Subgroups — C₁₉×#62337 #18068296

Order 4864.

1780 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3551	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3350	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3349	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3320	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3313	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3312	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3311	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3270	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3266	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3252	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3202	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3201	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3200	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3181	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3063	C₂	1	2	yes	maximal, complemented
17	C₁₉×#3059	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#3057	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#2932	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₉×#137	C₂²	1	2	yes	—
21	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
22	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#563	—	2	1	no	—
26	C₁₉×#563	—	2	1	no	—
27	C₁₉×#563	—	2	1	no	—
28	C₁₉×#560	—	2	1	no	—
29	C₁₉×#559	—	2	1	no	—
30	Q₈²×C₁₉	—	2	1	no	—
31	C₁₉×#556	C₂²	1	2	yes	—
32	C₁₉×#556	C₂²	1	2	yes	complemented
33	C₁₉×#555	—	2	1	no	—
34	C₁₉×#553	C₂²	1	2	yes	—
35	C₁₉×#552	C₂²	1	2	yes	—
36	C₁₉×#551	—	2	1	no	—
37	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
38	D₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
39	C₁₉×#548	C₂²	1	2	yes	—
40	C₁₉×#546	C₂²	1	2	yes	—
41	C₁₉×#542	—	2	2	no	—
42	C₁₉×#542	—	2	2	no	—
43	C₁₉×#540	—	2	2	no	—
44	C₁₉×#538	—	2	2	no	—
45	C₁₉×#537	C₂²	1	2	yes	—
46	C₁₉×#536	C₂²	1	1	yes	characteristic
47	C₁₉×#536	C₂²	1	1	yes	characteristic
48	C₁₉×#536	C₂²	1	1	yes	characteristic
49	C₁₉×#536	C₂²	1	2	yes	complemented
50	C₁₉×#535	C₂²	1	1	yes	characteristic
51	C₁₉×#533	C₂²	1	2	yes	complemented
52	C₁₉×#532	C₂²	1	1	yes	characteristic
53	C₁₉×#529	C₂²	1	2	yes	—
54	C₁₉×#501	C₂²	1	2	yes	complemented
55	C₁₉×#497	C₂²	1	2	yes	—
56	C₁₉×#491	C₂²	1	2	yes	complemented
57	C₁₉×#489	C₂²	1	2	yes	—
58	C₁₉×#485	C₂²	1	2	yes	—
59	C₁₉×#485	C₂²	1	2	yes	—
60	C₁₉×#485	C₂²	1	2	yes	complemented
61	C₁₉×#485	C₂²	1	2	yes	complemented
62	C₁₉×#484	C₂²	1	2	yes	complemented
63	C₁₉×#483	C₂²	1	2	yes	complemented
64	C₁₉×#482	C₂²	1	2	yes	—
65	C₁₉×#482	C₂²	1	2	yes	—
66	C₁₉×#479	C₂²	1	2	yes	complemented
67	C₁₉×#479	C₂²	1	2	yes	complemented
68	C₁₉×#477	C₂²	1	2	yes	complemented
69	C₁₉×#476	C₂²	1	2	yes	—
70	C₁₉×#470	C₂²	1	2	yes	—
71	C₁₉×#470	C₂²	1	2	yes	complemented
72	C₁₉×#470	C₂²	1	2	yes	complemented
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×#467	C₂²	1	2	yes	—
79	C₁₉×#467	C₂²	1	2	yes	complemented
80	C₁₉×#467	C₂²	1	2	yes	complemented
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	—
85	C₁₉×#465	C₂²	1	2	yes	—
86	C₁₉×#464	C₂²	1	2	yes	—
87	C₁₉×#464	C₂²	1	2	yes	—
88	C₁₉×#462	C₂²	1	2	yes	complemented
89	C₁₉×#461	C₂²	1	2	yes	—
90	C₁₉×#452	C₂²	1	2	yes	—
91	C₁₉×#452	C₂²	1	2	yes	—
92	C₁₉×#451	C₂²	1	2	yes	—
93	C₁₉×#451	C₂²	1	2	yes	complemented
94	C₁₉×#451	C₂²	1	2	yes	complemented
95	C₁₉×#450	C₂²	1	2	yes	—
96	C₁₉×#448	C₂²	1	2	yes	—
97	C₁₉×#448	C₂²	1	2	yes	—
98	C₁₉×#441	C₂²	1	2	yes	complemented
99	C₁₉×#441	C₂²	1	2	yes	complemented
100	C₁₉×#440	C₂²	1	2	yes	—
101	C₁₉×#440	C₂²	1	2	yes	—
102	C₁₉×#435	C₂²	1	2	yes	—
103	C₁₉×#435	C₂²	1	2	yes	—
104	C₁₉×#435	C₂²	1	2	yes	complemented
105	C₁₉×#435	C₂²	1	2	yes	complemented
106	C₁₉×#428	C₂²	1	2	yes	complemented
107	C₁₉×#427	C₂²	1	1	yes	characteristic
108	C₁₉×#427	C₂²	1	1	yes	characteristic, complemented
109	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
110	C₁₉×#419	C₂²	1	1	yes	characteristic
111	C₁₉×#419	C₂²	1	1	yes	characteristic, complemented
112	C₁₉×#419	C₂²	1	1	yes	characteristic, complemented
113	C₁₉×#418	C₂²	1	1	yes	characteristic
114	C₁₉×#416	C₂²	1	2	yes	—
115	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
116	C₁₉×#408	C₂²	1	1	yes	characteristic
117	C₁₉×#408	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₁₉	C₂³	1	2	yes	—
120	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
121	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
123	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
127	C₁₉×#137	—	4	4	no	—
128	C₂×Q₁₆×C₁₉	—	4	2	no	—
129	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
130	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
131	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
132	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
133	C₂×SD₁₆×C₁₉	—	4	2	no	—
134	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
135	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
138	C₁₉×#131	—	4	2	no	—
139	C₁₉×#131	—	4	2	no	—
140	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
141	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
142	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
143	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
144	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
146	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
147	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
150	C₁₉×C₄⋊Q₈	—	2	1	no	—
151	C₁₉×C₄⋊Q₈	—	2	1	no	—
152	C₁₉×C₄⋊Q₈	—	2	1	no	—
153	C₁₉×C₄⋊Q₈	—	2	2	no	—
154	C₁₉×C₄⋊Q₈	—	2	2	no	—
155	C₁₉×C₄⋊Q₈	—	2	2	no	—
156	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
157	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₁₉×#127	—	2	1	no	—
160	C₁₉×#127	D₄	1	1	yes	characteristic
161	C₁₉×#126	—	2	2	no	—
162	C₁₉×#126	—	2	2	no	—
163	C₁₉×#126	—	2	2	no	—
164	C₁₉×#126	—	2	2	no	—
165	C₁₉×#126	—	2	2	no	—
166	C₁₉×#126	—	2	2	no	—
167	C₁₉×#126	—	2	2	no	—
168	C₁₉×#125	—	2	2	no	—
169	C₁₉×#125	—	2	2	no	—
170	C₁₉×#125	C₂³	1	2	yes	—
171	C₁₉×#124	—	2	1	no	—
172	C₁₉×#124	—	2	1	no	—
173	C₁₉×#124	—	2	1	no	—
174	C₁₉×#124	—	2	1	no	—
175	C₁₉×#124	—	2	2	no	—
176	C₁₉×#124	—	2	2	no	—
177	C₁₉×#124	—	2	2	no	—
178	C₁₉×#124	—	2	2	no	—
179	C₁₉×#124	D₄	1	1	yes	characteristic
180	C₁₉×#124	D₄	1	1	yes	characteristic
181	C₁₉×#124	C₂³	1	2	yes	—
182	C₁₉×#123	—	2	1	no	—
183	C₁₉×#123	—	2	1	no	—
184	C₁₉×#123	—	2	1	no	—
185	C₁₉×#123	—	2	1	no	—
186	C₁₉×#123	—	2	1	no	—
187	C₁₉×#123	—	2	1	no	—
188	C₁₉×#123	—	2	2	no	—
189	C₁₉×#123	—	2	2	no	—
190	C₁₉×#123	—	2	2	no	—
191	C₁₉×#123	—	2	2	no	—
192	C₁₉×#123	—	2	2	no	—
193	C₁₉×#123	—	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	2	no	—
198	C₁₉×C₂²⋊Q₈	—	2	2	no	—
199	C₁₉×C₂²⋊Q₈	—	2	2	no	—
200	C₁₉×C₂²⋊Q₈	—	2	2	no	—
201	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₁₉×#121	—	2	2	no	—
211	C₁₉×#121	—	2	2	no	—
212	C₁₉×#121	—	2	2	no	—
213	C₁₉×#121	—	2	2	no	—
214	C₁₉×#121	—	2	2	no	—
215	C₁₉×#121	—	2	2	no	—
216	C₁₉×#121	D₄	1	2	yes	—
217	C₁₉×#121	D₄	1	2	yes	—
218	C₁₉×#121	C₂³	1	2	yes	—
219	C₁₉×#121	C₂³	1	2	yes	—
220	C₁₉×#121	C₂³	1	2	yes	—
221	C₁₉×#120	—	2	1	no	—
222	C₁₉×#120	—	2	1	no	—
223	C₁₉×#120	—	2	2	no	—
224	C₄×Q₈×C₁₉	—	2	2	no	—
225	C₄×Q₈×C₁₉	—	2	2	no	—
226	C₄×Q₈×C₁₉	—	2	2	no	—
227	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
228	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
229	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
230	C₄×D₄×C₁₉	—	2	2	no	—
231	C₄×D₄×C₁₉	—	2	2	no	—
232	C₄×D₄×C₁₉	—	2	2	no	—
233	C₄×D₄×C₁₉	—	2	2	no	—
234	C₄×D₄×C₁₉	—	2	2	no	—
235	C₄×D₄×C₁₉	C₂³	1	2	yes	—
236	C₄×D₄×C₁₉	C₂³	1	2	yes	—
237	C₄×D₄×C₁₉	C₂³	1	2	yes	—
238	C₁₉×#117	—	2	2	no	—
239	C₁₉×#117	—	2	2	no	—
240	C₁₉×#117	—	2	2	no	—
241	C₁₉×#117	C₂³	1	2	yes	—
242	C₁₉×#117	C₂³	1	1	yes	characteristic
243	C₁₉×#117	C₂³	1	1	yes	characteristic
244	C₁₉×#117	C₂³	1	1	yes	characteristic
245	C₁₉×#117	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
247	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
248	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
249	C₁₉×#107	C₂³	1	2	yes	—
250	C₁₉×#107	C₂³	1	2	yes	—
251	C₁₉×#107	C₂³	1	2	yes	—
252	C₁₉×#107	C₂³	1	2	yes	—
253	C₁₉×#106	C₂³	1	2	yes	—
254	C₁₉×#106	C₂³	1	2	yes	—
255	C₁₉×#106	C₂³	1	2	yes	—
256	C₁₉×#106	C₂³	1	2	yes	—
257	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
258	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
259	C₁₉×#103	C₂³	1	2	yes	—
260	C₁₉×#103	C₂³	1	2	yes	—
261	C₁₉×#103	C₂³	1	2	yes	—
262	C₁₉×#103	C₂³	1	2	yes	—
263	C₁₉×#103	C₂³	1	2	yes	—
264	C₁₉×#103	C₂³	1	2	yes	—
265	C₁₉×#103	C₂³	1	2	yes	—
266	C₁₉×#103	C₂³	1	2	yes	—
267	C₁₉×#103	C₂³	1	2	yes	—
268	C₁₉×#103	C₂³	1	2	yes	—
269	C₁₉×#103	C₂³	1	2	yes	—
270	C₁₉×#103	C₂³	1	2	yes	—
271	C₁₉×#102	C₂³	1	2	yes	—
272	C₁₉×#102	C₂³	1	2	yes	—
273	C₁₉×#102	C₂³	1	2	yes	—
274	C₁₉×#102	C₂³	1	2	yes	—
275	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₁₉×#97	C₂³	1	2	yes	—
280	C₁₉×#97	C₂³	1	2	yes	—
281	C₂⁴×C₁₉	—	2	1	no	—
282	#41×C₁₉	—	4	1	no	—
283	#41×C₁₉	—	4	1	no	—
284	#41×C₁₉	—	4	1	no	—
285	#41×C₁₉	—	4	1	no	—
286	#41×C₁₉	—	4	2	no	—
287	#41×C₁₉	—	4	2	no	—
288	C₂×Q₈×C₁₉	—	2	2	no	—
289	C₂×Q₈×C₁₉	—	2	1	no	—
290	C₂×Q₈×C₁₉	—	2	1	no	—
291	C₂×Q₈×C₁₉	—	2	1	no	—
292	C₂×Q₈×C₁₉	—	2	2	no	—
293	C₂×Q₈×C₁₉	—	4	1	no	—
294	C₂×Q₈×C₁₉	—	4	1	no	—
295	C₂×Q₈×C₁₉	—	4	1	no	—
296	C₂×Q₈×C₁₉	—	4	2	no	—
297	C₂×Q₈×C₁₉	—	4	1	no	—
298	C₂×Q₈×C₁₉	—	4	1	no	—
299	C₂×Q₈×C₁₉	—	4	1	no	—
300	C₂×Q₈×C₁₉	—	4	2	no	—
301	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
302	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
303	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
305	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
306	C₂×D₄×C₁₉	—	2	2	no	—
307	C₂×D₄×C₁₉	—	2	2	no	—
308	C₂×D₄×C₁₉	—	2	2	no	—
309	C₂×D₄×C₁₉	—	2	2	no	—
310	C₂×D₄×C₁₉	—	2	1	no	—
311	C₂×D₄×C₁₉	—	4	1	no	—
312	C₂×D₄×C₁₉	—	4	1	no	—
313	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
314	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
315	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
316	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
317	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
318	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
319	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
320	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₁₉	—	2	2	no	—
322	C₂²×C₄×C₁₉	—	2	1	no	—
323	C₂²×C₄×C₁₉	—	2	1	no	—
324	C₂²×C₄×C₁₉	—	2	2	no	—
325	C₂²×C₄×C₁₉	—	2	1	no	—
326	C₂²×C₄×C₁₉	—	2	2	no	—
327	C₂²×C₄×C₁₉	—	2	2	no	—
328	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
329	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
333	Q₁₆×C₁₉	—	2	4	no	—
334	Q₁₆×C₁₉	—	4	2	no	—
335	Q₁₆×C₁₉	—	4	2	no	—
336	Q₁₆×C₁₉	—	4	2	no	—
337	SD₁₆×C₁₉	—	2	4	no	—
338	SD₁₆×C₁₉	—	4	2	no	—
339	SD₁₆×C₁₉	—	4	2	no	—
340	SD₁₆×C₁₉	—	4	2	no	—
341	M₁₆×C₁₉	—	2	4	no	—
342	M₁₆×C₁₉	—	4	1	no	—
343	M₁₆×C₁₉	—	4	1	no	—
344	M₁₆×C₁₉	—	4	1	no	—
345	M₁₆×C₁₉	—	4	1	no	—
346	C₂×C₈×C₁₉	—	2	2	no	—
347	C₂×C₈×C₁₉	—	2	2	no	—
348	C₂×C₈×C₁₉	—	2	2	no	—
349	C₂×C₈×C₁₉	—	4	1	no	—
350	C₂×C₈×C₁₉	—	4	2	no	—
351	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
354	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
356	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
357	C₄⋊C₄×C₁₉	—	2	2	no	—
358	C₄⋊C₄×C₁₉	—	2	2	no	—
359	C₄⋊C₄×C₁₉	—	2	2	no	—
360	C₄⋊C₄×C₁₉	—	2	2	no	—
361	C₄⋊C₄×C₁₉	—	2	2	no	—
362	C₄⋊C₄×C₁₉	—	2	2	no	—
363	C₄⋊C₄×C₁₉	—	2	2	no	—
364	C₄⋊C₄×C₁₉	—	2	2	no	—
365	C₄⋊C₄×C₁₉	—	2	2	no	—
366	C₄⋊C₄×C₁₉	—	2	2	no	—
367	C₄⋊C₄×C₁₉	—	2	2	no	—
368	C₄⋊C₄×C₁₉	—	2	2	no	—
369	C₄⋊C₄×C₁₉	—	2	2	no	—
370	C₄⋊C₄×C₁₉	—	2	2	no	—
371	C₄⋊C₄×C₁₉	—	2	2	no	—
372	C₄⋊C₄×C₁₉	—	2	2	no	—
373	C₄⋊C₄×C₁₉	—	2	2	no	—
374	C₄⋊C₄×C₁₉	—	2	2	no	—
375	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
377	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
378	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
379	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
380	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
381	C₂²⋊C₄×C₁₉	—	2	2	no	—
382	C₂²⋊C₄×C₁₉	—	2	2	no	—
383	C₂²⋊C₄×C₁₉	—	2	2	no	—
384	C₂²⋊C₄×C₁₉	—	2	2	no	—
385	C₂²⋊C₄×C₁₉	—	2	1	no	—
386	C₂²⋊C₄×C₁₉	—	2	1	no	—
387	C₂²⋊C₄×C₁₉	—	2	1	no	—
388	C₂²⋊C₄×C₁₉	—	2	2	no	—
389	C₂²⋊C₄×C₁₉	—	2	1	no	—
390	C₂²⋊C₄×C₁₉	—	2	2	no	—
391	C₂²⋊C₄×C₁₉	—	2	2	no	—
392	C₂²⋊C₄×C₁₉	—	2	2	no	—
393	C₂²⋊C₄×C₁₉	—	2	2	no	—
394	C₂²⋊C₄×C₁₉	—	2	2	no	—
395	C₂²⋊C₄×C₁₉	—	2	2	no	—
396	C₂²⋊C₄×C₁₉	—	2	2	no	—
397	C₂²⋊C₄×C₁₉	—	2	2	no	—
398	C₂²⋊C₄×C₁₉	—	2	2	no	—
399	C₂²⋊C₄×C₁₉	—	2	2	no	—
400	C₂²⋊C₄×C₁₉	—	2	2	no	—
401	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
402	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
403	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
404	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
405	C₄²×C₁₉	—	2	1	no	—
406	C₄²×C₁₉	—	2	2	no	—
407	C₄²×C₁₉	—	2	2	no	—
408	C₄²×C₁₉	—	2	2	no	—
409	C₄²×C₁₉	—	2	1	no	—
410	C₄²×C₁₉	—	2	1	no	—
411	C₄²×C₁₉	—	2	1	no	—
412	C₄²×C₁₉	—	2	2	no	—
413	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
414	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
415	C₄²×C₁₉	C₂⁴	1	2	yes	—
416	#62337	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
417	C₂³×C₁₉	—	2	2	no	—
418	C₂³×C₁₉	—	8	1	no	—
419	C₂³×C₁₉	—	8	2	no	—
420	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
421	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
422	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
423	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
424	Q₈×C₁₉	—	2	2	no	—
425	Q₈×C₁₉	—	2	2	no	—
426	Q₈×C₁₉	—	2	2	no	—
427	Q₈×C₁₉	—	2	2	no	—
428	Q₈×C₁₉	—	2	2	no	—
429	Q₈×C₁₉	—	2	2	no	—
430	Q₈×C₁₉	—	4	1	no	—
431	Q₈×C₁₉	—	4	1	no	—
432	Q₈×C₁₉	—	4	4	no	—
433	Q₈×C₁₉	—	8	2	no	—
434	Q₈×C₁₉	—	8	1	no	—
435	Q₈×C₁₉	—	8	1	no	—
436	Q₈×C₁₉	—	8	1	no	—
437	D₄×C₁₉	—	2	2	no	—
438	D₄×C₁₉	—	2	2	no	—
439	D₄×C₁₉	—	4	2	no	—
440	D₄×C₁₉	—	4	2	no	—
441	D₄×C₁₉	—	4	2	no	—
442	D₄×C₁₉	—	4	1	no	—
443	D₄×C₁₉	—	4	1	no	—
444	D₄×C₁₉	—	4	1	no	—
445	D₄×C₁₉	—	4	1	no	—
446	D₄×C₁₉	—	8	1	no	—
447	D₄×C₁₉	—	8	2	no	—
448	D₄×C₁₉	—	8	2	no	—
449	D₄×C₁₉	—	8	2	no	—
450	D₄×C₁₉	—	8	2	no	—
451	C₂×C₄×C₁₉	—	2	1	no	—
452	C₂×C₄×C₁₉	—	2	1	no	—
453	C₂×C₄×C₁₉	—	2	1	no	—
454	C₂×C₄×C₁₉	—	2	2	no	—
455	C₂×C₄×C₁₉	—	2	1	no	—
456	C₂×C₄×C₁₉	—	2	1	no	—
457	C₂×C₄×C₁₉	—	2	1	no	—
458	C₂×C₄×C₁₉	—	2	2	no	—
459	C₂×C₄×C₁₉	—	2	2	no	—
460	C₂×C₄×C₁₉	—	2	2	no	—
461	C₂×C₄×C₁₉	—	2	2	no	—
462	C₂×C₄×C₁₉	—	2	2	no	—
463	C₂×C₄×C₁₉	—	2	2	no	—
464	C₂×C₄×C₁₉	—	2	2	no	—
465	C₂×C₄×C₁₉	—	2	2	no	—
466	C₂×C₄×C₁₉	—	4	2	no	—
467	C₂×C₄×C₁₉	—	8	2	no	—
468	C₂×C₄×C₁₉	—	8	2	no	—
469	C₂×C₄×C₁₉	—	8	2	no	—
470	C₂×C₄×C₁₉	—	8	1	no	—
471	C₂×C₄×C₁₉	—	8	1	no	—
472	C₂×C₄×C₁₉	—	8	2	no	—
473	C₂×C₄×C₁₉	—	8	1	no	—
474	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
478	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
479	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
481	C₈×C₁₉	—	2	1	no	—
482	C₈×C₁₉	—	2	1	no	—
483	C₈×C₁₉	—	2	1	no	—
484	C₈×C₁₉	—	2	2	no	—
485	C₈×C₁₉	—	2	2	no	—
486	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
487	#3551	C₂×C₁₉	1	1	yes	characteristic
488	#3550	C₂×C₁₉	1	1	yes	characteristic, complemented
489	#3350	C₂×C₁₉	1	2	yes	complemented
490	#3349	C₂×C₁₉	1	2	yes	complemented
491	#3320	C₂×C₁₉	1	2	yes	complemented
492	#3313	C₂×C₁₉	1	2	yes	complemented
493	#3312	C₂×C₁₉	1	2	yes	complemented
494	#3311	C₂×C₁₉	1	2	yes	complemented
495	#3270	C₂×C₁₉	1	2	yes	complemented
496	#3266	C₂×C₁₉	1	2	yes	complemented
497	#3252	C₂×C₁₉	1	2	yes	complemented
498	#3202	C₂×C₁₉	1	1	yes	characteristic, complemented
499	#3201	C₂×C₁₉	1	2	yes	complemented
500	#3200	C₂×C₁₉	1	1	yes	characteristic, complemented
501	#3181	C₂×C₁₉	1	2	yes	complemented
502	#3063	C₂×C₁₉	1	2	yes	complemented
503	#3059	C₂×C₁₉	1	1	yes	characteristic, complemented
504	#3057	C₂×C₁₉	1	1	yes	characteristic, complemented
505	#2932	C₂×C₁₉	1	1	yes	characteristic, complemented
506	C₂²×C₁₉	—	2	2	no	—
507	C₂²×C₁₉	—	2	2	no	—
508	C₂²×C₁₉	—	2	2	no	—
509	C₂²×C₁₉	—	2	2	no	—
510	C₂²×C₁₉	—	2	2	no	—
511	C₂²×C₁₉	—	2	1	no	—
512	C₂²×C₁₉	—	2	2	no	—
513	C₂²×C₁₉	—	2	1	no	—
514	C₂²×C₁₉	—	2	1	no	—
515	C₂²×C₁₉	—	4	2	no	—
516	C₂²×C₁₉	—	4	2	no	—
517	C₂²×C₁₉	—	4	2	no	—
518	C₂²×C₁₉	—	16	2	no	—
519	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
520	C₄×C₁₉	—	2	2	no	—
521	C₄×C₁₉	—	2	2	no	—
522	C₄×C₁₉	—	2	2	no	—
523	C₄×C₁₉	—	2	1	no	—
524	C₄×C₁₉	—	2	1	no	—
525	C₄×C₁₉	—	2	1	no	—
526	C₄×C₁₉	—	4	2	no	—
527	C₄×C₁₉	—	4	2	no	—
528	C₄×C₁₉	—	4	2	no	—
529	C₄×C₁₉	—	4	2	no	—
530	C₄×C₁₉	—	4	2	no	—
531	C₄×C₁₉	—	4	2	no	—
532	C₄×C₁₉	—	4	2	no	—
533	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
534	C₄×C₁₉	#585	1	1	yes	characteristic
535	C₂×#137	C₂²×C₁₉	1	2	yes	—
536	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
537	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
538	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
539	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic, complemented
540	#563	—	2	1	no	—
541	#563	—	2	1	no	—
542	#563	—	2	1	no	—
543	#560	—	2	1	no	—
544	#559	—	2	1	no	—
545	Q₈²	—	2	1	no	—
546	#556	C₂²×C₁₉	1	2	yes	—
547	#556	C₂²×C₁₉	1	2	yes	complemented
548	#555	—	2	1	no	—
549	#553	C₂²×C₁₉	1	2	yes	—
550	#552	C₂²×C₁₉	1	2	yes	—
551	#551	—	2	1	no	—
552	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
553	D₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
554	#548	C₂²×C₁₉	1	2	yes	—
555	#546	C₂²×C₁₉	1	2	yes	—
556	#542	—	2	2	no	—
557	#542	—	2	2	no	—
558	#540	—	2	2	no	—
559	#538	—	2	2	no	—
560	#537	C₂²×C₁₉	1	2	yes	—
561	#536	C₂²×C₁₉	1	1	yes	characteristic
562	#536	C₂²×C₁₉	1	1	yes	characteristic
563	#536	C₂²×C₁₉	1	1	yes	characteristic
564	#536	C₂²×C₁₉	1	2	yes	complemented
565	#535	C₂²×C₁₉	1	1	yes	characteristic
566	#533	C₂²×C₁₉	1	2	yes	complemented
567	#532	C₂²×C₁₉	1	1	yes	characteristic
568	#529	C₂²×C₁₉	1	2	yes	—
569	#501	C₂²×C₁₉	1	2	yes	complemented
570	#497	C₂²×C₁₉	1	2	yes	—
571	#491	C₂²×C₁₉	1	2	yes	complemented
572	#489	C₂²×C₁₉	1	2	yes	—
573	#485	C₂²×C₁₉	1	2	yes	—
574	#485	C₂²×C₁₉	1	2	yes	—
575	#485	C₂²×C₁₉	1	2	yes	complemented
576	#485	C₂²×C₁₉	1	2	yes	complemented
577	#484	C₂²×C₁₉	1	2	yes	complemented
578	#483	C₂²×C₁₉	1	2	yes	complemented
579	#482	C₂²×C₁₉	1	2	yes	—
580	#482	C₂²×C₁₉	1	2	yes	—
581	#479	C₂²×C₁₉	1	2	yes	complemented
582	#479	C₂²×C₁₉	1	2	yes	complemented
583	#477	C₂²×C₁₉	1	2	yes	complemented
584	#476	C₂²×C₁₉	1	2	yes	—
585	#470	C₂²×C₁₉	1	2	yes	—
586	#470	C₂²×C₁₉	1	2	yes	complemented
587	#470	C₂²×C₁₉	1	2	yes	complemented
588	#470	C₂²×C₁₉	1	2	yes	complemented
589	#468	C₂²×C₁₉	1	2	yes	—
590	#468	C₂²×C₁₉	1	2	yes	—
591	#468	C₂²×C₁₉	1	2	yes	—
592	#468	C₂²×C₁₉	1	2	yes	—
593	#467	C₂²×C₁₉	1	2	yes	—
594	#467	C₂²×C₁₉	1	2	yes	complemented
595	#467	C₂²×C₁₉	1	2	yes	complemented
596	#467	C₂²×C₁₉	1	2	yes	complemented
597	#465	C₂²×C₁₉	1	2	yes	—
598	#465	C₂²×C₁₉	1	2	yes	—
599	#465	C₂²×C₁₉	1	2	yes	—
600	#465	C₂²×C₁₉	1	2	yes	—
601	#464	C₂²×C₁₉	1	2	yes	—
602	#464	C₂²×C₁₉	1	2	yes	—
603	#462	C₂²×C₁₉	1	2	yes	complemented
604	#461	C₂²×C₁₉	1	2	yes	—
605	#452	C₂²×C₁₉	1	2	yes	—
606	#452	C₂²×C₁₉	1	2	yes	—
607	#451	C₂²×C₁₉	1	2	yes	—
608	#451	C₂²×C₁₉	1	2	yes	complemented
609	#451	C₂²×C₁₉	1	2	yes	complemented
610	#450	C₂²×C₁₉	1	2	yes	—
611	#448	C₂²×C₁₉	1	2	yes	—
612	#448	C₂²×C₁₉	1	2	yes	—
613	#441	C₂²×C₁₉	1	2	yes	complemented
614	#441	C₂²×C₁₉	1	2	yes	complemented
615	#440	C₂²×C₁₉	1	2	yes	—
616	#440	C₂²×C₁₉	1	2	yes	—
617	#435	C₂²×C₁₉	1	2	yes	—
618	#435	C₂²×C₁₉	1	2	yes	—
619	#435	C₂²×C₁₉	1	2	yes	complemented
620	#435	C₂²×C₁₉	1	2	yes	complemented
621	#428	C₂²×C₁₉	1	2	yes	complemented
622	#427	C₂²×C₁₉	1	1	yes	characteristic
623	#427	C₂²×C₁₉	1	1	yes	characteristic, complemented
624	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
625	#419	C₂²×C₁₉	1	1	yes	characteristic
626	#419	C₂²×C₁₉	1	1	yes	characteristic, complemented
627	#419	C₂²×C₁₉	1	1	yes	characteristic, complemented
628	#418	C₂²×C₁₉	1	1	yes	characteristic
629	#416	C₂²×C₁₉	1	2	yes	—
630	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
631	#408	C₂²×C₁₉	1	1	yes	characteristic
632	#408	C₂²×C₁₉	1	1	yes	characteristic, complemented
633	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic, complemented
634	C₂×C₁₉	—	4	1	no	—
635	C₂×C₁₉	—	4	2	no	—
636	C₂×C₁₉	—	4	1	no	—
637	C₂×C₁₉	—	4	1	no	—
638	C₂×C₁₉	—	8	2	no	—
639	C₂×C₁₉	#3496	1	1	yes	characteristic
640	C₂×C₁₉	#3586	1	2	yes	—
641	C₂×#41	C₂³×C₁₉	1	2	yes	—
642	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
643	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
644	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
645	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
646	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
647	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
648	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
649	#137	—	4	4	no	—
650	C₂×Q₁₆	—	4	2	no	—
651	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
652	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
653	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
654	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
655	C₂×SD₁₆	—	4	2	no	—
656	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
657	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
658	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
659	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
660	#131	—	4	2	no	—
661	#131	—	4	2	no	—
662	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
663	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
664	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
665	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
666	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
667	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
668	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
669	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
670	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
671	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
672	C₄⋊Q₈	—	2	1	no	—
673	C₄⋊Q₈	—	2	1	no	—
674	C₄⋊Q₈	—	2	1	no	—
675	C₄⋊Q₈	—	2	2	no	—
676	C₄⋊Q₈	—	2	2	no	—
677	C₄⋊Q₈	—	2	2	no	—
678	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
679	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
680	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
681	#127	—	2	1	no	—
682	#127	D₄×C₁₉	1	1	yes	characteristic
683	#126	—	2	2	no	—
684	#126	—	2	2	no	—
685	#126	—	2	2	no	—
686	#126	—	2	2	no	—
687	#126	—	2	2	no	—
688	#126	—	2	2	no	—
689	#126	—	2	2	no	—
690	#125	—	2	2	no	—
691	#125	—	2	2	no	—
692	#125	C₂³×C₁₉	1	2	yes	—
693	#124	—	2	1	no	—
694	#124	—	2	1	no	—
695	#124	—	2	1	no	—
696	#124	—	2	1	no	—
697	#124	—	2	2	no	—
698	#124	—	2	2	no	—
699	#124	—	2	2	no	—
700	#124	—	2	2	no	—
701	#124	D₄×C₁₉	1	1	yes	characteristic
702	#124	D₄×C₁₉	1	1	yes	characteristic
703	#124	C₂³×C₁₉	1	2	yes	—
704	#123	—	2	1	no	—
705	#123	—	2	1	no	—
706	#123	—	2	1	no	—
707	#123	—	2	1	no	—
708	#123	—	2	1	no	—
709	#123	—	2	1	no	—
710	#123	—	2	2	no	—
711	#123	—	2	2	no	—
712	#123	—	2	2	no	—
713	#123	—	2	2	no	—
714	#123	—	2	2	no	—
715	#123	—	2	2	no	—
716	C₂²⋊Q₈	—	2	2	no	—
717	C₂²⋊Q₈	—	2	2	no	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	—	2	2	no	—
720	C₂²⋊Q₈	—	2	2	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
724	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
725	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
726	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
727	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
728	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
729	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
730	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
731	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
732	#121	—	2	2	no	—
733	#121	—	2	2	no	—
734	#121	—	2	2	no	—
735	#121	—	2	2	no	—
736	#121	—	2	2	no	—
737	#121	—	2	2	no	—
738	#121	D₄×C₁₉	1	2	yes	—
739	#121	D₄×C₁₉	1	2	yes	—
740	#121	C₂³×C₁₉	1	2	yes	—
741	#121	C₂³×C₁₉	1	2	yes	—
742	#121	C₂³×C₁₉	1	2	yes	—
743	#120	—	2	1	no	—
744	#120	—	2	1	no	—
745	#120	—	2	2	no	—
746	C₄×Q₈	—	2	2	no	—
747	C₄×Q₈	—	2	2	no	—
748	C₄×Q₈	—	2	2	no	—
749	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
750	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
751	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
752	C₄×D₄	—	2	2	no	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	C₂³×C₁₉	1	2	yes	—
758	C₄×D₄	C₂³×C₁₉	1	2	yes	—
759	C₄×D₄	C₂³×C₁₉	1	2	yes	—
760	#117	—	2	2	no	—
761	#117	—	2	2	no	—
762	#117	—	2	2	no	—
763	#117	C₂³×C₁₉	1	1	yes	characteristic
764	#117	C₂³×C₁₉	1	1	yes	characteristic
765	#117	C₂³×C₁₉	1	1	yes	characteristic
766	#117	C₂³×C₁₉	1	1	yes	characteristic
767	#117	C₂³×C₁₉	1	2	yes	—
768	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
769	C₂×C₂²⋊C₄	—	2	2	no	—
770	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
771	#107	C₂³×C₁₉	1	2	yes	—
772	#107	C₂³×C₁₉	1	2	yes	—
773	#107	C₂³×C₁₉	1	2	yes	—
774	#107	C₂³×C₁₉	1	2	yes	—
775	#106	C₂³×C₁₉	1	2	yes	—
776	#106	C₂³×C₁₉	1	2	yes	—
777	#106	C₂³×C₁₉	1	2	yes	—
778	#106	C₂³×C₁₉	1	2	yes	—
779	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
780	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
781	#103	C₂³×C₁₉	1	2	yes	—
782	#103	C₂³×C₁₉	1	2	yes	—
783	#103	C₂³×C₁₉	1	2	yes	—
784	#103	C₂³×C₁₉	1	2	yes	—
785	#103	C₂³×C₁₉	1	2	yes	—
786	#103	C₂³×C₁₉	1	2	yes	—
787	#103	C₂³×C₁₉	1	2	yes	—
788	#103	C₂³×C₁₉	1	2	yes	—
789	#103	C₂³×C₁₉	1	2	yes	—
790	#103	C₂³×C₁₉	1	2	yes	—
791	#103	C₂³×C₁₉	1	2	yes	—
792	#103	C₂³×C₁₉	1	2	yes	—
793	#102	C₂³×C₁₉	1	2	yes	—
794	#102	C₂³×C₁₉	1	2	yes	—
795	#102	C₂³×C₁₉	1	2	yes	—
796	#102	C₂³×C₁₉	1	2	yes	—
797	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
798	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
799	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
800	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
801	#97	C₂³×C₁₉	1	2	yes	—
802	#97	C₂³×C₁₉	1	2	yes	—
803	C₁₉	#62337	1	1	yes	characteristic, direct product factor, Sylow
804	C₂⁴	—	2	1	no	—
805	#41	—	4	1	no	—
806	#41	—	4	1	no	—
807	#41	—	4	1	no	—
808	#41	—	4	1	no	—
809	#41	—	4	2	no	—
810	#41	—	4	2	no	—
811	C₂×Q₈	—	2	2	no	—
812	C₂×Q₈	—	2	1	no	—
813	C₂×Q₈	—	2	1	no	—
814	C₂×Q₈	—	2	1	no	—
815	C₂×Q₈	—	2	2	no	—
816	C₂×Q₈	—	4	1	no	—
817	C₂×Q₈	—	4	1	no	—
818	C₂×Q₈	—	4	1	no	—
819	C₂×Q₈	—	4	2	no	—
820	C₂×Q₈	—	4	1	no	—
821	C₂×Q₈	—	4	1	no	—
822	C₂×Q₈	—	4	1	no	—
823	C₂×Q₈	—	4	2	no	—
824	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
825	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
826	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
827	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
828	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	1	no	—
834	C₂×D₄	—	4	1	no	—
835	C₂×D₄	—	4	1	no	—
836	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
837	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
838	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
839	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
840	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
841	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
842	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
843	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
856	Q₁₆	—	2	4	no	—
857	Q₁₆	—	4	2	no	—
858	Q₁₆	—	4	2	no	—
859	Q₁₆	—	4	2	no	—
860	SD₁₆	—	2	4	no	—
861	SD₁₆	—	4	2	no	—
862	SD₁₆	—	4	2	no	—
863	SD₁₆	—	4	2	no	—
864	M₁₆	—	2	4	no	—
865	M₁₆	—	4	1	no	—
866	M₁₆	—	4	1	no	—
867	M₁₆	—	4	1	no	—
868	M₁₆	—	4	1	no	—
869	C₂×C₈	—	2	2	no	—
870	C₂×C₈	—	2	2	no	—
871	C₂×C₈	—	2	2	no	—
872	C₂×C₈	—	4	1	no	—
873	C₂×C₈	—	4	2	no	—
874	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
875	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
876	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
877	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
878	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
879	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
899	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
900	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
901	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
902	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
903	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	1	no	—
909	C₂²⋊C₄	—	2	1	no	—
910	C₂²⋊C₄	—	2	1	no	—
911	C₂²⋊C₄	—	2	1	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
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	C₂×D₄×C₁₉	1	2	yes	—
925	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
926	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
927	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
928	C₄²	—	2	1	no	—
929	C₄²	—	2	2	no	—
930	C₄²	—	2	2	no	—
931	C₄²	—	2	2	no	—
932	C₄²	—	2	1	no	—
933	C₄²	—	2	1	no	—
934	C₄²	—	2	1	no	—
935	C₄²	—	2	2	no	—
936	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
937	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
938	C₄²	C₂⁴×C₁₉	1	2	yes	—
939	C₂³	—	2	2	no	—
940	C₂³	—	8	1	no	—
941	C₂³	—	8	2	no	—
942	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
943	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
944	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
945	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
946	Q₈	—	2	2	no	—
947	Q₈	—	2	2	no	—
948	Q₈	—	2	2	no	—
949	Q₈	—	2	2	no	—
950	Q₈	—	2	2	no	—
951	Q₈	—	2	2	no	—
952	Q₈	—	4	1	no	—
953	Q₈	—	4	1	no	—
954	Q₈	—	4	4	no	—
955	Q₈	—	8	2	no	—
956	Q₈	—	8	1	no	—
957	Q₈	—	8	1	no	—
958	Q₈	—	8	1	no	—
959	D₄	—	2	2	no	—
960	D₄	—	2	2	no	—
961	D₄	—	4	2	no	—
962	D₄	—	4	1	no	—
963	D₄	—	4	1	no	—
964	D₄	—	4	1	no	—
965	D₄	—	4	1	no	—
966	D₄	—	4	2	no	—
967	D₄	—	4	2	no	—
968	D₄	—	8	1	no	—
969	D₄	—	8	2	no	—
970	D₄	—	8	2	no	—
971	D₄	—	8	2	no	—
972	D₄	—	8	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	4	2	no	—
989	C₂×C₄	—	8	2	no	—
990	C₂×C₄	—	8	2	no	—
991	C₂×C₄	—	8	1	no	—
992	C₂×C₄	—	8	1	no	—
993	C₂×C₄	—	8	2	no	—
994	C₂×C₄	—	8	1	no	—
995	C₂×C₄	—	8	2	no	—
996	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
997	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
998	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
999	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1000	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1001	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1002	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1003	C₈	—	2	1	no	—
1004	C₈	—	2	1	no	—
1005	C₈	—	2	1	no	—
1006	C₈	—	2	2	no	—
1007	C₈	—	2	2	no	—
1008	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	2	2	no	—
1018	C₂²	—	4	2	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	16	2	no	—
1022	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1023	C₄	—	2	2	no	—
1024	C₄	—	2	1	no	—
1025	C₄	—	2	1	no	—
1026	C₄	—	2	1	no	—
1027	C₄	—	2	2	no	—
1028	C₄	—	2	2	no	—
1029	C₄	—	4	2	no	—
1030	C₄	—	4	2	no	—
1031	C₄	—	4	2	no	—
1032	C₄	—	4	2	no	—
1033	C₄	—	4	2	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	2	no	—
1036	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1037	C₄	C₁₉×#585	1	1	yes	characteristic
1038	C₂	—	4	1	no	—
1039	C₂	—	4	1	no	—
1040	C₂	—	4	2	no	—
1041	C₂	—	4	1	no	—
1042	C₂	—	8	2	no	—
1043	C₂	C₁₉×#3496	1	1	yes	characteristic
1044	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×#3551	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#532 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3550	C₂	semidirect
3. C₁₉×#3350	C₂	semidirect
4. C₁₉×#3349	C₂	semidirect
5. C₁₉×#3320	C₂	semidirect
6. C₁₉×#3313	C₂	semidirect
7. C₁₉×#3312	C₂	semidirect
8. C₁₉×#3311	C₂	semidirect
9. C₁₉×#3270	C₂	semidirect
10. C₁₉×#3266	C₂	semidirect
11. C₁₉×#3252	C₂	semidirect
12. C₁₉×#3202	C₂	semidirect
13. C₁₉×#3201	C₂	semidirect
14. C₁₉×#3200	C₂	semidirect
15. C₁₉×#3181	C₂	semidirect
16. C₁₉×#3063	C₂	semidirect
17. C₁₉×#3059	C₂	semidirect
18. C₁₉×#3057	C₂	semidirect
19. C₁₉×#2932	C₂	semidirect
21. C₂²×Q₁₆×C₁₉	C₂²	semidirect
24. C₂×C₁₉×#131	C₂²	semidirect
32. C₁₉×#556	C₂²	semidirect
38. D₄×Q₈×C₁₉	C₂²	semidirect
49. C₁₉×#536	C₂²	semidirect
51. C₁₉×#533	C₂²	semidirect
54. C₁₉×#501	C₂²	semidirect
56. C₁₉×#491	C₂²	semidirect
60. C₁₉×#485	C₂²	semidirect
61. C₁₉×#485	C₂²	semidirect
62. C₁₉×#484	C₂²	semidirect
63. C₁₉×#483	C₂²	semidirect
66. C₁₉×#479	C₂²	semidirect
67. C₁₉×#479	C₂²	semidirect
68. C₁₉×#477	C₂²	semidirect
71. C₁₉×#470	C₂²	semidirect
72. C₁₉×#470	C₂²	semidirect
73. C₁₉×#470	C₂²	semidirect
79. C₁₉×#467	C₂²	semidirect
80. C₁₉×#467	C₂²	semidirect
81. C₁₉×#467	C₂²	semidirect
88. C₁₉×#462	C₂²	semidirect
93. C₁₉×#451	C₂²	semidirect
94. C₁₉×#451	C₂²	semidirect
98. C₁₉×#441	C₂²	semidirect
99. C₁₉×#441	C₂²	semidirect
104. C₁₉×#435	C₂²	semidirect
105. C₁₉×#435	C₂²	semidirect
106. C₁₉×#428	C₂²	semidirect
108. C₁₉×#427	C₂²	semidirect
109. C₁₉×#423	C₂²	semidirect
111. C₁₉×#419	C₂²	semidirect
112. C₁₉×#419	C₂²	semidirect
115. C₂×C₁₉×#103	C₂²	semidirect
117. C₁₉×#408	C₂²	semidirect
118. C₂×C₁₉×#97	C₂²	semidirect
416. #62337	C₁₉	direct (N × H)
488. #3550	C₂×C₁₉	semidirect
489. #3350	C₂×C₁₉	semidirect
490. #3349	C₂×C₁₉	semidirect
491. #3320	C₂×C₁₉	semidirect
492. #3313	C₂×C₁₉	semidirect
493. #3312	C₂×C₁₉	semidirect
494. #3311	C₂×C₁₉	semidirect
495. #3270	C₂×C₁₉	semidirect
496. #3266	C₂×C₁₉	semidirect
497. #3252	C₂×C₁₉	semidirect
498. #3202	C₂×C₁₉	semidirect
499. #3201	C₂×C₁₉	semidirect
500. #3200	C₂×C₁₉	semidirect
501. #3181	C₂×C₁₉	semidirect
502. #3063	C₂×C₁₉	semidirect
503. #3059	C₂×C₁₉	semidirect
504. #3057	C₂×C₁₉	semidirect
505. #2932	C₂×C₁₉	semidirect
536. C₂²×Q₁₆	C₂²×C₁₉	semidirect
539. C₂×#131	C₂²×C₁₉	semidirect
547. #556	C₂²×C₁₉	semidirect
553. D₄×Q₈	C₂²×C₁₉	semidirect
564. #536	C₂²×C₁₉	semidirect
566. #533	C₂²×C₁₉	semidirect
569. #501	C₂²×C₁₉	semidirect
571. #491	C₂²×C₁₉	semidirect
575. #485	C₂²×C₁₉	semidirect
576. #485	C₂²×C₁₉	semidirect
577. #484	C₂²×C₁₉	semidirect
578. #483	C₂²×C₁₉	semidirect
581. #479	C₂²×C₁₉	semidirect
582. #479	C₂²×C₁₉	semidirect
583. #477	C₂²×C₁₉	semidirect
586. #470	C₂²×C₁₉	semidirect
587. #470	C₂²×C₁₉	semidirect
588. #470	C₂²×C₁₉	semidirect
594. #467	C₂²×C₁₉	semidirect
595. #467	C₂²×C₁₉	semidirect
596. #467	C₂²×C₁₉	semidirect
603. #462	C₂²×C₁₉	semidirect
608. #451	C₂²×C₁₉	semidirect
609. #451	C₂²×C₁₉	semidirect
613. #441	C₂²×C₁₉	semidirect
614. #441	C₂²×C₁₉	semidirect
619. #435	C₂²×C₁₉	semidirect
620. #435	C₂²×C₁₉	semidirect
621. #428	C₂²×C₁₉	semidirect
623. #427	C₂²×C₁₉	semidirect
624. #423	C₂²×C₁₉	semidirect
626. #419	C₂²×C₁₉	semidirect
627. #419	C₂²×C₁₉	semidirect
630. C₂×#103	C₂²×C₁₉	semidirect
632. #408	C₂²×C₁₉	semidirect
633. C₂×#97	C₂²×C₁₉	semidirect
803. C₁₉	#62337	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×#3551	2
C₁₉×#3550	2
C₁₉×#3350	2
C₁₉×#3349	2
C₁₉×#3320	2
C₁₉×#3313	2
C₁₉×#3312	2
C₁₉×#3311	2
C₁₉×#3270	2
C₁₉×#3266	2
C₁₉×#3252	2
C₁₉×#3202	2
C₁₉×#3201	2
C₁₉×#3200	2
C₁₉×#3181	2
C₁₉×#3063	2
C₁₉×#3059	2
C₁₉×#3057	2
C₁₉×#2932	2
#62337	19

Subgroups — C19×#62337 #18068296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62337 #18068296