Subgroups — C₁₉×#62387 #18068346

Order 4864.

1712 conjugacy classes of subgroups.

The subgroup lattice has 916 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, complemented
2	C₁₉×#3548	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3399	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3397	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3389	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3388	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3376	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3370	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3368	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3366	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3260	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3259	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3257	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3251	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3180	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3179	C₂	1	2	yes	maximal, complemented
17	C₁₉×#3176	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#3174	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#2961	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#563	—	2	2	no	—
21	C₁₉×#562	—	2	2	no	—
22	C₁₉×#559	C₂²	1	2	yes	—
23	C₁₉×#557	C₂²	1	2	yes	—
24	C₁₉×#556	C₂²	1	2	yes	—
25	C₁₉×#554	C₂²	1	2	yes	—
26	C₁₉×#554	C₂²	1	2	yes	—
27	C₁₉×#554	C₂²	1	2	yes	—
28	C₁₉×#552	—	2	2	no	—
29	C₁₉×#550	C₂²	1	2	yes	—
30	C₁₉×#550	C₂²	1	2	yes	—
31	C₁₉×#547	—	2	2	no	—
32	C₁₉×#542	—	2	2	no	—
33	C₁₉×#542	C₂²	1	2	yes	—
34	C₁₉×#541	C₂²	1	1	yes	characteristic
35	C₁₉×#540	C₂²	1	1	yes	characteristic
36	C₁₉×#540	C₂²	1	1	yes	characteristic
37	C₁₉×#540	C₂²	1	1	yes	characteristic
38	C₁₉×#540	C₂²	1	2	yes	—
39	C₁₉×#539	—	2	2	no	—
40	C₁₉×#537	—	2	2	no	—
41	C₁₉×#537	—	2	2	no	—
42	C₁₉×#533	C₂²	1	1	yes	characteristic
43	C₁₉×#532	C₂²	1	2	yes	—
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×#496	C₂²	1	2	yes	—
50	C₁₉×#496	C₂²	1	2	yes	—
51	C₁₉×#493	C₂²	1	1	yes	characteristic
52	C₁₉×#492	C₂²	1	1	yes	characteristic
53	C₁₉×#491	C₂²	1	1	yes	characteristic
54	C₁₉×#490	C₂²	1	1	yes	characteristic
55	C₁₉×#490	C₂²	1	1	yes	characteristic
56	C₁₉×#490	C₂²	1	1	yes	characteristic
57	C₁₉×#490	C₂²	1	2	yes	—
58	C₁₉×#489	C₂²	1	2	yes	—
59	C₁₉×#488	C₂²	1	2	yes	—
60	C₁₉×#486	C₂²	1	2	yes	—
61	C₁₉×#479	C₂²	1	2	yes	—
62	C₁₉×#479	C₂²	1	2	yes	—
63	C₁₉×#478	C₂²	1	2	yes	—
64	C₁₉×#478	C₂²	1	2	yes	—
65	C₁₉×#478	C₂²	1	2	yes	—
66	C₁₉×#478	C₂²	1	2	yes	—
67	C₁₉×#478	C₂²	1	2	yes	—
68	C₁₉×#478	C₂²	1	2	yes	—
69	C₁₉×#476	C₂²	1	2	yes	—
70	C₁₉×#475	C₂²	1	2	yes	—
71	C₁₉×#474	C₂²	1	2	yes	—
72	C₁₉×#474	C₂²	1	2	yes	—
73	C₁₉×#469	C₂²	1	2	yes	—
74	C₁₉×#469	C₂²	1	2	yes	—
75	C₁₉×#468	C₂²	1	2	yes	—
76	C₁₉×#468	C₂²	1	2	yes	—
77	C₁₉×#466	C₂²	1	2	yes	—
78	C₁₉×#466	C₂²	1	2	yes	—
79	C₁₉×#465	C₂²	1	2	yes	—
80	C₁₉×#465	C₂²	1	2	yes	—
81	C₁₉×#463	C₂²	1	2	yes	—
82	C₁₉×#463	C₂²	1	2	yes	—
83	C₁₉×#463	C₂²	1	2	yes	—
84	C₁₉×#463	C₂²	1	2	yes	—
85	C₁₉×#461	C₂²	1	2	yes	—
86	C₁₉×#460	C₂²	1	2	yes	—
87	C₁₉×#460	C₂²	1	2	yes	—
88	C₁₉×#460	C₂²	1	2	yes	—
89	C₁₉×#459	C₂²	1	2	yes	—
90	C₁₉×#459	C₂²	1	2	yes	—
91	C₁₉×#459	C₂²	1	2	yes	—
92	C₁₉×#459	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×#442	C₂²	1	2	yes	—
98	C₁₉×#442	C₂²	1	2	yes	—
99	C₁₉×#442	C₂²	1	2	yes	—
100	C₁₉×#442	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×SD₁₆×C₁₉	C₂²	1	2	yes	—
106	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
107	C₄×D₈×C₁₉	C₂²	1	2	yes	—
108	C₄×D₈×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×#41×C₁₉	—	2	2	no	—
116	C₂×#41×C₁₉	—	2	2	no	—
117	C₂×#41×C₁₉	—	2	2	no	—
118	C₂×SD₁₆×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×D₈×C₁₉	C₂³	1	2	yes	—
123	C₂×D₈×C₁₉	C₂³	1	2	yes	—
124	C₂×D₈×C₁₉	C₂³	1	2	yes	—
125	C₂×D₈×C₁₉	C₂³	1	2	yes	—
126	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
130	C₁₉×C₄⋊Q₈	—	2	2	no	—
131	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
132	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
133	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
134	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₁₉×#127	C₂³	1	1	yes	characteristic
136	C₁₉×#127	C₂³	1	1	yes	characteristic
137	C₁₉×#127	C₂³	1	2	yes	—
138	C₁₉×#127	C₂³	1	2	yes	—
139	C₁₉×#127	C₂³	1	1	yes	characteristic
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×#125	—	2	2	no	—
146	C₁₉×#125	—	2	2	no	—
147	C₁₉×#125	—	2	2	no	—
148	C₁₉×#125	D₄	1	2	yes	—
149	C₁₉×#125	C₂³	1	1	yes	characteristic
150	C₁₉×#125	C₂³	1	1	yes	characteristic
151	C₁₉×#125	C₂³	1	2	yes	—
152	C₁₉×#125	C₂³	1	1	yes	characteristic
153	C₁₉×#125	C₂³	1	2	yes	—
154	C₁₉×#125	C₂³	1	1	yes	characteristic
155	C₁₉×#124	—	2	2	no	—
156	C₁₉×#124	—	2	2	no	—
157	C₁₉×#124	—	2	2	no	—
158	C₁₉×#124	C₂³	1	2	yes	—
159	C₁₉×#124	C₂³	1	2	yes	—
160	C₁₉×#123	—	2	2	no	—
161	C₁₉×#123	—	2	2	no	—
162	C₁₉×#123	—	2	2	no	—
163	C₁₉×#123	—	2	2	no	—
164	C₁₉×#123	—	2	2	no	—
165	C₁₉×#123	—	2	2	no	—
166	C₁₉×#123	—	2	2	no	—
167	C₁₉×#123	—	2	2	no	—
168	C₁₉×#123	—	2	2	no	—
169	C₁₉×C₂²⋊Q₈	—	2	2	no	—
170	C₁₉×C₂²⋊Q₈	—	2	2	no	—
171	C₁₉×C₂²⋊Q₈	—	2	2	no	—
172	C₁₉×C₂²⋊Q₈	—	2	2	no	—
173	C₁₉×C₂²⋊Q₈	—	2	2	no	—
174	C₁₉×C₂²⋊Q₈	—	2	2	no	—
175	C₁₉×C₂²⋊Q₈	—	2	2	no	—
176	C₁₉×C₂²⋊Q₈	—	2	2	no	—
177	C₁₉×C₂²⋊Q₈	—	2	2	no	—
178	C₁₉×C₂²⋊Q₈	—	2	2	no	—
179	C₁₉×C₂²⋊Q₈	—	2	2	no	—
180	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
181	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
182	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
183	C₁₉×#121	—	2	2	no	—
184	C₁₉×#121	—	2	2	no	—
185	C₁₉×#121	—	2	2	no	—
186	C₁₉×#121	—	2	2	no	—
187	C₁₉×#121	—	2	2	no	—
188	C₁₉×#121	—	2	2	no	—
189	C₁₉×#121	—	2	2	no	—
190	C₁₉×#121	—	2	2	no	—
191	C₁₉×#121	—	2	2	no	—
192	C₁₉×#121	—	2	2	no	—
193	C₁₉×#121	—	2	2	no	—
194	C₁₉×#121	—	2	2	no	—
195	C₁₉×#121	C₂³	1	2	yes	—
196	C₁₉×#121	C₂³	1	2	yes	—
197	C₁₉×#121	C₂³	1	2	yes	—
198	C₄×Q₈×C₁₉	—	2	2	no	—
199	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
200	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
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×D₄×C₁₉	—	2	2	no	—
205	C₄×D₄×C₁₉	—	2	2	no	—
206	C₄×D₄×C₁₉	—	2	2	no	—
207	C₄×D₄×C₁₉	C₂³	1	2	yes	—
208	C₄×D₄×C₁₉	C₂³	1	2	yes	—
209	C₄×D₄×C₁₉	C₂³	1	2	yes	—
210	C₄×D₄×C₁₉	C₂³	1	2	yes	—
211	C₄×D₄×C₁₉	C₂³	1	2	yes	—
212	C₄×D₄×C₁₉	C₂³	1	2	yes	—
213	C₄×D₄×C₁₉	C₂³	1	2	yes	—
214	C₄×D₄×C₁₉	C₂³	1	2	yes	—
215	C₄×D₄×C₁₉	C₂³	1	2	yes	—
216	C₁₉×#117	—	2	2	no	—
217	C₁₉×#117	—	2	2	no	—
218	C₁₉×#117	C₂³	1	1	yes	characteristic
219	C₁₉×#117	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
221	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
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×#102	C₂³	1	2	yes	—
243	C₁₉×#102	C₂³	1	2	yes	—
244	C₁₉×#102	C₂³	1	2	yes	—
245	C₁₉×#102	C₂³	1	2	yes	—
246	C₁₉×#102	C₂³	1	2	yes	—
247	C₁₉×#102	C₂³	1	2	yes	—
248	C₁₉×#102	C₂³	1	2	yes	—
249	C₁₉×#102	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	#41×C₁₉	—	8	4	no	—
263	#41×C₁₉	—	8	4	no	—
264	#41×C₁₉	—	8	4	no	—
265	C₂×Q₈×C₁₉	—	2	2	no	—
266	C₂×Q₈×C₁₉	—	2	2	no	—
267	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
268	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
269	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
270	C₂×D₄×C₁₉	—	2	2	no	—
271	C₂×D₄×C₁₉	—	2	2	no	—
272	C₂×D₄×C₁₉	—	2	2	no	—
273	C₂×D₄×C₁₉	—	2	2	no	—
274	C₂×D₄×C₁₉	—	2	2	no	—
275	C₂×D₄×C₁₉	—	2	2	no	—
276	C₂×D₄×C₁₉	—	2	2	no	—
277	C₂×D₄×C₁₉	—	2	2	no	—
278	C₂×D₄×C₁₉	—	2	2	no	—
279	C₂×D₄×C₁₉	—	2	2	no	—
280	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
281	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
282	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₁₉	—	2	2	no	—
284	C₂²×C₄×C₁₉	—	2	2	no	—
285	C₂²×C₄×C₁₉	—	2	2	no	—
286	C₂²×C₄×C₁₉	—	2	2	no	—
287	C₂²×C₄×C₁₉	—	2	2	no	—
288	C₂²×C₄×C₁₉	—	2	2	no	—
289	C₂²×C₄×C₁₉	—	2	2	no	—
290	C₂²×C₄×C₁₉	—	2	2	no	—
291	C₂²×C₄×C₁₉	—	2	2	no	—
292	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
293	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
294	SD₁₆×C₁₉	—	2	4	no	—
295	SD₁₆×C₁₉	—	4	2	no	—
296	SD₁₆×C₁₉	—	4	2	no	—
297	SD₁₆×C₁₉	—	4	2	no	—
298	D₈×C₁₉	—	2	4	no	—
299	D₈×C₁₉	—	4	2	no	—
300	D₈×C₁₉	—	4	2	no	—
301	D₈×C₁₉	—	4	2	no	—
302	M₁₆×C₁₉	—	4	1	no	—
303	M₁₆×C₁₉	—	4	1	no	—
304	C₂×C₈×C₁₉	—	2	2	no	—
305	C₂×C₈×C₁₉	—	4	1	no	—
306	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
307	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
308	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
309	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
310	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
311	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
325	C₄⋊C₄×C₁₉	—	2	2	no	—
326	C₄⋊C₄×C₁₉	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
333	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
334	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
335	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
336	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
337	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
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	—	2	2	no	—
348	C₂²⋊C₄×C₁₉	—	2	2	no	—
349	C₂²⋊C₄×C₁₉	—	2	2	no	—
350	C₂²⋊C₄×C₁₉	—	2	2	no	—
351	C₂²⋊C₄×C₁₉	—	2	2	no	—
352	C₂²⋊C₄×C₁₉	—	2	2	no	—
353	C₂²⋊C₄×C₁₉	—	2	2	no	—
354	C₂²⋊C₄×C₁₉	—	2	2	no	—
355	C₂²⋊C₄×C₁₉	—	2	2	no	—
356	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
357	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
358	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
359	C₄²×C₁₉	—	2	2	no	—
360	C₄²×C₁₉	—	2	2	no	—
361	C₄²×C₁₉	—	2	2	no	—
362	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
363	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
364	C₄²×C₁₉	C₂⁴	1	2	yes	—
365	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
366	C₄²×C₁₉	C₂⁴	1	2	yes	—
367	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
368	#62387	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
369	C₂³×C₁₉	—	2	2	no	—
370	C₂³×C₁₉	—	2	2	no	—
371	C₂³×C₁₉	—	2	2	no	—
372	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
373	Q₈×C₁₉	—	2	2	no	—
374	Q₈×C₁₉	—	2	2	no	—
375	Q₈×C₁₉	—	4	2	no	—
376	Q₈×C₁₉	—	4	2	no	—
377	Q₈×C₁₉	—	8	2	no	—
378	Q₈×C₁₉	—	8	2	no	—
379	D₄×C₁₉	—	2	2	no	—
380	D₄×C₁₉	—	2	2	no	—
381	D₄×C₁₉	—	2	2	no	—
382	D₄×C₁₉	—	2	2	no	—
383	D₄×C₁₉	—	2	2	no	—
384	D₄×C₁₉	—	2	2	no	—
385	D₄×C₁₉	—	4	4	no	—
386	D₄×C₁₉	—	8	2	no	—
387	D₄×C₁₉	—	8	2	no	—
388	D₄×C₁₉	—	8	2	no	—
389	D₄×C₁₉	—	8	2	no	—
390	D₄×C₁₉	—	8	2	no	—
391	D₄×C₁₉	—	8	2	no	—
392	D₄×C₁₉	—	8	2	no	—
393	D₄×C₁₉	—	8	2	no	—
394	D₄×C₁₉	—	8	2	no	—
395	C₂×C₄×C₁₉	—	2	1	no	—
396	C₂×C₄×C₁₉	—	2	1	no	—
397	C₂×C₄×C₁₉	—	2	2	no	—
398	C₂×C₄×C₁₉	—	2	2	no	—
399	C₂×C₄×C₁₉	—	2	2	no	—
400	C₂×C₄×C₁₉	—	2	2	no	—
401	C₂×C₄×C₁₉	—	2	2	no	—
402	C₂×C₄×C₁₉	—	4	2	no	—
403	C₂×C₄×C₁₉	—	4	4	no	—
404	C₂×C₄×C₁₉	—	4	4	no	—
405	C₂×C₄×C₁₉	—	8	2	no	—
406	C₂×C₄×C₁₉	—	8	2	no	—
407	C₂×C₄×C₁₉	—	8	2	no	—
408	C₂×C₄×C₁₉	—	8	2	no	—
409	C₂×C₄×C₁₉	—	8	2	no	—
410	C₂×C₄×C₁₉	—	8	2	no	—
411	C₂×C₄×C₁₉	—	8	2	no	—
412	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
420	C₈×C₁₉	—	2	1	no	—
421	C₈×C₁₉	—	2	2	no	—
422	C₈×C₁₉	—	2	1	no	—
423	C₈×C₁₉	—	2	2	no	—
424	C₈×C₁₉	—	2	1	no	—
425	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
426	#3557	C₂×C₁₉	1	1	yes	characteristic, complemented
427	#3548	C₂×C₁₉	1	1	yes	characteristic, complemented
428	#3399	C₂×C₁₉	1	2	yes	complemented
429	#3397	C₂×C₁₉	1	2	yes	complemented
430	#3389	C₂×C₁₉	1	2	yes	complemented
431	#3388	C₂×C₁₉	1	2	yes	complemented
432	#3376	C₂×C₁₉	1	2	yes	complemented
433	#3370	C₂×C₁₉	1	2	yes	complemented
434	#3368	C₂×C₁₉	1	2	yes	complemented
435	#3366	C₂×C₁₉	1	2	yes	complemented
436	#3260	C₂×C₁₉	1	1	yes	characteristic, complemented
437	#3259	C₂×C₁₉	1	1	yes	characteristic, complemented
438	#3257	C₂×C₁₉	1	2	yes	complemented
439	#3251	C₂×C₁₉	1	2	yes	complemented
440	#3180	C₂×C₁₉	1	2	yes	complemented
441	#3179	C₂×C₁₉	1	2	yes	complemented
442	#3176	C₂×C₁₉	1	1	yes	characteristic, complemented
443	#3174	C₂×C₁₉	1	1	yes	characteristic, complemented
444	#2961	C₂×C₁₉	1	1	yes	characteristic, complemented
445	C₂²×C₁₉	—	2	2	no	—
446	C₂²×C₁₉	—	2	1	no	—
447	C₂²×C₁₉	—	4	2	no	—
448	C₂²×C₁₉	—	4	2	no	—
449	C₂²×C₁₉	—	4	2	no	—
450	C₂²×C₁₉	—	4	2	no	—
451	C₂²×C₁₉	—	4	2	no	—
452	C₂²×C₁₉	—	4	2	no	—
453	C₂²×C₁₉	—	4	2	no	—
454	C₂²×C₁₉	—	4	2	no	—
455	C₂²×C₁₉	—	4	2	no	—
456	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
457	C₄×C₁₉	—	2	2	no	—
458	C₄×C₁₉	—	2	2	no	—
459	C₄×C₁₉	—	2	2	no	—
460	C₄×C₁₉	—	2	2	no	—
461	C₄×C₁₉	—	2	2	no	—
462	C₄×C₁₉	—	2	2	no	—
463	C₄×C₁₉	—	2	1	no	—
464	C₄×C₁₉	—	4	2	no	—
465	C₄×C₁₉	—	4	2	no	—
466	C₄×C₁₉	—	4	2	no	—
467	C₄×C₁₉	—	4	2	no	—
468	C₄×C₁₉	—	4	2	no	—
469	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
470	C₄×C₁₉	#585	1	1	yes	characteristic
471	#563	—	2	2	no	—
472	#562	—	2	2	no	—
473	#559	C₂²×C₁₉	1	2	yes	—
474	#557	C₂²×C₁₉	1	2	yes	—
475	#556	C₂²×C₁₉	1	2	yes	—
476	#554	C₂²×C₁₉	1	2	yes	—
477	#554	C₂²×C₁₉	1	2	yes	—
478	#554	C₂²×C₁₉	1	2	yes	—
479	#552	—	2	2	no	—
480	#550	C₂²×C₁₉	1	2	yes	—
481	#550	C₂²×C₁₉	1	2	yes	—
482	#547	—	2	2	no	—
483	#542	—	2	2	no	—
484	#542	C₂²×C₁₉	1	2	yes	—
485	#541	C₂²×C₁₉	1	1	yes	characteristic
486	#540	C₂²×C₁₉	1	1	yes	characteristic
487	#540	C₂²×C₁₉	1	1	yes	characteristic
488	#540	C₂²×C₁₉	1	1	yes	characteristic
489	#540	C₂²×C₁₉	1	2	yes	—
490	#539	—	2	2	no	—
491	#537	—	2	2	no	—
492	#537	—	2	2	no	—
493	#533	C₂²×C₁₉	1	1	yes	characteristic
494	#532	C₂²×C₁₉	1	2	yes	—
495	#529	C₂²×C₁₉	1	2	yes	—
496	#501	C₂²×C₁₉	1	2	yes	—
497	#501	C₂²×C₁₉	1	2	yes	—
498	#499	C₂²×C₁₉	1	1	yes	characteristic
499	#499	C₂²×C₁₉	1	1	yes	characteristic
500	#496	C₂²×C₁₉	1	2	yes	—
501	#496	C₂²×C₁₉	1	2	yes	—
502	#493	C₂²×C₁₉	1	1	yes	characteristic
503	#492	C₂²×C₁₉	1	1	yes	characteristic
504	#491	C₂²×C₁₉	1	1	yes	characteristic
505	#490	C₂²×C₁₉	1	1	yes	characteristic
506	#490	C₂²×C₁₉	1	2	yes	—
507	#490	C₂²×C₁₉	1	1	yes	characteristic
508	#490	C₂²×C₁₉	1	1	yes	characteristic
509	#489	C₂²×C₁₉	1	2	yes	—
510	#488	C₂²×C₁₉	1	2	yes	—
511	#486	C₂²×C₁₉	1	2	yes	—
512	#479	C₂²×C₁₉	1	2	yes	—
513	#479	C₂²×C₁₉	1	2	yes	—
514	#478	C₂²×C₁₉	1	2	yes	—
515	#478	C₂²×C₁₉	1	2	yes	—
516	#478	C₂²×C₁₉	1	2	yes	—
517	#478	C₂²×C₁₉	1	2	yes	—
518	#478	C₂²×C₁₉	1	2	yes	—
519	#478	C₂²×C₁₉	1	2	yes	—
520	#476	C₂²×C₁₉	1	2	yes	—
521	#475	C₂²×C₁₉	1	2	yes	—
522	#474	C₂²×C₁₉	1	2	yes	—
523	#474	C₂²×C₁₉	1	2	yes	—
524	#469	C₂²×C₁₉	1	2	yes	—
525	#469	C₂²×C₁₉	1	2	yes	—
526	#468	C₂²×C₁₉	1	2	yes	—
527	#468	C₂²×C₁₉	1	2	yes	—
528	#466	C₂²×C₁₉	1	2	yes	—
529	#466	C₂²×C₁₉	1	2	yes	—
530	#465	C₂²×C₁₉	1	2	yes	—
531	#465	C₂²×C₁₉	1	2	yes	—
532	#463	C₂²×C₁₉	1	2	yes	—
533	#463	C₂²×C₁₉	1	2	yes	—
534	#463	C₂²×C₁₉	1	2	yes	—
535	#463	C₂²×C₁₉	1	2	yes	—
536	#461	C₂²×C₁₉	1	2	yes	—
537	#460	C₂²×C₁₉	1	2	yes	—
538	#460	C₂²×C₁₉	1	2	yes	—
539	#460	C₂²×C₁₉	1	2	yes	—
540	#459	C₂²×C₁₉	1	2	yes	—
541	#459	C₂²×C₁₉	1	2	yes	—
542	#459	C₂²×C₁₉	1	2	yes	—
543	#459	C₂²×C₁₉	1	2	yes	—
544	#446	C₂²×C₁₉	1	2	yes	—
545	#446	C₂²×C₁₉	1	2	yes	—
546	#446	C₂²×C₁₉	1	2	yes	—
547	#446	C₂²×C₁₉	1	2	yes	—
548	#442	C₂²×C₁₉	1	2	yes	—
549	#442	C₂²×C₁₉	1	2	yes	—
550	#442	C₂²×C₁₉	1	2	yes	—
551	#442	C₂²×C₁₉	1	2	yes	—
552	#440	C₂²×C₁₉	1	2	yes	—
553	#440	C₂²×C₁₉	1	2	yes	—
554	#440	C₂²×C₁₉	1	2	yes	—
555	#440	C₂²×C₁₉	1	2	yes	—
556	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
557	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
558	C₄×D₈	C₂²×C₁₉	1	2	yes	—
559	C₄×D₈	C₂²×C₁₉	1	2	yes	—
560	#424	C₂²×C₁₉	1	1	yes	characteristic
561	#424	C₂²×C₁₉	1	1	yes	characteristic
562	#423	C₂²×C₁₉	1	1	yes	characteristic
563	#405	C₂²×C₁₉	1	1	yes	characteristic
564	#405	C₂²×C₁₉	1	1	yes	characteristic
565	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
566	C₂×C₁₉	—	4	1	no	—
567	C₂×C₁₉	—	8	2	no	—
568	C₂×C₁₉	—	8	2	no	—
569	C₂×C₁₉	—	8	2	no	—
570	C₂×C₁₉	#3497	1	1	yes	characteristic
571	C₂×C₁₉	#3585	1	2	yes	—
572	C₂×#41	—	2	2	no	—
573	C₂×#41	—	2	2	no	—
574	C₂×#41	—	2	2	no	—
575	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
576	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
577	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
578	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
579	C₂×D₈	C₂³×C₁₉	1	2	yes	—
580	C₂×D₈	C₂³×C₁₉	1	2	yes	—
581	C₂×D₈	C₂³×C₁₉	1	2	yes	—
582	C₂×D₈	C₂³×C₁₉	1	2	yes	—
583	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
584	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
585	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
586	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
587	C₄⋊Q₈	—	2	2	no	—
588	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
589	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
590	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
591	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
592	#127	C₂³×C₁₉	1	2	yes	—
593	#127	C₂³×C₁₉	1	1	yes	characteristic
594	#127	C₂³×C₁₉	1	2	yes	—
595	#127	C₂³×C₁₉	1	1	yes	characteristic
596	#127	C₂³×C₁₉	1	1	yes	characteristic
597	#126	—	2	2	no	—
598	#126	—	2	2	no	—
599	#126	—	2	2	no	—
600	#126	—	2	2	no	—
601	#126	—	2	2	no	—
602	#125	—	2	2	no	—
603	#125	—	2	2	no	—
604	#125	—	2	2	no	—
605	#125	D₄×C₁₉	1	2	yes	—
606	#125	C₂³×C₁₉	1	2	yes	—
607	#125	C₂³×C₁₉	1	1	yes	characteristic
608	#125	C₂³×C₁₉	1	2	yes	—
609	#125	C₂³×C₁₉	1	1	yes	characteristic
610	#125	C₂³×C₁₉	1	1	yes	characteristic
611	#125	C₂³×C₁₉	1	1	yes	characteristic
612	#124	—	2	2	no	—
613	#124	—	2	2	no	—
614	#124	—	2	2	no	—
615	#124	C₂³×C₁₉	1	2	yes	—
616	#124	C₂³×C₁₉	1	2	yes	—
617	#123	—	2	2	no	—
618	#123	—	2	2	no	—
619	#123	—	2	2	no	—
620	#123	—	2	2	no	—
621	#123	—	2	2	no	—
622	#123	—	2	2	no	—
623	#123	—	2	2	no	—
624	#123	—	2	2	no	—
625	#123	—	2	2	no	—
626	C₂²⋊Q₈	—	2	2	no	—
627	C₂²⋊Q₈	—	2	2	no	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	—	2	2	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
638	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
639	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
640	#121	—	2	2	no	—
641	#121	—	2	2	no	—
642	#121	—	2	2	no	—
643	#121	—	2	2	no	—
644	#121	—	2	2	no	—
645	#121	—	2	2	no	—
646	#121	—	2	2	no	—
647	#121	—	2	2	no	—
648	#121	—	2	2	no	—
649	#121	—	2	2	no	—
650	#121	—	2	2	no	—
651	#121	—	2	2	no	—
652	#121	C₂³×C₁₉	1	2	yes	—
653	#121	C₂³×C₁₉	1	2	yes	—
654	#121	C₂³×C₁₉	1	2	yes	—
655	C₄×Q₈	—	2	2	no	—
656	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
657	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
658	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
659	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
660	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
661	C₄×D₄	—	2	2	no	—
662	C₄×D₄	—	2	2	no	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	C₂³×C₁₉	1	2	yes	—
665	C₄×D₄	C₂³×C₁₉	1	2	yes	—
666	C₄×D₄	C₂³×C₁₉	1	2	yes	—
667	C₄×D₄	C₂³×C₁₉	1	2	yes	—
668	C₄×D₄	C₂³×C₁₉	1	2	yes	—
669	C₄×D₄	C₂³×C₁₉	1	2	yes	—
670	C₄×D₄	C₂³×C₁₉	1	2	yes	—
671	C₄×D₄	C₂³×C₁₉	1	2	yes	—
672	C₄×D₄	C₂³×C₁₉	1	2	yes	—
673	#117	—	2	2	no	—
674	#117	—	2	2	no	—
675	#117	C₂³×C₁₉	1	1	yes	characteristic
676	#117	C₂³×C₁₉	1	1	yes	characteristic
677	C₂×C₄⋊C₄	—	2	2	no	—
678	C₂×C₄⋊C₄	—	2	2	no	—
679	C₂×C₄⋊C₄	—	2	2	no	—
680	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
681	#107	C₂³×C₁₉	1	2	yes	—
682	#107	C₂³×C₁₉	1	2	yes	—
683	#107	C₂³×C₁₉	1	2	yes	—
684	#107	C₂³×C₁₉	1	2	yes	—
685	#106	C₂³×C₁₉	1	2	yes	—
686	#106	C₂³×C₁₉	1	2	yes	—
687	#106	C₂³×C₁₉	1	2	yes	—
688	#106	C₂³×C₁₉	1	2	yes	—
689	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
690	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
691	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
692	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
693	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
694	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
695	#103	C₂³×C₁₉	1	2	yes	—
696	#103	C₂³×C₁₉	1	2	yes	—
697	#103	C₂³×C₁₉	1	2	yes	—
698	#103	C₂³×C₁₉	1	2	yes	—
699	#102	C₂³×C₁₉	1	2	yes	—
700	#102	C₂³×C₁₉	1	2	yes	—
701	#102	C₂³×C₁₉	1	2	yes	—
702	#102	C₂³×C₁₉	1	2	yes	—
703	#102	C₂³×C₁₉	1	2	yes	—
704	#102	C₂³×C₁₉	1	2	yes	—
705	#102	C₂³×C₁₉	1	2	yes	—
706	#102	C₂³×C₁₉	1	2	yes	—
707	#102	C₂³×C₁₉	1	2	yes	—
708	#102	C₂³×C₁₉	1	2	yes	—
709	#102	C₂³×C₁₉	1	2	yes	—
710	#102	C₂³×C₁₉	1	2	yes	—
711	#97	C₂³×C₁₉	1	2	yes	—
712	#97	C₂³×C₁₉	1	2	yes	—
713	#97	C₂³×C₁₉	1	1	yes	characteristic
714	#97	C₂³×C₁₉	1	2	yes	—
715	#97	C₂³×C₁₉	1	1	yes	characteristic
716	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
717	C₄×C₈	C₂³×C₁₉	1	2	yes	—
718	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
719	C₁₉	#62387	1	1	yes	characteristic, direct product factor, Sylow
720	#41	—	8	4	no	—
721	#41	—	8	4	no	—
722	#41	—	8	4	no	—
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	2	2	no	—
725	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
726	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
727	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
739	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
740	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
752	SD₁₆	—	2	4	no	—
753	SD₁₆	—	4	2	no	—
754	SD₁₆	—	4	2	no	—
755	SD₁₆	—	4	2	no	—
756	D₈	—	2	4	no	—
757	D₈	—	4	2	no	—
758	D₈	—	4	2	no	—
759	D₈	—	4	2	no	—
760	M₁₆	—	4	1	no	—
761	M₁₆	—	4	1	no	—
762	C₂×C₈	—	2	2	no	—
763	C₂×C₈	—	4	1	no	—
764	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
765	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
766	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
767	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
768	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
769	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
786	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
787	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
788	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
789	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
790	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
791	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
792	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
794	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
795	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
796	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
797	C₂²⋊C₄	—	2	2	no	—
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	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
815	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
816	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
821	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
822	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
823	C₄²	C₂⁴×C₁₉	1	2	yes	—
824	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
825	C₄²	C₂⁴×C₁₉	1	2	yes	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
830	Q₈	—	2	2	no	—
831	Q₈	—	2	2	no	—
832	Q₈	—	4	2	no	—
833	Q₈	—	4	2	no	—
834	Q₈	—	8	2	no	—
835	Q₈	—	8	2	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	2	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	2	no	—
841	D₄	—	2	2	no	—
842	D₄	—	4	4	no	—
843	D₄	—	8	2	no	—
844	D₄	—	8	2	no	—
845	D₄	—	8	2	no	—
846	D₄	—	8	2	no	—
847	D₄	—	8	2	no	—
848	D₄	—	8	2	no	—
849	D₄	—	8	2	no	—
850	D₄	—	8	2	no	—
851	D₄	—	8	2	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	4	4	no	—
861	C₂×C₄	—	4	4	no	—
862	C₂×C₄	—	8	2	no	—
863	C₂×C₄	—	8	2	no	—
864	C₂×C₄	—	8	2	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	—	8	2	no	—
867	C₂×C₄	—	8	2	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
870	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
872	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
873	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
874	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
875	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
876	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
877	C₈	—	2	1	no	—
878	C₈	—	2	2	no	—
879	C₈	—	2	1	no	—
880	C₈	—	2	2	no	—
881	C₈	—	2	1	no	—
882	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
883	C₂²	—	2	1	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
895	C₄	—	2	1	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
908	C₄	C₁₉×#585	1	1	yes	characteristic
909	C₂	—	4	1	no	—
910	C₂	—	8	2	no	—
911	C₂	—	8	2	no	—
912	C₂	—	8	2	no	—
913	C₂	C₁₉×#3497	1	1	yes	characteristic
914	C₂	C₁₉×#3585	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3557	C₂	semidirect
2. C₁₉×#3548	C₂	semidirect
3. C₁₉×#3399	C₂	semidirect
4. C₁₉×#3397	C₂	semidirect
5. C₁₉×#3389	C₂	semidirect
6. C₁₉×#3388	C₂	semidirect
7. C₁₉×#3376	C₂	semidirect
8. C₁₉×#3370	C₂	semidirect
9. C₁₉×#3368	C₂	semidirect
10. C₁₉×#3366	C₂	semidirect
11. C₁₉×#3260	C₂	semidirect
12. C₁₉×#3259	C₂	semidirect
13. C₁₉×#3257	C₂	semidirect
14. C₁₉×#3251	C₂	semidirect
15. C₁₉×#3180	C₂	semidirect
16. C₁₉×#3179	C₂	semidirect
17. C₁₉×#3176	C₂	semidirect
18. C₁₉×#3174	C₂	semidirect
19. C₁₉×#2961	C₂	semidirect
368. #62387	C₁₉	direct (N × H)
426. #3557	C₂×C₁₉	semidirect
427. #3548	C₂×C₁₉	semidirect
428. #3399	C₂×C₁₉	semidirect
429. #3397	C₂×C₁₉	semidirect
430. #3389	C₂×C₁₉	semidirect
431. #3388	C₂×C₁₉	semidirect
432. #3376	C₂×C₁₉	semidirect
433. #3370	C₂×C₁₉	semidirect
434. #3368	C₂×C₁₉	semidirect
435. #3366	C₂×C₁₉	semidirect
436. #3260	C₂×C₁₉	semidirect
437. #3259	C₂×C₁₉	semidirect
438. #3257	C₂×C₁₉	semidirect
439. #3251	C₂×C₁₉	semidirect
440. #3180	C₂×C₁₉	semidirect
441. #3179	C₂×C₁₉	semidirect
442. #3176	C₂×C₁₉	semidirect
443. #3174	C₂×C₁₉	semidirect
444. #2961	C₂×C₁₉	semidirect
719. C₁₉	#62387	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×#3548	2
C₁₉×#3399	2
C₁₉×#3397	2
C₁₉×#3389	2
C₁₉×#3388	2
C₁₉×#3376	2
C₁₉×#3370	2
C₁₉×#3368	2
C₁₉×#3366	2
C₁₉×#3260	2
C₁₉×#3259	2
C₁₉×#3257	2
C₁₉×#3251	2
C₁₉×#3180	2
C₁₉×#3179	2
C₁₉×#3176	2
C₁₉×#3174	2
C₁₉×#2961	2
#62387	19

Subgroups — C19×#62387 #18068346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62387 #18068346