Subgroups — C₁₉×#22506 #18028465

Order 4864.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3475	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2290	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1995	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1986	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1897	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1896	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1871	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1871	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1826	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1826	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1806	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1759	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1733	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#556	C₄	1	1	yes	characteristic, complemented
19	C₁₉×#555	C₄	1	1	yes	characteristic, complemented
20	C₁₉×#554	C₄	1	1	yes	characteristic, complemented
21	C₁₉×#553	C₄	1	1	yes	characteristic, complemented
22	C₁₉×#553	C₄	1	1	yes	characteristic, complemented
23	C₁₉×#552	—	2	1	no	—
24	C₁₉×#552	C₄	1	1	yes	characteristic, complemented
25	C₁₉×#552	C₄	1	1	yes	characteristic, complemented
26	C₁₉×#551	—	2	1	no	—
27	C₁₉×#551	—	2	1	no	—
28	C₁₉×#547	C₄	1	1	yes	characteristic, complemented
29	C₁₉×#546	—	2	1	no	—
30	C₁₉×#533	C₂²	1	1	yes	characteristic
31	C₁₉×#529	—	2	1	no	—
32	C₁₉×#529	—	2	1	no	—
33	C₁₉×#529	—	2	1	no	—
34	C₁₉×#525	C₂²	1	1	yes	characteristic
35	C₁₉×#525	C₂²	1	1	yes	characteristic
36	C₄×#41×C₁₉	—	2	1	no	—
37	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#436	—	2	1	no	—
44	C₁₉×#435	—	2	1	no	—
45	C₁₉×#435	—	2	1	no	—
46	C₈×D₄×C₁₉	—	2	1	no	—
47	C₁₉×#423	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
49	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
51	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
52	C₁₉×#407	C₂²	1	1	yes	characteristic
53	C₁₉×#407	C₂²	1	1	yes	characteristic
54	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
55	C₁₉×#388	—	2	1	no	—
56	C₁₉×#387	—	2	1	no	—
57	C₁₉×#386	—	2	1	no	—
58	C₁₉×#385	—	2	1	no	—
59	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
60	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
61	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
62	C₁₉×#376	C₂²	1	1	yes	characteristic
63	C₁₉×#339	C₂²	1	1	yes	characteristic
64	C₁₉×#339	C₂²	1	1	yes	characteristic
65	C₁₉×#339	C₂²	1	1	yes	characteristic
66	C₁₉×#339	C₂²	1	1	yes	characteristic
67	C₁₉×#339	C₂²	1	1	yes	characteristic
68	C₁₉×#339	C₂²	1	1	yes	characteristic
69	C₁₉×#339	C₂²	1	1	yes	characteristic
70	C₁₉×#339	C₂²	1	1	yes	characteristic
71	C₁₉×#339	C₂²	1	1	yes	characteristic
72	C₁₉×#339	C₂²	1	1	yes	characteristic
73	C₁₉×#339	C₂²	1	1	yes	characteristic
74	C₁₉×#339	C₂²	1	1	yes	characteristic
75	C₂×#41×C₁₉	—	2	1	no	—
76	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
78	C₂³×C₄×C₁₉	—	2	1	no	—
79	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×M₁₆×C₁₉	—	2	1	no	—
82	C₂×M₁₆×C₁₉	—	2	1	no	—
83	C₂×M₁₆×C₁₉	—	2	2	no	—
84	C₂×M₁₆×C₁₉	—	2	2	no	—
85	C₂×M₁₆×C₁₉	—	4	1	no	—
86	C₂×M₁₆×C₁₉	—	4	1	no	—
87	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₉	—	2	1	no	—
92	C₂²×C₈×C₁₉	—	2	1	no	—
93	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
94	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
95	C₁₉×#126	—	2	1	no	—
96	C₁₉×#126	—	2	1	no	—
97	C₁₉×#126	—	2	1	no	—
98	C₁₉×#126	—	2	1	no	—
99	C₁₉×#126	—	2	1	no	—
100	C₁₉×#126	—	2	1	no	—
101	C₁₉×#125	—	2	1	no	—
102	C₁₉×#125	—	2	1	no	—
103	C₁₉×#125	—	2	1	no	—
104	C₁₉×#125	C₂×C₄	1	1	yes	characteristic, complemented
105	C₁₉×#125	C₂×C₄	1	1	yes	characteristic, complemented
106	C₁₉×#124	—	2	1	no	—
107	C₁₉×#124	—	2	1	no	—
108	C₁₉×#124	—	2	1	no	—
109	C₁₉×#123	—	2	1	no	—
110	C₁₉×#123	—	2	1	no	—
111	C₁₉×#123	—	2	1	no	—
112	C₁₉×#123	—	2	1	no	—
113	C₁₉×#123	—	2	1	no	—
114	C₁₉×#123	—	2	1	no	—
115	C₁₉×#123	—	2	1	no	—
116	C₁₉×#123	—	2	1	no	—
117	C₁₉×C₂²⋊Q₈	—	2	1	no	—
118	C₁₉×C₂²⋊Q₈	—	2	1	no	—
119	C₁₉×C₂²⋊Q₈	—	2	1	no	—
120	C₁₉×C₂²⋊Q₈	—	2	1	no	—
121	C₁₉×C₂²⋊Q₈	—	2	1	no	—
122	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
123	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
124	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
125	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
126	C₁₉×#121	—	2	1	no	—
127	C₁₉×#121	—	2	1	no	—
128	C₁₉×#121	—	2	1	no	—
129	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
130	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
131	C₁₉×#121	C₂×C₄	1	1	yes	characteristic, complemented
132	C₁₉×#121	C₂×C₄	1	1	yes	characteristic, complemented
133	C₁₉×#120	—	2	1	no	—
134	C₁₉×#120	—	2	1	no	—
135	C₄×Q₈×C₁₉	—	2	1	no	—
136	C₄×Q₈×C₁₉	—	2	1	no	—
137	C₄×Q₈×C₁₉	—	2	1	no	—
138	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
139	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
140	C₄×D₄×C₁₉	—	2	1	no	—
141	C₄×D₄×C₁₉	—	2	1	no	—
142	C₄×D₄×C₁₉	—	2	1	no	—
143	C₄×D₄×C₁₉	—	2	1	no	—
144	C₄×D₄×C₁₉	—	2	1	no	—
145	C₄×D₄×C₁₉	—	2	1	no	—
146	C₄×D₄×C₁₉	—	2	1	no	—
147	C₄×D₄×C₁₉	—	2	1	no	—
148	C₄×D₄×C₁₉	—	2	1	no	—
149	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
150	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
151	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
152	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
153	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
154	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
155	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
156	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
157	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
158	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
159	C₁₉×#117	—	2	1	no	—
160	C₁₉×#117	—	2	1	no	—
161	C₁₉×#117	—	2	1	no	—
162	C₁₉×#117	—	2	1	no	—
163	C₁₉×#117	—	2	1	no	—
164	C₁₉×#117	—	2	1	no	—
165	C₁₉×#117	—	2	1	no	—
166	C₁₉×#117	—	2	1	no	—
167	C₁₉×#117	—	2	2	no	—
168	C₁₉×#117	—	4	1	no	—
169	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
170	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
171	C₁₉×#117	C₂×C₄	1	1	yes	characteristic, complemented
172	C₁₉×#117	C₂×C₄	1	1	yes	characteristic, complemented
173	C₁₉×#117	C₂³	1	1	yes	characteristic
174	C₁₉×#117	C₂³	1	1	yes	characteristic
175	C₁₉×#117	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
181	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
182	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
185	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
186	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
187	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
188	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₁₉	—	2	1	no	—
191	C₂×C₄²×C₁₉	—	2	1	no	—
192	C₂×C₄²×C₁₉	—	2	1	no	—
193	C₂×C₄²×C₁₉	—	2	2	no	—
194	C₂×C₄²×C₁₉	—	2	1	no	—
195	C₂×C₄²×C₁₉	—	4	1	no	—
196	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
201	C₁₉×C₄⋊C₈	—	2	1	no	—
202	C₁₉×C₄⋊C₈	—	2	1	no	—
203	C₁₉×#104	—	2	2	no	—
204	C₁₉×#104	—	2	2	no	—
205	C₁₉×#104	—	4	1	no	—
206	C₁₉×#104	—	4	1	no	—
207	C₁₉×C₂²⋊C₈	—	2	1	no	—
208	C₁₉×C₂²⋊C₈	—	2	1	no	—
209	C₁₉×C₂²⋊C₈	—	2	1	no	—
210	C₁₉×C₂²⋊C₈	—	2	1	no	—
211	C₁₉×#97	—	2	1	no	—
212	C₄×C₈×C₁₉	—	2	1	no	—
213	C₁₉×#95	—	2	1	no	—
214	C₁₉×#95	—	2	1	no	—
215	C₁₉×#95	—	2	1	no	—
216	C₁₉×#95	—	2	1	no	—
217	C₁₉×#95	—	2	1	no	—
218	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
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	4	no	—
225	C₂×Q₈×C₁₉	—	2	1	no	—
226	C₂×Q₈×C₁₉	—	2	1	no	—
227	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
228	C₂×D₄×C₁₉	—	2	1	no	—
229	C₂×D₄×C₁₉	—	2	1	no	—
230	C₂×D₄×C₁₉	—	2	1	no	—
231	C₂×D₄×C₁₉	—	2	1	no	—
232	C₂×D₄×C₁₉	—	2	1	no	—
233	C₂×D₄×C₁₉	—	4	2	no	—
234	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
235	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
236	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
237	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
238	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
239	C₂²×C₄×C₁₉	—	2	1	no	—
240	C₂²×C₄×C₁₉	—	2	1	no	—
241	C₂²×C₄×C₁₉	—	2	1	no	—
242	C₂²×C₄×C₁₉	—	2	1	no	—
243	C₂²×C₄×C₁₉	—	2	1	no	—
244	C₂²×C₄×C₁₉	—	2	1	no	—
245	C₂²×C₄×C₁₉	—	2	1	no	—
246	C₂²×C₄×C₁₉	—	2	1	no	—
247	C₂²×C₄×C₁₉	—	2	1	no	—
248	C₂²×C₄×C₁₉	—	2	1	no	—
249	C₂²×C₄×C₁₉	—	2	1	no	—
250	C₂²×C₄×C₁₉	—	2	1	no	—
251	C₂²×C₄×C₁₉	—	2	1	no	—
252	C₂²×C₄×C₁₉	—	2	1	no	—
253	C₂²×C₄×C₁₉	—	2	1	no	—
254	C₂²×C₄×C₁₉	—	2	1	no	—
255	C₂²×C₄×C₁₉	—	2	1	no	—
256	C₂²×C₄×C₁₉	—	2	1	no	—
257	C₂²×C₄×C₁₉	—	2	1	no	—
258	C₂²×C₄×C₁₉	—	4	2	no	—
259	C₂²×C₄×C₁₉	—	4	2	no	—
260	C₂²×C₄×C₁₉	—	4	2	no	—
261	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
262	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
263	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
264	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
265	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
274	M₁₆×C₁₉	—	2	1	no	—
275	M₁₆×C₁₉	—	2	1	no	—
276	M₁₆×C₁₉	—	2	1	no	—
277	M₁₆×C₁₉	—	2	1	no	—
278	M₁₆×C₁₉	—	2	1	no	—
279	M₁₆×C₁₉	—	2	1	no	—
280	M₁₆×C₁₉	—	2	1	no	—
281	M₁₆×C₁₉	—	4	2	no	—
282	M₁₆×C₁₉	—	4	2	no	—
283	M₁₆×C₁₉	#41	1	2	yes	complemented
284	C₂×C₈×C₁₉	—	2	1	no	—
285	C₂×C₈×C₁₉	—	2	1	no	—
286	C₂×C₈×C₁₉	—	2	1	no	—
287	C₂×C₈×C₁₉	—	2	1	no	—
288	C₂×C₈×C₁₉	—	4	2	no	—
289	C₂×C₈×C₁₉	—	4	2	no	—
290	C₄⋊C₄×C₁₉	—	2	1	no	—
291	C₄⋊C₄×C₁₉	—	2	1	no	—
292	C₄⋊C₄×C₁₉	—	2	1	no	—
293	C₄⋊C₄×C₁₉	—	2	1	no	—
294	C₄⋊C₄×C₁₉	—	2	1	no	—
295	C₄⋊C₄×C₁₉	—	2	1	no	—
296	C₄⋊C₄×C₁₉	—	2	1	no	—
297	C₄⋊C₄×C₁₉	—	2	1	no	—
298	C₄⋊C₄×C₁₉	—	2	1	no	—
299	C₄⋊C₄×C₁₉	—	2	1	no	—
300	C₄⋊C₄×C₁₉	—	2	1	no	—
301	C₄⋊C₄×C₁₉	—	2	1	no	—
302	C₄⋊C₄×C₁₉	—	2	1	no	—
303	C₄⋊C₄×C₁₉	—	2	1	no	—
304	C₄⋊C₄×C₁₉	—	2	1	no	—
305	C₄⋊C₄×C₁₉	—	2	1	no	—
306	C₄⋊C₄×C₁₉	—	4	2	no	—
307	C₄⋊C₄×C₁₉	—	4	2	no	—
308	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
309	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
310	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
311	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
312	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
313	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
314	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
315	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
316	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
317	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
318	C₂²⋊C₄×C₁₉	—	2	1	no	—
319	C₂²⋊C₄×C₁₉	—	2	1	no	—
320	C₂²⋊C₄×C₁₉	—	2	1	no	—
321	C₂²⋊C₄×C₁₉	—	2	1	no	—
322	C₂²⋊C₄×C₁₉	—	2	1	no	—
323	C₂²⋊C₄×C₁₉	—	2	1	no	—
324	C₂²⋊C₄×C₁₉	—	2	1	no	—
325	C₂²⋊C₄×C₁₉	—	2	1	no	—
326	C₂²⋊C₄×C₁₉	—	2	1	no	—
327	C₂²⋊C₄×C₁₉	—	2	1	no	—
328	C₂²⋊C₄×C₁₉	—	2	1	no	—
329	C₂²⋊C₄×C₁₉	—	2	1	no	—
330	C₂²⋊C₄×C₁₉	—	2	1	no	—
331	C₂²⋊C₄×C₁₉	—	2	1	no	—
332	C₂²⋊C₄×C₁₉	—	2	1	no	—
333	C₂²⋊C₄×C₁₉	—	2	1	no	—
334	C₂²⋊C₄×C₁₉	—	2	1	no	—
335	C₂²⋊C₄×C₁₉	—	4	2	no	—
336	C₂²⋊C₄×C₁₉	—	4	2	no	—
337	C₂²⋊C₄×C₁₉	—	4	2	no	—
338	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
339	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
340	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
341	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
342	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
343	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
344	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
345	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
346	C₄²×C₁₉	—	2	1	no	—
347	C₄²×C₁₉	—	2	1	no	—
348	C₄²×C₁₉	—	2	1	no	—
349	C₄²×C₁₉	—	2	1	no	—
350	C₄²×C₁₉	—	2	1	no	—
351	C₄²×C₁₉	—	2	1	no	—
352	C₄²×C₁₉	—	2	1	no	—
353	C₄²×C₁₉	—	2	1	no	—
354	C₄²×C₁₉	—	2	1	no	—
355	C₄²×C₁₉	—	2	1	no	—
356	C₄²×C₁₉	—	2	1	no	—
357	C₄²×C₁₉	—	2	1	no	—
358	C₄²×C₁₉	—	2	1	no	—
359	C₄²×C₁₉	—	2	1	no	—
360	C₄²×C₁₉	—	2	1	no	—
361	C₄²×C₁₉	—	2	1	no	—
362	C₄²×C₁₉	—	4	2	no	—
363	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
364	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
365	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
366	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
367	C₄²×C₁₉	#41	1	2	yes	complemented
368	#22506	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	1	no	—
375	C₂³×C₁₉	—	4	1	no	—
376	C₂³×C₁₉	—	4	1	no	—
377	C₂³×C₁₉	—	4	1	no	—
378	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
379	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
380	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
381	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
382	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
383	Q₈×C₁₉	—	2	1	no	—
384	Q₈×C₁₉	—	2	1	no	—
385	Q₈×C₁₉	—	4	2	no	—
386	Q₈×C₁₉	—	8	1	no	—
387	D₄×C₁₉	—	2	2	no	—
388	D₄×C₁₉	—	2	2	no	—
389	D₄×C₁₉	—	2	1	no	—
390	D₄×C₁₉	—	2	1	no	—
391	D₄×C₁₉	—	4	1	no	—
392	D₄×C₁₉	—	4	1	no	—
393	D₄×C₁₉	—	4	2	no	—
394	D₄×C₁₉	—	4	1	no	—
395	D₄×C₁₉	—	4	1	no	—
396	D₄×C₁₉	—	4	2	no	—
397	D₄×C₁₉	—	8	1	no	—
398	D₄×C₁₉	—	8	1	no	—
399	C₂×C₄×C₁₉	—	2	1	no	—
400	C₂×C₄×C₁₉	—	2	1	no	—
401	C₂×C₄×C₁₉	—	2	1	no	—
402	C₂×C₄×C₁₉	—	2	1	no	—
403	C₂×C₄×C₁₉	—	2	1	no	—
404	C₂×C₄×C₁₉	—	2	1	no	—
405	C₂×C₄×C₁₉	—	2	1	no	—
406	C₂×C₄×C₁₉	—	2	1	no	—
407	C₂×C₄×C₁₉	—	2	1	no	—
408	C₂×C₄×C₁₉	—	2	1	no	—
409	C₂×C₄×C₁₉	—	2	1	no	—
410	C₂×C₄×C₁₉	—	2	1	no	—
411	C₂×C₄×C₁₉	—	2	1	no	—
412	C₂×C₄×C₁₉	—	2	1	no	—
413	C₂×C₄×C₁₉	—	2	1	no	—
414	C₂×C₄×C₁₉	—	2	1	no	—
415	C₂×C₄×C₁₉	—	2	1	no	—
416	C₂×C₄×C₁₉	—	2	1	no	—
417	C₂×C₄×C₁₉	—	2	1	no	—
418	C₂×C₄×C₁₉	—	2	1	no	—
419	C₂×C₄×C₁₉	—	2	2	no	—
420	C₂×C₄×C₁₉	—	2	1	no	—
421	C₂×C₄×C₁₉	—	2	1	no	—
422	C₂×C₄×C₁₉	—	2	1	no	—
423	C₂×C₄×C₁₉	—	2	1	no	—
424	C₂×C₄×C₁₉	—	2	1	no	—
425	C₂×C₄×C₁₉	—	2	1	no	—
426	C₂×C₄×C₁₉	—	2	1	no	—
427	C₂×C₄×C₁₉	—	2	2	no	—
428	C₂×C₄×C₁₉	—	4	1	no	—
429	C₂×C₄×C₁₉	—	4	1	no	—
430	C₂×C₄×C₁₉	—	4	2	no	—
431	C₂×C₄×C₁₉	—	4	1	no	—
432	C₂×C₄×C₁₉	—	4	1	no	—
433	C₂×C₄×C₁₉	—	4	1	no	—
434	C₂×C₄×C₁₉	—	4	2	no	—
435	C₂×C₄×C₁₉	—	4	8	no	—
436	C₂×C₄×C₁₉	—	4	1	no	—
437	C₂×C₄×C₁₉	—	4	2	no	—
438	C₂×C₄×C₁₉	—	4	1	no	—
439	C₂×C₄×C₁₉	—	4	1	no	—
440	C₂×C₄×C₁₉	—	4	1	no	—
441	C₂×C₄×C₁₉	—	4	1	no	—
442	C₂×C₄×C₁₉	—	4	1	no	—
443	C₂×C₄×C₁₉	—	4	1	no	—
444	C₂×C₄×C₁₉	—	4	1	no	—
445	C₂×C₄×C₁₉	—	4	1	no	—
446	C₂×C₄×C₁₉	—	8	1	no	—
447	C₂×C₄×C₁₉	—	8	1	no	—
448	C₂×C₄×C₁₉	—	8	1	no	—
449	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
450	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
451	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
452	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
453	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
454	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
455	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
456	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
457	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
458	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
460	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
461	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
462	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
463	C₈×C₁₉	—	2	2	no	—
464	C₈×C₁₉	—	4	1	no	—
465	C₈×C₁₉	—	4	1	no	—
466	C₈×C₁₉	—	4	1	no	—
467	#3475	C₂×C₁₉	1	1	yes	characteristic
468	D₄×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
469	#2290	C₂×C₁₉	1	1	yes	characteristic, complemented
470	#1995	C₂×C₁₉	1	1	yes	characteristic, complemented
471	#1986	C₂×C₁₉	1	1	yes	characteristic, complemented
472	#1897	C₂×C₁₉	1	1	yes	characteristic, complemented
473	#1896	C₂×C₁₉	1	1	yes	characteristic, complemented
474	#1871	C₂×C₁₉	1	1	yes	characteristic, complemented
475	#1871	C₂×C₁₉	1	1	yes	characteristic, complemented
476	#1826	C₂×C₁₉	1	1	yes	characteristic, complemented
477	#1826	C₂×C₁₉	1	1	yes	characteristic, complemented
478	#1806	C₂×C₁₉	1	1	yes	characteristic, complemented
479	#1759	C₂×C₁₉	1	1	yes	characteristic, complemented
480	#1733	C₂×C₁₉	1	1	yes	characteristic, complemented
481	C₂×#339	C₂×C₁₉	1	1	yes	characteristic, complemented
482	C₂²×C₁₉	—	2	1	no	—
483	C₂²×C₁₉	—	2	1	no	—
484	C₂²×C₁₉	—	2	1	no	—
485	C₂²×C₁₉	—	2	1	no	—
486	C₂²×C₁₉	—	2	1	no	—
487	C₂²×C₁₉	—	2	1	no	—
488	C₂²×C₁₉	—	2	1	no	—
489	C₂²×C₁₉	—	2	1	no	—
490	C₂²×C₁₉	—	2	1	no	—
491	C₂²×C₁₉	—	2	1	no	—
492	C₂²×C₁₉	—	2	1	no	—
493	C₂²×C₁₉	—	2	1	no	—
494	C₂²×C₁₉	—	2	1	no	—
495	C₂²×C₁₉	—	4	2	no	—
496	C₂²×C₁₉	—	4	2	no	—
497	C₂²×C₁₉	—	4	1	no	—
498	C₂²×C₁₉	—	4	1	no	—
499	C₂²×C₁₉	—	4	1	no	—
500	C₂²×C₁₉	—	8	1	no	—
501	C₂²×C₁₉	—	8	1	no	—
502	C₂²×C₁₉	#421	1	2	yes	—
503	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
504	C₂²×C₁₉	#546	1	1	yes	characteristic
505	C₂²×C₁₉	#547	1	1	yes	characteristic
506	C₄×C₁₉	—	2	1	no	—
507	C₄×C₁₉	—	2	1	no	—
508	C₄×C₁₉	—	2	1	no	—
509	C₄×C₁₉	—	2	1	no	—
510	C₄×C₁₉	—	2	1	no	—
511	C₄×C₁₉	—	2	1	no	—
512	C₄×C₁₉	—	2	1	no	—
513	C₄×C₁₉	—	2	1	no	—
514	C₄×C₁₉	—	4	2	no	—
515	C₄×C₁₉	—	4	2	no	—
516	C₄×C₁₉	—	4	1	no	—
517	C₄×C₁₉	—	4	1	no	—
518	C₄×C₁₉	—	4	1	no	—
519	C₄×C₁₉	—	4	1	no	—
520	C₄×C₁₉	—	4	1	no	—
521	C₄×C₁₉	—	4	1	no	—
522	C₄×C₁₉	—	4	1	no	—
523	C₄×C₁₉	—	8	1	no	—
524	C₄×C₁₉	—	8	1	no	—
525	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
526	C₄×C₁₉	#520	1	1	yes	characteristic
527	C₄×C₁₉	#546	1	1	yes	characteristic
528	C₄×C₁₉	#547	1	1	yes	characteristic
529	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
530	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
531	#556	C₄×C₁₉	1	1	yes	characteristic, complemented
532	#555	C₄×C₁₉	1	1	yes	characteristic, complemented
533	#554	C₄×C₁₉	1	1	yes	characteristic, complemented
534	#553	C₄×C₁₉	1	1	yes	characteristic, complemented
535	#553	C₄×C₁₉	1	1	yes	characteristic, complemented
536	#552	—	2	1	no	—
537	#552	C₄×C₁₉	1	1	yes	characteristic, complemented
538	#552	C₄×C₁₉	1	1	yes	characteristic, complemented
539	#551	—	2	1	no	—
540	#551	—	2	1	no	—
541	#547	C₄×C₁₉	1	1	yes	characteristic, complemented
542	#546	—	2	1	no	—
543	#533	C₂²×C₁₉	1	1	yes	characteristic
544	#529	—	2	1	no	—
545	#529	—	2	1	no	—
546	#529	—	2	1	no	—
547	#525	C₂²×C₁₉	1	1	yes	characteristic
548	#525	C₂²×C₁₉	1	1	yes	characteristic
549	C₄×#41	—	2	1	no	—
550	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
551	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
552	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
553	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
554	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
555	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
556	#436	—	2	1	no	—
557	#435	—	2	1	no	—
558	#435	—	2	1	no	—
559	C₈×D₄	—	2	1	no	—
560	#423	C₂²×C₁₉	1	1	yes	characteristic
561	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
562	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
563	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
564	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
565	#407	C₂²×C₁₉	1	1	yes	characteristic
566	#407	C₂²×C₁₉	1	1	yes	characteristic
567	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
568	#388	—	2	1	no	—
569	#387	—	2	1	no	—
570	#386	—	2	1	no	—
571	#385	—	2	1	no	—
572	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
573	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
574	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
575	#376	C₂²×C₁₉	1	1	yes	characteristic
576	#339	C₂²×C₁₉	1	1	yes	characteristic
577	#339	C₂²×C₁₉	1	1	yes	characteristic
578	#339	C₂²×C₁₉	1	1	yes	characteristic
579	#339	C₂²×C₁₉	1	1	yes	characteristic
580	#339	C₂²×C₁₉	1	1	yes	characteristic
581	#339	C₂²×C₁₉	1	1	yes	characteristic
582	#339	C₂²×C₁₉	1	1	yes	characteristic
583	#339	C₂²×C₁₉	1	1	yes	characteristic
584	#339	C₂²×C₁₉	1	1	yes	characteristic
585	#339	C₂²×C₁₉	1	1	yes	characteristic
586	#339	C₂²×C₁₉	1	1	yes	characteristic
587	#339	C₂²×C₁₉	1	1	yes	characteristic
588	C₂×C₁₉	—	2	1	no	—
589	C₂×C₁₉	—	2	1	no	—
590	C₂×C₁₉	—	2	2	no	—
591	C₂×C₁₉	—	4	1	no	—
592	C₂×C₁₉	—	4	1	no	—
593	C₂×C₁₉	—	4	1	no	—
594	C₂×C₁₉	—	8	1	no	—
595	C₂×C₁₉	#2339	1	1	yes	characteristic
596	C₂×C₁₉	C₂×#421	1	1	yes	characteristic
597	C₂×C₁₉	#2901	1	1	yes	characteristic
598	C₂×#41	—	2	1	no	—
599	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
600	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
601	C₂³×C₄	—	2	1	no	—
602	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
603	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
604	C₂×M₁₆	—	2	1	no	—
605	C₂×M₁₆	—	2	1	no	—
606	C₂×M₁₆	—	2	2	no	—
607	C₂×M₁₆	—	2	2	no	—
608	C₂×M₁₆	—	4	1	no	—
609	C₂×M₁₆	—	4	1	no	—
610	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
611	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
612	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
613	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
614	C₂²×C₈	—	2	1	no	—
615	C₂²×C₈	—	2	1	no	—
616	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
617	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
618	#126	—	2	1	no	—
619	#126	—	2	1	no	—
620	#126	—	2	1	no	—
621	#126	—	2	1	no	—
622	#126	—	2	1	no	—
623	#126	—	2	1	no	—
624	#125	—	2	1	no	—
625	#125	—	2	1	no	—
626	#125	—	2	1	no	—
627	#125	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
628	#125	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
629	#124	—	2	1	no	—
630	#124	—	2	1	no	—
631	#124	—	2	1	no	—
632	#123	—	2	1	no	—
633	#123	—	2	1	no	—
634	#123	—	2	1	no	—
635	#123	—	2	1	no	—
636	#123	—	2	1	no	—
637	#123	—	2	1	no	—
638	#123	—	2	1	no	—
639	#123	—	2	1	no	—
640	C₂²⋊Q₈	—	2	1	no	—
641	C₂²⋊Q₈	—	2	1	no	—
642	C₂²⋊Q₈	—	2	1	no	—
643	C₂²⋊Q₈	—	2	1	no	—
644	C₂²⋊Q₈	—	2	1	no	—
645	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
646	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
647	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
648	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
649	#121	—	2	1	no	—
650	#121	—	2	1	no	—
651	#121	—	2	1	no	—
652	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
653	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
654	#121	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
655	#121	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
656	#120	—	2	1	no	—
657	#120	—	2	1	no	—
658	C₄×Q₈	—	2	1	no	—
659	C₄×Q₈	—	2	1	no	—
660	C₄×Q₈	—	2	1	no	—
661	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
662	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
663	C₄×D₄	—	2	1	no	—
664	C₄×D₄	—	2	1	no	—
665	C₄×D₄	—	2	1	no	—
666	C₄×D₄	—	2	1	no	—
667	C₄×D₄	—	2	1	no	—
668	C₄×D₄	—	2	1	no	—
669	C₄×D₄	—	2	1	no	—
670	C₄×D₄	—	2	1	no	—
671	C₄×D₄	—	2	1	no	—
672	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
673	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
674	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
675	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
676	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
677	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
678	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
679	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
680	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
681	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
682	#117	—	2	1	no	—
683	#117	—	2	1	no	—
684	#117	—	2	1	no	—
685	#117	—	2	1	no	—
686	#117	—	2	1	no	—
687	#117	—	2	1	no	—
688	#117	—	2	1	no	—
689	#117	—	2	1	no	—
690	#117	—	2	2	no	—
691	#117	—	4	1	no	—
692	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
693	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
694	#117	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
695	#117	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
696	#117	C₂³×C₁₉	1	1	yes	characteristic
697	#117	C₂³×C₁₉	1	1	yes	characteristic
698	#117	C₂³×C₁₉	1	1	yes	characteristic
699	C₂×C₄⋊C₄	—	2	1	no	—
700	C₂×C₄⋊C₄	—	2	1	no	—
701	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
702	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
704	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
705	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
706	C₂×C₂²⋊C₄	—	2	1	no	—
707	C₂×C₂²⋊C₄	—	2	1	no	—
708	C₂×C₂²⋊C₄	—	2	1	no	—
709	C₂×C₂²⋊C₄	—	2	1	no	—
710	C₂×C₂²⋊C₄	—	2	1	no	—
711	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
712	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
713	C₂×C₄²	—	2	1	no	—
714	C₂×C₄²	—	2	1	no	—
715	C₂×C₄²	—	2	1	no	—
716	C₂×C₄²	—	2	2	no	—
717	C₂×C₄²	—	2	1	no	—
718	C₂×C₄²	—	4	1	no	—
719	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
720	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
721	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
722	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
723	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
724	C₄⋊C₈	—	2	1	no	—
725	C₄⋊C₈	—	2	1	no	—
726	#104	—	2	2	no	—
727	#104	—	2	2	no	—
728	#104	—	4	1	no	—
729	#104	—	4	1	no	—
730	C₂²⋊C₈	—	2	1	no	—
731	C₂²⋊C₈	—	2	1	no	—
732	C₂²⋊C₈	—	2	1	no	—
733	C₂²⋊C₈	—	2	1	no	—
734	#97	—	2	1	no	—
735	C₄×C₈	—	2	1	no	—
736	#95	—	2	1	no	—
737	#95	—	2	1	no	—
738	#95	—	2	1	no	—
739	#95	—	2	1	no	—
740	#95	—	2	1	no	—
741	C₁₉	#22506	1	1	yes	characteristic, direct product factor, Sylow
742	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
743	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
744	#41	—	2	1	no	—
745	#41	—	2	1	no	—
746	#41	—	2	1	no	—
747	#41	—	2	1	no	—
748	#41	—	4	4	no	—
749	C₂×Q₈	—	2	1	no	—
750	C₂×Q₈	—	2	1	no	—
751	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	1	no	—
754	C₂×D₄	—	2	1	no	—
755	C₂×D₄	—	2	1	no	—
756	C₂×D₄	—	2	1	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
759	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
760	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
761	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
762	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
763	C₂²×C₄	—	2	1	no	—
764	C₂²×C₄	—	2	1	no	—
765	C₂²×C₄	—	2	1	no	—
766	C₂²×C₄	—	2	1	no	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	1	no	—
771	C₂²×C₄	—	2	1	no	—
772	C₂²×C₄	—	2	1	no	—
773	C₂²×C₄	—	2	1	no	—
774	C₂²×C₄	—	2	1	no	—
775	C₂²×C₄	—	2	1	no	—
776	C₂²×C₄	—	2	1	no	—
777	C₂²×C₄	—	2	1	no	—
778	C₂²×C₄	—	2	1	no	—
779	C₂²×C₄	—	2	1	no	—
780	C₂²×C₄	—	2	1	no	—
781	C₂²×C₄	—	2	1	no	—
782	C₂²×C₄	—	4	2	no	—
783	C₂²×C₄	—	4	2	no	—
784	C₂²×C₄	—	4	2	no	—
785	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
786	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
787	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
788	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
789	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
790	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
791	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
792	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
793	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
794	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
795	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
796	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
798	M₁₆	—	2	1	no	—
799	M₁₆	—	2	1	no	—
800	M₁₆	—	2	1	no	—
801	M₁₆	—	2	1	no	—
802	M₁₆	—	2	1	no	—
803	M₁₆	—	2	1	no	—
804	M₁₆	—	2	1	no	—
805	M₁₆	—	4	2	no	—
806	M₁₆	—	4	2	no	—
807	M₁₆	#41×C₁₉	1	2	yes	complemented
808	C₂×C₈	—	2	1	no	—
809	C₂×C₈	—	2	1	no	—
810	C₂×C₈	—	2	1	no	—
811	C₂×C₈	—	2	1	no	—
812	C₂×C₈	—	4	2	no	—
813	C₂×C₈	—	4	2	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	1	no	—
820	C₄⋊C₄	—	2	1	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	1	no	—
824	C₄⋊C₄	—	2	1	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	1	no	—
828	C₄⋊C₄	—	2	1	no	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	4	2	no	—
831	C₄⋊C₄	—	4	2	no	—
832	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
833	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
834	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
835	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
836	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
837	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
838	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
839	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
840	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
841	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
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	1	no	—
847	C₂²⋊C₄	—	2	1	no	—
848	C₂²⋊C₄	—	2	1	no	—
849	C₂²⋊C₄	—	2	1	no	—
850	C₂²⋊C₄	—	2	1	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	—	2	1	no	—
857	C₂²⋊C₄	—	2	1	no	—
858	C₂²⋊C₄	—	2	1	no	—
859	C₂²⋊C₄	—	4	2	no	—
860	C₂²⋊C₄	—	4	2	no	—
861	C₂²⋊C₄	—	4	2	no	—
862	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
863	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
864	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
865	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
866	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
867	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
868	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
869	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
870	C₄²	—	2	1	no	—
871	C₄²	—	2	1	no	—
872	C₄²	—	2	1	no	—
873	C₄²	—	2	1	no	—
874	C₄²	—	2	1	no	—
875	C₄²	—	2	1	no	—
876	C₄²	—	2	1	no	—
877	C₄²	—	2	1	no	—
878	C₄²	—	2	1	no	—
879	C₄²	—	2	1	no	—
880	C₄²	—	2	1	no	—
881	C₄²	—	2	1	no	—
882	C₄²	—	2	1	no	—
883	C₄²	—	2	1	no	—
884	C₄²	—	2	1	no	—
885	C₄²	—	2	1	no	—
886	C₄²	—	4	2	no	—
887	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
888	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
889	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
890	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
891	C₄²	#41×C₁₉	1	2	yes	complemented
892	C₂³	—	2	2	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	1	no	—
898	C₂³	—	4	1	no	—
899	C₂³	—	4	1	no	—
900	C₂³	—	4	1	no	—
901	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
902	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
903	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
904	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
905	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
906	Q₈	—	2	1	no	—
907	Q₈	—	2	1	no	—
908	Q₈	—	4	2	no	—
909	Q₈	—	8	1	no	—
910	D₄	—	2	2	no	—
911	D₄	—	2	2	no	—
912	D₄	—	2	1	no	—
913	D₄	—	2	1	no	—
914	D₄	—	4	1	no	—
915	D₄	—	4	1	no	—
916	D₄	—	4	2	no	—
917	D₄	—	4	2	no	—
918	D₄	—	4	1	no	—
919	D₄	—	4	1	no	—
920	D₄	—	8	1	no	—
921	D₄	—	8	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	4	1	no	—
952	C₂×C₄	—	4	1	no	—
953	C₂×C₄	—	4	2	no	—
954	C₂×C₄	—	4	1	no	—
955	C₂×C₄	—	4	1	no	—
956	C₂×C₄	—	4	1	no	—
957	C₂×C₄	—	4	2	no	—
958	C₂×C₄	—	4	8	no	—
959	C₂×C₄	—	4	2	no	—
960	C₂×C₄	—	4	1	no	—
961	C₂×C₄	—	4	1	no	—
962	C₂×C₄	—	4	1	no	—
963	C₂×C₄	—	4	1	no	—
964	C₂×C₄	—	4	1	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	1	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	8	1	no	—
970	C₂×C₄	—	8	1	no	—
971	C₂×C₄	—	8	1	no	—
972	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
973	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
974	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
975	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
976	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
977	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
978	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
979	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
980	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
981	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
982	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
983	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
984	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
985	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
986	C₈	—	2	2	no	—
987	C₈	—	4	1	no	—
988	C₈	—	4	1	no	—
989	C₈	—	4	1	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	2	1	no	—
993	C₂²	—	2	1	no	—
994	C₂²	—	2	1	no	—
995	C₂²	—	2	1	no	—
996	C₂²	—	2	1	no	—
997	C₂²	—	2	1	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	1	no	—
1000	C₂²	—	2	1	no	—
1001	C₂²	—	2	1	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	1	no	—
1008	C₂²	—	8	1	no	—
1009	C₂²	—	8	1	no	—
1010	C₂²	C₁₉×#421	1	2	yes	—
1011	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1012	C₂²	C₁₉×#546	1	1	yes	characteristic
1013	C₂²	C₁₉×#547	1	1	yes	characteristic
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	2	1	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	2	1	no	—
1021	C₄	—	2	1	no	—
1022	C₄	—	4	2	no	—
1023	C₄	—	4	2	no	—
1024	C₄	—	4	1	no	—
1025	C₄	—	4	1	no	—
1026	C₄	—	4	1	no	—
1027	C₄	—	4	1	no	—
1028	C₄	—	4	1	no	—
1029	C₄	—	4	1	no	—
1030	C₄	—	4	1	no	—
1031	C₄	—	8	1	no	—
1032	C₄	—	8	1	no	—
1033	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
1034	C₄	C₁₉×#520	1	1	yes	characteristic
1035	C₄	C₁₉×#546	1	1	yes	characteristic
1036	C₄	C₁₉×#547	1	1	yes	characteristic
1037	C₂	—	2	1	no	—
1038	C₂	—	2	1	no	—
1039	C₂	—	2	2	no	—
1040	C₂	—	4	1	no	—
1041	C₂	—	4	1	no	—
1042	C₂	—	4	1	no	—
1043	C₂	—	8	1	no	—
1044	C₂	C₁₉×#2339	1	1	yes	characteristic
1045	C₂	C₂×C₁₉×#421	1	1	yes	characteristic
1046	C₂	C₁₉×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
prime radical	C₁₉×#3475	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×M₁₆×C₁₉	C₂	semidirect
3. C₁₉×#2290	C₂	semidirect
4. C₁₉×#1995	C₂	semidirect
5. C₁₉×#1986	C₂	semidirect
6. C₁₉×#1897	C₂	semidirect
7. C₁₉×#1896	C₂	semidirect
8. C₁₉×#1871	C₂	semidirect
9. C₁₉×#1871	C₂	semidirect
10. C₁₉×#1826	C₂	semidirect
11. C₁₉×#1826	C₂	semidirect
12. C₁₉×#1806	C₂	semidirect
13. C₁₉×#1759	C₂	semidirect
14. C₁₉×#1733	C₂	semidirect
15. C₂×C₁₉×#339	C₂	semidirect
18. C₁₉×#556	C₄	semidirect
19. C₁₉×#555	C₄	semidirect
20. C₁₉×#554	C₄	semidirect
21. C₁₉×#553	C₄	semidirect
22. C₁₉×#553	C₄	semidirect
24. C₁₉×#552	C₄	semidirect
25. C₁₉×#552	C₄	semidirect
28. C₁₉×#547	C₄	semidirect
93. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
94. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
104. C₁₉×#125	C₂×C₄	semidirect
105. C₁₉×#125	C₂×C₄	semidirect
124. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
125. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
131. C₁₉×#121	C₂×C₄	semidirect
132. C₁₉×#121	C₂×C₄	semidirect
138. C₄×Q₈×C₁₉	C₂×C₄	semidirect
139. C₄×Q₈×C₁₉	C₂×C₄	semidirect
153. C₄×D₄×C₁₉	C₂×C₄	semidirect
154. C₄×D₄×C₁₉	C₂×C₄	semidirect
171. C₁₉×#117	C₂×C₄	semidirect
172. C₁₉×#117	C₂×C₄	semidirect
180. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
181. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
283. M₁₆×C₁₉	#41	semidirect
367. C₄²×C₁₉	#41	semidirect
368. #22506	C₁₉	direct (N × H)
468. D₄×M₁₆	C₂×C₁₉	semidirect
469. #2290	C₂×C₁₉	semidirect
470. #1995	C₂×C₁₉	semidirect
471. #1986	C₂×C₁₉	semidirect
472. #1897	C₂×C₁₉	semidirect
473. #1896	C₂×C₁₉	semidirect
474. #1871	C₂×C₁₉	semidirect
475. #1871	C₂×C₁₉	semidirect
476. #1826	C₂×C₁₉	semidirect
477. #1826	C₂×C₁₉	semidirect
478. #1806	C₂×C₁₉	semidirect
479. #1759	C₂×C₁₉	semidirect
480. #1733	C₂×C₁₉	semidirect
481. C₂×#339	C₂×C₁₉	semidirect
531. #556	C₄×C₁₉	semidirect
532. #555	C₄×C₁₉	semidirect
533. #554	C₄×C₁₉	semidirect
534. #553	C₄×C₁₉	semidirect
535. #553	C₄×C₁₉	semidirect
537. #552	C₄×C₁₉	semidirect
538. #552	C₄×C₁₉	semidirect
541. #547	C₄×C₁₉	semidirect
616. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
617. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
627. #125	C₂×C₄×C₁₉	semidirect
628. #125	C₂×C₄×C₁₉	semidirect
647. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
648. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
654. #121	C₂×C₄×C₁₉	semidirect
655. #121	C₂×C₄×C₁₉	semidirect
661. C₄×Q₈	C₂×C₄×C₁₉	semidirect
662. C₄×Q₈	C₂×C₄×C₁₉	semidirect
676. C₄×D₄	C₂×C₄×C₁₉	semidirect
677. C₄×D₄	C₂×C₄×C₁₉	semidirect
694. #117	C₂×C₄×C₁₉	semidirect
695. #117	C₂×C₄×C₁₉	semidirect
703. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
704. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
741. C₁₉	#22506	direct (N × H)
807. M₁₆	#41×C₁₉	semidirect
891. C₄²	#41×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3475	2
D₄×M₁₆×C₁₉	2
C₁₉×#2290	2
C₁₉×#1995	2
C₁₉×#1986	2
C₁₉×#1897	2
C₁₉×#1896	2
C₁₉×#1871	2
C₁₉×#1826	2
C₁₉×#1806	2
C₁₉×#1759	2
C₁₉×#1733	2
C₂×C₁₉×#339	2
#22506	19

Subgroups — C19×#22506 #18028465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22506 #18028465