Subgroups — C₁₉×#61607 #18067566

Order 4864.

2112 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3331	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3316	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3314	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3299	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3278	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3276	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3270	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3266	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3216	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3210	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3196	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3190	C₂	1	2	yes	maximal, complemented
19	C₁₉×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#3007	C₂	1	2	yes	maximal, complemented
22	C₂×C₁₉×#452	C₂	1	2	yes	maximal, complemented
23	C₁₉×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₁₉	C₂²	1	2	yes	—
25	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
26	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
27	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
28	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
29	C₁₉×#554	—	2	1	no	—
30	C₁₉×#554	—	2	2	no	—
31	C₁₉×#554	—	2	1	no	—
32	C₁₉×#554	C₂²	1	1	yes	characteristic
33	C₁₉×#554	C₂²	1	2	yes	complemented
34	C₁₉×#554	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#550	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
39	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#548	C₂²	1	2	yes	—
41	C₁₉×#547	—	2	1	no	—
42	C₁₉×#547	C₂²	1	1	yes	characteristic
43	C₁₉×#546	—	2	2	no	—
44	C₁₉×#546	C₂²	1	2	yes	—
45	D₄²×C₁₉	—	2	1	no	—
46	D₄²×C₁₉	C₂²	1	1	yes	characteristic
47	C₁₉×#544	—	2	1	no	—
48	C₁₉×#543	—	2	2	no	—
49	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×#532	—	2	1	no	—
52	C₁₉×#532	C₂²	1	1	yes	characteristic
53	C₁₉×#525	—	2	2	no	—
54	C₁₉×#525	C₂²	1	2	yes	—
55	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
56	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
57	C₁₉×#518	—	2	1	no	—
58	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₁₉	—	2	1	no	—
60	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
61	C₁₉×#497	C₂²	1	2	yes	complemented
62	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#489	C₂²	1	2	yes	complemented
65	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#485	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#485	C₂²	1	2	yes	complemented
69	C₁₉×#485	C₂²	1	1	yes	characteristic, complemented
70	C₁₉×#484	C₂²	1	2	yes	complemented
71	C₁₉×#483	C₂²	1	2	yes	complemented
72	C₁₉×#481	C₂²	1	2	yes	complemented
73	C₁₉×#480	C₂²	1	2	yes	complemented
74	C₁₉×#477	C₂²	1	1	yes	characteristic, complemented
75	C₁₉×#476	C₂²	1	1	yes	characteristic, complemented
76	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
77	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
78	C₁₉×#470	C₂²	1	2	yes	complemented
79	C₁₉×#470	C₂²	1	2	yes	complemented
80	C₁₉×#468	C₂²	1	2	yes	complemented
81	C₁₉×#468	C₂²	1	2	yes	complemented
82	C₁₉×#467	C₂²	1	2	yes	complemented
83	C₁₉×#467	C₂²	1	2	yes	complemented
84	C₁₉×#465	C₂²	1	2	yes	complemented
85	C₁₉×#465	C₂²	1	2	yes	complemented
86	C₁₉×#464	C₂²	1	2	yes	complemented
87	C₁₉×#464	C₂²	1	2	yes	complemented
88	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
89	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
90	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
91	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
92	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
93	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
94	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
95	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
96	C₁₉×#452	C₂²	1	1	yes	characteristic
97	C₁₉×#452	C₂²	1	2	yes	—
98	C₁₉×#452	C₂²	1	1	yes	characteristic
99	C₁₉×#452	C₂²	1	2	yes	complemented
100	C₁₉×#452	C₂²	1	2	yes	complemented
101	C₁₉×#452	C₂²	1	2	yes	complemented
102	C₁₉×#452	C₂²	1	2	yes	complemented
103	C₁₉×#452	C₂²	1	2	yes	complemented
104	C₁₉×#452	C₂²	1	2	yes	complemented
105	C₁₉×#452	C₂²	1	2	yes	complemented
106	C₁₉×#452	C₂²	1	2	yes	complemented
107	C₁₉×#451	C₂²	1	2	yes	complemented
108	C₁₉×#451	C₂²	1	2	yes	complemented
109	C₁₉×#451	C₂²	1	2	yes	complemented
110	C₁₉×#451	C₂²	1	2	yes	complemented
111	C₁₉×#450	C₂²	1	2	yes	complemented
112	C₁₉×#450	C₂²	1	2	yes	complemented
113	C₁₉×#448	C₂²	1	2	yes	complemented
114	C₁₉×#448	C₂²	1	2	yes	complemented
115	C₁₉×#441	C₂²	1	2	yes	complemented
116	C₁₉×#440	C₂²	1	2	yes	complemented
117	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
121	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
122	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
123	C₁₉×#435	C₂²	1	2	yes	complemented
124	C₁₉×#435	C₂²	1	2	yes	complemented
125	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
126	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
127	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
128	C₁₉×#431	C₂²	1	1	yes	characteristic, complemented
129	C₁₉×#417	C₂²	1	2	yes	complemented
130	C₁₉×#417	C₂²	1	2	yes	complemented
131	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
132	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
133	C₁₉×#407	C₂²	1	2	yes	complemented
134	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
135	C₂×#41×C₁₉	—	2	2	no	—
136	C₂×#41×C₁₉	—	2	2	no	—
137	C₂×#41×C₁₉	—	4	4	no	—
138	C₂×#41×C₁₉	—	4	4	no	—
139	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
140	C₂×#41×C₁₉	C₂³	1	2	yes	—
141	C₂×#41×C₁₉	C₂³	1	2	yes	—
142	C₂×#41×C₁₉	C₂³	1	2	yes	—
143	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
144	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
145	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
146	C₂²×D₄×C₁₉	—	2	2	no	—
147	C₂²×D₄×C₁₉	—	2	1	no	—
148	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
149	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
150	C₂³×C₄×C₁₉	—	2	2	no	—
151	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
152	C₁₉×#137	—	4	4	no	—
153	C₁₉×#137	—	4	4	no	—
154	C₂×Q₁₆×C₁₉	—	4	4	no	—
155	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
156	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
157	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
158	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
161	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₁₉	—	4	4	no	—
163	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
165	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
167	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
168	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
169	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
170	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
171	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
172	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
173	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
174	C₁₉×C₄⋊Q₈	—	2	1	no	—
175	C₁₉×C₄⋊Q₈	—	2	1	no	—
176	C₁₉×C₄⋊Q₈	—	2	1	no	—
177	C₁₉×C₄⋊Q₈	—	2	2	no	—
178	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
181	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
182	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
183	C₁₉×#127	—	2	1	no	—
184	C₁₉×#127	C₂³	1	1	yes	characteristic
185	C₁₉×#125	—	2	1	no	—
186	C₁₉×#125	—	2	1	no	—
187	C₁₉×#125	—	2	2	no	—
188	C₁₉×#125	—	2	1	no	—
189	C₁₉×#125	—	2	1	no	—
190	C₁₉×#124	—	2	2	no	—
191	C₁₉×#124	C₂³	1	2	yes	—
192	C₁₉×#123	—	2	2	no	—
193	C₁₉×#123	—	2	2	no	—
194	C₁₉×#123	—	2	2	no	—
195	C₁₉×C₂²⋊Q₈	—	2	2	no	—
196	C₁₉×C₂²⋊Q₈	—	2	2	no	—
197	C₁₉×C₂²⋊Q₈	—	2	2	no	—
198	C₁₉×C₂²⋊Q₈	—	2	2	no	—
199	C₁₉×C₂²⋊Q₈	—	2	1	no	—
200	C₁₉×C₂²⋊Q₈	—	2	1	no	—
201	C₁₉×C₂²⋊Q₈	—	2	2	no	—
202	C₁₉×C₂²⋊Q₈	—	2	2	no	—
203	C₁₉×C₂²⋊Q₈	—	2	2	no	—
204	C₁₉×C₂²⋊Q₈	—	2	2	no	—
205	C₁₉×C₂²⋊Q₈	—	2	2	no	—
206	C₁₉×C₂²⋊Q₈	—	2	2	no	—
207	C₁₉×C₂²⋊Q₈	—	2	2	no	—
208	C₁₉×C₂²⋊Q₈	—	2	2	no	—
209	C₁₉×C₂²⋊Q₈	—	2	2	no	—
210	C₁₉×C₂²⋊Q₈	—	2	2	no	—
211	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₁₉×#121	—	2	2	no	—
221	C₁₉×#121	—	2	1	no	—
222	C₁₉×#121	—	2	1	no	—
223	C₁₉×#121	—	2	1	no	—
224	C₁₉×#121	—	2	1	no	—
225	C₁₉×#121	—	2	2	no	—
226	C₁₉×#121	—	2	2	no	—
227	C₁₉×#121	C₂³	1	2	yes	—
228	C₁₉×#121	C₂³	1	2	yes	—
229	C₁₉×#120	—	2	2	no	—
230	C₁₉×#120	—	2	2	no	—
231	C₁₉×#120	—	2	2	no	—
232	C₄×Q₈×C₁₉	—	2	1	no	—
233	C₄×Q₈×C₁₉	—	2	1	no	—
234	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
238	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₁₉	—	2	1	no	—
240	C₄×D₄×C₁₉	—	2	1	no	—
241	C₄×D₄×C₁₉	—	2	2	no	—
242	C₄×D₄×C₁₉	—	2	1	no	—
243	C₄×D₄×C₁₉	—	2	1	no	—
244	C₄×D₄×C₁₉	—	2	2	no	—
245	C₄×D₄×C₁₉	—	2	1	no	—
246	C₄×D₄×C₁₉	—	2	2	no	—
247	C₄×D₄×C₁₉	—	2	1	no	—
248	C₄×D₄×C₁₉	—	2	1	no	—
249	C₄×D₄×C₁₉	—	2	2	no	—
250	C₄×D₄×C₁₉	—	2	1	no	—
251	C₄×D₄×C₁₉	—	2	2	no	—
252	C₄×D₄×C₁₉	—	2	1	no	—
253	C₄×D₄×C₁₉	—	2	1	no	—
254	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
255	C₄×D₄×C₁₉	D₄	1	2	yes	—
256	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
257	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₁₉	C₂³	1	2	yes	—
261	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
262	C₁₉×#117	—	2	1	no	—
263	C₁₉×#117	—	2	1	no	—
264	C₁₉×#117	—	2	1	no	—
265	C₁₉×#117	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
267	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
268	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
269	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
272	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
273	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
274	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
276	C₂×C₄²×C₁₉	—	2	1	no	—
277	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
278	C₁₉×#107	C₂³	1	1	yes	characteristic
279	C₁₉×#107	C₂³	1	1	yes	characteristic
280	C₁₉×#107	C₂³	1	2	yes	—
281	C₁₉×#106	C₂³	1	1	yes	characteristic
282	C₁₉×#106	C₂³	1	1	yes	characteristic
283	C₁₉×#106	C₂³	1	2	yes	—
284	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₁₉×#103	C₂³	1	1	yes	characteristic
289	C₁₉×#103	C₂³	1	2	yes	—
290	C₁₉×#103	C₂³	1	2	yes	—
291	C₁₉×#103	C₂³	1	2	yes	—
292	C₁₉×#103	C₂³	1	1	yes	characteristic
293	C₁₉×#103	C₂³	1	2	yes	—
294	C₁₉×#103	C₂³	1	2	yes	—
295	C₁₉×#103	C₂³	1	1	yes	characteristic
296	C₁₉×#103	C₂³	1	1	yes	characteristic
297	C₁₉×#103	C₂³	1	1	yes	characteristic
298	C₁₉×#103	C₂³	1	1	yes	characteristic
299	C₁₉×#103	C₂³	1	2	yes	—
300	C₁₉×#103	C₂³	1	2	yes	—
301	C₁₉×#102	C₂³	1	1	yes	characteristic
302	C₁₉×#102	C₂³	1	2	yes	—
303	C₁₉×#102	C₂³	1	2	yes	—
304	C₁₉×#102	C₂³	1	2	yes	—
305	C₁₉×#102	C₂³	1	1	yes	characteristic
306	C₁₉×#102	C₂³	1	2	yes	—
307	C₁₉×#102	C₂³	1	2	yes	—
308	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
313	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₁₉×#97	C₂³	1	2	yes	—
316	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
318	C₂⁴×C₁₉	—	2	2	no	—
319	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
320	#41×C₁₉	—	2	2	no	—
321	#41×C₁₉	—	2	2	no	—
322	#41×C₁₉	—	2	4	no	—
323	#41×C₁₉	—	2	4	no	—
324	#41×C₁₉	—	4	2	no	—
325	#41×C₁₉	—	4	2	no	—
326	#41×C₁₉	—	4	2	no	—
327	#41×C₁₉	—	4	2	no	—
328	#41×C₁₉	—	4	8	no	—
329	#41×C₁₉	—	4	8	no	—
330	C₂×Q₈×C₁₉	—	2	2	no	—
331	C₂×Q₈×C₁₉	—	2	1	no	—
332	C₂×Q₈×C₁₉	—	2	1	no	—
333	C₂×Q₈×C₁₉	—	2	2	no	—
334	C₂×Q₈×C₁₉	—	2	2	no	—
335	C₂×Q₈×C₁₉	—	2	4	no	—
336	C₂×Q₈×C₁₉	—	4	2	no	—
337	C₂×Q₈×C₁₉	—	4	2	no	—
338	C₂×Q₈×C₁₉	—	4	2	no	—
339	C₂×Q₈×C₁₉	—	4	2	no	—
340	C₂×Q₈×C₁₉	—	4	2	no	—
341	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
342	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
343	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
344	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
345	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₁₉	—	2	1	no	—
347	C₂×D₄×C₁₉	—	2	4	no	—
348	C₂×D₄×C₁₉	—	2	4	no	—
349	C₂×D₄×C₁₉	—	2	2	no	—
350	C₂×D₄×C₁₉	—	2	2	no	—
351	C₂×D₄×C₁₉	—	2	2	no	—
352	C₂×D₄×C₁₉	—	2	2	no	—
353	C₂×D₄×C₁₉	—	2	2	no	—
354	C₂×D₄×C₁₉	—	2	1	no	—
355	C₂×D₄×C₁₉	—	2	2	no	—
356	C₂×D₄×C₁₉	—	2	1	no	—
357	C₂×D₄×C₁₉	—	4	2	no	—
358	C₂×D₄×C₁₉	—	4	8	no	—
359	C₂×D₄×C₁₉	—	4	4	no	—
360	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
361	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
362	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
363	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
364	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₁₉	—	2	1	no	—
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	1	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	1	no	—
376	C₂²×C₄×C₁₉	—	4	2	no	—
377	C₂²×C₄×C₁₉	—	4	2	no	—
378	C₂²×C₄×C₁₉	—	4	8	no	—
379	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
382	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
383	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
384	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
386	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
387	Q₁₆×C₁₉	—	2	2	no	—
388	Q₁₆×C₁₉	—	2	4	no	—
389	Q₁₆×C₁₉	—	2	2	no	—
390	Q₁₆×C₁₉	—	4	2	no	—
391	Q₁₆×C₁₉	—	4	2	no	—
392	Q₁₆×C₁₉	—	4	2	no	—
393	Q₁₆×C₁₉	—	4	2	no	—
394	SD₁₆×C₁₉	—	2	2	no	—
395	SD₁₆×C₁₉	—	2	4	no	—
396	SD₁₆×C₁₉	—	2	2	no	—
397	SD₁₆×C₁₉	—	4	2	no	—
398	SD₁₆×C₁₉	—	4	2	no	—
399	SD₁₆×C₁₉	—	4	2	no	—
400	SD₁₆×C₁₉	—	4	2	no	—
401	M₁₆×C₁₉	—	4	2	no	—
402	M₁₆×C₁₉	—	4	2	no	—
403	C₂×C₈×C₁₉	—	4	2	no	—
404	C₂×C₈×C₁₉	—	4	2	no	—
405	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
408	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
409	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
410	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₁₉	—	2	1	no	—
412	C₄⋊C₄×C₁₉	—	2	2	no	—
413	C₄⋊C₄×C₁₉	—	2	1	no	—
414	C₄⋊C₄×C₁₉	—	2	1	no	—
415	C₄⋊C₄×C₁₉	—	2	2	no	—
416	C₄⋊C₄×C₁₉	—	2	2	no	—
417	C₄⋊C₄×C₁₉	—	2	2	no	—
418	C₄⋊C₄×C₁₉	—	2	2	no	—
419	C₄⋊C₄×C₁₉	—	2	2	no	—
420	C₄⋊C₄×C₁₉	—	2	2	no	—
421	C₄⋊C₄×C₁₉	—	2	2	no	—
422	C₄⋊C₄×C₁₉	—	2	1	no	—
423	C₄⋊C₄×C₁₉	—	2	1	no	—
424	C₄⋊C₄×C₁₉	—	2	1	no	—
425	C₄⋊C₄×C₁₉	—	2	1	no	—
426	C₄⋊C₄×C₁₉	—	2	1	no	—
427	C₄⋊C₄×C₁₉	—	2	1	no	—
428	C₄⋊C₄×C₁₉	—	2	1	no	—
429	C₄⋊C₄×C₁₉	—	2	2	no	—
430	C₄⋊C₄×C₁₉	—	2	1	no	—
431	C₄⋊C₄×C₁₉	—	2	1	no	—
432	C₄⋊C₄×C₁₉	—	2	2	no	—
433	C₄⋊C₄×C₁₉	—	2	1	no	—
434	C₄⋊C₄×C₁₉	—	2	1	no	—
435	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
438	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
440	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
442	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
443	C₂²⋊C₄×C₁₉	—	2	1	no	—
444	C₂²⋊C₄×C₁₉	—	2	2	no	—
445	C₂²⋊C₄×C₁₉	—	2	1	no	—
446	C₂²⋊C₄×C₁₉	—	2	2	no	—
447	C₂²⋊C₄×C₁₉	—	2	2	no	—
448	C₂²⋊C₄×C₁₉	—	2	2	no	—
449	C₂²⋊C₄×C₁₉	—	2	2	no	—
450	C₂²⋊C₄×C₁₉	—	2	2	no	—
451	C₂²⋊C₄×C₁₉	—	2	1	no	—
452	C₂²⋊C₄×C₁₉	—	2	2	no	—
453	C₂²⋊C₄×C₁₉	—	2	2	no	—
454	C₂²⋊C₄×C₁₉	—	2	2	no	—
455	C₂²⋊C₄×C₁₉	—	2	1	no	—
456	C₂²⋊C₄×C₁₉	—	2	1	no	—
457	C₂²⋊C₄×C₁₉	—	2	2	no	—
458	C₂²⋊C₄×C₁₉	—	2	2	no	—
459	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
460	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
463	C₄²×C₁₉	—	2	1	no	—
464	C₄²×C₁₉	—	2	1	no	—
465	C₄²×C₁₉	—	2	1	no	—
466	C₄²×C₁₉	—	2	2	no	—
467	C₄²×C₁₉	—	2	1	no	—
468	C₄²×C₁₉	—	2	1	no	—
469	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
470	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
472	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
473	#61607	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
474	C₂³×C₁₉	—	2	1	no	—
475	C₂³×C₁₉	—	2	4	no	—
476	C₂³×C₁₉	—	2	2	no	—
477	C₂³×C₁₉	—	4	2	no	—
478	C₂³×C₁₉	—	4	2	no	—
479	C₂³×C₁₉	—	4	4	no	—
480	C₂³×C₁₉	—	4	4	no	—
481	C₂³×C₁₉	—	8	2	no	—
482	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
483	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
484	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
485	Q₈×C₁₉	—	2	1	no	—
486	Q₈×C₁₉	—	2	1	no	—
487	Q₈×C₁₉	—	2	2	no	—
488	Q₈×C₁₉	—	2	1	no	—
489	Q₈×C₁₉	—	2	1	no	—
490	Q₈×C₁₉	—	2	2	no	—
491	Q₈×C₁₉	—	2	1	no	—
492	Q₈×C₁₉	—	2	2	no	—
493	Q₈×C₁₉	—	2	2	no	—
494	Q₈×C₁₉	—	4	4	no	—
495	Q₈×C₁₉	—	8	1	no	—
496	Q₈×C₁₉	—	8	1	no	—
497	Q₈×C₁₉	—	8	2	no	—
498	Q₈×C₁₉	—	8	2	no	—
499	Q₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
500	D₄×C₁₉	—	2	4	no	—
501	D₄×C₁₉	—	2	4	no	—
502	D₄×C₁₉	—	2	2	no	—
503	D₄×C₁₉	—	2	1	no	—
504	D₄×C₁₉	—	2	2	no	—
505	D₄×C₁₉	—	2	2	no	—
506	D₄×C₁₉	—	4	4	no	—
507	D₄×C₁₉	—	4	4	no	—
508	D₄×C₁₉	—	4	4	no	—
509	D₄×C₁₉	—	4	4	no	—
510	D₄×C₁₉	—	4	4	no	—
511	D₄×C₁₉	—	4	2	no	—
512	D₄×C₁₉	—	8	1	no	—
513	D₄×C₁₉	—	8	2	no	—
514	D₄×C₁₉	#137	1	4	yes	complemented
515	D₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
516	C₂×C₄×C₁₉	—	2	4	no	—
517	C₂×C₄×C₁₉	—	2	1	no	—
518	C₂×C₄×C₁₉	—	2	2	no	—
519	C₂×C₄×C₁₉	—	2	2	no	—
520	C₂×C₄×C₁₉	—	2	2	no	—
521	C₂×C₄×C₁₉	—	2	2	no	—
522	C₂×C₄×C₁₉	—	2	2	no	—
523	C₂×C₄×C₁₉	—	2	1	no	—
524	C₂×C₄×C₁₉	—	2	1	no	—
525	C₂×C₄×C₁₉	—	2	1	no	—
526	C₂×C₄×C₁₉	—	2	1	no	—
527	C₂×C₄×C₁₉	—	2	2	no	—
528	C₂×C₄×C₁₉	—	2	1	no	—
529	C₂×C₄×C₁₉	—	2	1	no	—
530	C₂×C₄×C₁₉	—	2	1	no	—
531	C₂×C₄×C₁₉	—	2	2	no	—
532	C₂×C₄×C₁₉	—	2	1	no	—
533	C₂×C₄×C₁₉	—	2	2	no	—
534	C₂×C₄×C₁₉	—	4	2	no	—
535	C₂×C₄×C₁₉	—	4	2	no	—
536	C₂×C₄×C₁₉	—	4	2	no	—
537	C₂×C₄×C₁₉	—	4	1	no	—
538	C₂×C₄×C₁₉	—	4	4	no	—
539	C₂×C₄×C₁₉	—	4	4	no	—
540	C₂×C₄×C₁₉	—	4	4	no	—
541	C₂×C₄×C₁₉	—	4	4	no	—
542	C₂×C₄×C₁₉	—	4	2	no	—
543	C₂×C₄×C₁₉	—	8	1	no	—
544	C₂×C₄×C₁₉	—	8	2	no	—
545	C₂×C₄×C₁₉	—	8	2	no	—
546	C₂×C₄×C₁₉	—	8	2	no	—
547	C₂×C₄×C₁₉	—	8	2	no	—
548	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
553	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
554	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
556	C₈×C₁₉	—	2	1	no	—
557	C₈×C₁₉	—	2	1	no	—
558	C₈×C₁₉	—	2	2	no	—
559	C₈×C₁₉	—	2	2	no	—
560	C₈×C₁₉	—	2	1	no	—
561	C₈×C₁₉	—	2	1	no	—
562	#3501	C₂×C₁₉	1	1	yes	characteristic, complemented
563	D₄×#41	C₂×C₁₉	1	1	yes	characteristic
564	#3333	C₂×C₁₉	1	1	yes	characteristic, complemented
565	#3331	C₂×C₁₉	1	1	yes	characteristic, complemented
566	#3316	C₂×C₁₉	1	2	yes	complemented
567	#3314	C₂×C₁₉	1	2	yes	complemented
568	#3299	C₂×C₁₉	1	1	yes	characteristic, complemented
569	#3295	C₂×C₁₉	1	1	yes	characteristic, complemented
570	D₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
571	D₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
572	#3278	C₂×C₁₉	1	1	yes	characteristic, complemented
573	#3276	C₂×C₁₉	1	1	yes	characteristic, complemented
574	#3270	C₂×C₁₉	1	2	yes	complemented
575	#3266	C₂×C₁₉	1	2	yes	complemented
576	#3216	C₂×C₁₉	1	1	yes	characteristic, complemented
577	#3210	C₂×C₁₉	1	1	yes	characteristic, complemented
578	#3196	C₂×C₁₉	1	2	yes	complemented
579	#3190	C₂×C₁₉	1	2	yes	complemented
580	#3116	C₂×C₁₉	1	1	yes	characteristic, complemented
581	#3107	C₂×C₁₉	1	1	yes	characteristic, complemented
582	#3007	C₂×C₁₉	1	2	yes	complemented
583	C₂×#452	C₂×C₁₉	1	2	yes	complemented
584	#2974	C₂×C₁₉	1	1	yes	characteristic, complemented
585	C₂²×C₁₉	—	2	2	no	—
586	C₂²×C₁₉	—	2	2	no	—
587	C₂²×C₁₉	—	2	1	no	—
588	C₂²×C₁₉	—	2	2	no	—
589	C₂²×C₁₉	—	2	1	no	—
590	C₂²×C₁₉	—	2	2	no	—
591	C₂²×C₁₉	—	2	2	no	—
592	C₂²×C₁₉	—	2	1	no	—
593	C₂²×C₁₉	—	2	2	no	—
594	C₂²×C₁₉	—	4	1	no	—
595	C₂²×C₁₉	—	4	1	no	—
596	C₂²×C₁₉	—	4	2	no	—
597	C₂²×C₁₉	—	4	2	no	—
598	C₂²×C₁₉	—	4	2	no	—
599	C₂²×C₁₉	—	8	4	no	—
600	C₂²×C₁₉	—	8	8	no	—
601	C₂²×C₁₉	C₂×#137	1	4	yes	—
602	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
603	C₄×C₁₉	—	2	1	no	—
604	C₄×C₁₉	—	2	1	no	—
605	C₄×C₁₉	—	2	1	no	—
606	C₄×C₁₉	—	2	2	no	—
607	C₄×C₁₉	—	2	2	no	—
608	C₄×C₁₉	—	2	2	no	—
609	C₄×C₁₉	—	2	1	no	—
610	C₄×C₁₉	—	4	1	no	—
611	C₄×C₁₉	—	4	2	no	—
612	C₄×C₁₉	—	4	1	no	—
613	C₄×C₁₉	—	4	1	no	—
614	C₄×C₁₉	—	4	2	no	—
615	C₄×C₁₉	—	4	1	no	—
616	C₄×C₁₉	—	4	2	no	—
617	C₄×C₁₉	—	4	1	no	—
618	C₄×C₁₉	—	4	1	no	—
619	C₄×C₁₉	C₂×#137	1	2	yes	—
620	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
621	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
622	C₂²×#41	C₂²×C₁₉	1	2	yes	—
623	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
624	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
625	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
626	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
627	#554	—	2	1	no	—
628	#554	—	2	2	no	—
629	#554	—	2	1	no	—
630	#554	C₂²×C₁₉	1	1	yes	characteristic
631	#554	C₂²×C₁₉	1	1	yes	characteristic, complemented
632	#554	C₂²×C₁₉	1	2	yes	complemented
633	#550	C₂²×C₁₉	1	1	yes	characteristic
634	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
635	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
636	D₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
637	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
638	#548	C₂²×C₁₉	1	2	yes	—
639	#547	—	2	1	no	—
640	#547	C₂²×C₁₉	1	1	yes	characteristic
641	#546	—	2	2	no	—
642	#546	C₂²×C₁₉	1	2	yes	—
643	D₄²	—	2	1	no	—
644	D₄²	C₂²×C₁₉	1	1	yes	characteristic
645	#544	—	2	1	no	—
646	#543	—	2	2	no	—
647	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
648	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
649	#532	—	2	1	no	—
650	#532	C₂²×C₁₉	1	1	yes	characteristic
651	#525	—	2	2	no	—
652	#525	C₂²×C₁₉	1	2	yes	—
653	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	complemented
654	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	complemented
655	#518	—	2	1	no	—
656	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
657	C₂×C₄×D₄	—	2	1	no	—
658	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
659	#497	C₂²×C₁₉	1	2	yes	complemented
660	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
661	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
662	#489	C₂²×C₁₉	1	2	yes	complemented
663	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
664	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
665	#485	C₂²×C₁₉	1	1	yes	characteristic, complemented
666	#485	C₂²×C₁₉	1	1	yes	characteristic, complemented
667	#485	C₂²×C₁₉	1	2	yes	complemented
668	#484	C₂²×C₁₉	1	2	yes	complemented
669	#483	C₂²×C₁₉	1	2	yes	complemented
670	#481	C₂²×C₁₉	1	2	yes	complemented
671	#480	C₂²×C₁₉	1	2	yes	complemented
672	#477	C₂²×C₁₉	1	1	yes	characteristic, complemented
673	#476	C₂²×C₁₉	1	1	yes	characteristic, complemented
674	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
675	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
676	#470	C₂²×C₁₉	1	2	yes	complemented
677	#470	C₂²×C₁₉	1	2	yes	complemented
678	#468	C₂²×C₁₉	1	2	yes	complemented
679	#468	C₂²×C₁₉	1	2	yes	complemented
680	#467	C₂²×C₁₉	1	2	yes	complemented
681	#467	C₂²×C₁₉	1	2	yes	complemented
682	#465	C₂²×C₁₉	1	2	yes	complemented
683	#465	C₂²×C₁₉	1	2	yes	complemented
684	#464	C₂²×C₁₉	1	2	yes	complemented
685	#464	C₂²×C₁₉	1	2	yes	complemented
686	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
687	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
688	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
689	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
690	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
691	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
692	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
693	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
694	#452	C₂²×C₁₉	1	1	yes	characteristic
695	#452	C₂²×C₁₉	1	1	yes	characteristic
696	#452	C₂²×C₁₉	1	2	yes	—
697	#452	C₂²×C₁₉	1	2	yes	complemented
698	#452	C₂²×C₁₉	1	2	yes	complemented
699	#452	C₂²×C₁₉	1	2	yes	complemented
700	#452	C₂²×C₁₉	1	2	yes	complemented
701	#452	C₂²×C₁₉	1	2	yes	complemented
702	#452	C₂²×C₁₉	1	2	yes	complemented
703	#452	C₂²×C₁₉	1	2	yes	complemented
704	#452	C₂²×C₁₉	1	2	yes	complemented
705	#451	C₂²×C₁₉	1	2	yes	complemented
706	#451	C₂²×C₁₉	1	2	yes	complemented
707	#451	C₂²×C₁₉	1	2	yes	complemented
708	#451	C₂²×C₁₉	1	2	yes	complemented
709	#450	C₂²×C₁₉	1	2	yes	complemented
710	#450	C₂²×C₁₉	1	2	yes	complemented
711	#448	C₂²×C₁₉	1	2	yes	complemented
712	#448	C₂²×C₁₉	1	2	yes	complemented
713	#441	C₂²×C₁₉	1	2	yes	complemented
714	#440	C₂²×C₁₉	1	2	yes	complemented
715	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
716	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
717	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
718	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
719	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
720	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
721	#435	C₂²×C₁₉	1	2	yes	complemented
722	#435	C₂²×C₁₉	1	2	yes	complemented
723	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
724	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
725	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
726	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
727	#417	C₂²×C₁₉	1	2	yes	complemented
728	#417	C₂²×C₁₉	1	2	yes	complemented
729	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
730	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
731	#407	C₂²×C₁₉	1	2	yes	complemented
732	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	complemented
733	C₂×C₁₉	—	2	4	no	—
734	C₂×C₁₉	—	4	2	no	—
735	C₂×C₁₉	—	4	1	no	—
736	C₂×C₁₉	—	4	2	no	—
737	C₂×C₁₉	—	8	2	no	—
738	C₂×C₁₉	#3484	1	1	yes	characteristic
739	C₂×C₁₉	C₂²×#137	1	1	yes	characteristic
740	C₂×C₁₉	#3584	1	1	yes	characteristic
741	C₂×#41	—	2	2	no	—
742	C₂×#41	—	2	2	no	—
743	C₂×#41	—	4	4	no	—
744	C₂×#41	—	4	4	no	—
745	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
746	C₂×#41	C₂³×C₁₉	1	2	yes	—
747	C₂×#41	C₂³×C₁₉	1	2	yes	—
748	C₂×#41	C₂³×C₁₉	1	2	yes	—
749	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
750	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
751	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
752	C₂²×D₄	—	2	2	no	—
753	C₂²×D₄	—	2	1	no	—
754	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
755	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
756	C₂³×C₄	—	2	2	no	—
757	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
758	#137	—	4	4	no	—
759	#137	—	4	4	no	—
760	C₂×Q₁₆	—	4	4	no	—
761	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
762	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
763	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
764	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
765	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
766	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
767	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
768	C₂×SD₁₆	—	4	4	no	—
769	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
770	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
771	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
772	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
773	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
776	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
777	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
778	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
779	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
780	C₄⋊Q₈	—	2	1	no	—
781	C₄⋊Q₈	—	2	1	no	—
782	C₄⋊Q₈	—	2	1	no	—
783	C₄⋊Q₈	—	2	2	no	—
784	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
785	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
786	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
787	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
788	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
789	#127	—	2	1	no	—
790	#127	C₂³×C₁₉	1	1	yes	characteristic
791	#125	—	2	1	no	—
792	#125	—	2	1	no	—
793	#125	—	2	2	no	—
794	#125	—	2	1	no	—
795	#125	—	2	1	no	—
796	#124	—	2	2	no	—
797	#124	C₂³×C₁₉	1	2	yes	—
798	#123	—	2	2	no	—
799	#123	—	2	2	no	—
800	#123	—	2	2	no	—
801	C₂²⋊Q₈	—	2	2	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	—	2	2	no	—
804	C₂²⋊Q₈	—	2	2	no	—
805	C₂²⋊Q₈	—	2	1	no	—
806	C₂²⋊Q₈	—	2	1	no	—
807	C₂²⋊Q₈	—	2	2	no	—
808	C₂²⋊Q₈	—	2	2	no	—
809	C₂²⋊Q₈	—	2	2	no	—
810	C₂²⋊Q₈	—	2	2	no	—
811	C₂²⋊Q₈	—	2	2	no	—
812	C₂²⋊Q₈	—	2	2	no	—
813	C₂²⋊Q₈	—	2	2	no	—
814	C₂²⋊Q₈	—	2	2	no	—
815	C₂²⋊Q₈	—	2	2	no	—
816	C₂²⋊Q₈	—	2	2	no	—
817	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
818	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
819	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
820	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
821	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
822	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
823	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
824	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
825	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
826	#121	—	2	2	no	—
827	#121	—	2	1	no	—
828	#121	—	2	1	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	2	no	—
832	#121	—	2	2	no	—
833	#121	C₂³×C₁₉	1	2	yes	—
834	#121	C₂³×C₁₉	1	2	yes	—
835	#120	—	2	2	no	—
836	#120	—	2	2	no	—
837	#120	—	2	2	no	—
838	C₄×Q₈	—	2	1	no	—
839	C₄×Q₈	—	2	1	no	—
840	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
841	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
842	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
843	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
844	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
845	C₄×D₄	—	2	1	no	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	2	no	—
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	2	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	2	no	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	—	2	2	no	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	—	2	2	no	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
861	C₄×D₄	D₄×C₁₉	1	2	yes	—
862	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
863	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
864	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
865	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
866	C₄×D₄	C₂³×C₁₉	1	2	yes	—
867	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
868	#117	—	2	1	no	—
869	#117	—	2	1	no	—
870	#117	—	2	1	no	—
871	#117	C₂³×C₁₉	1	1	yes	characteristic
872	C₂×C₄⋊C₄	—	2	2	no	—
873	C₂×C₄⋊C₄	—	2	2	no	—
874	C₂×C₄⋊C₄	—	2	1	no	—
875	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
876	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
877	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
878	C₂×C₂²⋊C₄	—	2	2	no	—
879	C₂×C₂²⋊C₄	—	2	2	no	—
880	C₂×C₂²⋊C₄	—	2	2	no	—
881	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
882	C₂×C₄²	—	2	1	no	—
883	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
884	#107	C₂³×C₁₉	1	1	yes	characteristic
885	#107	C₂³×C₁₉	1	1	yes	characteristic
886	#107	C₂³×C₁₉	1	2	yes	—
887	#106	C₂³×C₁₉	1	1	yes	characteristic
888	#106	C₂³×C₁₉	1	1	yes	characteristic
889	#106	C₂³×C₁₉	1	2	yes	—
890	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
891	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
892	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
893	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
894	#103	C₂³×C₁₉	1	1	yes	characteristic
895	#103	C₂³×C₁₉	1	2	yes	—
896	#103	C₂³×C₁₉	1	2	yes	—
897	#103	C₂³×C₁₉	1	2	yes	—
898	#103	C₂³×C₁₉	1	1	yes	characteristic
899	#103	C₂³×C₁₉	1	2	yes	—
900	#103	C₂³×C₁₉	1	2	yes	—
901	#103	C₂³×C₁₉	1	1	yes	characteristic
902	#103	C₂³×C₁₉	1	1	yes	characteristic
903	#103	C₂³×C₁₉	1	1	yes	characteristic
904	#103	C₂³×C₁₉	1	1	yes	characteristic
905	#103	C₂³×C₁₉	1	2	yes	—
906	#103	C₂³×C₁₉	1	2	yes	—
907	#102	C₂³×C₁₉	1	1	yes	characteristic
908	#102	C₂³×C₁₉	1	2	yes	—
909	#102	C₂³×C₁₉	1	2	yes	—
910	#102	C₂³×C₁₉	1	2	yes	—
911	#102	C₂³×C₁₉	1	1	yes	characteristic
912	#102	C₂³×C₁₉	1	2	yes	—
913	#102	C₂³×C₁₉	1	2	yes	—
914	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
915	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
916	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
917	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
918	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
919	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
920	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
921	#97	C₂³×C₁₉	1	2	yes	—
922	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
923	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
924	C₁₉	#61607	1	1	yes	characteristic, direct product factor, Sylow
925	C₂⁴	—	2	2	no	—
926	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
927	#41	—	2	2	no	—
928	#41	—	2	2	no	—
929	#41	—	2	4	no	—
930	#41	—	2	4	no	—
931	#41	—	4	2	no	—
932	#41	—	4	2	no	—
933	#41	—	4	2	no	—
934	#41	—	4	2	no	—
935	#41	—	4	8	no	—
936	#41	—	4	8	no	—
937	C₂×Q₈	—	2	2	no	—
938	C₂×Q₈	—	2	1	no	—
939	C₂×Q₈	—	2	1	no	—
940	C₂×Q₈	—	2	2	no	—
941	C₂×Q₈	—	2	2	no	—
942	C₂×Q₈	—	2	4	no	—
943	C₂×Q₈	—	4	2	no	—
944	C₂×Q₈	—	4	2	no	—
945	C₂×Q₈	—	4	2	no	—
946	C₂×Q₈	—	4	2	no	—
947	C₂×Q₈	—	4	2	no	—
948	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
949	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
950	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
951	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
952	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	2	4	no	—
955	C₂×D₄	—	2	4	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	2	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	1	no	—
964	C₂×D₄	—	4	2	no	—
965	C₂×D₄	—	4	8	no	—
966	C₂×D₄	—	4	4	no	—
967	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
968	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
969	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
970	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
971	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	2	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	2	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	2	no	—
980	C₂²×C₄	—	2	2	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	1	no	—
983	C₂²×C₄	—	4	2	no	—
984	C₂²×C₄	—	4	2	no	—
985	C₂²×C₄	—	4	8	no	—
986	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
987	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
988	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
989	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
990	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
991	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
992	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
993	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
994	Q₁₆	—	2	2	no	—
995	Q₁₆	—	2	4	no	—
996	Q₁₆	—	2	2	no	—
997	Q₁₆	—	4	2	no	—
998	Q₁₆	—	4	2	no	—
999	Q₁₆	—	4	2	no	—
1000	Q₁₆	—	4	2	no	—
1001	SD₁₆	—	2	2	no	—
1002	SD₁₆	—	2	4	no	—
1003	SD₁₆	—	2	2	no	—
1004	SD₁₆	—	4	2	no	—
1005	SD₁₆	—	4	2	no	—
1006	SD₁₆	—	4	2	no	—
1007	SD₁₆	—	4	2	no	—
1008	M₁₆	—	4	2	no	—
1009	M₁₆	—	4	2	no	—
1010	C₂×C₈	—	4	2	no	—
1011	C₂×C₈	—	4	2	no	—
1012	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1013	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1014	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1015	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1016	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
1017	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	2	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1043	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1044	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1045	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1046	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1047	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1048	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1049	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1067	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1068	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1069	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1070	C₄²	—	2	1	no	—
1071	C₄²	—	2	1	no	—
1072	C₄²	—	2	1	no	—
1073	C₄²	—	2	2	no	—
1074	C₄²	—	2	1	no	—
1075	C₄²	—	2	1	no	—
1076	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1077	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1078	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1079	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1080	C₂³	—	2	1	no	—
1081	C₂³	—	2	4	no	—
1082	C₂³	—	2	2	no	—
1083	C₂³	—	4	2	no	—
1084	C₂³	—	4	2	no	—
1085	C₂³	—	4	4	no	—
1086	C₂³	—	4	4	no	—
1087	C₂³	—	8	2	no	—
1088	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1089	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1090	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1091	Q₈	—	2	1	no	—
1092	Q₈	—	2	1	no	—
1093	Q₈	—	2	2	no	—
1094	Q₈	—	2	1	no	—
1095	Q₈	—	2	1	no	—
1096	Q₈	—	2	2	no	—
1097	Q₈	—	2	1	no	—
1098	Q₈	—	2	2	no	—
1099	Q₈	—	2	2	no	—
1100	Q₈	—	4	4	no	—
1101	Q₈	—	8	2	no	—
1102	Q₈	—	8	2	no	—
1103	Q₈	—	8	1	no	—
1104	Q₈	—	8	1	no	—
1105	Q₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
1106	D₄	—	2	4	no	—
1107	D₄	—	2	4	no	—
1108	D₄	—	2	2	no	—
1109	D₄	—	2	1	no	—
1110	D₄	—	2	2	no	—
1111	D₄	—	2	2	no	—
1112	D₄	—	4	4	no	—
1113	D₄	—	4	4	no	—
1114	D₄	—	4	4	no	—
1115	D₄	—	4	4	no	—
1116	D₄	—	4	4	no	—
1117	D₄	—	4	2	no	—
1118	D₄	—	8	1	no	—
1119	D₄	—	8	2	no	—
1120	D₄	C₁₉×#137	1	4	yes	complemented
1121	D₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
1122	C₂×C₄	—	2	4	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	2	no	—
1143	C₂×C₄	—	4	1	no	—
1144	C₂×C₄	—	4	4	no	—
1145	C₂×C₄	—	4	4	no	—
1146	C₂×C₄	—	4	4	no	—
1147	C₂×C₄	—	4	4	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	8	1	no	—
1150	C₂×C₄	—	8	2	no	—
1151	C₂×C₄	—	8	2	no	—
1152	C₂×C₄	—	8	2	no	—
1153	C₂×C₄	—	8	2	no	—
1154	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1155	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1156	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1157	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1158	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1159	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1160	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1161	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1162	C₈	—	2	1	no	—
1163	C₈	—	2	1	no	—
1164	C₈	—	2	2	no	—
1165	C₈	—	2	2	no	—
1166	C₈	—	2	1	no	—
1167	C₈	—	2	1	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	2	1	no	—
1171	C₂²	—	2	2	no	—
1172	C₂²	—	2	2	no	—
1173	C₂²	—	2	1	no	—
1174	C₂²	—	2	2	no	—
1175	C₂²	—	2	1	no	—
1176	C₂²	—	2	2	no	—
1177	C₂²	—	4	1	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	2	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	8	4	no	—
1183	C₂²	—	8	8	no	—
1184	C₂²	C₂×C₁₉×#137	1	4	yes	—
1185	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1186	C₄	—	2	1	no	—
1187	C₄	—	2	2	no	—
1188	C₄	—	2	2	no	—
1189	C₄	—	2	2	no	—
1190	C₄	—	2	1	no	—
1191	C₄	—	2	1	no	—
1192	C₄	—	2	1	no	—
1193	C₄	—	4	2	no	—
1194	C₄	—	4	1	no	—
1195	C₄	—	4	2	no	—
1196	C₄	—	4	1	no	—
1197	C₄	—	4	1	no	—
1198	C₄	—	4	1	no	—
1199	C₄	—	4	2	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	1	no	—
1202	C₄	C₂×C₁₉×#137	1	2	yes	—
1203	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1204	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1205	C₂	—	2	4	no	—
1206	C₂	—	4	1	no	—
1207	C₂	—	4	2	no	—
1208	C₂	—	4	2	no	—
1209	C₂	—	8	2	no	—
1210	C₂	C₁₉×#3484	1	1	yes	characteristic
1211	C₂	C₂²×C₁₉×#137	1	1	yes	characteristic
1212	C₂	C₁₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	D₄×#41×C₁₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3501	C₂	semidirect
3. C₁₉×#3333	C₂	semidirect
4. C₁₉×#3331	C₂	semidirect
5. C₁₉×#3316	C₂	semidirect
6. C₁₉×#3314	C₂	semidirect
7. C₁₉×#3299	C₂	semidirect
8. C₁₉×#3295	C₂	semidirect
9. D₄×Q₁₆×C₁₉	C₂	semidirect
10. D₄×SD₁₆×C₁₉	C₂	semidirect
11. C₁₉×#3278	C₂	semidirect
12. C₁₉×#3276	C₂	semidirect
13. C₁₉×#3270	C₂	semidirect
14. C₁₉×#3266	C₂	semidirect
15. C₁₉×#3216	C₂	semidirect
16. C₁₉×#3210	C₂	semidirect
17. C₁₉×#3196	C₂	semidirect
18. C₁₉×#3190	C₂	semidirect
19. C₁₉×#3116	C₂	semidirect
20. C₁₉×#3107	C₂	semidirect
21. C₁₉×#3007	C₂	semidirect
22. C₂×C₁₉×#452	C₂	semidirect
23. C₁₉×#2974	C₂	semidirect
25. C₂×C₁₉×#137	C₂²	semidirect
26. C₂×C₁₉×#137	C₂²	semidirect
27. C₂²×Q₁₆×C₁₉	C₂²	semidirect
28. C₂²×SD₁₆×C₁₉	C₂²	semidirect
33. C₁₉×#554	C₂²	semidirect
34. C₁₉×#554	C₂²	semidirect
38. D₄×Q₈×C₁₉	C₂²	semidirect
39. D₄×Q₈×C₁₉	C₂²	semidirect
49. C₁₉×#533	C₂²	semidirect
50. C₁₉×#533	C₂²	semidirect
55. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
56. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
61. C₁₉×#497	C₂²	semidirect
62. C₁₉×#494	C₂²	semidirect
63. C₁₉×#492	C₂²	semidirect
64. C₁₉×#489	C₂²	semidirect
65. C₁₉×#487	C₂²	semidirect
66. C₁₉×#486	C₂²	semidirect
67. C₁₉×#485	C₂²	semidirect
68. C₁₉×#485	C₂²	semidirect
69. C₁₉×#485	C₂²	semidirect
70. C₁₉×#484	C₂²	semidirect
71. C₁₉×#483	C₂²	semidirect
72. C₁₉×#481	C₂²	semidirect
73. C₁₉×#480	C₂²	semidirect
74. C₁₉×#477	C₂²	semidirect
75. C₁₉×#476	C₂²	semidirect
76. C₁₉×#475	C₂²	semidirect
77. C₁₉×#474	C₂²	semidirect
78. C₁₉×#470	C₂²	semidirect
79. C₁₉×#470	C₂²	semidirect
80. C₁₉×#468	C₂²	semidirect
81. C₁₉×#468	C₂²	semidirect
82. C₁₉×#467	C₂²	semidirect
83. C₁₉×#467	C₂²	semidirect
84. C₁₉×#465	C₂²	semidirect
85. C₁₉×#465	C₂²	semidirect
86. C₁₉×#464	C₂²	semidirect
87. C₁₉×#464	C₂²	semidirect
88. C₁₉×#462	C₂²	semidirect
89. C₁₉×#462	C₂²	semidirect
90. C₁₉×#462	C₂²	semidirect
91. C₁₉×#462	C₂²	semidirect
92. C₁₉×#461	C₂²	semidirect
93. C₁₉×#461	C₂²	semidirect
94. C₁₉×#460	C₂²	semidirect
95. C₁₉×#460	C₂²	semidirect
99. C₁₉×#452	C₂²	semidirect
100. C₁₉×#452	C₂²	semidirect
101. C₁₉×#452	C₂²	semidirect
102. C₁₉×#452	C₂²	semidirect
103. C₁₉×#452	C₂²	semidirect
104. C₁₉×#452	C₂²	semidirect
105. C₁₉×#452	C₂²	semidirect
106. C₁₉×#452	C₂²	semidirect
107. C₁₉×#451	C₂²	semidirect
108. C₁₉×#451	C₂²	semidirect
109. C₁₉×#451	C₂²	semidirect
110. C₁₉×#451	C₂²	semidirect
111. C₁₉×#450	C₂²	semidirect
112. C₁₉×#450	C₂²	semidirect
113. C₁₉×#448	C₂²	semidirect
114. C₁₉×#448	C₂²	semidirect
115. C₁₉×#441	C₂²	semidirect
116. C₁₉×#440	C₂²	semidirect
117. C₄×Q₁₆×C₁₉	C₂²	semidirect
118. C₄×Q₁₆×C₁₉	C₂²	semidirect
119. C₄×SD₁₆×C₁₉	C₂²	semidirect
120. C₄×SD₁₆×C₁₉	C₂²	semidirect
121. C₁₉×#436	C₂²	semidirect
122. C₁₉×#436	C₂²	semidirect
123. C₁₉×#435	C₂²	semidirect
124. C₁₉×#435	C₂²	semidirect
127. C₁₉×#432	C₂²	semidirect
128. C₁₉×#431	C₂²	semidirect
129. C₁₉×#417	C₂²	semidirect
130. C₁₉×#417	C₂²	semidirect
131. C₂×C₁₉×#103	C₂²	semidirect
132. C₂×C₁₉×#102	C₂²	semidirect
133. C₁₉×#407	C₂²	semidirect
134. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
473. #61607	C₁₉	direct (N × H)
514. D₄×C₁₉	#137	semidirect
562. #3501	C₂×C₁₉	semidirect
564. #3333	C₂×C₁₉	semidirect
565. #3331	C₂×C₁₉	semidirect
566. #3316	C₂×C₁₉	semidirect
567. #3314	C₂×C₁₉	semidirect
568. #3299	C₂×C₁₉	semidirect
569. #3295	C₂×C₁₉	semidirect
570. D₄×Q₁₆	C₂×C₁₉	semidirect
571. D₄×SD₁₆	C₂×C₁₉	semidirect
572. #3278	C₂×C₁₉	semidirect
573. #3276	C₂×C₁₉	semidirect
574. #3270	C₂×C₁₉	semidirect
575. #3266	C₂×C₁₉	semidirect
576. #3216	C₂×C₁₉	semidirect
577. #3210	C₂×C₁₉	semidirect
578. #3196	C₂×C₁₉	semidirect
579. #3190	C₂×C₁₉	semidirect
580. #3116	C₂×C₁₉	semidirect
581. #3107	C₂×C₁₉	semidirect
582. #3007	C₂×C₁₉	semidirect
583. C₂×#452	C₂×C₁₉	semidirect
584. #2974	C₂×C₁₉	semidirect
623. C₂×#137	C₂²×C₁₉	semidirect
624. C₂×#137	C₂²×C₁₉	semidirect
625. C₂²×Q₁₆	C₂²×C₁₉	semidirect
626. C₂²×SD₁₆	C₂²×C₁₉	semidirect
631. #554	C₂²×C₁₉	semidirect
632. #554	C₂²×C₁₉	semidirect
636. D₄×Q₈	C₂²×C₁₉	semidirect
637. D₄×Q₈	C₂²×C₁₉	semidirect
647. #533	C₂²×C₁₉	semidirect
648. #533	C₂²×C₁₉	semidirect
653. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
654. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
659. #497	C₂²×C₁₉	semidirect
660. #494	C₂²×C₁₉	semidirect
661. #492	C₂²×C₁₉	semidirect
662. #489	C₂²×C₁₉	semidirect
663. #487	C₂²×C₁₉	semidirect
664. #486	C₂²×C₁₉	semidirect
665. #485	C₂²×C₁₉	semidirect
666. #485	C₂²×C₁₉	semidirect
667. #485	C₂²×C₁₉	semidirect
668. #484	C₂²×C₁₉	semidirect
669. #483	C₂²×C₁₉	semidirect
670. #481	C₂²×C₁₉	semidirect
671. #480	C₂²×C₁₉	semidirect
672. #477	C₂²×C₁₉	semidirect
673. #476	C₂²×C₁₉	semidirect
674. #475	C₂²×C₁₉	semidirect
675. #474	C₂²×C₁₉	semidirect
676. #470	C₂²×C₁₉	semidirect
677. #470	C₂²×C₁₉	semidirect
678. #468	C₂²×C₁₉	semidirect
679. #468	C₂²×C₁₉	semidirect
680. #467	C₂²×C₁₉	semidirect
681. #467	C₂²×C₁₉	semidirect
682. #465	C₂²×C₁₉	semidirect
683. #465	C₂²×C₁₉	semidirect
684. #464	C₂²×C₁₉	semidirect
685. #464	C₂²×C₁₉	semidirect
686. #462	C₂²×C₁₉	semidirect
687. #462	C₂²×C₁₉	semidirect
688. #462	C₂²×C₁₉	semidirect
689. #462	C₂²×C₁₉	semidirect
690. #461	C₂²×C₁₉	semidirect
691. #461	C₂²×C₁₉	semidirect
692. #460	C₂²×C₁₉	semidirect
693. #460	C₂²×C₁₉	semidirect
697. #452	C₂²×C₁₉	semidirect
698. #452	C₂²×C₁₉	semidirect
699. #452	C₂²×C₁₉	semidirect
700. #452	C₂²×C₁₉	semidirect
701. #452	C₂²×C₁₉	semidirect
702. #452	C₂²×C₁₉	semidirect
703. #452	C₂²×C₁₉	semidirect
704. #452	C₂²×C₁₉	semidirect
705. #451	C₂²×C₁₉	semidirect
706. #451	C₂²×C₁₉	semidirect
707. #451	C₂²×C₁₉	semidirect
708. #451	C₂²×C₁₉	semidirect
709. #450	C₂²×C₁₉	semidirect
710. #450	C₂²×C₁₉	semidirect
711. #448	C₂²×C₁₉	semidirect
712. #448	C₂²×C₁₉	semidirect
713. #441	C₂²×C₁₉	semidirect
714. #440	C₂²×C₁₉	semidirect
715. C₄×Q₁₆	C₂²×C₁₉	semidirect
716. C₄×Q₁₆	C₂²×C₁₉	semidirect
717. C₄×SD₁₆	C₂²×C₁₉	semidirect
718. C₄×SD₁₆	C₂²×C₁₉	semidirect
719. #436	C₂²×C₁₉	semidirect
720. #436	C₂²×C₁₉	semidirect
721. #435	C₂²×C₁₉	semidirect
722. #435	C₂²×C₁₉	semidirect
725. #432	C₂²×C₁₉	semidirect
726. #431	C₂²×C₁₉	semidirect
727. #417	C₂²×C₁₉	semidirect
728. #417	C₂²×C₁₉	semidirect
729. C₂×#103	C₂²×C₁₉	semidirect
730. C₂×#102	C₂²×C₁₉	semidirect
731. #407	C₂²×C₁₉	semidirect
732. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
924. C₁₉	#61607	direct (N × H)
1120. D₄	C₁₉×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3501	2
D₄×#41×C₁₉	2
C₁₉×#3333	2
C₁₉×#3331	2
C₁₉×#3316	2
C₁₉×#3314	2
C₁₉×#3299	2
C₁₉×#3295	2
D₄×Q₁₆×C₁₉	2
D₄×SD₁₆×C₁₉	2
C₁₉×#3278	2
C₁₉×#3276	2
C₁₉×#3270	2
C₁₉×#3266	2
C₁₉×#3216	2
C₁₉×#3210	2
C₁₉×#3196	2
C₁₉×#3190	2
C₁₉×#3116	2
C₁₉×#3107	2
C₁₉×#3007	2
C₂×C₁₉×#452	2
C₁₉×#2974	2
#61607	19

Subgroups — C19×#61607 #18067566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61607 #18067566