×#103	C₂³	1	2	yes	—
246	C₁₉×#103	C₂³	1	2	yes	—
247	C₁₉×#103	C₂³	1	2	yes	—
248	C₁₉×#103	C₂³	1	2	yes	—
249	C₁₉×#103	C₂³	1	2	yes	—
250	C₁₉×#103	C₂³	1	2	yes	—
251	C₁₉×#103	C₂³	1	2	yes	—
252	C₁₉×#103	C₂³	1	2	yes	—
253	C₁₉×#103	C₂³	1	2	yes	—
254	C₁₉×#102	C₂³	1	2	yes	—
255	C₁₉×#102	C₂³	1	2	yes	—
256	C₁₉×#102	C₂³	1	2	yes	—
257	C₁₉×#102	C₂³	1	2	yes	—
258	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
260	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
261	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
262	C₁₉×#97	C₂³	1	1	yes	characteristic
263	C₁₉×#97	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
266	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
267	#41×C₁₉	—	4	1	no	—
268	#41×C₁₉	—	4	1	no	—
269	#41×C₁₉	—	4	2	no	—
270	#41×C₁₉	—	4	2	no	—
271	#41×C₁₉	—	4	2	no	—
272	#41×C₁₉	—	4	2	no	—
273	C₂×Q₈×C₁₉	—	2	2	no	—
274	C₂×Q₈×C₁₉	—	2	2	no	—
275	C₂×Q₈×C₁₉	—	4	2	no	—
276	C₂×Q₈×C₁₉	—	4	2	no	—
277	C₂×Q₈×C₁₉	—	4	2	no	—
278	C₂×Q₈×C₁₉	—	4	2	no	—
279	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
280	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
281	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
282	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
283	C₂×D₄×C₁₉	—	2	2	no	—
284	C₂×D₄×C₁₉	—	2	2	no	—
285	C₂×D₄×C₁₉	—	2	2	no	—
286	C₂×D₄×C₁₉	—	2	2	no	—
287	C₂×D₄×C₁₉	—	2	2	no	—
288	C₂×D₄×C₁₉	—	2	2	no	—
289	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
290	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
291	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
292	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
293	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₁₉	—	2	2	no	—
295	C₂²×C₄×C₁₉	—	2	2	no	—
296	C₂²×C₄×C₁₉	—	2	2	no	—
297	C₂²×C₄×C₁₉	—	2	2	no	—
298	C₂²×C₄×C₁₉	—	2	2	no	—
299	C₂²×C₄×C₁₉	—	2	2	no	—
300	C₂²×C₄×C₁₉	—	2	2	no	—
301	C₂²×C₄×C₁₉	—	4	1	no	—
302	C₂²×C₄×C₁₉	—	4	1	no	—
303	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
304	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
308	Q₁₆×C₁₉	—	2	4	no	—
309	Q₁₆×C₁₉	—	4	2	no	—
310	Q₁₆×C₁₉	—	4	2	no	—
311	Q₁₆×C₁₉	—	4	2	no	—
312	SD₁₆×C₁₉	—	2	4	no	—
313	SD₁₆×C₁₉	—	4	2	no	—
314	SD₁₆×C₁₉	—	4	2	no	—
315	SD₁₆×C₁₉	—	4	2	no	—
316	M₁₆×C₁₉	—	2	4	no	—
317	M₁₆×C₁₉	—	2	4	no	—
318	M₁₆×C₁₉	—	4	2	no	—
319	M₁₆×C₁₉	—	4	1	no	—
320	M₁₆×C₁₉	—	4	1	no	—
321	C₂×C₈×C₁₉	—	2	2	no	—
322	C₂×C₈×C₁₉	—	4	1	no	—
323	C₂×C₈×C₁₉	—	4	2	no	—
324	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
325	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
326	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
327	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
328	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
329	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
330	C₄⋊C₄×C₁₉	—	2	2	no	—
331	C₄⋊C₄×C₁₉	—	2	2	no	—
332	C₄⋊C₄×C₁₉	—	2	2	no	—
333	C₄⋊C₄×C₁₉	—	2	2	no	—
334	C₄⋊C₄×C₁₉	—	2	2	no	—
335	C₄⋊C₄×C₁₉	—	2	2	no	—
336	C₄⋊C₄×C₁₉	—	2	2	no	—
337	C₄⋊C₄×C₁₉	—	2	2	no	—
338	C₄⋊C₄×C₁₉	—	2	2	no	—
339	C₄⋊C₄×C₁₉	—	2	2	no	—
340	C₄⋊C₄×C₁₉	—	2	2	no	—
341	C₄⋊C₄×C₁₉	—	2	2	no	—
342	C₄⋊C₄×C₁₉	—	2	2	no	—
343	C₄⋊C₄×C₁₉	—	2	2	no	—
344	C₄⋊C₄×C₁₉	—	2	2	no	—
345	C₄⋊C₄×C₁₉	—	2	2	no	—
346	C₄⋊C₄×C₁₉	—	2	2	no	—
347	C₄⋊C₄×C₁₉	—	2	2	no	—
348	C₄⋊C₄×C₁₉	—	2	2	no	—
349	C₄⋊C₄×C₁₉	—	2	2	no	—
350	C₄⋊C₄×C₁₉	—	2	2	no	—
351	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
352	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
353	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
354	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
355	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
356	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
357	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
358	C₂²⋊C₄×C₁₉	—	2	2	no	—
359	C₂²⋊C₄×C₁₉	—	2	2	no	—
360	C₂²⋊C₄×C₁₉	—	2	2	no	—
361	C₂²⋊C₄×C₁₉	—	2	2	no	—
362	C₂²⋊C₄×C₁₉	—	2	2	no	—
363	C₂²⋊C₄×C₁₉	—	2	2	no	—
364	C₂²⋊C₄×C₁₉	—	2	2	no	—
365	C₂²⋊C₄×C₁₉	—	2	2	no	—
366	C₂²⋊C₄×C₁₉	—	2	2	no	—
367	C₂²⋊C₄×C₁₉	—	2	2	no	—
368	C₂²⋊C₄×C₁₉	—	2	2	no	—
369	C₂²⋊C₄×C₁₉	—	2	2	no	—
370	C₂²⋊C₄×C₁₉	—	2	2	no	—
371	C₂²⋊C₄×C₁₉	—	2	2	no	—
372	C₂²⋊C₄×C₁₉	—	2	2	no	—
373	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
374	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
375	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
376	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
377	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
378	C₄²×C₁₉	—	2	2	no	—
379	C₄²×C₁₉	—	2	2	no	—
380	C₄²×C₁₉	—	2	2	no	—
381	C₄²×C₁₉	—	2	2	no	—
382	C₄²×C₁₉	—	2	2	no	—
383	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
384	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
385	#62293	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
386	C₂³×C₁₉	—	2	2	no	—
387	C₂³×C₁₉	—	4	1	no	—
388	C₂³×C₁₉	—	4	2	no	—
389	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
390	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
391	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
392	Q₈×C₁₉	—	2	2	no	—
393	Q₈×C₁₉	—	2	2	no	—
394	Q₈×C₁₉	—	2	2	no	—
395	Q₈×C₁₉	—	2	2	no	—
396	Q₈×C₁₉	—	2	2	no	—
397	Q₈×C₁₉	—	2	2	no	—
398	Q₈×C₁₉	—	4	1	no	—
399	Q₈×C₁₉	—	8	2	no	—
400	Q₈×C₁₉	—	8	2	no	—
401	D₄×C₁₉	—	2	2	no	—
402	D₄×C₁₉	—	2	2	no	—
403	D₄×C₁₉	—	4	2	no	—
404	D₄×C₁₉	—	4	2	no	—
405	D₄×C₁₉	—	4	1	no	—
406	D₄×C₁₉	—	4	2	no	—
407	D₄×C₁₉	—	8	2	no	—
408	D₄×C₁₉	—	8	2	no	—
409	D₄×C₁₉	—	8	2	no	—
410	D₄×C₁₉	—	8	2	no	—
411	D₄×C₁₉	—	8	2	no	—
412	D₄×C₁₉	—	8	2	no	—
413	C₂×C₄×C₁₉	—	2	1	no	—
414	C₂×C₄×C₁₉	—	2	2	no	—
415	C₂×C₄×C₁₉	—	2	2	no	—
416	C₂×C₄×C₁₉	—	2	1	no	—
417	C₂×C₄×C₁₉	—	2	2	no	—
418	C₂×C₄×C₁₉	—	2	2	no	—
419	C₂×C₄×C₁₉	—	2	2	no	—
420	C₂×C₄×C₁₉	—	2	2	no	—
421	C₂×C₄×C₁₉	—	2	2	no	—
422	C₂×C₄×C₁₉	—	2	2	no	—
423	C₂×C₄×C₁₉	—	2	2	no	—
424	C₂×C₄×C₁₉	—	2	2	no	—
425	C₂×C₄×C₁₉	—	2	2	no	—
426	C₂×C₄×C₁₉	—	4	1	no	—
427	C₂×C₄×C₁₉	—	4	2	no	—
428	C₂×C₄×C₁₉	—	4	4	no	—
429	C₂×C₄×C₁₉	—	8	2	no	—
430	C₂×C₄×C₁₉	—	8	2	no	—
431	C₂×C₄×C₁₉	—	8	2	no	—
432	C₂×C₄×C₁₉	—	8	2	no	—
433	C₂×C₄×C₁₉	—	8	2	no	—
434	C₂×C₄×C₁₉	—	8	2	no	—
435	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
437	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
438	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
439	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
441	C₈×C₁₉	—	2	1	no	—
442	C₈×C₁₉	—	2	2	no	—
443	C₈×C₁₉	—	2	2	no	—
444	C₈×C₁₉	—	2	1	no	—
445	C₈×C₁₉	—	2	1	no	—
446	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
447	#3539	C₂×C₁₉	1	1	yes	characteristic
448	#3538	C₂×C₁₉	1	1	yes	characteristic, complemented
449	#3352	C₂×C₁₉	1	2	yes	complemented
450	#3351	C₂×C₁₉	1	2	yes	complemented
451	#3320	C₂×C₁₉	1	2	yes	complemented
452	#3317	C₂×C₁₉	1	2	yes	complemented
453	#3315	C₂×C₁₉	1	2	yes	complemented
454	#3312	C₂×C₁₉	1	2	yes	complemented
455	#3278	C₂×C₁₉	1	2	yes	complemented
456	#3276	C₂×C₁₉	1	2	yes	complemented
457	#3261	C₂×C₁₉	1	1	yes	characteristic, complemented
458	#3260	C₂×C₁₉	1	1	yes	characteristic, complemented
459	#3201	C₂×C₁₉	1	2	yes	complemented
460	#3196	C₂×C₁₉	1	2	yes	complemented
461	#3177	C₂×C₁₉	1	1	yes	characteristic, complemented
462	#3174	C₂×C₁₉	1	1	yes	characteristic, complemented
463	#3063	C₂×C₁₉	1	2	yes	complemented
464	#3056	C₂×C₁₉	1	2	yes	complemented
465	#2930	C₂×C₁₉	1	1	yes	characteristic, complemented
466	C₂²×C₁₉	—	2	2	no	—
467	C₂²×C₁₉	—	2	2	no	—
468	C₂²×C₁₉	—	2	2	no	—
469	C₂²×C₁₉	—	2	2	no	—
470	C₂²×C₁₉	—	2	2	no	—
471	C₂²×C₁₉	—	2	2	no	—
472	C₂²×C₁₉	—	2	1	no	—
473	C₂²×C₁₉	—	2	2	no	—
474	C₂²×C₁₉	—	4	2	no	—
475	C₂²×C₁₉	—	4	2	no	—
476	C₂²×C₁₉	—	4	2	no	—
477	C₂²×C₁₉	—	8	2	no	—
478	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
479	C₄×C₁₉	—	2	2	no	—
480	C₄×C₁₉	—	2	2	no	—
481	C₄×C₁₉	—	2	2	no	—
482	C₄×C₁₉	—	2	1	no	—
483	C₄×C₁₉	—	2	2	no	—
484	C₄×C₁₉	—	4	2	no	—
485	C₄×C₁₉	—	4	2	no	—
486	C₄×C₁₉	—	4	2	no	—
487	C₄×C₁₉	—	4	2	no	—
488	C₄×C₁₉	—	4	2	no	—
489	C₄×C₁₉	—	4	2	no	—
490	C₄×C₁₉	—	4	2	no	—
491	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
492	C₄×C₁₉	#585	1	1	yes	characteristic
493	C₂×#137	C₂²×C₁₉	1	2	yes	—
494	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
495	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
496	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
497	#563	—	2	2	no	—
498	#560	—	2	2	no	—
499	#553	—	2	2	no	—
500	#553	C₂²×C₁₉	1	2	yes	—
501	#552	C₂²×C₁₉	1	2	yes	—
502	#552	C₂²×C₁₉	1	2	yes	—
503	#552	C₂²×C₁₉	1	2	yes	—
504	#551	—	2	2	no	—
505	#550	C₂²×C₁₉	1	2	yes	—
506	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
507	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
508	#547	C₂²×C₁₉	1	2	yes	—
509	#544	—	2	2	no	—
510	#541	C₂²×C₁₉	1	1	yes	characteristic
511	#541	C₂²×C₁₉	1	1	yes	characteristic
512	#541	C₂²×C₁₉	1	1	yes	characteristic
513	#540	—	2	2	no	—
514	#540	C₂²×C₁₉	1	1	yes	characteristic
515	#539	—	2	2	no	—
516	#539	—	2	2	no	—
517	#537	C₂²×C₁₉	1	2	yes	—
518	#536	C₂²×C₁₉	1	2	yes	—
519	#525	C₂²×C₁₉	1	2	yes	—
520	#525	C₂²×C₁₉	1	1	yes	characteristic
521	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
522	#499	C₂²×C₁₉	1	1	yes	characteristic, complemented
523	#499	C₂²×C₁₉	1	1	yes	characteristic, complemented
524	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
525	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
526	#491	C₂²×C₁₉	1	1	yes	characteristic, complemented
527	#491	C₂²×C₁₉	1	1	yes	characteristic, complemented
528	#491	C₂²×C₁₉	1	1	yes	characteristic, complemented
529	#490	C₂²×C₁₉	1	1	yes	characteristic, complemented
530	#485	C₂²×C₁₉	1	2	yes	—
531	#485	C₂²×C₁₉	1	2	yes	—
532	#485	C₂²×C₁₉	1	2	yes	complemented
533	#484	C₂²×C₁₉	1	2	yes	—
534	#484	C₂²×C₁₉	1	2	yes	complemented
535	#483	C₂²×C₁₉	1	2	yes	complemented
536	#482	C₂²×C₁₉	1	2	yes	complemented
537	#481	C₂²×C₁₉	1	2	yes	—
538	#479	C₂²×C₁₉	1	2	yes	complemented
539	#479	C₂²×C₁₉	1	2	yes	complemented
540	#479	C₂²×C₁₉	1	2	yes	complemented
541	#478	C₂²×C₁₉	1	2	yes	complemented
542	#470	C₂²×C₁₉	1	2	yes	—
543	#470	C₂²×C₁₉	1	2	yes	—
544	#470	C₂²×C₁₉	1	2	yes	—
545	#470	C₂²×C₁₉	1	2	yes	—
546	#470	C₂²×C₁₉	1	2	yes	complemented
547	#468	C₂²×C₁₉	1	2	yes	—
548	#468	C₂²×C₁₉	1	2	yes	—
549	#468	C₂²×C₁₉	1	2	yes	—
550	#468	C₂²×C₁₉	1	2	yes	—
551	#468	C₂²×C₁₉	1	2	yes	complemented
552	#467	C₂²×C₁₉	1	2	yes	—
553	#467	C₂²×C₁₉	1	2	yes	—
554	#467	C₂²×C₁₉	1	2	yes	complemented
555	#465	C₂²×C₁₉	1	2	yes	—
556	#465	C₂²×C₁₉	1	2	yes	—
557	#465	C₂²×C₁₉	1	2	yes	complemented
558	#462	C₂²×C₁₉	1	2	yes	complemented
559	#462	C₂²×C₁₉	1	2	yes	complemented
560	#461	C₂²×C₁₉	1	2	yes	complemented
561	#460	C₂²×C₁₉	1	2	yes	complemented
562	#452	C₂²×C₁₉	1	2	yes	—
563	#452	C₂²×C₁₉	1	2	yes	—
564	#452	C₂²×C₁₉	1	2	yes	complemented
565	#452	C₂²×C₁₉	1	2	yes	complemented
566	#451	C₂²×C₁₉	1	2	yes	—
567	#451	C₂²×C₁₉	1	2	yes	complemented
568	#448	C₂²×C₁₉	1	2	yes	—
569	#448	C₂²×C₁₉	1	2	yes	complemented
570	#441	C₂²×C₁₉	1	2	yes	complemented
571	#440	C₂²×C₁₉	1	2	yes	complemented
572	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
573	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
574	#436	C₂²×C₁₉	1	2	yes	—
575	#436	C₂²×C₁₉	1	2	yes	—
576	#435	C₂²×C₁₉	1	2	yes	—
577	#435	C₂²×C₁₉	1	2	yes	—
578	#428	C₂²×C₁₉	1	2	yes	—
579	#428	C₂²×C₁₉	1	2	yes	complemented
580	#424	C₂²×C₁₉	1	1	yes	characteristic
581	#419	C₂²×C₁₉	1	2	yes	—
582	#417	C₂²×C₁₉	1	2	yes	—
583	#416	C₂²×C₁₉	1	2	yes	complemented
584	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
585	#408	C₂²×C₁₉	1	1	yes	characteristic
586	#407	C₂²×C₁₉	1	1	yes	characteristic
587	#405	C₂²×C₁₉	1	1	yes	characteristic
588	C₂×C₁₉	—	4	2	no	—
589	C₂×C₁₉	—	4	2	no	—
590	C₂×C₁₉	—	4	1	no	—
591	C₂×C₁₉	—	8	2	no	—
592	C₂×C₁₉	#3496	1	1	yes	characteristic
593	C₂×C₁₉	#3586	1	2	yes	—
594	C₂×#41	C₂³×C₁₉	1	2	yes	—
595	C₂×#41	C₂³×C₁₉	1	2	yes	—
596	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
597	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
598	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
599	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
600	#137	—	4	4	no	—
601	#137	—	4	4	no	—
602	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
603	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
604	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
605	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
606	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
607	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
608	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
609	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
610	#131	—	4	2	no	—
611	C₂×M₁₆	—	4	2	no	—
612	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
613	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
614	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
615	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
616	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
617	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
618	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
619	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
620	C₄⋊Q₈	—	2	2	no	—
621	C₄⋊Q₈	—	2	2	no	—
622	C₄⋊Q₈	—	2	2	no	—
623	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
624	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
625	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
626	#127	—	2	2	no	—
627	#127	C₂³×C₁₉	1	1	yes	characteristic
628	#126	—	2	2	no	—
629	#126	—	2	2	no	—
630	#126	—	2	2	no	—
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#126	—	2	2	no	—
635	#125	—	2	2	no	—
636	#125	—	2	2	no	—
637	#125	—	2	2	no	—
638	#125	—	2	2	no	—
639	#125	—	2	2	no	—
640	#125	—	2	2	no	—
641	#125	C₂³×C₁₉	1	1	yes	characteristic
642	#125	C₂³×C₁₉	1	1	yes	characteristic
643	#125	C₂³×C₁₉	1	1	yes	characteristic
644	#125	C₂³×C₁₉	1	1	yes	characteristic
645	#124	—	2	2	no	—
646	#123	—	2	2	no	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	#123	—	2	2	no	—
652	#123	—	2	2	no	—
653	#123	—	2	2	no	—
654	#123	—	2	2	no	—
655	#123	—	2	2	no	—
656	#123	D₄×C₁₉	1	2	yes	—
657	C₂²⋊Q₈	—	2	2	no	—
658	C₂²⋊Q₈	—	2	2	no	—
659	C₂²⋊Q₈	—	2	2	no	—
660	C₂²⋊Q₈	—	2	2	no	—
661	C₂²⋊Q₈	—	2	2	no	—
662	C₂²⋊Q₈	—	2	2	no	—
663	C₂²⋊Q₈	—	2	2	no	—
664	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
665	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
666	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
667	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
668	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
669	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
670	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
671	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
672	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
673	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
674	#121	—	2	2	no	—
675	#121	—	2	2	no	—
676	#121	—	2	2	no	—
677	#121	—	2	2	no	—
678	#121	—	2	2	no	—
679	#121	—	2	2	no	—
680	#121	—	2	2	no	—
681	#121	—	2	2	no	—
682	#121	D₄×C₁₉	1	2	yes	—
683	#121	C₂³×C₁₉	1	2	yes	—
684	#121	C₂³×C₁₉	1	2	yes	—
685	#121	C₂³×C₁₉	1	2	yes	—
686	#120	—	2	2	no	—
687	#120	D₄×C₁₉	1	2	yes	—
688	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
689	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
690	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
691	C₄×D₄	—	2	2	no	—
692	C₄×D₄	—	2	2	no	—
693	C₄×D₄	—	2	2	no	—
694	C₄×D₄	—	2	2	no	—
695	C₄×D₄	—	2	2	no	—
696	C₄×D₄	—	2	2	no	—
697	C₄×D₄	C₂³×C₁₉	1	2	yes	—
698	C₄×D₄	C₂³×C₁₉	1	2	yes	—
699	C₄×D₄	C₂³×C₁₉	1	2	yes	—
700	#117	—	2	2	no	—
701	#117	—	2	2	no	—
702	#117	—	2	2	no	—
703	#117	C₂³×C₁₉	1	2	yes	—
704	#117	C₂³×C₁₉	1	2	yes	—
705	#117	C₂³×C₁₉	1	1	yes	characteristic
706	C₂×C₄⋊C₄	—	2	2	no	—
707	C₂×C₄⋊C₄	—	2	2	no	—
708	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
709	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
710	C₂×C₂²⋊C₄	—	2	2	no	—
711	#107	C₂³×C₁₉	1	2	yes	—
712	#107	C₂³×C₁₉	1	2	yes	—
713	#107	C₂³×C₁₉	1	2	yes	—
714	#107	C₂³×C₁₉	1	2	yes	—
715	#106	C₂³×C₁₉	1	2	yes	—
716	#106	C₂³×C₁₉	1	2	yes	—
717	#106	C₂³×C₁₉	1	2	yes	—
718	#106	C₂³×C₁₉	1	2	yes	—
719	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
720	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
721	#103	C₂³×C₁₉	1	2	yes	—
722	#103	C₂³×C₁₉	1	2	yes	—
723	#103	C₂³×C₁₉	1	2	yes	—
724	#103	C₂³×C₁₉	1	2	yes	—
725	#103	C₂³×C₁₉	1	2	yes	—
726	#103	C₂³×C₁₉	1	2	yes	—
727	#103	C₂³×C₁₉	1	2	yes	—
728	#103	C₂³×C₁₉	1	2	yes	—
729	#103	C₂³×C₁₉	1	2	yes	—
730	#103	C₂³×C₁₉	1	2	yes	—
731	#103	C₂³×C₁₉	1	2	yes	—
732	#103	C₂³×C₁₉	1	2	yes	—
733	#102	C₂³×C₁₉	1	2	yes	—
734	#102	C₂³×C₁₉	1	2	yes	—
735	#102	C₂³×C₁₉	1	2	yes	—
736	#102	C₂³×C₁₉	1	2	yes	—
737	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
738	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
739	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
740	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
741	#97	C₂³×C₁₉	1	1	yes	characteristic
742	#97	C₂³×C₁₉	1	1	yes	characteristic
743	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
744	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
745	C₁₉	#62293	1	1	yes	characteristic, direct product factor, Sylow
746	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
747	#41	—	4	1	no	—
748	#41	—	4	1	no	—
749	#41	—	4	2	no	—
750	#41	—	4	2	no	—
751	#41	—	4	2	no	—
752	#41	—	4	2	no	—
753	C₂×Q₈	—	2	2	no	—
754	C₂×Q₈	—	2	2	no	—
755	C₂×Q₈	—	4	2	no	—
756	C₂×Q₈	—	4	2	no	—
757	C₂×Q₈	—	4	2	no	—
758	C₂×Q₈	—	4	2	no	—
759	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
760	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
761	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
762	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
770	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
771	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
772	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
773	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	4	1	no	—
782	C₂²×C₄	—	4	1	no	—
783	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
784	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
788	Q₁₆	—	2	4	no	—
789	Q₁₆	—	4	2	no	—
790	Q₁₆	—	4	2	no	—
791	Q₁₆	—	4	2	no	—
792	SD₁₆	—	2	4	no	—
793	SD₁₆	—	4	2	no	—
794	SD₁₆	—	4	2	no	—
795	SD₁₆	—	4	2	no	—
796	M₁₆	—	2	4	no	—
797	M₁₆	—	2	4	no	—
798	M₁₆	—	4	2	no	—
799	M₁₆	—	4	1	no	—
800	M₁₆	—	4	1	no	—
801	C₂×C₈	—	2	2	no	—
802	C₂×C₈	—	4	1	no	—
803	C₂×C₈	—	4	2	no	—
804	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
805	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
806	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
807	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
808	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
809	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
832	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
833	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
834	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
835	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
836	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
837	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
854	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
855	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
856	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
857	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
858	C₄²	—	2	2	no	—
859	C₄²	—	2	2	no	—
860	C₄²	—	2	2	no	—
861	C₄²	—	2	2	no	—
862	C₄²	—	2	2	no	—
863	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
864	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
865	C₂³	—	2	2	no	—
866	C₂³	—	4	1	no	—
867	C₂³	—	4	2	no	—
868	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
869	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
870	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
871	Q₈	—	2	2	no	—
872	Q₈	—	2	2	no	—
873	Q₈	—	2	2	no	—
874	Q₈	—	2	2	no	—
875	Q₈	—	2	2	no	—
876	Q₈	—	2	2	no	—
877	Q₈	—	4	1	no	—
878	Q₈	—	8	2	no	—
879	Q₈	—	8	2	no	—
880	D₄	—	2	2	no	—
881	D₄	—	2	2	no	—
882	D₄	—	4	1	no	—
883	D₄	—	4	2	no	—
884	D₄	—	4	2	no	—
885	D₄	—	4	2	no	—
886	D₄	—	8	2	no	—
887	D₄	—	8	2	no	—
888	D₄	—	8	2	no	—
889	D₄	—	8	2	no	—
890	D₄	—	8	2	no	—
891	D₄	—	8	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	4	1	no	—
906	C₂×C₄	—	4	2	no	—
907	C₂×C₄	—	4	4	no	—
908	C₂×C₄	—	8	2	no	—
909	C₂×C₄	—	8	2	no	—
910	C₂×C₄	—	8	2	no	—
911	C₂×C₄	—	8	2	no	—
912	C₂×C₄	—	8	2	no	—
913	C₂×C₄	—	8	2	no	—
914	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
915	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
916	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
917	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
918	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
919	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
920	C₈	—	2	1	no	—
921	C₈	—	2	2	no	—
922	C₈	—	2	2	no	—
923	C₈	—	2	1	no	—
924	C₈	—	2	1	no	—
925	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	8	2	no	—
938	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
939	C₄	—	2	2	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	2	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	2	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	2	no	—
951	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
952	C₄	C₁₉×#585	1	1	yes	characteristic
953	C₂	—	4	2	no	—
954	C₂	—	4	1	no	—
955	C₂	—	4	2	no	—
956	C₂	—	8	2	no	—
957	C₂	C₁₉×#3496	1	1	yes	characteristic
958	C₂	C₁₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3539	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#525 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3538	C₂	semidirect
3. C₁₉×#3352	C₂	semidirect
4. C₁₉×#3351	C₂	semidirect
5. C₁₉×#3320	C₂	semidirect
6. C₁₉×#3317	C₂	semidirect
7. C₁₉×#3315	C₂	semidirect
8. C₁₉×#3312	C₂	semidirect
9. C₁₉×#3278	C₂	semidirect
10. C₁₉×#3276	C₂	semidirect
11. C₁₉×#3261	C₂	semidirect
12. C₁₉×#3260	C₂	semidirect
13. C₁₉×#3201	C₂	semidirect
14. C₁₉×#3196	C₂	semidirect
15. C₁₉×#3177	C₂	semidirect
16. C₁₉×#3174	C₂	semidirect
17. C₁₉×#3063	C₂	semidirect
18. C₁₉×#3056	C₂	semidirect
19. C₁₉×#2930	C₂	semidirect
21. C₂×C₁₉×#137	C₂²	semidirect
49. C₁₉×#499	C₂²	semidirect
50. C₁₉×#499	C₂²	semidirect
51. C₁₉×#494	C₂²	semidirect
52. C₁₉×#492	C₂²	semidirect
53. C₁₉×#491	C₂²	semidirect
54. C₁₉×#491	C₂²	semidirect
55. C₁₉×#491	C₂²	semidirect
56. C₁₉×#490	C₂²	semidirect
59. C₁₉×#485	C₂²	semidirect
61. C₁₉×#484	C₂²	semidirect
62. C₁₉×#483	C₂²	semidirect
63. C₁₉×#482	C₂²	semidirect
65. C₁₉×#479	C₂²	semidirect
66. C₁₉×#479	C₂²	semidirect
67. C₁₉×#479	C₂²	semidirect
68. C₁₉×#478	C₂²	semidirect
73. C₁₉×#470	C₂²	semidirect
78. C₁₉×#468	C₂²	semidirect
81. C₁₉×#467	C₂²	semidirect
84. C₁₉×#465	C₂²	semidirect
85. C₁₉×#462	C₂²	semidirect
86. C₁₉×#462	C₂²	semidirect
87. C₁₉×#461	C₂²	semidirect
88. C₁₉×#460	C₂²	semidirect
91. C₁₉×#452	C₂²	semidirect
92. C₁₉×#452	C₂²	semidirect
94. C₁₉×#451	C₂²	semidirect
96. C₁₉×#448	C₂²	semidirect
97. C₁₉×#441	C₂²	semidirect
98. C₁₉×#440	C₂²	semidirect
99. C₄×Q₁₆×C₁₉	C₂²	semidirect
100. C₄×SD₁₆×C₁₉	C₂²	semidirect
106. C₁₉×#428	C₂²	semidirect
110. C₁₉×#416	C₂²	semidirect
111. C₂×C₁₉×#103	C₂²	semidirect
385. #62293	C₁₉	direct (N × H)
448. #3538	C₂×C₁₉	semidirect
449. #3352	C₂×C₁₉	semidirect
450. #3351	C₂×C₁₉	semidirect
451. #3320	C₂×C₁₉	semidirect
452. #3317	C₂×C₁₉	semidirect
453. #3315	C₂×C₁₉	semidirect
454. #3312	C₂×C₁₉	semidirect
455. #3278	C₂×C₁₉	semidirect
456. #3276	C₂×C₁₉	semidirect
457. #3261	C₂×C₁₉	semidirect
458. #3260	C₂×C₁₉	semidirect
459. #3201	C₂×C₁₉	semidirect
460. #3196	C₂×C₁₉	semidirect
461. #3177	C₂×C₁₉	semidirect
462. #3174	C₂×C₁₉	semidirect
463. #3063	C₂×C₁₉	semidirect
464. #3056	C₂×C₁₉	semidirect
465. #2930	C₂×C₁₉	semidirect
494. C₂×#137	C₂²×C₁₉	semidirect
522. #499	C₂²×C₁₉	semidirect
523. #499	C₂²×C₁₉	semidirect
524. #494	C₂²×C₁₉	semidirect
525. #492	C₂²×C₁₉	semidirect
526. #491	C₂²×C₁₉	semidirect
527. #491	C₂²×C₁₉	semidirect
528. #491	C₂²×C₁₉	semidirect
529. #490	C₂²×C₁₉	semidirect
532. #485	C₂²×C₁₉	semidirect
534. #484	C₂²×C₁₉	semidirect
535. #483	C₂²×C₁₉	semidirect
536. #482	C₂²×C₁₉	semidirect
538. #479	C₂²×C₁₉	semidirect
539. #479	C₂²×C₁₉	semidirect
540. #479	C₂²×C₁₉	semidirect
541. #478	C₂²×C₁₉	semidirect
546. #470	C₂²×C₁₉	semidirect
551. #468	C₂²×C₁₉	semidirect
554. #467	C₂²×C₁₉	semidirect
557. #465	C₂²×C₁₉	semidirect
558. #462	C₂²×C₁₉	semidirect
559. #462	C₂²×C₁₉	semidirect
560. #461	C₂²×C₁₉	semidirect
561. #460	C₂²×C₁₉	semidirect
564. #452	C₂²×C₁₉	semidirect
565. #452	C₂²×C₁₉	semidirect
567. #451	C₂²×C₁₉	semidirect
569. #448	C₂²×C₁₉	semidirect
570. #441	C₂²×C₁₉	semidirect
571. #440	C₂²×C₁₉	semidirect
572. C₄×Q₁₆	C₂²×C₁₉	semidirect
573. C₄×SD₁₆	C₂²×C₁₉	semidirect
579. #428	C₂²×C₁₉	semidirect
583. #416	C₂²×C₁₉	semidirect
584. C₂×#103	C₂²×C₁₉	semidirect
745. C₁₉	#62293	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×#3539	2
C₁₉×#3538	2
C₁₉×#3352	2
C₁₉×#3351	2
C₁₉×#3320	2
C₁₉×#3317	2
C₁₉×#3315	2
C₁₉×#3312	2
C₁₉×#3278	2
C₁₉×#3276	2
C₁₉×#3261	2
C₁₉×#3260	2
C₁₉×#3201	2
C₁₉×#3196	2
C₁₉×#3177	2
C₁₉×#3174	2
C₁₉×#3063	2
C₁₉×#3056	2
C₁₉×#2930	2
#62293	19

Subgroups — C19×#62293 #18068252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62293 #18068252