Subgroups — C₁₉×#62237 #18068196

Order 4864.

1634 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3515	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3388	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3374	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3352	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3344	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3344	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3331	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3315	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3315	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3261	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3255	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3242	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3236	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3120	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3116	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3084	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3080	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#2995	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#564	—	2	1	no	—
21	C₁₉×#563	—	2	1	no	—
22	C₁₉×#557	C₂²	1	1	yes	characteristic
23	C₁₉×#557	C₂²	1	2	yes	—
24	C₁₉×#554	C₂²	1	1	yes	characteristic
25	C₁₉×#554	C₂²	1	1	yes	characteristic
26	C₁₉×#554	C₂²	1	2	yes	—
27	C₁₉×#553	—	2	1	no	—
28	C₁₉×#552	—	2	2	no	—
29	C₁₉×#552	—	2	2	no	—
30	C₁₉×#552	—	2	1	no	—
31	C₁₉×#552	C₂²	1	2	yes	—
32	C₁₉×#552	C₂²	1	2	yes	—
33	C₁₉×#552	C₂²	1	2	yes	—
34	C₁₉×#547	C₂²	1	1	yes	characteristic
35	C₁₉×#547	C₂²	1	2	yes	—
36	C₁₉×#544	—	2	1	no	—
37	C₁₉×#544	C₂²	1	2	yes	—
38	C₁₉×#541	—	2	2	no	—
39	C₁₉×#541	C₂²	1	2	yes	—
40	C₁₉×#541	C₂²	1	2	yes	—
41	C₁₉×#539	—	2	2	no	—
42	C₁₉×#539	—	2	1	no	—
43	C₁₉×#533	C₂²	1	1	yes	characteristic
44	C₁₉×#533	C₂²	1	1	yes	characteristic
45	C₁₉×#529	—	2	1	no	—
46	C₁₉×#529	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#125	—	2	1	no	—
48	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
49	C₁₉×#520	C₂²	1	2	yes	—
50	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
51	C₁₉×#501	C₂²	1	2	yes	—
52	C₁₉×#501	C₂²	1	2	yes	—
53	C₁₉×#499	C₂²	1	2	yes	—
54	C₁₉×#491	C₂²	1	2	yes	—
55	C₁₉×#491	C₂²	1	2	yes	—
56	C₁₉×#487	C₂²	1	2	yes	—
57	C₁₉×#485	C₂²	1	2	yes	—
58	C₁₉×#485	C₂²	1	2	yes	—
59	C₁₉×#485	C₂²	1	2	yes	—
60	C₁₉×#484	C₂²	1	2	yes	—
61	C₁₉×#484	C₂²	1	2	yes	—
62	C₁₉×#484	C₂²	1	2	yes	—
63	C₁₉×#483	C₂²	1	2	yes	—
64	C₁₉×#483	C₂²	1	2	yes	—
65	C₁₉×#483	C₂²	1	2	yes	—
66	C₁₉×#479	C₂²	1	2	yes	—
67	C₁₉×#479	C₂²	1	2	yes	—
68	C₁₉×#479	C₂²	1	2	yes	—
69	C₁₉×#479	C₂²	1	2	yes	—
70	C₁₉×#479	C₂²	1	2	yes	—
71	C₁₉×#479	C₂²	1	2	yes	—
72	C₁₉×#479	C₂²	1	2	yes	—
73	C₁₉×#478	C₂²	1	2	yes	—
74	C₁₉×#478	C₂²	1	2	yes	—
75	C₁₉×#478	C₂²	1	2	yes	—
76	C₁₉×#477	C₂²	1	1	yes	characteristic
77	C₁₉×#476	C₂²	1	2	yes	—
78	C₁₉×#476	C₂²	1	1	yes	characteristic
79	C₁₉×#475	C₂²	1	2	yes	—
80	C₁₉×#475	C₂²	1	2	yes	—
81	C₁₉×#475	C₂²	1	2	yes	—
82	C₁₉×#470	C₂²	1	2	yes	—
83	C₁₉×#470	C₂²	1	2	yes	—
84	C₁₉×#470	C₂²	1	2	yes	—
85	C₁₉×#470	C₂²	1	2	yes	—
86	C₁₉×#467	C₂²	1	2	yes	—
87	C₁₉×#467	C₂²	1	2	yes	—
88	C₁₉×#462	C₂²	1	2	yes	—
89	C₁₉×#462	C₂²	1	2	yes	—
90	C₁₉×#462	C₂²	1	1	yes	characteristic
91	C₁₉×#462	C₂²	1	2	yes	—
92	C₁₉×#462	C₂²	1	2	yes	—
93	C₁₉×#461	C₂²	1	1	yes	characteristic
94	C₁₉×#452	C₂²	1	2	yes	—
95	C₁₉×#452	C₂²	1	2	yes	—
96	C₁₉×#452	C₂²	1	2	yes	—
97	C₁₉×#446	C₂²	1	2	yes	—
98	C₁₉×#441	C₂²	1	2	yes	—
99	C₁₉×#441	C₂²	1	2	yes	—
100	C₁₉×#440	C₂²	1	2	yes	—
101	C₁₉×#440	C₂²	1	2	yes	—
102	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
103	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
104	C₁₉×#436	C₂²	1	2	yes	—
105	C₁₉×#435	C₂²	1	2	yes	—
106	C₁₉×#435	C₂²	1	2	yes	—
107	C₁₉×#433	C₂²	1	2	yes	—
108	C₁₉×#432	C₂²	1	1	yes	characteristic
109	C₁₉×#428	C₂²	1	1	yes	characteristic
110	C₁₉×#428	C₂²	1	1	yes	characteristic
111	C₁₉×#428	C₂²	1	2	yes	—
112	C₂×C₁₉×#106	C₂²	1	2	yes	—
113	C₁₉×#424	C₂²	1	2	yes	—
114	C₁₉×#423	C₂²	1	1	yes	characteristic
115	C₁₉×#417	C₂²	1	1	yes	characteristic
116	C₁₉×#417	C₂²	1	2	yes	—
117	C₁₉×#417	C₂²	1	1	yes	characteristic
118	C₁₉×#416	C₂²	1	2	yes	—
119	C₂×#41×C₁₉	C₂³	1	2	yes	—
120	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
125	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
128	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
129	C₁₉×C₄⋊Q₈	—	2	2	no	—
130	C₁₉×C₄⋊Q₈	—	2	2	no	—
131	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
132	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
133	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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×#126	—	2	2	no	—
138	C₁₉×#126	—	2	2	no	—
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	D₄	1	2	yes	—
145	C₁₉×#125	—	2	2	no	—
146	C₁₉×#125	—	2	2	no	—
147	C₁₉×#125	—	2	1	no	—
148	C₁₉×#125	—	2	1	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	1	no	—
160	C₁₉×#125	—	2	1	no	—
161	C₁₉×#125	—	2	1	no	—
162	C₁₉×#125	—	2	1	no	—
163	C₁₉×#125	D₄	1	1	yes	characteristic
164	C₁₉×#125	C₂³	1	2	yes	—
165	C₁₉×#125	C₂³	1	2	yes	—
166	C₁₉×#125	C₂³	1	2	yes	—
167	C₁₉×#125	C₂³	1	2	yes	—
168	C₁₉×#124	D₄	1	1	yes	characteristic
169	C₁₉×#123	—	2	2	no	—
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	D₄	1	2	yes	—
176	C₁₉×C₂²⋊Q₈	—	2	1	no	—
177	C₁₉×C₂²⋊Q₈	—	2	1	no	—
178	C₁₉×C₂²⋊Q₈	—	2	1	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	D₄	1	1	yes	characteristic
186	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
187	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
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×#121	—	2	1	no	—
193	C₁₉×#121	—	2	2	no	—
194	C₁₉×#121	D₄	1	1	yes	characteristic
195	C₄×Q₈×C₁₉	—	2	1	no	—
196	C₄×Q₈×C₁₉	—	2	2	no	—
197	C₄×Q₈×C₁₉	—	2	1	no	—
198	C₄×Q₈×C₁₉	—	2	1	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	1	yes	characteristic
204	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
205	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
207	C₄×D₄×C₁₉	—	2	1	no	—
208	C₄×D₄×C₁₉	—	2	2	no	—
209	C₄×D₄×C₁₉	—	2	1	no	—
210	C₄×D₄×C₁₉	—	2	1	no	—
211	C₄×D₄×C₁₉	—	2	2	no	—
212	C₄×D₄×C₁₉	—	2	2	no	—
213	C₄×D₄×C₁₉	C₂³	1	2	yes	—
214	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
215	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
216	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₁₉	C₂³	1	2	yes	—
218	C₁₉×#117	—	2	1	no	—
219	C₁₉×#117	—	2	1	no	—
220	C₁₉×#117	—	2	2	no	—
221	C₁₉×#117	—	2	2	no	—
222	C₁₉×#117	—	2	2	no	—
223	C₁₉×#117	—	2	2	no	—
224	C₁₉×#117	—	2	1	no	—
225	C₁₉×#117	C₂³	1	2	yes	—
226	C₁₉×#117	C₂³	1	1	yes	characteristic
227	C₁₉×#117	C₂³	1	2	yes	—
228	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
229	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
230	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
231	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
232	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
233	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
234	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
238	C₂×C₄²×C₁₉	—	2	1	no	—
239	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
240	C₁₉×#107	C₂³	1	2	yes	—
241	C₁₉×#107	C₂³	1	2	yes	—
242	C₁₉×#107	C₂³	1	2	yes	—
243	C₁₉×#107	C₂³	1	2	yes	—
244	C₁₉×#107	C₂³	1	2	yes	—
245	C₁₉×#106	C₂³	1	2	yes	—
246	C₁₉×#106	C₂³	1	2	yes	—
247	C₁₉×#106	C₂³	1	2	yes	—
248	C₁₉×#106	C₂³	1	2	yes	—
249	C₁₉×#106	C₂³	1	2	yes	—
250	C₁₉×#106	C₂³	1	2	yes	—
251	C₁₉×#106	C₂³	1	2	yes	—
252	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
253	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
254	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
256	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
257	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₁₉×#103	C₂³	1	2	yes	—
259	C₁₉×#103	C₂³	1	2	yes	—
260	C₁₉×#103	C₂³	1	2	yes	—
261	C₁₉×#103	C₂³	1	2	yes	—
262	C₁₉×#103	C₂³	1	2	yes	—
263	C₁₉×#103	C₂³	1	2	yes	—
264	C₁₉×#103	C₂³	1	2	yes	—
265	C₁₉×#103	C₂³	1	2	yes	—
266	C₁₉×#103	C₂³	1	2	yes	—
267	C₁₉×#103	C₂³	1	2	yes	—
268	C₁₉×#103	C₂³	1	2	yes	—
269	C₁₉×#103	C₂³	1	2	yes	—
270	C₁₉×#103	C₂³	1	2	yes	—
271	C₁₉×#102	C₂³	1	2	yes	—
272	C₁₉×#102	C₂³	1	2	yes	—
273	C₁₉×#102	C₂³	1	2	yes	—
274	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₁₉×#97	C₂³	1	2	yes	—
278	C₁₉×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₁₉	C₂³	1	2	yes	—
280	#41×C₁₉	—	2	4	no	—
281	#41×C₁₉	—	2	2	no	—
282	#41×C₁₉	—	4	2	no	—
283	#41×C₁₉	—	4	1	no	—
284	C₂×Q₈×C₁₉	—	2	1	no	—
285	C₂×Q₈×C₁₉	—	2	1	no	—
286	C₂×Q₈×C₁₉	—	2	2	no	—
287	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
288	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
289	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
290	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
291	C₂×D₄×C₁₉	—	2	2	no	—
292	C₂×D₄×C₁₉	—	2	1	no	—
293	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
294	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
295	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₁₉	—	2	1	no	—
297	C₂²×C₄×C₁₉	—	2	1	no	—
298	C₂²×C₄×C₁₉	—	2	2	no	—
299	C₂²×C₄×C₁₉	—	2	2	no	—
300	C₂²×C₄×C₁₉	—	2	1	no	—
301	C₂²×C₄×C₁₉	—	2	1	no	—
302	C₂²×C₄×C₁₉	—	2	2	no	—
303	C₂²×C₄×C₁₉	—	2	1	no	—
304	C₂²×C₄×C₁₉	—	2	2	no	—
305	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
309	Q₁₆×C₁₉	—	4	2	no	—
310	Q₁₆×C₁₉	—	4	2	no	—
311	Q₁₆×C₁₉	—	4	2	no	—
312	SD₁₆×C₁₉	—	2	4	no	—
313	M₁₆×C₁₉	—	4	1	no	—
314	M₁₆×C₁₉	—	4	2	no	—
315	M₁₆×C₁₉	—	4	1	no	—
316	C₂×C₈×C₁₉	—	4	2	no	—
317	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
318	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
319	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
320	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
321	C₄⋊C₄×C₁₉	—	2	2	no	—
322	C₄⋊C₄×C₁₉	—	2	1	no	—
323	C₄⋊C₄×C₁₉	—	2	1	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	—	2	2	no	—
328	C₄⋊C₄×C₁₉	—	2	2	no	—
329	C₄⋊C₄×C₁₉	—	2	2	no	—
330	C₄⋊C₄×C₁₉	—	2	2	no	—
331	C₄⋊C₄×C₁₉	—	2	2	no	—
332	C₄⋊C₄×C₁₉	—	2	2	no	—
333	C₄⋊C₄×C₁₉	—	2	2	no	—
334	C₄⋊C₄×C₁₉	—	2	2	no	—
335	C₄⋊C₄×C₁₉	—	2	1	no	—
336	C₄⋊C₄×C₁₉	—	2	2	no	—
337	C₄⋊C₄×C₁₉	—	2	1	no	—
338	C₄⋊C₄×C₁₉	—	2	1	no	—
339	C₄⋊C₄×C₁₉	—	2	1	no	—
340	C₄⋊C₄×C₁₉	—	2	1	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	1	no	—
346	C₄⋊C₄×C₁₉	—	2	2	no	—
347	C₄⋊C₄×C₁₉	—	2	2	no	—
348	C₄⋊C₄×C₁₉	—	2	1	no	—
349	C₄⋊C₄×C₁₉	—	2	2	no	—
350	C₄⋊C₄×C₁₉	—	2	1	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	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
357	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	1	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	1	no	—
376	C₂²⋊C₄×C₁₉	—	2	1	no	—
377	C₂²⋊C₄×C₁₉	—	2	2	no	—
378	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
379	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
380	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
381	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
382	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
383	C₄²×C₁₉	—	2	1	no	—
384	C₄²×C₁₉	—	2	1	no	—
385	C₄²×C₁₉	—	2	1	no	—
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	—	2	2	no	—
392	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
395	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
396	C₄²×C₁₉	C₂⁴	1	2	yes	—
397	#62237	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
398	C₂³×C₁₉	—	2	1	no	—
399	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
400	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
401	Q₈×C₁₉	—	2	2	no	—
402	Q₈×C₁₉	—	2	2	no	—
403	Q₈×C₁₉	—	2	1	no	—
404	Q₈×C₁₉	—	2	2	no	—
405	Q₈×C₁₉	—	2	1	no	—
406	Q₈×C₁₉	—	2	2	no	—
407	Q₈×C₁₉	—	4	1	no	—
408	Q₈×C₁₉	—	8	1	no	—
409	Q₈×C₁₉	—	8	1	no	—
410	Q₈×C₁₉	—	8	2	no	—
411	D₄×C₁₉	—	2	1	no	—
412	D₄×C₁₉	—	4	1	no	—
413	D₄×C₁₉	—	4	2	no	—
414	D₄×C₁₉	—	4	4	no	—
415	D₄×C₁₉	—	4	2	no	—
416	D₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
417	C₂×C₄×C₁₉	—	2	1	no	—
418	C₂×C₄×C₁₉	—	2	2	no	—
419	C₂×C₄×C₁₉	—	2	2	no	—
420	C₂×C₄×C₁₉	—	2	1	no	—
421	C₂×C₄×C₁₉	—	2	1	no	—
422	C₂×C₄×C₁₉	—	2	2	no	—
423	C₂×C₄×C₁₉	—	2	1	no	—
424	C₂×C₄×C₁₉	—	2	2	no	—
425	C₂×C₄×C₁₉	—	2	1	no	—
426	C₂×C₄×C₁₉	—	2	2	no	—
427	C₂×C₄×C₁₉	—	2	2	no	—
428	C₂×C₄×C₁₉	—	2	2	no	—
429	C₂×C₄×C₁₉	—	2	2	no	—
430	C₂×C₄×C₁₉	—	4	1	no	—
431	C₂×C₄×C₁₉	—	4	1	no	—
432	C₂×C₄×C₁₉	—	4	2	no	—
433	C₂×C₄×C₁₉	—	4	4	no	—
434	C₂×C₄×C₁₉	—	4	2	no	—
435	C₂×C₄×C₁₉	—	4	2	no	—
436	C₂×C₄×C₁₉	—	8	1	no	—
437	C₂×C₄×C₁₉	—	8	2	no	—
438	C₂×C₄×C₁₉	—	8	2	no	—
439	C₂×C₄×C₁₉	—	8	1	no	—
440	C₂×C₄×C₁₉	—	8	2	no	—
441	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
448	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
449	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
450	C₈×C₁₉	—	2	2	no	—
451	C₈×C₁₉	—	2	2	no	—
452	C₈×C₁₉	—	2	2	no	—
453	C₈×C₁₉	—	2	2	no	—
454	#3563	C₂×C₁₉	1	1	yes	characteristic, complemented
455	#3515	C₂×C₁₉	1	1	yes	characteristic
456	#3388	C₂×C₁₉	1	2	yes	complemented
457	#3374	C₂×C₁₉	1	2	yes	complemented
458	#3352	C₂×C₁₉	1	2	yes	complemented
459	#3344	C₂×C₁₉	1	2	yes	complemented
460	#3344	C₂×C₁₉	1	2	yes	complemented
461	#3331	C₂×C₁₉	1	2	yes	complemented
462	#3315	C₂×C₁₉	1	2	yes	complemented
463	#3315	C₂×C₁₉	1	2	yes	complemented
464	#3261	C₂×C₁₉	1	2	yes	complemented
465	#3255	C₂×C₁₉	1	1	yes	characteristic, complemented
466	#3242	C₂×C₁₉	1	2	yes	complemented
467	#3236	C₂×C₁₉	1	1	yes	characteristic, complemented
468	#3120	C₂×C₁₉	1	2	yes	complemented
469	#3116	C₂×C₁₉	1	1	yes	characteristic, complemented
470	#3084	C₂×C₁₉	1	2	yes	complemented
471	#3080	C₂×C₁₉	1	1	yes	characteristic, complemented
472	#2995	C₂×C₁₉	1	1	yes	characteristic, complemented
473	C₂²×C₁₉	—	2	1	no	—
474	C₂²×C₁₉	—	2	1	no	—
475	C₂²×C₁₉	—	2	2	no	—
476	C₂²×C₁₉	—	2	2	no	—
477	C₂²×C₁₉	—	2	2	no	—
478	C₂²×C₁₉	—	2	1	no	—
479	C₂²×C₁₉	—	2	2	no	—
480	C₂²×C₁₉	—	4	1	no	—
481	C₂²×C₁₉	—	4	1	no	—
482	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
483	C₄×C₁₉	—	2	1	no	—
484	C₄×C₁₉	—	2	1	no	—
485	C₄×C₁₉	—	2	1	no	—
486	C₄×C₁₉	—	2	1	no	—
487	C₄×C₁₉	—	2	2	no	—
488	C₄×C₁₉	—	2	2	no	—
489	C₄×C₁₉	—	2	2	no	—
490	C₄×C₁₉	—	2	1	no	—
491	C₄×C₁₉	—	4	1	no	—
492	C₄×C₁₉	—	4	2	no	—
493	C₄×C₁₉	—	4	1	no	—
494	C₄×C₁₉	—	4	2	no	—
495	C₄×C₁₉	—	4	2	no	—
496	C₄×C₁₉	—	4	2	no	—
497	C₄×C₁₉	—	4	1	no	—
498	C₄×C₁₉	—	4	2	no	—
499	C₄×C₁₉	—	4	2	no	—
500	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
501	C₄×C₁₉	#585	1	1	yes	characteristic
502	#564	—	2	1	no	—
503	#563	—	2	1	no	—
504	#557	C₂²×C₁₉	1	1	yes	characteristic
505	#557	C₂²×C₁₉	1	2	yes	—
506	#554	C₂²×C₁₉	1	1	yes	characteristic
507	#554	C₂²×C₁₉	1	2	yes	—
508	#554	C₂²×C₁₉	1	1	yes	characteristic
509	#553	—	2	1	no	—
510	#552	—	2	2	no	—
511	#552	—	2	2	no	—
512	#552	—	2	1	no	—
513	#552	C₂²×C₁₉	1	2	yes	—
514	#552	C₂²×C₁₉	1	2	yes	—
515	#552	C₂²×C₁₉	1	2	yes	—
516	#547	C₂²×C₁₉	1	2	yes	—
517	#547	C₂²×C₁₉	1	1	yes	characteristic
518	#544	—	2	1	no	—
519	#544	C₂²×C₁₉	1	2	yes	—
520	#541	—	2	2	no	—
521	#541	C₂²×C₁₉	1	2	yes	—
522	#541	C₂²×C₁₉	1	2	yes	—
523	#539	—	2	2	no	—
524	#539	—	2	1	no	—
525	#533	C₂²×C₁₉	1	1	yes	characteristic
526	#533	C₂²×C₁₉	1	1	yes	characteristic
527	#529	—	2	1	no	—
528	#529	C₂²×C₁₉	1	1	yes	characteristic
529	C₂×#125	—	2	1	no	—
530	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
531	#520	C₂²×C₁₉	1	2	yes	—
532	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
533	#501	C₂²×C₁₉	1	2	yes	—
534	#501	C₂²×C₁₉	1	2	yes	—
535	#499	C₂²×C₁₉	1	2	yes	—
536	#491	C₂²×C₁₉	1	2	yes	—
537	#491	C₂²×C₁₉	1	2	yes	—
538	#487	C₂²×C₁₉	1	2	yes	—
539	#485	C₂²×C₁₉	1	2	yes	—
540	#485	C₂²×C₁₉	1	2	yes	—
541	#485	C₂²×C₁₉	1	2	yes	—
542	#484	C₂²×C₁₉	1	2	yes	—
543	#484	C₂²×C₁₉	1	2	yes	—
544	#484	C₂²×C₁₉	1	2	yes	—
545	#483	C₂²×C₁₉	1	2	yes	—
546	#483	C₂²×C₁₉	1	2	yes	—
547	#483	C₂²×C₁₉	1	2	yes	—
548	#479	C₂²×C₁₉	1	2	yes	—
549	#479	C₂²×C₁₉	1	2	yes	—
550	#479	C₂²×C₁₉	1	2	yes	—
551	#479	C₂²×C₁₉	1	2	yes	—
552	#479	C₂²×C₁₉	1	2	yes	—
553	#479	C₂²×C₁₉	1	2	yes	—
554	#479	C₂²×C₁₉	1	2	yes	—
555	#478	C₂²×C₁₉	1	2	yes	—
556	#478	C₂²×C₁₉	1	2	yes	—
557	#478	C₂²×C₁₉	1	2	yes	—
558	#477	C₂²×C₁₉	1	1	yes	characteristic
559	#476	C₂²×C₁₉	1	2	yes	—
560	#476	C₂²×C₁₉	1	1	yes	characteristic
561	#475	C₂²×C₁₉	1	2	yes	—
562	#475	C₂²×C₁₉	1	2	yes	—
563	#475	C₂²×C₁₉	1	2	yes	—
564	#470	C₂²×C₁₉	1	2	yes	—
565	#470	C₂²×C₁₉	1	2	yes	—
566	#470	C₂²×C₁₉	1	2	yes	—
567	#470	C₂²×C₁₉	1	2	yes	—
568	#467	C₂²×C₁₉	1	2	yes	—
569	#467	C₂²×C₁₉	1	2	yes	—
570	#462	C₂²×C₁₉	1	2	yes	—
571	#462	C₂²×C₁₉	1	1	yes	characteristic
572	#462	C₂²×C₁₉	1	2	yes	—
573	#462	C₂²×C₁₉	1	2	yes	—
574	#462	C₂²×C₁₉	1	2	yes	—
575	#461	C₂²×C₁₉	1	1	yes	characteristic
576	#452	C₂²×C₁₉	1	2	yes	—
577	#452	C₂²×C₁₉	1	2	yes	—
578	#452	C₂²×C₁₉	1	2	yes	—
579	#446	C₂²×C₁₉	1	2	yes	—
580	#441	C₂²×C₁₉	1	2	yes	—
581	#441	C₂²×C₁₉	1	2	yes	—
582	#440	C₂²×C₁₉	1	2	yes	—
583	#440	C₂²×C₁₉	1	2	yes	—
584	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
585	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
586	#436	C₂²×C₁₉	1	2	yes	—
587	#435	C₂²×C₁₉	1	2	yes	—
588	#435	C₂²×C₁₉	1	2	yes	—
589	#433	C₂²×C₁₉	1	2	yes	—
590	#432	C₂²×C₁₉	1	1	yes	characteristic
591	#428	C₂²×C₁₉	1	1	yes	characteristic
592	#428	C₂²×C₁₉	1	1	yes	characteristic
593	#428	C₂²×C₁₉	1	2	yes	—
594	C₂×#106	C₂²×C₁₉	1	2	yes	—
595	#424	C₂²×C₁₉	1	2	yes	—
596	#423	C₂²×C₁₉	1	1	yes	characteristic
597	#417	C₂²×C₁₉	1	1	yes	characteristic
598	#417	C₂²×C₁₉	1	2	yes	—
599	#417	C₂²×C₁₉	1	1	yes	characteristic
600	#416	C₂²×C₁₉	1	2	yes	—
601	C₂×C₁₉	—	4	1	no	—
602	C₂×C₁₉	—	4	2	no	—
603	C₂×C₁₉	—	4	2	no	—
604	C₂×C₁₉	#3489	1	1	yes	characteristic
605	C₂×C₁₉	#3586	1	1	yes	characteristic
606	C₂×C₁₉	#3586	1	1	yes	characteristic
607	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
608	C₂×#41	C₂³×C₁₉	1	2	yes	—
609	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
610	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
611	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
612	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
613	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
614	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
615	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
616	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
617	C₄⋊Q₈	—	2	2	no	—
618	C₄⋊Q₈	—	2	2	no	—
619	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
620	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
621	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
622	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
623	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
624	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
625	#126	—	2	2	no	—
626	#126	—	2	2	no	—
627	#126	—	2	2	no	—
628	#126	—	2	2	no	—
629	#126	—	2	2	no	—
630	#126	—	2	2	no	—
631	#126	—	2	2	no	—
632	#126	D₄×C₁₉	1	2	yes	—
633	#125	—	2	2	no	—
634	#125	—	2	2	no	—
635	#125	—	2	1	no	—
636	#125	—	2	1	no	—
637	#125	—	2	2	no	—
638	#125	—	2	2	no	—
639	#125	—	2	2	no	—
640	#125	—	2	2	no	—
641	#125	—	2	2	no	—
642	#125	—	2	2	no	—
643	#125	—	2	2	no	—
644	#125	—	2	2	no	—
645	#125	—	2	2	no	—
646	#125	—	2	2	no	—
647	#125	—	2	1	no	—
648	#125	—	2	1	no	—
649	#125	—	2	1	no	—
650	#125	—	2	1	no	—
651	#125	D₄×C₁₉	1	1	yes	characteristic
652	#125	C₂³×C₁₉	1	2	yes	—
653	#125	C₂³×C₁₉	1	2	yes	—
654	#125	C₂³×C₁₉	1	2	yes	—
655	#125	C₂³×C₁₉	1	2	yes	—
656	#124	D₄×C₁₉	1	1	yes	characteristic
657	#123	—	2	2	no	—
658	#123	—	2	2	no	—
659	#123	—	2	2	no	—
660	#123	—	2	2	no	—
661	#123	—	2	2	no	—
662	#123	—	2	2	no	—
663	#123	D₄×C₁₉	1	2	yes	—
664	C₂²⋊Q₈	—	2	1	no	—
665	C₂²⋊Q₈	—	2	1	no	—
666	C₂²⋊Q₈	—	2	1	no	—
667	C₂²⋊Q₈	—	2	2	no	—
668	C₂²⋊Q₈	—	2	2	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	2	no	—
672	C₂²⋊Q₈	—	2	2	no	—
673	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
674	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
675	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
676	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
677	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
678	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
679	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
680	#121	—	2	1	no	—
681	#121	—	2	2	no	—
682	#121	D₄×C₁₉	1	1	yes	characteristic
683	C₄×Q₈	—	2	1	no	—
684	C₄×Q₈	—	2	2	no	—
685	C₄×Q₈	—	2	1	no	—
686	C₄×Q₈	—	2	1	no	—
687	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
688	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
689	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
690	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
691	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
692	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
693	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
694	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
695	C₄×D₄	—	2	1	no	—
696	C₄×D₄	—	2	2	no	—
697	C₄×D₄	—	2	1	no	—
698	C₄×D₄	—	2	1	no	—
699	C₄×D₄	—	2	2	no	—
700	C₄×D₄	—	2	2	no	—
701	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
702	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
703	C₄×D₄	C₂³×C₁₉	1	2	yes	—
704	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
705	C₄×D₄	C₂³×C₁₉	1	2	yes	—
706	#117	—	2	1	no	—
707	#117	—	2	1	no	—
708	#117	—	2	2	no	—
709	#117	—	2	2	no	—
710	#117	—	2	2	no	—
711	#117	—	2	2	no	—
712	#117	—	2	1	no	—
713	#117	C₂³×C₁₉	1	1	yes	characteristic
714	#117	C₂³×C₁₉	1	2	yes	—
715	#117	C₂³×C₁₉	1	2	yes	—
716	C₂×C₄⋊C₄	—	2	1	no	—
717	C₂×C₄⋊C₄	—	2	1	no	—
718	C₂×C₄⋊C₄	—	2	2	no	—
719	C₂×C₄⋊C₄	—	2	1	no	—
720	C₂×C₄⋊C₄	—	2	2	no	—
721	C₂×C₄⋊C₄	—	2	1	no	—
722	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
723	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
724	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
725	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
726	C₂×C₄²	—	2	1	no	—
727	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
728	#107	C₂³×C₁₉	1	2	yes	—
729	#107	C₂³×C₁₉	1	2	yes	—
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	2	yes	—
735	#106	C₂³×C₁₉	1	2	yes	—
736	#106	C₂³×C₁₉	1	2	yes	—
737	#106	C₂³×C₁₉	1	2	yes	—
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	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
743	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
744	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
745	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
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	#103	C₂³×C₁₉	1	2	yes	—
755	#103	C₂³×C₁₉	1	2	yes	—
756	#103	C₂³×C₁₉	1	2	yes	—
757	#103	C₂³×C₁₉	1	2	yes	—
758	#103	C₂³×C₁₉	1	2	yes	—
759	#102	C₂³×C₁₉	1	2	yes	—
760	#102	C₂³×C₁₉	1	2	yes	—
761	#102	C₂³×C₁₉	1	2	yes	—
762	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
763	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
764	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
765	#97	C₂³×C₁₉	1	2	yes	—
766	#97	C₂³×C₁₉	1	2	yes	—
767	C₄×C₈	C₂³×C₁₉	1	2	yes	—
768	C₁₉	#62237	1	1	yes	characteristic, direct product factor, Sylow
769	#41	—	2	2	no	—
770	#41	—	2	4	no	—
771	#41	—	4	2	no	—
772	#41	—	4	1	no	—
773	C₂×Q₈	—	2	1	no	—
774	C₂×Q₈	—	2	1	no	—
775	C₂×Q₈	—	2	2	no	—
776	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
777	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
778	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
779	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
780	C₂×D₄	—	2	2	no	—
781	C₂×D₄	—	2	1	no	—
782	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
783	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
784	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
785	C₂²×C₄	—	2	1	no	—
786	C₂²×C₄	—	2	1	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	1	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
795	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
798	Q₁₆	—	4	2	no	—
799	Q₁₆	—	4	2	no	—
800	Q₁₆	—	4	2	no	—
801	SD₁₆	—	2	4	no	—
802	M₁₆	—	4	1	no	—
803	M₁₆	—	4	2	no	—
804	M₁₆	—	4	1	no	—
805	C₂×C₈	—	4	2	no	—
806	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
807	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
808	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
809	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	1	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	1	no	—
828	C₄⋊C₄	—	2	1	no	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	1	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	1	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	1	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	C₂×D₄×C₁₉	1	2	yes	—
845	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
846	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
847	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
848	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
849	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
850	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
851	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
852	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
853	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
854	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
855	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	1	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	1	no	—
865	C₂²⋊C₄	—	2	1	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
868	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
869	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
870	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
871	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
872	C₄²	—	2	1	no	—
873	C₄²	—	2	1	no	—
874	C₄²	—	2	1	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	—	2	2	no	—
881	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
882	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
883	C₄²	C₂⁴×C₁₉	1	2	yes	—
884	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
885	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
886	C₂³	—	2	1	no	—
887	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
888	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
889	Q₈	—	2	2	no	—
890	Q₈	—	2	2	no	—
891	Q₈	—	2	1	no	—
892	Q₈	—	2	2	no	—
893	Q₈	—	2	1	no	—
894	Q₈	—	2	2	no	—
895	Q₈	—	4	1	no	—
896	Q₈	—	8	1	no	—
897	Q₈	—	8	1	no	—
898	Q₈	—	8	2	no	—
899	D₄	—	2	1	no	—
900	D₄	—	4	1	no	—
901	D₄	—	4	2	no	—
902	D₄	—	4	4	no	—
903	D₄	—	4	2	no	—
904	D₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	2	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	4	2	no	—
923	C₂×C₄	—	4	2	no	—
924	C₂×C₄	—	8	1	no	—
925	C₂×C₄	—	8	2	no	—
926	C₂×C₄	—	8	2	no	—
927	C₂×C₄	—	8	1	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
931	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
932	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
933	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
936	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
937	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
938	C₈	—	2	2	no	—
939	C₈	—	2	2	no	—
940	C₈	—	2	2	no	—
941	C₈	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	4	1	no	—
950	C₂²	—	4	1	no	—
951	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
952	C₄	—	2	2	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	4	1	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	1	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
970	C₄	C₁₉×#585	1	1	yes	characteristic
971	C₂	—	4	1	no	—
972	C₂	—	4	2	no	—
973	C₂	—	4	2	no	—
974	C₂	C₁₉×#3489	1	1	yes	characteristic
975	C₂	C₁₉×#3586	1	1	yes	characteristic
976	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×#3515	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3563	C₂	semidirect
3. C₁₉×#3388	C₂	semidirect
4. C₁₉×#3374	C₂	semidirect
5. C₁₉×#3352	C₂	semidirect
6. C₁₉×#3344	C₂	semidirect
7. C₁₉×#3344	C₂	semidirect
8. C₁₉×#3331	C₂	semidirect
9. C₁₉×#3315	C₂	semidirect
10. C₁₉×#3315	C₂	semidirect
11. C₁₉×#3261	C₂	semidirect
12. C₁₉×#3255	C₂	semidirect
13. C₁₉×#3242	C₂	semidirect
14. C₁₉×#3236	C₂	semidirect
15. C₁₉×#3120	C₂	semidirect
16. C₁₉×#3116	C₂	semidirect
17. C₁₉×#3084	C₂	semidirect
18. C₁₉×#3080	C₂	semidirect
19. C₁₉×#2995	C₂	semidirect
397. #62237	C₁₉	direct (N × H)
454. #3563	C₂×C₁₉	semidirect
456. #3388	C₂×C₁₉	semidirect
457. #3374	C₂×C₁₉	semidirect
458. #3352	C₂×C₁₉	semidirect
459. #3344	C₂×C₁₉	semidirect
460. #3344	C₂×C₁₉	semidirect
461. #3331	C₂×C₁₉	semidirect
462. #3315	C₂×C₁₉	semidirect
463. #3315	C₂×C₁₉	semidirect
464. #3261	C₂×C₁₉	semidirect
465. #3255	C₂×C₁₉	semidirect
466. #3242	C₂×C₁₉	semidirect
467. #3236	C₂×C₁₉	semidirect
468. #3120	C₂×C₁₉	semidirect
469. #3116	C₂×C₁₉	semidirect
470. #3084	C₂×C₁₉	semidirect
471. #3080	C₂×C₁₉	semidirect
472. #2995	C₂×C₁₉	semidirect
768. C₁₉	#62237	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×#3563	2
C₁₉×#3515	2
C₁₉×#3388	2
C₁₉×#3374	2
C₁₉×#3352	2
C₁₉×#3344	2
C₁₉×#3331	2
C₁₉×#3315	2
C₁₉×#3261	2
C₁₉×#3255	2
C₁₉×#3242	2
C₁₉×#3236	2
C₁₉×#3120	2
C₁₉×#3116	2
C₁₉×#3084	2
C₁₉×#3080	2
C₁₉×#2995	2
#62237	19

Subgroups — C19×#62237 #18068196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62237 #18068196