Subgroups — C₁₉×#62259 #18068218

Order 4864.

2130 conjugacy classes of subgroups.

The subgroup lattice has 854 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×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3354	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3353	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3332	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3330	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3325	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3324	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3274	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3272	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3245	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3188	C₂	1	4	yes	maximal, complemented
14	C₁₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3055	C₂	1	4	yes	maximal, complemented
17	C₂×C₁₉×#436	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₉×H(5,𝔽₂)	—	2	1	no	—
19	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
20	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	complemented
21	C₁₉×#559	—	2	2	no	—
22	C₁₉×#556	C₂²	1	2	yes	complemented
23	C₁₉×#555	C₂²	1	2	yes	complemented
24	C₁₉×#553	—	2	2	no	—
25	C₁₉×#550	C₂²	1	2	yes	complemented
26	C₁₉×#547	C₂²	1	2	yes	—
27	C₁₉×#547	C₂²	1	2	yes	—
28	C₁₉×#547	C₂²	1	2	yes	complemented
29	C₁₉×#546	—	2	2	no	—
30	C₁₉×#546	—	2	2	no	—
31	D₄²×C₁₉	C₂²	1	2	yes	—
32	D₄²×C₁₉	C₂²	1	2	yes	—
33	C₁₉×#538	—	2	2	no	—
34	C₁₉×#537	—	2	1	no	—
35	C₁₉×#535	—	2	1	no	—
36	C₁₉×#534	—	2	2	no	—
37	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#532	C₂²	1	1	yes	characteristic
39	C₁₉×#532	C₂²	1	1	yes	characteristic
40	C₁₉×#532	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#525	C₂²	1	4	yes	complemented
42	C₂×C₁₉×#121	C₂²	1	4	yes	—
43	C₁₉×#520	—	2	1	no	—
44	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#493	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
52	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#484	C₂²	1	4	yes	complemented
54	C₁₉×#482	C₂²	1	4	yes	complemented
55	C₁₉×#482	C₂²	1	4	yes	complemented
56	C₁₉×#481	C₂²	1	4	yes	complemented
57	C₁₉×#476	C₂²	1	2	yes	complemented
58	C₁₉×#475	C₂²	1	2	yes	complemented
59	C₁₉×#474	C₂²	1	2	yes	complemented
60	C₁₉×#474	C₂²	1	2	yes	complemented
61	C₁₉×#469	C₂²	1	4	yes	complemented
62	C₁₉×#469	C₂²	1	4	yes	complemented
63	C₁₉×#468	C₂²	1	4	yes	complemented
64	C₁₉×#468	C₂²	1	4	yes	complemented
65	C₁₉×#466	C₂²	1	2	yes	complemented
66	C₁₉×#466	C₂²	1	2	yes	complemented
67	C₁₉×#466	C₂²	1	4	yes	complemented
68	C₁₉×#465	C₂²	1	2	yes	complemented
69	C₁₉×#465	C₂²	1	2	yes	complemented
70	C₁₉×#465	C₂²	1	4	yes	complemented
71	C₁₉×#461	C₂²	1	2	yes	complemented
72	C₁₉×#460	C₂²	1	2	yes	complemented
73	C₁₉×#459	C₂²	1	2	yes	complemented
74	C₁₉×#459	C₂²	1	2	yes	complemented
75	C₁₉×#450	C₂²	1	4	yes	complemented
76	C₁₉×#449	C₂²	1	4	yes	complemented
77	C₁₉×#449	C₂²	1	4	yes	complemented
78	C₁₉×#447	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
80	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
81	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
82	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
83	C₁₉×#436	C₂²	1	2	yes	complemented
84	C₁₉×#436	C₂²	1	2	yes	complemented
85	C₁₉×#436	C₂²	1	2	yes	complemented
86	C₁₉×#436	C₂²	1	2	yes	complemented
87	C₁₉×#428	C₂²	1	4	yes	complemented
88	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
89	C₁₉×#418	C₂²	1	4	yes	complemented
90	C₁₉×#417	C₂²	1	4	yes	complemented
91	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
92	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
93	C₁₉×H(5,𝔽₂)	—	4	8	no	—
94	C₂×#41×C₁₉	—	2	2	no	—
95	C₂×#41×C₁₉	—	2	2	no	—
96	C₂×#41×C₁₉	—	2	1	no	—
97	C₂×#41×C₁₉	—	2	1	no	—
98	C₂×#41×C₁₉	—	2	1	no	—
99	C₂×#41×C₁₉	C₂³	1	4	yes	—
100	C₂²×D₄×C₁₉	—	2	4	no	—
101	C₂²×D₄×C₁₉	—	2	2	no	—
102	C₂²×D₄×C₁₉	—	2	2	no	—
103	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
104	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
105	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
106	C₁₉×AGL(1,ℤ/8)	—	4	8	no	—
107	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
110	C₂×D₈×C₁₉	C₂³	1	2	yes	—
111	C₂×D₈×C₁₉	C₂³	1	2	yes	—
112	C₂×D₈×C₁₉	C₂³	1	4	yes	—
113	C₂×M₁₆×C₁₉	—	4	4	no	—
114	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
115	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
116	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₁₉×#127	—	2	2	no	—
125	C₁₉×#127	C₂³	1	1	yes	characteristic
126	C₁₉×#127	C₂³	1	1	yes	characteristic
127	C₁₉×#127	C₂³	1	1	yes	characteristic
128	C₁₉×#126	—	2	4	no	—
129	C₁₉×#125	—	2	1	no	—
130	C₁₉×#124	—	2	2	no	—
131	C₁₉×#124	—	2	4	no	—
132	C₁₉×#124	—	2	1	no	—
133	C₁₉×#124	—	2	1	no	—
134	C₁₉×#124	—	2	1	no	—
135	C₁₉×#123	—	2	4	no	—
136	C₁₉×#123	—	2	4	no	—
137	C₁₉×#123	—	2	4	no	—
138	C₁₉×#123	—	2	4	no	—
139	C₁₉×C₂²⋊Q₈	—	2	1	no	—
140	C₁₉×C₂²⋊Q₈	—	2	2	no	—
141	C₁₉×C₂²⋊Q₈	—	2	2	no	—
142	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
143	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₁₉×#121	—	2	2	no	—
145	C₁₉×#121	—	2	2	no	—
146	C₁₉×#121	—	2	4	no	—
147	C₁₉×#121	—	2	4	no	—
148	C₁₉×#121	—	2	1	no	—
149	C₁₉×#121	—	2	1	no	—
150	C₁₉×#121	—	2	1	no	—
151	C₁₉×#121	—	2	2	no	—
152	C₁₉×#121	—	2	2	no	—
153	C₁₉×#121	—	2	4	no	—
154	C₁₉×#121	C₂³	1	4	yes	—
155	C₁₉×#121	C₂³	1	4	yes	—
156	C₁₉×#121	C₂³	1	4	yes	—
157	C₁₉×#121	C₂³	1	2	yes	—
158	C₁₉×#121	C₂³	1	2	yes	—
159	C₁₉×#121	C₂³	1	2	yes	—
160	C₁₉×#120	—	2	4	no	—
161	C₁₉×#120	—	2	4	no	—
162	C₁₉×#120	—	2	4	no	—
163	C₄×Q₈×C₁₉	—	2	2	no	—
164	C₄×Q₈×C₁₉	—	2	1	no	—
165	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
166	C₄×D₄×C₁₉	—	2	4	no	—
167	C₄×D₄×C₁₉	—	2	4	no	—
168	C₄×D₄×C₁₉	—	2	2	no	—
169	C₄×D₄×C₁₉	—	2	1	no	—
170	C₄×D₄×C₁₉	—	2	1	no	—
171	C₄×D₄×C₁₉	—	2	1	no	—
172	C₄×D₄×C₁₉	D₄	1	2	yes	—
173	C₄×D₄×C₁₉	D₄	1	2	yes	—
174	C₄×D₄×C₁₉	C₂³	1	2	yes	—
175	C₄×D₄×C₁₉	C₂³	1	2	yes	—
176	C₄×D₄×C₁₉	C₂³	1	2	yes	—
177	C₄×D₄×C₁₉	C₂³	1	2	yes	—
178	C₄×D₄×C₁₉	C₂³	1	2	yes	—
179	C₁₉×#117	—	2	1	no	—
180	C₁₉×#117	—	2	2	no	—
181	C₁₉×#117	C₂³	1	4	yes	—
182	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
185	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
186	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
187	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
188	C₁₉×#107	C₂³	1	2	yes	—
189	C₁₉×#107	C₂³	1	4	yes	—
190	C₁₉×#107	C₂³	1	2	yes	—
191	C₁₉×#106	C₂³	1	2	yes	—
192	C₁₉×#106	C₂³	1	4	yes	—
193	C₁₉×#106	C₂³	1	2	yes	—
194	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
195	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
196	C₁₉×#103	C₂³	1	2	yes	—
197	C₁₉×#103	C₂³	1	4	yes	—
198	C₁₉×#103	C₂³	1	2	yes	—
199	C₁₉×#102	C₂³	1	2	yes	—
200	C₁₉×#102	C₂³	1	4	yes	—
201	C₁₉×#102	C₂³	1	2	yes	—
202	C₁₉×#102	C₂³	1	2	yes	—
203	C₁₉×#102	C₂³	1	4	yes	—
204	C₁₉×#102	C₂³	1	4	yes	—
205	C₁₉×#102	C₂³	1	2	yes	—
206	C₁₉×#102	C₂³	1	2	yes	—
207	C₁₉×#102	C₂³	1	2	yes	—
208	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
209	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
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	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
214	C₂⁴×C₁₉	—	2	4	no	—
215	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
216	#41×C₁₉	—	4	4	no	—
217	#41×C₁₉	—	4	4	no	—
218	#41×C₁₉	—	4	8	no	—
219	#41×C₁₉	—	4	8	no	—
220	#41×C₁₉	—	4	4	no	—
221	#41×C₁₉	—	4	4	no	—
222	#41×C₁₉	—	4	4	no	—
223	C₂×Q₈×C₁₉	—	2	1	no	—
224	C₂×Q₈×C₁₉	—	2	1	no	—
225	C₂×Q₈×C₁₉	—	2	1	no	—
226	C₂×Q₈×C₁₉	—	2	1	no	—
227	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
228	C₂×D₄×C₁₉	—	2	2	no	—
229	C₂×D₄×C₁₉	—	2	4	no	—
230	C₂×D₄×C₁₉	—	2	4	no	—
231	C₂×D₄×C₁₉	—	2	2	no	—
232	C₂×D₄×C₁₉	—	2	2	no	—
233	C₂×D₄×C₁₉	—	2	4	no	—
234	C₂×D₄×C₁₉	—	2	4	no	—
235	C₂×D₄×C₁₉	—	2	4	no	—
236	C₂×D₄×C₁₉	—	2	1	no	—
237	C₂×D₄×C₁₉	—	2	1	no	—
238	C₂×D₄×C₁₉	—	2	1	no	—
239	C₂×D₄×C₁₉	—	2	1	no	—
240	C₂×D₄×C₁₉	—	2	1	no	—
241	C₂×D₄×C₁₉	—	2	1	no	—
242	C₂×D₄×C₁₉	—	2	4	no	—
243	C₂×D₄×C₁₉	—	4	4	no	—
244	C₂×D₄×C₁₉	—	4	4	no	—
245	C₂×D₄×C₁₉	—	4	8	no	—
246	C₂×D₄×C₁₉	—	4	8	no	—
247	C₂×D₄×C₁₉	—	4	16	no	—
248	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
250	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
251	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
252	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₉	—	2	4	no	—
254	C₂²×C₄×C₁₉	—	2	2	no	—
255	C₂²×C₄×C₁₉	—	2	2	no	—
256	C₂²×C₄×C₁₉	—	2	2	no	—
257	C₂²×C₄×C₁₉	—	2	4	no	—
258	C₂²×C₄×C₁₉	—	4	2	no	—
259	C₂²×C₄×C₁₉	—	4	2	no	—
260	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
262	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
266	SD₁₆×C₁₉	—	2	4	no	—
267	SD₁₆×C₁₉	—	4	2	no	—
268	SD₁₆×C₁₉	—	4	4	no	—
269	D₈×C₁₉	—	2	4	no	—
270	D₈×C₁₉	—	4	2	no	—
271	D₈×C₁₉	—	4	4	no	—
272	M₁₆×C₁₉	—	2	8	no	—
273	M₁₆×C₁₉	—	4	4	no	—
274	C₂×C₈×C₁₉	—	2	2	no	—
275	C₂×C₈×C₁₉	—	4	1	no	—
276	C₂×C₈×C₁₉	—	4	2	no	—
277	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
278	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
279	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
280	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
281	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
282	C₄⋊C₄×C₁₉	—	2	1	no	—
283	C₄⋊C₄×C₁₉	—	2	4	no	—
284	C₄⋊C₄×C₁₉	—	2	4	no	—
285	C₄⋊C₄×C₁₉	—	2	1	no	—
286	C₄⋊C₄×C₁₉	—	2	2	no	—
287	C₄⋊C₄×C₁₉	—	2	1	no	—
288	C₄⋊C₄×C₁₉	—	2	1	no	—
289	C₄⋊C₄×C₁₉	—	2	1	no	—
290	C₄⋊C₄×C₁₉	—	2	1	no	—
291	C₄⋊C₄×C₁₉	—	2	2	no	—
292	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
293	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
295	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
296	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
298	C₂²⋊C₄×C₁₉	—	2	2	no	—
299	C₂²⋊C₄×C₁₉	—	2	4	no	—
300	C₂²⋊C₄×C₁₉	—	2	4	no	—
301	C₂²⋊C₄×C₁₉	—	2	2	no	—
302	C₂²⋊C₄×C₁₉	—	2	2	no	—
303	C₂²⋊C₄×C₁₉	—	2	4	no	—
304	C₂²⋊C₄×C₁₉	—	2	4	no	—
305	C₂²⋊C₄×C₁₉	—	2	4	no	—
306	C₂²⋊C₄×C₁₉	—	2	2	no	—
307	C₂²⋊C₄×C₁₉	—	2	2	no	—
308	C₂²⋊C₄×C₁₉	—	2	2	no	—
309	C₂²⋊C₄×C₁₉	—	2	2	no	—
310	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
311	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
312	C₄²×C₁₉	—	2	4	no	—
313	C₄²×C₁₉	—	2	2	no	—
314	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
317	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
318	#62259	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₂³×C₁₉	—	2	4	no	—
320	C₂³×C₁₉	—	2	2	no	—
321	C₂³×C₁₉	—	2	2	no	—
322	C₂³×C₁₉	—	2	2	no	—
323	C₂³×C₁₉	—	4	2	no	—
324	C₂³×C₁₉	—	4	2	no	—
325	C₂³×C₁₉	—	4	8	no	—
326	C₂³×C₁₉	—	8	4	no	—
327	C₂³×C₁₉	—	8	4	no	—
328	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
329	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
330	Q₈×C₁₉	—	2	2	no	—
331	Q₈×C₁₉	—	2	2	no	—
332	Q₈×C₁₉	—	4	2	no	—
333	Q₈×C₁₉	—	4	2	no	—
334	Q₈×C₁₉	—	4	2	no	—
335	Q₈×C₁₉	—	8	1	no	—
336	D₄×C₁₉	—	2	4	no	—
337	D₄×C₁₉	—	2	4	no	—
338	D₄×C₁₉	—	2	2	no	—
339	D₄×C₁₉	—	2	2	no	—
340	D₄×C₁₉	—	2	2	no	—
341	D₄×C₁₉	—	2	2	no	—
342	D₄×C₁₉	—	2	2	no	—
343	D₄×C₁₉	—	2	2	no	—
344	D₄×C₁₉	—	4	8	no	—
345	D₄×C₁₉	—	4	8	no	—
346	D₄×C₁₉	—	4	4	no	—
347	D₄×C₁₉	—	4	4	no	—
348	D₄×C₁₉	—	4	4	no	—
349	D₄×C₁₉	—	4	2	no	—
350	D₄×C₁₉	—	4	2	no	—
351	D₄×C₁₉	—	4	2	no	—
352	D₄×C₁₉	—	8	1	no	—
353	D₄×C₁₉	—	8	1	no	—
354	D₄×C₁₉	—	8	1	no	—
355	D₄×C₁₉	—	8	4	no	—
356	D₄×C₁₉	—	8	4	no	—
357	D₄×C₁₉	—	8	4	no	—
358	C₂×C₄×C₁₉	—	2	1	no	—
359	C₂×C₄×C₁₉	—	2	4	no	—
360	C₂×C₄×C₁₉	—	2	1	no	—
361	C₂×C₄×C₁₉	—	2	4	no	—
362	C₂×C₄×C₁₉	—	2	2	no	—
363	C₂×C₄×C₁₉	—	2	2	no	—
364	C₂×C₄×C₁₉	—	2	2	no	—
365	C₂×C₄×C₁₉	—	2	2	no	—
366	C₂×C₄×C₁₉	—	2	2	no	—
367	C₂×C₄×C₁₉	—	4	4	no	—
368	C₂×C₄×C₁₉	—	4	2	no	—
369	C₂×C₄×C₁₉	—	4	1	no	—
370	C₂×C₄×C₁₉	—	4	8	no	—
371	C₂×C₄×C₁₉	—	4	4	no	—
372	C₂×C₄×C₁₉	—	4	4	no	—
373	C₂×C₄×C₁₉	—	4	4	no	—
374	C₂×C₄×C₁₉	—	8	4	no	—
375	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	complemented
376	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
377	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
383	C₈×C₁₉	—	2	1	no	—
384	C₈×C₁₉	—	2	4	no	—
385	C₈×C₁₉	—	2	1	no	—
386	C₈×C₁₉	—	2	1	no	—
387	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	complemented
388	#3506	C₂×C₁₉	1	1	yes	characteristic, complemented
389	#3496	C₂×C₁₉	1	1	yes	characteristic, complemented
390	#3354	C₂×C₁₉	1	2	yes	complemented
391	#3353	C₂×C₁₉	1	2	yes	complemented
392	#3332	C₂×C₁₉	1	2	yes	complemented
393	#3330	C₂×C₁₉	1	2	yes	complemented
394	#3325	C₂×C₁₉	1	2	yes	complemented
395	#3324	C₂×C₁₉	1	2	yes	complemented
396	#3274	C₂×C₁₉	1	2	yes	complemented
397	#3272	C₂×C₁₉	1	2	yes	complemented
398	#3246	C₂×C₁₉	1	1	yes	characteristic, complemented
399	#3245	C₂×C₁₉	1	1	yes	characteristic, complemented
400	#3188	C₂×C₁₉	1	4	yes	complemented
401	#3169	C₂×C₁₉	1	1	yes	characteristic, complemented
402	#3167	C₂×C₁₉	1	1	yes	characteristic, complemented
403	#3055	C₂×C₁₉	1	4	yes	complemented
404	C₂×#436	C₂×C₁₉	1	1	yes	characteristic, complemented
405	C₂²×C₁₉	—	2	1	no	—
406	C₂²×C₁₉	—	2	1	no	—
407	C₂²×C₁₉	—	2	4	no	—
408	C₂²×C₁₉	—	2	4	no	—
409	C₂²×C₁₉	—	2	4	no	—
410	C₂²×C₁₉	—	4	2	no	—
411	C₂²×C₁₉	—	4	2	no	—
412	C₂²×C₁₉	—	4	2	no	—
413	C₂²×C₁₉	—	4	2	no	—
414	C₂²×C₁₉	—	4	2	no	—
415	C₂²×C₁₉	—	4	2	no	—
416	C₂²×C₁₉	—	4	2	no	—
417	C₂²×C₁₉	—	4	2	no	—
418	C₂²×C₁₉	—	4	2	no	—
419	C₂²×C₁₉	—	8	4	no	—
420	C₂²×C₁₉	—	16	8	no	—
421	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
422	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
423	C₄×C₁₉	—	2	1	no	—
424	C₄×C₁₉	—	2	1	no	—
425	C₄×C₁₉	—	2	1	no	—
426	C₄×C₁₉	—	2	4	no	—
427	C₄×C₁₉	—	4	2	no	—
428	C₄×C₁₉	—	4	2	no	—
429	C₄×C₁₉	—	4	2	no	—
430	C₄×C₁₉	—	4	2	no	—
431	C₄×C₁₉	—	4	2	no	—
432	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
433	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
434	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
435	C₄×C₁₉	#585	1	1	yes	characteristic
436	C₂×H(5,𝔽₂)	—	2	1	no	—
437	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	complemented
438	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	complemented
439	#559	—	2	2	no	—
440	#556	C₂²×C₁₉	1	2	yes	complemented
441	#555	C₂²×C₁₉	1	2	yes	complemented
442	#553	—	2	2	no	—
443	#550	C₂²×C₁₉	1	2	yes	complemented
444	#547	C₂²×C₁₉	1	2	yes	—
445	#547	C₂²×C₁₉	1	2	yes	—
446	#547	C₂²×C₁₉	1	2	yes	complemented
447	#546	—	2	2	no	—
448	#546	—	2	2	no	—
449	D₄²	C₂²×C₁₉	1	2	yes	—
450	D₄²	C₂²×C₁₉	1	2	yes	—
451	#538	—	2	2	no	—
452	#537	—	2	1	no	—
453	#535	—	2	1	no	—
454	#534	—	2	2	no	—
455	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
456	#532	C₂²×C₁₉	1	1	yes	characteristic
457	#532	C₂²×C₁₉	1	1	yes	characteristic
458	#532	C₂²×C₁₉	1	1	yes	characteristic, complemented
459	#525	C₂²×C₁₉	1	4	yes	complemented
460	C₂×#121	C₂²×C₁₉	1	4	yes	—
461	#520	—	2	1	no	—
462	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
463	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
464	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
465	#493	C₂²×C₁₉	1	1	yes	characteristic, complemented
466	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
467	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
468	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
469	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
470	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
471	#484	C₂²×C₁₉	1	4	yes	complemented
472	#482	C₂²×C₁₉	1	4	yes	complemented
473	#482	C₂²×C₁₉	1	4	yes	complemented
474	#481	C₂²×C₁₉	1	4	yes	complemented
475	#476	C₂²×C₁₉	1	2	yes	complemented
476	#475	C₂²×C₁₉	1	2	yes	complemented
477	#474	C₂²×C₁₉	1	2	yes	complemented
478	#474	C₂²×C₁₉	1	2	yes	complemented
479	#469	C₂²×C₁₉	1	4	yes	complemented
480	#469	C₂²×C₁₉	1	4	yes	complemented
481	#468	C₂²×C₁₉	1	4	yes	complemented
482	#468	C₂²×C₁₉	1	4	yes	complemented
483	#466	C₂²×C₁₉	1	2	yes	complemented
484	#466	C₂²×C₁₉	1	2	yes	complemented
485	#466	C₂²×C₁₉	1	4	yes	complemented
486	#465	C₂²×C₁₉	1	2	yes	complemented
487	#465	C₂²×C₁₉	1	2	yes	complemented
488	#465	C₂²×C₁₉	1	4	yes	complemented
489	#461	C₂²×C₁₉	1	2	yes	complemented
490	#460	C₂²×C₁₉	1	2	yes	complemented
491	#459	C₂²×C₁₉	1	2	yes	complemented
492	#459	C₂²×C₁₉	1	2	yes	complemented
493	#450	C₂²×C₁₉	1	4	yes	complemented
494	#449	C₂²×C₁₉	1	4	yes	complemented
495	#449	C₂²×C₁₉	1	4	yes	complemented
496	#447	C₂²×C₁₉	1	4	yes	complemented
497	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
498	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
499	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
500	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
501	#436	C₂²×C₁₉	1	2	yes	complemented
502	#436	C₂²×C₁₉	1	2	yes	complemented
503	#436	C₂²×C₁₉	1	2	yes	complemented
504	#436	C₂²×C₁₉	1	2	yes	complemented
505	#428	C₂²×C₁₉	1	4	yes	complemented
506	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
507	#418	C₂²×C₁₉	1	4	yes	complemented
508	#417	C₂²×C₁₉	1	4	yes	complemented
509	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	complemented
510	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
511	C₂×C₁₉	—	2	2	no	—
512	C₂×C₁₉	—	4	4	no	—
513	C₂×C₁₉	—	8	2	no	—
514	C₂×C₁₉	—	8	2	no	—
515	C₂×C₁₉	—	8	2	no	—
516	C₂×C₁₉	#3496	1	1	yes	characteristic
517	C₂×C₁₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
518	C₂×C₁₉	#3584	1	1	yes	characteristic
519	H(5,𝔽₂)	—	4	8	no	—
520	C₂×#41	—	2	2	no	—
521	C₂×#41	—	2	2	no	—
522	C₂×#41	—	2	1	no	—
523	C₂×#41	—	2	1	no	—
524	C₂×#41	—	2	1	no	—
525	C₂×#41	C₂³×C₁₉	1	4	yes	—
526	C₂²×D₄	—	2	4	no	—
527	C₂²×D₄	—	2	2	no	—
528	C₂²×D₄	—	2	2	no	—
529	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
530	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
531	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
532	AGL(1,ℤ/8)	—	4	8	no	—
533	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
534	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
535	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
536	C₂×D₈	C₂³×C₁₉	1	2	yes	—
537	C₂×D₈	C₂³×C₁₉	1	4	yes	—
538	C₂×D₈	C₂³×C₁₉	1	2	yes	—
539	C₂×M₁₆	—	4	4	no	—
540	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
541	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
542	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
543	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
544	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
545	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
546	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
547	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
548	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
549	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
550	#127	—	2	2	no	—
551	#127	C₂³×C₁₉	1	1	yes	characteristic
552	#127	C₂³×C₁₉	1	1	yes	characteristic
553	#127	C₂³×C₁₉	1	1	yes	characteristic
554	#126	—	2	4	no	—
555	#125	—	2	1	no	—
556	#124	—	2	2	no	—
557	#124	—	2	4	no	—
558	#124	—	2	1	no	—
559	#124	—	2	1	no	—
560	#124	—	2	1	no	—
561	#123	—	2	4	no	—
562	#123	—	2	4	no	—
563	#123	—	2	4	no	—
564	#123	—	2	4	no	—
565	C₂²⋊Q₈	—	2	1	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
569	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
570	#121	—	2	2	no	—
571	#121	—	2	2	no	—
572	#121	—	2	4	no	—
573	#121	—	2	4	no	—
574	#121	—	2	1	no	—
575	#121	—	2	1	no	—
576	#121	—	2	1	no	—
577	#121	—	2	2	no	—
578	#121	—	2	2	no	—
579	#121	—	2	4	no	—
580	#121	C₂³×C₁₉	1	2	yes	—
581	#121	C₂³×C₁₉	1	2	yes	—
582	#121	C₂³×C₁₉	1	4	yes	—
583	#121	C₂³×C₁₉	1	4	yes	—
584	#121	C₂³×C₁₉	1	2	yes	—
585	#121	C₂³×C₁₉	1	4	yes	—
586	#120	—	2	4	no	—
587	#120	—	2	4	no	—
588	#120	—	2	4	no	—
589	C₄×Q₈	—	2	2	no	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
592	C₄×D₄	—	2	4	no	—
593	C₄×D₄	—	2	4	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	D₄×C₁₉	1	2	yes	—
599	C₄×D₄	D₄×C₁₉	1	2	yes	—
600	C₄×D₄	C₂³×C₁₉	1	2	yes	—
601	C₄×D₄	C₂³×C₁₉	1	2	yes	—
602	C₄×D₄	C₂³×C₁₉	1	2	yes	—
603	C₄×D₄	C₂³×C₁₉	1	2	yes	—
604	C₄×D₄	C₂³×C₁₉	1	2	yes	—
605	#117	—	2	1	no	—
606	#117	—	2	2	no	—
607	#117	C₂³×C₁₉	1	4	yes	—
608	C₂×C₄⋊C₄	—	2	2	no	—
609	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
611	C₂×C₂²⋊C₄	—	2	4	no	—
612	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
613	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
614	#107	C₂³×C₁₉	1	2	yes	—
615	#107	C₂³×C₁₉	1	4	yes	—
616	#107	C₂³×C₁₉	1	2	yes	—
617	#106	C₂³×C₁₉	1	2	yes	—
618	#106	C₂³×C₁₉	1	4	yes	—
619	#106	C₂³×C₁₉	1	2	yes	—
620	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
621	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
622	#103	C₂³×C₁₉	1	2	yes	—
623	#103	C₂³×C₁₉	1	4	yes	—
624	#103	C₂³×C₁₉	1	2	yes	—
625	#102	C₂³×C₁₉	1	2	yes	—
626	#102	C₂³×C₁₉	1	4	yes	—
627	#102	C₂³×C₁₉	1	2	yes	—
628	#102	C₂³×C₁₉	1	2	yes	—
629	#102	C₂³×C₁₉	1	4	yes	—
630	#102	C₂³×C₁₉	1	4	yes	—
631	#102	C₂³×C₁₉	1	2	yes	—
632	#102	C₂³×C₁₉	1	2	yes	—
633	#102	C₂³×C₁₉	1	2	yes	—
634	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
635	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
636	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
637	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
638	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
639	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
640	C₁₉	#62259	1	1	yes	characteristic, direct product factor, Sylow
641	C₂⁴	—	2	4	no	—
642	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
643	#41	—	4	4	no	—
644	#41	—	4	4	no	—
645	#41	—	4	8	no	—
646	#41	—	4	8	no	—
647	#41	—	4	4	no	—
648	#41	—	4	4	no	—
649	#41	—	4	4	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	1	no	—
653	C₂×Q₈	—	2	1	no	—
654	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	4	no	—
657	C₂×D₄	—	2	4	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	4	4	no	—
671	C₂×D₄	—	4	4	no	—
672	C₂×D₄	—	4	8	no	—
673	C₂×D₄	—	4	8	no	—
674	C₂×D₄	—	4	16	no	—
675	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
676	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
677	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
678	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
679	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
689	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
690	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
692	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
693	SD₁₆	—	2	4	no	—
694	SD₁₆	—	4	2	no	—
695	SD₁₆	—	4	4	no	—
696	D₈	—	2	4	no	—
697	D₈	—	4	2	no	—
698	D₈	—	4	4	no	—
699	M₁₆	—	2	8	no	—
700	M₁₆	—	4	4	no	—
701	C₂×C₈	—	2	2	no	—
702	C₂×C₈	—	4	1	no	—
703	C₂×C₈	—	4	2	no	—
704	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
705	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
706	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
707	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
708	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
720	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
721	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
723	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
738	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
739	C₄²	—	2	4	no	—
740	C₄²	—	2	2	no	—
741	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
742	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
743	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
744	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
745	C₂³	—	2	4	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	4	2	no	—
750	C₂³	—	4	2	no	—
751	C₂³	—	4	8	no	—
752	C₂³	—	8	4	no	—
753	C₂³	—	8	4	no	—
754	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
755	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
756	Q₈	—	2	2	no	—
757	Q₈	—	2	2	no	—
758	Q₈	—	4	2	no	—
759	Q₈	—	4	2	no	—
760	Q₈	—	4	2	no	—
761	Q₈	—	8	1	no	—
762	D₄	—	2	4	no	—
763	D₄	—	2	4	no	—
764	D₄	—	2	2	no	—
765	D₄	—	2	2	no	—
766	D₄	—	2	2	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	4	8	no	—
771	D₄	—	4	8	no	—
772	D₄	—	4	4	no	—
773	D₄	—	4	4	no	—
774	D₄	—	4	4	no	—
775	D₄	—	4	2	no	—
776	D₄	—	4	2	no	—
777	D₄	—	4	2	no	—
778	D₄	—	8	4	no	—
779	D₄	—	8	1	no	—
780	D₄	—	8	1	no	—
781	D₄	—	8	1	no	—
782	D₄	—	8	4	no	—
783	D₄	—	8	4	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	4	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	—	4	4	no	—
798	C₂×C₄	—	4	4	no	—
799	C₂×C₄	—	4	4	no	—
800	C₂×C₄	—	8	4	no	—
801	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	complemented
802	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
803	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
808	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
809	C₈	—	2	1	no	—
810	C₈	—	2	4	no	—
811	C₈	—	2	1	no	—
812	C₈	—	2	1	no	—
813	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	complemented
814	C₂²	—	2	1	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	2	4	no	—
818	C₂²	—	2	4	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	8	4	no	—
829	C₂²	—	16	8	no	—
830	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
831	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
832	C₄	—	2	1	no	—
833	C₄	—	2	4	no	—
834	C₄	—	2	1	no	—
835	C₄	—	2	1	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
842	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
843	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
844	C₄	C₁₉×#585	1	1	yes	characteristic
845	C₂	—	2	2	no	—
846	C₂	—	4	4	no	—
847	C₂	—	8	2	no	—
848	C₂	—	8	2	no	—
849	C₂	—	8	2	no	—
850	C₂	C₁₉×#3496	1	1	yes	characteristic
851	C₂	C₂²×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
852	C₂	C₁₉×#3584	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 ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3506	C₂	semidirect
2. C₁₉×#3496	C₂	semidirect
3. C₁₉×#3354	C₂	semidirect
4. C₁₉×#3353	C₂	semidirect
5. C₁₉×#3332	C₂	semidirect
6. C₁₉×#3330	C₂	semidirect
7. C₁₉×#3325	C₂	semidirect
8. C₁₉×#3324	C₂	semidirect
9. C₁₉×#3274	C₂	semidirect
10. C₁₉×#3272	C₂	semidirect
11. C₁₉×#3246	C₂	semidirect
12. C₁₉×#3245	C₂	semidirect
13. C₁₉×#3188	C₂	semidirect
14. C₁₉×#3169	C₂	semidirect
15. C₁₉×#3167	C₂	semidirect
16. C₁₉×#3055	C₂	semidirect
17. C₂×C₁₉×#436	C₂	semidirect
19. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂²×M₁₆×C₁₉	C₂²	semidirect
22. C₁₉×#556	C₂²	semidirect
23. C₁₉×#555	C₂²	semidirect
25. C₁₉×#550	C₂²	semidirect
28. C₁₉×#547	C₂²	semidirect
37. C₁₉×#533	C₂²	semidirect
40. C₁₉×#532	C₂²	semidirect
41. C₁₉×#525	C₂²	semidirect
45. C₁₉×#500	C₂²	semidirect
46. C₁₉×#498	C₂²	semidirect
47. C₁₉×#493	C₂²	semidirect
48. C₁₉×#492	C₂²	semidirect
49. C₁₉×#487	C₂²	semidirect
50. C₁₉×#486	C₂²	semidirect
51. C₁₉×#486	C₂²	semidirect
52. C₁₉×#486	C₂²	semidirect
53. C₁₉×#484	C₂²	semidirect
54. C₁₉×#482	C₂²	semidirect
55. C₁₉×#482	C₂²	semidirect
56. C₁₉×#481	C₂²	semidirect
57. C₁₉×#476	C₂²	semidirect
58. C₁₉×#475	C₂²	semidirect
59. C₁₉×#474	C₂²	semidirect
60. C₁₉×#474	C₂²	semidirect
61. C₁₉×#469	C₂²	semidirect
62. C₁₉×#469	C₂²	semidirect
63. C₁₉×#468	C₂²	semidirect
64. C₁₉×#468	C₂²	semidirect
65. C₁₉×#466	C₂²	semidirect
66. C₁₉×#466	C₂²	semidirect
67. C₁₉×#466	C₂²	semidirect
68. C₁₉×#465	C₂²	semidirect
69. C₁₉×#465	C₂²	semidirect
70. C₁₉×#465	C₂²	semidirect
71. C₁₉×#461	C₂²	semidirect
72. C₁₉×#460	C₂²	semidirect
73. C₁₉×#459	C₂²	semidirect
74. C₁₉×#459	C₂²	semidirect
75. C₁₉×#450	C₂²	semidirect
76. C₁₉×#449	C₂²	semidirect
77. C₁₉×#449	C₂²	semidirect
78. C₁₉×#447	C₂²	semidirect
79. C₄×SD₁₆×C₁₉	C₂²	semidirect
80. C₄×SD₁₆×C₁₉	C₂²	semidirect
81. C₄×D₈×C₁₉	C₂²	semidirect
82. C₄×D₈×C₁₉	C₂²	semidirect
83. C₁₉×#436	C₂²	semidirect
84. C₁₉×#436	C₂²	semidirect
85. C₁₉×#436	C₂²	semidirect
86. C₁₉×#436	C₂²	semidirect
87. C₁₉×#428	C₂²	semidirect
88. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
89. C₁₉×#418	C₂²	semidirect
90. C₁₉×#417	C₂²	semidirect
91. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
92. C₂×C₄×C₈×C₁₉	C₂²	semidirect
318. #62259	C₁₉	direct (N × H)
375. C₂×C₄×C₁₉	AGL(1,ℤ/8)	semidirect
387. C₈×C₁₉	H(5,𝔽₂)	semidirect
388. #3506	C₂×C₁₉	semidirect
389. #3496	C₂×C₁₉	semidirect
390. #3354	C₂×C₁₉	semidirect
391. #3353	C₂×C₁₉	semidirect
392. #3332	C₂×C₁₉	semidirect
393. #3330	C₂×C₁₉	semidirect
394. #3325	C₂×C₁₉	semidirect
395. #3324	C₂×C₁₉	semidirect
396. #3274	C₂×C₁₉	semidirect
397. #3272	C₂×C₁₉	semidirect
398. #3246	C₂×C₁₉	semidirect
399. #3245	C₂×C₁₉	semidirect
400. #3188	C₂×C₁₉	semidirect
401. #3169	C₂×C₁₉	semidirect
402. #3167	C₂×C₁₉	semidirect
403. #3055	C₂×C₁₉	semidirect
404. C₂×#436	C₂×C₁₉	semidirect
437. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
438. C₂²×M₁₆	C₂²×C₁₉	semidirect
440. #556	C₂²×C₁₉	semidirect
441. #555	C₂²×C₁₉	semidirect
443. #550	C₂²×C₁₉	semidirect
446. #547	C₂²×C₁₉	semidirect
455. #533	C₂²×C₁₉	semidirect
458. #532	C₂²×C₁₉	semidirect
459. #525	C₂²×C₁₉	semidirect
463. #500	C₂²×C₁₉	semidirect
464. #498	C₂²×C₁₉	semidirect
465. #493	C₂²×C₁₉	semidirect
466. #492	C₂²×C₁₉	semidirect
467. #487	C₂²×C₁₉	semidirect
468. #486	C₂²×C₁₉	semidirect
469. #486	C₂²×C₁₉	semidirect
470. #486	C₂²×C₁₉	semidirect
471. #484	C₂²×C₁₉	semidirect
472. #482	C₂²×C₁₉	semidirect
473. #482	C₂²×C₁₉	semidirect
474. #481	C₂²×C₁₉	semidirect
475. #476	C₂²×C₁₉	semidirect
476. #475	C₂²×C₁₉	semidirect
477. #474	C₂²×C₁₉	semidirect
478. #474	C₂²×C₁₉	semidirect
479. #469	C₂²×C₁₉	semidirect
480. #469	C₂²×C₁₉	semidirect
481. #468	C₂²×C₁₉	semidirect
482. #468	C₂²×C₁₉	semidirect
483. #466	C₂²×C₁₉	semidirect
484. #466	C₂²×C₁₉	semidirect
485. #466	C₂²×C₁₉	semidirect
486. #465	C₂²×C₁₉	semidirect
487. #465	C₂²×C₁₉	semidirect
488. #465	C₂²×C₁₉	semidirect
489. #461	C₂²×C₁₉	semidirect
490. #460	C₂²×C₁₉	semidirect
491. #459	C₂²×C₁₉	semidirect
492. #459	C₂²×C₁₉	semidirect
493. #450	C₂²×C₁₉	semidirect
494. #449	C₂²×C₁₉	semidirect
495. #449	C₂²×C₁₉	semidirect
496. #447	C₂²×C₁₉	semidirect
497. C₄×SD₁₆	C₂²×C₁₉	semidirect
498. C₄×SD₁₆	C₂²×C₁₉	semidirect
499. C₄×D₈	C₂²×C₁₉	semidirect
500. C₄×D₈	C₂²×C₁₉	semidirect
501. #436	C₂²×C₁₉	semidirect
502. #436	C₂²×C₁₉	semidirect
503. #436	C₂²×C₁₉	semidirect
504. #436	C₂²×C₁₉	semidirect
505. #428	C₂²×C₁₉	semidirect
506. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
507. #418	C₂²×C₁₉	semidirect
508. #417	C₂²×C₁₉	semidirect
509. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
510. C₂×C₄×C₈	C₂²×C₁₉	semidirect
640. C₁₉	#62259	direct (N × H)
801. C₂×C₄	C₁₉×AGL(1,ℤ/8)	semidirect
813. C₈	C₁₉×H(5,𝔽₂)	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×#3496	2
C₁₉×#3354	2
C₁₉×#3353	2
C₁₉×#3332	2
C₁₉×#3330	2
C₁₉×#3325	2
C₁₉×#3324	2
C₁₉×#3274	2
C₁₉×#3272	2
C₁₉×#3246	2
C₁₉×#3245	2
C₁₉×#3188	2
C₁₉×#3169	2
C₁₉×#3167	2
C₁₉×#3055	2
C₂×C₁₉×#436	2
#62259	19

Subgroups — C19×#62259 #18068218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62259 #18068218