Subgroups — C₁₉×#24464 #18030423

Order 4864.

1600 conjugacy classes of subgroups.

The subgroup lattice has 1100 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	C₂²×C₁₉×#104	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2856	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2039	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×#1896	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1883	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1859	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	—	2	2	no	—
37	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#520	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#469	—	2	1	no	—
42	C₁₉×#468	—	2	1	no	—
43	C₁₉×#466	—	2	1	no	—
44	C₁₉×#465	—	2	1	no	—
45	C₁₉×#453	—	2	4	no	—
46	C₁₉×#449	—	2	1	no	—
47	C₁₉×#449	—	2	1	no	—
48	C₁₉×#448	—	2	1	no	—
49	C₁₉×#447	—	2	1	no	—
50	C₁₉×#428	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₁₉×#104	—	2	4	no	—
52	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
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	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#418	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#417	C₂²	1	1	yes	characteristic
60	C₁₉×#417	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#417	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#407	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#390	—	2	2	no	—
66	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#384	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	2	no	—
97	C₂²×D₄×C₁₉	—	2	1	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	—	2	1	no	—
104	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
106	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
107	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
108	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
109	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
110	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
111	C₂×SD₁₆×C₁₉	—	2	1	no	—
112	C₂×SD₁₆×C₁₉	—	2	1	no	—
113	C₂×SD₁₆×C₁₉	—	2	1	no	—
114	C₂×D₈×C₁₉	—	2	1	no	—
115	C₂×D₈×C₁₉	—	2	1	no	—
116	C₂×D₈×C₁₉	—	2	1	no	—
117	C₂×M₁₆×C₁₉	—	2	1	no	—
118	C₂×M₁₆×C₁₉	—	2	2	no	—
119	C₂×M₁₆×C₁₉	—	4	1	no	—
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	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₁₉	—	2	1	no	—
125	C₁₉×#127	—	2	2	no	—
126	C₁₉×#127	—	2	1	no	—
127	C₁₉×#127	—	2	2	no	—
128	C₁₉×#127	—	4	1	no	—
129	C₁₉×#124	—	2	2	no	—
130	C₁₉×#124	—	2	1	no	—
131	C₁₉×#123	—	2	2	no	—
132	C₁₉×#123	—	2	1	no	—
133	C₁₉×C₂²⋊Q₈	—	2	2	no	—
134	C₁₉×C₂²⋊Q₈	—	2	1	no	—
135	C₁₉×C₂²⋊Q₈	—	2	1	no	—
136	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
137	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
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	2	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	1	no	—
149	C₁₉×#121	—	2	2	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	—	2	1	no	—
156	C₁₉×#121	—	4	8	no	—
157	C₁₉×#121	D₄	1	1	yes	characteristic, complemented
158	C₁₉×#121	D₄	1	1	yes	characteristic, complemented
159	C₁₉×#120	—	2	2	no	—
160	C₁₉×#120	—	2	2	no	—
161	C₁₉×#120	—	2	2	no	—
162	C₁₉×#120	—	2	1	no	—
163	C₁₉×#120	—	2	2	no	—
164	C₄×Q₈×C₁₉	—	2	1	no	—
165	C₄×D₄×C₁₉	—	2	2	no	—
166	C₄×D₄×C₁₉	—	2	2	no	—
167	C₄×D₄×C₁₉	—	2	1	no	—
168	C₄×D₄×C₁₉	—	2	2	no	—
169	C₄×D₄×C₁₉	—	2	1	no	—
170	C₄×D₄×C₁₉	—	2	1	no	—
171	C₁₉×#117	—	2	1	no	—
172	C₁₉×#117	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₂×C₄⋊C₄×C₁₉	—	2	2	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	2	no	—
179	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
180	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
181	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
182	C₂×C₄²×C₁₉	—	2	2	no	—
183	C₂×C₄²×C₁₉	—	2	1	no	—
184	C₂×C₄²×C₁₉	—	4	1	no	—
185	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
187	C₁₉×#107	—	2	1	no	—
188	C₁₉×#106	—	2	1	no	—
189	C₁₉×#104	—	2	2	no	—
190	C₁₉×#104	—	2	2	no	—
191	C₁₉×#104	—	2	2	no	—
192	C₁₉×#104	—	2	2	no	—
193	C₁₉×#104	—	4	1	no	—
194	C₁₉×#104	D₄	1	4	yes	complemented
195	C₁₉×#103	—	2	1	no	—
196	C₁₉×#103	—	2	1	no	—
197	C₁₉×#103	—	2	1	no	—
198	C₁₉×#102	—	2	1	no	—
199	C₁₉×#102	—	2	1	no	—
200	C₁₉×#102	—	2	1	no	—
201	C₁₉×#102	—	2	1	no	—
202	C₁₉×#102	—	2	1	no	—
203	C₁₉×#100	—	2	2	no	—
204	C₁₉×#100	—	4	1	no	—
205	C₁₉×C₂²⋊C₈	—	2	1	no	—
206	C₁₉×C₂²⋊C₈	—	2	1	no	—
207	C₂⁴×C₁₉	—	2	2	no	—
208	C₂⁴×C₁₉	—	2	1	no	—
209	C₂⁴×C₁₉	—	2	1	no	—
210	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
212	#41×C₁₉	—	2	1	no	—
213	#41×C₁₉	—	2	1	no	—
214	#41×C₁₉	—	2	2	no	—
215	#41×C₁₉	—	2	2	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	—	2	1	no	—
224	#41×C₁₉	—	4	2	no	—
225	#41×C₁₉	—	4	2	no	—
226	#41×C₁₉	—	4	1	no	—
227	#41×C₁₉	—	4	1	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	—	4	2	no	—
234	#41×C₁₉	C₂×D₄	1	2	yes	—
235	#41×C₁₉	#41	1	2	yes	—
236	C₂×Q₈×C₁₉	—	2	1	no	—
237	C₂×Q₈×C₁₉	—	2	2	no	—
238	C₂×Q₈×C₁₉	—	4	1	no	—
239	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
242	C₂×D₄×C₁₉	—	2	1	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	2	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	1	no	—
252	C₂×D₄×C₁₉	—	2	2	no	—
253	C₂×D₄×C₁₉	—	2	2	no	—
254	C₂×D₄×C₁₉	—	2	2	no	—
255	C₂×D₄×C₁₉	—	2	1	no	—
256	C₂×D₄×C₁₉	—	2	2	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	—	2	1	no	—
270	C₂×D₄×C₁₉	—	4	1	no	—
271	C₂×D₄×C₁₉	—	4	2	no	—
272	C₂×D₄×C₁₉	—	4	2	no	—
273	C₂×D₄×C₁₉	—	4	4	no	—
274	C₂×D₄×C₁₉	—	4	4	no	—
275	C₂×D₄×C₁₉	—	4	4	no	—
276	C₂×D₄×C₁₉	—	4	2	no	—
277	C₂×D₄×C₁₉	—	4	2	no	—
278	C₂×D₄×C₁₉	—	4	4	no	—
279	C₂×D₄×C₁₉	—	4	4	no	—
280	C₂×D₄×C₁₉	—	4	2	no	—
281	C₂×D₄×C₁₉	—	4	2	no	—
282	C₂×D₄×C₁₉	—	4	4	no	—
283	C₂×D₄×C₁₉	—	4	4	no	—
284	C₂×D₄×C₁₉	—	4	1	no	—
285	C₂×D₄×C₁₉	—	4	1	no	—
286	C₂×D₄×C₁₉	—	8	4	no	—
287	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
288	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
289	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	1	no	—
295	C₂²×C₄×C₁₉	—	2	1	no	—
296	C₂²×C₄×C₁₉	—	2	2	no	—
297	C₂²×C₄×C₁₉	—	2	4	no	—
298	C₂²×C₄×C₁₉	—	2	1	no	—
299	C₂²×C₄×C₁₉	—	2	1	no	—
300	C₂²×C₄×C₁₉	—	2	2	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	—	2	1	no	—
305	C₂²×C₄×C₁₉	—	2	1	no	—
306	C₂²×C₄×C₁₉	—	4	2	no	—
307	C₂²×C₄×C₁₉	—	4	2	no	—
308	C₂²×C₄×C₁₉	—	4	2	no	—
309	C₂²×C₄×C₁₉	—	4	2	no	—
310	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
316	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
317	SD₁₆×C₁₉	—	4	2	no	—
318	SD₁₆×C₁₉	—	4	2	no	—
319	SD₁₆×C₁₉	—	4	2	no	—
320	D₈×C₁₉	—	4	2	no	—
321	D₈×C₁₉	—	4	2	no	—
322	D₈×C₁₉	—	4	2	no	—
323	M₁₆×C₁₉	—	2	1	no	—
324	M₁₆×C₁₉	—	2	1	no	—
325	M₁₆×C₁₉	—	2	1	no	—
326	M₁₆×C₁₉	—	2	1	no	—
327	M₁₆×C₁₉	—	2	1	no	—
328	M₁₆×C₁₉	—	2	1	no	—
329	M₁₆×C₁₉	—	2	1	no	—
330	M₁₆×C₁₉	—	4	2	no	—
331	M₁₆×C₁₉	C₂×D₄	1	2	yes	complemented
332	C₂×C₈×C₁₉	—	2	1	no	—
333	C₂×C₈×C₁₉	—	2	1	no	—
334	C₂×C₈×C₁₉	—	2	1	no	—
335	C₂×C₈×C₁₉	—	2	1	no	—
336	C₂×C₈×C₁₉	—	4	2	no	—
337	C₄⋊C₄×C₁₉	—	2	2	no	—
338	C₄⋊C₄×C₁₉	—	2	2	no	—
339	C₄⋊C₄×C₁₉	—	2	1	no	—
340	C₄⋊C₄×C₁₉	—	2	1	no	—
341	C₄⋊C₄×C₁₉	—	2	1	no	—
342	C₄⋊C₄×C₁₉	—	2	1	no	—
343	C₄⋊C₄×C₁₉	—	2	1	no	—
344	C₄⋊C₄×C₁₉	—	2	1	no	—
345	C₄⋊C₄×C₁₉	—	4	4	no	—
346	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
347	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
348	C₂²⋊C₄×C₁₉	—	2	2	no	—
349	C₂²⋊C₄×C₁₉	—	2	2	no	—
350	C₂²⋊C₄×C₁₉	—	2	2	no	—
351	C₂²⋊C₄×C₁₉	—	2	2	no	—
352	C₂²⋊C₄×C₁₉	—	2	2	no	—
353	C₂²⋊C₄×C₁₉	—	2	1	no	—
354	C₂²⋊C₄×C₁₉	—	2	1	no	—
355	C₂²⋊C₄×C₁₉	—	2	1	no	—
356	C₂²⋊C₄×C₁₉	—	2	1	no	—
357	C₂²⋊C₄×C₁₉	—	2	2	no	—
358	C₂²⋊C₄×C₁₉	—	2	2	no	—
359	C₂²⋊C₄×C₁₉	—	2	1	no	—
360	C₂²⋊C₄×C₁₉	—	4	4	no	—
361	C₂²⋊C₄×C₁₉	—	4	4	no	—
362	C₂²⋊C₄×C₁₉	—	4	1	no	—
363	C₂²⋊C₄×C₁₉	—	4	1	no	—
364	C₄²×C₁₉	—	2	2	no	—
365	C₄²×C₁₉	—	2	1	no	—
366	C₄²×C₁₉	—	2	1	no	—
367	C₄²×C₁₉	—	2	1	no	—
368	C₄²×C₁₉	—	2	1	no	—
369	C₄²×C₁₉	—	4	2	no	—
370	C₄²×C₁₉	C₂×D₄	1	2	yes	complemented
371	#24464	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
372	C₂³×C₁₉	—	2	1	no	—
373	C₂³×C₁₉	—	2	1	no	—
374	C₂³×C₁₉	—	2	1	no	—
375	C₂³×C₁₉	—	2	2	no	—
376	C₂³×C₁₉	—	2	2	no	—
377	C₂³×C₁₉	—	2	1	no	—
378	C₂³×C₁₉	—	2	1	no	—
379	C₂³×C₁₉	—	2	2	no	—
380	C₂³×C₁₉	—	2	2	no	—
381	C₂³×C₁₉	—	4	1	no	—
382	C₂³×C₁₉	—	4	2	no	—
383	C₂³×C₁₉	—	4	4	no	—
384	C₂³×C₁₉	—	4	2	no	—
385	C₂³×C₁₉	—	4	2	no	—
386	C₂³×C₁₉	—	4	2	no	—
387	C₂³×C₁₉	—	4	2	no	—
388	C₂³×C₁₉	—	4	2	no	—
389	C₂³×C₁₉	—	4	1	no	—
390	C₂³×C₁₉	—	4	1	no	—
391	C₂³×C₁₉	—	4	1	no	—
392	C₂³×C₁₉	—	8	1	no	—
393	C₂³×C₁₉	—	8	2	no	—
394	C₂³×C₁₉	—	8	2	no	—
395	C₂³×C₁₉	#120	1	1	yes	characteristic
396	C₂³×C₁₉	#120	1	1	yes	characteristic
397	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
398	Q₈×C₁₉	—	2	1	no	—
399	Q₈×C₁₉	—	2	1	no	—
400	Q₈×C₁₉	—	2	1	no	—
401	Q₈×C₁₉	—	2	1	no	—
402	Q₈×C₁₉	—	2	1	no	—
403	Q₈×C₁₉	—	4	2	no	—
404	Q₈×C₁₉	#121	1	2	yes	complemented
405	D₄×C₁₉	—	2	2	no	—
406	D₄×C₁₉	—	2	2	no	—
407	D₄×C₁₉	—	2	1	no	—
408	D₄×C₁₉	—	2	1	no	—
409	D₄×C₁₉	—	2	1	no	—
410	D₄×C₁₉	—	2	1	no	—
411	D₄×C₁₉	—	2	1	no	—
412	D₄×C₁₉	—	4	2	no	—
413	D₄×C₁₉	—	4	2	no	—
414	D₄×C₁₉	—	4	4	no	—
415	D₄×C₁₉	—	4	2	no	—
416	D₄×C₁₉	—	4	4	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	4	no	—
422	D₄×C₁₉	—	4	2	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	—	4	1	no	—
428	D₄×C₁₉	—	4	1	no	—
429	D₄×C₁₉	—	4	1	no	—
430	D₄×C₁₉	—	4	1	no	—
431	D₄×C₁₉	—	8	8	no	—
432	D₄×C₁₉	—	8	1	no	—
433	D₄×C₁₉	—	8	2	no	—
434	D₄×C₁₉	—	8	2	no	—
435	D₄×C₁₉	—	8	2	no	—
436	D₄×C₁₉	—	8	2	no	—
437	D₄×C₁₉	—	8	2	no	—
438	D₄×C₁₉	—	8	2	no	—
439	D₄×C₁₉	#121	1	2	yes	complemented
440	C₂×C₄×C₁₉	—	2	2	no	—
441	C₂×C₄×C₁₉	—	2	2	no	—
442	C₂×C₄×C₁₉	—	2	1	no	—
443	C₂×C₄×C₁₉	—	2	2	no	—
444	C₂×C₄×C₁₉	—	2	1	no	—
445	C₂×C₄×C₁₉	—	2	1	no	—
446	C₂×C₄×C₁₉	—	2	1	no	—
447	C₂×C₄×C₁₉	—	2	1	no	—
448	C₂×C₄×C₁₉	—	2	1	no	—
449	C₂×C₄×C₁₉	—	2	1	no	—
450	C₂×C₄×C₁₉	—	2	1	no	—
451	C₂×C₄×C₁₉	—	2	1	no	—
452	C₂×C₄×C₁₉	—	2	2	no	—
453	C₂×C₄×C₁₉	—	2	1	no	—
454	C₂×C₄×C₁₉	—	2	1	no	—
455	C₂×C₄×C₁₉	—	2	2	no	—
456	C₂×C₄×C₁₉	—	2	2	no	—
457	C₂×C₄×C₁₉	—	2	1	no	—
458	C₂×C₄×C₁₉	—	2	2	no	—
459	C₂×C₄×C₁₉	—	2	1	no	—
460	C₂×C₄×C₁₉	—	2	1	no	—
461	C₂×C₄×C₁₉	—	2	1	no	—
462	C₂×C₄×C₁₉	—	4	2	no	—
463	C₂×C₄×C₁₉	—	4	2	no	—
464	C₂×C₄×C₁₉	—	4	2	no	—
465	C₂×C₄×C₁₉	—	4	8	no	—
466	C₂×C₄×C₁₉	—	4	4	no	—
467	C₂×C₄×C₁₉	—	4	1	no	—
468	C₂×C₄×C₁₉	—	4	1	no	—
469	C₂×C₄×C₁₉	—	4	1	no	—
470	C₂×C₄×C₁₉	—	4	1	no	—
471	C₂×C₄×C₁₉	—	4	1	no	—
472	C₂×C₄×C₁₉	—	4	1	no	—
473	C₂×C₄×C₁₉	—	4	2	no	—
474	C₂×C₄×C₁₉	—	4	2	no	—
475	C₂×C₄×C₁₉	—	4	1	no	—
476	C₂×C₄×C₁₉	—	8	2	no	—
477	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
478	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
479	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
483	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
484	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
485	C₈×C₁₉	—	2	2	no	—
486	C₈×C₁₉	—	4	1	no	—
487	C₈×C₁₉	—	4	1	no	—
488	C₈×C₁₉	—	4	1	no	—
489	#3488	C₂×C₁₉	1	1	yes	characteristic, complemented
490	#3055	C₂×C₁₉	1	1	yes	characteristic, complemented
491	C₂×#453	C₂×C₁₉	1	1	yes	characteristic, complemented
492	#3006	C₂×C₁₉	1	1	yes	characteristic, complemented
493	C₂²×#104	C₂×C₁₉	1	1	yes	characteristic, complemented
494	#2856	C₂×C₁₉	1	1	yes	characteristic, complemented
495	#2039	C₂×C₁₉	1	1	yes	characteristic, complemented
496	#2037	C₂×C₁₉	1	1	yes	characteristic, complemented
497	#2006	C₂×C₁₉	1	1	yes	characteristic, complemented
498	#2002	C₂×C₁₉	1	1	yes	characteristic, complemented
499	#1900	C₂×C₁₉	1	1	yes	characteristic, complemented
500	#1896	C₂×C₁₉	1	1	yes	characteristic, complemented
501	#1883	C₂×C₁₉	1	1	yes	characteristic, complemented
502	#1859	C₂×C₁₉	1	1	yes	characteristic, complemented
503	#1792	C₂×C₁₉	1	1	yes	characteristic, complemented
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	—	2	1	no	—
509	C₂²×C₁₉	—	2	2	no	—
510	C₂²×C₁₉	—	2	1	no	—
511	C₂²×C₁₉	—	2	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	1	no	—
518	C₂²×C₁₉	—	4	2	no	—
519	C₂²×C₁₉	—	4	2	no	—
520	C₂²×C₁₉	—	4	1	no	—
521	C₂²×C₁₉	—	4	1	no	—
522	C₂²×C₁₉	—	4	1	no	—
523	C₂²×C₁₉	—	4	2	no	—
524	C₂²×C₁₉	—	4	1	no	—
525	C₂²×C₁₉	—	8	4	no	—
526	C₂²×C₁₉	—	8	2	no	—
527	C₂²×C₁₉	—	8	2	no	—
528	C₂²×C₁₉	—	8	2	no	—
529	C₂²×C₁₉	—	8	2	no	—
530	C₂²×C₁₉	—	8	1	no	—
531	C₂²×C₁₉	—	8	1	no	—
532	C₂²×C₁₉	—	8	1	no	—
533	C₂²×C₁₉	—	16	4	no	—
534	C₂²×C₁₉	#453	1	2	yes	complemented
535	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
536	C₂²×C₁₉	D₄²	1	1	yes	characteristic
537	C₂²×C₁₉	#546	1	1	yes	characteristic
538	C₄×C₁₉	—	2	4	no	—
539	C₄×C₁₉	—	2	1	no	—
540	C₄×C₁₉	—	2	1	no	—
541	C₄×C₁₉	—	2	2	no	—
542	C₄×C₁₉	—	4	2	no	—
543	C₄×C₁₉	—	4	1	no	—
544	C₄×C₁₉	—	4	1	no	—
545	C₄×C₁₉	—	4	2	no	—
546	C₄×C₁₉	—	4	1	no	—
547	C₄×C₁₉	—	4	1	no	—
548	C₄×C₁₉	—	8	1	no	—
549	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
550	C₄×C₁₉	#534	1	1	yes	characteristic
551	C₄×C₁₉	D₄²	1	1	yes	characteristic
552	C₄×C₁₉	#546	1	1	yes	characteristic
553	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
554	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
555	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
556	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic, complemented
557	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic, complemented
558	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
559	#550	—	2	1	no	—
560	#548	—	2	1	no	—
561	#546	—	2	1	no	—
562	#546	—	2	2	no	—
563	D₄²	—	2	2	no	—
564	D₄²	—	2	1	no	—
565	#537	—	2	1	no	—
566	#537	C₂²×C₁₉	1	1	yes	characteristic
567	#535	—	2	1	no	—
568	#535	C₂²×C₁₉	1	1	yes	characteristic
569	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic, complemented
570	#525	—	2	1	no	—
571	#525	C₂²×C₁₉	1	1	yes	characteristic
572	C₂×#121	—	2	1	no	—
573	C₂×#121	—	2	2	no	—
574	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
575	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic, complemented
576	#520	C₂²×C₁₉	1	1	yes	characteristic
577	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
578	#469	—	2	1	no	—
579	#468	—	2	1	no	—
580	#466	—	2	1	no	—
581	#465	—	2	1	no	—
582	#453	—	2	4	no	—
583	#449	—	2	1	no	—
584	#449	—	2	1	no	—
585	#448	—	2	1	no	—
586	#447	—	2	1	no	—
587	#428	C₂²×C₁₉	1	1	yes	characteristic, complemented
588	C₂×#104	—	2	4	no	—
589	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
590	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
591	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
592	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
593	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
594	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
595	#418	C₂²×C₁₉	1	1	yes	characteristic, complemented
596	#417	C₂²×C₁₉	1	1	yes	characteristic
597	#417	C₂²×C₁₉	1	1	yes	characteristic, complemented
598	#417	C₂²×C₁₉	1	1	yes	characteristic, complemented
599	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic, complemented
600	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic, complemented
601	#407	C₂²×C₁₉	1	1	yes	characteristic, complemented
602	#390	—	2	2	no	—
603	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
604	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
605	#384	C₂²×C₁₉	1	1	yes	characteristic, complemented
606	#343	C₂²×C₁₉	1	1	yes	characteristic, complemented
607	#343	C₂²×C₁₉	1	1	yes	characteristic, complemented
608	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
609	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
610	C₂×C₁₉	—	2	1	no	—
611	C₂×C₁₉	—	2	1	no	—
612	C₂×C₁₉	—	2	2	no	—
613	C₂×C₁₉	—	4	1	no	—
614	C₂×C₁₉	—	4	2	no	—
615	C₂×C₁₉	—	8	1	no	—
616	C₂×C₁₉	—	8	2	no	—
617	C₂×C₁₉	—	8	1	no	—
618	C₂×C₁₉	—	16	1	no	—
619	C₂×C₁₉	#2410	1	1	yes	characteristic
620	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
621	C₂×C₁₉	#3018	1	1	yes	characteristic
622	H(5,𝔽₂)	—	2	2	no	—
623	H(5,𝔽₂)	—	2	2	no	—
624	H(5,𝔽₂)	—	4	1	no	—
625	H(5,𝔽₂)	—	4	1	no	—
626	C₂×#41	—	2	1	no	—
627	C₂×#41	—	2	1	no	—
628	C₂×#41	—	2	1	no	—
629	C₂×#41	—	2	1	no	—
630	C₂×#41	—	2	2	no	—
631	C₂×#41	—	2	2	no	—
632	C₂×#41	—	4	1	no	—
633	C₂×#41	—	4	1	no	—
634	C₂×#41	D₄×C₁₉	1	1	yes	characteristic, complemented
635	C₂×#41	D₄×C₁₉	1	1	yes	characteristic, complemented
636	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
637	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
638	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
639	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
640	C₂²×D₄	—	2	1	no	—
641	C₂²×D₄	—	2	2	no	—
642	C₂²×D₄	—	2	2	no	—
643	C₂²×D₄	—	2	1	no	—
644	C₂²×D₄	—	2	1	no	—
645	C₂²×D₄	—	2	1	no	—
646	C₂²×D₄	—	2	2	no	—
647	C₂²×D₄	D₄×C₁₉	1	2	yes	—
648	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic, complemented
649	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
650	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
651	C₂³×C₄	—	2	1	no	—
652	C₂³×C₄	—	2	1	no	—
653	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
654	AGL(1,ℤ/8)	—	2	2	no	—
655	AGL(1,ℤ/8)	—	2	2	no	—
656	AGL(1,ℤ/8)	—	2	2	no	—
657	AGL(1,ℤ/8)	—	4	1	no	—
658	AGL(1,ℤ/8)	—	4	1	no	—
659	AGL(1,ℤ/8)	—	4	1	no	—
660	C₂×SD₁₆	—	2	1	no	—
661	C₂×SD₁₆	—	2	1	no	—
662	C₂×SD₁₆	—	2	1	no	—
663	C₂×D₈	—	2	1	no	—
664	C₂×D₈	—	2	1	no	—
665	C₂×D₈	—	2	1	no	—
666	C₂×M₁₆	—	2	1	no	—
667	C₂×M₁₆	—	2	2	no	—
668	C₂×M₁₆	—	4	1	no	—
669	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
670	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
671	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
672	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
673	C₂²×C₈	—	2	1	no	—
674	#127	—	2	2	no	—
675	#127	—	2	1	no	—
676	#127	—	2	2	no	—
677	#127	—	4	1	no	—
678	#124	—	2	2	no	—
679	#124	—	2	1	no	—
680	#123	—	2	2	no	—
681	#123	—	2	1	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	1	no	—
684	C₂²⋊Q₈	—	2	1	no	—
685	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
686	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
687	#121	—	2	2	no	—
688	#121	—	2	2	no	—
689	#121	—	2	2	no	—
690	#121	—	2	2	no	—
691	#121	—	2	2	no	—
692	#121	—	2	1	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	2	no	—
699	#121	—	2	1	no	—
700	#121	—	2	1	no	—
701	#121	—	2	1	no	—
702	#121	—	2	1	no	—
703	#121	—	2	1	no	—
704	#121	—	2	1	no	—
705	#121	—	4	8	no	—
706	#121	D₄×C₁₉	1	1	yes	characteristic, complemented
707	#121	D₄×C₁₉	1	1	yes	characteristic, complemented
708	#120	—	2	2	no	—
709	#120	—	2	2	no	—
710	#120	—	2	2	no	—
711	#120	—	2	1	no	—
712	#120	—	2	2	no	—
713	C₄×Q₈	—	2	1	no	—
714	C₄×D₄	—	2	2	no	—
715	C₄×D₄	—	2	2	no	—
716	C₄×D₄	—	2	1	no	—
717	C₄×D₄	—	2	2	no	—
718	C₄×D₄	—	2	1	no	—
719	C₄×D₄	—	2	1	no	—
720	#117	—	2	1	no	—
721	#117	C₂³×C₁₉	1	1	yes	characteristic
722	C₂×C₄⋊C₄	—	2	1	no	—
723	C₂×C₄⋊C₄	—	2	2	no	—
724	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
725	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	—	2	2	no	—
727	C₂×C₂²⋊C₄	—	2	2	no	—
728	C₂×C₂²⋊C₄	—	2	2	no	—
729	C₂×C₂²⋊C₄	—	2	1	no	—
730	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
731	C₂×C₄²	—	2	2	no	—
732	C₂×C₄²	—	2	1	no	—
733	C₂×C₄²	—	4	1	no	—
734	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
735	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
736	#107	—	2	1	no	—
737	#106	—	2	1	no	—
738	#104	—	2	2	no	—
739	#104	—	2	2	no	—
740	#104	—	2	2	no	—
741	#104	—	2	2	no	—
742	#104	—	4	1	no	—
743	#104	D₄×C₁₉	1	4	yes	complemented
744	#103	—	2	1	no	—
745	#103	—	2	1	no	—
746	#103	—	2	1	no	—
747	#102	—	2	1	no	—
748	#102	—	2	1	no	—
749	#102	—	2	1	no	—
750	#102	—	2	1	no	—
751	#102	—	2	1	no	—
752	#100	—	2	2	no	—
753	#100	—	4	1	no	—
754	C₂²⋊C₈	—	2	1	no	—
755	C₂²⋊C₈	—	2	1	no	—
756	C₁₉	#24464	1	1	yes	characteristic, direct product factor, Sylow
757	C₂⁴	—	2	2	no	—
758	C₂⁴	—	2	1	no	—
759	C₂⁴	—	2	1	no	—
760	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
761	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
762	#41	—	2	1	no	—
763	#41	—	2	1	no	—
764	#41	—	2	2	no	—
765	#41	—	2	2	no	—
766	#41	—	2	1	no	—
767	#41	—	2	1	no	—
768	#41	—	2	1	no	—
769	#41	—	2	1	no	—
770	#41	—	2	1	no	—
771	#41	—	2	1	no	—
772	#41	—	2	1	no	—
773	#41	—	2	1	no	—
774	#41	—	4	2	no	—
775	#41	—	4	2	no	—
776	#41	—	4	1	no	—
777	#41	—	4	1	no	—
778	#41	—	4	2	no	—
779	#41	—	4	2	no	—
780	#41	—	4	2	no	—
781	#41	—	4	2	no	—
782	#41	—	4	2	no	—
783	#41	—	4	2	no	—
784	#41	C₂×D₄×C₁₉	1	2	yes	—
785	#41	#41×C₁₉	1	2	yes	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	2	no	—
788	C₂×Q₈	—	4	1	no	—
789	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
790	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
791	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
792	C₂×D₄	—	2	1	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	1	no	—
801	C₂×D₄	—	2	1	no	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	2	2	no	—
804	C₂×D₄	—	2	2	no	—
805	C₂×D₄	—	2	1	no	—
806	C₂×D₄	—	2	2	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	—	2	1	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	1	no	—
817	C₂×D₄	—	2	1	no	—
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	1	no	—
820	C₂×D₄	—	4	1	no	—
821	C₂×D₄	—	4	2	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	—	4	4	no	—
824	C₂×D₄	—	4	4	no	—
825	C₂×D₄	—	4	4	no	—
826	C₂×D₄	—	4	2	no	—
827	C₂×D₄	—	4	2	no	—
828	C₂×D₄	—	4	4	no	—
829	C₂×D₄	—	4	4	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂×D₄	—	4	4	no	—
833	C₂×D₄	—	4	4	no	—
834	C₂×D₄	—	4	1	no	—
835	C₂×D₄	—	4	1	no	—
836	C₂×D₄	—	8	4	no	—
837	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
838	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
839	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	2	1	no	—
842	C₂²×C₄	—	2	1	no	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	2	1	no	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	4	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	1	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	1	no	—
852	C₂²×C₄	—	2	1	no	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
861	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
862	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
863	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
864	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
865	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
866	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
867	SD₁₆	—	4	2	no	—
868	SD₁₆	—	4	2	no	—
869	SD₁₆	—	4	2	no	—
870	D₈	—	4	2	no	—
871	D₈	—	4	2	no	—
872	D₈	—	4	2	no	—
873	M₁₆	—	2	1	no	—
874	M₁₆	—	2	1	no	—
875	M₁₆	—	2	1	no	—
876	M₁₆	—	2	1	no	—
877	M₁₆	—	2	1	no	—
878	M₁₆	—	2	1	no	—
879	M₁₆	—	2	1	no	—
880	M₁₆	—	4	2	no	—
881	M₁₆	C₂×D₄×C₁₉	1	2	yes	complemented
882	C₂×C₈	—	2	1	no	—
883	C₂×C₈	—	2	1	no	—
884	C₂×C₈	—	2	1	no	—
885	C₂×C₈	—	2	1	no	—
886	C₂×C₈	—	4	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	1	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	4	4	no	—
896	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
897	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	1	no	—
904	C₂²⋊C₄	—	2	1	no	—
905	C₂²⋊C₄	—	2	1	no	—
906	C₂²⋊C₄	—	2	1	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	1	no	—
910	C₂²⋊C₄	—	4	4	no	—
911	C₂²⋊C₄	—	4	4	no	—
912	C₂²⋊C₄	—	4	1	no	—
913	C₂²⋊C₄	—	4	1	no	—
914	C₄²	—	2	2	no	—
915	C₄²	—	2	1	no	—
916	C₄²	—	2	1	no	—
917	C₄²	—	2	1	no	—
918	C₄²	—	2	1	no	—
919	C₄²	—	4	2	no	—
920	C₄²	C₂×D₄×C₁₉	1	2	yes	complemented
921	C₂³	—	2	2	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	1	no	—
924	C₂³	—	2	1	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	1	no	—
927	C₂³	—	2	1	no	—
928	C₂³	—	2	2	no	—
929	C₂³	—	2	2	no	—
930	C₂³	—	4	1	no	—
931	C₂³	—	4	2	no	—
932	C₂³	—	4	4	no	—
933	C₂³	—	4	2	no	—
934	C₂³	—	4	2	no	—
935	C₂³	—	4	2	no	—
936	C₂³	—	4	2	no	—
937	C₂³	—	4	2	no	—
938	C₂³	—	4	1	no	—
939	C₂³	—	4	1	no	—
940	C₂³	—	4	1	no	—
941	C₂³	—	8	1	no	—
942	C₂³	—	8	2	no	—
943	C₂³	—	8	2	no	—
944	C₂³	C₁₉×#120	1	1	yes	characteristic
945	C₂³	C₁₉×#120	1	1	yes	characteristic
946	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
947	Q₈	—	2	1	no	—
948	Q₈	—	2	1	no	—
949	Q₈	—	2	1	no	—
950	Q₈	—	2	1	no	—
951	Q₈	—	2	1	no	—
952	Q₈	—	4	2	no	—
953	Q₈	C₁₉×#121	1	2	yes	complemented
954	D₄	—	2	2	no	—
955	D₄	—	2	2	no	—
956	D₄	—	2	1	no	—
957	D₄	—	2	1	no	—
958	D₄	—	2	1	no	—
959	D₄	—	2	1	no	—
960	D₄	—	2	1	no	—
961	D₄	—	4	2	no	—
962	D₄	—	4	2	no	—
963	D₄	—	4	4	no	—
964	D₄	—	4	2	no	—
965	D₄	—	4	4	no	—
966	D₄	—	4	4	no	—
967	D₄	—	4	2	no	—
968	D₄	—	4	1	no	—
969	D₄	—	4	1	no	—
970	D₄	—	4	1	no	—
971	D₄	—	4	1	no	—
972	D₄	—	4	1	no	—
973	D₄	—	4	1	no	—
974	D₄	—	4	1	no	—
975	D₄	—	4	1	no	—
976	D₄	—	4	1	no	—
977	D₄	—	4	1	no	—
978	D₄	—	4	1	no	—
979	D₄	—	4	1	no	—
980	D₄	—	8	8	no	—
981	D₄	—	8	2	no	—
982	D₄	—	8	1	no	—
983	D₄	—	8	2	no	—
984	D₄	—	8	2	no	—
985	D₄	—	8	2	no	—
986	D₄	—	8	2	no	—
987	D₄	—	8	2	no	—
988	D₄	C₁₉×#121	1	2	yes	complemented
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	4	2	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	4	2	no	—
1014	C₂×C₄	—	4	8	no	—
1015	C₂×C₄	—	4	4	no	—
1016	C₂×C₄	—	4	1	no	—
1017	C₂×C₄	—	4	1	no	—
1018	C₂×C₄	—	4	1	no	—
1019	C₂×C₄	—	4	1	no	—
1020	C₂×C₄	—	4	1	no	—
1021	C₂×C₄	—	4	1	no	—
1022	C₂×C₄	—	4	2	no	—
1023	C₂×C₄	—	4	2	no	—
1024	C₂×C₄	—	4	1	no	—
1025	C₂×C₄	—	8	2	no	—
1026	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
1027	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
1028	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1029	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1030	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1031	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
1032	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1033	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1034	C₈	—	2	2	no	—
1035	C₈	—	4	1	no	—
1036	C₈	—	4	1	no	—
1037	C₈	—	4	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	2	1	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	2	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	2	1	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	—	4	1	no	—
1050	C₂²	—	4	1	no	—
1051	C₂²	—	4	1	no	—
1052	C₂²	—	4	2	no	—
1053	C₂²	—	4	2	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	1	no	—
1059	C₂²	—	8	4	no	—
1060	C₂²	—	8	2	no	—
1061	C₂²	—	8	2	no	—
1062	C₂²	—	8	2	no	—
1063	C₂²	—	8	2	no	—
1064	C₂²	—	8	1	no	—
1065	C₂²	—	8	1	no	—
1066	C₂²	—	8	1	no	—
1067	C₂²	—	16	4	no	—
1068	C₂²	C₁₉×#453	1	2	yes	complemented
1069	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
1070	C₂²	D₄²×C₁₉	1	1	yes	characteristic
1071	C₂²	C₁₉×#546	1	1	yes	characteristic
1072	C₄	—	2	4	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	4	2	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	2	no	—
1080	C₄	—	4	1	no	—
1081	C₄	—	4	1	no	—
1082	C₄	—	8	1	no	—
1083	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
1084	C₄	C₁₉×#534	1	1	yes	characteristic
1085	C₄	D₄²×C₁₉	1	1	yes	characteristic
1086	C₄	C₁₉×#546	1	1	yes	characteristic
1087	C₂	—	2	1	no	—
1088	C₂	—	2	1	no	—
1089	C₂	—	2	2	no	—
1090	C₂	—	4	1	no	—
1091	C₂	—	4	2	no	—
1092	C₂	—	8	1	no	—
1093	C₂	—	8	2	no	—
1094	C₂	—	8	1	no	—
1095	C₂	—	16	1	no	—
1096	C₂	C₁₉×#2410	1	1	yes	characteristic
1097	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
1098	C₂	C₁₉×#3018	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. C₂²×C₁₉×#104	C₂	semidirect
6. C₁₉×#2856	C₂	semidirect
7. C₁₉×#2039	C₂	semidirect
8. C₁₉×#2037	C₂	semidirect
9. C₁₉×#2006	C₂	semidirect
10. C₁₉×#2002	C₂	semidirect
11. C₁₉×#1900	C₂	semidirect
12. C₁₉×#1896	C₂	semidirect
13. C₁₉×#1883	C₂	semidirect
14. C₁₉×#1859	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
38. C₂×C₁₉×#121	C₂²	semidirect
40. C₂²×C₄²×C₁₉	C₂²	semidirect
50. C₁₉×#428	C₂²	semidirect
54. C₂×C₁₉×#104	C₂²	semidirect
55. C₂×C₁₉×#104	C₂²	semidirect
56. C₂×C₁₉×#104	C₂²	semidirect
57. C₂×C₁₉×#104	C₂²	semidirect
58. C₁₉×#418	C₂²	semidirect
60. C₁₉×#417	C₂²	semidirect
61. C₁₉×#417	C₂²	semidirect
62. C₂×C₁₉×#100	C₂²	semidirect
63. C₂×C₁₉×#100	C₂²	semidirect
64. C₁₉×#407	C₂²	semidirect
66. C₁₉×#390	C₂²	semidirect
67. C₁₉×#390	C₂²	semidirect
68. C₁₉×#384	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
136. C₁₉×C₂²⋊Q₈	D₄	semidirect
137. C₁₉×C₂²⋊Q₈	D₄	semidirect
157. C₁₉×#121	D₄	semidirect
158. C₁₉×#121	D₄	semidirect
194. C₁₉×#104	D₄	semidirect
331. M₁₆×C₁₉	C₂×D₄	semidirect
370. C₄²×C₁₉	C₂×D₄	semidirect
371. #24464	C₁₉	direct (N × H)
404. Q₈×C₁₉	#121	semidirect
439. D₄×C₁₉	#121	semidirect
489. #3488	C₂×C₁₉	semidirect
490. #3055	C₂×C₁₉	semidirect
491. C₂×#453	C₂×C₁₉	semidirect
492. #3006	C₂×C₁₉	semidirect
493. C₂²×#104	C₂×C₁₉	semidirect
494. #2856	C₂×C₁₉	semidirect
495. #2039	C₂×C₁₉	semidirect
496. #2037	C₂×C₁₉	semidirect
497. #2006	C₂×C₁₉	semidirect
498. #2002	C₂×C₁₉	semidirect
499. #1900	C₂×C₁₉	semidirect
500. #1896	C₂×C₁₉	semidirect
501. #1883	C₂×C₁₉	semidirect
502. #1859	C₂×C₁₉	semidirect
503. #1792	C₂×C₁₉	semidirect
534. C₂²×C₁₉	#453	semidirect
556. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
557. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
558. C₂²×M₁₆	C₂²×C₁₉	semidirect
569. C₂×#127	C₂²×C₁₉	semidirect
575. C₂×#121	C₂²×C₁₉	semidirect
577. C₂²×C₄²	C₂²×C₁₉	semidirect
587. #428	C₂²×C₁₉	semidirect
591. C₂×#104	C₂²×C₁₉	semidirect
592. C₂×#104	C₂²×C₁₉	semidirect
593. C₂×#104	C₂²×C₁₉	semidirect
594. C₂×#104	C₂²×C₁₉	semidirect
595. #418	C₂²×C₁₉	semidirect
597. #417	C₂²×C₁₉	semidirect
598. #417	C₂²×C₁₉	semidirect
599. C₂×#100	C₂²×C₁₉	semidirect
600. C₂×#100	C₂²×C₁₉	semidirect
601. #407	C₂²×C₁₉	semidirect
603. #390	C₂²×C₁₉	semidirect
604. #390	C₂²×C₁₉	semidirect
605. #384	C₂²×C₁₉	semidirect
606. #343	C₂²×C₁₉	semidirect
607. #343	C₂²×C₁₉	semidirect
608. #339	C₂²×C₁₉	semidirect
609. #339	C₂²×C₁₉	semidirect
634. C₂×#41	D₄×C₁₉	semidirect
635. C₂×#41	D₄×C₁₉	semidirect
639. C₂²×Q₈	D₄×C₁₉	semidirect
648. C₂²×D₄	D₄×C₁₉	semidirect
685. C₂²⋊Q₈	D₄×C₁₉	semidirect
686. C₂²⋊Q₈	D₄×C₁₉	semidirect
706. #121	D₄×C₁₉	semidirect
707. #121	D₄×C₁₉	semidirect
743. #104	D₄×C₁₉	semidirect
756. C₁₉	#24464	direct (N × H)
881. M₁₆	C₂×D₄×C₁₉	semidirect
920. C₄²	C₂×D₄×C₁₉	semidirect
953. Q₈	C₁₉×#121	semidirect
988. D₄	C₁₉×#121	semidirect
1068. C₂²	C₁₉×#453	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
C₂²×C₁₉×#104	2
C₁₉×#2856	2
C₁₉×#2039	2
C₁₉×#2037	2
C₁₉×#2006	2
C₁₉×#2002	2
C₁₉×#1900	2
C₁₉×#1896	2
C₁₉×#1883	2
C₁₉×#1859	2
C₁₉×#1792	2
#24464	19

Subgroups — C19×#24464 #18030423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24464 #18030423