Subgroups — C₁₉×#61347 #18067306

Order 4864.

1846 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3373	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3371	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3369	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3366	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3362	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3360	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#3136	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3084	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₉×#476	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3045	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3035	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#2952	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#135	C₂²	1	2	yes	—
20	C₁₉×#559	C₂²	1	4	yes	—
21	Q₈²×C₁₉	C₂²	1	2	yes	complemented
22	C₁₉×#557	C₂²	1	2	yes	complemented
23	C₁₉×#556	C₂²	1	2	yes	—
24	C₁₉×#555	—	2	1	no	—
25	C₁₉×#554	—	2	2	no	—
26	C₁₉×#554	C₂²	1	2	yes	complemented
27	C₁₉×#553	—	2	2	no	—
28	C₁₉×#550	C₂²	1	2	yes	—
29	D₄×Q₈×C₁₉	—	2	2	no	—
30	D₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
31	C₁₉×#547	—	2	1	no	—
32	C₁₉×#544	—	2	2	no	—
33	C₁₉×#544	C₂²	1	2	yes	—
34	C₁₉×#538	—	2	2	no	—
35	C₁₉×#535	C₂²	1	2	yes	—
36	C₁₉×#533	—	2	1	no	—
37	C₁₉×#533	C₂²	1	1	yes	characteristic
38	C₁₉×#532	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
40	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₁₉×#525	—	2	2	no	—
42	C₁₉×#520	C₂²	1	2	yes	—
43	C₁₉×#520	C₂²	1	2	yes	—
44	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
46	C₁₉×#490	C₂²	1	4	yes	—
47	C₁₉×#489	C₂²	1	4	yes	—
48	C₁₉×#489	C₂²	1	4	yes	complemented
49	C₁₉×#488	C₂²	1	4	yes	—
50	C₁₉×#487	C₂²	1	2	yes	complemented
51	C₁₉×#486	C₂²	1	4	yes	—
52	C₁₉×#486	C₂²	1	2	yes	complemented
53	C₁₉×#479	C₂²	1	4	yes	complemented
54	C₁₉×#478	C₂²	1	4	yes	complemented
55	C₁₉×#476	C₂²	1	2	yes	—
56	C₁₉×#476	C₂²	1	2	yes	—
57	C₁₉×#476	C₂²	1	4	yes	—
58	C₁₉×#476	C₂²	1	4	yes	complemented
59	C₁₉×#475	C₂²	1	4	yes	complemented
60	C₁₉×#464	C₂²	1	4	yes	—
61	C₁₉×#464	C₂²	1	2	yes	complemented
62	C₁₉×#463	C₂²	1	4	yes	—
63	C₁₉×#463	C₂²	1	2	yes	complemented
64	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#460	C₂²	1	4	yes	—
67	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#459	C₂²	1	4	yes	—
69	C₁₉×#459	C₂²	1	1	yes	characteristic, complemented
70	C₁₉×#446	C₂²	1	2	yes	complemented
71	C₁₉×#446	C₂²	1	4	yes	complemented
72	C₈×Q₈×C₁₉	C₂²	1	2	yes	complemented
73	C₁₉×#442	C₂²	1	2	yes	—
74	C₁₉×#442	C₂²	1	4	yes	complemented
75	C₁₉×#441	C₂²	1	4	yes	complemented
76	C₁₉×#440	C₂²	1	2	yes	—
77	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
78	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	complemented
80	C₄×D₈×C₁₉	C₂²	1	2	yes	—
81	C₁₉×#428	C₂²	1	1	yes	characteristic
82	C₂×C₁₉×#106	C₂²	1	2	yes	—
83	C₁₉×#424	C₂²	1	2	yes	—
84	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
85	C₁₉×#418	C₂²	1	1	yes	characteristic
86	C₁₉×#417	C₂²	1	1	yes	characteristic
87	C₁₉×#417	C₂²	1	2	yes	—
88	C₁₉×#417	C₂²	1	2	yes	—
89	C₁₉×#416	C₂²	1	2	yes	—
90	C₂×C₁₉×#102	C₂²	1	2	yes	—
91	C₁₉×#405	C₂²	1	2	yes	—
92	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
93	C₂×#41×C₁₉	—	2	2	no	—
94	C₂×#41×C₁₉	C₂³	1	2	yes	—
95	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₉	—	2	2	no	—
97	C₂²×Q₈×C₁₉	—	2	1	no	—
98	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₉	—	2	1	no	—
100	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
101	C₁₉×#135	—	2	8	no	—
102	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
105	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
106	C₂×D₈×C₁₉	C₂³	1	2	yes	—
107	C₂×D₈×C₁₉	C₂³	1	2	yes	—
108	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
111	C₁₉×C₄⋊Q₈	—	2	2	no	—
112	C₁₉×C₄⋊Q₈	—	2	2	no	—
113	C₁₉×C₄⋊Q₈	—	2	2	no	—
114	C₁₉×C₄⋊Q₈	—	2	4	no	—
115	C₁₉×C₄⋊Q₈	—	2	1	no	—
116	C₁₉×C₄⋊Q₈	—	2	1	no	—
117	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
118	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
119	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
121	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
123	C₁₉×#127	C₂³	1	4	yes	—
124	C₁₉×#127	C₂³	1	1	yes	characteristic
125	C₁₉×#126	—	2	4	no	—
126	C₁₉×#125	—	2	2	no	—
127	C₁₉×#125	—	2	4	no	—
128	C₁₉×#125	D₄	1	2	yes	—
129	C₁₉×#125	C₂³	1	4	yes	—
130	C₁₉×#124	—	2	4	no	—
131	C₁₉×#124	C₂³	1	4	yes	—
132	C₁₉×#124	C₂³	1	2	yes	—
133	C₁₉×#123	—	2	4	no	—
134	C₁₉×#123	—	2	4	no	—
135	C₁₉×C₂²⋊Q₈	—	2	2	no	—
136	C₁₉×C₂²⋊Q₈	—	2	2	no	—
137	C₁₉×C₂²⋊Q₈	—	2	2	no	—
138	C₁₉×C₂²⋊Q₈	—	2	4	no	—
139	C₁₉×C₂²⋊Q₈	—	2	4	no	—
140	C₁₉×C₂²⋊Q₈	—	2	4	no	—
141	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
142	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
143	C₁₉×#121	—	2	1	no	—
144	C₁₉×#121	—	2	1	no	—
145	C₁₉×#121	—	2	2	no	—
146	C₁₉×#121	—	2	2	no	—
147	C₁₉×#121	—	2	2	no	—
148	C₁₉×#121	—	2	4	no	—
149	C₁₉×#120	—	2	4	no	—
150	C₄×Q₈×C₁₉	—	2	2	no	—
151	C₄×Q₈×C₁₉	—	2	2	no	—
152	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
153	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
154	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
155	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
156	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
157	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
158	C₄×D₄×C₁₉	—	2	1	no	—
159	C₄×D₄×C₁₉	—	2	1	no	—
160	C₄×D₄×C₁₉	—	2	4	no	—
161	C₄×D₄×C₁₉	—	2	4	no	—
162	C₄×D₄×C₁₉	—	2	4	no	—
163	C₄×D₄×C₁₉	—	2	1	no	—
164	C₄×D₄×C₁₉	—	2	1	no	—
165	C₄×D₄×C₁₉	—	2	1	no	—
166	C₄×D₄×C₁₉	—	2	1	no	—
167	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₁₉	C₂³	1	2	yes	—
169	C₄×D₄×C₁₉	C₂³	1	4	yes	—
170	C₄×D₄×C₁₉	C₂³	1	4	yes	—
171	C₄×D₄×C₁₉	C₂³	1	2	yes	—
172	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
173	C₁₉×#117	—	2	2	no	—
174	C₁₉×#117	—	2	2	no	—
175	C₁₉×#117	—	2	2	no	—
176	C₁₉×#117	—	2	1	no	—
177	C₁₉×#117	C₂³	1	1	yes	characteristic
178	C₁₉×#117	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
186	C₂×C₄²×C₁₉	—	2	1	no	—
187	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
188	C₁₉×#107	C₂³	1	2	yes	—
189	C₁₉×#106	C₂³	1	4	yes	—
190	C₁₉×#106	C₂³	1	4	yes	—
191	C₁₉×#106	C₂³	1	2	yes	—
192	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
194	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
195	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
196	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
197	C₁₉×#103	C₂³	1	2	yes	—
198	C₁₉×#103	C₂³	1	2	yes	—
199	C₁₉×#103	C₂³	1	2	yes	—
200	C₁₉×#103	C₂³	1	4	yes	—
201	C₁₉×#103	C₂³	1	4	yes	—
202	C₁₉×#102	C₂³	1	4	yes	—
203	C₁₉×#102	C₂³	1	4	yes	—
204	C₁₉×#102	C₂³	1	2	yes	—
205	C₁₉×#102	C₂³	1	2	yes	—
206	C₁₉×#102	C₂³	1	2	yes	—
207	C₁₉×#102	C₂³	1	4	yes	—
208	C₁₉×#102	C₂³	1	4	yes	—
209	C₁₉×#102	C₂³	1	2	yes	—
210	C₁₉×#102	C₂³	1	2	yes	—
211	C₁₉×#97	C₂³	1	2	yes	—
212	C₁₉×#97	C₂³	1	4	yes	—
213	C₄×C₈×C₁₉	C₂³	1	2	yes	—
214	C₄×C₈×C₁₉	C₂³	1	4	yes	—
215	C₂⁴×C₁₉	—	2	1	no	—
216	#41×C₁₉	—	2	2	no	—
217	#41×C₁₉	—	2	4	no	—
218	#41×C₁₉	—	2	4	no	—
219	#41×C₁₉	—	8	4	no	—
220	#41×C₁₉	#41	1	4	yes	complemented
221	C₂×Q₈×C₁₉	—	2	2	no	—
222	C₂×Q₈×C₁₉	—	2	4	no	—
223	C₂×Q₈×C₁₉	—	2	2	no	—
224	C₂×Q₈×C₁₉	—	8	2	no	—
225	C₂×Q₈×C₁₉	—	8	4	no	—
226	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
229	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
230	C₂×D₄×C₁₉	—	2	1	no	—
231	C₂×D₄×C₁₉	—	2	2	no	—
232	C₂×D₄×C₁₉	—	2	1	no	—
233	C₂×D₄×C₁₉	—	2	1	no	—
234	C₂×D₄×C₁₉	—	2	4	no	—
235	C₂×D₄×C₁₉	—	2	1	no	—
236	C₂×D₄×C₁₉	—	2	4	no	—
237	C₂×D₄×C₁₉	—	2	2	no	—
238	C₂×D₄×C₁₉	—	2	2	no	—
239	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
240	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
241	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₉	—	2	1	no	—
243	C₂²×C₄×C₁₉	—	2	1	no	—
244	C₂²×C₄×C₁₉	—	2	2	no	—
245	C₂²×C₄×C₁₉	—	2	1	no	—
246	C₂²×C₄×C₁₉	—	2	1	no	—
247	C₂²×C₄×C₁₉	—	2	2	no	—
248	C₂²×C₄×C₁₉	—	2	2	no	—
249	C₂²×C₄×C₁₉	—	2	4	no	—
250	C₂²×C₄×C₁₉	—	2	4	no	—
251	C₂²×C₄×C₁₉	—	2	2	no	—
252	C₂²×C₄×C₁₉	—	8	2	no	—
253	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
256	Q₁₆×C₁₉	—	2	4	no	—
257	SD₁₆×C₁₉	—	2	4	no	—
258	SD₁₆×C₁₉	—	2	4	no	—
259	SD₁₆×C₁₉	—	2	4	no	—
260	D₈×C₁₉	—	2	4	no	—
261	D₈×C₁₉	—	2	4	no	—
262	M₁₆×C₁₉	—	2	2	no	—
263	M₁₆×C₁₉	—	2	2	no	—
264	C₂×C₈×C₁₉	—	2	4	no	—
265	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
266	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
267	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
268	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₁₉	—	2	1	no	—
270	C₄⋊C₄×C₁₉	—	2	2	no	—
271	C₄⋊C₄×C₁₉	—	2	2	no	—
272	C₄⋊C₄×C₁₉	—	2	4	no	—
273	C₄⋊C₄×C₁₉	—	2	4	no	—
274	C₄⋊C₄×C₁₉	—	2	2	no	—
275	C₄⋊C₄×C₁₉	—	2	4	no	—
276	C₄⋊C₄×C₁₉	—	2	1	no	—
277	C₄⋊C₄×C₁₉	—	2	1	no	—
278	C₄⋊C₄×C₁₉	—	2	1	no	—
279	C₄⋊C₄×C₁₉	—	2	1	no	—
280	C₄⋊C₄×C₁₉	—	2	4	no	—
281	C₄⋊C₄×C₁₉	—	2	4	no	—
282	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
283	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
284	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
286	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
287	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
288	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
290	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
291	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
292	C₂²⋊C₄×C₁₉	—	2	1	no	—
293	C₂²⋊C₄×C₁₉	—	2	2	no	—
294	C₂²⋊C₄×C₁₉	—	2	2	no	—
295	C₂²⋊C₄×C₁₉	—	2	4	no	—
296	C₂²⋊C₄×C₁₉	—	2	1	no	—
297	C₂²⋊C₄×C₁₉	—	2	1	no	—
298	C₂²⋊C₄×C₁₉	—	2	4	no	—
299	C₂²⋊C₄×C₁₉	—	2	4	no	—
300	C₂²⋊C₄×C₁₉	—	2	2	no	—
301	C₂²⋊C₄×C₁₉	—	2	4	no	—
302	C₂²⋊C₄×C₁₉	—	2	2	no	—
303	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
304	C₄²×C₁₉	—	2	1	no	—
305	C₄²×C₁₉	—	2	1	no	—
306	C₄²×C₁₉	—	2	1	no	—
307	C₄²×C₁₉	—	2	4	no	—
308	C₄²×C₁₉	—	2	4	no	—
309	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
312	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
313	C₄²×C₁₉	C₂⁴	1	4	yes	—
314	#61347	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂³×C₁₉	—	2	1	no	—
316	C₂³×C₁₉	—	2	2	no	—
317	C₂³×C₁₉	—	2	2	no	—
318	C₂³×C₁₉	—	4	2	no	—
319	C₂³×C₁₉	—	8	1	no	—
320	C₂³×C₁₉	—	8	1	no	—
321	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
322	Q₈×C₁₉	—	2	4	no	—
323	Q₈×C₁₉	—	2	1	no	—
324	Q₈×C₁₉	—	2	2	no	—
325	Q₈×C₁₉	—	2	2	no	—
326	Q₈×C₁₉	—	4	2	no	—
327	Q₈×C₁₉	—	4	4	no	—
328	Q₈×C₁₉	—	8	2	no	—
329	Q₈×C₁₉	—	8	4	no	—
330	Q₈×C₁₉	C₂×#41	1	2	yes	—
331	D₄×C₁₉	—	2	4	no	—
332	D₄×C₁₉	—	2	2	no	—
333	D₄×C₁₉	—	2	2	no	—
334	D₄×C₁₉	—	2	1	no	—
335	D₄×C₁₉	—	2	2	no	—
336	D₄×C₁₉	—	2	2	no	—
337	D₄×C₁₉	—	4	4	no	—
338	D₄×C₁₉	—	4	2	no	—
339	D₄×C₁₉	—	4	2	no	—
340	D₄×C₁₉	—	8	1	no	—
341	D₄×C₁₉	—	8	4	no	—
342	D₄×C₁₉	—	8	4	no	—
343	D₄×C₁₉	C₂×#41	1	2	yes	—
344	C₂×C₄×C₁₉	—	2	1	no	—
345	C₂×C₄×C₁₉	—	2	4	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	1	no	—
350	C₂×C₄×C₁₉	—	2	1	no	—
351	C₂×C₄×C₁₉	—	2	4	no	—
352	C₂×C₄×C₁₉	—	4	1	no	—
353	C₂×C₄×C₁₉	—	4	2	no	—
354	C₂×C₄×C₁₉	—	4	4	no	—
355	C₂×C₄×C₁₉	—	4	2	no	—
356	C₂×C₄×C₁₉	—	4	4	no	—
357	C₂×C₄×C₁₉	—	8	2	no	—
358	C₂×C₄×C₁₉	—	8	4	no	—
359	C₂×C₄×C₁₉	—	8	4	no	—
360	C₂×C₄×C₁₉	—	8	1	no	—
361	C₂×C₄×C₁₉	—	8	2	no	—
362	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
364	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
365	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
370	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
371	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
372	C₈×C₁₉	—	2	2	no	—
373	C₈×C₁₉	—	2	2	no	—
374	C₈×C₁₉	—	2	2	no	—
375	C₈×C₁₉	—	2	2	no	—
376	#3506	C₂×C₁₉	1	1	yes	characteristic, complemented
377	#3503	C₂×C₁₉	1	1	yes	characteristic, complemented
378	#3373	C₂×C₁₉	1	4	yes	complemented
379	#3371	C₂×C₁₉	1	4	yes	complemented
380	#3369	C₂×C₁₉	1	2	yes	complemented
381	#3366	C₂×C₁₉	1	2	yes	complemented
382	#3362	C₂×C₁₉	1	2	yes	complemented
383	#3360	C₂×C₁₉	1	2	yes	complemented
384	#3141	C₂×C₁₉	1	1	yes	characteristic, complemented
385	#3136	C₂×C₁₉	1	2	yes	complemented
386	#3084	C₂×C₁₉	1	2	yes	complemented
387	C₂×#476	C₂×C₁₉	1	1	yes	characteristic, complemented
388	#3045	C₂×C₁₉	1	2	yes	complemented
389	#3035	C₂×C₁₉	1	1	yes	characteristic, complemented
390	#2962	C₂×C₁₉	1	1	yes	characteristic, complemented
391	#2952	C₂×C₁₉	1	2	yes	complemented
392	C₄×AGL(1,ℤ/8)	C₂×C₁₉	1	1	yes	characteristic, complemented
393	C₂²×C₁₉	—	2	1	no	—
394	C₂²×C₁₉	—	2	1	no	—
395	C₂²×C₁₉	—	2	2	no	—
396	C₂²×C₁₉	—	4	1	no	—
397	C₂²×C₁₉	—	4	1	no	—
398	C₂²×C₁₉	—	4	2	no	—
399	C₂²×C₁₉	—	4	2	no	—
400	C₂²×C₁₉	—	4	2	no	—
401	C₂²×C₁₉	—	4	2	no	—
402	C₂²×C₁₉	—	4	2	no	—
403	C₂²×C₁₉	—	4	2	no	—
404	C₂²×C₁₉	—	8	4	no	—
405	C₂²×C₁₉	#548	1	2	yes	—
406	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
407	C₄×C₁₉	—	2	1	no	—
408	C₄×C₁₉	—	2	1	no	—
409	C₄×C₁₉	—	2	4	no	—
410	C₄×C₁₉	—	2	2	no	—
411	C₄×C₁₉	—	2	1	no	—
412	C₄×C₁₉	—	2	4	no	—
413	C₄×C₁₉	—	4	1	no	—
414	C₄×C₁₉	—	4	4	no	—
415	C₄×C₁₉	—	4	2	no	—
416	C₄×C₁₉	—	4	1	no	—
417	C₄×C₁₉	—	4	2	no	—
418	C₄×C₁₉	#548	1	2	yes	—
419	C₄×C₁₉	#577	1	2	yes	—
420	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
421	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
422	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
423	C₂×#135	C₂²×C₁₉	1	2	yes	—
424	#559	C₂²×C₁₉	1	4	yes	—
425	Q₈²	C₂²×C₁₉	1	2	yes	complemented
426	#557	C₂²×C₁₉	1	2	yes	complemented
427	#556	C₂²×C₁₉	1	2	yes	—
428	#555	—	2	1	no	—
429	#554	—	2	2	no	—
430	#554	C₂²×C₁₉	1	2	yes	complemented
431	#553	—	2	2	no	—
432	#550	C₂²×C₁₉	1	2	yes	—
433	D₄×Q₈	—	2	2	no	—
434	D₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
435	#547	—	2	1	no	—
436	#544	—	2	2	no	—
437	#544	C₂²×C₁₉	1	2	yes	—
438	#538	—	2	2	no	—
439	#535	C₂²×C₁₉	1	2	yes	—
440	#533	—	2	1	no	—
441	#533	C₂²×C₁₉	1	1	yes	characteristic
442	#532	C₂²×C₁₉	1	1	yes	characteristic
443	C₂×C₄⋊Q₈	—	2	1	no	—
444	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
445	#525	—	2	2	no	—
446	#520	C₂²×C₁₉	1	2	yes	—
447	#520	C₂²×C₁₉	1	2	yes	—
448	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
449	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
450	#490	C₂²×C₁₉	1	4	yes	—
451	#489	C₂²×C₁₉	1	4	yes	—
452	#489	C₂²×C₁₉	1	4	yes	complemented
453	#488	C₂²×C₁₉	1	4	yes	—
454	#487	C₂²×C₁₉	1	2	yes	complemented
455	#486	C₂²×C₁₉	1	4	yes	—
456	#486	C₂²×C₁₉	1	2	yes	complemented
457	#479	C₂²×C₁₉	1	4	yes	complemented
458	#478	C₂²×C₁₉	1	4	yes	complemented
459	#476	C₂²×C₁₉	1	2	yes	—
460	#476	C₂²×C₁₉	1	2	yes	—
461	#476	C₂²×C₁₉	1	4	yes	—
462	#476	C₂²×C₁₉	1	4	yes	complemented
463	#475	C₂²×C₁₉	1	4	yes	complemented
464	#464	C₂²×C₁₉	1	4	yes	—
465	#464	C₂²×C₁₉	1	2	yes	complemented
466	#463	C₂²×C₁₉	1	4	yes	—
467	#463	C₂²×C₁₉	1	2	yes	complemented
468	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
469	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
470	#460	C₂²×C₁₉	1	4	yes	—
471	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
472	#459	C₂²×C₁₉	1	4	yes	—
473	#459	C₂²×C₁₉	1	1	yes	characteristic, complemented
474	#446	C₂²×C₁₉	1	2	yes	complemented
475	#446	C₂²×C₁₉	1	4	yes	complemented
476	C₈×Q₈	C₂²×C₁₉	1	2	yes	complemented
477	#442	C₂²×C₁₉	1	2	yes	—
478	#442	C₂²×C₁₉	1	4	yes	complemented
479	#441	C₂²×C₁₉	1	4	yes	complemented
480	#440	C₂²×C₁₉	1	2	yes	—
481	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
482	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	complemented
483	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	complemented
484	C₄×D₈	C₂²×C₁₉	1	2	yes	—
485	#428	C₂²×C₁₉	1	1	yes	characteristic
486	C₂×#106	C₂²×C₁₉	1	2	yes	—
487	#424	C₂²×C₁₉	1	2	yes	—
488	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
489	#418	C₂²×C₁₉	1	1	yes	characteristic
490	#417	C₂²×C₁₉	1	2	yes	—
491	#417	C₂²×C₁₉	1	2	yes	—
492	#417	C₂²×C₁₉	1	1	yes	characteristic
493	#416	C₂²×C₁₉	1	2	yes	—
494	C₂×#102	C₂²×C₁₉	1	2	yes	—
495	#405	C₂²×C₁₉	1	2	yes	—
496	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
497	C₂×C₁₉	—	2	2	no	—
498	C₂×C₁₉	—	4	2	no	—
499	C₂×C₁₉	—	8	2	no	—
500	C₂×C₁₉	—	8	2	no	—
501	C₂×C₁₉	C₂×#548	1	1	yes	characteristic
502	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
503	C₂×C₁₉	#3585	1	1	yes	characteristic
504	C₂×#41	—	2	2	no	—
505	C₂×#41	C₂³×C₁₉	1	2	yes	—
506	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
507	C₂²×Q₈	—	2	2	no	—
508	C₂²×Q₈	—	2	1	no	—
509	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
510	C₂³×C₄	—	2	1	no	—
511	AGL(1,ℤ/8)	—	2	4	no	—
512	#135	—	2	8	no	—
513	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
514	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
515	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
516	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
517	C₂×D₈	C₂³×C₁₉	1	2	yes	—
518	C₂×D₈	C₂³×C₁₉	1	2	yes	—
519	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
520	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
521	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
522	C₄⋊Q₈	—	2	2	no	—
523	C₄⋊Q₈	—	2	2	no	—
524	C₄⋊Q₈	—	2	2	no	—
525	C₄⋊Q₈	—	2	4	no	—
526	C₄⋊Q₈	—	2	1	no	—
527	C₄⋊Q₈	—	2	1	no	—
528	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
529	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
532	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
534	#127	C₂³×C₁₉	1	1	yes	characteristic
535	#127	C₂³×C₁₉	1	4	yes	—
536	#126	—	2	4	no	—
537	#125	—	2	2	no	—
538	#125	—	2	4	no	—
539	#125	D₄×C₁₉	1	2	yes	—
540	#125	C₂³×C₁₉	1	4	yes	—
541	#124	—	2	4	no	—
542	#124	C₂³×C₁₉	1	2	yes	—
543	#124	C₂³×C₁₉	1	4	yes	—
544	#123	—	2	4	no	—
545	#123	—	2	4	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	4	no	—
550	C₂²⋊Q₈	—	2	4	no	—
551	C₂²⋊Q₈	—	2	4	no	—
552	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
553	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
554	#121	—	2	1	no	—
555	#121	—	2	1	no	—
556	#121	—	2	2	no	—
557	#121	—	2	2	no	—
558	#121	—	2	2	no	—
559	#121	—	2	4	no	—
560	#120	—	2	4	no	—
561	C₄×Q₈	—	2	2	no	—
562	C₄×Q₈	—	2	2	no	—
563	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
564	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
565	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
566	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
567	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
568	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	4	no	—
572	C₄×D₄	—	2	4	no	—
573	C₄×D₄	—	2	4	no	—
574	C₄×D₄	—	2	1	no	—
575	C₄×D₄	—	2	1	no	—
576	C₄×D₄	—	2	1	no	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	C₂³×C₁₉	1	2	yes	—
579	C₄×D₄	C₂³×C₁₉	1	2	yes	—
580	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
581	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
582	C₄×D₄	C₂³×C₁₉	1	4	yes	—
583	C₄×D₄	C₂³×C₁₉	1	4	yes	—
584	#117	—	2	2	no	—
585	#117	—	2	2	no	—
586	#117	—	2	2	no	—
587	#117	—	2	1	no	—
588	#117	C₂³×C₁₉	1	1	yes	characteristic
589	#117	C₂³×C₁₉	1	2	yes	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	2	no	—
592	C₂×C₄⋊C₄	—	2	2	no	—
593	C₂×C₄⋊C₄	—	2	2	no	—
594	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
596	C₂×C₂²⋊C₄	—	2	1	no	—
597	C₂×C₄²	—	2	1	no	—
598	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
599	#107	C₂³×C₁₉	1	2	yes	—
600	#106	C₂³×C₁₉	1	4	yes	—
601	#106	C₂³×C₁₉	1	4	yes	—
602	#106	C₂³×C₁₉	1	2	yes	—
603	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
604	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
605	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
606	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
607	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
608	#103	C₂³×C₁₉	1	2	yes	—
609	#103	C₂³×C₁₉	1	2	yes	—
610	#103	C₂³×C₁₉	1	2	yes	—
611	#103	C₂³×C₁₉	1	4	yes	—
612	#103	C₂³×C₁₉	1	4	yes	—
613	#102	C₂³×C₁₉	1	4	yes	—
614	#102	C₂³×C₁₉	1	4	yes	—
615	#102	C₂³×C₁₉	1	2	yes	—
616	#102	C₂³×C₁₉	1	2	yes	—
617	#102	C₂³×C₁₉	1	2	yes	—
618	#102	C₂³×C₁₉	1	4	yes	—
619	#102	C₂³×C₁₉	1	4	yes	—
620	#102	C₂³×C₁₉	1	2	yes	—
621	#102	C₂³×C₁₉	1	2	yes	—
622	#97	C₂³×C₁₉	1	2	yes	—
623	#97	C₂³×C₁₉	1	4	yes	—
624	C₄×C₈	C₂³×C₁₉	1	2	yes	—
625	C₄×C₈	C₂³×C₁₉	1	4	yes	—
626	C₁₉	#61347	1	1	yes	characteristic, direct product factor, Sylow
627	C₂⁴	—	2	1	no	—
628	#41	—	2	2	no	—
629	#41	—	2	4	no	—
630	#41	—	2	4	no	—
631	#41	—	8	4	no	—
632	#41	#41×C₁₉	1	4	yes	complemented
633	C₂×Q₈	—	2	2	no	—
634	C₂×Q₈	—	2	4	no	—
635	C₂×Q₈	—	2	2	no	—
636	C₂×Q₈	—	8	2	no	—
637	C₂×Q₈	—	8	4	no	—
638	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
639	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
640	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
641	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
652	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
653	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	8	2	no	—
665	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
668	Q₁₆	—	2	4	no	—
669	SD₁₆	—	2	4	no	—
670	SD₁₆	—	2	4	no	—
671	SD₁₆	—	2	4	no	—
672	D₈	—	2	4	no	—
673	D₈	—	2	4	no	—
674	M₁₆	—	2	2	no	—
675	M₁₆	—	2	2	no	—
676	C₂×C₈	—	2	4	no	—
677	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
678	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
679	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
680	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
695	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
696	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
697	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
698	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
699	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
700	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
701	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
702	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
703	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
716	C₄²	—	2	1	no	—
717	C₄²	—	2	1	no	—
718	C₄²	—	2	1	no	—
719	C₄²	—	2	4	no	—
720	C₄²	—	2	4	no	—
721	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
722	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
723	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
724	C₄²	C₂⁴×C₁₉	1	4	yes	—
725	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
726	C₂³	—	2	1	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	4	2	no	—
730	C₂³	—	8	1	no	—
731	C₂³	—	8	1	no	—
732	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
733	Q₈	—	2	4	no	—
734	Q₈	—	2	1	no	—
735	Q₈	—	2	2	no	—
736	Q₈	—	2	2	no	—
737	Q₈	—	4	2	no	—
738	Q₈	—	4	4	no	—
739	Q₈	—	8	2	no	—
740	Q₈	—	8	4	no	—
741	Q₈	C₂×#41×C₁₉	1	2	yes	—
742	D₄	—	2	4	no	—
743	D₄	—	2	2	no	—
744	D₄	—	2	2	no	—
745	D₄	—	2	1	no	—
746	D₄	—	2	2	no	—
747	D₄	—	2	2	no	—
748	D₄	—	4	4	no	—
749	D₄	—	4	2	no	—
750	D₄	—	4	2	no	—
751	D₄	—	8	4	no	—
752	D₄	—	8	1	no	—
753	D₄	—	8	4	no	—
754	D₄	C₂×#41×C₁₉	1	2	yes	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	—	8	2	no	—
769	C₂×C₄	—	8	4	no	—
770	C₂×C₄	—	8	4	no	—
771	C₂×C₄	—	8	1	no	—
772	C₂×C₄	—	8	2	no	—
773	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
774	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
775	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
776	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
777	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
778	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
780	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
781	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
782	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
783	C₈	—	2	2	no	—
784	C₈	—	2	2	no	—
785	C₈	—	2	2	no	—
786	C₈	—	2	2	no	—
787	C₂²	—	2	1	no	—
788	C₂²	—	2	1	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	8	4	no	—
799	C₂²	C₁₉×#548	1	2	yes	—
800	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
801	C₄	—	2	2	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	4	no	—
804	C₄	—	2	1	no	—
805	C₄	—	2	1	no	—
806	C₄	—	2	4	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	1	no	—
811	C₄	—	4	4	no	—
812	C₄	C₁₉×#548	1	2	yes	—
813	C₄	C₁₉×#577	1	2	yes	—
814	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
815	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
816	C₂	—	2	2	no	—
817	C₂	—	4	2	no	—
818	C₂	—	8	2	no	—
819	C₂	—	8	2	no	—
820	C₂	C₂×C₁₉×#548	1	1	yes	characteristic
821	C₂	C₂×C₁₉×#577	1	1	yes	characteristic
822	C₂	C₁₉×#3585	1	1	yes	characteristic

	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×#3506	C₂	semidirect
2. C₁₉×#3503	C₂	semidirect
3. C₁₉×#3373	C₂	semidirect
4. C₁₉×#3371	C₂	semidirect
5. C₁₉×#3369	C₂	semidirect
6. C₁₉×#3366	C₂	semidirect
7. C₁₉×#3362	C₂	semidirect
8. C₁₉×#3360	C₂	semidirect
9. C₁₉×#3141	C₂	semidirect
10. C₁₉×#3136	C₂	semidirect
11. C₁₉×#3084	C₂	semidirect
12. C₂×C₁₉×#476	C₂	semidirect
13. C₁₉×#3045	C₂	semidirect
14. C₁₉×#3035	C₂	semidirect
15. C₁₉×#2962	C₂	semidirect
16. C₁₉×#2952	C₂	semidirect
17. C₄×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
21. Q₈²×C₁₉	C₂²	semidirect
22. C₁₉×#557	C₂²	semidirect
26. C₁₉×#554	C₂²	semidirect
30. D₄×Q₈×C₁₉	C₂²	semidirect
48. C₁₉×#489	C₂²	semidirect
50. C₁₉×#487	C₂²	semidirect
52. C₁₉×#486	C₂²	semidirect
53. C₁₉×#479	C₂²	semidirect
54. C₁₉×#478	C₂²	semidirect
58. C₁₉×#476	C₂²	semidirect
59. C₁₉×#475	C₂²	semidirect
61. C₁₉×#464	C₂²	semidirect
63. C₁₉×#463	C₂²	semidirect
64. C₁₉×#462	C₂²	semidirect
65. C₁₉×#461	C₂²	semidirect
67. C₁₉×#460	C₂²	semidirect
69. C₁₉×#459	C₂²	semidirect
70. C₁₉×#446	C₂²	semidirect
71. C₁₉×#446	C₂²	semidirect
72. C₈×Q₈×C₁₉	C₂²	semidirect
74. C₁₉×#442	C₂²	semidirect
75. C₁₉×#441	C₂²	semidirect
78. C₄×SD₁₆×C₁₉	C₂²	semidirect
79. C₄×SD₁₆×C₁₉	C₂²	semidirect
220. #41×C₁₉	#41	semidirect
314. #61347	C₁₉	direct (N × H)
376. #3506	C₂×C₁₉	semidirect
377. #3503	C₂×C₁₉	semidirect
378. #3373	C₂×C₁₉	semidirect
379. #3371	C₂×C₁₉	semidirect
380. #3369	C₂×C₁₉	semidirect
381. #3366	C₂×C₁₉	semidirect
382. #3362	C₂×C₁₉	semidirect
383. #3360	C₂×C₁₉	semidirect
384. #3141	C₂×C₁₉	semidirect
385. #3136	C₂×C₁₉	semidirect
386. #3084	C₂×C₁₉	semidirect
387. C₂×#476	C₂×C₁₉	semidirect
388. #3045	C₂×C₁₉	semidirect
389. #3035	C₂×C₁₉	semidirect
390. #2962	C₂×C₁₉	semidirect
391. #2952	C₂×C₁₉	semidirect
392. C₄×AGL(1,ℤ/8)	C₂×C₁₉	semidirect
425. Q₈²	C₂²×C₁₉	semidirect
426. #557	C₂²×C₁₉	semidirect
430. #554	C₂²×C₁₉	semidirect
434. D₄×Q₈	C₂²×C₁₉	semidirect
452. #489	C₂²×C₁₉	semidirect
454. #487	C₂²×C₁₉	semidirect
456. #486	C₂²×C₁₉	semidirect
457. #479	C₂²×C₁₉	semidirect
458. #478	C₂²×C₁₉	semidirect
462. #476	C₂²×C₁₉	semidirect
463. #475	C₂²×C₁₉	semidirect
465. #464	C₂²×C₁₉	semidirect
467. #463	C₂²×C₁₉	semidirect
468. #462	C₂²×C₁₉	semidirect
469. #461	C₂²×C₁₉	semidirect
471. #460	C₂²×C₁₉	semidirect
473. #459	C₂²×C₁₉	semidirect
474. #446	C₂²×C₁₉	semidirect
475. #446	C₂²×C₁₉	semidirect
476. C₈×Q₈	C₂²×C₁₉	semidirect
478. #442	C₂²×C₁₉	semidirect
479. #441	C₂²×C₁₉	semidirect
482. C₄×SD₁₆	C₂²×C₁₉	semidirect
483. C₄×SD₁₆	C₂²×C₁₉	semidirect
626. C₁₉	#61347	direct (N × H)
632. #41	#41×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3506	2
C₁₉×#3503	2
C₁₉×#3373	2
C₁₉×#3371	2
C₁₉×#3369	2
C₁₉×#3366	2
C₁₉×#3362	2
C₁₉×#3360	2
C₁₉×#3141	2
C₁₉×#3136	2
C₁₉×#3084	2
C₂×C₁₉×#476	2
C₁₉×#3045	2
C₁₉×#3035	2
C₁₉×#2962	2
C₁₉×#2952	2
C₄×C₁₉×AGL(1,ℤ/8)	2
#61347	19

Subgroups — C19×#61347 #18067306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61347 #18067306