Subgroups — C₁₉×#61950 #18067909

Order 4864.

1878 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3393	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3360	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3303	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3300	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3283	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3282	C₂	1	4	yes	maximal, complemented
9	C₁₉×#3248	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3212	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3107	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3100	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3035	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#2988	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₉×#135	C₂²	1	4	yes	—
19	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
20	C₁₉×#556	C₂²	1	1	yes	characteristic
21	C₁₉×#556	C₂²	1	2	yes	complemented
22	C₁₉×#555	—	2	1	no	—
23	C₁₉×#555	C₂²	1	1	yes	characteristic
24	C₁₉×#554	—	2	1	no	—
25	C₁₉×#554	C₂²	1	1	yes	characteristic
26	C₁₉×#553	—	2	1	no	—
27	C₁₉×#553	—	2	2	no	—
28	C₁₉×#552	—	2	1	no	—
29	C₁₉×#552	C₂²	1	2	yes	—
30	C₁₉×#551	—	2	2	no	—
31	C₁₉×#548	C₂²	1	4	yes	—
32	C₁₉×#547	C₂²	1	1	yes	characteristic
33	C₁₉×#547	C₂²	1	2	yes	complemented
34	C₁₉×#546	C₂²	1	2	yes	—
35	C₁₉×#542	—	2	2	no	—
36	C₁₉×#537	—	2	1	no	—
37	C₁₉×#533	C₂²	1	1	yes	characteristic
38	C₁₉×#533	C₂²	1	2	yes	complemented
39	C₁₉×#532	C₂²	1	1	yes	characteristic
40	C₁₉×#532	C₂²	1	2	yes	complemented
41	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
42	C₁₉×#529	—	2	2	no	—
43	C₁₉×#529	C₂²	1	2	yes	—
44	C₁₉×#525	—	2	1	no	—
45	C₁₉×#520	—	2	1	no	—
46	C₄×#41×C₁₉	C₂²	1	2	yes	—
47	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₂×C₁₉×#117	—	2	1	no	—
50	C₁₉×#495	C₂²	1	4	yes	—
51	C₁₉×#494	C₂²	1	2	yes	complemented
52	C₁₉×#488	C₂²	1	4	yes	complemented
53	C₁₉×#487	C₂²	1	2	yes	complemented
54	C₁₉×#485	C₂²	1	4	yes	complemented
55	C₁₉×#480	C₂²	1	2	yes	—
56	C₁₉×#479	C₂²	1	4	yes	complemented
57	C₁₉×#476	C₂²	1	2	yes	complemented
58	C₁₉×#475	C₂²	1	2	yes	complemented
59	C₁₉×#474	C₂²	1	1	yes	characteristic
60	C₁₉×#474	C₂²	1	1	yes	characteristic
61	C₁₉×#467	C₂²	1	4	yes	complemented
62	C₁₉×#465	C₂²	1	4	yes	—
63	C₁₉×#465	C₂²	1	4	yes	—
64	C₁₉×#464	C₂²	1	4	yes	—
65	C₁₉×#464	C₂²	1	4	yes	complemented
66	C₁₉×#463	C₂²	1	4	yes	—
67	C₁₉×#462	C₂²	1	2	yes	complemented
68	C₁₉×#462	C₂²	1	2	yes	complemented
69	C₁₉×#461	C₂²	1	2	yes	—
70	C₁₉×#461	C₂²	1	2	yes	—
71	C₁₉×#461	C₂²	1	2	yes	—
72	C₁₉×#461	C₂²	1	2	yes	—
73	C₁₉×#461	C₂²	1	2	yes	complemented
74	C₁₉×#460	C₂²	1	2	yes	complemented
75	C₁₉×#459	C₂²	1	1	yes	characteristic
76	C₁₉×#459	C₂²	1	1	yes	characteristic
77	C₁₉×#452	C₂²	1	4	yes	—
78	C₁₉×#452	C₂²	1	4	yes	complemented
79	C₁₉×#451	C₂²	1	4	yes	—
80	C₁₉×#449	C₂²	1	4	yes	—
81	C₁₉×#447	C₂²	1	2	yes	—
82	C₈×Q₈×C₁₉	C₂²	1	2	yes	complemented
83	C₄×Q₁₆×C₁₉	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
85	C₄×D₈×C₁₉	C₂²	1	2	yes	—
86	C₄×D₈×C₁₉	C₂²	1	2	yes	—
87	C₈×D₄×C₁₉	C₂²	1	4	yes	—
88	C₈×D₄×C₁₉	C₂²	1	2	yes	complemented
89	C₁₉×#431	C₂²	1	1	yes	characteristic
90	C₁₉×#431	C₂²	1	2	yes	complemented
91	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
92	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
93	C₁₉×#416	C₂²	1	4	yes	complemented
94	C₂×C₁₉×#103	C₂²	1	2	yes	—
95	C₂×#41×C₁₉	—	2	1	no	—
96	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
97	C₂×#41×C₁₉	C₂³	1	2	yes	—
98	C₂×#41×C₁₉	C₂³	1	4	yes	—
99	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
100	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₉	—	2	1	no	—
102	C₁₉×#135	—	4	8	no	—
103	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
104	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₁₉	—	4	4	no	—
106	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
109	C₂×D₈×C₁₉	C₂³	1	2	yes	—
110	C₂×D₈×C₁₉	C₂³	1	2	yes	—
111	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
112	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
113	C₁₉×C₄⋊Q₈	—	2	1	no	—
114	C₁₉×C₄⋊Q₈	—	2	1	no	—
115	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₉×#127	C₂³	1	1	yes	characteristic
121	C₁₉×#126	—	2	2	no	—
122	C₁₉×#126	—	2	4	no	—
123	C₁₉×#126	—	2	2	no	—
124	C₁₉×#126	—	2	2	no	—
125	C₁₉×#125	—	2	2	no	—
126	C₁₉×#125	—	2	1	no	—
127	C₁₉×#125	—	2	2	no	—
128	C₁₉×#125	C₂³	1	2	yes	—
129	C₁₉×#124	—	2	2	no	—
130	C₁₉×#124	—	2	4	no	—
131	C₁₉×#124	—	2	1	no	—
132	C₁₉×#124	C₂³	1	4	yes	—
133	C₁₉×#124	C₂³	1	2	yes	—
134	C₁₉×#123	—	2	2	no	—
135	C₁₉×#123	—	2	2	no	—
136	C₁₉×#123	—	2	2	no	—
137	C₁₉×#123	—	2	2	no	—
138	C₁₉×#123	—	2	4	no	—
139	C₁₉×C₂²⋊Q₈	—	2	1	no	—
140	C₁₉×C₂²⋊Q₈	—	2	1	no	—
141	C₁₉×C₂²⋊Q₈	—	2	2	no	—
142	C₁₉×C₂²⋊Q₈	—	2	1	no	—
143	C₁₉×C₂²⋊Q₈	—	2	2	no	—
144	C₁₉×C₂²⋊Q₈	—	2	2	no	—
145	C₁₉×C₂²⋊Q₈	—	2	4	no	—
146	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₁₉×#121	—	2	1	no	—
150	C₁₉×#121	—	2	1	no	—
151	C₁₉×#121	—	2	2	no	—
152	C₁₉×#121	—	2	4	no	—
153	C₁₉×#121	—	2	1	no	—
154	C₁₉×#121	—	2	2	no	—
155	C₁₉×#121	—	2	2	no	—
156	C₁₉×#121	—	2	2	no	—
157	C₁₉×#121	C₂³	1	2	yes	—
158	C₁₉×#121	C₂³	1	2	yes	—
159	C₁₉×#120	—	2	2	no	—
160	C₄×Q₈×C₁₉	—	2	2	no	—
161	C₄×Q₈×C₁₉	—	2	1	no	—
162	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
164	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
165	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
166	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₁₉	—	2	2	no	—
168	C₄×D₄×C₁₉	—	2	2	no	—
169	C₄×D₄×C₁₉	—	2	2	no	—
170	C₄×D₄×C₁₉	—	2	4	no	—
171	C₄×D₄×C₁₉	—	2	1	no	—
172	C₄×D₄×C₁₉	—	2	1	no	—
173	C₄×D₄×C₁₉	—	2	2	no	—
174	C₄×D₄×C₁₉	—	2	1	no	—
175	C₄×D₄×C₁₉	—	2	2	no	—
176	C₄×D₄×C₁₉	D₄	1	2	yes	—
177	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
178	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₁₉	C₂³	1	2	yes	—
181	C₄×D₄×C₁₉	C₂³	1	2	yes	—
182	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₁₉	C₂³	1	2	yes	—
185	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
186	C₁₉×#117	—	2	1	no	—
187	C₁₉×#117	—	2	2	no	—
188	C₁₉×#117	—	2	1	no	—
189	C₁₉×#117	—	2	1	no	—
190	C₁₉×#117	—	2	2	no	—
191	C₁₉×#117	—	2	2	no	—
192	C₁₉×#117	—	2	2	no	—
193	C₁₉×#117	—	2	2	no	—
194	C₁₉×#117	D₄	1	1	yes	characteristic
195	C₁₉×#117	D₄	1	2	yes	—
196	C₁₉×#117	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
202	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
204	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂×C₄²×C₁₉	—	2	2	no	—
206	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
208	C₁₉×#107	C₂³	1	2	yes	—
209	C₁₉×#107	C₂³	1	2	yes	—
210	C₁₉×#106	C₂³	1	4	yes	—
211	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
212	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
215	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₁₉×#103	C₂³	1	4	yes	—
217	C₁₉×#103	C₂³	1	4	yes	—
218	C₁₉×#103	C₂³	1	4	yes	—
219	C₁₉×#103	C₂³	1	4	yes	—
220	C₁₉×#103	C₂³	1	4	yes	—
221	C₁₉×#102	C₂³	1	2	yes	—
222	C₁₉×#102	C₂³	1	4	yes	—
223	C₁₉×#102	C₂³	1	2	yes	—
224	C₁₉×#102	C₂³	1	2	yes	—
225	C₁₉×#102	C₂³	1	2	yes	—
226	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₄×C₈×C₁₉	C₂³	1	2	yes	—
229	C₄×C₈×C₁₉	C₂³	1	4	yes	—
230	C₂⁴×C₁₉	—	2	1	no	—
231	#41×C₁₉	—	2	4	no	—
232	#41×C₁₉	—	2	4	no	—
233	#41×C₁₉	—	4	2	no	—
234	#41×C₁₉	—	4	4	no	—
235	#41×C₁₉	—	4	4	no	—
236	#41×C₁₉	—	4	4	no	—
237	C₂×Q₈×C₁₉	—	2	1	no	—
238	C₂×Q₈×C₁₉	—	2	1	no	—
239	C₂×Q₈×C₁₉	—	2	2	no	—
240	C₂×Q₈×C₁₉	—	4	2	no	—
241	C₂×Q₈×C₁₉	—	4	2	no	—
242	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
244	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
245	C₂×D₄×C₁₉	—	2	2	no	—
246	C₂×D₄×C₁₉	—	2	2	no	—
247	C₂×D₄×C₁₉	—	2	2	no	—
248	C₂×D₄×C₁₉	—	2	2	no	—
249	C₂×D₄×C₁₉	—	2	4	no	—
250	C₂×D₄×C₁₉	—	2	1	no	—
251	C₂×D₄×C₁₉	—	2	1	no	—
252	C₂×D₄×C₁₉	—	2	1	no	—
253	C₂×D₄×C₁₉	—	4	1	no	—
254	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
255	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
258	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₉	—	2	1	no	—
260	C₂²×C₄×C₁₉	—	2	2	no	—
261	C₂²×C₄×C₁₉	—	2	1	no	—
262	C₂²×C₄×C₁₉	—	2	2	no	—
263	C₂²×C₄×C₁₉	—	2	1	no	—
264	C₂²×C₄×C₁₉	—	2	2	no	—
265	C₂²×C₄×C₁₉	—	2	1	no	—
266	C₂²×C₄×C₁₉	—	2	1	no	—
267	C₂²×C₄×C₁₉	—	2	2	no	—
268	C₂²×C₄×C₁₉	—	2	4	no	—
269	C₂²×C₄×C₁₉	—	4	4	no	—
270	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
276	Q₁₆×C₁₉	—	4	4	no	—
277	Q₁₆×C₁₉	—	4	4	no	—
278	SD₁₆×C₁₉	—	2	8	no	—
279	SD₁₆×C₁₉	—	4	4	no	—
280	SD₁₆×C₁₉	—	4	4	no	—
281	D₈×C₁₉	—	2	4	no	—
282	D₈×C₁₉	—	4	2	no	—
283	C₂×C₈×C₁₉	—	4	2	no	—
284	C₂×C₈×C₁₉	—	4	4	no	—
285	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
286	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
287	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₁₉	—	2	2	no	—
289	C₄⋊C₄×C₁₉	—	2	1	no	—
290	C₄⋊C₄×C₁₉	—	2	1	no	—
291	C₄⋊C₄×C₁₉	—	2	2	no	—
292	C₄⋊C₄×C₁₉	—	2	2	no	—
293	C₄⋊C₄×C₁₉	—	2	2	no	—
294	C₄⋊C₄×C₁₉	—	2	2	no	—
295	C₄⋊C₄×C₁₉	—	2	4	no	—
296	C₄⋊C₄×C₁₉	—	2	2	no	—
297	C₄⋊C₄×C₁₉	—	2	1	no	—
298	C₄⋊C₄×C₁₉	—	2	1	no	—
299	C₄⋊C₄×C₁₉	—	2	2	no	—
300	C₄⋊C₄×C₁₉	—	2	2	no	—
301	C₄⋊C₄×C₁₉	—	2	2	no	—
302	C₄⋊C₄×C₁₉	—	2	2	no	—
303	C₄⋊C₄×C₁₉	—	2	1	no	—
304	C₄⋊C₄×C₁₉	—	2	4	no	—
305	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
306	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
307	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
308	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
313	C₂²⋊C₄×C₁₉	—	2	2	no	—
314	C₂²⋊C₄×C₁₉	—	2	4	no	—
315	C₂²⋊C₄×C₁₉	—	2	2	no	—
316	C₂²⋊C₄×C₁₉	—	2	2	no	—
317	C₂²⋊C₄×C₁₉	—	2	1	no	—
318	C₂²⋊C₄×C₁₉	—	2	2	no	—
319	C₂²⋊C₄×C₁₉	—	2	2	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	4	no	—
324	C₂²⋊C₄×C₁₉	—	2	2	no	—
325	C₂²⋊C₄×C₁₉	—	2	2	no	—
326	C₂²⋊C₄×C₁₉	—	2	4	no	—
327	C₂²⋊C₄×C₁₉	—	2	2	no	—
328	C₂²⋊C₄×C₁₉	—	2	2	no	—
329	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
332	C₄²×C₁₉	—	2	2	no	—
333	C₄²×C₁₉	—	2	2	no	—
334	C₄²×C₁₉	—	2	2	no	—
335	C₄²×C₁₉	—	2	4	no	—
336	C₄²×C₁₉	C₂×D₄	1	2	yes	—
337	C₄²×C₁₉	C₂×D₄	1	2	yes	—
338	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
341	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
342	C₄²×C₁₉	C₂⁴	1	2	yes	—
343	#61950	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂³×C₁₉	—	2	1	no	—
345	C₂³×C₁₉	—	2	1	no	—
346	C₂³×C₁₉	—	2	2	no	—
347	C₂³×C₁₉	—	4	2	no	—
348	C₂³×C₁₉	—	4	2	no	—
349	C₂³×C₁₉	—	8	1	no	—
350	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
351	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
352	Q₈×C₁₉	—	2	2	no	—
353	Q₈×C₁₉	—	2	4	no	—
354	Q₈×C₁₉	—	2	2	no	—
355	Q₈×C₁₉	—	2	2	no	—
356	Q₈×C₁₉	—	2	4	no	—
357	Q₈×C₁₉	—	4	2	no	—
358	Q₈×C₁₉	—	8	1	no	—
359	Q₈×C₁₉	—	8	2	no	—
360	D₄×C₁₉	—	2	4	no	—
361	D₄×C₁₉	—	2	2	no	—
362	D₄×C₁₉	—	2	2	no	—
363	D₄×C₁₉	—	2	1	no	—
364	D₄×C₁₉	—	2	1	no	—
365	D₄×C₁₉	—	2	1	no	—
366	D₄×C₁₉	—	2	2	no	—
367	D₄×C₁₉	—	4	2	no	—
368	D₄×C₁₉	—	4	2	no	—
369	D₄×C₁₉	—	4	4	no	—
370	D₄×C₁₉	—	4	4	no	—
371	D₄×C₁₉	—	4	2	no	—
372	D₄×C₁₉	—	8	2	no	—
373	D₄×C₁₉	—	8	4	no	—
374	D₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
375	C₂×C₄×C₁₉	—	2	4	no	—
376	C₂×C₄×C₁₉	—	2	1	no	—
377	C₂×C₄×C₁₉	—	2	2	no	—
378	C₂×C₄×C₁₉	—	2	1	no	—
379	C₂×C₄×C₁₉	—	2	2	no	—
380	C₂×C₄×C₁₉	—	2	1	no	—
381	C₂×C₄×C₁₉	—	2	2	no	—
382	C₂×C₄×C₁₉	—	2	2	no	—
383	C₂×C₄×C₁₉	—	2	2	no	—
384	C₂×C₄×C₁₉	—	2	4	no	—
385	C₂×C₄×C₁₉	—	2	1	no	—
386	C₂×C₄×C₁₉	—	4	2	no	—
387	C₂×C₄×C₁₉	—	4	1	no	—
388	C₂×C₄×C₁₉	—	4	4	no	—
389	C₂×C₄×C₁₉	—	4	2	no	—
390	C₂×C₄×C₁₉	—	4	2	no	—
391	C₂×C₄×C₁₉	—	4	2	no	—
392	C₂×C₄×C₁₉	—	4	2	no	—
393	C₂×C₄×C₁₉	—	4	2	no	—
394	C₂×C₄×C₁₉	—	4	4	no	—
395	C₂×C₄×C₁₉	—	8	2	no	—
396	C₂×C₄×C₁₉	—	8	4	no	—
397	C₂×C₄×C₁₉	—	8	2	no	—
398	C₂×C₄×C₁₉	#135	1	4	yes	complemented
399	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
408	C₈×C₁₉	—	2	2	no	—
409	C₈×C₁₉	—	2	4	no	—
410	C₈×C₁₉	—	2	2	no	—
411	#3511	C₂×C₁₉	1	1	yes	characteristic, complemented
412	#3475	C₂×C₁₉	1	1	yes	characteristic, complemented
413	#3393	C₂×C₁₉	1	2	yes	complemented
414	#3360	C₂×C₁₉	1	2	yes	complemented
415	#3303	C₂×C₁₉	1	2	yes	complemented
416	#3300	C₂×C₁₉	1	4	yes	complemented
417	#3283	C₂×C₁₉	1	2	yes	complemented
418	#3282	C₂×C₁₉	1	4	yes	complemented
419	#3248	C₂×C₁₉	1	2	yes	complemented
420	#3246	C₂×C₁₉	1	1	yes	characteristic, complemented
421	#3212	C₂×C₁₉	1	2	yes	complemented
422	#3209	C₂×C₁₉	1	1	yes	characteristic, complemented
423	#3107	C₂×C₁₉	1	2	yes	complemented
424	#3100	C₂×C₁₉	1	1	yes	characteristic, complemented
425	#3035	C₂×C₁₉	1	2	yes	complemented
426	C₂×#461	C₂×C₁₉	1	1	yes	characteristic, complemented
427	#2988	C₂×C₁₉	1	1	yes	characteristic, complemented
428	C₂²×C₁₉	—	2	1	no	—
429	C₂²×C₁₉	—	2	1	no	—
430	C₂²×C₁₉	—	2	2	no	—
431	C₂²×C₁₉	—	2	2	no	—
432	C₂²×C₁₉	—	2	2	no	—
433	C₂²×C₁₉	—	2	2	no	—
434	C₂²×C₁₉	—	4	1	no	—
435	C₂²×C₁₉	—	4	1	no	—
436	C₂²×C₁₉	—	4	2	no	—
437	C₂²×C₁₉	—	4	1	no	—
438	C₂²×C₁₉	—	4	2	no	—
439	C₂²×C₁₉	—	4	1	no	—
440	C₂²×C₁₉	—	4	1	no	—
441	C₂²×C₁₉	—	4	2	no	—
442	C₂²×C₁₉	—	8	4	no	—
443	C₂²×C₁₉	C₂×#135	1	2	yes	—
444	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
445	C₄×C₁₉	—	2	1	no	—
446	C₄×C₁₉	—	2	2	no	—
447	C₄×C₁₉	—	2	1	no	—
448	C₄×C₁₉	—	2	2	no	—
449	C₄×C₁₉	—	2	1	no	—
450	C₄×C₁₉	—	2	2	no	—
451	C₄×C₁₉	—	4	2	no	—
452	C₄×C₁₉	—	4	2	no	—
453	C₄×C₁₉	—	4	4	no	—
454	C₄×C₁₉	—	4	1	no	—
455	C₄×C₁₉	—	4	1	no	—
456	C₄×C₁₉	—	4	2	no	—
457	C₄×C₁₉	C₂×#135	1	2	yes	—
458	C₄×C₁₉	C₂×#135	1	2	yes	—
459	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
460	C₄×C₁₉	#585	1	1	yes	characteristic
461	C₂×#135	C₂²×C₁₉	1	4	yes	—
462	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
463	#556	C₂²×C₁₉	1	1	yes	characteristic
464	#556	C₂²×C₁₉	1	2	yes	complemented
465	#555	—	2	1	no	—
466	#555	C₂²×C₁₉	1	1	yes	characteristic
467	#554	—	2	1	no	—
468	#554	C₂²×C₁₉	1	1	yes	characteristic
469	#553	—	2	1	no	—
470	#553	—	2	2	no	—
471	#552	—	2	1	no	—
472	#552	C₂²×C₁₉	1	2	yes	—
473	#551	—	2	2	no	—
474	#548	C₂²×C₁₉	1	4	yes	—
475	#547	C₂²×C₁₉	1	1	yes	characteristic
476	#547	C₂²×C₁₉	1	2	yes	complemented
477	#546	C₂²×C₁₉	1	2	yes	—
478	#542	—	2	2	no	—
479	#537	—	2	1	no	—
480	#533	C₂²×C₁₉	1	1	yes	characteristic
481	#533	C₂²×C₁₉	1	2	yes	complemented
482	#532	C₂²×C₁₉	1	1	yes	characteristic
483	#532	C₂²×C₁₉	1	2	yes	complemented
484	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
485	#529	—	2	2	no	—
486	#529	C₂²×C₁₉	1	2	yes	—
487	#525	—	2	1	no	—
488	#520	—	2	1	no	—
489	C₄×#41	C₂²×C₁₉	1	2	yes	—
490	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
491	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
492	C₂×#117	—	2	1	no	—
493	#495	C₂²×C₁₉	1	4	yes	—
494	#494	C₂²×C₁₉	1	2	yes	complemented
495	#488	C₂²×C₁₉	1	4	yes	complemented
496	#487	C₂²×C₁₉	1	2	yes	complemented
497	#485	C₂²×C₁₉	1	4	yes	complemented
498	#480	C₂²×C₁₉	1	2	yes	—
499	#479	C₂²×C₁₉	1	4	yes	complemented
500	#476	C₂²×C₁₉	1	2	yes	complemented
501	#475	C₂²×C₁₉	1	2	yes	complemented
502	#474	C₂²×C₁₉	1	1	yes	characteristic
503	#474	C₂²×C₁₉	1	1	yes	characteristic
504	#467	C₂²×C₁₉	1	4	yes	complemented
505	#465	C₂²×C₁₉	1	4	yes	—
506	#465	C₂²×C₁₉	1	4	yes	—
507	#464	C₂²×C₁₉	1	4	yes	—
508	#464	C₂²×C₁₉	1	4	yes	complemented
509	#463	C₂²×C₁₉	1	4	yes	—
510	#462	C₂²×C₁₉	1	2	yes	complemented
511	#462	C₂²×C₁₉	1	2	yes	complemented
512	#461	C₂²×C₁₉	1	2	yes	—
513	#461	C₂²×C₁₉	1	2	yes	—
514	#461	C₂²×C₁₉	1	2	yes	—
515	#461	C₂²×C₁₉	1	2	yes	—
516	#461	C₂²×C₁₉	1	2	yes	complemented
517	#460	C₂²×C₁₉	1	2	yes	complemented
518	#459	C₂²×C₁₉	1	1	yes	characteristic
519	#459	C₂²×C₁₉	1	1	yes	characteristic
520	#452	C₂²×C₁₉	1	4	yes	—
521	#452	C₂²×C₁₉	1	4	yes	complemented
522	#451	C₂²×C₁₉	1	4	yes	—
523	#449	C₂²×C₁₉	1	4	yes	—
524	#447	C₂²×C₁₉	1	2	yes	—
525	C₈×Q₈	C₂²×C₁₉	1	2	yes	complemented
526	C₄×Q₁₆	C₂²×C₁₉	1	4	yes	complemented
527	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
528	C₄×D₈	C₂²×C₁₉	1	2	yes	—
529	C₄×D₈	C₂²×C₁₉	1	2	yes	—
530	C₈×D₄	C₂²×C₁₉	1	4	yes	—
531	C₈×D₄	C₂²×C₁₉	1	2	yes	complemented
532	#431	C₂²×C₁₉	1	1	yes	characteristic
533	#431	C₂²×C₁₉	1	2	yes	complemented
534	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
535	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
536	#416	C₂²×C₁₉	1	4	yes	complemented
537	C₂×#103	C₂²×C₁₉	1	2	yes	—
538	C₂×C₁₉	—	2	2	no	—
539	C₂×C₁₉	—	4	2	no	—
540	C₂×C₁₉	—	4	2	no	—
541	C₂×C₁₉	—	8	2	no	—
542	C₂×C₁₉	—	8	1	no	—
543	C₂×C₁₉	#3488	1	1	yes	characteristic
544	C₂×C₁₉	C₂²×#135	1	1	yes	characteristic
545	C₂×C₁₉	#3586	1	1	yes	characteristic
546	C₂×#41	—	2	1	no	—
547	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
548	C₂×#41	C₂³×C₁₉	1	2	yes	—
549	C₂×#41	C₂³×C₁₉	1	4	yes	—
550	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
551	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
552	C₂³×C₄	—	2	1	no	—
553	#135	—	4	8	no	—
554	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
555	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
556	C₂×SD₁₆	—	4	4	no	—
557	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
558	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
559	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
560	C₂×D₈	C₂³×C₁₉	1	2	yes	—
561	C₂×D₈	C₂³×C₁₉	1	2	yes	—
562	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
563	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
564	C₄⋊Q₈	—	2	1	no	—
565	C₄⋊Q₈	—	2	1	no	—
566	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
567	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
568	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
569	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
570	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
571	#127	C₂³×C₁₉	1	1	yes	characteristic
572	#126	—	2	2	no	—
573	#126	—	2	4	no	—
574	#126	—	2	2	no	—
575	#126	—	2	2	no	—
576	#125	—	2	2	no	—
577	#125	—	2	1	no	—
578	#125	—	2	2	no	—
579	#125	C₂³×C₁₉	1	2	yes	—
580	#124	—	2	2	no	—
581	#124	—	2	4	no	—
582	#124	—	2	1	no	—
583	#124	C₂³×C₁₉	1	2	yes	—
584	#124	C₂³×C₁₉	1	4	yes	—
585	#123	—	2	2	no	—
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	#123	—	2	2	no	—
589	#123	—	2	4	no	—
590	C₂²⋊Q₈	—	2	1	no	—
591	C₂²⋊Q₈	—	2	1	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	4	no	—
597	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
598	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
599	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
600	#121	—	2	1	no	—
601	#121	—	2	1	no	—
602	#121	—	2	2	no	—
603	#121	—	2	4	no	—
604	#121	—	2	1	no	—
605	#121	—	2	2	no	—
606	#121	—	2	2	no	—
607	#121	—	2	2	no	—
608	#121	C₂³×C₁₉	1	2	yes	—
609	#121	C₂³×C₁₉	1	2	yes	—
610	#120	—	2	2	no	—
611	C₄×Q₈	—	2	2	no	—
612	C₄×Q₈	—	2	1	no	—
613	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
614	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
615	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
616	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
617	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	4	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	D₄×C₁₉	1	2	yes	—
628	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
629	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
630	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
631	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
632	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
633	C₄×D₄	C₂³×C₁₉	1	2	yes	—
634	C₄×D₄	C₂³×C₁₉	1	2	yes	—
635	C₄×D₄	C₂³×C₁₉	1	2	yes	—
636	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
637	#117	—	2	1	no	—
638	#117	—	2	2	no	—
639	#117	—	2	1	no	—
640	#117	—	2	1	no	—
641	#117	—	2	2	no	—
642	#117	—	2	2	no	—
643	#117	—	2	2	no	—
644	#117	—	2	2	no	—
645	#117	D₄×C₁₉	1	1	yes	characteristic
646	#117	D₄×C₁₉	1	2	yes	—
647	#117	C₂³×C₁₉	1	2	yes	—
648	C₂×C₄⋊C₄	—	2	1	no	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	—	2	1	no	—
652	C₂×C₄⋊C₄	—	2	2	no	—
653	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	—	2	2	no	—
656	C₂×C₄²	—	2	2	no	—
657	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
659	#107	C₂³×C₁₉	1	2	yes	—
660	#107	C₂³×C₁₉	1	2	yes	—
661	#106	C₂³×C₁₉	1	4	yes	—
662	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
663	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
664	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
665	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
666	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
667	#103	C₂³×C₁₉	1	4	yes	—
668	#103	C₂³×C₁₉	1	4	yes	—
669	#103	C₂³×C₁₉	1	4	yes	—
670	#103	C₂³×C₁₉	1	4	yes	—
671	#103	C₂³×C₁₉	1	4	yes	—
672	#102	C₂³×C₁₉	1	2	yes	—
673	#102	C₂³×C₁₉	1	4	yes	—
674	#102	C₂³×C₁₉	1	2	yes	—
675	#102	C₂³×C₁₉	1	2	yes	—
676	#102	C₂³×C₁₉	1	2	yes	—
677	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
678	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
679	C₄×C₈	C₂³×C₁₉	1	2	yes	—
680	C₄×C₈	C₂³×C₁₉	1	4	yes	—
681	C₁₉	#61950	1	1	yes	characteristic, direct product factor, Sylow
682	C₂⁴	—	2	1	no	—
683	#41	—	2	4	no	—
684	#41	—	2	4	no	—
685	#41	—	4	2	no	—
686	#41	—	4	4	no	—
687	#41	—	4	4	no	—
688	#41	—	4	4	no	—
689	C₂×Q₈	—	2	1	no	—
690	C₂×Q₈	—	2	1	no	—
691	C₂×Q₈	—	2	2	no	—
692	C₂×Q₈	—	4	2	no	—
693	C₂×Q₈	—	4	2	no	—
694	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
695	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
696	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	4	1	no	—
706	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
707	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
708	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
709	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
710	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	4	4	no	—
722	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
723	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
724	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
725	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
728	Q₁₆	—	4	4	no	—
729	Q₁₆	—	4	4	no	—
730	SD₁₆	—	2	8	no	—
731	SD₁₆	—	4	4	no	—
732	SD₁₆	—	4	4	no	—
733	D₈	—	2	4	no	—
734	D₈	—	4	2	no	—
735	C₂×C₈	—	4	2	no	—
736	C₂×C₈	—	4	4	no	—
737	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
738	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
739	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
758	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
759	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
760	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
761	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
762	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
763	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
764	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	1	no	—
773	C₂²⋊C₄	—	2	1	no	—
774	C₂²⋊C₄	—	2	1	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
782	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
783	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	4	no	—
788	C₄²	C₂×D₄×C₁₉	1	2	yes	—
789	C₄²	C₂×D₄×C₁₉	1	2	yes	—
790	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
791	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
792	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
793	C₄²	C₂⁴×C₁₉	1	2	yes	—
794	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
795	C₂³	—	2	1	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	4	2	no	—
799	C₂³	—	4	2	no	—
800	C₂³	—	8	1	no	—
801	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
802	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
803	Q₈	—	2	2	no	—
804	Q₈	—	2	4	no	—
805	Q₈	—	2	2	no	—
806	Q₈	—	2	2	no	—
807	Q₈	—	2	4	no	—
808	Q₈	—	4	2	no	—
809	Q₈	—	8	2	no	—
810	Q₈	—	8	1	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	2	no	—
814	D₄	—	2	1	no	—
815	D₄	—	2	1	no	—
816	D₄	—	2	1	no	—
817	D₄	—	2	2	no	—
818	D₄	—	4	2	no	—
819	D₄	—	4	2	no	—
820	D₄	—	4	4	no	—
821	D₄	—	4	4	no	—
822	D₄	—	4	2	no	—
823	D₄	—	8	4	no	—
824	D₄	—	8	2	no	—
825	D₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	4	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	4	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	2	no	—
842	C₂×C₄	—	4	2	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	4	2	no	—
845	C₂×C₄	—	4	4	no	—
846	C₂×C₄	—	8	4	no	—
847	C₂×C₄	—	8	2	no	—
848	C₂×C₄	—	8	2	no	—
849	C₂×C₄	C₁₉×#135	1	4	yes	complemented
850	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
851	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
852	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
853	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
854	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
855	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
856	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
857	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
858	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
859	C₈	—	2	2	no	—
860	C₈	—	2	4	no	—
861	C₈	—	2	2	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	8	4	no	—
877	C₂²	C₂×C₁₉×#135	1	2	yes	—
878	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
879	C₄	—	2	2	no	—
880	C₄	—	2	1	no	—
881	C₄	—	2	2	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	1	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	4	no	—
887	C₄	—	4	1	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	2	no	—
891	C₄	C₂×C₁₉×#135	1	2	yes	—
892	C₄	C₂×C₁₉×#135	1	2	yes	—
893	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
894	C₄	C₁₉×#585	1	1	yes	characteristic
895	C₂	—	2	2	no	—
896	C₂	—	4	2	no	—
897	C₂	—	4	2	no	—
898	C₂	—	8	1	no	—
899	C₂	—	8	2	no	—
900	C₂	C₁₉×#3488	1	1	yes	characteristic
901	C₂	C₂²×C₁₉×#135	1	1	yes	characteristic
902	C₂	C₁₉×#3586	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 ◁ C₄×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3511	C₂	semidirect
2. C₁₉×#3475	C₂	semidirect
3. C₁₉×#3393	C₂	semidirect
4. C₁₉×#3360	C₂	semidirect
5. C₁₉×#3303	C₂	semidirect
6. C₁₉×#3300	C₂	semidirect
7. C₁₉×#3283	C₂	semidirect
8. C₁₉×#3282	C₂	semidirect
9. C₁₉×#3248	C₂	semidirect
10. C₁₉×#3246	C₂	semidirect
11. C₁₉×#3212	C₂	semidirect
12. C₁₉×#3209	C₂	semidirect
13. C₁₉×#3107	C₂	semidirect
14. C₁₉×#3100	C₂	semidirect
15. C₁₉×#3035	C₂	semidirect
16. C₂×C₁₉×#461	C₂	semidirect
17. C₁₉×#2988	C₂	semidirect
21. C₁₉×#556	C₂²	semidirect
33. C₁₉×#547	C₂²	semidirect
38. C₁₉×#533	C₂²	semidirect
40. C₁₉×#532	C₂²	semidirect
51. C₁₉×#494	C₂²	semidirect
52. C₁₉×#488	C₂²	semidirect
53. C₁₉×#487	C₂²	semidirect
54. C₁₉×#485	C₂²	semidirect
56. C₁₉×#479	C₂²	semidirect
57. C₁₉×#476	C₂²	semidirect
58. C₁₉×#475	C₂²	semidirect
61. C₁₉×#467	C₂²	semidirect
65. C₁₉×#464	C₂²	semidirect
67. C₁₉×#462	C₂²	semidirect
68. C₁₉×#462	C₂²	semidirect
73. C₁₉×#461	C₂²	semidirect
74. C₁₉×#460	C₂²	semidirect
78. C₁₉×#452	C₂²	semidirect
82. C₈×Q₈×C₁₉	C₂²	semidirect
83. C₄×Q₁₆×C₁₉	C₂²	semidirect
88. C₈×D₄×C₁₉	C₂²	semidirect
90. C₁₉×#431	C₂²	semidirect
92. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
93. C₁₉×#416	C₂²	semidirect
343. #61950	C₁₉	direct (N × H)
398. C₂×C₄×C₁₉	#135	semidirect
411. #3511	C₂×C₁₉	semidirect
412. #3475	C₂×C₁₉	semidirect
413. #3393	C₂×C₁₉	semidirect
414. #3360	C₂×C₁₉	semidirect
415. #3303	C₂×C₁₉	semidirect
416. #3300	C₂×C₁₉	semidirect
417. #3283	C₂×C₁₉	semidirect
418. #3282	C₂×C₁₉	semidirect
419. #3248	C₂×C₁₉	semidirect
420. #3246	C₂×C₁₉	semidirect
421. #3212	C₂×C₁₉	semidirect
422. #3209	C₂×C₁₉	semidirect
423. #3107	C₂×C₁₉	semidirect
424. #3100	C₂×C₁₉	semidirect
425. #3035	C₂×C₁₉	semidirect
426. C₂×#461	C₂×C₁₉	semidirect
427. #2988	C₂×C₁₉	semidirect
464. #556	C₂²×C₁₉	semidirect
476. #547	C₂²×C₁₉	semidirect
481. #533	C₂²×C₁₉	semidirect
483. #532	C₂²×C₁₉	semidirect
494. #494	C₂²×C₁₉	semidirect
495. #488	C₂²×C₁₉	semidirect
496. #487	C₂²×C₁₉	semidirect
497. #485	C₂²×C₁₉	semidirect
499. #479	C₂²×C₁₉	semidirect
500. #476	C₂²×C₁₉	semidirect
501. #475	C₂²×C₁₉	semidirect
504. #467	C₂²×C₁₉	semidirect
508. #464	C₂²×C₁₉	semidirect
510. #462	C₂²×C₁₉	semidirect
511. #462	C₂²×C₁₉	semidirect
516. #461	C₂²×C₁₉	semidirect
517. #460	C₂²×C₁₉	semidirect
521. #452	C₂²×C₁₉	semidirect
525. C₈×Q₈	C₂²×C₁₉	semidirect
526. C₄×Q₁₆	C₂²×C₁₉	semidirect
531. C₈×D₄	C₂²×C₁₉	semidirect
533. #431	C₂²×C₁₉	semidirect
535. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
536. #416	C₂²×C₁₉	semidirect
681. C₁₉	#61950	direct (N × H)
849. C₂×C₄	C₁₉×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3511	2
C₁₉×#3475	2
C₁₉×#3393	2
C₁₉×#3360	2
C₁₉×#3303	2
C₁₉×#3300	2
C₁₉×#3283	2
C₁₉×#3282	2
C₁₉×#3248	2
C₁₉×#3246	2
C₁₉×#3212	2
C₁₉×#3209	2
C₁₉×#3107	2
C₁₉×#3100	2
C₁₉×#3035	2
C₂×C₁₉×#461	2
C₁₉×#2988	2
#61950	19

Subgroups — C19×#61950 #18067909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61950 #18067909