Subgroups — C₁₉×#24468 #18030427

Order 4864.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3488	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3055	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#453	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3006	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#421	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2619	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2040	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2037	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2006	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2002	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1900	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1897	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1883	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1860	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1792	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
21	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×#550	—	2	1	no	—
23	C₁₉×#548	—	2	1	no	—
24	C₁₉×#546	—	2	1	no	—
25	C₁₉×#546	—	2	2	no	—
26	D₄²×C₁₉	—	2	2	no	—
27	D₄²×C₁₉	—	2	1	no	—
28	C₁₉×#537	—	2	1	no	—
29	C₁₉×#537	C₂²	1	1	yes	characteristic
30	C₁₉×#535	—	2	1	no	—
31	C₁₉×#535	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#525	—	2	1	no	—
34	C₁₉×#525	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#121	—	2	1	no	—
36	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#520	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#469	—	2	1	no	—
41	C₁₉×#468	—	2	1	no	—
42	C₁₉×#466	—	2	1	no	—
43	C₁₉×#465	—	2	1	no	—
44	C₁₉×#453	—	2	4	no	—
45	C₁₉×#449	—	2	1	no	—
46	C₁₉×#449	—	2	1	no	—
47	C₁₉×#448	—	2	1	no	—
48	C₁₉×#447	—	2	1	no	—
49	C₁₉×#428	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#421	—	2	4	no	—
51	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#418	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#417	C₂²	1	1	yes	characteristic
59	C₁₉×#417	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#417	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#407	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#394	—	2	2	no	—
65	C₁₉×#392	—	2	2	no	—
66	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#382	C₂²	1	1	yes	characteristic, complemented
69	C₁₉×#343	C₂²	1	1	yes	characteristic, complemented
70	C₁₉×#343	C₂²	1	1	yes	characteristic, complemented
71	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
72	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
73	C₁₉×H(5,𝔽₂)	—	2	2	no	—
74	C₁₉×H(5,𝔽₂)	—	2	2	no	—
75	C₁₉×H(5,𝔽₂)	—	4	1	no	—
76	C₁₉×H(5,𝔽₂)	—	4	1	no	—
77	C₂×#41×C₁₉	—	2	1	no	—
78	C₂×#41×C₁₉	—	2	1	no	—
79	C₂×#41×C₁₉	—	2	1	no	—
80	C₂×#41×C₁₉	—	2	1	no	—
81	C₂×#41×C₁₉	—	2	2	no	—
82	C₂×#41×C₁₉	—	2	2	no	—
83	C₂×#41×C₁₉	—	4	1	no	—
84	C₂×#41×C₁₉	—	4	1	no	—
85	C₂×#41×C₁₉	D₄	1	1	yes	characteristic, complemented
86	C₂×#41×C₁₉	D₄	1	1	yes	characteristic, complemented
87	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic, complemented
91	C₂²×D₄×C₁₉	—	2	1	no	—
92	C₂²×D₄×C₁₉	—	2	2	no	—
93	C₂²×D₄×C₁₉	—	2	2	no	—
94	C₂²×D₄×C₁₉	—	2	1	no	—
95	C₂²×D₄×C₁₉	—	2	1	no	—
96	C₂²×D₄×C₁₉	—	2	1	no	—
97	C₂²×D₄×C₁₉	—	2	2	no	—
98	C₂²×D₄×C₁₉	D₄	1	2	yes	—
99	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic, complemented
100	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₉	—	2	1	no	—
103	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
105	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
106	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
107	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
108	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
109	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
110	C₂×SD₁₆×C₁₉	—	2	1	no	—
111	C₂×SD₁₆×C₁₉	—	2	1	no	—
112	C₂×SD₁₆×C₁₉	—	2	1	no	—
113	C₂×D₈×C₁₉	—	2	1	no	—
114	C₂×D₈×C₁₉	—	2	1	no	—
115	C₂×D₈×C₁₉	—	2	1	no	—
116	C₂×M₁₆×C₁₉	—	2	1	no	—
117	C₂×M₁₆×C₁₉	—	2	2	no	—
118	C₂×M₁₆×C₁₉	—	4	1	no	—
119	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
120	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
121	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
122	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₁₉	—	2	1	no	—
124	C₁₉×#127	—	2	2	no	—
125	C₁₉×#127	—	2	1	no	—
126	C₁₉×#127	—	2	2	no	—
127	C₁₉×#127	—	4	1	no	—
128	C₁₉×#124	—	2	2	no	—
129	C₁₉×#124	—	2	1	no	—
130	C₁₉×#123	—	2	2	no	—
131	C₁₉×#123	—	2	1	no	—
132	C₁₉×C₂²⋊Q₈	—	2	2	no	—
133	C₁₉×C₂²⋊Q₈	—	2	1	no	—
134	C₁₉×C₂²⋊Q₈	—	2	1	no	—
135	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
136	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
137	C₁₉×#121	—	2	2	no	—
138	C₁₉×#121	—	2	2	no	—
139	C₁₉×#121	—	2	2	no	—
140	C₁₉×#121	—	2	2	no	—
141	C₁₉×#121	—	2	2	no	—
142	C₁₉×#121	—	2	1	no	—
143	C₁₉×#121	—	2	1	no	—
144	C₁₉×#121	—	2	1	no	—
145	C₁₉×#121	—	2	1	no	—
146	C₁₉×#121	—	2	1	no	—
147	C₁₉×#121	—	2	1	no	—
148	C₁₉×#121	—	2	2	no	—
149	C₁₉×#121	—	2	1	no	—
150	C₁₉×#121	—	2	1	no	—
151	C₁₉×#121	—	2	1	no	—
152	C₁₉×#121	—	2	1	no	—
153	C₁₉×#121	—	2	1	no	—
154	C₁₉×#121	—	2	1	no	—
155	C₁₉×#121	D₄	1	1	yes	characteristic, complemented
156	C₁₉×#121	D₄	1	1	yes	characteristic, complemented
157	C₁₉×#120	—	2	2	no	—
158	C₁₉×#120	—	2	2	no	—
159	C₁₉×#120	—	2	2	no	—
160	C₁₉×#120	—	2	1	no	—
161	C₁₉×#120	—	2	2	no	—
162	C₄×Q₈×C₁₉	—	2	1	no	—
163	C₄×D₄×C₁₉	—	2	2	no	—
164	C₄×D₄×C₁₉	—	2	2	no	—
165	C₄×D₄×C₁₉	—	2	1	no	—
166	C₄×D₄×C₁₉	—	2	2	no	—
167	C₄×D₄×C₁₉	—	2	1	no	—
168	C₄×D₄×C₁₉	—	2	1	no	—
169	C₁₉×#117	—	2	1	no	—
170	C₁₉×#117	—	2	2	no	—
171	C₁₉×#117	—	4	1	no	—
172	C₁₉×#117	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
178	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
179	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
180	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
181	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
182	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
183	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
185	C₁₉×#107	—	2	1	no	—
186	C₁₉×#106	—	2	1	no	—
187	C₁₉×#104	—	2	2	no	—
188	C₁₉×#104	—	2	2	no	—
189	C₁₉×#104	—	2	2	no	—
190	C₁₉×#104	—	2	2	no	—
191	C₁₉×#104	—	4	1	no	—
192	C₁₉×#104	D₄	1	4	yes	complemented
193	C₁₉×#103	—	2	1	no	—
194	C₁₉×#103	—	2	1	no	—
195	C₁₉×#103	—	2	1	no	—
196	C₁₉×#102	—	2	1	no	—
197	C₁₉×#102	—	2	1	no	—
198	C₁₉×#102	—	2	1	no	—
199	C₁₉×#102	—	2	1	no	—
200	C₁₉×#102	—	2	1	no	—
201	C₁₉×#100	—	2	2	no	—
202	C₁₉×#100	—	4	1	no	—
203	C₁₉×C₂²⋊C₈	—	2	1	no	—
204	C₁₉×C₂²⋊C₈	—	2	1	no	—
205	C₁₉×#95	—	2	2	no	—
206	C₂⁴×C₁₉	—	2	2	no	—
207	C₂⁴×C₁₉	—	2	1	no	—
208	C₂⁴×C₁₉	—	2	1	no	—
209	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
210	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
211	#41×C₁₉	—	2	1	no	—
212	#41×C₁₉	—	2	1	no	—
213	#41×C₁₉	—	2	2	no	—
214	#41×C₁₉	—	2	2	no	—
215	#41×C₁₉	—	2	1	no	—
216	#41×C₁₉	—	2	1	no	—
217	#41×C₁₉	—	2	1	no	—
218	#41×C₁₉	—	2	1	no	—
219	#41×C₁₉	—	2	1	no	—
220	#41×C₁₉	—	2	1	no	—
221	#41×C₁₉	—	2	1	no	—
222	#41×C₁₉	—	2	1	no	—
223	#41×C₁₉	—	4	2	no	—
224	#41×C₁₉	—	4	2	no	—
225	#41×C₁₉	—	4	1	no	—
226	#41×C₁₉	—	4	1	no	—
227	#41×C₁₉	—	4	2	no	—
228	#41×C₁₉	—	4	2	no	—
229	#41×C₁₉	—	4	2	no	—
230	#41×C₁₉	—	4	2	no	—
231	#41×C₁₉	—	4	2	no	—
232	#41×C₁₉	—	4	2	no	—
233	#41×C₁₉	C₂×D₄	1	2	yes	—
234	#41×C₁₉	#41	1	2	yes	—
235	C₂×Q₈×C₁₉	—	2	1	no	—
236	C₂×Q₈×C₁₉	—	2	2	no	—
237	C₂×Q₈×C₁₉	—	4	1	no	—
238	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
241	C₂×D₄×C₁₉	—	2	1	no	—
242	C₂×D₄×C₁₉	—	2	2	no	—
243	C₂×D₄×C₁₉	—	2	2	no	—
244	C₂×D₄×C₁₉	—	2	2	no	—
245	C₂×D₄×C₁₉	—	2	2	no	—
246	C₂×D₄×C₁₉	—	2	1	no	—
247	C₂×D₄×C₁₉	—	2	1	no	—
248	C₂×D₄×C₁₉	—	2	1	no	—
249	C₂×D₄×C₁₉	—	2	1	no	—
250	C₂×D₄×C₁₉	—	2	1	no	—
251	C₂×D₄×C₁₉	—	2	2	no	—
252	C₂×D₄×C₁₉	—	2	2	no	—
253	C₂×D₄×C₁₉	—	2	2	no	—
254	C₂×D₄×C₁₉	—	2	1	no	—
255	C₂×D₄×C₁₉	—	2	2	no	—
256	C₂×D₄×C₁₉	—	2	1	no	—
257	C₂×D₄×C₁₉	—	2	1	no	—
258	C₂×D₄×C₁₉	—	2	1	no	—
259	C₂×D₄×C₁₉	—	2	1	no	—
260	C₂×D₄×C₁₉	—	2	1	no	—
261	C₂×D₄×C₁₉	—	2	1	no	—
262	C₂×D₄×C₁₉	—	2	1	no	—
263	C₂×D₄×C₁₉	—	2	1	no	—
264	C₂×D₄×C₁₉	—	2	1	no	—
265	C₂×D₄×C₁₉	—	2	1	no	—
266	C₂×D₄×C₁₉	—	2	1	no	—
267	C₂×D₄×C₁₉	—	2	1	no	—
268	C₂×D₄×C₁₉	—	2	1	no	—
269	C₂×D₄×C₁₉	—	4	1	no	—
270	C₂×D₄×C₁₉	—	4	2	no	—
271	C₂×D₄×C₁₉	—	4	2	no	—
272	C₂×D₄×C₁₉	—	4	4	no	—
273	C₂×D₄×C₁₉	—	4	2	no	—
274	C₂×D₄×C₁₉	—	4	2	no	—
275	C₂×D₄×C₁₉	—	4	4	no	—
276	C₂×D₄×C₁₉	—	4	4	no	—
277	C₂×D₄×C₁₉	—	4	2	no	—
278	C₂×D₄×C₁₉	—	4	2	no	—
279	C₂×D₄×C₁₉	—	4	1	no	—
280	C₂×D₄×C₁₉	—	4	1	no	—
281	C₂×D₄×C₁₉	—	8	2	no	—
282	C₂×D₄×C₁₉	—	8	2	no	—
283	C₂×D₄×C₁₉	—	8	2	no	—
284	C₂×D₄×C₁₉	—	8	2	no	—
285	C₂×D₄×C₁₉	—	8	4	no	—
286	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
287	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
288	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₁₉	—	2	1	no	—
290	C₂²×C₄×C₁₉	—	2	1	no	—
291	C₂²×C₄×C₁₉	—	2	1	no	—
292	C₂²×C₄×C₁₉	—	2	1	no	—
293	C₂²×C₄×C₁₉	—	2	1	no	—
294	C₂²×C₄×C₁₉	—	2	2	no	—
295	C₂²×C₄×C₁₉	—	2	1	no	—
296	C₂²×C₄×C₁₉	—	2	1	no	—
297	C₂²×C₄×C₁₉	—	2	2	no	—
298	C₂²×C₄×C₁₉	—	2	1	no	—
299	C₂²×C₄×C₁₉	—	2	1	no	—
300	C₂²×C₄×C₁₉	—	2	1	no	—
301	C₂²×C₄×C₁₉	—	2	1	no	—
302	C₂²×C₄×C₁₉	—	2	1	no	—
303	C₂²×C₄×C₁₉	—	2	1	no	—
304	C₂²×C₄×C₁₉	—	4	2	no	—
305	C₂²×C₄×C₁₉	—	4	2	no	—
306	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
312	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
313	SD₁₆×C₁₉	—	4	2	no	—
314	SD₁₆×C₁₉	—	4	2	no	—
315	SD₁₆×C₁₉	—	4	2	no	—
316	D₈×C₁₉	—	4	2	no	—
317	D₈×C₁₉	—	4	2	no	—
318	D₈×C₁₉	—	4	2	no	—
319	M₁₆×C₁₉	—	2	1	no	—
320	M₁₆×C₁₉	—	2	1	no	—
321	M₁₆×C₁₉	—	2	1	no	—
322	M₁₆×C₁₉	—	2	1	no	—
323	M₁₆×C₁₉	—	2	1	no	—
324	M₁₆×C₁₉	—	2	1	no	—
325	M₁₆×C₁₉	—	2	1	no	—
326	M₁₆×C₁₉	—	4	2	no	—
327	M₁₆×C₁₉	C₂×D₄	1	2	yes	complemented
328	C₂×C₈×C₁₉	—	2	1	no	—
329	C₂×C₈×C₁₉	—	2	1	no	—
330	C₂×C₈×C₁₉	—	2	1	no	—
331	C₂×C₈×C₁₉	—	2	1	no	—
332	C₂×C₈×C₁₉	—	4	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	1	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	—	4	2	no	—
342	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
343	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
344	C₂²⋊C₄×C₁₉	—	2	2	no	—
345	C₂²⋊C₄×C₁₉	—	2	2	no	—
346	C₂²⋊C₄×C₁₉	—	2	2	no	—
347	C₂²⋊C₄×C₁₉	—	2	2	no	—
348	C₂²⋊C₄×C₁₉	—	2	2	no	—
349	C₂²⋊C₄×C₁₉	—	2	1	no	—
350	C₂²⋊C₄×C₁₉	—	2	1	no	—
351	C₂²⋊C₄×C₁₉	—	2	1	no	—
352	C₂²⋊C₄×C₁₉	—	2	1	no	—
353	C₂²⋊C₄×C₁₉	—	2	2	no	—
354	C₂²⋊C₄×C₁₉	—	2	2	no	—
355	C₂²⋊C₄×C₁₉	—	2	1	no	—
356	C₂²⋊C₄×C₁₉	—	4	2	no	—
357	C₂²⋊C₄×C₁₉	—	4	1	no	—
358	C₂²⋊C₄×C₁₉	—	4	1	no	—
359	C₂²⋊C₄×C₁₉	—	8	2	no	—
360	C₂²⋊C₄×C₁₉	—	8	2	no	—
361	C₄²×C₁₉	—	2	2	no	—
362	C₄²×C₁₉	—	2	1	no	—
363	C₄²×C₁₉	—	2	1	no	—
364	C₄²×C₁₉	—	2	1	no	—
365	C₄²×C₁₉	—	2	1	no	—
366	C₄²×C₁₉	C₂×D₄	1	2	yes	complemented
367	#24468	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
368	C₂³×C₁₉	—	2	1	no	—
369	C₂³×C₁₉	—	2	1	no	—
370	C₂³×C₁₉	—	2	1	no	—
371	C₂³×C₁₉	—	2	2	no	—
372	C₂³×C₁₉	—	2	1	no	—
373	C₂³×C₁₉	—	2	1	no	—
374	C₂³×C₁₉	—	2	2	no	—
375	C₂³×C₁₉	—	2	2	no	—
376	C₂³×C₁₉	—	4	1	no	—
377	C₂³×C₁₉	—	4	1	no	—
378	C₂³×C₁₉	—	4	2	no	—
379	C₂³×C₁₉	—	4	2	no	—
380	C₂³×C₁₉	—	4	4	no	—
381	C₂³×C₁₉	—	4	2	no	—
382	C₂³×C₁₉	—	4	2	no	—
383	C₂³×C₁₉	—	4	2	no	—
384	C₂³×C₁₉	—	4	2	no	—
385	C₂³×C₁₉	—	4	1	no	—
386	C₂³×C₁₉	—	4	1	no	—
387	C₂³×C₁₉	—	4	1	no	—
388	C₂³×C₁₉	—	8	1	no	—
389	C₂³×C₁₉	—	8	2	no	—
390	C₂³×C₁₉	—	8	2	no	—
391	C₂³×C₁₉	#120	1	1	yes	characteristic
392	C₂³×C₁₉	#120	1	1	yes	characteristic
393	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
394	Q₈×C₁₉	—	2	1	no	—
395	Q₈×C₁₉	—	2	1	no	—
396	Q₈×C₁₉	—	2	1	no	—
397	Q₈×C₁₉	—	2	1	no	—
398	Q₈×C₁₉	—	2	1	no	—
399	Q₈×C₁₉	—	4	2	no	—
400	Q₈×C₁₉	#121	1	2	yes	—
401	D₄×C₁₉	—	2	2	no	—
402	D₄×C₁₉	—	2	2	no	—
403	D₄×C₁₉	—	2	1	no	—
404	D₄×C₁₉	—	2	1	no	—
405	D₄×C₁₉	—	2	1	no	—
406	D₄×C₁₉	—	2	1	no	—
407	D₄×C₁₉	—	2	1	no	—
408	D₄×C₁₉	—	4	2	no	—
409	D₄×C₁₉	—	4	2	no	—
410	D₄×C₁₉	—	4	4	no	—
411	D₄×C₁₉	—	4	2	no	—
412	D₄×C₁₉	—	4	4	no	—
413	D₄×C₁₉	—	4	4	no	—
414	D₄×C₁₉	—	4	2	no	—
415	D₄×C₁₉	—	4	1	no	—
416	D₄×C₁₉	—	4	1	no	—
417	D₄×C₁₉	—	4	1	no	—
418	D₄×C₁₉	—	4	1	no	—
419	D₄×C₁₉	—	4	1	no	—
420	D₄×C₁₉	—	4	1	no	—
421	D₄×C₁₉	—	4	1	no	—
422	D₄×C₁₉	—	4	1	no	—
423	D₄×C₁₉	—	4	1	no	—
424	D₄×C₁₉	—	4	1	no	—
425	D₄×C₁₉	—	4	1	no	—
426	D₄×C₁₉	—	4	1	no	—
427	D₄×C₁₉	—	8	1	no	—
428	D₄×C₁₉	—	8	2	no	—
429	D₄×C₁₉	—	8	2	no	—
430	D₄×C₁₉	—	8	2	no	—
431	D₄×C₁₉	—	8	2	no	—
432	D₄×C₁₉	—	8	8	no	—
433	D₄×C₁₉	—	8	2	no	—
434	D₄×C₁₉	—	8	2	no	—
435	D₄×C₁₉	#121	1	2	yes	—
436	C₂×C₄×C₁₉	—	2	1	no	—
437	C₂×C₄×C₁₉	—	2	1	no	—
438	C₂×C₄×C₁₉	—	2	1	no	—
439	C₂×C₄×C₁₉	—	2	1	no	—
440	C₂×C₄×C₁₉	—	2	1	no	—
441	C₂×C₄×C₁₉	—	2	1	no	—
442	C₂×C₄×C₁₉	—	2	1	no	—
443	C₂×C₄×C₁₉	—	2	1	no	—
444	C₂×C₄×C₁₉	—	2	1	no	—
445	C₂×C₄×C₁₉	—	2	2	no	—
446	C₂×C₄×C₁₉	—	2	1	no	—
447	C₂×C₄×C₁₉	—	2	1	no	—
448	C₂×C₄×C₁₉	—	2	2	no	—
449	C₂×C₄×C₁₉	—	2	1	no	—
450	C₂×C₄×C₁₉	—	2	2	no	—
451	C₂×C₄×C₁₉	—	2	1	no	—
452	C₂×C₄×C₁₉	—	2	1	no	—
453	C₂×C₄×C₁₉	—	2	1	no	—
454	C₂×C₄×C₁₉	—	2	2	no	—
455	C₂×C₄×C₁₉	—	4	2	no	—
456	C₂×C₄×C₁₉	—	4	2	no	—
457	C₂×C₄×C₁₉	—	4	2	no	—
458	C₂×C₄×C₁₉	—	4	4	no	—
459	C₂×C₄×C₁₉	—	4	1	no	—
460	C₂×C₄×C₁₉	—	4	1	no	—
461	C₂×C₄×C₁₉	—	4	1	no	—
462	C₂×C₄×C₁₉	—	4	1	no	—
463	C₂×C₄×C₁₉	—	4	1	no	—
464	C₂×C₄×C₁₉	—	4	1	no	—
465	C₂×C₄×C₁₉	—	4	2	no	—
466	C₂×C₄×C₁₉	—	4	1	no	—
467	C₂×C₄×C₁₉	—	4	1	no	—
468	C₂×C₄×C₁₉	—	4	2	no	—
469	C₂×C₄×C₁₉	—	4	1	no	—
470	C₂×C₄×C₁₉	—	4	1	no	—
471	C₂×C₄×C₁₉	—	8	2	no	—
472	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
473	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
474	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
478	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
479	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
480	C₈×C₁₉	—	2	2	no	—
481	C₈×C₁₉	—	4	1	no	—
482	C₈×C₁₉	—	4	1	no	—
483	C₈×C₁₉	—	4	1	no	—
484	#3488	C₂×C₁₉	1	1	yes	characteristic, complemented
485	#3055	C₂×C₁₉	1	1	yes	characteristic, complemented
486	C₂×#453	C₂×C₁₉	1	1	yes	characteristic, complemented
487	#3006	C₂×C₁₉	1	1	yes	characteristic, complemented
488	C₂×#421	C₂×C₁₉	1	1	yes	characteristic, complemented
489	#2619	C₂×C₁₉	1	1	yes	characteristic, complemented
490	#2040	C₂×C₁₉	1	1	yes	characteristic, complemented
491	#2037	C₂×C₁₉	1	1	yes	characteristic, complemented
492	#2006	C₂×C₁₉	1	1	yes	characteristic, complemented
493	#2002	C₂×C₁₉	1	1	yes	characteristic, complemented
494	#1900	C₂×C₁₉	1	1	yes	characteristic, complemented
495	#1897	C₂×C₁₉	1	1	yes	characteristic, complemented
496	#1883	C₂×C₁₉	1	1	yes	characteristic, complemented
497	#1860	C₂×C₁₉	1	1	yes	characteristic, complemented
498	#1792	C₂×C₁₉	1	1	yes	characteristic, complemented
499	C₂²×C₁₉	—	2	1	no	—
500	C₂²×C₁₉	—	2	1	no	—
501	C₂²×C₁₉	—	2	1	no	—
502	C₂²×C₁₉	—	2	1	no	—
503	C₂²×C₁₉	—	2	2	no	—
504	C₂²×C₁₉	—	2	1	no	—
505	C₂²×C₁₉	—	2	1	no	—
506	C₂²×C₁₉	—	2	1	no	—
507	C₂²×C₁₉	—	2	1	no	—
508	C₂²×C₁₉	—	4	1	no	—
509	C₂²×C₁₉	—	4	1	no	—
510	C₂²×C₁₉	—	4	1	no	—
511	C₂²×C₁₉	—	4	1	no	—
512	C₂²×C₁₉	—	4	2	no	—
513	C₂²×C₁₉	—	4	2	no	—
514	C₂²×C₁₉	—	4	1	no	—
515	C₂²×C₁₉	—	4	1	no	—
516	C₂²×C₁₉	—	4	1	no	—
517	C₂²×C₁₉	—	4	2	no	—
518	C₂²×C₁₉	—	4	1	no	—
519	C₂²×C₁₉	—	8	1	no	—
520	C₂²×C₁₉	—	8	1	no	—
521	C₂²×C₁₉	—	8	2	no	—
522	C₂²×C₁₉	—	8	2	no	—
523	C₂²×C₁₉	—	8	2	no	—
524	C₂²×C₁₉	—	8	2	no	—
525	C₂²×C₁₉	—	8	4	no	—
526	C₂²×C₁₉	—	8	1	no	—
527	C₂²×C₁₉	—	8	1	no	—
528	C₂²×C₁₉	—	8	1	no	—
529	C₂²×C₁₉	—	16	4	no	—
530	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
531	C₂²×C₁₉	D₄²	1	1	yes	characteristic
532	C₂²×C₁₉	#546	1	1	yes	characteristic
533	C₄×C₁₉	—	2	1	no	—
534	C₄×C₁₉	—	2	1	no	—
535	C₄×C₁₉	—	2	2	no	—
536	C₄×C₁₉	—	4	2	no	—
537	C₄×C₁₉	—	4	1	no	—
538	C₄×C₁₉	—	4	1	no	—
539	C₄×C₁₉	—	4	2	no	—
540	C₄×C₁₉	—	4	1	no	—
541	C₄×C₁₉	—	4	1	no	—
542	C₄×C₁₉	—	8	1	no	—
543	C₄×C₁₉	—	8	1	no	—
544	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
545	C₄×C₁₉	#534	1	1	yes	characteristic
546	C₄×C₁₉	D₄²	1	1	yes	characteristic
547	C₄×C₁₉	#546	1	1	yes	characteristic
548	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
549	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
550	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
551	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic, complemented
552	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic, complemented
553	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
554	#550	—	2	1	no	—
555	#548	—	2	1	no	—
556	#546	—	2	1	no	—
557	#546	—	2	2	no	—
558	D₄²	—	2	2	no	—
559	D₄²	—	2	1	no	—
560	#537	—	2	1	no	—
561	#537	C₂²×C₁₉	1	1	yes	characteristic
562	#535	—	2	1	no	—
563	#535	C₂²×C₁₉	1	1	yes	characteristic
564	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic, complemented
565	#525	—	2	1	no	—
566	#525	C₂²×C₁₉	1	1	yes	characteristic
567	C₂×#121	—	2	1	no	—
568	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
569	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic, complemented
570	#520	C₂²×C₁₉	1	1	yes	characteristic
571	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
572	#469	—	2	1	no	—
573	#468	—	2	1	no	—
574	#466	—	2	1	no	—
575	#465	—	2	1	no	—
576	#453	—	2	4	no	—
577	#449	—	2	1	no	—
578	#449	—	2	1	no	—
579	#448	—	2	1	no	—
580	#447	—	2	1	no	—
581	#428	C₂²×C₁₉	1	1	yes	characteristic, complemented
582	#421	—	2	4	no	—
583	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
584	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
585	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
586	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
587	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
588	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
589	#418	C₂²×C₁₉	1	1	yes	characteristic, complemented
590	#417	C₂²×C₁₉	1	1	yes	characteristic
591	#417	C₂²×C₁₉	1	1	yes	characteristic, complemented
592	#417	C₂²×C₁₉	1	1	yes	characteristic, complemented
593	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic, complemented
594	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic, complemented
595	#407	C₂²×C₁₉	1	1	yes	characteristic, complemented
596	#394	—	2	2	no	—
597	#392	—	2	2	no	—
598	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
599	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
600	#382	C₂²×C₁₉	1	1	yes	characteristic, complemented
601	#343	C₂²×C₁₉	1	1	yes	characteristic, complemented
602	#343	C₂²×C₁₉	1	1	yes	characteristic, complemented
603	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
604	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
605	C₂×C₁₉	—	2	1	no	—
606	C₂×C₁₉	—	2	1	no	—
607	C₂×C₁₉	—	4	1	no	—
608	C₂×C₁₉	—	4	1	no	—
609	C₂×C₁₉	—	4	2	no	—
610	C₂×C₁₉	—	8	1	no	—
611	C₂×C₁₉	—	8	2	no	—
612	C₂×C₁₉	—	8	1	no	—
613	C₂×C₁₉	—	16	1	no	—
614	C₂×C₁₉	#2410	1	1	yes	characteristic
615	C₂×C₁₉	#3019	1	1	yes	characteristic
616	C₂×C₁₉	#3021	1	1	yes	characteristic
617	H(5,𝔽₂)	—	2	2	no	—
618	H(5,𝔽₂)	—	2	2	no	—
619	H(5,𝔽₂)	—	4	1	no	—
620	H(5,𝔽₂)	—	4	1	no	—
621	C₂×#41	—	2	1	no	—
622	C₂×#41	—	2	1	no	—
623	C₂×#41	—	2	1	no	—
624	C₂×#41	—	2	1	no	—
625	C₂×#41	—	2	2	no	—
626	C₂×#41	—	2	2	no	—
627	C₂×#41	—	4	1	no	—
628	C₂×#41	—	4	1	no	—
629	C₂×#41	D₄×C₁₉	1	1	yes	characteristic, complemented
630	C₂×#41	D₄×C₁₉	1	1	yes	characteristic, complemented
631	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
632	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
633	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
634	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
635	C₂²×D₄	—	2	1	no	—
636	C₂²×D₄	—	2	2	no	—
637	C₂²×D₄	—	2	2	no	—
638	C₂²×D₄	—	2	1	no	—
639	C₂²×D₄	—	2	1	no	—
640	C₂²×D₄	—	2	1	no	—
641	C₂²×D₄	—	2	2	no	—
642	C₂²×D₄	D₄×C₁₉	1	2	yes	—
643	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic, complemented
644	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
645	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
646	C₂³×C₄	—	2	1	no	—
647	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
648	AGL(1,ℤ/8)	—	2	2	no	—
649	AGL(1,ℤ/8)	—	2	2	no	—
650	AGL(1,ℤ/8)	—	2	2	no	—
651	AGL(1,ℤ/8)	—	4	1	no	—
652	AGL(1,ℤ/8)	—	4	1	no	—
653	AGL(1,ℤ/8)	—	4	1	no	—
654	C₂×SD₁₆	—	2	1	no	—
655	C₂×SD₁₆	—	2	1	no	—
656	C₂×SD₁₆	—	2	1	no	—
657	C₂×D₈	—	2	1	no	—
658	C₂×D₈	—	2	1	no	—
659	C₂×D₈	—	2	1	no	—
660	C₂×M₁₆	—	2	1	no	—
661	C₂×M₁₆	—	2	2	no	—
662	C₂×M₁₆	—	4	1	no	—
663	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
664	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
665	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
666	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
667	C₂²×C₈	—	2	1	no	—
668	#127	—	2	2	no	—
669	#127	—	2	1	no	—
670	#127	—	2	2	no	—
671	#127	—	4	1	no	—
672	#124	—	2	2	no	—
673	#124	—	2	1	no	—
674	#123	—	2	2	no	—
675	#123	—	2	1	no	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	—	2	1	no	—
678	C₂²⋊Q₈	—	2	1	no	—
679	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
680	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
681	#121	—	2	2	no	—
682	#121	—	2	2	no	—
683	#121	—	2	2	no	—
684	#121	—	2	2	no	—
685	#121	—	2	2	no	—
686	#121	—	2	1	no	—
687	#121	—	2	1	no	—
688	#121	—	2	1	no	—
689	#121	—	2	1	no	—
690	#121	—	2	1	no	—
691	#121	—	2	1	no	—
692	#121	—	2	2	no	—
693	#121	—	2	1	no	—
694	#121	—	2	1	no	—
695	#121	—	2	1	no	—
696	#121	—	2	1	no	—
697	#121	—	2	1	no	—
698	#121	—	2	1	no	—
699	#121	D₄×C₁₉	1	1	yes	characteristic, complemented
700	#121	D₄×C₁₉	1	1	yes	characteristic, complemented
701	#120	—	2	2	no	—
702	#120	—	2	2	no	—
703	#120	—	2	2	no	—
704	#120	—	2	1	no	—
705	#120	—	2	2	no	—
706	C₄×Q₈	—	2	1	no	—
707	C₄×D₄	—	2	2	no	—
708	C₄×D₄	—	2	2	no	—
709	C₄×D₄	—	2	1	no	—
710	C₄×D₄	—	2	2	no	—
711	C₄×D₄	—	2	1	no	—
712	C₄×D₄	—	2	1	no	—
713	#117	—	2	1	no	—
714	#117	—	2	2	no	—
715	#117	—	4	1	no	—
716	#117	C₂³×C₁₉	1	1	yes	characteristic
717	C₂×C₄⋊C₄	—	2	1	no	—
718	C₂×C₄⋊C₄	—	2	1	no	—
719	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
721	C₂×C₂²⋊C₄	—	2	2	no	—
722	C₂×C₂²⋊C₄	—	2	1	no	—
723	C₂×C₂²⋊C₄	—	2	1	no	—
724	C₂×C₂²⋊C₄	—	2	2	no	—
725	C₂×C₂²⋊C₄	—	2	2	no	—
726	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
727	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
728	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
729	#107	—	2	1	no	—
730	#106	—	2	1	no	—
731	#104	—	2	2	no	—
732	#104	—	2	2	no	—
733	#104	—	2	2	no	—
734	#104	—	2	2	no	—
735	#104	—	4	1	no	—
736	#104	D₄×C₁₉	1	4	yes	complemented
737	#103	—	2	1	no	—
738	#103	—	2	1	no	—
739	#103	—	2	1	no	—
740	#102	—	2	1	no	—
741	#102	—	2	1	no	—
742	#102	—	2	1	no	—
743	#102	—	2	1	no	—
744	#102	—	2	1	no	—
745	#100	—	2	2	no	—
746	#100	—	4	1	no	—
747	C₂²⋊C₈	—	2	1	no	—
748	C₂²⋊C₈	—	2	1	no	—
749	#95	—	2	2	no	—
750	C₁₉	#24468	1	1	yes	characteristic, direct product factor, Sylow
751	C₂⁴	—	2	2	no	—
752	C₂⁴	—	2	1	no	—
753	C₂⁴	—	2	1	no	—
754	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
755	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
756	#41	—	2	1	no	—
757	#41	—	2	1	no	—
758	#41	—	2	2	no	—
759	#41	—	2	2	no	—
760	#41	—	2	1	no	—
761	#41	—	2	1	no	—
762	#41	—	2	1	no	—
763	#41	—	2	1	no	—
764	#41	—	2	1	no	—
765	#41	—	2	1	no	—
766	#41	—	2	1	no	—
767	#41	—	2	1	no	—
768	#41	—	4	2	no	—
769	#41	—	4	2	no	—
770	#41	—	4	1	no	—
771	#41	—	4	1	no	—
772	#41	—	4	2	no	—
773	#41	—	4	2	no	—
774	#41	—	4	2	no	—
775	#41	—	4	2	no	—
776	#41	—	4	2	no	—
777	#41	—	4	2	no	—
778	#41	C₂×D₄×C₁₉	1	2	yes	—
779	#41	#41×C₁₉	1	2	yes	—
780	C₂×Q₈	—	2	1	no	—
781	C₂×Q₈	—	2	2	no	—
782	C₂×Q₈	—	4	1	no	—
783	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
784	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
785	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
786	C₂×D₄	—	2	1	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	2	no	—
791	C₂×D₄	—	2	1	no	—
792	C₂×D₄	—	2	1	no	—
793	C₂×D₄	—	2	1	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	1	no	—
802	C₂×D₄	—	2	1	no	—
803	C₂×D₄	—	2	1	no	—
804	C₂×D₄	—	2	1	no	—
805	C₂×D₄	—	2	1	no	—
806	C₂×D₄	—	2	1	no	—
807	C₂×D₄	—	2	1	no	—
808	C₂×D₄	—	2	1	no	—
809	C₂×D₄	—	2	1	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	1	no	—
813	C₂×D₄	—	2	1	no	—
814	C₂×D₄	—	4	1	no	—
815	C₂×D₄	—	4	2	no	—
816	C₂×D₄	—	4	2	no	—
817	C₂×D₄	—	4	4	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	—	4	2	no	—
820	C₂×D₄	—	4	4	no	—
821	C₂×D₄	—	4	4	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	—	4	2	no	—
824	C₂×D₄	—	4	1	no	—
825	C₂×D₄	—	4	1	no	—
826	C₂×D₄	—	8	2	no	—
827	C₂×D₄	—	8	2	no	—
828	C₂×D₄	—	8	2	no	—
829	C₂×D₄	—	8	2	no	—
830	C₂×D₄	—	8	4	no	—
831	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
832	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
833	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	1	no	—
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	2	1	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	2	1	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	2	1	no	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	4	2	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
852	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
853	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
854	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
855	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
856	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
858	SD₁₆	—	4	2	no	—
859	SD₁₆	—	4	2	no	—
860	SD₁₆	—	4	2	no	—
861	D₈	—	4	2	no	—
862	D₈	—	4	2	no	—
863	D₈	—	4	2	no	—
864	M₁₆	—	2	1	no	—
865	M₁₆	—	2	1	no	—
866	M₁₆	—	2	1	no	—
867	M₁₆	—	2	1	no	—
868	M₁₆	—	2	1	no	—
869	M₁₆	—	2	1	no	—
870	M₁₆	—	2	1	no	—
871	M₁₆	—	4	2	no	—
872	M₁₆	C₂×D₄×C₁₉	1	2	yes	complemented
873	C₂×C₈	—	2	1	no	—
874	C₂×C₈	—	2	1	no	—
875	C₂×C₈	—	2	1	no	—
876	C₂×C₈	—	2	1	no	—
877	C₂×C₈	—	4	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	1	no	—
881	C₄⋊C₄	—	2	1	no	—
882	C₄⋊C₄	—	2	1	no	—
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	4	2	no	—
887	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
888	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	1	no	—
895	C₂²⋊C₄	—	2	1	no	—
896	C₂²⋊C₄	—	2	1	no	—
897	C₂²⋊C₄	—	2	1	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	1	no	—
901	C₂²⋊C₄	—	4	2	no	—
902	C₂²⋊C₄	—	4	1	no	—
903	C₂²⋊C₄	—	4	1	no	—
904	C₂²⋊C₄	—	8	2	no	—
905	C₂²⋊C₄	—	8	2	no	—
906	C₄²	—	2	2	no	—
907	C₄²	—	2	1	no	—
908	C₄²	—	2	1	no	—
909	C₄²	—	2	1	no	—
910	C₄²	—	2	1	no	—
911	C₄²	C₂×D₄×C₁₉	1	2	yes	complemented
912	C₂³	—	2	1	no	—
913	C₂³	—	2	1	no	—
914	C₂³	—	2	1	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	4	1	no	—
921	C₂³	—	4	1	no	—
922	C₂³	—	4	2	no	—
923	C₂³	—	4	2	no	—
924	C₂³	—	4	4	no	—
925	C₂³	—	4	2	no	—
926	C₂³	—	4	2	no	—
927	C₂³	—	4	2	no	—
928	C₂³	—	4	2	no	—
929	C₂³	—	4	1	no	—
930	C₂³	—	4	1	no	—
931	C₂³	—	4	1	no	—
932	C₂³	—	8	1	no	—
933	C₂³	—	8	2	no	—
934	C₂³	—	8	2	no	—
935	C₂³	C₁₉×#120	1	1	yes	characteristic
936	C₂³	C₁₉×#120	1	1	yes	characteristic
937	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
938	Q₈	—	2	1	no	—
939	Q₈	—	2	1	no	—
940	Q₈	—	2	1	no	—
941	Q₈	—	2	1	no	—
942	Q₈	—	2	1	no	—
943	Q₈	—	4	2	no	—
944	Q₈	C₁₉×#121	1	2	yes	—
945	D₄	—	2	2	no	—
946	D₄	—	2	2	no	—
947	D₄	—	2	1	no	—
948	D₄	—	2	1	no	—
949	D₄	—	2	1	no	—
950	D₄	—	2	1	no	—
951	D₄	—	2	1	no	—
952	D₄	—	4	2	no	—
953	D₄	—	4	2	no	—
954	D₄	—	4	4	no	—
955	D₄	—	4	2	no	—
956	D₄	—	4	4	no	—
957	D₄	—	4	4	no	—
958	D₄	—	4	2	no	—
959	D₄	—	4	1	no	—
960	D₄	—	4	1	no	—
961	D₄	—	4	1	no	—
962	D₄	—	4	1	no	—
963	D₄	—	4	1	no	—
964	D₄	—	4	1	no	—
965	D₄	—	4	1	no	—
966	D₄	—	4	1	no	—
967	D₄	—	4	1	no	—
968	D₄	—	4	1	no	—
969	D₄	—	4	1	no	—
970	D₄	—	4	1	no	—
971	D₄	—	8	2	no	—
972	D₄	—	8	1	no	—
973	D₄	—	8	2	no	—
974	D₄	—	8	2	no	—
975	D₄	—	8	2	no	—
976	D₄	—	8	8	no	—
977	D₄	—	8	2	no	—
978	D₄	—	8	2	no	—
979	D₄	C₁₉×#121	1	2	yes	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	4	2	no	—
1000	C₂×C₄	—	4	2	no	—
1001	C₂×C₄	—	4	2	no	—
1002	C₂×C₄	—	4	4	no	—
1003	C₂×C₄	—	4	1	no	—
1004	C₂×C₄	—	4	1	no	—
1005	C₂×C₄	—	4	1	no	—
1006	C₂×C₄	—	4	1	no	—
1007	C₂×C₄	—	4	1	no	—
1008	C₂×C₄	—	4	1	no	—
1009	C₂×C₄	—	4	2	no	—
1010	C₂×C₄	—	4	1	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	4	1	no	—
1014	C₂×C₄	—	4	1	no	—
1015	C₂×C₄	—	8	2	no	—
1016	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
1017	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
1018	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1019	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1020	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1021	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
1022	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1023	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1024	C₈	—	2	2	no	—
1025	C₈	—	4	1	no	—
1026	C₈	—	4	1	no	—
1027	C₈	—	4	1	no	—
1028	C₂²	—	2	1	no	—
1029	C₂²	—	2	1	no	—
1030	C₂²	—	2	1	no	—
1031	C₂²	—	2	1	no	—
1032	C₂²	—	2	2	no	—
1033	C₂²	—	2	1	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	4	1	no	—
1038	C₂²	—	4	1	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	2	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	—	4	1	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	8	1	no	—
1049	C₂²	—	8	1	no	—
1050	C₂²	—	8	2	no	—
1051	C₂²	—	8	2	no	—
1052	C₂²	—	8	2	no	—
1053	C₂²	—	8	2	no	—
1054	C₂²	—	8	4	no	—
1055	C₂²	—	8	1	no	—
1056	C₂²	—	8	1	no	—
1057	C₂²	—	8	1	no	—
1058	C₂²	—	16	4	no	—
1059	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
1060	C₂²	D₄²×C₁₉	1	1	yes	characteristic
1061	C₂²	C₁₉×#546	1	1	yes	characteristic
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	1	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	8	1	no	—
1072	C₄	—	8	1	no	—
1073	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
1074	C₄	C₁₉×#534	1	1	yes	characteristic
1075	C₄	D₄²×C₁₉	1	1	yes	characteristic
1076	C₄	C₁₉×#546	1	1	yes	characteristic
1077	C₂	—	2	1	no	—
1078	C₂	—	2	1	no	—
1079	C₂	—	4	1	no	—
1080	C₂	—	4	1	no	—
1081	C₂	—	4	2	no	—
1082	C₂	—	8	1	no	—
1083	C₂	—	8	2	no	—
1084	C₂	—	8	1	no	—
1085	C₂	—	16	1	no	—
1086	C₂	C₁₉×#2410	1	1	yes	characteristic
1087	C₂	C₁₉×#3019	1	1	yes	characteristic
1088	C₂	C₁₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3488	C₂	semidirect
2. C₁₉×#3055	C₂	semidirect
3. C₂×C₁₉×#453	C₂	semidirect
4. C₁₉×#3006	C₂	semidirect
5. C₂×C₁₉×#421	C₂	semidirect
6. C₁₉×#2619	C₂	semidirect
7. C₁₉×#2040	C₂	semidirect
8. C₁₉×#2037	C₂	semidirect
9. C₁₉×#2006	C₂	semidirect
10. C₁₉×#2002	C₂	semidirect
11. C₁₉×#1900	C₂	semidirect
12. C₁₉×#1897	C₂	semidirect
13. C₁₉×#1883	C₂	semidirect
14. C₁₉×#1860	C₂	semidirect
15. C₁₉×#1792	C₂	semidirect
19. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂²×M₁₆×C₁₉	C₂²	semidirect
32. C₂×C₁₉×#127	C₂²	semidirect
37. C₂×C₁₉×#121	C₂²	semidirect
39. C₂×C₁₉×#117	C₂²	semidirect
49. C₁₉×#428	C₂²	semidirect
53. C₂×C₁₉×#104	C₂²	semidirect
54. C₂×C₁₉×#104	C₂²	semidirect
55. C₂×C₁₉×#104	C₂²	semidirect
56. C₂×C₁₉×#104	C₂²	semidirect
57. C₁₉×#418	C₂²	semidirect
59. C₁₉×#417	C₂²	semidirect
60. C₁₉×#417	C₂²	semidirect
61. C₂×C₁₉×#100	C₂²	semidirect
62. C₂×C₁₉×#100	C₂²	semidirect
63. C₁₉×#407	C₂²	semidirect
66. C₁₉×#390	C₂²	semidirect
67. C₁₉×#390	C₂²	semidirect
68. C₁₉×#382	C₂²	semidirect
69. C₁₉×#343	C₂²	semidirect
70. C₁₉×#343	C₂²	semidirect
71. C₁₉×#339	C₂²	semidirect
72. C₁₉×#339	C₂²	semidirect
85. C₂×#41×C₁₉	D₄	semidirect
86. C₂×#41×C₁₉	D₄	semidirect
90. C₂²×Q₈×C₁₉	D₄	semidirect
99. C₂²×D₄×C₁₉	D₄	semidirect
135. C₁₉×C₂²⋊Q₈	D₄	semidirect
136. C₁₉×C₂²⋊Q₈	D₄	semidirect
155. C₁₉×#121	D₄	semidirect
156. C₁₉×#121	D₄	semidirect
192. C₁₉×#104	D₄	semidirect
327. M₁₆×C₁₉	C₂×D₄	semidirect
366. C₄²×C₁₉	C₂×D₄	semidirect
367. #24468	C₁₉	direct (N × H)
484. #3488	C₂×C₁₉	semidirect
485. #3055	C₂×C₁₉	semidirect
486. C₂×#453	C₂×C₁₉	semidirect
487. #3006	C₂×C₁₉	semidirect
488. C₂×#421	C₂×C₁₉	semidirect
489. #2619	C₂×C₁₉	semidirect
490. #2040	C₂×C₁₉	semidirect
491. #2037	C₂×C₁₉	semidirect
492. #2006	C₂×C₁₉	semidirect
493. #2002	C₂×C₁₉	semidirect
494. #1900	C₂×C₁₉	semidirect
495. #1897	C₂×C₁₉	semidirect
496. #1883	C₂×C₁₉	semidirect
497. #1860	C₂×C₁₉	semidirect
498. #1792	C₂×C₁₉	semidirect
551. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
552. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
553. C₂²×M₁₆	C₂²×C₁₉	semidirect
564. C₂×#127	C₂²×C₁₉	semidirect
569. C₂×#121	C₂²×C₁₉	semidirect
571. C₂×#117	C₂²×C₁₉	semidirect
581. #428	C₂²×C₁₉	semidirect
585. C₂×#104	C₂²×C₁₉	semidirect
586. C₂×#104	C₂²×C₁₉	semidirect
587. C₂×#104	C₂²×C₁₉	semidirect
588. C₂×#104	C₂²×C₁₉	semidirect
589. #418	C₂²×C₁₉	semidirect
591. #417	C₂²×C₁₉	semidirect
592. #417	C₂²×C₁₉	semidirect
593. C₂×#100	C₂²×C₁₉	semidirect
594. C₂×#100	C₂²×C₁₉	semidirect
595. #407	C₂²×C₁₉	semidirect
598. #390	C₂²×C₁₉	semidirect
599. #390	C₂²×C₁₉	semidirect
600. #382	C₂²×C₁₉	semidirect
601. #343	C₂²×C₁₉	semidirect
602. #343	C₂²×C₁₉	semidirect
603. #339	C₂²×C₁₉	semidirect
604. #339	C₂²×C₁₉	semidirect
629. C₂×#41	D₄×C₁₉	semidirect
630. C₂×#41	D₄×C₁₉	semidirect
634. C₂²×Q₈	D₄×C₁₉	semidirect
643. C₂²×D₄	D₄×C₁₉	semidirect
679. C₂²⋊Q₈	D₄×C₁₉	semidirect
680. C₂²⋊Q₈	D₄×C₁₉	semidirect
699. #121	D₄×C₁₉	semidirect
700. #121	D₄×C₁₉	semidirect
736. #104	D₄×C₁₉	semidirect
750. C₁₉	#24468	direct (N × H)
872. M₁₆	C₂×D₄×C₁₉	semidirect
911. C₄²	C₂×D₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3488	2
C₁₉×#3055	2
C₂×C₁₉×#453	2
C₁₉×#3006	2
C₂×C₁₉×#421	2
C₁₉×#2619	2
C₁₉×#2040	2
C₁₉×#2037	2
C₁₉×#2006	2
C₁₉×#2002	2
C₁₉×#1900	2
C₁₉×#1897	2
C₁₉×#1883	2
C₁₉×#1860	2
C₁₉×#1792	2
#24468	19

Subgroups — C19×#24468 #18030427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24468 #18030427