Subgroups — C₁₉×#62407 #18068366

Order 4864.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3401	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3393	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3387	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3384	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#3371	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3369	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3369	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3367	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3360	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3359	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3263	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3258	C₂	1	2	yes	maximal, complemented
17	C₁₉×#3248	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#3185	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#3178	C₂	1	2	yes	maximal, complemented
21	C₁₉×#3173	C₂	1	2	yes	maximal, complemented
22	C₁₉×#3171	C₂	1	1	yes	maximal, characteristic
23	C₁₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₉×#563	—	2	2	no	—
25	C₁₉×#563	—	2	2	no	—
26	C₁₉×#559	C₂²	1	2	yes	—
27	Q₈²×C₁₉	C₂²	1	2	yes	—
28	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#557	C₂²	1	1	yes	characteristic
30	C₁₉×#557	C₂²	1	2	yes	—
31	C₁₉×#556	—	2	1	no	—
32	C₁₉×#556	—	2	1	no	—
33	C₁₉×#556	C₂²	1	1	yes	characteristic
34	C₁₉×#556	C₂²	1	1	yes	characteristic
35	C₁₉×#556	C₂²	1	1	yes	characteristic
36	C₁₉×#556	C₂²	1	2	yes	—
37	C₁₉×#554	C₂²	1	1	yes	characteristic
38	C₁₉×#552	—	2	1	no	—
39	D₄×Q₈×C₁₉	—	2	1	no	—
40	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
42	C₁₉×#544	—	2	1	no	—
43	C₁₉×#542	—	2	2	no	—
44	C₁₉×#542	C₂²	1	2	yes	—
45	C₁₉×#542	C₂²	1	2	yes	—
46	C₁₉×#542	C₂²	1	2	yes	—
47	C₁₉×#541	—	2	1	no	—
48	C₁₉×#541	—	2	2	no	—
49	C₁₉×#541	C₂²	1	2	yes	—
50	C₁₉×#536	—	2	1	no	—
51	C₁₉×#536	—	2	1	no	—
52	C₁₉×#533	C₂²	1	1	yes	characteristic
53	C₁₉×#533	C₂²	1	1	yes	characteristic
54	C₁₉×#533	C₂²	1	1	yes	characteristic
55	C₁₉×#532	C₂²	1	1	yes	characteristic
56	C₁₉×#529	C₂²	1	1	yes	characteristic
57	C₁₉×#501	C₂²	1	1	yes	characteristic
58	C₁₉×#501	C₂²	1	2	yes	—
59	C₁₉×#498	C₂²	1	2	yes	—
60	C₁₉×#498	C₂²	1	1	yes	characteristic
61	C₁₉×#497	C₂²	1	2	yes	—
62	C₁₉×#496	C₂²	1	1	yes	characteristic
63	C₁₉×#495	C₂²	1	2	yes	—
64	C₁₉×#494	C₂²	1	1	yes	characteristic
65	C₁₉×#490	C₂²	1	1	yes	characteristic
66	C₁₉×#489	C₂²	1	1	yes	characteristic
67	C₁₉×#489	C₂²	1	2	yes	—
68	C₁₉×#489	C₂²	1	2	yes	—
69	C₁₉×#488	C₂²	1	2	yes	—
70	C₁₉×#487	C₂²	1	2	yes	—
71	C₁₉×#487	C₂²	1	1	yes	characteristic
72	C₁₉×#487	C₂²	1	1	yes	characteristic
73	C₁₉×#479	C₂²	1	2	yes	—
74	C₁₉×#479	C₂²	1	2	yes	—
75	C₁₉×#478	C₂²	1	2	yes	—
76	C₁₉×#477	C₂²	1	2	yes	—
77	C₁₉×#476	C₂²	1	1	yes	characteristic
78	C₁₉×#476	C₂²	1	1	yes	characteristic
79	C₁₉×#476	C₂²	1	2	yes	—
80	C₁₉×#476	C₂²	1	2	yes	—
81	C₁₉×#475	C₂²	1	2	yes	—
82	C₁₉×#475	C₂²	1	1	yes	characteristic
83	C₁₉×#475	C₂²	1	2	yes	—
84	C₁₉×#475	C₂²	1	2	yes	—
85	C₁₉×#475	C₂²	1	2	yes	—
86	C₁₉×#474	C₂²	1	1	yes	characteristic
87	C₁₉×#470	C₂²	1	2	yes	—
88	C₁₉×#470	C₂²	1	2	yes	—
89	C₁₉×#469	C₂²	1	1	yes	characteristic
90	C₁₉×#469	C₂²	1	1	yes	characteristic
91	C₁₉×#468	C₂²	1	1	yes	characteristic
92	C₁₉×#468	C₂²	1	1	yes	characteristic
93	C₁₉×#467	C₂²	1	2	yes	—
94	C₁₉×#465	C₂²	1	2	yes	—
95	C₁₉×#465	C₂²	1	2	yes	—
96	C₁₉×#465	C₂²	1	2	yes	—
97	C₁₉×#464	C₂²	1	2	yes	—
98	C₁₉×#464	C₂²	1	2	yes	—
99	C₁₉×#464	C₂²	1	2	yes	—
100	C₁₉×#464	C₂²	1	2	yes	—
101	C₁₉×#464	C₂²	1	2	yes	—
102	C₁₉×#463	C₂²	1	2	yes	—
103	C₁₉×#463	C₂²	1	2	yes	—
104	C₁₉×#462	C₂²	1	1	yes	characteristic
105	C₁₉×#462	C₂²	1	2	yes	—
106	C₁₉×#461	C₂²	1	1	yes	characteristic
107	C₁₉×#461	C₂²	1	1	yes	characteristic
108	C₁₉×#461	C₂²	1	1	yes	characteristic
109	C₁₉×#461	C₂²	1	2	yes	—
110	C₁₉×#460	C₂²	1	2	yes	—
111	C₁₉×#446	C₂²	1	1	yes	characteristic
112	C₁₉×#446	C₂²	1	2	yes	—
113	C₁₉×#446	C₂²	1	1	yes	characteristic
114	C₁₉×#446	C₂²	1	2	yes	—
115	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
117	C₁₉×#442	C₂²	1	2	yes	—
118	C₁₉×#441	C₂²	1	2	yes	—
119	C₁₉×#441	C₂²	1	2	yes	—
120	C₁₉×#441	C₂²	1	2	yes	—
121	C₁₉×#441	C₂²	1	2	yes	—
122	C₁₉×#440	C₂²	1	2	yes	—
123	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
124	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
125	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
128	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
129	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
131	C₁₉×#424	C₂²	1	2	yes	—
132	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
133	C₁₉×#405	C₂²	1	2	yes	—
134	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
135	C₂×#41×C₁₉	—	2	1	no	—
136	C₂²×Q₈×C₁₉	—	2	1	no	—
137	C₂²×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
139	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
146	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
151	C₁₉×C₄⋊Q₈	—	2	2	no	—
152	C₁₉×C₄⋊Q₈	—	2	2	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	—	2	1	no	—
157	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
158	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
159	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₁₉×#127	C₂³	1	1	yes	characteristic
169	C₁₉×#126	—	2	2	no	—
170	C₁₉×#126	—	2	2	no	—
171	C₁₉×#126	—	2	2	no	—
172	C₁₉×#126	—	2	2	no	—
173	C₁₉×#126	—	2	2	no	—
174	C₁₉×#126	—	2	2	no	—
175	C₁₉×#126	—	2	2	no	—
176	C₁₉×#126	—	2	2	no	—
177	C₁₉×#126	—	2	2	no	—
178	C₁₉×#126	—	2	2	no	—
179	C₁₉×#126	—	2	1	no	—
180	C₁₉×#125	—	2	2	no	—
181	C₁₉×#125	—	2	2	no	—
182	C₁₉×#125	—	2	2	no	—
183	C₁₉×#125	—	2	2	no	—
184	C₁₉×#125	—	2	2	no	—
185	C₁₉×#125	—	2	1	no	—
186	C₁₉×#125	—	2	1	no	—
187	C₁₉×#125	—	2	1	no	—
188	C₁₉×#125	D₄	1	2	yes	—
189	C₁₉×#125	C₂³	1	2	yes	—
190	C₁₉×#125	C₂³	1	1	yes	characteristic
191	C₁₉×#124	—	2	2	no	—
192	C₁₉×#124	—	2	2	no	—
193	C₁₉×#124	—	2	2	no	—
194	C₁₉×#124	—	2	2	no	—
195	C₁₉×#124	—	2	1	no	—
196	C₁₉×#124	C₂³	1	2	yes	—
197	C₁₉×#124	C₂³	1	2	yes	—
198	C₁₉×#124	C₂³	1	2	yes	—
199	C₁₉×#124	C₂³	1	1	yes	characteristic
200	C₁₉×#123	—	2	1	no	—
201	C₁₉×#123	—	2	2	no	—
202	C₁₉×#123	—	2	2	no	—
203	C₁₉×#123	—	2	2	no	—
204	C₁₉×#123	—	2	2	no	—
205	C₁₉×#123	—	2	2	no	—
206	C₁₉×C₂²⋊Q₈	—	2	1	no	—
207	C₁₉×C₂²⋊Q₈	—	2	1	no	—
208	C₁₉×C₂²⋊Q₈	—	2	1	no	—
209	C₁₉×C₂²⋊Q₈	—	2	1	no	—
210	C₁₉×C₂²⋊Q₈	—	2	2	no	—
211	C₁₉×C₂²⋊Q₈	—	2	1	no	—
212	C₁₉×C₂²⋊Q₈	—	2	1	no	—
213	C₁₉×C₂²⋊Q₈	—	2	1	no	—
214	C₁₉×C₂²⋊Q₈	—	2	1	no	—
215	C₁₉×C₂²⋊Q₈	—	2	2	no	—
216	C₁₉×C₂²⋊Q₈	—	2	2	no	—
217	C₁₉×C₂²⋊Q₈	—	2	2	no	—
218	C₁₉×C₂²⋊Q₈	—	2	2	no	—
219	C₁₉×C₂²⋊Q₈	—	2	2	no	—
220	C₁₉×C₂²⋊Q₈	—	2	2	no	—
221	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
222	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
223	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
224	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
226	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
227	C₁₉×#121	—	2	1	no	—
228	C₁₉×#121	C₂³	1	1	yes	characteristic
229	C₁₉×#121	C₂³	1	1	yes	characteristic
230	C₁₉×#121	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₁₉	—	2	1	no	—
232	C₄×Q₈×C₁₉	—	2	1	no	—
233	C₄×Q₈×C₁₉	—	2	2	no	—
234	C₄×Q₈×C₁₉	—	2	2	no	—
235	C₄×Q₈×C₁₉	—	2	1	no	—
236	C₄×Q₈×C₁₉	—	2	1	no	—
237	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
239	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
240	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
241	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
242	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
243	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
244	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
245	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
246	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
248	C₄×D₄×C₁₉	—	2	1	no	—
249	C₄×D₄×C₁₉	—	2	2	no	—
250	C₄×D₄×C₁₉	—	2	1	no	—
251	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₁₉	C₂³	1	2	yes	—
255	C₄×D₄×C₁₉	C₂³	1	2	yes	—
256	C₄×D₄×C₁₉	C₂³	1	2	yes	—
257	C₁₉×#117	—	2	1	no	—
258	C₁₉×#117	—	2	1	no	—
259	C₁₉×#117	—	2	1	no	—
260	C₁₉×#117	—	2	1	no	—
261	C₁₉×#117	—	2	2	no	—
262	C₁₉×#117	—	2	1	no	—
263	C₁₉×#117	—	2	1	no	—
264	C₁₉×#117	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
266	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
267	C₁₉×#107	C₂³	1	1	yes	characteristic
268	C₁₉×#107	C₂³	1	1	yes	characteristic
269	C₁₉×#107	C₂³	1	2	yes	—
270	C₁₉×#106	C₂³	1	1	yes	characteristic
271	C₁₉×#106	C₂³	1	2	yes	—
272	C₁₉×#106	C₂³	1	2	yes	—
273	C₁₉×#106	C₂³	1	2	yes	—
274	C₁₉×#106	C₂³	1	1	yes	characteristic
275	C₁₉×#106	C₂³	1	2	yes	—
276	C₁₉×#106	C₂³	1	2	yes	—
277	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
279	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
282	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
283	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
284	C₁₉×#103	C₂³	1	2	yes	—
285	C₁₉×#103	C₂³	1	1	yes	characteristic
286	C₁₉×#103	C₂³	1	2	yes	—
287	C₁₉×#103	C₂³	1	2	yes	—
288	C₁₉×#103	C₂³	1	1	yes	characteristic
289	C₁₉×#103	C₂³	1	2	yes	—
290	C₁₉×#103	C₂³	1	2	yes	—
291	C₁₉×#103	C₂³	1	2	yes	—
292	C₁₉×#103	C₂³	1	2	yes	—
293	C₁₉×#103	C₂³	1	2	yes	—
294	C₁₉×#103	C₂³	1	2	yes	—
295	C₁₉×#102	C₂³	1	1	yes	characteristic
296	C₁₉×#102	C₂³	1	1	yes	characteristic
297	C₁₉×#102	C₂³	1	1	yes	characteristic
298	C₁₉×#102	C₂³	1	1	yes	characteristic
299	C₁₉×#102	C₂³	1	1	yes	characteristic
300	C₁₉×#102	C₂³	1	2	yes	—
301	C₁₉×#102	C₂³	1	1	yes	characteristic
302	C₁₉×#102	C₂³	1	2	yes	—
303	C₁₉×#102	C₂³	1	2	yes	—
304	C₁₉×#97	C₂³	1	1	yes	characteristic
305	C₁₉×#97	C₂³	1	1	yes	characteristic
306	C₁₉×#97	C₂³	1	2	yes	—
307	C₁₉×#97	C₂³	1	2	yes	—
308	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₁₉	C₂³	1	2	yes	—
311	C₄×C₈×C₁₉	C₂³	1	2	yes	—
312	#41×C₁₉	—	8	2	no	—
313	C₂×Q₈×C₁₉	—	2	1	no	—
314	C₂×Q₈×C₁₉	—	2	1	no	—
315	C₂×Q₈×C₁₉	—	2	2	no	—
316	C₂×Q₈×C₁₉	—	2	2	no	—
317	C₂×Q₈×C₁₉	—	2	2	no	—
318	C₂×Q₈×C₁₉	—	2	1	no	—
319	C₂×Q₈×C₁₉	—	8	2	no	—
320	C₂×Q₈×C₁₉	—	8	2	no	—
321	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
324	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
327	C₂×D₄×C₁₉	—	2	1	no	—
328	C₂×D₄×C₁₉	—	2	1	no	—
329	C₂×D₄×C₁₉	—	2	1	no	—
330	C₂×D₄×C₁₉	—	2	1	no	—
331	C₂×D₄×C₁₉	—	2	1	no	—
332	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₁₉	—	2	1	no	—
336	C₂²×C₄×C₁₉	—	2	1	no	—
337	C₂²×C₄×C₁₉	—	2	1	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	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
344	Q₁₆×C₁₉	—	2	4	no	—
345	Q₁₆×C₁₉	—	4	2	no	—
346	Q₁₆×C₁₉	—	4	2	no	—
347	SD₁₆×C₁₉	—	2	2	no	—
348	SD₁₆×C₁₉	—	4	2	no	—
349	SD₁₆×C₁₉	—	4	2	no	—
350	SD₁₆×C₁₉	—	4	2	no	—
351	SD₁₆×C₁₉	—	4	1	no	—
352	D₈×C₁₉	—	2	2	no	—
353	D₈×C₁₉	—	4	1	no	—
354	M₁₆×C₁₉	—	2	2	no	—
355	M₁₆×C₁₉	—	4	1	no	—
356	C₂×C₈×C₁₉	—	4	2	no	—
357	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
358	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
359	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
363	C₄⋊C₄×C₁₉	—	2	1	no	—
364	C₄⋊C₄×C₁₉	—	2	2	no	—
365	C₄⋊C₄×C₁₉	—	2	1	no	—
366	C₄⋊C₄×C₁₉	—	2	1	no	—
367	C₄⋊C₄×C₁₉	—	2	1	no	—
368	C₄⋊C₄×C₁₉	—	2	2	no	—
369	C₄⋊C₄×C₁₉	—	2	1	no	—
370	C₄⋊C₄×C₁₉	—	2	1	no	—
371	C₄⋊C₄×C₁₉	—	2	1	no	—
372	C₄⋊C₄×C₁₉	—	2	1	no	—
373	C₄⋊C₄×C₁₉	—	2	1	no	—
374	C₄⋊C₄×C₁₉	—	2	2	no	—
375	C₄⋊C₄×C₁₉	—	2	2	no	—
376	C₄⋊C₄×C₁₉	—	2	2	no	—
377	C₄⋊C₄×C₁₉	—	2	2	no	—
378	C₄⋊C₄×C₁₉	—	2	2	no	—
379	C₄⋊C₄×C₁₉	—	2	1	no	—
380	C₄⋊C₄×C₁₉	—	2	2	no	—
381	C₄⋊C₄×C₁₉	—	2	2	no	—
382	C₄⋊C₄×C₁₉	—	2	2	no	—
383	C₄⋊C₄×C₁₉	—	2	2	no	—
384	C₄⋊C₄×C₁₉	—	2	2	no	—
385	C₄⋊C₄×C₁₉	—	2	2	no	—
386	C₄⋊C₄×C₁₉	—	2	2	no	—
387	C₄⋊C₄×C₁₉	—	2	2	no	—
388	C₄⋊C₄×C₁₉	—	2	2	no	—
389	C₄⋊C₄×C₁₉	—	2	1	no	—
390	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
391	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
405	C₂²⋊C₄×C₁₉	—	2	2	no	—
406	C₂²⋊C₄×C₁₉	—	2	2	no	—
407	C₂²⋊C₄×C₁₉	—	2	1	no	—
408	C₂²⋊C₄×C₁₉	—	2	1	no	—
409	C₂²⋊C₄×C₁₉	—	2	1	no	—
410	C₂²⋊C₄×C₁₉	—	2	1	no	—
411	C₂²⋊C₄×C₁₉	—	2	2	no	—
412	C₂²⋊C₄×C₁₉	—	2	2	no	—
413	C₂²⋊C₄×C₁₉	—	2	2	no	—
414	C₂²⋊C₄×C₁₉	—	2	2	no	—
415	C₂²⋊C₄×C₁₉	—	2	1	no	—
416	C₂²⋊C₄×C₁₉	—	2	1	no	—
417	C₂²⋊C₄×C₁₉	—	2	2	no	—
418	C₂²⋊C₄×C₁₉	—	2	2	no	—
419	C₂²⋊C₄×C₁₉	—	2	1	no	—
420	C₂²⋊C₄×C₁₉	—	2	1	no	—
421	C₂²⋊C₄×C₁₉	—	2	2	no	—
422	C₂²⋊C₄×C₁₉	—	2	2	no	—
423	C₂²⋊C₄×C₁₉	—	2	1	no	—
424	C₂²⋊C₄×C₁₉	—	2	2	no	—
425	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
427	C₄²×C₁₉	—	2	2	no	—
428	C₄²×C₁₉	—	2	2	no	—
429	C₄²×C₁₉	—	2	1	no	—
430	C₄²×C₁₉	—	2	2	no	—
431	C₄²×C₁₉	—	2	2	no	—
432	C₄²×C₁₉	—	2	2	no	—
433	C₄²×C₁₉	—	2	2	no	—
434	C₄²×C₁₉	—	2	2	no	—
435	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
438	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
439	C₄²×C₁₉	C₂⁴	1	2	yes	—
440	C₄²×C₁₉	C₂⁴	1	2	yes	—
441	#62407	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
442	C₂³×C₁₉	—	2	1	no	—
443	C₂³×C₁₉	—	2	1	no	—
444	C₂³×C₁₉	—	2	1	no	—
445	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
446	Q₈×C₁₉	—	2	2	no	—
447	Q₈×C₁₉	—	2	2	no	—
448	Q₈×C₁₉	—	2	1	no	—
449	Q₈×C₁₉	—	2	2	no	—
450	Q₈×C₁₉	—	2	2	no	—
451	Q₈×C₁₉	—	2	2	no	—
452	Q₈×C₁₉	—	2	2	no	—
453	Q₈×C₁₉	—	2	1	no	—
454	Q₈×C₁₉	—	4	2	no	—
455	Q₈×C₁₉	—	4	2	no	—
456	Q₈×C₁₉	—	8	1	no	—
457	Q₈×C₁₉	—	8	2	no	—
458	Q₈×C₁₉	—	8	2	no	—
459	Q₈×C₁₉	—	8	2	no	—
460	Q₈×C₁₉	—	8	1	no	—
461	D₄×C₁₉	—	2	1	no	—
462	D₄×C₁₉	—	2	1	no	—
463	D₄×C₁₉	—	2	1	no	—
464	D₄×C₁₉	—	2	1	no	—
465	D₄×C₁₉	—	2	1	no	—
466	D₄×C₁₉	—	2	1	no	—
467	D₄×C₁₉	—	4	2	no	—
468	D₄×C₁₉	—	8	1	no	—
469	D₄×C₁₉	—	8	1	no	—
470	D₄×C₁₉	—	8	1	no	—
471	D₄×C₁₉	—	8	1	no	—
472	C₂×C₄×C₁₉	—	2	2	no	—
473	C₂×C₄×C₁₉	—	2	1	no	—
474	C₂×C₄×C₁₉	—	2	1	no	—
475	C₂×C₄×C₁₉	—	2	2	no	—
476	C₂×C₄×C₁₉	—	2	2	no	—
477	C₂×C₄×C₁₉	—	2	1	no	—
478	C₂×C₄×C₁₉	—	2	1	no	—
479	C₂×C₄×C₁₉	—	2	1	no	—
480	C₂×C₄×C₁₉	—	2	2	no	—
481	C₂×C₄×C₁₉	—	2	1	no	—
482	C₂×C₄×C₁₉	—	2	1	no	—
483	C₂×C₄×C₁₉	—	2	2	no	—
484	C₂×C₄×C₁₉	—	4	1	no	—
485	C₂×C₄×C₁₉	—	4	2	no	—
486	C₂×C₄×C₁₉	—	4	2	no	—
487	C₂×C₄×C₁₉	—	4	2	no	—
488	C₂×C₄×C₁₉	—	8	2	no	—
489	C₂×C₄×C₁₉	—	8	2	no	—
490	C₂×C₄×C₁₉	—	8	2	no	—
491	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
501	C₈×C₁₉	—	2	1	no	—
502	C₈×C₁₉	—	2	2	no	—
503	C₈×C₁₉	—	2	2	no	—
504	C₈×C₁₉	—	2	1	no	—
505	C₈×C₁₉	—	2	1	no	—
506	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
507	#3555	C₂×C₁₉	1	1	yes	characteristic, complemented
508	#3550	C₂×C₁₉	1	1	yes	characteristic, complemented
509	#3401	C₂×C₁₉	1	2	yes	complemented
510	#3398	C₂×C₁₉	1	1	yes	characteristic, complemented
511	#3393	C₂×C₁₉	1	1	yes	characteristic, complemented
512	#3387	C₂×C₁₉	1	2	yes	complemented
513	#3384	C₂×C₁₉	1	1	yes	characteristic, complemented
514	Q₈×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
515	#3371	C₂×C₁₉	1	2	yes	complemented
516	#3369	C₂×C₁₉	1	1	yes	characteristic, complemented
517	#3369	C₂×C₁₉	1	2	yes	complemented
518	#3367	C₂×C₁₉	1	1	yes	characteristic, complemented
519	#3360	C₂×C₁₉	1	1	yes	characteristic, complemented
520	#3359	C₂×C₁₉	1	1	yes	characteristic, complemented
521	#3263	C₂×C₁₉	1	2	yes	complemented
522	#3258	C₂×C₁₉	1	2	yes	complemented
523	#3248	C₂×C₁₉	1	1	yes	characteristic, complemented
524	#3246	C₂×C₁₉	1	1	yes	characteristic, complemented
525	#3185	C₂×C₁₉	1	1	yes	characteristic, complemented
526	#3178	C₂×C₁₉	1	2	yes	complemented
527	#3173	C₂×C₁₉	1	2	yes	complemented
528	#3171	C₂×C₁₉	1	1	yes	characteristic
529	#2962	C₂×C₁₉	1	1	yes	characteristic, complemented
530	C₂²×C₁₉	—	2	1	no	—
531	C₂²×C₁₉	—	2	1	no	—
532	C₂²×C₁₉	—	2	1	no	—
533	C₂²×C₁₉	—	4	1	no	—
534	C₂²×C₁₉	—	4	1	no	—
535	C₂²×C₁₉	—	4	1	no	—
536	C₂²×C₁₉	—	4	1	no	—
537	C₂²×C₁₉	—	4	1	no	—
538	C₂²×C₁₉	—	4	1	no	—
539	C₂²×C₁₉	—	4	1	no	—
540	C₂²×C₁₉	—	4	1	no	—
541	C₂²×C₁₉	—	4	1	no	—
542	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
543	C₄×C₁₉	—	2	1	no	—
544	C₄×C₁₉	—	2	1	no	—
545	C₄×C₁₉	—	2	2	no	—
546	C₄×C₁₉	—	2	2	no	—
547	C₄×C₁₉	—	2	1	no	—
548	C₄×C₁₉	—	2	1	no	—
549	C₄×C₁₉	—	2	2	no	—
550	C₄×C₁₉	—	2	2	no	—
551	C₄×C₁₉	—	4	2	no	—
552	C₄×C₁₉	—	4	1	no	—
553	C₄×C₁₉	—	4	2	no	—
554	C₄×C₁₉	—	4	1	no	—
555	C₄×C₁₉	—	4	2	no	—
556	C₄×C₁₉	—	4	1	no	—
557	C₄×C₁₉	—	4	1	no	—
558	C₄×C₁₉	—	4	1	no	—
559	C₄×C₁₉	—	4	2	no	—
560	C₄×C₁₉	#577	1	2	yes	—
561	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
562	C₄×C₁₉	#585	1	1	yes	characteristic
563	#563	—	2	2	no	—
564	#563	—	2	2	no	—
565	#559	C₂²×C₁₉	1	2	yes	—
566	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
567	Q₈²	C₂²×C₁₉	1	2	yes	—
568	#557	C₂²×C₁₉	1	1	yes	characteristic
569	#557	C₂²×C₁₉	1	2	yes	—
570	#556	—	2	1	no	—
571	#556	—	2	1	no	—
572	#556	C₂²×C₁₉	1	1	yes	characteristic
573	#556	C₂²×C₁₉	1	1	yes	characteristic
574	#556	C₂²×C₁₉	1	1	yes	characteristic
575	#556	C₂²×C₁₉	1	2	yes	—
576	#554	C₂²×C₁₉	1	1	yes	characteristic
577	#552	—	2	1	no	—
578	D₄×Q₈	—	2	1	no	—
579	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
580	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
581	#544	—	2	1	no	—
582	#542	—	2	2	no	—
583	#542	C₂²×C₁₉	1	2	yes	—
584	#542	C₂²×C₁₉	1	2	yes	—
585	#542	C₂²×C₁₉	1	2	yes	—
586	#541	—	2	1	no	—
587	#541	—	2	2	no	—
588	#541	C₂²×C₁₉	1	2	yes	—
589	#536	—	2	1	no	—
590	#536	—	2	1	no	—
591	#533	C₂²×C₁₉	1	1	yes	characteristic
592	#533	C₂²×C₁₉	1	1	yes	characteristic
593	#533	C₂²×C₁₉	1	1	yes	characteristic
594	#532	C₂²×C₁₉	1	1	yes	characteristic
595	#529	C₂²×C₁₉	1	1	yes	characteristic
596	#501	C₂²×C₁₉	1	2	yes	—
597	#501	C₂²×C₁₉	1	1	yes	characteristic
598	#498	C₂²×C₁₉	1	1	yes	characteristic
599	#498	C₂²×C₁₉	1	2	yes	—
600	#497	C₂²×C₁₉	1	2	yes	—
601	#496	C₂²×C₁₉	1	1	yes	characteristic
602	#495	C₂²×C₁₉	1	2	yes	—
603	#494	C₂²×C₁₉	1	1	yes	characteristic
604	#490	C₂²×C₁₉	1	1	yes	characteristic
605	#489	C₂²×C₁₉	1	2	yes	—
606	#489	C₂²×C₁₉	1	1	yes	characteristic
607	#489	C₂²×C₁₉	1	2	yes	—
608	#488	C₂²×C₁₉	1	2	yes	—
609	#487	C₂²×C₁₉	1	1	yes	characteristic
610	#487	C₂²×C₁₉	1	2	yes	—
611	#487	C₂²×C₁₉	1	1	yes	characteristic
612	#479	C₂²×C₁₉	1	2	yes	—
613	#479	C₂²×C₁₉	1	2	yes	—
614	#478	C₂²×C₁₉	1	2	yes	—
615	#477	C₂²×C₁₉	1	2	yes	—
616	#476	C₂²×C₁₉	1	1	yes	characteristic
617	#476	C₂²×C₁₉	1	1	yes	characteristic
618	#476	C₂²×C₁₉	1	2	yes	—
619	#476	C₂²×C₁₉	1	2	yes	—
620	#475	C₂²×C₁₉	1	1	yes	characteristic
621	#475	C₂²×C₁₉	1	2	yes	—
622	#475	C₂²×C₁₉	1	2	yes	—
623	#475	C₂²×C₁₉	1	2	yes	—
624	#475	C₂²×C₁₉	1	2	yes	—
625	#474	C₂²×C₁₉	1	1	yes	characteristic
626	#470	C₂²×C₁₉	1	2	yes	—
627	#470	C₂²×C₁₉	1	2	yes	—
628	#469	C₂²×C₁₉	1	1	yes	characteristic
629	#469	C₂²×C₁₉	1	1	yes	characteristic
630	#468	C₂²×C₁₉	1	1	yes	characteristic
631	#468	C₂²×C₁₉	1	1	yes	characteristic
632	#467	C₂²×C₁₉	1	2	yes	—
633	#465	C₂²×C₁₉	1	2	yes	—
634	#465	C₂²×C₁₉	1	2	yes	—
635	#465	C₂²×C₁₉	1	2	yes	—
636	#464	C₂²×C₁₉	1	2	yes	—
637	#464	C₂²×C₁₉	1	2	yes	—
638	#464	C₂²×C₁₉	1	2	yes	—
639	#464	C₂²×C₁₉	1	2	yes	—
640	#464	C₂²×C₁₉	1	2	yes	—
641	#463	C₂²×C₁₉	1	2	yes	—
642	#463	C₂²×C₁₉	1	2	yes	—
643	#462	C₂²×C₁₉	1	1	yes	characteristic
644	#462	C₂²×C₁₉	1	2	yes	—
645	#461	C₂²×C₁₉	1	1	yes	characteristic
646	#461	C₂²×C₁₉	1	2	yes	—
647	#461	C₂²×C₁₉	1	1	yes	characteristic
648	#461	C₂²×C₁₉	1	1	yes	characteristic
649	#460	C₂²×C₁₉	1	2	yes	—
650	#446	C₂²×C₁₉	1	1	yes	characteristic
651	#446	C₂²×C₁₉	1	2	yes	—
652	#446	C₂²×C₁₉	1	1	yes	characteristic
653	#446	C₂²×C₁₉	1	2	yes	—
654	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
655	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
656	#442	C₂²×C₁₉	1	2	yes	—
657	#441	C₂²×C₁₉	1	2	yes	—
658	#441	C₂²×C₁₉	1	2	yes	—
659	#441	C₂²×C₁₉	1	2	yes	—
660	#441	C₂²×C₁₉	1	2	yes	—
661	#440	C₂²×C₁₉	1	2	yes	—
662	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
663	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
664	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
665	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
666	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
667	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
668	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
669	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
670	#424	C₂²×C₁₉	1	2	yes	—
671	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
672	#405	C₂²×C₁₉	1	2	yes	—
673	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
674	C₂×C₁₉	—	4	1	no	—
675	C₂×C₁₉	—	8	1	no	—
676	C₂×C₁₉	—	8	1	no	—
677	C₂×C₁₉	—	8	1	no	—
678	C₂×C₁₉	#3497	1	1	yes	characteristic
679	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
680	C₂×C₁₉	#3586	1	1	yes	characteristic
681	C₂×#41	—	2	1	no	—
682	C₂²×Q₈	—	2	1	no	—
683	C₂²×Q₈	—	2	1	no	—
684	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
685	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
686	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
688	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
689	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
690	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
691	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
692	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
693	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
694	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
695	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
696	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
697	C₄⋊Q₈	—	2	2	no	—
698	C₄⋊Q₈	—	2	2	no	—
699	C₄⋊Q₈	—	2	2	no	—
700	C₄⋊Q₈	—	2	2	no	—
701	C₄⋊Q₈	—	2	2	no	—
702	C₄⋊Q₈	—	2	1	no	—
703	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
704	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
706	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
708	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
712	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
713	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
714	#127	C₂³×C₁₉	1	1	yes	characteristic
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#126	—	2	1	no	—
726	#125	—	2	2	no	—
727	#125	—	2	2	no	—
728	#125	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	—	2	2	no	—
731	#125	—	2	1	no	—
732	#125	—	2	1	no	—
733	#125	—	2	1	no	—
734	#125	D₄×C₁₉	1	2	yes	—
735	#125	C₂³×C₁₉	1	1	yes	characteristic
736	#125	C₂³×C₁₉	1	2	yes	—
737	#124	—	2	2	no	—
738	#124	—	2	2	no	—
739	#124	—	2	2	no	—
740	#124	—	2	2	no	—
741	#124	—	2	1	no	—
742	#124	C₂³×C₁₉	1	1	yes	characteristic
743	#124	C₂³×C₁₉	1	2	yes	—
744	#124	C₂³×C₁₉	1	2	yes	—
745	#124	C₂³×C₁₉	1	2	yes	—
746	#123	—	2	1	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
768	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
769	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
770	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
771	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
772	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
773	#121	—	2	1	no	—
774	#121	C₂³×C₁₉	1	1	yes	characteristic
775	#121	C₂³×C₁₉	1	1	yes	characteristic
776	#121	C₂³×C₁₉	1	1	yes	characteristic
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	2	no	—
780	C₄×Q₈	—	2	2	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
785	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
786	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
787	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
788	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
789	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
790	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
791	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
792	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
793	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₁₉	1	2	yes	—
801	C₄×D₄	C₂³×C₁₉	1	2	yes	—
802	C₄×D₄	C₂³×C₁₉	1	2	yes	—
803	#117	—	2	1	no	—
804	#117	—	2	1	no	—
805	#117	—	2	1	no	—
806	#117	—	2	1	no	—
807	#117	—	2	2	no	—
808	#117	—	2	1	no	—
809	#117	—	2	1	no	—
810	#117	C₂³×C₁₉	1	2	yes	—
811	C₂×C₄⋊C₄	—	2	1	no	—
812	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
813	#107	C₂³×C₁₉	1	1	yes	characteristic
814	#107	C₂³×C₁₉	1	1	yes	characteristic
815	#107	C₂³×C₁₉	1	2	yes	—
816	#106	C₂³×C₁₉	1	1	yes	characteristic
817	#106	C₂³×C₁₉	1	2	yes	—
818	#106	C₂³×C₁₉	1	2	yes	—
819	#106	C₂³×C₁₉	1	2	yes	—
820	#106	C₂³×C₁₉	1	1	yes	characteristic
821	#106	C₂³×C₁₉	1	2	yes	—
822	#106	C₂³×C₁₉	1	2	yes	—
823	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
824	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
825	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
827	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
828	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
829	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
830	#103	C₂³×C₁₉	1	2	yes	—
831	#103	C₂³×C₁₉	1	1	yes	characteristic
832	#103	C₂³×C₁₉	1	2	yes	—
833	#103	C₂³×C₁₉	1	2	yes	—
834	#103	C₂³×C₁₉	1	1	yes	characteristic
835	#103	C₂³×C₁₉	1	2	yes	—
836	#103	C₂³×C₁₉	1	2	yes	—
837	#103	C₂³×C₁₉	1	2	yes	—
838	#103	C₂³×C₁₉	1	2	yes	—
839	#103	C₂³×C₁₉	1	2	yes	—
840	#103	C₂³×C₁₉	1	2	yes	—
841	#102	C₂³×C₁₉	1	1	yes	characteristic
842	#102	C₂³×C₁₉	1	1	yes	characteristic
843	#102	C₂³×C₁₉	1	1	yes	characteristic
844	#102	C₂³×C₁₉	1	1	yes	characteristic
845	#102	C₂³×C₁₉	1	1	yes	characteristic
846	#102	C₂³×C₁₉	1	2	yes	—
847	#102	C₂³×C₁₉	1	1	yes	characteristic
848	#102	C₂³×C₁₉	1	2	yes	—
849	#102	C₂³×C₁₉	1	2	yes	—
850	#97	C₂³×C₁₉	1	1	yes	characteristic
851	#97	C₂³×C₁₉	1	1	yes	characteristic
852	#97	C₂³×C₁₉	1	2	yes	—
853	#97	C₂³×C₁₉	1	2	yes	—
854	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
855	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
856	C₄×C₈	C₂³×C₁₉	1	2	yes	—
857	C₄×C₈	C₂³×C₁₉	1	2	yes	—
858	C₁₉	#62407	1	1	yes	characteristic, direct product factor, Sylow
859	#41	—	8	2	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	1	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	—	2	1	no	—
866	C₂×Q₈	—	8	2	no	—
867	C₂×Q₈	—	8	2	no	—
868	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
869	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
870	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
871	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
872	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
873	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	—	2	1	no	—
876	C₂×D₄	—	2	1	no	—
877	C₂×D₄	—	2	1	no	—
878	C₂×D₄	—	2	1	no	—
879	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
880	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
881	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	1	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
889	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
891	Q₁₆	—	2	4	no	—
892	Q₁₆	—	4	2	no	—
893	Q₁₆	—	4	2	no	—
894	SD₁₆	—	2	2	no	—
895	SD₁₆	—	4	2	no	—
896	SD₁₆	—	4	2	no	—
897	SD₁₆	—	4	2	no	—
898	SD₁₆	—	4	1	no	—
899	D₈	—	2	2	no	—
900	D₈	—	4	1	no	—
901	M₁₆	—	2	2	no	—
902	M₁₆	—	4	1	no	—
903	C₂×C₈	—	4	2	no	—
904	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
905	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
906	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
907	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
908	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
909	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
938	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
939	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
940	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
941	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
942	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
943	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
946	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
949	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
950	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
951	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
973	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
983	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
984	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
985	C₄²	C₂⁴×C₁₉	1	2	yes	—
986	C₄²	C₂⁴×C₁₉	1	2	yes	—
987	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
988	C₂³	—	2	1	no	—
989	C₂³	—	2	1	no	—
990	C₂³	—	2	1	no	—
991	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
992	Q₈	—	2	2	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	2	2	no	—
996	Q₈	—	2	2	no	—
997	Q₈	—	2	2	no	—
998	Q₈	—	2	2	no	—
999	Q₈	—	2	1	no	—
1000	Q₈	—	4	2	no	—
1001	Q₈	—	4	2	no	—
1002	Q₈	—	8	2	no	—
1003	Q₈	—	8	2	no	—
1004	Q₈	—	8	1	no	—
1005	Q₈	—	8	1	no	—
1006	Q₈	—	8	2	no	—
1007	D₄	—	2	1	no	—
1008	D₄	—	2	1	no	—
1009	D₄	—	2	1	no	—
1010	D₄	—	2	1	no	—
1011	D₄	—	2	1	no	—
1012	D₄	—	2	1	no	—
1013	D₄	—	4	2	no	—
1014	D₄	—	8	1	no	—
1015	D₄	—	8	1	no	—
1016	D₄	—	8	1	no	—
1017	D₄	—	8	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	4	1	no	—
1031	C₂×C₄	—	4	2	no	—
1032	C₂×C₄	—	4	2	no	—
1033	C₂×C₄	—	4	2	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	—	8	2	no	—
1036	C₂×C₄	—	8	2	no	—
1037	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1038	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1039	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1040	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1041	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1042	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1043	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1044	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1045	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1046	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1047	C₈	—	2	1	no	—
1048	C₈	—	2	2	no	—
1049	C₈	—	2	2	no	—
1050	C₈	—	2	1	no	—
1051	C₈	—	2	1	no	—
1052	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	2	1	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	4	1	no	—
1059	C₂²	—	4	1	no	—
1060	C₂²	—	4	1	no	—
1061	C₂²	—	4	1	no	—
1062	C₂²	—	4	1	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1066	C₄	—	2	1	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	2	2	no	—
1069	C₄	—	2	2	no	—
1070	C₄	—	2	1	no	—
1071	C₄	—	2	1	no	—
1072	C₄	—	2	2	no	—
1073	C₄	—	2	2	no	—
1074	C₄	—	4	2	no	—
1075	C₄	—	4	1	no	—
1076	C₄	—	4	2	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	2	no	—
1081	C₄	—	4	2	no	—
1082	C₄	—	4	1	no	—
1083	C₄	C₁₉×#577	1	2	yes	—
1084	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
1085	C₄	C₁₉×#585	1	1	yes	characteristic
1086	C₂	—	4	1	no	—
1087	C₂	—	8	1	no	—
1088	C₂	—	8	1	no	—
1089	C₂	—	8	1	no	—
1090	C₂	C₁₉×#3497	1	1	yes	characteristic
1091	C₂	C₂×C₁₉×#577	1	1	yes	characteristic
1092	C₂	C₁₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3171	C₂
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×#3555	C₂	semidirect
2. C₁₉×#3550	C₂	semidirect
3. C₁₉×#3401	C₂	semidirect
4. C₁₉×#3398	C₂	semidirect
5. C₁₉×#3393	C₂	semidirect
6. C₁₉×#3387	C₂	semidirect
7. C₁₉×#3384	C₂	semidirect
8. Q₈×SD₁₆×C₁₉	C₂	semidirect
9. C₁₉×#3371	C₂	semidirect
10. C₁₉×#3369	C₂	semidirect
11. C₁₉×#3369	C₂	semidirect
12. C₁₉×#3367	C₂	semidirect
13. C₁₉×#3360	C₂	semidirect
14. C₁₉×#3359	C₂	semidirect
15. C₁₉×#3263	C₂	semidirect
16. C₁₉×#3258	C₂	semidirect
17. C₁₉×#3248	C₂	semidirect
18. C₁₉×#3246	C₂	semidirect
19. C₁₉×#3185	C₂	semidirect
20. C₁₉×#3178	C₂	semidirect
21. C₁₉×#3173	C₂	semidirect
23. C₁₉×#2962	C₂	semidirect
441. #62407	C₁₉	direct (N × H)
507. #3555	C₂×C₁₉	semidirect
508. #3550	C₂×C₁₉	semidirect
509. #3401	C₂×C₁₉	semidirect
510. #3398	C₂×C₁₉	semidirect
511. #3393	C₂×C₁₉	semidirect
512. #3387	C₂×C₁₉	semidirect
513. #3384	C₂×C₁₉	semidirect
514. Q₈×SD₁₆	C₂×C₁₉	semidirect
515. #3371	C₂×C₁₉	semidirect
516. #3369	C₂×C₁₉	semidirect
517. #3369	C₂×C₁₉	semidirect
518. #3367	C₂×C₁₉	semidirect
519. #3360	C₂×C₁₉	semidirect
520. #3359	C₂×C₁₉	semidirect
521. #3263	C₂×C₁₉	semidirect
522. #3258	C₂×C₁₉	semidirect
523. #3248	C₂×C₁₉	semidirect
524. #3246	C₂×C₁₉	semidirect
525. #3185	C₂×C₁₉	semidirect
526. #3178	C₂×C₁₉	semidirect
527. #3173	C₂×C₁₉	semidirect
529. #2962	C₂×C₁₉	semidirect
858. C₁₉	#62407	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×#3555	2
C₁₉×#3550	2
C₁₉×#3401	2
C₁₉×#3398	2
C₁₉×#3393	2
C₁₉×#3387	2
C₁₉×#3384	2
Q₈×SD₁₆×C₁₉	2
C₁₉×#3371	2
C₁₉×#3369	2
C₁₉×#3367	2
C₁₉×#3360	2
C₁₉×#3359	2
C₁₉×#3263	2
C₁₉×#3258	2
C₁₉×#3248	2
C₁₉×#3246	2
C₁₉×#3185	2
C₁₉×#3178	2
C₁₉×#3173	2
C₁₉×#3171	2
C₁₉×#2962	2
#62407	19

Subgroups — C19×#62407 #18068366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62407 #18068366