Subgroups — C₁₉×#62279 #18068238

Order 4864.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3541	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3349	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3346	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3302	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3301	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3300	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3299	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3270	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3269	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3262	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3261	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3203	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3202	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3196	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3178	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3063	C₂	1	2	yes	maximal, complemented
17	C₁₉×#3050	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#2929	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
21	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
22	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
24	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#563	—	2	2	no	—
26	C₁₉×#562	—	2	2	no	—
27	C₁₉×#556	C₂²	1	2	yes	—
28	C₁₉×#554	—	2	2	no	—
29	C₁₉×#554	C₂²	1	2	yes	—
30	C₁₉×#553	—	2	2	no	—
31	C₁₉×#553	C₂²	1	2	yes	—
32	C₁₉×#552	C₂²	1	2	yes	—
33	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
34	C₁₉×#548	C₂²	1	2	yes	—
35	C₁₉×#548	C₂²	1	2	yes	—
36	C₁₉×#547	C₂²	1	2	yes	—
37	C₁₉×#542	—	2	2	no	—
38	C₁₉×#542	C₂²	1	2	yes	—
39	C₁₉×#541	C₂²	1	2	yes	—
40	C₁₉×#539	—	2	2	no	—
41	C₁₉×#538	—	2	2	no	—
42	C₁₉×#538	—	2	2	no	—
43	C₁₉×#537	C₂²	1	2	yes	—
44	C₁₉×#536	C₂²	1	2	yes	—
45	C₁₉×#525	C₂²	1	2	yes	—
46	C₁₉×#525	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
48	C₁₉×#501	C₂²	1	2	yes	complemented
49	C₁₉×#497	C₂²	1	2	yes	complemented
50	C₁₉×#488	C₂²	1	2	yes	complemented
51	C₁₉×#487	C₂²	1	2	yes	complemented
52	C₁₉×#485	C₂²	1	2	yes	—
53	C₁₉×#485	C₂²	1	2	yes	—
54	C₁₉×#485	C₂²	1	2	yes	complemented
55	C₁₉×#485	C₂²	1	2	yes	complemented
56	C₁₉×#484	C₂²	1	2	yes	—
57	C₁₉×#484	C₂²	1	2	yes	complemented
58	C₁₉×#481	C₂²	1	2	yes	—
59	C₁₉×#480	C₂²	1	2	yes	complemented
60	C₁₉×#479	C₂²	1	2	yes	complemented
61	C₁₉×#479	C₂²	1	2	yes	complemented
62	C₁₉×#477	C₂²	1	2	yes	complemented
63	C₁₉×#474	C₂²	1	2	yes	complemented
64	C₁₉×#470	C₂²	1	2	yes	—
65	C₁₉×#470	C₂²	1	2	yes	—
66	C₁₉×#470	C₂²	1	2	yes	complemented
67	C₁₉×#468	C₂²	1	2	yes	—
68	C₁₉×#468	C₂²	1	2	yes	—
69	C₁₉×#468	C₂²	1	2	yes	complemented
70	C₁₉×#467	C₂²	1	2	yes	—
71	C₁₉×#467	C₂²	1	1	yes	characteristic
72	C₁₉×#467	C₂²	1	1	yes	characteristic
73	C₁₉×#467	C₂²	1	1	yes	characteristic
74	C₁₉×#467	C₂²	1	2	yes	—
75	C₁₉×#467	C₂²	1	1	yes	characteristic
76	C₁₉×#467	C₂²	1	1	yes	characteristic
77	C₁₉×#467	C₂²	1	1	yes	characteristic
78	C₁₉×#467	C₂²	1	2	yes	complemented
79	C₁₉×#466	C₂²	1	1	yes	characteristic
80	C₁₉×#466	C₂²	1	1	yes	characteristic
81	C₁₉×#465	C₂²	1	2	yes	—
82	C₁₉×#465	C₂²	1	2	yes	—
83	C₁₉×#465	C₂²	1	2	yes	complemented
84	C₁₉×#464	C₂²	1	2	yes	complemented
85	C₁₉×#463	C₂²	1	2	yes	complemented
86	C₁₉×#462	C₂²	1	2	yes	complemented
87	C₁₉×#462	C₂²	1	2	yes	complemented
88	C₁₉×#452	C₂²	1	2	yes	—
89	C₁₉×#452	C₂²	1	2	yes	—
90	C₁₉×#452	C₂²	1	2	yes	complemented
91	C₁₉×#451	C₂²	1	2	yes	—
92	C₁₉×#451	C₂²	1	2	yes	complemented
93	C₁₉×#451	C₂²	1	2	yes	complemented
94	C₁₉×#449	C₂²	1	2	yes	complemented
95	C₁₉×#448	C₂²	1	2	yes	—
96	C₁₉×#441	C₂²	1	2	yes	complemented
97	C₁₉×#440	C₂²	1	2	yes	complemented
98	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
99	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
100	C₁₉×#435	C₂²	1	2	yes	—
101	C₁₉×#435	C₂²	1	2	yes	—
102	C₈×D₄×C₁₉	C₂²	1	2	yes	—
103	C₈×D₄×C₁₉	C₂²	1	2	yes	—
104	C₁₉×#428	C₂²	1	2	yes	complemented
105	C₁₉×#427	C₂²	1	1	yes	characteristic
106	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
107	C₁₉×#424	C₂²	1	1	yes	characteristic
108	C₁₉×#416	C₂²	1	2	yes	—
109	C₁₉×#416	C₂²	1	2	yes	complemented
110	C₂×C₁₉×#103	C₂²	1	2	yes	—
111	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
112	C₁₉×#408	C₂²	1	1	yes	characteristic
113	C₁₉×#407	C₂²	1	1	yes	characteristic
114	C₁₉×#405	C₂²	1	1	yes	characteristic
115	C₂×#41×C₁₉	C₂³	1	2	yes	—
116	C₂×#41×C₁₉	C₂³	1	2	yes	—
117	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
118	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
119	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
121	C₁₉×#137	—	4	4	no	—
122	C₁₉×#135	—	4	2	no	—
123	C₂×Q₁₆×C₁₉	—	4	2	no	—
124	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
126	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
127	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
129	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
130	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
132	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
133	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
134	C₁₉×#131	—	4	2	no	—
135	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
136	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₁₉	—	4	2	no	—
139	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
145	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
146	C₁₉×C₄⋊Q₈	—	2	2	no	—
147	C₁₉×C₄⋊Q₈	—	2	2	no	—
148	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
149	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
150	C₁₉×#126	—	2	2	no	—
151	C₁₉×#126	—	2	2	no	—
152	C₁₉×#126	—	2	2	no	—
153	C₁₉×#126	—	2	2	no	—
154	C₁₉×#126	—	2	2	no	—
155	C₁₉×#126	—	2	2	no	—
156	C₁₉×#126	—	2	2	no	—
157	C₁₉×#125	—	2	2	no	—
158	C₁₉×#125	—	2	2	no	—
159	C₁₉×#125	—	2	2	no	—
160	C₁₉×#125	—	2	2	no	—
161	C₁₉×#125	C₂³	1	2	yes	—
162	C₁₉×#124	—	2	2	no	—
163	C₁₉×#124	—	2	2	no	—
164	C₁₉×#124	—	2	2	no	—
165	C₁₉×#124	—	2	2	no	—
166	C₁₉×#124	—	2	2	no	—
167	C₁₉×#124	C₂³	1	2	yes	—
168	C₁₉×#123	—	2	2	no	—
169	C₁₉×#123	—	2	2	no	—
170	C₁₉×#123	—	2	2	no	—
171	C₁₉×#123	—	2	2	no	—
172	C₁₉×#123	—	2	2	no	—
173	C₁₉×#123	—	2	2	no	—
174	C₁₉×#123	—	2	2	no	—
175	C₁₉×#123	—	2	2	no	—
176	C₁₉×#123	D₄	1	2	yes	—
177	C₁₉×C₂²⋊Q₈	—	2	2	no	—
178	C₁₉×C₂²⋊Q₈	—	2	2	no	—
179	C₁₉×C₂²⋊Q₈	—	2	2	no	—
180	C₁₉×C₂²⋊Q₈	—	2	2	no	—
181	C₁₉×C₂²⋊Q₈	—	2	2	no	—
182	C₁₉×C₂²⋊Q₈	—	2	2	no	—
183	C₁₉×C₂²⋊Q₈	—	2	2	no	—
184	C₁₉×C₂²⋊Q₈	—	2	2	no	—
185	C₁₉×C₂²⋊Q₈	—	2	2	no	—
186	C₁₉×C₂²⋊Q₈	—	2	2	no	—
187	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
188	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
189	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₁₉×#121	—	2	2	no	—
199	C₁₉×#121	—	2	2	no	—
200	C₁₉×#121	—	2	2	no	—
201	C₁₉×#121	—	2	2	no	—
202	C₁₉×#121	—	2	2	no	—
203	C₁₉×#121	—	2	2	no	—
204	C₁₉×#121	—	2	2	no	—
205	C₁₉×#121	D₄	1	1	yes	characteristic
206	C₁₉×#121	D₄	1	1	yes	characteristic
207	C₁₉×#121	C₂³	1	2	yes	—
208	C₁₉×#121	C₂³	1	2	yes	—
209	C₁₉×#121	C₂³	1	2	yes	—
210	C₁₉×#120	—	2	2	no	—
211	C₁₉×#120	D₄	1	2	yes	—
212	C₄×Q₈×C₁₉	—	2	2	no	—
213	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
214	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
215	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
216	C₄×D₄×C₁₉	—	2	2	no	—
217	C₄×D₄×C₁₉	—	2	2	no	—
218	C₄×D₄×C₁₉	—	2	2	no	—
219	C₄×D₄×C₁₉	—	2	2	no	—
220	C₄×D₄×C₁₉	—	2	2	no	—
221	C₄×D₄×C₁₉	—	2	2	no	—
222	C₄×D₄×C₁₉	—	2	2	no	—
223	C₄×D₄×C₁₉	C₂³	1	2	yes	—
224	C₄×D₄×C₁₉	C₂³	1	2	yes	—
225	C₄×D₄×C₁₉	C₂³	1	2	yes	—
226	C₁₉×#117	—	2	2	no	—
227	C₁₉×#117	C₂³	1	2	yes	—
228	C₁₉×#117	C₂³	1	2	yes	—
229	C₁₉×#117	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
231	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
232	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
234	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
235	C₁₉×#107	C₂³	1	2	yes	—
236	C₁₉×#107	C₂³	1	1	yes	characteristic
237	C₁₉×#107	C₂³	1	1	yes	characteristic
238	C₁₉×#107	C₂³	1	1	yes	characteristic
239	C₁₉×#107	C₂³	1	1	yes	characteristic
240	C₁₉×#107	C₂³	1	2	yes	—
241	C₁₉×#107	C₂³	1	2	yes	—
242	C₁₉×#106	C₂³	1	2	yes	—
243	C₁₉×#106	C₂³	1	2	yes	—
244	C₁₉×#106	C₂³	1	2	yes	—
245	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
246	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
247	C₁₉×#103	C₂³	1	2	yes	—
248	C₁₉×#103	C₂³	1	2	yes	—
249	C₁₉×#103	C₂³	1	2	yes	—
250	C₁₉×#103	C₂³	1	2	yes	—
251	C₁₉×#103	C₂³	1	2	yes	—
252	C₁₉×#103	C₂³	1	2	yes	—
253	C₁₉×#103	C₂³	1	2	yes	—
254	C₁₉×#103	C₂³	1	2	yes	—
255	C₁₉×#103	C₂³	1	2	yes	—
256	C₁₉×#103	C₂³	1	2	yes	—
257	C₁₉×#103	C₂³	1	2	yes	—
258	C₁₉×#103	C₂³	1	2	yes	—
259	C₁₉×#102	C₂³	1	2	yes	—
260	C₁₉×#102	C₂³	1	2	yes	—
261	C₁₉×#102	C₂³	1	2	yes	—
262	C₁₉×#102	C₂³	1	2	yes	—
263	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
264	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
265	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
266	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
267	C₁₉×#97	C₂³	1	2	yes	—
268	C₄×C₈×C₁₉	C₂³	1	2	yes	—
269	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
270	#41×C₁₉	—	4	1	no	—
271	#41×C₁₉	—	4	1	no	—
272	#41×C₁₉	—	4	2	no	—
273	#41×C₁₉	—	4	2	no	—
274	#41×C₁₉	—	4	2	no	—
275	#41×C₁₉	—	4	2	no	—
276	C₂×Q₈×C₁₉	—	2	2	no	—
277	C₂×Q₈×C₁₉	—	2	2	no	—
278	C₂×Q₈×C₁₉	—	2	2	no	—
279	C₂×Q₈×C₁₉	—	4	2	no	—
280	C₂×Q₈×C₁₉	—	4	2	no	—
281	C₂×Q₈×C₁₉	—	4	2	no	—
282	C₂×Q₈×C₁₉	—	4	2	no	—
283	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
284	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
285	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
286	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
287	C₂×D₄×C₁₉	—	2	2	no	—
288	C₂×D₄×C₁₉	—	2	2	no	—
289	C₂×D₄×C₁₉	—	2	2	no	—
290	C₂×D₄×C₁₉	—	2	2	no	—
291	C₂×D₄×C₁₉	—	2	2	no	—
292	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
293	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
294	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
295	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
296	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₁₉	—	2	2	no	—
298	C₂²×C₄×C₁₉	—	2	2	no	—
299	C₂²×C₄×C₁₉	—	2	2	no	—
300	C₂²×C₄×C₁₉	—	2	2	no	—
301	C₂²×C₄×C₁₉	—	2	2	no	—
302	C₂²×C₄×C₁₉	—	2	2	no	—
303	C₂²×C₄×C₁₉	—	2	2	no	—
304	C₂²×C₄×C₁₉	—	4	1	no	—
305	C₂²×C₄×C₁₉	—	4	1	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	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
313	Q₁₆×C₁₉	—	2	4	no	—
314	Q₁₆×C₁₉	—	4	1	no	—
315	Q₁₆×C₁₉	—	4	1	no	—
316	Q₁₆×C₁₉	—	4	2	no	—
317	Q₁₆×C₁₉	—	4	1	no	—
318	Q₁₆×C₁₉	—	4	2	no	—
319	SD₁₆×C₁₉	—	2	4	no	—
320	SD₁₆×C₁₉	—	4	2	no	—
321	SD₁₆×C₁₉	—	4	2	no	—
322	D₈×C₁₉	—	4	1	no	—
323	M₁₆×C₁₉	—	2	4	no	—
324	M₁₆×C₁₉	—	4	1	no	—
325	M₁₆×C₁₉	—	4	1	no	—
326	C₂×C₈×C₁₉	—	2	2	no	—
327	C₂×C₈×C₁₉	—	2	2	no	—
328	C₂×C₈×C₁₉	—	2	2	no	—
329	C₂×C₈×C₁₉	—	4	1	no	—
330	C₂×C₈×C₁₉	—	4	1	no	—
331	C₂×C₈×C₁₉	—	4	1	no	—
332	C₂×C₈×C₁₉	—	4	2	no	—
333	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
334	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
335	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
336	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
337	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
338	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
339	C₄⋊C₄×C₁₉	—	2	2	no	—
340	C₄⋊C₄×C₁₉	—	2	2	no	—
341	C₄⋊C₄×C₁₉	—	2	2	no	—
342	C₄⋊C₄×C₁₉	—	2	2	no	—
343	C₄⋊C₄×C₁₉	—	2	2	no	—
344	C₄⋊C₄×C₁₉	—	2	2	no	—
345	C₄⋊C₄×C₁₉	—	2	2	no	—
346	C₄⋊C₄×C₁₉	—	2	2	no	—
347	C₄⋊C₄×C₁₉	—	2	2	no	—
348	C₄⋊C₄×C₁₉	—	2	2	no	—
349	C₄⋊C₄×C₁₉	—	2	2	no	—
350	C₄⋊C₄×C₁₉	—	2	2	no	—
351	C₄⋊C₄×C₁₉	—	2	2	no	—
352	C₄⋊C₄×C₁₉	—	2	2	no	—
353	C₄⋊C₄×C₁₉	—	2	2	no	—
354	C₄⋊C₄×C₁₉	—	2	2	no	—
355	C₄⋊C₄×C₁₉	—	2	2	no	—
356	C₄⋊C₄×C₁₉	—	2	2	no	—
357	C₄⋊C₄×C₁₉	—	2	2	no	—
358	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
360	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
366	C₂²⋊C₄×C₁₉	—	2	2	no	—
367	C₂²⋊C₄×C₁₉	—	2	2	no	—
368	C₂²⋊C₄×C₁₉	—	2	2	no	—
369	C₂²⋊C₄×C₁₉	—	2	2	no	—
370	C₂²⋊C₄×C₁₉	—	2	2	no	—
371	C₂²⋊C₄×C₁₉	—	2	2	no	—
372	C₂²⋊C₄×C₁₉	—	2	2	no	—
373	C₂²⋊C₄×C₁₉	—	2	2	no	—
374	C₂²⋊C₄×C₁₉	—	2	2	no	—
375	C₂²⋊C₄×C₁₉	—	2	2	no	—
376	C₂²⋊C₄×C₁₉	—	2	2	no	—
377	C₂²⋊C₄×C₁₉	—	2	2	no	—
378	C₂²⋊C₄×C₁₉	—	2	2	no	—
379	C₂²⋊C₄×C₁₉	—	2	2	no	—
380	C₂²⋊C₄×C₁₉	—	2	2	no	—
381	C₂²⋊C₄×C₁₉	—	2	2	no	—
382	C₂²⋊C₄×C₁₉	—	2	2	no	—
383	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
384	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
385	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
386	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
387	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
388	C₄²×C₁₉	—	2	2	no	—
389	C₄²×C₁₉	—	2	2	no	—
390	C₄²×C₁₉	—	2	2	no	—
391	C₄²×C₁₉	—	2	2	no	—
392	C₄²×C₁₉	—	2	2	no	—
393	C₄²×C₁₉	C₂⁴	1	2	yes	—
394	#62279	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
395	C₂³×C₁₉	—	2	2	no	—
396	C₂³×C₁₉	—	2	2	no	—
397	C₂³×C₁₉	—	4	1	no	—
398	C₂³×C₁₉	—	4	1	no	—
399	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
400	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
401	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
402	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
403	Q₈×C₁₉	—	2	2	no	—
404	Q₈×C₁₉	—	2	2	no	—
405	Q₈×C₁₉	—	2	2	no	—
406	Q₈×C₁₉	—	2	2	no	—
407	Q₈×C₁₉	—	2	2	no	—
408	Q₈×C₁₉	—	2	2	no	—
409	Q₈×C₁₉	—	4	1	no	—
410	Q₈×C₁₉	—	8	2	no	—
411	Q₈×C₁₉	—	8	2	no	—
412	Q₈×C₁₉	—	8	2	no	—
413	D₄×C₁₉	—	2	4	no	—
414	D₄×C₁₉	—	2	2	no	—
415	D₄×C₁₉	—	2	2	no	—
416	D₄×C₁₉	—	4	2	no	—
417	D₄×C₁₉	—	4	1	no	—
418	D₄×C₁₉	—	4	2	no	—
419	D₄×C₁₉	—	4	4	no	—
420	D₄×C₁₉	—	8	2	no	—
421	D₄×C₁₉	—	8	2	no	—
422	D₄×C₁₉	—	8	2	no	—
423	D₄×C₁₉	—	8	2	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	—	2	1	no	—
429	C₂×C₄×C₁₉	—	2	1	no	—
430	C₂×C₄×C₁₉	—	2	1	no	—
431	C₂×C₄×C₁₉	—	2	2	no	—
432	C₂×C₄×C₁₉	—	2	2	no	—
433	C₂×C₄×C₁₉	—	2	2	no	—
434	C₂×C₄×C₁₉	—	2	2	no	—
435	C₂×C₄×C₁₉	—	2	2	no	—
436	C₂×C₄×C₁₉	—	2	2	no	—
437	C₂×C₄×C₁₉	—	2	2	no	—
438	C₂×C₄×C₁₉	—	2	2	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	—	8	2	no	—
443	C₂×C₄×C₁₉	—	8	2	no	—
444	C₂×C₄×C₁₉	—	8	2	no	—
445	C₂×C₄×C₁₉	—	8	2	no	—
446	C₂×C₄×C₁₉	—	8	2	no	—
447	C₂×C₄×C₁₉	—	8	2	no	—
448	C₂×C₄×C₁₉	—	8	2	no	—
449	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
450	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
456	C₈×C₁₉	—	2	1	no	—
457	C₈×C₁₉	—	2	1	no	—
458	C₈×C₁₉	—	2	1	no	—
459	C₈×C₁₉	—	2	2	no	—
460	C₈×C₁₉	—	2	2	no	—
461	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
462	#3541	C₂×C₁₉	1	2	yes	complemented
463	#3349	C₂×C₁₉	1	2	yes	complemented
464	#3346	C₂×C₁₉	1	2	yes	complemented
465	#3302	C₂×C₁₉	1	2	yes	complemented
466	#3301	C₂×C₁₉	1	2	yes	complemented
467	#3300	C₂×C₁₉	1	2	yes	complemented
468	#3299	C₂×C₁₉	1	2	yes	complemented
469	#3270	C₂×C₁₉	1	2	yes	complemented
470	#3269	C₂×C₁₉	1	2	yes	complemented
471	#3262	C₂×C₁₉	1	1	yes	characteristic, complemented
472	#3261	C₂×C₁₉	1	1	yes	characteristic, complemented
473	#3203	C₂×C₁₉	1	1	yes	characteristic, complemented
474	#3202	C₂×C₁₉	1	1	yes	characteristic, complemented
475	#3196	C₂×C₁₉	1	2	yes	complemented
476	#3178	C₂×C₁₉	1	2	yes	complemented
477	#3063	C₂×C₁₉	1	2	yes	complemented
478	#3050	C₂×C₁₉	1	1	yes	characteristic, complemented
479	C₂×#467	C₂×C₁₉	1	1	yes	characteristic, complemented
480	#2929	C₂×C₁₉	1	1	yes	characteristic, complemented
481	C₂²×C₁₉	—	2	1	no	—
482	C₂²×C₁₉	—	2	1	no	—
483	C₂²×C₁₉	—	2	2	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	2	no	—
489	C₂²×C₁₉	—	2	2	no	—
490	C₂²×C₁₉	—	2	1	no	—
491	C₂²×C₁₉	—	2	1	no	—
492	C₂²×C₁₉	—	4	4	no	—
493	C₂²×C₁₉	—	4	2	no	—
494	C₂²×C₁₉	—	4	2	no	—
495	C₂²×C₁₉	—	4	2	no	—
496	C₂²×C₁₉	#578	1	2	yes	—
497	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
498	C₄×C₁₉	—	2	2	no	—
499	C₄×C₁₉	—	2	1	no	—
500	C₄×C₁₉	—	2	1	no	—
501	C₄×C₁₉	—	2	1	no	—
502	C₄×C₁₉	—	2	2	no	—
503	C₄×C₁₉	—	2	2	no	—
504	C₄×C₁₉	—	4	2	no	—
505	C₄×C₁₉	—	4	2	no	—
506	C₄×C₁₉	—	4	2	no	—
507	C₄×C₁₉	—	4	2	no	—
508	C₄×C₁₉	—	4	2	no	—
509	C₄×C₁₉	—	4	2	no	—
510	C₄×C₁₉	—	4	2	no	—
511	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
512	C₄×C₁₉	#585	1	1	yes	characteristic
513	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
514	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
515	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
516	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
517	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
518	#563	—	2	2	no	—
519	#562	—	2	2	no	—
520	#556	C₂²×C₁₉	1	2	yes	—
521	#554	—	2	2	no	—
522	#554	C₂²×C₁₉	1	2	yes	—
523	#553	—	2	2	no	—
524	#553	C₂²×C₁₉	1	2	yes	—
525	#552	C₂²×C₁₉	1	2	yes	—
526	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
527	#548	C₂²×C₁₉	1	2	yes	—
528	#548	C₂²×C₁₉	1	2	yes	—
529	#547	C₂²×C₁₉	1	2	yes	—
530	#542	—	2	2	no	—
531	#542	C₂²×C₁₉	1	2	yes	—
532	#541	C₂²×C₁₉	1	2	yes	—
533	#539	—	2	2	no	—
534	#538	—	2	2	no	—
535	#538	—	2	2	no	—
536	#537	C₂²×C₁₉	1	2	yes	—
537	#536	C₂²×C₁₉	1	2	yes	—
538	#525	C₂²×C₁₉	1	2	yes	—
539	#525	C₂²×C₁₉	1	1	yes	characteristic
540	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
541	#501	C₂²×C₁₉	1	2	yes	complemented
542	#497	C₂²×C₁₉	1	2	yes	complemented
543	#488	C₂²×C₁₉	1	2	yes	complemented
544	#487	C₂²×C₁₉	1	2	yes	complemented
545	#485	C₂²×C₁₉	1	2	yes	—
546	#485	C₂²×C₁₉	1	2	yes	—
547	#485	C₂²×C₁₉	1	2	yes	complemented
548	#485	C₂²×C₁₉	1	2	yes	complemented
549	#484	C₂²×C₁₉	1	2	yes	—
550	#484	C₂²×C₁₉	1	2	yes	complemented
551	#481	C₂²×C₁₉	1	2	yes	—
552	#480	C₂²×C₁₉	1	2	yes	complemented
553	#479	C₂²×C₁₉	1	2	yes	complemented
554	#479	C₂²×C₁₉	1	2	yes	complemented
555	#477	C₂²×C₁₉	1	2	yes	complemented
556	#474	C₂²×C₁₉	1	2	yes	complemented
557	#470	C₂²×C₁₉	1	2	yes	—
558	#470	C₂²×C₁₉	1	2	yes	—
559	#470	C₂²×C₁₉	1	2	yes	complemented
560	#468	C₂²×C₁₉	1	2	yes	—
561	#468	C₂²×C₁₉	1	2	yes	—
562	#468	C₂²×C₁₉	1	2	yes	complemented
563	#467	C₂²×C₁₉	1	2	yes	—
564	#467	C₂²×C₁₉	1	2	yes	—
565	#467	C₂²×C₁₉	1	1	yes	characteristic
566	#467	C₂²×C₁₉	1	1	yes	characteristic
567	#467	C₂²×C₁₉	1	1	yes	characteristic
568	#467	C₂²×C₁₉	1	1	yes	characteristic
569	#467	C₂²×C₁₉	1	1	yes	characteristic
570	#467	C₂²×C₁₉	1	1	yes	characteristic
571	#467	C₂²×C₁₉	1	2	yes	complemented
572	#466	C₂²×C₁₉	1	1	yes	characteristic
573	#466	C₂²×C₁₉	1	1	yes	characteristic
574	#465	C₂²×C₁₉	1	2	yes	—
575	#465	C₂²×C₁₉	1	2	yes	—
576	#465	C₂²×C₁₉	1	2	yes	complemented
577	#464	C₂²×C₁₉	1	2	yes	complemented
578	#463	C₂²×C₁₉	1	2	yes	complemented
579	#462	C₂²×C₁₉	1	2	yes	complemented
580	#462	C₂²×C₁₉	1	2	yes	complemented
581	#452	C₂²×C₁₉	1	2	yes	—
582	#452	C₂²×C₁₉	1	2	yes	—
583	#452	C₂²×C₁₉	1	2	yes	complemented
584	#451	C₂²×C₁₉	1	2	yes	—
585	#451	C₂²×C₁₉	1	2	yes	complemented
586	#451	C₂²×C₁₉	1	2	yes	complemented
587	#449	C₂²×C₁₉	1	2	yes	complemented
588	#448	C₂²×C₁₉	1	2	yes	—
589	#441	C₂²×C₁₉	1	2	yes	complemented
590	#440	C₂²×C₁₉	1	2	yes	complemented
591	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
592	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
593	#435	C₂²×C₁₉	1	2	yes	—
594	#435	C₂²×C₁₉	1	2	yes	—
595	C₈×D₄	C₂²×C₁₉	1	2	yes	—
596	C₈×D₄	C₂²×C₁₉	1	2	yes	—
597	#428	C₂²×C₁₉	1	2	yes	complemented
598	#427	C₂²×C₁₉	1	1	yes	characteristic
599	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
600	#424	C₂²×C₁₉	1	1	yes	characteristic
601	#416	C₂²×C₁₉	1	2	yes	—
602	#416	C₂²×C₁₉	1	2	yes	complemented
603	C₂×#103	C₂²×C₁₉	1	2	yes	—
604	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
605	#408	C₂²×C₁₉	1	1	yes	characteristic
606	#407	C₂²×C₁₉	1	1	yes	characteristic
607	#405	C₂²×C₁₉	1	1	yes	characteristic
608	C₂×C₁₉	—	2	2	no	—
609	C₂×C₁₉	—	4	2	no	—
610	C₂×C₁₉	—	4	1	no	—
611	C₂×C₁₉	—	4	1	no	—
612	C₂×C₁₉	—	8	2	no	—
613	C₂×C₁₉	#3496	1	1	yes	characteristic
614	C₂×C₁₉	C₂×#578	1	1	yes	characteristic
615	C₂×C₁₉	#3584	1	1	yes	characteristic
616	C₂×#41	C₂³×C₁₉	1	2	yes	—
617	C₂×#41	C₂³×C₁₉	1	2	yes	—
618	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
619	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
620	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
621	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
622	#137	—	4	4	no	—
623	#135	—	4	2	no	—
624	C₂×Q₁₆	—	4	2	no	—
625	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
626	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
627	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
628	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
629	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
630	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
631	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
632	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
633	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
634	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
635	#131	—	4	2	no	—
636	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
637	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
638	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
639	C₂²×C₈	—	4	2	no	—
640	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
641	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
642	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
643	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
644	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
645	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
646	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
647	C₄⋊Q₈	—	2	2	no	—
648	C₄⋊Q₈	—	2	2	no	—
649	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
650	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
651	#126	—	2	2	no	—
652	#126	—	2	2	no	—
653	#126	—	2	2	no	—
654	#126	—	2	2	no	—
655	#126	—	2	2	no	—
656	#126	—	2	2	no	—
657	#126	—	2	2	no	—
658	#125	—	2	2	no	—
659	#125	—	2	2	no	—
660	#125	—	2	2	no	—
661	#125	—	2	2	no	—
662	#125	C₂³×C₁₉	1	2	yes	—
663	#124	—	2	2	no	—
664	#124	—	2	2	no	—
665	#124	—	2	2	no	—
666	#124	—	2	2	no	—
667	#124	—	2	2	no	—
668	#124	C₂³×C₁₉	1	2	yes	—
669	#123	—	2	2	no	—
670	#123	—	2	2	no	—
671	#123	—	2	2	no	—
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	D₄×C₁₉	1	2	yes	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
689	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
690	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
691	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
692	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
693	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
694	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
695	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
696	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
697	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
698	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	—	2	2	no	—
703	#121	—	2	2	no	—
704	#121	—	2	2	no	—
705	#121	—	2	2	no	—
706	#121	D₄×C₁₉	1	1	yes	characteristic
707	#121	D₄×C₁₉	1	1	yes	characteristic
708	#121	C₂³×C₁₉	1	2	yes	—
709	#121	C₂³×C₁₉	1	2	yes	—
710	#121	C₂³×C₁₉	1	2	yes	—
711	#120	—	2	2	no	—
712	#120	D₄×C₁₉	1	2	yes	—
713	C₄×Q₈	—	2	2	no	—
714	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
715	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
716	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
717	C₄×D₄	—	2	2	no	—
718	C₄×D₄	—	2	2	no	—
719	C₄×D₄	—	2	2	no	—
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	C₂³×C₁₉	1	2	yes	—
725	C₄×D₄	C₂³×C₁₉	1	2	yes	—
726	C₄×D₄	C₂³×C₁₉	1	2	yes	—
727	#117	—	2	2	no	—
728	#117	C₂³×C₁₉	1	2	yes	—
729	#117	C₂³×C₁₉	1	2	yes	—
730	#117	C₂³×C₁₉	1	1	yes	characteristic
731	C₂×C₄⋊C₄	—	2	2	no	—
732	C₂×C₄⋊C₄	—	2	2	no	—
733	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
734	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
735	C₂×C₂²⋊C₄	—	2	2	no	—
736	#107	C₂³×C₁₉	1	2	yes	—
737	#107	C₂³×C₁₉	1	1	yes	characteristic
738	#107	C₂³×C₁₉	1	1	yes	characteristic
739	#107	C₂³×C₁₉	1	1	yes	characteristic
740	#107	C₂³×C₁₉	1	1	yes	characteristic
741	#107	C₂³×C₁₉	1	2	yes	—
742	#107	C₂³×C₁₉	1	2	yes	—
743	#106	C₂³×C₁₉	1	2	yes	—
744	#106	C₂³×C₁₉	1	2	yes	—
745	#106	C₂³×C₁₉	1	2	yes	—
746	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
747	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
748	#103	C₂³×C₁₉	1	2	yes	—
749	#103	C₂³×C₁₉	1	2	yes	—
750	#103	C₂³×C₁₉	1	2	yes	—
751	#103	C₂³×C₁₉	1	2	yes	—
752	#103	C₂³×C₁₉	1	2	yes	—
753	#103	C₂³×C₁₉	1	2	yes	—
754	#103	C₂³×C₁₉	1	2	yes	—
755	#103	C₂³×C₁₉	1	2	yes	—
756	#103	C₂³×C₁₉	1	2	yes	—
757	#103	C₂³×C₁₉	1	2	yes	—
758	#103	C₂³×C₁₉	1	2	yes	—
759	#103	C₂³×C₁₉	1	2	yes	—
760	#102	C₂³×C₁₉	1	2	yes	—
761	#102	C₂³×C₁₉	1	2	yes	—
762	#102	C₂³×C₁₉	1	2	yes	—
763	#102	C₂³×C₁₉	1	2	yes	—
764	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
765	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
766	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
767	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
768	#97	C₂³×C₁₉	1	2	yes	—
769	C₄×C₈	C₂³×C₁₉	1	2	yes	—
770	C₁₉	#62279	1	1	yes	characteristic, direct product factor, Sylow
771	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
772	#41	—	4	1	no	—
773	#41	—	4	1	no	—
774	#41	—	4	2	no	—
775	#41	—	4	2	no	—
776	#41	—	4	2	no	—
777	#41	—	4	2	no	—
778	C₂×Q₈	—	2	2	no	—
779	C₂×Q₈	—	2	2	no	—
780	C₂×Q₈	—	2	2	no	—
781	C₂×Q₈	—	4	2	no	—
782	C₂×Q₈	—	4	2	no	—
783	C₂×Q₈	—	4	2	no	—
784	C₂×Q₈	—	4	2	no	—
785	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
786	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
787	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
788	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	2	no	—
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
795	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
796	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
797	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
798	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	4	1	no	—
807	C₂²×C₄	—	4	1	no	—
808	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
809	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
810	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
813	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
815	Q₁₆	—	2	4	no	—
816	Q₁₆	—	4	1	no	—
817	Q₁₆	—	4	1	no	—
818	Q₁₆	—	4	2	no	—
819	Q₁₆	—	4	1	no	—
820	Q₁₆	—	4	2	no	—
821	SD₁₆	—	2	4	no	—
822	SD₁₆	—	4	2	no	—
823	SD₁₆	—	4	2	no	—
824	D₈	—	4	1	no	—
825	M₁₆	—	2	4	no	—
826	M₁₆	—	4	1	no	—
827	M₁₆	—	4	1	no	—
828	C₂×C₈	—	2	2	no	—
829	C₂×C₈	—	2	2	no	—
830	C₂×C₈	—	2	2	no	—
831	C₂×C₈	—	4	1	no	—
832	C₂×C₈	—	4	1	no	—
833	C₂×C₈	—	4	1	no	—
834	C₂×C₈	—	4	2	no	—
835	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
836	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
837	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
838	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
839	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
840	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
861	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
862	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
863	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
864	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
865	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
866	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
867	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
886	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
887	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
888	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
889	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
890	C₄²	—	2	2	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	2	no	—
895	C₄²	C₂⁴×C₁₉	1	2	yes	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	4	1	no	—
899	C₂³	—	4	1	no	—
900	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
901	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
902	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
903	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
904	Q₈	—	2	2	no	—
905	Q₈	—	2	2	no	—
906	Q₈	—	2	2	no	—
907	Q₈	—	2	2	no	—
908	Q₈	—	2	2	no	—
909	Q₈	—	2	2	no	—
910	Q₈	—	4	1	no	—
911	Q₈	—	8	2	no	—
912	Q₈	—	8	2	no	—
913	Q₈	—	8	2	no	—
914	D₄	—	2	4	no	—
915	D₄	—	2	2	no	—
916	D₄	—	2	2	no	—
917	D₄	—	4	1	no	—
918	D₄	—	4	2	no	—
919	D₄	—	4	2	no	—
920	D₄	—	4	4	no	—
921	D₄	—	8	2	no	—
922	D₄	—	8	2	no	—
923	D₄	—	8	2	no	—
924	D₄	—	8	2	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	4	1	no	—
941	C₂×C₄	—	4	1	no	—
942	C₂×C₄	—	4	1	no	—
943	C₂×C₄	—	8	2	no	—
944	C₂×C₄	—	8	2	no	—
945	C₂×C₄	—	8	2	no	—
946	C₂×C₄	—	8	2	no	—
947	C₂×C₄	—	8	2	no	—
948	C₂×C₄	—	8	2	no	—
949	C₂×C₄	—	8	2	no	—
950	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
951	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
952	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
953	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
954	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
955	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
956	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
957	C₈	—	2	1	no	—
958	C₈	—	2	1	no	—
959	C₈	—	2	1	no	—
960	C₈	—	2	2	no	—
961	C₈	—	2	2	no	—
962	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	1	no	—
965	C₂²	—	2	1	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	2	no	—
968	C₂²	—	2	2	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	2	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	4	4	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	2	no	—
978	C₂²	C₁₉×#578	1	2	yes	—
979	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	2	no	—
984	C₄	—	2	2	no	—
985	C₄	—	2	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	2	no	—
993	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
994	C₄	C₁₉×#585	1	1	yes	characteristic
995	C₂	—	2	2	no	—
996	C₂	—	4	1	no	—
997	C₂	—	4	1	no	—
998	C₂	—	4	2	no	—
999	C₂	—	8	2	no	—
1000	C₂	C₁₉×#3496	1	1	yes	characteristic
1001	C₂	C₂×C₁₉×#578	1	1	yes	characteristic
1002	C₂	C₁₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3541	C₂	semidirect
2. C₁₉×#3349	C₂	semidirect
3. C₁₉×#3346	C₂	semidirect
4. C₁₉×#3302	C₂	semidirect
5. C₁₉×#3301	C₂	semidirect
6. C₁₉×#3300	C₂	semidirect
7. C₁₉×#3299	C₂	semidirect
8. C₁₉×#3270	C₂	semidirect
9. C₁₉×#3269	C₂	semidirect
10. C₁₉×#3262	C₂	semidirect
11. C₁₉×#3261	C₂	semidirect
12. C₁₉×#3203	C₂	semidirect
13. C₁₉×#3202	C₂	semidirect
14. C₁₉×#3196	C₂	semidirect
15. C₁₉×#3178	C₂	semidirect
16. C₁₉×#3063	C₂	semidirect
17. C₁₉×#3050	C₂	semidirect
18. C₂×C₁₉×#467	C₂	semidirect
19. C₁₉×#2929	C₂	semidirect
20. C₂×C₁₉×#137	C₂²	semidirect
48. C₁₉×#501	C₂²	semidirect
49. C₁₉×#497	C₂²	semidirect
50. C₁₉×#488	C₂²	semidirect
51. C₁₉×#487	C₂²	semidirect
54. C₁₉×#485	C₂²	semidirect
55. C₁₉×#485	C₂²	semidirect
57. C₁₉×#484	C₂²	semidirect
59. C₁₉×#480	C₂²	semidirect
60. C₁₉×#479	C₂²	semidirect
61. C₁₉×#479	C₂²	semidirect
62. C₁₉×#477	C₂²	semidirect
63. C₁₉×#474	C₂²	semidirect
66. C₁₉×#470	C₂²	semidirect
69. C₁₉×#468	C₂²	semidirect
78. C₁₉×#467	C₂²	semidirect
83. C₁₉×#465	C₂²	semidirect
84. C₁₉×#464	C₂²	semidirect
85. C₁₉×#463	C₂²	semidirect
86. C₁₉×#462	C₂²	semidirect
87. C₁₉×#462	C₂²	semidirect
90. C₁₉×#452	C₂²	semidirect
92. C₁₉×#451	C₂²	semidirect
93. C₁₉×#451	C₂²	semidirect
94. C₁₉×#449	C₂²	semidirect
96. C₁₉×#441	C₂²	semidirect
97. C₁₉×#440	C₂²	semidirect
98. C₄×Q₁₆×C₁₉	C₂²	semidirect
99. C₄×SD₁₆×C₁₉	C₂²	semidirect
104. C₁₉×#428	C₂²	semidirect
109. C₁₉×#416	C₂²	semidirect
111. C₂×C₁₉×#103	C₂²	semidirect
394. #62279	C₁₉	direct (N × H)
462. #3541	C₂×C₁₉	semidirect
463. #3349	C₂×C₁₉	semidirect
464. #3346	C₂×C₁₉	semidirect
465. #3302	C₂×C₁₉	semidirect
466. #3301	C₂×C₁₉	semidirect
467. #3300	C₂×C₁₉	semidirect
468. #3299	C₂×C₁₉	semidirect
469. #3270	C₂×C₁₉	semidirect
470. #3269	C₂×C₁₉	semidirect
471. #3262	C₂×C₁₉	semidirect
472. #3261	C₂×C₁₉	semidirect
473. #3203	C₂×C₁₉	semidirect
474. #3202	C₂×C₁₉	semidirect
475. #3196	C₂×C₁₉	semidirect
476. #3178	C₂×C₁₉	semidirect
477. #3063	C₂×C₁₉	semidirect
478. #3050	C₂×C₁₉	semidirect
479. C₂×#467	C₂×C₁₉	semidirect
480. #2929	C₂×C₁₉	semidirect
513. C₂×#137	C₂²×C₁₉	semidirect
541. #501	C₂²×C₁₉	semidirect
542. #497	C₂²×C₁₉	semidirect
543. #488	C₂²×C₁₉	semidirect
544. #487	C₂²×C₁₉	semidirect
547. #485	C₂²×C₁₉	semidirect
548. #485	C₂²×C₁₉	semidirect
550. #484	C₂²×C₁₉	semidirect
552. #480	C₂²×C₁₉	semidirect
553. #479	C₂²×C₁₉	semidirect
554. #479	C₂²×C₁₉	semidirect
555. #477	C₂²×C₁₉	semidirect
556. #474	C₂²×C₁₉	semidirect
559. #470	C₂²×C₁₉	semidirect
562. #468	C₂²×C₁₉	semidirect
571. #467	C₂²×C₁₉	semidirect
576. #465	C₂²×C₁₉	semidirect
577. #464	C₂²×C₁₉	semidirect
578. #463	C₂²×C₁₉	semidirect
579. #462	C₂²×C₁₉	semidirect
580. #462	C₂²×C₁₉	semidirect
583. #452	C₂²×C₁₉	semidirect
585. #451	C₂²×C₁₉	semidirect
586. #451	C₂²×C₁₉	semidirect
587. #449	C₂²×C₁₉	semidirect
589. #441	C₂²×C₁₉	semidirect
590. #440	C₂²×C₁₉	semidirect
591. C₄×Q₁₆	C₂²×C₁₉	semidirect
592. C₄×SD₁₆	C₂²×C₁₉	semidirect
597. #428	C₂²×C₁₉	semidirect
602. #416	C₂²×C₁₉	semidirect
604. C₂×#103	C₂²×C₁₉	semidirect
770. C₁₉	#62279	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3541	2
C₁₉×#3349	2
C₁₉×#3346	2
C₁₉×#3302	2
C₁₉×#3301	2
C₁₉×#3300	2
C₁₉×#3299	2
C₁₉×#3270	2
C₁₉×#3269	2
C₁₉×#3262	2
C₁₉×#3261	2
C₁₉×#3203	2
C₁₉×#3202	2
C₁₉×#3196	2
C₁₉×#3178	2
C₁₉×#3063	2
C₁₉×#3050	2
C₂×C₁₉×#467	2
C₁₉×#2929	2
#62279	19

Subgroups — C19×#62279 #18068238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62279 #18068238