Subgroups — C₁₉×#62388 #18068347

Order 4864.

1600 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3557	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3400	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3398	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3390	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3388	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3377	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3374	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3372	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3371	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
13	C₁₉×#3258	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3252	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3181	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3178	C₂	1	2	yes	maximal, complemented
17	C₁₉×#3177	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#3174	C₂	1	1	yes	maximal, characteristic
19	C₁₉×#2961	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#564	—	2	2	no	—
21	C₁₉×#563	—	2	2	no	—
22	C₁₉×#559	C₂²	1	2	yes	—
23	C₁₉×#557	—	2	2	no	—
24	C₁₉×#557	C₂²	1	2	yes	—
25	C₁₉×#557	C₂²	1	2	yes	—
26	C₁₉×#557	C₂²	1	2	yes	—
27	C₁₉×#557	C₂²	1	2	yes	—
28	C₁₉×#557	C₂²	1	2	yes	—
29	C₁₉×#556	C₂²	1	2	yes	—
30	C₁₉×#554	C₂²	1	2	yes	—
31	C₁₉×#552	—	2	2	no	—
32	C₁₉×#542	—	2	2	no	—
33	C₁₉×#542	C₂²	1	2	yes	—
34	C₁₉×#541	—	2	2	no	—
35	C₁₉×#541	—	2	2	no	—
36	C₁₉×#541	C₂²	1	1	yes	characteristic
37	C₁₉×#541	C₂²	1	1	yes	characteristic
38	C₁₉×#541	C₂²	1	1	yes	characteristic
39	C₁₉×#541	C₂²	1	2	yes	—
40	C₁₉×#540	C₂²	1	1	yes	characteristic
41	C₁₉×#539	—	2	2	no	—
42	C₁₉×#533	C₂²	1	2	yes	—
43	C₁₉×#533	C₂²	1	1	yes	characteristic
44	C₁₉×#529	C₂²	1	2	yes	—
45	C₁₉×#501	C₂²	1	2	yes	—
46	C₁₉×#501	C₂²	1	2	yes	—
47	C₁₉×#499	C₂²	1	1	yes	characteristic
48	C₁₉×#499	C₂²	1	1	yes	characteristic
49	C₁₉×#497	C₂²	1	2	yes	—
50	C₁₉×#497	C₂²	1	2	yes	—
51	C₁₉×#494	C₂²	1	1	yes	characteristic
52	C₁₉×#492	C₂²	1	1	yes	characteristic
53	C₁₉×#491	C₂²	1	1	yes	characteristic
54	C₁₉×#491	C₂²	1	1	yes	characteristic
55	C₁₉×#491	C₂²	1	1	yes	characteristic
56	C₁₉×#491	C₂²	1	2	yes	—
57	C₁₉×#490	C₂²	1	1	yes	characteristic
58	C₁₉×#489	C₂²	1	2	yes	—
59	C₁₉×#488	C₂²	1	2	yes	—
60	C₁₉×#487	C₂²	1	2	yes	—
61	C₁₉×#479	C₂²	1	2	yes	—
62	C₁₉×#479	C₂²	1	2	yes	—
63	C₁₉×#479	C₂²	1	2	yes	—
64	C₁₉×#479	C₂²	1	2	yes	—
65	C₁₉×#479	C₂²	1	2	yes	—
66	C₁₉×#479	C₂²	1	2	yes	—
67	C₁₉×#478	C₂²	1	2	yes	—
68	C₁₉×#478	C₂²	1	2	yes	—
69	C₁₉×#477	C₂²	1	2	yes	—
70	C₁₉×#477	C₂²	1	2	yes	—
71	C₁₉×#476	C₂²	1	2	yes	—
72	C₁₉×#475	C₂²	1	2	yes	—
73	C₁₉×#470	C₂²	1	2	yes	—
74	C₁₉×#470	C₂²	1	2	yes	—
75	C₁₉×#468	C₂²	1	2	yes	—
76	C₁₉×#468	C₂²	1	2	yes	—
77	C₁₉×#467	C₂²	1	2	yes	—
78	C₁₉×#467	C₂²	1	2	yes	—
79	C₁₉×#465	C₂²	1	2	yes	—
80	C₁₉×#465	C₂²	1	2	yes	—
81	C₁₉×#464	C₂²	1	2	yes	—
82	C₁₉×#464	C₂²	1	2	yes	—
83	C₁₉×#464	C₂²	1	2	yes	—
84	C₁₉×#464	C₂²	1	2	yes	—
85	C₁₉×#462	C₂²	1	2	yes	—
86	C₁₉×#462	C₂²	1	2	yes	—
87	C₁₉×#462	C₂²	1	2	yes	—
88	C₁₉×#462	C₂²	1	2	yes	—
89	C₁₉×#461	C₂²	1	2	yes	—
90	C₁₉×#461	C₂²	1	2	yes	—
91	C₁₉×#461	C₂²	1	2	yes	—
92	C₁₉×#460	C₂²	1	2	yes	—
93	C₁₉×#446	C₂²	1	2	yes	—
94	C₁₉×#446	C₂²	1	2	yes	—
95	C₁₉×#446	C₂²	1	2	yes	—
96	C₁₉×#446	C₂²	1	2	yes	—
97	C₁₉×#441	C₂²	1	2	yes	—
98	C₁₉×#441	C₂²	1	2	yes	—
99	C₁₉×#441	C₂²	1	2	yes	—
100	C₁₉×#441	C₂²	1	2	yes	—
101	C₁₉×#440	C₂²	1	2	yes	—
102	C₁₉×#440	C₂²	1	2	yes	—
103	C₁₉×#440	C₂²	1	2	yes	—
104	C₁₉×#440	C₂²	1	2	yes	—
105	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
106	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
107	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
108	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
109	C₁₉×#424	C₂²	1	1	yes	characteristic
110	C₁₉×#424	C₂²	1	1	yes	characteristic
111	C₁₉×#423	C₂²	1	1	yes	characteristic
112	C₁₉×#405	C₂²	1	1	yes	characteristic
113	C₁₉×#405	C₂²	1	1	yes	characteristic
114	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
115	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
116	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
117	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
118	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
119	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
120	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
121	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
122	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
123	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
125	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
127	C₁₉×C₄⋊Q₈	—	2	2	no	—
128	C₁₉×C₄⋊Q₈	—	2	2	no	—
129	C₁₉×C₄⋊Q₈	—	2	2	no	—
130	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
131	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
132	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
133	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
134	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
135	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
136	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₁₉×#127	C₂³	1	1	yes	characteristic
139	C₁₉×#126	—	2	2	no	—
140	C₁₉×#126	—	2	2	no	—
141	C₁₉×#126	—	2	2	no	—
142	C₁₉×#126	—	2	2	no	—
143	C₁₉×#126	—	2	2	no	—
144	C₁₉×#126	—	2	2	no	—
145	C₁₉×#126	—	2	2	no	—
146	C₁₉×#126	—	2	2	no	—
147	C₁₉×#126	—	2	2	no	—
148	C₁₉×#125	—	2	2	no	—
149	C₁₉×#125	—	2	2	no	—
150	C₁₉×#125	—	2	2	no	—
151	C₁₉×#125	—	2	2	no	—
152	C₁₉×#125	—	2	2	no	—
153	C₁₉×#125	—	2	2	no	—
154	C₁₉×#125	—	2	2	no	—
155	C₁₉×#125	—	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	—	2	2	no	—
163	C₁₉×#125	—	2	2	no	—
164	C₁₉×#125	—	2	2	no	—
165	C₁₉×#125	—	2	2	no	—
166	C₁₉×#125	D₄	1	2	yes	—
167	C₁₉×#125	C₂³	1	1	yes	characteristic
168	C₁₉×#125	C₂³	1	2	yes	—
169	C₁₉×#125	C₂³	1	1	yes	characteristic
170	C₁₉×#125	C₂³	1	1	yes	characteristic
171	C₁₉×#125	C₂³	1	1	yes	characteristic
172	C₁₉×#125	C₂³	1	2	yes	—
173	C₁₉×#124	—	2	2	no	—
174	C₁₉×#124	—	2	2	no	—
175	C₁₉×#124	C₂³	1	2	yes	—
176	C₁₉×#124	C₂³	1	2	yes	—
177	C₁₉×#123	—	2	2	no	—
178	C₁₉×#123	—	2	2	no	—
179	C₁₉×#123	—	2	2	no	—
180	C₁₉×#123	—	2	2	no	—
181	C₁₉×#123	—	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	D₄	1	2	yes	—
189	C₁₉×C₂²⋊Q₈	D₄	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×#121	—	2	2	no	—
194	C₁₉×#121	C₂³	1	2	yes	—
195	C₄×Q₈×C₁₉	—	2	2	no	—
196	C₄×Q₈×C₁₉	—	2	2	no	—
197	C₄×Q₈×C₁₉	—	2	2	no	—
198	C₄×Q₈×C₁₉	—	2	2	no	—
199	C₄×Q₈×C₁₉	—	2	2	no	—
200	C₄×Q₈×C₁₉	—	2	2	no	—
201	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
202	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
203	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
204	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
205	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
206	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
207	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
208	C₄×Q₈×C₁₉	C₂³	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	C₂³	1	2	yes	—
215	C₄×D₄×C₁₉	C₂³	1	2	yes	—
216	C₄×D₄×C₁₉	C₂³	1	2	yes	—
217	C₁₉×#117	—	2	2	no	—
218	C₁₉×#117	—	2	2	no	—
219	C₁₉×#117	—	2	2	no	—
220	C₁₉×#117	C₂³	1	1	yes	characteristic
221	C₁₉×#117	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
223	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
224	C₁₉×#107	C₂³	1	2	yes	—
225	C₁₉×#107	C₂³	1	2	yes	—
226	C₁₉×#107	C₂³	1	2	yes	—
227	C₁₉×#107	C₂³	1	2	yes	—
228	C₁₉×#106	C₂³	1	2	yes	—
229	C₁₉×#106	C₂³	1	2	yes	—
230	C₁₉×#106	C₂³	1	2	yes	—
231	C₁₉×#106	C₂³	1	2	yes	—
232	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
233	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
234	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
235	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
236	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
237	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
238	C₁₉×#103	C₂³	1	2	yes	—
239	C₁₉×#103	C₂³	1	2	yes	—
240	C₁₉×#103	C₂³	1	2	yes	—
241	C₁₉×#103	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×#102	C₂³	1	2	yes	—
251	C₁₉×#102	C₂³	1	2	yes	—
252	C₁₉×#102	C₂³	1	2	yes	—
253	C₁₉×#102	C₂³	1	2	yes	—
254	C₁₉×#97	C₂³	1	2	yes	—
255	C₁₉×#97	C₂³	1	2	yes	—
256	C₁₉×#97	C₂³	1	1	yes	characteristic
257	C₁₉×#97	C₂³	1	2	yes	—
258	C₁₉×#97	C₂³	1	1	yes	characteristic
259	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
260	C₄×C₈×C₁₉	C₂³	1	2	yes	—
261	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
262	C₂×Q₈×C₁₉	—	2	2	no	—
263	C₂×Q₈×C₁₉	—	2	2	no	—
264	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
265	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
266	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
267	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
268	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
269	C₂×D₄×C₁₉	—	2	2	no	—
270	C₂×D₄×C₁₉	—	2	2	no	—
271	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₉	—	2	2	no	—
273	C₂²×C₄×C₁₉	—	2	2	no	—
274	C₂²×C₄×C₁₉	—	2	2	no	—
275	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
277	Q₁₆×C₁₉	—	2	4	no	—
278	Q₁₆×C₁₉	—	4	2	no	—
279	Q₁₆×C₁₉	—	4	2	no	—
280	Q₁₆×C₁₉	—	4	2	no	—
281	SD₁₆×C₁₉	—	2	4	no	—
282	SD₁₆×C₁₉	—	4	2	no	—
283	SD₁₆×C₁₉	—	4	2	no	—
284	SD₁₆×C₁₉	—	4	2	no	—
285	M₁₆×C₁₉	—	4	1	no	—
286	M₁₆×C₁₉	—	4	1	no	—
287	C₂×C₈×C₁₉	—	2	2	no	—
288	C₂×C₈×C₁₉	—	4	1	no	—
289	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
290	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
291	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
292	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
293	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
294	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
295	C₄⋊C₄×C₁₉	—	2	2	no	—
296	C₄⋊C₄×C₁₉	—	2	2	no	—
297	C₄⋊C₄×C₁₉	—	2	2	no	—
298	C₄⋊C₄×C₁₉	—	2	2	no	—
299	C₄⋊C₄×C₁₉	—	2	2	no	—
300	C₄⋊C₄×C₁₉	—	2	2	no	—
301	C₄⋊C₄×C₁₉	—	2	2	no	—
302	C₄⋊C₄×C₁₉	—	2	2	no	—
303	C₄⋊C₄×C₁₉	—	2	2	no	—
304	C₄⋊C₄×C₁₉	—	2	2	no	—
305	C₄⋊C₄×C₁₉	—	2	2	no	—
306	C₄⋊C₄×C₁₉	—	2	2	no	—
307	C₄⋊C₄×C₁₉	—	2	2	no	—
308	C₄⋊C₄×C₁₉	—	2	2	no	—
309	C₄⋊C₄×C₁₉	—	2	2	no	—
310	C₄⋊C₄×C₁₉	—	2	2	no	—
311	C₄⋊C₄×C₁₉	—	2	2	no	—
312	C₄⋊C₄×C₁₉	—	2	2	no	—
313	C₄⋊C₄×C₁₉	—	2	2	no	—
314	C₄⋊C₄×C₁₉	—	2	2	no	—
315	C₄⋊C₄×C₁₉	—	2	2	no	—
316	C₄⋊C₄×C₁₉	—	2	2	no	—
317	C₄⋊C₄×C₁₉	—	2	2	no	—
318	C₄⋊C₄×C₁₉	—	2	2	no	—
319	C₄⋊C₄×C₁₉	—	2	2	no	—
320	C₄⋊C₄×C₁₉	—	2	2	no	—
321	C₄⋊C₄×C₁₉	—	2	2	no	—
322	C₄⋊C₄×C₁₉	—	2	2	no	—
323	C₄⋊C₄×C₁₉	—	2	2	no	—
324	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
325	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
326	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
327	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
328	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
329	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
330	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
331	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
332	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
333	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
334	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
335	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
336	C₂²⋊C₄×C₁₉	—	2	2	no	—
337	C₂²⋊C₄×C₁₉	—	2	2	no	—
338	C₂²⋊C₄×C₁₉	—	2	2	no	—
339	C₂²⋊C₄×C₁₉	—	2	2	no	—
340	C₂²⋊C₄×C₁₉	—	2	2	no	—
341	C₂²⋊C₄×C₁₉	—	2	2	no	—
342	C₂²⋊C₄×C₁₉	—	2	2	no	—
343	C₂²⋊C₄×C₁₉	—	2	2	no	—
344	C₂²⋊C₄×C₁₉	—	2	2	no	—
345	C₂²⋊C₄×C₁₉	—	2	2	no	—
346	C₂²⋊C₄×C₁₉	—	2	2	no	—
347	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
348	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
349	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
350	C₄²×C₁₉	—	2	2	no	—
351	C₄²×C₁₉	—	2	2	no	—
352	C₄²×C₁₉	—	2	2	no	—
353	C₄²×C₁₉	—	2	2	no	—
354	C₄²×C₁₉	—	2	2	no	—
355	C₄²×C₁₉	—	2	2	no	—
356	C₄²×C₁₉	—	2	2	no	—
357	C₄²×C₁₉	—	2	2	no	—
358	C₄²×C₁₉	—	2	2	no	—
359	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
360	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
361	C₄²×C₁₉	C₂⁴	1	2	yes	—
362	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
363	C₄²×C₁₉	C₂⁴	1	2	yes	—
364	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
365	#62388	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
366	C₂³×C₁₉	—	2	2	no	—
367	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
368	Q₈×C₁₉	—	2	2	no	—
369	Q₈×C₁₉	—	2	2	no	—
370	Q₈×C₁₉	—	2	2	no	—
371	Q₈×C₁₉	—	2	2	no	—
372	Q₈×C₁₉	—	2	2	no	—
373	Q₈×C₁₉	—	2	2	no	—
374	Q₈×C₁₉	—	4	2	no	—
375	Q₈×C₁₉	—	4	2	no	—
376	Q₈×C₁₉	—	4	4	no	—
377	Q₈×C₁₉	—	8	2	no	—
378	D₄×C₁₉	—	2	2	no	—
379	D₄×C₁₉	—	2	2	no	—
380	D₄×C₁₉	—	8	2	no	—
381	D₄×C₁₉	—	8	2	no	—
382	C₂×C₄×C₁₉	—	2	1	no	—
383	C₂×C₄×C₁₉	—	2	1	no	—
384	C₂×C₄×C₁₉	—	2	2	no	—
385	C₂×C₄×C₁₉	—	2	2	no	—
386	C₂×C₄×C₁₉	—	2	2	no	—
387	C₂×C₄×C₁₉	—	2	2	no	—
388	C₂×C₄×C₁₉	—	2	2	no	—
389	C₂×C₄×C₁₉	—	2	2	no	—
390	C₂×C₄×C₁₉	—	2	2	no	—
391	C₂×C₄×C₁₉	—	4	2	no	—
392	C₂×C₄×C₁₉	—	8	2	no	—
393	C₂×C₄×C₁₉	—	8	2	no	—
394	C₂×C₄×C₁₉	—	8	2	no	—
395	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
403	C₈×C₁₉	—	2	1	no	—
404	C₈×C₁₉	—	2	2	no	—
405	C₈×C₁₉	—	2	1	no	—
406	C₈×C₁₉	—	2	2	no	—
407	C₈×C₁₉	—	2	1	no	—
408	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
409	#3557	C₂×C₁₉	1	1	yes	characteristic
410	#3556	C₂×C₁₉	1	1	yes	characteristic, complemented
411	#3400	C₂×C₁₉	1	2	yes	complemented
412	#3398	C₂×C₁₉	1	2	yes	complemented
413	#3390	C₂×C₁₉	1	2	yes	complemented
414	#3388	C₂×C₁₉	1	2	yes	complemented
415	#3377	C₂×C₁₉	1	2	yes	complemented
416	#3374	C₂×C₁₉	1	2	yes	complemented
417	#3372	C₂×C₁₉	1	2	yes	complemented
418	#3371	C₂×C₁₉	1	2	yes	complemented
419	#3261	C₂×C₁₉	1	1	yes	characteristic, complemented
420	#3260	C₂×C₁₉	1	1	yes	characteristic
421	#3258	C₂×C₁₉	1	2	yes	complemented
422	#3252	C₂×C₁₉	1	2	yes	complemented
423	#3181	C₂×C₁₉	1	2	yes	complemented
424	#3178	C₂×C₁₉	1	2	yes	complemented
425	#3177	C₂×C₁₉	1	1	yes	characteristic, complemented
426	#3174	C₂×C₁₉	1	1	yes	characteristic
427	#2961	C₂×C₁₉	1	1	yes	characteristic, complemented
428	C₂²×C₁₉	—	2	2	no	—
429	C₂²×C₁₉	—	2	1	no	—
430	C₂²×C₁₉	—	4	2	no	—
431	C₂²×C₁₉	—	4	2	no	—
432	C₂²×C₁₉	—	4	2	no	—
433	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
434	C₄×C₁₉	—	2	2	no	—
435	C₄×C₁₉	—	2	2	no	—
436	C₄×C₁₉	—	2	2	no	—
437	C₄×C₁₉	—	2	2	no	—
438	C₄×C₁₉	—	2	2	no	—
439	C₄×C₁₉	—	2	2	no	—
440	C₄×C₁₉	—	2	1	no	—
441	C₄×C₁₉	—	4	2	no	—
442	C₄×C₁₉	—	4	2	no	—
443	C₄×C₁₉	—	4	2	no	—
444	C₄×C₁₉	—	4	2	no	—
445	C₄×C₁₉	—	4	2	no	—
446	C₄×C₁₉	—	4	2	no	—
447	C₄×C₁₉	—	4	2	no	—
448	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
449	C₄×C₁₉	#585	1	1	yes	characteristic
450	#564	—	2	2	no	—
451	#563	—	2	2	no	—
452	#559	C₂²×C₁₉	1	2	yes	—
453	#557	—	2	2	no	—
454	#557	C₂²×C₁₉	1	2	yes	—
455	#557	C₂²×C₁₉	1	2	yes	—
456	#557	C₂²×C₁₉	1	2	yes	—
457	#557	C₂²×C₁₉	1	2	yes	—
458	#557	C₂²×C₁₉	1	2	yes	—
459	#556	C₂²×C₁₉	1	2	yes	—
460	#554	C₂²×C₁₉	1	2	yes	—
461	#552	—	2	2	no	—
462	#542	—	2	2	no	—
463	#542	C₂²×C₁₉	1	2	yes	—
464	#541	—	2	2	no	—
465	#541	—	2	2	no	—
466	#541	C₂²×C₁₉	1	1	yes	characteristic
467	#541	C₂²×C₁₉	1	1	yes	characteristic
468	#541	C₂²×C₁₉	1	1	yes	characteristic
469	#541	C₂²×C₁₉	1	2	yes	—
470	#540	C₂²×C₁₉	1	1	yes	characteristic
471	#539	—	2	2	no	—
472	#533	C₂²×C₁₉	1	2	yes	—
473	#533	C₂²×C₁₉	1	1	yes	characteristic
474	#529	C₂²×C₁₉	1	2	yes	—
475	#501	C₂²×C₁₉	1	2	yes	—
476	#501	C₂²×C₁₉	1	2	yes	—
477	#499	C₂²×C₁₉	1	1	yes	characteristic
478	#499	C₂²×C₁₉	1	1	yes	characteristic
479	#497	C₂²×C₁₉	1	2	yes	—
480	#497	C₂²×C₁₉	1	2	yes	—
481	#494	C₂²×C₁₉	1	1	yes	characteristic
482	#492	C₂²×C₁₉	1	1	yes	characteristic
483	#491	C₂²×C₁₉	1	1	yes	characteristic
484	#491	C₂²×C₁₉	1	2	yes	—
485	#491	C₂²×C₁₉	1	1	yes	characteristic
486	#491	C₂²×C₁₉	1	1	yes	characteristic
487	#490	C₂²×C₁₉	1	1	yes	characteristic
488	#489	C₂²×C₁₉	1	2	yes	—
489	#488	C₂²×C₁₉	1	2	yes	—
490	#487	C₂²×C₁₉	1	2	yes	—
491	#479	C₂²×C₁₉	1	2	yes	—
492	#479	C₂²×C₁₉	1	2	yes	—
493	#479	C₂²×C₁₉	1	2	yes	—
494	#479	C₂²×C₁₉	1	2	yes	—
495	#479	C₂²×C₁₉	1	2	yes	—
496	#479	C₂²×C₁₉	1	2	yes	—
497	#478	C₂²×C₁₉	1	2	yes	—
498	#478	C₂²×C₁₉	1	2	yes	—
499	#477	C₂²×C₁₉	1	2	yes	—
500	#477	C₂²×C₁₉	1	2	yes	—
501	#476	C₂²×C₁₉	1	2	yes	—
502	#475	C₂²×C₁₉	1	2	yes	—
503	#470	C₂²×C₁₉	1	2	yes	—
504	#470	C₂²×C₁₉	1	2	yes	—
505	#468	C₂²×C₁₉	1	2	yes	—
506	#468	C₂²×C₁₉	1	2	yes	—
507	#467	C₂²×C₁₉	1	2	yes	—
508	#467	C₂²×C₁₉	1	2	yes	—
509	#465	C₂²×C₁₉	1	2	yes	—
510	#465	C₂²×C₁₉	1	2	yes	—
511	#464	C₂²×C₁₉	1	2	yes	—
512	#464	C₂²×C₁₉	1	2	yes	—
513	#464	C₂²×C₁₉	1	2	yes	—
514	#464	C₂²×C₁₉	1	2	yes	—
515	#462	C₂²×C₁₉	1	2	yes	—
516	#462	C₂²×C₁₉	1	2	yes	—
517	#462	C₂²×C₁₉	1	2	yes	—
518	#462	C₂²×C₁₉	1	2	yes	—
519	#461	C₂²×C₁₉	1	2	yes	—
520	#461	C₂²×C₁₉	1	2	yes	—
521	#461	C₂²×C₁₉	1	2	yes	—
522	#460	C₂²×C₁₉	1	2	yes	—
523	#446	C₂²×C₁₉	1	2	yes	—
524	#446	C₂²×C₁₉	1	2	yes	—
525	#446	C₂²×C₁₉	1	2	yes	—
526	#446	C₂²×C₁₉	1	2	yes	—
527	#441	C₂²×C₁₉	1	2	yes	—
528	#441	C₂²×C₁₉	1	2	yes	—
529	#441	C₂²×C₁₉	1	2	yes	—
530	#441	C₂²×C₁₉	1	2	yes	—
531	#440	C₂²×C₁₉	1	2	yes	—
532	#440	C₂²×C₁₉	1	2	yes	—
533	#440	C₂²×C₁₉	1	2	yes	—
534	#440	C₂²×C₁₉	1	2	yes	—
535	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
536	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
537	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
538	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
539	#424	C₂²×C₁₉	1	1	yes	characteristic
540	#424	C₂²×C₁₉	1	1	yes	characteristic
541	#423	C₂²×C₁₉	1	1	yes	characteristic
542	#405	C₂²×C₁₉	1	1	yes	characteristic
543	#405	C₂²×C₁₉	1	1	yes	characteristic
544	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
545	C₂×C₁₉	—	4	1	no	—
546	C₂×C₁₉	—	8	2	no	—
547	C₂×C₁₉	#3497	1	1	yes	characteristic
548	C₂×C₁₉	#3586	1	2	yes	—
549	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
550	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
551	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
552	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
553	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
554	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
555	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
556	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
557	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
558	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
559	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
560	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
561	C₄⋊Q₈	—	2	2	no	—
562	C₄⋊Q₈	—	2	2	no	—
563	C₄⋊Q₈	—	2	2	no	—
564	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
565	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
566	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
567	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
568	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
569	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
570	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
571	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
572	#127	C₂³×C₁₉	1	1	yes	characteristic
573	#126	—	2	2	no	—
574	#126	—	2	2	no	—
575	#126	—	2	2	no	—
576	#126	—	2	2	no	—
577	#126	—	2	2	no	—
578	#126	—	2	2	no	—
579	#126	—	2	2	no	—
580	#126	—	2	2	no	—
581	#126	—	2	2	no	—
582	#125	—	2	2	no	—
583	#125	—	2	2	no	—
584	#125	—	2	2	no	—
585	#125	—	2	2	no	—
586	#125	—	2	2	no	—
587	#125	—	2	2	no	—
588	#125	—	2	2	no	—
589	#125	—	2	2	no	—
590	#125	—	2	2	no	—
591	#125	—	2	2	no	—
592	#125	—	2	2	no	—
593	#125	—	2	2	no	—
594	#125	—	2	2	no	—
595	#125	—	2	2	no	—
596	#125	—	2	2	no	—
597	#125	—	2	2	no	—
598	#125	—	2	2	no	—
599	#125	—	2	2	no	—
600	#125	D₄×C₁₉	1	2	yes	—
601	#125	C₂³×C₁₉	1	2	yes	—
602	#125	C₂³×C₁₉	1	1	yes	characteristic
603	#125	C₂³×C₁₉	1	1	yes	characteristic
604	#125	C₂³×C₁₉	1	1	yes	characteristic
605	#125	C₂³×C₁₉	1	2	yes	—
606	#125	C₂³×C₁₉	1	1	yes	characteristic
607	#124	—	2	2	no	—
608	#124	—	2	2	no	—
609	#124	C₂³×C₁₉	1	2	yes	—
610	#124	C₂³×C₁₉	1	2	yes	—
611	#123	—	2	2	no	—
612	#123	—	2	2	no	—
613	#123	—	2	2	no	—
614	#123	—	2	2	no	—
615	#123	—	2	2	no	—
616	C₂²⋊Q₈	—	2	2	no	—
617	C₂²⋊Q₈	—	2	2	no	—
618	C₂²⋊Q₈	—	2	2	no	—
619	C₂²⋊Q₈	—	2	2	no	—
620	C₂²⋊Q₈	—	2	2	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
623	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
624	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
625	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
626	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
627	#121	—	2	2	no	—
628	#121	C₂³×C₁₉	1	2	yes	—
629	C₄×Q₈	—	2	2	no	—
630	C₄×Q₈	—	2	2	no	—
631	C₄×Q₈	—	2	2	no	—
632	C₄×Q₈	—	2	2	no	—
633	C₄×Q₈	—	2	2	no	—
634	C₄×Q₈	—	2	2	no	—
635	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
636	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
637	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
638	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
639	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
640	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
641	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
642	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
643	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
644	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
645	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	C₂³×C₁₉	1	2	yes	—
649	C₄×D₄	C₂³×C₁₉	1	2	yes	—
650	C₄×D₄	C₂³×C₁₉	1	2	yes	—
651	#117	—	2	2	no	—
652	#117	—	2	2	no	—
653	#117	—	2	2	no	—
654	#117	C₂³×C₁₉	1	1	yes	characteristic
655	#117	C₂³×C₁₉	1	1	yes	characteristic
656	C₂×C₄⋊C₄	—	2	2	no	—
657	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
658	#107	C₂³×C₁₉	1	2	yes	—
659	#107	C₂³×C₁₉	1	2	yes	—
660	#107	C₂³×C₁₉	1	2	yes	—
661	#107	C₂³×C₁₉	1	2	yes	—
662	#106	C₂³×C₁₉	1	2	yes	—
663	#106	C₂³×C₁₉	1	2	yes	—
664	#106	C₂³×C₁₉	1	2	yes	—
665	#106	C₂³×C₁₉	1	2	yes	—
666	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
667	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
668	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
669	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
670	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
671	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
672	#103	C₂³×C₁₉	1	2	yes	—
673	#103	C₂³×C₁₉	1	2	yes	—
674	#103	C₂³×C₁₉	1	2	yes	—
675	#103	C₂³×C₁₉	1	2	yes	—
676	#103	C₂³×C₁₉	1	2	yes	—
677	#103	C₂³×C₁₉	1	2	yes	—
678	#103	C₂³×C₁₉	1	2	yes	—
679	#103	C₂³×C₁₉	1	2	yes	—
680	#103	C₂³×C₁₉	1	2	yes	—
681	#103	C₂³×C₁₉	1	2	yes	—
682	#103	C₂³×C₁₉	1	2	yes	—
683	#103	C₂³×C₁₉	1	2	yes	—
684	#102	C₂³×C₁₉	1	2	yes	—
685	#102	C₂³×C₁₉	1	2	yes	—
686	#102	C₂³×C₁₉	1	2	yes	—
687	#102	C₂³×C₁₉	1	2	yes	—
688	#97	C₂³×C₁₉	1	2	yes	—
689	#97	C₂³×C₁₉	1	2	yes	—
690	#97	C₂³×C₁₉	1	1	yes	characteristic
691	#97	C₂³×C₁₉	1	2	yes	—
692	#97	C₂³×C₁₉	1	1	yes	characteristic
693	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
694	C₄×C₈	C₂³×C₁₉	1	2	yes	—
695	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
696	C₁₉	#62388	1	1	yes	characteristic, direct product factor, Sylow
697	C₂×Q₈	—	2	2	no	—
698	C₂×Q₈	—	2	2	no	—
699	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
700	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
701	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
702	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
703	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
712	Q₁₆	—	2	4	no	—
713	Q₁₆	—	4	2	no	—
714	Q₁₆	—	4	2	no	—
715	Q₁₆	—	4	2	no	—
716	SD₁₆	—	2	4	no	—
717	SD₁₆	—	4	2	no	—
718	SD₁₆	—	4	2	no	—
719	SD₁₆	—	4	2	no	—
720	M₁₆	—	4	1	no	—
721	M₁₆	—	4	1	no	—
722	C₂×C₈	—	2	2	no	—
723	C₂×C₈	—	4	1	no	—
724	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
725	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
726	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
727	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
728	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
729	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
760	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
761	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
762	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
763	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
764	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
765	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
766	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
767	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
768	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
769	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
770	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
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	—	2	2	no	—
782	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
783	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
784	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	2	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
795	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
796	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
797	C₄²	C₂⁴×C₁₉	1	2	yes	—
798	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
799	C₄²	C₂⁴×C₁₉	1	2	yes	—
800	C₂³	—	2	2	no	—
801	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
802	Q₈	—	2	2	no	—
803	Q₈	—	2	2	no	—
804	Q₈	—	2	2	no	—
805	Q₈	—	2	2	no	—
806	Q₈	—	2	2	no	—
807	Q₈	—	2	2	no	—
808	Q₈	—	4	2	no	—
809	Q₈	—	4	2	no	—
810	Q₈	—	4	4	no	—
811	Q₈	—	8	2	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	2	no	—
814	D₄	—	8	2	no	—
815	D₄	—	8	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	8	2	no	—
827	C₂×C₄	—	8	2	no	—
828	C₂×C₄	—	8	2	no	—
829	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
830	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
831	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
832	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
833	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
834	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
835	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
836	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
837	C₈	—	2	1	no	—
838	C₈	—	2	2	no	—
839	C₈	—	2	1	no	—
840	C₈	—	2	2	no	—
841	C₈	—	2	1	no	—
842	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
843	C₂²	—	2	1	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
849	C₄	—	2	1	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	2	no	—
855	C₄	—	2	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
864	C₄	C₁₉×#585	1	1	yes	characteristic
865	C₂	—	4	1	no	—
866	C₂	—	8	2	no	—
867	C₂	C₁₉×#3497	1	1	yes	characteristic
868	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×#540	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3556	C₂	semidirect
3. C₁₉×#3400	C₂	semidirect
4. C₁₉×#3398	C₂	semidirect
5. C₁₉×#3390	C₂	semidirect
6. C₁₉×#3388	C₂	semidirect
7. C₁₉×#3377	C₂	semidirect
8. C₁₉×#3374	C₂	semidirect
9. C₁₉×#3372	C₂	semidirect
10. C₁₉×#3371	C₂	semidirect
11. C₁₉×#3261	C₂	semidirect
13. C₁₉×#3258	C₂	semidirect
14. C₁₉×#3252	C₂	semidirect
15. C₁₉×#3181	C₂	semidirect
16. C₁₉×#3178	C₂	semidirect
17. C₁₉×#3177	C₂	semidirect
19. C₁₉×#2961	C₂	semidirect
365. #62388	C₁₉	direct (N × H)
410. #3556	C₂×C₁₉	semidirect
411. #3400	C₂×C₁₉	semidirect
412. #3398	C₂×C₁₉	semidirect
413. #3390	C₂×C₁₉	semidirect
414. #3388	C₂×C₁₉	semidirect
415. #3377	C₂×C₁₉	semidirect
416. #3374	C₂×C₁₉	semidirect
417. #3372	C₂×C₁₉	semidirect
418. #3371	C₂×C₁₉	semidirect
419. #3261	C₂×C₁₉	semidirect
421. #3258	C₂×C₁₉	semidirect
422. #3252	C₂×C₁₉	semidirect
423. #3181	C₂×C₁₉	semidirect
424. #3178	C₂×C₁₉	semidirect
425. #3177	C₂×C₁₉	semidirect
427. #2961	C₂×C₁₉	semidirect
696. C₁₉	#62388	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×#3557	2
C₁₉×#3556	2
C₁₉×#3400	2
C₁₉×#3398	2
C₁₉×#3390	2
C₁₉×#3388	2
C₁₉×#3377	2
C₁₉×#3374	2
C₁₉×#3372	2
C₁₉×#3371	2
C₁₉×#3261	2
C₁₉×#3260	2
C₁₉×#3258	2
C₁₉×#3252	2
C₁₉×#3181	2
C₁₉×#3178	2
C₁₉×#3177	2
C₁₉×#3174	2
C₁₉×#2961	2
#62388	19

Subgroups — C19×#62388 #18068347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62388 #18068347