Subgroups — C₁₉×#62343 #18068302

Order 4864.

1820 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3548	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3356	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3353	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3304	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3302	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3299	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3298	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3278	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3276	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3255	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3201	C₂	1	4	yes	maximal, complemented
14	C₁₉×#3170	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3063	C₂	1	4	yes	maximal, complemented
17	C₁₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₉×#137	C₂²	1	4	yes	—
19	C₂×C₁₉×#131	C₂²	1	2	yes	—
20	C₁₉×#563	—	2	2	no	—
21	C₁₉×#562	—	2	2	no	—
22	C₁₉×#559	—	2	1	no	—
23	Q₈²×C₁₉	—	2	1	no	—
24	C₁₉×#556	C₂²	1	2	yes	—
25	C₁₉×#556	C₂²	1	2	yes	—
26	C₁₉×#554	—	2	1	no	—
27	C₁₉×#554	C₂²	1	2	yes	—
28	C₁₉×#550	—	2	1	no	—
29	C₁₉×#550	C₂²	1	2	yes	—
30	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
31	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
32	C₁₉×#547	C₂²	1	2	yes	—
33	C₁₉×#547	C₂²	1	2	yes	—
34	C₁₉×#542	—	2	2	no	—
35	C₁₉×#542	—	2	2	no	—
36	C₁₉×#540	—	2	2	no	—
37	C₁₉×#537	—	2	2	no	—
38	C₁₉×#537	C₂²	1	4	yes	—
39	C₁₉×#536	C₂²	1	4	yes	—
40	C₁₉×#533	C₂²	1	1	yes	characteristic
41	C₁₉×#533	C₂²	1	1	yes	characteristic
42	C₁₉×#533	C₂²	1	1	yes	characteristic
43	C₁₉×#532	C₂²	1	1	yes	characteristic
44	C₁₉×#532	C₂²	1	1	yes	characteristic
45	C₁₉×#500	C₂²	1	1	yes	characteristic
46	C₁₉×#498	C₂²	1	1	yes	characteristic
47	C₁₉×#494	C₂²	1	1	yes	characteristic
48	C₁₉×#492	C₂²	1	1	yes	characteristic
49	C₁₉×#487	C₂²	1	1	yes	characteristic
50	C₁₉×#487	C₂²	1	1	yes	characteristic
51	C₁₉×#487	C₂²	1	1	yes	characteristic
52	C₁₉×#486	C₂²	1	1	yes	characteristic
53	C₁₉×#485	C₂²	1	4	yes	—
54	C₁₉×#484	C₂²	1	4	yes	—
55	C₁₉×#483	C₂²	1	4	yes	—
56	C₁₉×#482	C₂²	1	4	yes	—
57	C₁₉×#477	C₂²	1	2	yes	—
58	C₁₉×#475	C₂²	1	2	yes	—
59	C₁₉×#475	C₂²	1	2	yes	—
60	C₁₉×#474	C₂²	1	2	yes	—
61	C₁₉×#470	C₂²	1	4	yes	—
62	C₁₉×#470	C₂²	1	4	yes	—
63	C₁₉×#468	C₂²	1	4	yes	—
64	C₁₉×#468	C₂²	1	4	yes	—
65	C₁₉×#467	C₂²	1	2	yes	—
66	C₁₉×#467	C₂²	1	2	yes	—
67	C₁₉×#467	C₂²	1	4	yes	—
68	C₁₉×#465	C₂²	1	2	yes	—
69	C₁₉×#465	C₂²	1	2	yes	—
70	C₁₉×#465	C₂²	1	4	yes	—
71	C₁₉×#462	C₂²	1	2	yes	—
72	C₁₉×#462	C₂²	1	2	yes	—
73	C₁₉×#461	C₂²	1	2	yes	—
74	C₁₉×#460	C₂²	1	2	yes	—
75	C₁₉×#452	C₂²	1	4	yes	—
76	C₁₉×#452	C₂²	1	4	yes	—
77	C₁₉×#451	C₂²	1	4	yes	—
78	C₁₉×#448	C₂²	1	4	yes	—
79	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
80	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
81	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
82	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
83	C₁₉×#436	C₂²	1	2	yes	—
84	C₁₉×#436	C₂²	1	2	yes	—
85	C₈×D₄×C₁₉	C₂²	1	2	yes	—
86	C₈×D₄×C₁₉	C₂²	1	2	yes	—
87	C₁₉×#428	C₂²	1	4	yes	—
88	C₁₉×#423	C₂²	1	1	yes	characteristic
89	C₁₉×#416	C₂²	1	4	yes	—
90	C₂×C₁₉×#103	C₂²	1	4	yes	—
91	C₁₉×#408	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
93	C₂×#41×C₁₉	—	2	2	no	—
94	C₂×#41×C₁₉	—	2	1	no	—
95	C₂×#41×C₁₉	C₂³	1	4	yes	—
96	C₂×#41×C₁₉	C₂³	1	2	yes	—
97	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
98	C₁₉×#137	—	4	8	no	—
99	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
100	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
105	C₁₉×#131	—	4	4	no	—
106	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
107	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
108	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
111	C₁₉×C₄⋊Q₈	—	2	4	no	—
112	C₁₉×C₄⋊Q₈	—	2	2	no	—
113	C₁₉×C₄⋊Q₈	—	2	2	no	—
114	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
115	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₁₉×#127	—	2	2	no	—
123	C₁₉×#127	D₄	1	1	yes	characteristic
124	C₁₉×#127	C₂³	1	1	yes	characteristic
125	C₁₉×#126	—	2	4	no	—
126	C₁₉×#126	—	2	4	no	—
127	C₁₉×#125	—	2	2	no	—
128	C₁₉×#125	—	2	1	no	—
129	C₁₉×#125	—	2	1	no	—
130	C₁₉×#125	—	2	1	no	—
131	C₁₉×#124	—	2	4	no	—
132	C₁₉×#124	—	2	2	no	—
133	C₁₉×#124	—	2	2	no	—
134	C₁₉×#124	—	2	1	no	—
135	C₁₉×#124	D₄	1	2	yes	—
136	C₁₉×#123	—	2	4	no	—
137	C₁₉×#123	—	2	4	no	—
138	C₁₉×#123	—	2	4	no	—
139	C₁₉×#123	—	2	4	no	—
140	C₁₉×C₂²⋊Q₈	—	2	4	no	—
141	C₁₉×C₂²⋊Q₈	—	2	1	no	—
142	C₁₉×C₂²⋊Q₈	—	2	1	no	—
143	C₁₉×C₂²⋊Q₈	—	2	1	no	—
144	C₁₉×C₂²⋊Q₈	—	2	2	no	—
145	C₁₉×C₂²⋊Q₈	—	2	4	no	—
146	C₁₉×C₂²⋊Q₈	—	2	4	no	—
147	C₁₉×C₂²⋊Q₈	—	2	4	no	—
148	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
149	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
150	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
151	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₁₉×#121	—	2	4	no	—
155	C₁₉×#121	—	2	4	no	—
156	C₁₉×#121	—	2	2	no	—
157	C₁₉×#121	—	2	4	no	—
158	C₁₉×#121	—	2	1	no	—
159	C₁₉×#121	—	2	4	no	—
160	C₁₉×#121	D₄	1	2	yes	—
161	C₁₉×#121	D₄	1	2	yes	—
162	C₁₉×#121	C₂³	1	4	yes	—
163	C₁₉×#121	C₂³	1	2	yes	—
164	C₄×Q₈×C₁₉	—	2	2	no	—
165	C₄×Q₈×C₁₉	—	2	2	no	—
166	C₄×Q₈×C₁₉	—	2	1	no	—
167	C₄×Q₈×C₁₉	—	2	1	no	—
168	C₄×Q₈×C₁₉	—	2	1	no	—
169	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
170	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
171	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
172	C₄×D₄×C₁₉	—	2	2	no	—
173	C₄×D₄×C₁₉	—	2	2	no	—
174	C₄×D₄×C₁₉	—	2	2	no	—
175	C₄×D₄×C₁₉	—	2	2	no	—
176	C₄×D₄×C₁₉	—	2	1	no	—
177	C₄×D₄×C₁₉	C₂³	1	2	yes	—
178	C₄×D₄×C₁₉	C₂³	1	2	yes	—
179	C₄×D₄×C₁₉	C₂³	1	2	yes	—
180	C₁₉×#117	—	2	1	no	—
181	C₁₉×#117	—	2	1	no	—
182	C₁₉×#117	—	2	1	no	—
183	C₁₉×#117	C₂³	1	4	yes	—
184	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
186	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
187	C₁₉×#107	C₂³	1	2	yes	—
188	C₁₉×#107	C₂³	1	4	yes	—
189	C₁₉×#107	C₂³	1	2	yes	—
190	C₁₉×#106	C₂³	1	2	yes	—
191	C₁₉×#106	C₂³	1	4	yes	—
192	C₁₉×#106	C₂³	1	2	yes	—
193	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
194	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
195	C₁₉×#103	C₂³	1	2	yes	—
196	C₁₉×#103	C₂³	1	2	yes	—
197	C₁₉×#103	C₂³	1	4	yes	—
198	C₁₉×#103	C₂³	1	4	yes	—
199	C₁₉×#103	C₂³	1	2	yes	—
200	C₁₉×#103	C₂³	1	4	yes	—
201	C₁₉×#103	C₂³	1	2	yes	—
202	C₁₉×#103	C₂³	1	2	yes	—
203	C₁₉×#103	C₂³	1	2	yes	—
204	C₁₉×#102	C₂³	1	2	yes	—
205	C₁₉×#102	C₂³	1	4	yes	—
206	C₁₉×#102	C₂³	1	2	yes	—
207	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
208	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
209	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
213	#41×C₁₉	—	4	2	no	—
214	#41×C₁₉	—	4	2	no	—
215	#41×C₁₉	—	4	4	no	—
216	#41×C₁₉	—	4	4	no	—
217	#41×C₁₉	—	8	2	no	—
218	#41×C₁₉	—	8	4	no	—
219	C₂×Q₈×C₁₉	—	2	1	no	—
220	C₂×Q₈×C₁₉	—	2	1	no	—
221	C₂×Q₈×C₁₉	—	2	1	no	—
222	C₂×Q₈×C₁₉	—	2	1	no	—
223	C₂×Q₈×C₁₉	—	2	4	no	—
224	C₂×Q₈×C₁₉	—	4	4	no	—
225	C₂×Q₈×C₁₉	—	4	4	no	—
226	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
228	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
229	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
230	C₂×D₄×C₁₉	—	2	2	no	—
231	C₂×D₄×C₁₉	—	2	4	no	—
232	C₂×D₄×C₁₉	—	2	4	no	—
233	C₂×D₄×C₁₉	—	2	1	no	—
234	C₂×D₄×C₁₉	—	2	1	no	—
235	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
238	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
239	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₉	—	2	4	no	—
241	C₂²×C₄×C₁₉	—	2	4	no	—
242	C₂²×C₄×C₁₉	—	2	2	no	—
243	C₂²×C₄×C₁₉	—	2	4	no	—
244	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
248	Q₁₆×C₁₉	—	2	4	no	—
249	Q₁₆×C₁₉	—	4	2	no	—
250	Q₁₆×C₁₉	—	4	4	no	—
251	SD₁₆×C₁₉	—	2	4	no	—
252	SD₁₆×C₁₉	—	4	2	no	—
253	SD₁₆×C₁₉	—	4	4	no	—
254	M₁₆×C₁₉	—	2	8	no	—
255	M₁₆×C₁₉	—	4	2	no	—
256	C₂×C₈×C₁₉	—	2	2	no	—
257	C₂×C₈×C₁₉	—	4	1	no	—
258	C₂×C₈×C₁₉	—	4	4	no	—
259	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
260	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
261	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
262	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
263	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
264	C₄⋊C₄×C₁₉	—	2	1	no	—
265	C₄⋊C₄×C₁₉	—	2	4	no	—
266	C₄⋊C₄×C₁₉	—	2	4	no	—
267	C₄⋊C₄×C₁₉	—	2	1	no	—
268	C₄⋊C₄×C₁₉	—	2	1	no	—
269	C₄⋊C₄×C₁₉	—	2	1	no	—
270	C₄⋊C₄×C₁₉	—	2	1	no	—
271	C₄⋊C₄×C₁₉	—	2	1	no	—
272	C₄⋊C₄×C₁₉	—	2	1	no	—
273	C₄⋊C₄×C₁₉	—	2	1	no	—
274	C₄⋊C₄×C₁₉	—	2	1	no	—
275	C₄⋊C₄×C₁₉	—	2	1	no	—
276	C₄⋊C₄×C₁₉	—	2	2	no	—
277	C₄⋊C₄×C₁₉	—	2	4	no	—
278	C₄⋊C₄×C₁₉	—	2	4	no	—
279	C₄⋊C₄×C₁₉	—	2	2	no	—
280	C₄⋊C₄×C₁₉	—	2	2	no	—
281	C₄⋊C₄×C₁₉	—	2	2	no	—
282	C₄⋊C₄×C₁₉	—	2	2	no	—
283	C₄⋊C₄×C₁₉	—	2	2	no	—
284	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
286	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
290	C₂²⋊C₄×C₁₉	—	2	2	no	—
291	C₂²⋊C₄×C₁₉	—	2	2	no	—
292	C₂²⋊C₄×C₁₉	—	2	2	no	—
293	C₂²⋊C₄×C₁₉	—	2	4	no	—
294	C₂²⋊C₄×C₁₉	—	2	4	no	—
295	C₂²⋊C₄×C₁₉	—	2	4	no	—
296	C₂²⋊C₄×C₁₉	—	2	4	no	—
297	C₂²⋊C₄×C₁₉	—	2	4	no	—
298	C₂²⋊C₄×C₁₉	—	2	2	no	—
299	C₂²⋊C₄×C₁₉	—	2	2	no	—
300	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
301	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
302	C₄²×C₁₉	—	2	2	no	—
303	C₄²×C₁₉	—	2	2	no	—
304	C₄²×C₁₉	—	2	2	no	—
305	C₄²×C₁₉	—	2	4	no	—
306	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
309	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
310	#62343	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
311	C₂³×C₁₉	—	2	2	no	—
312	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
313	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
314	Q₈×C₁₉	—	2	2	no	—
315	Q₈×C₁₉	—	2	2	no	—
316	Q₈×C₁₉	—	2	2	no	—
317	Q₈×C₁₉	—	2	2	no	—
318	Q₈×C₁₉	—	2	2	no	—
319	Q₈×C₁₉	—	2	2	no	—
320	Q₈×C₁₉	—	4	2	no	—
321	Q₈×C₁₉	—	4	2	no	—
322	Q₈×C₁₉	—	4	2	no	—
323	Q₈×C₁₉	—	4	2	no	—
324	Q₈×C₁₉	—	8	4	no	—
325	Q₈×C₁₉	—	8	1	no	—
326	D₄×C₁₉	—	2	4	no	—
327	D₄×C₁₉	—	2	4	no	—
328	D₄×C₁₉	—	2	2	no	—
329	D₄×C₁₉	—	2	2	no	—
330	D₄×C₁₉	—	4	4	no	—
331	D₄×C₁₉	—	4	2	no	—
332	D₄×C₁₉	—	4	2	no	—
333	D₄×C₁₉	—	8	1	no	—
334	D₄×C₁₉	—	8	4	no	—
335	D₄×C₁₉	—	8	2	no	—
336	D₄×C₁₉	—	8	4	no	—
337	C₂×C₄×C₁₉	—	2	2	no	—
338	C₂×C₄×C₁₉	—	2	2	no	—
339	C₂×C₄×C₁₉	—	2	1	no	—
340	C₂×C₄×C₁₉	—	2	4	no	—
341	C₂×C₄×C₁₉	—	2	1	no	—
342	C₂×C₄×C₁₉	—	2	4	no	—
343	C₂×C₄×C₁₉	—	2	2	no	—
344	C₂×C₄×C₁₉	—	2	2	no	—
345	C₂×C₄×C₁₉	—	2	2	no	—
346	C₂×C₄×C₁₉	—	2	2	no	—
347	C₂×C₄×C₁₉	—	2	2	no	—
348	C₂×C₄×C₁₉	—	2	2	no	—
349	C₂×C₄×C₁₉	—	2	2	no	—
350	C₂×C₄×C₁₉	—	4	4	no	—
351	C₂×C₄×C₁₉	—	8	4	no	—
352	C₂×C₄×C₁₉	—	8	4	no	—
353	C₂×C₄×C₁₉	—	8	4	no	—
354	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
355	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
361	C₈×C₁₉	—	2	1	no	—
362	C₈×C₁₉	—	2	4	no	—
363	C₈×C₁₉	—	2	1	no	—
364	C₈×C₁₉	—	2	1	no	—
365	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
366	#3550	C₂×C₁₉	1	1	yes	characteristic, complemented
367	#3548	C₂×C₁₉	1	1	yes	characteristic
368	#3356	C₂×C₁₉	1	2	yes	complemented
369	#3353	C₂×C₁₉	1	2	yes	complemented
370	#3304	C₂×C₁₉	1	2	yes	complemented
371	#3302	C₂×C₁₉	1	2	yes	complemented
372	#3299	C₂×C₁₉	1	2	yes	complemented
373	#3298	C₂×C₁₉	1	2	yes	complemented
374	#3278	C₂×C₁₉	1	2	yes	complemented
375	#3276	C₂×C₁₉	1	2	yes	complemented
376	#3255	C₂×C₁₉	1	1	yes	characteristic, complemented
377	#3254	C₂×C₁₉	1	1	yes	characteristic, complemented
378	#3201	C₂×C₁₉	1	4	yes	complemented
379	#3170	C₂×C₁₉	1	1	yes	characteristic, complemented
380	#3167	C₂×C₁₉	1	1	yes	characteristic, complemented
381	#3063	C₂×C₁₉	1	4	yes	complemented
382	#2931	C₂×C₁₉	1	1	yes	characteristic, complemented
383	C₂²×C₁₉	—	2	4	no	—
384	C₂²×C₁₉	—	2	1	no	—
385	C₂²×C₁₉	—	2	1	no	—
386	C₂²×C₁₉	—	2	4	no	—
387	C₂²×C₁₉	—	2	1	no	—
388	C₂²×C₁₉	—	2	4	no	—
389	C₂²×C₁₉	—	4	2	no	—
390	C₂²×C₁₉	—	4	2	no	—
391	C₂²×C₁₉	—	4	2	no	—
392	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
393	C₄×C₁₉	—	2	4	no	—
394	C₄×C₁₉	—	2	1	no	—
395	C₄×C₁₉	—	2	1	no	—
396	C₄×C₁₉	—	2	1	no	—
397	C₄×C₁₉	—	4	2	no	—
398	C₄×C₁₉	—	4	2	no	—
399	C₄×C₁₉	—	4	2	no	—
400	C₄×C₁₉	—	4	2	no	—
401	C₄×C₁₉	—	4	2	no	—
402	C₄×C₁₉	—	4	2	no	—
403	C₄×C₁₉	—	4	2	no	—
404	C₄×C₁₉	#577	1	2	yes	—
405	C₄×C₁₉	#578	1	2	yes	—
406	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
407	C₄×C₁₉	#585	1	1	yes	characteristic
408	C₂×#137	C₂²×C₁₉	1	4	yes	—
409	C₂×#131	C₂²×C₁₉	1	2	yes	—
410	#563	—	2	2	no	—
411	#562	—	2	2	no	—
412	#559	—	2	1	no	—
413	Q₈²	—	2	1	no	—
414	#556	C₂²×C₁₉	1	2	yes	—
415	#556	C₂²×C₁₉	1	2	yes	—
416	#554	—	2	1	no	—
417	#554	C₂²×C₁₉	1	2	yes	—
418	#550	—	2	1	no	—
419	#550	C₂²×C₁₉	1	2	yes	—
420	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
421	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
422	#547	C₂²×C₁₉	1	2	yes	—
423	#547	C₂²×C₁₉	1	2	yes	—
424	#542	—	2	2	no	—
425	#542	—	2	2	no	—
426	#540	—	2	2	no	—
427	#537	—	2	2	no	—
428	#537	C₂²×C₁₉	1	4	yes	—
429	#536	C₂²×C₁₉	1	4	yes	—
430	#533	C₂²×C₁₉	1	1	yes	characteristic
431	#533	C₂²×C₁₉	1	1	yes	characteristic
432	#533	C₂²×C₁₉	1	1	yes	characteristic
433	#532	C₂²×C₁₉	1	1	yes	characteristic
434	#532	C₂²×C₁₉	1	1	yes	characteristic
435	#500	C₂²×C₁₉	1	1	yes	characteristic
436	#498	C₂²×C₁₉	1	1	yes	characteristic
437	#494	C₂²×C₁₉	1	1	yes	characteristic
438	#492	C₂²×C₁₉	1	1	yes	characteristic
439	#487	C₂²×C₁₉	1	1	yes	characteristic
440	#487	C₂²×C₁₉	1	1	yes	characteristic
441	#487	C₂²×C₁₉	1	1	yes	characteristic
442	#486	C₂²×C₁₉	1	1	yes	characteristic
443	#485	C₂²×C₁₉	1	4	yes	—
444	#484	C₂²×C₁₉	1	4	yes	—
445	#483	C₂²×C₁₉	1	4	yes	—
446	#482	C₂²×C₁₉	1	4	yes	—
447	#477	C₂²×C₁₉	1	2	yes	—
448	#475	C₂²×C₁₉	1	2	yes	—
449	#475	C₂²×C₁₉	1	2	yes	—
450	#474	C₂²×C₁₉	1	2	yes	—
451	#470	C₂²×C₁₉	1	4	yes	—
452	#470	C₂²×C₁₉	1	4	yes	—
453	#468	C₂²×C₁₉	1	4	yes	—
454	#468	C₂²×C₁₉	1	4	yes	—
455	#467	C₂²×C₁₉	1	2	yes	—
456	#467	C₂²×C₁₉	1	2	yes	—
457	#467	C₂²×C₁₉	1	4	yes	—
458	#465	C₂²×C₁₉	1	2	yes	—
459	#465	C₂²×C₁₉	1	2	yes	—
460	#465	C₂²×C₁₉	1	4	yes	—
461	#462	C₂²×C₁₉	1	2	yes	—
462	#462	C₂²×C₁₉	1	2	yes	—
463	#461	C₂²×C₁₉	1	2	yes	—
464	#460	C₂²×C₁₉	1	2	yes	—
465	#452	C₂²×C₁₉	1	4	yes	—
466	#452	C₂²×C₁₉	1	4	yes	—
467	#451	C₂²×C₁₉	1	4	yes	—
468	#448	C₂²×C₁₉	1	4	yes	—
469	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
470	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
471	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
472	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
473	#436	C₂²×C₁₉	1	2	yes	—
474	#436	C₂²×C₁₉	1	2	yes	—
475	C₈×D₄	C₂²×C₁₉	1	2	yes	—
476	C₈×D₄	C₂²×C₁₉	1	2	yes	—
477	#428	C₂²×C₁₉	1	4	yes	—
478	#423	C₂²×C₁₉	1	1	yes	characteristic
479	#416	C₂²×C₁₉	1	4	yes	—
480	C₂×#103	C₂²×C₁₉	1	4	yes	—
481	#408	C₂²×C₁₉	1	2	yes	—
482	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
483	C₂×C₁₉	—	4	4	no	—
484	C₂×C₁₉	—	4	1	no	—
485	C₂×C₁₉	—	8	2	no	—
486	C₂×C₁₉	#3496	1	1	yes	characteristic
487	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
488	C₂×C₁₉	C₂×#578	1	1	yes	characteristic
489	C₂×#41	—	2	2	no	—
490	C₂×#41	—	2	1	no	—
491	C₂×#41	C₂³×C₁₉	1	4	yes	—
492	C₂×#41	C₂³×C₁₉	1	2	yes	—
493	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
494	#137	—	4	8	no	—
495	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
496	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
497	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
498	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
499	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
500	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
501	#131	—	4	4	no	—
502	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
503	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
504	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
505	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
506	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
507	C₄⋊Q₈	—	2	4	no	—
508	C₄⋊Q₈	—	2	2	no	—
509	C₄⋊Q₈	—	2	2	no	—
510	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
511	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
512	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
513	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
517	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
518	#127	—	2	2	no	—
519	#127	D₄×C₁₉	1	1	yes	characteristic
520	#127	C₂³×C₁₉	1	1	yes	characteristic
521	#126	—	2	4	no	—
522	#126	—	2	4	no	—
523	#125	—	2	2	no	—
524	#125	—	2	1	no	—
525	#125	—	2	1	no	—
526	#125	—	2	1	no	—
527	#124	—	2	4	no	—
528	#124	—	2	2	no	—
529	#124	—	2	2	no	—
530	#124	—	2	1	no	—
531	#124	D₄×C₁₉	1	2	yes	—
532	#123	—	2	4	no	—
533	#123	—	2	4	no	—
534	#123	—	2	4	no	—
535	#123	—	2	4	no	—
536	C₂²⋊Q₈	—	2	4	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	C₂²⋊Q₈	—	2	4	no	—
543	C₂²⋊Q₈	—	2	4	no	—
544	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
545	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
546	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
547	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
548	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
549	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
550	#121	—	2	4	no	—
551	#121	—	2	4	no	—
552	#121	—	2	2	no	—
553	#121	—	2	4	no	—
554	#121	—	2	1	no	—
555	#121	—	2	4	no	—
556	#121	D₄×C₁₉	1	2	yes	—
557	#121	D₄×C₁₉	1	2	yes	—
558	#121	C₂³×C₁₉	1	2	yes	—
559	#121	C₂³×C₁₉	1	4	yes	—
560	C₄×Q₈	—	2	2	no	—
561	C₄×Q₈	—	2	2	no	—
562	C₄×Q₈	—	2	1	no	—
563	C₄×Q₈	—	2	1	no	—
564	C₄×Q₈	—	2	1	no	—
565	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
566	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
567	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	C₂³×C₁₉	1	2	yes	—
574	C₄×D₄	C₂³×C₁₉	1	2	yes	—
575	C₄×D₄	C₂³×C₁₉	1	2	yes	—
576	#117	—	2	1	no	—
577	#117	—	2	1	no	—
578	#117	—	2	1	no	—
579	#117	C₂³×C₁₉	1	4	yes	—
580	C₂×C₄⋊C₄	—	2	2	no	—
581	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
582	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
583	#107	C₂³×C₁₉	1	2	yes	—
584	#107	C₂³×C₁₉	1	4	yes	—
585	#107	C₂³×C₁₉	1	2	yes	—
586	#106	C₂³×C₁₉	1	2	yes	—
587	#106	C₂³×C₁₉	1	4	yes	—
588	#106	C₂³×C₁₉	1	2	yes	—
589	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
590	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
591	#103	C₂³×C₁₉	1	2	yes	—
592	#103	C₂³×C₁₉	1	2	yes	—
593	#103	C₂³×C₁₉	1	4	yes	—
594	#103	C₂³×C₁₉	1	4	yes	—
595	#103	C₂³×C₁₉	1	2	yes	—
596	#103	C₂³×C₁₉	1	4	yes	—
597	#103	C₂³×C₁₉	1	2	yes	—
598	#103	C₂³×C₁₉	1	2	yes	—
599	#103	C₂³×C₁₉	1	2	yes	—
600	#102	C₂³×C₁₉	1	2	yes	—
601	#102	C₂³×C₁₉	1	4	yes	—
602	#102	C₂³×C₁₉	1	2	yes	—
603	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
604	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
605	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
606	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
607	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
608	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
609	C₁₉	#62343	1	1	yes	characteristic, direct product factor, Sylow
610	#41	—	4	2	no	—
611	#41	—	4	2	no	—
612	#41	—	4	4	no	—
613	#41	—	4	4	no	—
614	#41	—	8	2	no	—
615	#41	—	8	4	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	4	no	—
621	C₂×Q₈	—	4	4	no	—
622	C₂×Q₈	—	4	4	no	—
623	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
624	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
625	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
626	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
633	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
634	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
635	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
636	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
644	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
645	Q₁₆	—	2	4	no	—
646	Q₁₆	—	4	2	no	—
647	Q₁₆	—	4	4	no	—
648	SD₁₆	—	2	4	no	—
649	SD₁₆	—	4	2	no	—
650	SD₁₆	—	4	4	no	—
651	M₁₆	—	2	8	no	—
652	M₁₆	—	4	2	no	—
653	C₂×C₈	—	2	2	no	—
654	C₂×C₈	—	4	1	no	—
655	C₂×C₈	—	4	4	no	—
656	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
657	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
658	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
659	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
660	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
682	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
685	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
686	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
698	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
699	C₄²	—	2	2	no	—
700	C₄²	—	2	2	no	—
701	C₄²	—	2	2	no	—
702	C₄²	—	2	4	no	—
703	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
704	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
705	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
706	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
707	C₂³	—	2	2	no	—
708	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
709	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
710	Q₈	—	2	2	no	—
711	Q₈	—	2	2	no	—
712	Q₈	—	2	2	no	—
713	Q₈	—	2	2	no	—
714	Q₈	—	2	2	no	—
715	Q₈	—	2	2	no	—
716	Q₈	—	4	2	no	—
717	Q₈	—	4	2	no	—
718	Q₈	—	4	2	no	—
719	Q₈	—	4	2	no	—
720	Q₈	—	8	4	no	—
721	Q₈	—	8	1	no	—
722	D₄	—	2	4	no	—
723	D₄	—	2	4	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	4	4	no	—
727	D₄	—	4	2	no	—
728	D₄	—	4	2	no	—
729	D₄	—	8	1	no	—
730	D₄	—	8	4	no	—
731	D₄	—	8	2	no	—
732	D₄	—	8	4	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	4	4	no	—
747	C₂×C₄	—	8	4	no	—
748	C₂×C₄	—	8	4	no	—
749	C₂×C₄	—	8	4	no	—
750	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
751	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
754	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
756	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
757	C₈	—	2	1	no	—
758	C₈	—	2	4	no	—
759	C₈	—	2	1	no	—
760	C₈	—	2	1	no	—
761	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
762	C₂²	—	2	4	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	4	no	—
766	C₂²	—	2	1	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
772	C₄	—	2	4	no	—
773	C₄	—	2	1	no	—
774	C₄	—	2	1	no	—
775	C₄	—	2	1	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	C₁₉×#577	1	2	yes	—
784	C₄	C₁₉×#578	1	2	yes	—
785	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
786	C₄	C₁₉×#585	1	1	yes	characteristic
787	C₂	—	4	4	no	—
788	C₂	—	4	1	no	—
789	C₂	—	8	2	no	—
790	C₂	C₁₉×#3496	1	1	yes	characteristic
791	C₂	C₂×C₁₉×#577	1	1	yes	characteristic
792	C₂	C₂×C₁₉×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3548	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3550	C₂	semidirect
3. C₁₉×#3356	C₂	semidirect
4. C₁₉×#3353	C₂	semidirect
5. C₁₉×#3304	C₂	semidirect
6. C₁₉×#3302	C₂	semidirect
7. C₁₉×#3299	C₂	semidirect
8. C₁₉×#3298	C₂	semidirect
9. C₁₉×#3278	C₂	semidirect
10. C₁₉×#3276	C₂	semidirect
11. C₁₉×#3255	C₂	semidirect
12. C₁₉×#3254	C₂	semidirect
13. C₁₉×#3201	C₂	semidirect
14. C₁₉×#3170	C₂	semidirect
15. C₁₉×#3167	C₂	semidirect
16. C₁₉×#3063	C₂	semidirect
17. C₁₉×#2931	C₂	semidirect
310. #62343	C₁₉	direct (N × H)
366. #3550	C₂×C₁₉	semidirect
368. #3356	C₂×C₁₉	semidirect
369. #3353	C₂×C₁₉	semidirect
370. #3304	C₂×C₁₉	semidirect
371. #3302	C₂×C₁₉	semidirect
372. #3299	C₂×C₁₉	semidirect
373. #3298	C₂×C₁₉	semidirect
374. #3278	C₂×C₁₉	semidirect
375. #3276	C₂×C₁₉	semidirect
376. #3255	C₂×C₁₉	semidirect
377. #3254	C₂×C₁₉	semidirect
378. #3201	C₂×C₁₉	semidirect
379. #3170	C₂×C₁₉	semidirect
380. #3167	C₂×C₁₉	semidirect
381. #3063	C₂×C₁₉	semidirect
382. #2931	C₂×C₁₉	semidirect
609. C₁₉	#62343	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×#3550	2
C₁₉×#3548	2
C₁₉×#3356	2
C₁₉×#3353	2
C₁₉×#3304	2
C₁₉×#3302	2
C₁₉×#3299	2
C₁₉×#3298	2
C₁₉×#3278	2
C₁₉×#3276	2
C₁₉×#3255	2
C₁₉×#3254	2
C₁₉×#3201	2
C₁₉×#3170	2
C₁₉×#3167	2
C₁₉×#3063	2
C₁₉×#2931	2
#62343	19

Subgroups — C19×#62343 #18068302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62343 #18068302