Subgroups — C₁₉×#62335 #18068294

Order 4864.

1776 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3547	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3348	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3344	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3321	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3316	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3315	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3312	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3270	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3269	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3256	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3255	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3204	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3202	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3201	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3181	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3063	C₂	1	2	yes	maximal, complemented
17	C₁₉×#3060	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#3059	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	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
22	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
25	C₁₉×#562	—	2	2	no	—
26	C₁₉×#562	—	2	2	no	—
27	C₁₉×#555	—	2	2	no	—
28	C₁₉×#555	C₂²	1	2	yes	—
29	C₁₉×#554	C₂²	1	2	yes	—
30	C₁₉×#553	—	2	2	no	—
31	C₁₉×#552	C₂²	1	2	yes	—
32	C₁₉×#552	C₂²	1	2	yes	—
33	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
34	C₁₉×#548	C₂²	1	2	yes	—
35	C₁₉×#548	C₂²	1	2	yes	—
36	C₁₉×#547	C₂²	1	2	yes	—
37	C₁₉×#544	—	2	2	no	—
38	C₁₉×#542	—	2	2	no	—
39	C₁₉×#542	—	2	2	no	—
40	C₁₉×#540	—	2	2	no	—
41	C₁₉×#537	C₂²	1	2	yes	—
42	C₁₉×#537	C₂²	1	2	yes	—
43	C₁₉×#536	C₂²	1	2	yes	—
44	C₁₉×#536	C₂²	1	2	yes	—
45	C₁₉×#533	C₂²	1	2	yes	—
46	C₁₉×#532	C₂²	1	1	yes	characteristic
47	C₁₉×#529	C₂²	1	2	yes	—
48	C₁₉×#501	C₂²	1	2	yes	—
49	C₁₉×#497	C₂²	1	2	yes	—
50	C₁₉×#491	C₂²	1	2	yes	—
51	C₁₉×#489	C₂²	1	2	yes	—
52	C₁₉×#485	C₂²	1	2	yes	—
53	C₁₉×#485	C₂²	1	2	yes	—
54	C₁₉×#485	C₂²	1	2	yes	—
55	C₁₉×#484	C₂²	1	2	yes	—
56	C₁₉×#483	C₂²	1	2	yes	—
57	C₁₉×#483	C₂²	1	2	yes	—
58	C₁₉×#482	C₂²	1	2	yes	—
59	C₁₉×#481	C₂²	1	2	yes	—
60	C₁₉×#479	C₂²	1	2	yes	—
61	C₁₉×#478	C₂²	1	2	yes	—
62	C₁₉×#475	C₂²	1	2	yes	—
63	C₁₉×#475	C₂²	1	2	yes	—
64	C₁₉×#470	C₂²	1	2	yes	—
65	C₁₉×#470	C₂²	1	1	yes	characteristic
66	C₁₉×#470	C₂²	1	1	yes	characteristic
67	C₁₉×#470	C₂²	1	1	yes	characteristic
68	C₁₉×#470	C₂²	1	2	yes	—
69	C₁₉×#470	C₂²	1	1	yes	characteristic
70	C₁₉×#470	C₂²	1	1	yes	characteristic
71	C₁₉×#470	C₂²	1	1	yes	characteristic
72	C₁₉×#469	C₂²	1	1	yes	characteristic
73	C₁₉×#469	C₂²	1	1	yes	characteristic
74	C₁₉×#468	C₂²	1	2	yes	—
75	C₁₉×#468	C₂²	1	2	yes	—
76	C₁₉×#467	C₂²	1	2	yes	—
77	C₁₉×#467	C₂²	1	2	yes	—
78	C₁₉×#467	C₂²	1	2	yes	—
79	C₁₉×#467	C₂²	1	2	yes	—
80	C₁₉×#465	C₂²	1	2	yes	—
81	C₁₉×#465	C₂²	1	2	yes	—
82	C₁₉×#465	C₂²	1	2	yes	—
83	C₁₉×#465	C₂²	1	2	yes	—
84	C₁₉×#464	C₂²	1	2	yes	—
85	C₁₉×#463	C₂²	1	2	yes	—
86	C₁₉×#462	C₂²	1	2	yes	—
87	C₁₉×#462	C₂²	1	2	yes	—
88	C₁₉×#452	C₂²	1	2	yes	—
89	C₁₉×#452	C₂²	1	2	yes	—
90	C₁₉×#452	C₂²	1	2	yes	—
91	C₁₉×#451	C₂²	1	2	yes	—
92	C₁₉×#451	C₂²	1	2	yes	—
93	C₁₉×#451	C₂²	1	2	yes	—
94	C₁₉×#449	C₂²	1	2	yes	—
95	C₁₉×#448	C₂²	1	2	yes	—
96	C₁₉×#441	C₂²	1	2	yes	—
97	C₁₉×#441	C₂²	1	2	yes	—
98	C₁₉×#440	C₂²	1	2	yes	—
99	C₁₉×#440	C₂²	1	2	yes	—
100	C₁₉×#435	C₂²	1	2	yes	—
101	C₁₉×#435	C₂²	1	2	yes	—
102	C₁₉×#435	C₂²	1	2	yes	—
103	C₁₉×#435	C₂²	1	2	yes	—
104	C₁₉×#428	C₂²	1	2	yes	—
105	C₁₉×#427	C₂²	1	1	yes	characteristic
106	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
107	C₁₉×#423	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	—
111	C₂×C₁₉×#103	C₂²	1	2	yes	—
112	C₁₉×#408	C₂²	1	1	yes	characteristic
113	C₁₉×#408	C₂²	1	1	yes	characteristic
114	C₂×C₁₉×#97	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	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
119	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
120	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
121	C₁₉×#137	—	4	4	no	—
122	C₁₉×#135	—	4	2	no	—
123	C₂×Q₁₆×C₁₉	—	4	2	no	—
124	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
126	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
129	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
130	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
132	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
133	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
134	C₁₉×#131	—	4	2	no	—
135	C₁₉×#131	—	4	2	no	—
136	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
137	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
146	C₁₉×C₄⋊Q₈	—	2	2	no	—
147	C₁₉×C₄⋊Q₈	—	2	2	no	—
148	C₁₉×C₄⋊Q₈	—	2	2	no	—
149	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
150	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
151	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
152	C₁₉×#127	D₄	1	1	yes	characteristic
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	C₂³	1	2	yes	—
161	C₁₉×#124	—	2	2	no	—
162	C₁₉×#124	—	2	2	no	—
163	C₁₉×#124	—	2	2	no	—
164	C₁₉×#124	—	2	2	no	—
165	C₁₉×#124	—	2	2	no	—
166	C₁₉×#124	—	2	2	no	—
167	C₁₉×#124	D₄	1	1	yes	characteristic
168	C₁₉×#124	D₄	1	1	yes	characteristic
169	C₁₉×#124	C₂³	1	2	yes	—
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	—	2	2	no	—
178	C₁₉×#123	—	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	—	2	2	no	—
186	C₁₉×C₂²⋊Q₈	—	2	2	no	—
187	C₁₉×C₂²⋊Q₈	—	2	2	no	—
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×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
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	—	2	2	no	—
204	C₁₉×#121	—	2	2	no	—
205	C₁₉×#121	—	2	2	no	—
206	C₁₉×#121	—	2	2	no	—
207	C₁₉×#121	D₄	1	2	yes	—
208	C₁₉×#121	D₄	1	2	yes	—
209	C₁₉×#121	C₂³	1	2	yes	—
210	C₁₉×#121	C₂³	1	2	yes	—
211	C₁₉×#121	C₂³	1	2	yes	—
212	C₄×Q₈×C₁₉	—	2	2	no	—
213	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
214	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
215	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
216	C₄×D₄×C₁₉	—	2	2	no	—
217	C₄×D₄×C₁₉	—	2	2	no	—
218	C₄×D₄×C₁₉	—	2	2	no	—
219	C₄×D₄×C₁₉	—	2	2	no	—
220	C₄×D₄×C₁₉	—	2	2	no	—
221	C₄×D₄×C₁₉	C₂³	1	2	yes	—
222	C₄×D₄×C₁₉	C₂³	1	2	yes	—
223	C₄×D₄×C₁₉	C₂³	1	2	yes	—
224	C₁₉×#117	—	2	2	no	—
225	C₁₉×#117	—	2	2	no	—
226	C₁₉×#117	—	2	2	no	—
227	C₁₉×#117	—	2	2	no	—
228	C₁₉×#117	—	2	2	no	—
229	C₁₉×#117	C₂³	1	2	yes	—
230	C₁₉×#117	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
232	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
234	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
235	C₁₉×#107	C₂³	1	2	yes	—
236	C₁₉×#107	C₂³	1	2	yes	—
237	C₁₉×#107	C₂³	1	2	yes	—
238	C₁₉×#106	C₂³	1	2	yes	—
239	C₁₉×#106	C₂³	1	1	yes	characteristic
240	C₁₉×#106	C₂³	1	1	yes	characteristic
241	C₁₉×#106	C₂³	1	1	yes	characteristic
242	C₁₉×#106	C₂³	1	1	yes	characteristic
243	C₁₉×#106	C₂³	1	2	yes	—
244	C₁₉×#106	C₂³	1	2	yes	—
245	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
246	C₁₉×C₄⋊C₈	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×#103	C₂³	1	2	yes	—
255	C₁₉×#103	C₂³	1	2	yes	—
256	C₁₉×#103	C₂³	1	2	yes	—
257	C₁₉×#103	C₂³	1	2	yes	—
258	C₁₉×#103	C₂³	1	2	yes	—
259	C₁₉×#102	C₂³	1	2	yes	—
260	C₁₉×#102	C₂³	1	2	yes	—
261	C₁₉×#102	C₂³	1	2	yes	—
262	C₁₉×#102	C₂³	1	2	yes	—
263	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
264	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
265	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
266	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
267	C₁₉×#97	C₂³	1	2	yes	—
268	C₁₉×#97	C₂³	1	2	yes	—
269	#41×C₁₉	—	4	1	no	—
270	#41×C₁₉	—	4	1	no	—
271	#41×C₁₉	—	4	1	no	—
272	#41×C₁₉	—	4	1	no	—
273	#41×C₁₉	—	4	2	no	—
274	#41×C₁₉	—	4	2	no	—
275	#41×C₁₉	—	4	2	no	—
276	#41×C₁₉	—	4	2	no	—
277	C₂×Q₈×C₁₉	—	2	2	no	—
278	C₂×Q₈×C₁₉	—	2	2	no	—
279	C₂×Q₈×C₁₉	—	2	2	no	—
280	C₂×Q₈×C₁₉	—	4	2	no	—
281	C₂×Q₈×C₁₉	—	4	2	no	—
282	C₂×Q₈×C₁₉	—	4	2	no	—
283	C₂×Q₈×C₁₉	—	4	2	no	—
284	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
285	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
286	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
287	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
288	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
289	C₂×D₄×C₁₉	—	2	2	no	—
290	C₂×D₄×C₁₉	—	2	2	no	—
291	C₂×D₄×C₁₉	—	2	2	no	—
292	C₂×D₄×C₁₉	—	2	2	no	—
293	C₂×D₄×C₁₉	—	2	2	no	—
294	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
295	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
296	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
297	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
298	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
299	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
300	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
301	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₁₉	—	2	2	no	—
303	C₂²×C₄×C₁₉	—	2	2	no	—
304	C₂²×C₄×C₁₉	—	2	2	no	—
305	C₂²×C₄×C₁₉	—	2	2	no	—
306	C₂²×C₄×C₁₉	—	2	2	no	—
307	C₂²×C₄×C₁₉	—	2	2	no	—
308	C₂²×C₄×C₁₉	—	2	2	no	—
309	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
310	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
314	Q₁₆×C₁₉	—	2	4	no	—
315	Q₁₆×C₁₉	—	4	1	no	—
316	Q₁₆×C₁₉	—	4	1	no	—
317	Q₁₆×C₁₉	—	4	2	no	—
318	Q₁₆×C₁₉	—	4	1	no	—
319	Q₁₆×C₁₉	—	4	2	no	—
320	SD₁₆×C₁₉	—	2	4	no	—
321	SD₁₆×C₁₉	—	4	2	no	—
322	SD₁₆×C₁₉	—	4	2	no	—
323	D₈×C₁₉	—	4	1	no	—
324	M₁₆×C₁₉	—	2	4	no	—
325	M₁₆×C₁₉	—	4	1	no	—
326	M₁₆×C₁₉	—	4	1	no	—
327	M₁₆×C₁₉	—	4	1	no	—
328	M₁₆×C₁₉	—	4	1	no	—
329	C₂×C₈×C₁₉	—	2	2	no	—
330	C₂×C₈×C₁₉	—	2	2	no	—
331	C₂×C₈×C₁₉	—	2	2	no	—
332	C₂×C₈×C₁₉	—	4	1	no	—
333	C₂×C₈×C₁₉	—	4	2	no	—
334	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
335	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
336	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
337	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
338	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
339	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
352	C₄⋊C₄×C₁₉	—	2	2	no	—
353	C₄⋊C₄×C₁₉	—	2	2	no	—
354	C₄⋊C₄×C₁₉	—	2	2	no	—
355	C₄⋊C₄×C₁₉	—	2	2	no	—
356	C₄⋊C₄×C₁₉	—	2	2	no	—
357	C₄⋊C₄×C₁₉	—	2	2	no	—
358	C₄⋊C₄×C₁₉	—	2	2	no	—
359	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
362	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
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	—	2	2	no	—
374	C₂²⋊C₄×C₁₉	—	2	2	no	—
375	C₂²⋊C₄×C₁₉	—	2	2	no	—
376	C₂²⋊C₄×C₁₉	—	2	2	no	—
377	C₂²⋊C₄×C₁₉	—	2	2	no	—
378	C₂²⋊C₄×C₁₉	—	2	2	no	—
379	C₂²⋊C₄×C₁₉	—	2	2	no	—
380	C₂²⋊C₄×C₁₉	—	2	2	no	—
381	C₂²⋊C₄×C₁₉	—	2	2	no	—
382	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
383	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
384	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
385	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
386	C₄²×C₁₉	—	2	2	no	—
387	C₄²×C₁₉	—	2	2	no	—
388	C₄²×C₁₉	—	2	2	no	—
389	C₄²×C₁₉	—	2	2	no	—
390	C₄²×C₁₉	—	2	2	no	—
391	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
392	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₁₉	C₂⁴	1	2	yes	—
394	#62335	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
395	C₂³×C₁₉	—	2	2	no	—
396	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
397	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
398	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
399	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
400	Q₈×C₁₉	—	2	2	no	—
401	Q₈×C₁₉	—	2	2	no	—
402	Q₈×C₁₉	—	2	2	no	—
403	Q₈×C₁₉	—	2	2	no	—
404	Q₈×C₁₉	—	2	2	no	—
405	Q₈×C₁₉	—	2	2	no	—
406	Q₈×C₁₉	—	4	1	no	—
407	Q₈×C₁₉	—	4	1	no	—
408	Q₈×C₁₉	—	8	2	no	—
409	Q₈×C₁₉	—	8	2	no	—
410	Q₈×C₁₉	—	8	2	no	—
411	D₄×C₁₉	—	2	2	no	—
412	D₄×C₁₉	—	2	2	no	—
413	D₄×C₁₉	—	4	2	no	—
414	D₄×C₁₉	—	4	2	no	—
415	D₄×C₁₉	—	4	1	no	—
416	D₄×C₁₉	—	4	2	no	—
417	D₄×C₁₉	—	4	1	no	—
418	D₄×C₁₉	—	4	1	no	—
419	D₄×C₁₉	—	4	1	no	—
420	D₄×C₁₉	—	8	2	no	—
421	D₄×C₁₉	—	8	2	no	—
422	D₄×C₁₉	—	8	2	no	—
423	D₄×C₁₉	—	8	2	no	—
424	D₄×C₁₉	—	8	2	no	—
425	C₂×C₄×C₁₉	—	2	1	no	—
426	C₂×C₄×C₁₉	—	2	1	no	—
427	C₂×C₄×C₁₉	—	2	1	no	—
428	C₂×C₄×C₁₉	—	2	2	no	—
429	C₂×C₄×C₁₉	—	2	1	no	—
430	C₂×C₄×C₁₉	—	2	1	no	—
431	C₂×C₄×C₁₉	—	2	2	no	—
432	C₂×C₄×C₁₉	—	2	1	no	—
433	C₂×C₄×C₁₉	—	2	2	no	—
434	C₂×C₄×C₁₉	—	2	2	no	—
435	C₂×C₄×C₁₉	—	2	2	no	—
436	C₂×C₄×C₁₉	—	2	2	no	—
437	C₂×C₄×C₁₉	—	2	2	no	—
438	C₂×C₄×C₁₉	—	2	2	no	—
439	C₂×C₄×C₁₉	—	2	2	no	—
440	C₂×C₄×C₁₉	—	4	2	no	—
441	C₂×C₄×C₁₉	—	4	4	no	—
442	C₂×C₄×C₁₉	—	8	2	no	—
443	C₂×C₄×C₁₉	—	8	2	no	—
444	C₂×C₄×C₁₉	—	8	2	no	—
445	C₂×C₄×C₁₉	—	8	2	no	—
446	C₂×C₄×C₁₉	—	8	2	no	—
447	C₂×C₄×C₁₉	—	8	2	no	—
448	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
449	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
451	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
455	C₈×C₁₉	—	2	1	no	—
456	C₈×C₁₉	—	2	1	no	—
457	C₈×C₁₉	—	2	1	no	—
458	C₈×C₁₉	—	2	2	no	—
459	C₈×C₁₉	—	2	2	no	—
460	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
461	#3547	C₂×C₁₉	1	2	yes	complemented
462	#3348	C₂×C₁₉	1	2	yes	complemented
463	#3344	C₂×C₁₉	1	2	yes	complemented
464	#3321	C₂×C₁₉	1	2	yes	complemented
465	#3316	C₂×C₁₉	1	2	yes	complemented
466	#3315	C₂×C₁₉	1	2	yes	complemented
467	#3312	C₂×C₁₉	1	2	yes	complemented
468	#3270	C₂×C₁₉	1	2	yes	complemented
469	#3269	C₂×C₁₉	1	2	yes	complemented
470	#3256	C₂×C₁₉	1	1	yes	characteristic, complemented
471	#3255	C₂×C₁₉	1	1	yes	characteristic, complemented
472	#3204	C₂×C₁₉	1	1	yes	characteristic, complemented
473	#3202	C₂×C₁₉	1	1	yes	characteristic, complemented
474	#3201	C₂×C₁₉	1	2	yes	complemented
475	#3181	C₂×C₁₉	1	2	yes	complemented
476	#3063	C₂×C₁₉	1	2	yes	complemented
477	#3060	C₂×C₁₉	1	1	yes	characteristic, complemented
478	#3059	C₂×C₁₉	1	1	yes	characteristic, complemented
479	#2932	C₂×C₁₉	1	1	yes	characteristic, complemented
480	C₂²×C₁₉	—	2	2	no	—
481	C₂²×C₁₉	—	2	2	no	—
482	C₂²×C₁₉	—	2	2	no	—
483	C₂²×C₁₉	—	2	2	no	—
484	C₂²×C₁₉	—	2	2	no	—
485	C₂²×C₁₉	—	2	1	no	—
486	C₂²×C₁₉	—	2	2	no	—
487	C₂²×C₁₉	—	2	1	no	—
488	C₂²×C₁₉	—	2	1	no	—
489	C₂²×C₁₉	—	4	2	no	—
490	C₂²×C₁₉	—	4	2	no	—
491	C₂²×C₁₉	—	4	2	no	—
492	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
493	C₄×C₁₉	—	2	2	no	—
494	C₄×C₁₉	—	2	2	no	—
495	C₄×C₁₉	—	2	1	no	—
496	C₄×C₁₉	—	2	2	no	—
497	C₄×C₁₉	—	2	1	no	—
498	C₄×C₁₉	—	2	1	no	—
499	C₄×C₁₉	—	4	2	no	—
500	C₄×C₁₉	—	4	2	no	—
501	C₄×C₁₉	—	4	2	no	—
502	C₄×C₁₉	—	4	2	no	—
503	C₄×C₁₉	—	4	2	no	—
504	C₄×C₁₉	—	4	2	no	—
505	C₄×C₁₉	—	4	2	no	—
506	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
507	C₄×C₁₉	#585	1	1	yes	characteristic
508	C₂×#137	C₂²×C₁₉	1	2	yes	—
509	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
510	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
511	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
512	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
513	#562	—	2	2	no	—
514	#562	—	2	2	no	—
515	#555	—	2	2	no	—
516	#555	C₂²×C₁₉	1	2	yes	—
517	#554	C₂²×C₁₉	1	2	yes	—
518	#553	—	2	2	no	—
519	#552	C₂²×C₁₉	1	2	yes	—
520	#552	C₂²×C₁₉	1	2	yes	—
521	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
522	#548	C₂²×C₁₉	1	2	yes	—
523	#548	C₂²×C₁₉	1	2	yes	—
524	#547	C₂²×C₁₉	1	2	yes	—
525	#544	—	2	2	no	—
526	#542	—	2	2	no	—
527	#542	—	2	2	no	—
528	#540	—	2	2	no	—
529	#537	C₂²×C₁₉	1	2	yes	—
530	#537	C₂²×C₁₉	1	2	yes	—
531	#536	C₂²×C₁₉	1	2	yes	—
532	#536	C₂²×C₁₉	1	2	yes	—
533	#533	C₂²×C₁₉	1	2	yes	—
534	#532	C₂²×C₁₉	1	1	yes	characteristic
535	#529	C₂²×C₁₉	1	2	yes	—
536	#501	C₂²×C₁₉	1	2	yes	—
537	#497	C₂²×C₁₉	1	2	yes	—
538	#491	C₂²×C₁₉	1	2	yes	—
539	#489	C₂²×C₁₉	1	2	yes	—
540	#485	C₂²×C₁₉	1	2	yes	—
541	#485	C₂²×C₁₉	1	2	yes	—
542	#485	C₂²×C₁₉	1	2	yes	—
543	#484	C₂²×C₁₉	1	2	yes	—
544	#483	C₂²×C₁₉	1	2	yes	—
545	#483	C₂²×C₁₉	1	2	yes	—
546	#482	C₂²×C₁₉	1	2	yes	—
547	#481	C₂²×C₁₉	1	2	yes	—
548	#479	C₂²×C₁₉	1	2	yes	—
549	#478	C₂²×C₁₉	1	2	yes	—
550	#475	C₂²×C₁₉	1	2	yes	—
551	#475	C₂²×C₁₉	1	2	yes	—
552	#470	C₂²×C₁₉	1	2	yes	—
553	#470	C₂²×C₁₉	1	2	yes	—
554	#470	C₂²×C₁₉	1	1	yes	characteristic
555	#470	C₂²×C₁₉	1	1	yes	characteristic
556	#470	C₂²×C₁₉	1	1	yes	characteristic
557	#470	C₂²×C₁₉	1	1	yes	characteristic
558	#470	C₂²×C₁₉	1	1	yes	characteristic
559	#470	C₂²×C₁₉	1	1	yes	characteristic
560	#469	C₂²×C₁₉	1	1	yes	characteristic
561	#469	C₂²×C₁₉	1	1	yes	characteristic
562	#468	C₂²×C₁₉	1	2	yes	—
563	#468	C₂²×C₁₉	1	2	yes	—
564	#467	C₂²×C₁₉	1	2	yes	—
565	#467	C₂²×C₁₉	1	2	yes	—
566	#467	C₂²×C₁₉	1	2	yes	—
567	#467	C₂²×C₁₉	1	2	yes	—
568	#465	C₂²×C₁₉	1	2	yes	—
569	#465	C₂²×C₁₉	1	2	yes	—
570	#465	C₂²×C₁₉	1	2	yes	—
571	#465	C₂²×C₁₉	1	2	yes	—
572	#464	C₂²×C₁₉	1	2	yes	—
573	#463	C₂²×C₁₉	1	2	yes	—
574	#462	C₂²×C₁₉	1	2	yes	—
575	#462	C₂²×C₁₉	1	2	yes	—
576	#452	C₂²×C₁₉	1	2	yes	—
577	#452	C₂²×C₁₉	1	2	yes	—
578	#452	C₂²×C₁₉	1	2	yes	—
579	#451	C₂²×C₁₉	1	2	yes	—
580	#451	C₂²×C₁₉	1	2	yes	—
581	#451	C₂²×C₁₉	1	2	yes	—
582	#449	C₂²×C₁₉	1	2	yes	—
583	#448	C₂²×C₁₉	1	2	yes	—
584	#441	C₂²×C₁₉	1	2	yes	—
585	#441	C₂²×C₁₉	1	2	yes	—
586	#440	C₂²×C₁₉	1	2	yes	—
587	#440	C₂²×C₁₉	1	2	yes	—
588	#435	C₂²×C₁₉	1	2	yes	—
589	#435	C₂²×C₁₉	1	2	yes	—
590	#435	C₂²×C₁₉	1	2	yes	—
591	#435	C₂²×C₁₉	1	2	yes	—
592	#428	C₂²×C₁₉	1	2	yes	—
593	#427	C₂²×C₁₉	1	1	yes	characteristic
594	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
595	#423	C₂²×C₁₉	1	1	yes	characteristic
596	#419	C₂²×C₁₉	1	2	yes	—
597	#417	C₂²×C₁₉	1	2	yes	—
598	#416	C₂²×C₁₉	1	2	yes	—
599	C₂×#103	C₂²×C₁₉	1	2	yes	—
600	#408	C₂²×C₁₉	1	1	yes	characteristic
601	#408	C₂²×C₁₉	1	1	yes	characteristic
602	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
603	C₂×C₁₉	—	4	1	no	—
604	C₂×C₁₉	—	4	1	no	—
605	C₂×C₁₉	—	4	2	no	—
606	C₂×C₁₉	—	4	1	no	—
607	C₂×C₁₉	—	8	2	no	—
608	C₂×C₁₉	#3496	1	1	yes	characteristic
609	C₂×C₁₉	#3586	1	2	yes	—
610	C₂×#41	C₂³×C₁₉	1	2	yes	—
611	C₂×#41	C₂³×C₁₉	1	2	yes	—
612	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
613	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
614	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
615	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
616	#137	—	4	4	no	—
617	#135	—	4	2	no	—
618	C₂×Q₁₆	—	4	2	no	—
619	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
620	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
621	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
622	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
623	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
624	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
625	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
626	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
627	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
628	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
629	#131	—	4	2	no	—
630	#131	—	4	2	no	—
631	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
632	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
633	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
634	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
635	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
636	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
637	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
638	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
639	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
640	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
641	C₄⋊Q₈	—	2	2	no	—
642	C₄⋊Q₈	—	2	2	no	—
643	C₄⋊Q₈	—	2	2	no	—
644	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
645	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
646	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
647	#127	D₄×C₁₉	1	1	yes	characteristic
648	#126	—	2	2	no	—
649	#126	—	2	2	no	—
650	#126	—	2	2	no	—
651	#125	—	2	2	no	—
652	#125	—	2	2	no	—
653	#125	—	2	2	no	—
654	#125	—	2	2	no	—
655	#125	C₂³×C₁₉	1	2	yes	—
656	#124	—	2	2	no	—
657	#124	—	2	2	no	—
658	#124	—	2	2	no	—
659	#124	—	2	2	no	—
660	#124	—	2	2	no	—
661	#124	—	2	2	no	—
662	#124	D₄×C₁₉	1	1	yes	characteristic
663	#124	D₄×C₁₉	1	1	yes	characteristic
664	#124	C₂³×C₁₉	1	2	yes	—
665	#123	—	2	2	no	—
666	#123	—	2	2	no	—
667	#123	—	2	2	no	—
668	#123	—	2	2	no	—
669	#123	—	2	2	no	—
670	#123	—	2	2	no	—
671	#123	—	2	2	no	—
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
684	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
685	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
686	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
687	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
688	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
689	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
690	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
691	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
692	#121	—	2	2	no	—
693	#121	—	2	2	no	—
694	#121	—	2	2	no	—
695	#121	—	2	2	no	—
696	#121	—	2	2	no	—
697	#121	—	2	2	no	—
698	#121	—	2	2	no	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	D₄×C₁₉	1	2	yes	—
703	#121	D₄×C₁₉	1	2	yes	—
704	#121	C₂³×C₁₉	1	2	yes	—
705	#121	C₂³×C₁₉	1	2	yes	—
706	#121	C₂³×C₁₉	1	2	yes	—
707	C₄×Q₈	—	2	2	no	—
708	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
709	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
710	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
711	C₄×D₄	—	2	2	no	—
712	C₄×D₄	—	2	2	no	—
713	C₄×D₄	—	2	2	no	—
714	C₄×D₄	—	2	2	no	—
715	C₄×D₄	—	2	2	no	—
716	C₄×D₄	C₂³×C₁₉	1	2	yes	—
717	C₄×D₄	C₂³×C₁₉	1	2	yes	—
718	C₄×D₄	C₂³×C₁₉	1	2	yes	—
719	#117	—	2	2	no	—
720	#117	—	2	2	no	—
721	#117	—	2	2	no	—
722	#117	—	2	2	no	—
723	#117	—	2	2	no	—
724	#117	C₂³×C₁₉	1	2	yes	—
725	#117	C₂³×C₁₉	1	2	yes	—
726	C₂×C₄⋊C₄	—	2	2	no	—
727	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
729	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
730	#107	C₂³×C₁₉	1	2	yes	—
731	#107	C₂³×C₁₉	1	2	yes	—
732	#107	C₂³×C₁₉	1	2	yes	—
733	#106	C₂³×C₁₉	1	2	yes	—
734	#106	C₂³×C₁₉	1	1	yes	characteristic
735	#106	C₂³×C₁₉	1	1	yes	characteristic
736	#106	C₂³×C₁₉	1	1	yes	characteristic
737	#106	C₂³×C₁₉	1	1	yes	characteristic
738	#106	C₂³×C₁₉	1	2	yes	—
739	#106	C₂³×C₁₉	1	2	yes	—
740	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
741	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
742	#103	C₂³×C₁₉	1	2	yes	—
743	#103	C₂³×C₁₉	1	2	yes	—
744	#103	C₂³×C₁₉	1	2	yes	—
745	#103	C₂³×C₁₉	1	2	yes	—
746	#103	C₂³×C₁₉	1	2	yes	—
747	#103	C₂³×C₁₉	1	2	yes	—
748	#103	C₂³×C₁₉	1	2	yes	—
749	#103	C₂³×C₁₉	1	2	yes	—
750	#103	C₂³×C₁₉	1	2	yes	—
751	#103	C₂³×C₁₉	1	2	yes	—
752	#103	C₂³×C₁₉	1	2	yes	—
753	#103	C₂³×C₁₉	1	2	yes	—
754	#102	C₂³×C₁₉	1	2	yes	—
755	#102	C₂³×C₁₉	1	2	yes	—
756	#102	C₂³×C₁₉	1	2	yes	—
757	#102	C₂³×C₁₉	1	2	yes	—
758	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
759	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
760	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
761	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
762	#97	C₂³×C₁₉	1	2	yes	—
763	#97	C₂³×C₁₉	1	2	yes	—
764	C₁₉	#62335	1	1	yes	characteristic, direct product factor, Sylow
765	#41	—	4	1	no	—
766	#41	—	4	1	no	—
767	#41	—	4	1	no	—
768	#41	—	4	1	no	—
769	#41	—	4	2	no	—
770	#41	—	4	2	no	—
771	#41	—	4	2	no	—
772	#41	—	4	2	no	—
773	C₂×Q₈	—	2	2	no	—
774	C₂×Q₈	—	2	2	no	—
775	C₂×Q₈	—	2	2	no	—
776	C₂×Q₈	—	4	2	no	—
777	C₂×Q₈	—	4	2	no	—
778	C₂×Q₈	—	4	2	no	—
779	C₂×Q₈	—	4	2	no	—
780	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
781	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
782	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
783	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
784	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
791	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
792	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
793	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
794	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
795	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
796	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
797	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
808	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
810	Q₁₆	—	2	4	no	—
811	Q₁₆	—	4	1	no	—
812	Q₁₆	—	4	1	no	—
813	Q₁₆	—	4	2	no	—
814	Q₁₆	—	4	1	no	—
815	Q₁₆	—	4	2	no	—
816	SD₁₆	—	2	4	no	—
817	SD₁₆	—	4	2	no	—
818	SD₁₆	—	4	2	no	—
819	D₈	—	4	1	no	—
820	M₁₆	—	2	4	no	—
821	M₁₆	—	4	1	no	—
822	M₁₆	—	4	1	no	—
823	M₁₆	—	4	1	no	—
824	M₁₆	—	4	1	no	—
825	C₂×C₈	—	2	2	no	—
826	C₂×C₈	—	2	2	no	—
827	C₂×C₈	—	2	2	no	—
828	C₂×C₈	—	4	1	no	—
829	C₂×C₈	—	4	2	no	—
830	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
831	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
832	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
833	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
834	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
835	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
856	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
857	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
858	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
859	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
860	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
879	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
880	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
881	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	2	no	—
887	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
888	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
889	C₄²	C₂⁴×C₁₉	1	2	yes	—
890	C₂³	—	2	2	no	—
891	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
892	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
893	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
894	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
895	Q₈	—	2	2	no	—
896	Q₈	—	2	2	no	—
897	Q₈	—	2	2	no	—
898	Q₈	—	2	2	no	—
899	Q₈	—	2	2	no	—
900	Q₈	—	2	2	no	—
901	Q₈	—	4	1	no	—
902	Q₈	—	4	1	no	—
903	Q₈	—	8	2	no	—
904	Q₈	—	8	2	no	—
905	Q₈	—	8	2	no	—
906	D₄	—	2	2	no	—
907	D₄	—	2	2	no	—
908	D₄	—	4	1	no	—
909	D₄	—	4	2	no	—
910	D₄	—	4	1	no	—
911	D₄	—	4	1	no	—
912	D₄	—	4	1	no	—
913	D₄	—	4	2	no	—
914	D₄	—	4	2	no	—
915	D₄	—	8	2	no	—
916	D₄	—	8	2	no	—
917	D₄	—	8	2	no	—
918	D₄	—	8	2	no	—
919	D₄	—	8	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	4	2	no	—
936	C₂×C₄	—	4	4	no	—
937	C₂×C₄	—	8	2	no	—
938	C₂×C₄	—	8	2	no	—
939	C₂×C₄	—	8	2	no	—
940	C₂×C₄	—	8	2	no	—
941	C₂×C₄	—	8	2	no	—
942	C₂×C₄	—	8	2	no	—
943	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
944	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
945	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
946	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
947	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
948	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
949	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
950	C₈	—	2	1	no	—
951	C₈	—	2	1	no	—
952	C₈	—	2	1	no	—
953	C₈	—	2	2	no	—
954	C₈	—	2	2	no	—
955	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	2	2	no	—
963	C₂²	—	2	2	no	—
964	C₂²	—	2	2	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	2	no	—
968	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
969	C₄	—	2	1	no	—
970	C₄	—	2	2	no	—
971	C₄	—	2	1	no	—
972	C₄	—	2	1	no	—
973	C₄	—	2	2	no	—
974	C₄	—	2	2	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	2	no	—
979	C₄	—	4	2	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	2	no	—
982	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
983	C₄	C₁₉×#585	1	1	yes	characteristic
984	C₂	—	4	1	no	—
985	C₂	—	4	2	no	—
986	C₂	—	4	1	no	—
987	C₂	—	4	1	no	—
988	C₂	—	8	2	no	—
989	C₂	C₁₉×#3496	1	1	yes	characteristic
990	C₂	C₁₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3547	C₂	semidirect
2. C₁₉×#3348	C₂	semidirect
3. C₁₉×#3344	C₂	semidirect
4. C₁₉×#3321	C₂	semidirect
5. C₁₉×#3316	C₂	semidirect
6. C₁₉×#3315	C₂	semidirect
7. C₁₉×#3312	C₂	semidirect
8. C₁₉×#3270	C₂	semidirect
9. C₁₉×#3269	C₂	semidirect
10. C₁₉×#3256	C₂	semidirect
11. C₁₉×#3255	C₂	semidirect
12. C₁₉×#3204	C₂	semidirect
13. C₁₉×#3202	C₂	semidirect
14. C₁₉×#3201	C₂	semidirect
15. C₁₉×#3181	C₂	semidirect
16. C₁₉×#3063	C₂	semidirect
17. C₁₉×#3060	C₂	semidirect
18. C₁₉×#3059	C₂	semidirect
19. C₁₉×#2932	C₂	semidirect
394. #62335	C₁₉	direct (N × H)
461. #3547	C₂×C₁₉	semidirect
462. #3348	C₂×C₁₉	semidirect
463. #3344	C₂×C₁₉	semidirect
464. #3321	C₂×C₁₉	semidirect
465. #3316	C₂×C₁₉	semidirect
466. #3315	C₂×C₁₉	semidirect
467. #3312	C₂×C₁₉	semidirect
468. #3270	C₂×C₁₉	semidirect
469. #3269	C₂×C₁₉	semidirect
470. #3256	C₂×C₁₉	semidirect
471. #3255	C₂×C₁₉	semidirect
472. #3204	C₂×C₁₉	semidirect
473. #3202	C₂×C₁₉	semidirect
474. #3201	C₂×C₁₉	semidirect
475. #3181	C₂×C₁₉	semidirect
476. #3063	C₂×C₁₉	semidirect
477. #3060	C₂×C₁₉	semidirect
478. #3059	C₂×C₁₉	semidirect
479. #2932	C₂×C₁₉	semidirect
764. C₁₉	#62335	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×#3547	2
C₁₉×#3348	2
C₁₉×#3344	2
C₁₉×#3321	2
C₁₉×#3316	2
C₁₉×#3315	2
C₁₉×#3312	2
C₁₉×#3270	2
C₁₉×#3269	2
C₁₉×#3256	2
C₁₉×#3255	2
C₁₉×#3204	2
C₁₉×#3202	2
C₁₉×#3201	2
C₁₉×#3181	2
C₁₉×#3063	2
C₁₉×#3060	2
C₁₉×#3059	2
C₁₉×#2932	2
#62335	19

Subgroups — C19×#62335 #18068294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62335 #18068294