Subgroups — C₁₉×#62295 #18068254

Order 4864.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3353	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3343	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3330	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3324	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3310	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3308	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3298	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3294	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3265	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3194	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3193	C₂	1	2	yes	maximal, complemented
19	C₁₉×#3182	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#3171	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#3055	C₂	1	2	yes	maximal, complemented
22	C₂×C₁₉×#468	C₂	1	2	yes	maximal, complemented
23	D₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₉×H(5,𝔽₂)	—	2	1	no	—
25	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
27	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	complemented
28	C₁₉×#556	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#554	—	2	1	no	—
30	C₁₉×#552	C₂²	1	2	yes	complemented
31	C₁₉×#551	—	2	2	no	—
32	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#548	C₂²	1	2	yes	complemented
34	C₁₉×#547	C₂²	1	1	yes	characteristic
35	C₁₉×#547	C₂²	1	2	yes	—
36	C₁₉×#547	C₂²	1	1	yes	characteristic
37	C₁₉×#547	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#547	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#546	—	2	1	no	—
40	C₁₉×#546	—	2	1	no	—
41	C₁₉×#546	—	2	2	no	—
42	C₁₉×#546	—	2	1	no	—
43	D₄²×C₁₉	C₂²	1	2	yes	—
44	D₄²×C₁₉	C₂²	1	1	yes	characteristic
45	D₄²×C₁₉	C₂²	1	1	yes	characteristic
46	C₁₉×#542	—	2	1	no	—
47	C₁₉×#539	—	2	2	no	—
48	C₁₉×#537	—	2	1	no	—
49	C₁₉×#534	—	2	2	no	—
50	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×#532	C₂²	1	1	yes	characteristic
52	C₁₉×#532	C₂²	1	1	yes	characteristic
53	C₁₉×#529	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#525	C₂²	1	2	yes	complemented
55	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
56	C₂×C₁₉×#121	C₂²	1	2	yes	—
57	C₂×C₁₉×#121	C₂²	1	2	yes	—
58	C₁₉×#520	—	2	1	no	—
59	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
60	C₁₉×#501	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#496	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#490	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#489	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#484	C₂²	1	2	yes	complemented
69	C₁₉×#484	C₂²	1	2	yes	complemented
70	C₁₉×#483	C₂²	1	2	yes	complemented
71	C₁₉×#482	C₂²	1	2	yes	complemented
72	C₁₉×#482	C₂²	1	2	yes	complemented
73	C₁₉×#480	C₂²	1	2	yes	complemented
74	C₁₉×#480	C₂²	1	2	yes	complemented
75	C₁₉×#480	C₂²	1	2	yes	complemented
76	C₁₉×#478	C₂²	1	2	yes	complemented
77	C₁₉×#477	C₂²	1	2	yes	complemented
78	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
79	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
80	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
81	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
82	C₁₉×#469	C₂²	1	1	yes	characteristic, complemented
83	C₁₉×#469	C₂²	1	1	yes	characteristic, complemented
84	C₁₉×#469	C₂²	1	2	yes	complemented
85	C₁₉×#468	C₂²	1	1	yes	characteristic, complemented
86	C₁₉×#468	C₂²	1	1	yes	characteristic, complemented
87	C₁₉×#468	C₂²	1	2	yes	complemented
88	C₁₉×#468	C₂²	1	2	yes	complemented
89	C₁₉×#468	C₂²	1	2	yes	complemented
90	C₁₉×#468	C₂²	1	2	yes	complemented
91	C₁₉×#468	C₂²	1	2	yes	complemented
92	C₁₉×#468	C₂²	1	2	yes	complemented
93	C₁₉×#468	C₂²	1	2	yes	complemented
94	C₁₉×#468	C₂²	1	2	yes	complemented
95	C₁₉×#468	C₂²	1	2	yes	complemented
96	C₁₉×#466	C₂²	1	2	yes	complemented
97	C₁₉×#466	C₂²	1	2	yes	complemented
98	C₁₉×#465	C₂²	1	2	yes	complemented
99	C₁₉×#465	C₂²	1	2	yes	complemented
100	C₁₉×#463	C₂²	1	2	yes	complemented
101	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
102	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
103	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
104	C₁₉×#460	C₂²	1	2	yes	complemented
105	C₁₉×#459	C₂²	1	1	yes	characteristic, complemented
106	C₁₉×#450	C₂²	1	2	yes	complemented
107	C₁₉×#450	C₂²	1	2	yes	complemented
108	C₁₉×#450	C₂²	1	2	yes	complemented
109	C₁₉×#449	C₂²	1	2	yes	complemented
110	C₁₉×#449	C₂²	1	2	yes	complemented
111	C₁₉×#448	C₂²	1	2	yes	complemented
112	C₁₉×#448	C₂²	1	2	yes	complemented
113	C₁₉×#447	C₂²	1	2	yes	complemented
114	C₁₉×#440	C₂²	1	2	yes	complemented
115	C₁₉×#440	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
120	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
121	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
122	C₁₉×#435	C₂²	1	2	yes	complemented
123	C₁₉×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
125	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
126	C₁₉×#428	C₂²	1	2	yes	complemented
127	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
128	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
129	C₁₉×#418	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	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
135	C₁₉×H(5,𝔽₂)	—	4	8	no	—
136	C₂×#41×C₁₉	—	2	1	no	—
137	C₂×#41×C₁₉	—	2	2	no	—
138	C₂×#41×C₁₉	—	2	1	no	—
139	C₂×#41×C₁₉	—	2	1	no	—
140	C₂×#41×C₁₉	—	2	1	no	—
141	C₂×#41×C₁₉	—	2	1	no	—
142	C₂×#41×C₁₉	C₂³	1	2	yes	—
143	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
144	C₂²×D₄×C₁₉	—	2	2	no	—
145	C₂²×D₄×C₁₉	—	2	2	no	—
146	C₂²×D₄×C₁₉	—	2	2	no	—
147	C₂²×D₄×C₁₉	—	2	1	no	—
148	C₂²×D₄×C₁₉	—	2	1	no	—
149	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
150	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
151	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
152	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
153	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
154	C₂×SD₁₆×C₁₉	—	4	4	no	—
155	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
162	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
163	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
164	C₂×D₈×C₁₉	C₂³	1	2	yes	—
165	C₂×M₁₆×C₁₉	—	4	4	no	—
166	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
167	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
168	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
170	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
171	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
172	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
173	C₁₉×C₄⋊Q₈	—	2	1	no	—
174	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
175	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
176	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
177	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
178	C₁₉×#127	C₂³	1	1	yes	characteristic
179	C₁₉×#127	C₂³	1	1	yes	characteristic
180	C₁₉×#126	—	2	2	no	—
181	C₁₉×#126	—	2	2	no	—
182	C₁₉×#126	—	2	1	no	—
183	C₁₉×#125	—	2	2	no	—
184	C₁₉×#125	—	2	1	no	—
185	C₁₉×#125	C₂³	1	1	yes	characteristic
186	C₁₉×#124	—	2	1	no	—
187	C₁₉×#124	—	2	2	no	—
188	C₁₉×#124	—	2	1	no	—
189	C₁₉×#124	—	2	1	no	—
190	C₁₉×#124	C₂³	1	1	yes	characteristic
191	C₁₉×#123	—	2	2	no	—
192	C₁₉×#123	—	2	2	no	—
193	C₁₉×#123	—	2	1	no	—
194	C₁₉×#123	—	2	2	no	—
195	C₁₉×#123	—	2	2	no	—
196	C₁₉×#123	—	2	2	no	—
197	C₁₉×#123	—	2	2	no	—
198	C₁₉×#123	—	2	2	no	—
199	C₁₉×#123	—	2	2	no	—
200	C₁₉×C₂²⋊Q₈	—	2	2	no	—
201	C₁₉×C₂²⋊Q₈	—	2	2	no	—
202	C₁₉×C₂²⋊Q₈	—	2	1	no	—
203	C₁₉×C₂²⋊Q₈	—	2	1	no	—
204	C₁₉×C₂²⋊Q₈	—	2	2	no	—
205	C₁₉×C₂²⋊Q₈	—	2	1	no	—
206	C₁₉×C₂²⋊Q₈	—	2	2	no	—
207	C₁₉×C₂²⋊Q₈	—	2	1	no	—
208	C₁₉×C₂²⋊Q₈	—	2	2	no	—
209	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₁₉×#121	—	2	2	no	—
215	C₁₉×#121	—	2	1	no	—
216	C₁₉×#121	—	2	2	no	—
217	C₁₉×#121	—	2	2	no	—
218	C₁₉×#121	—	2	2	no	—
219	C₁₉×#121	—	2	2	no	—
220	C₁₉×#121	—	2	1	no	—
221	C₁₉×#121	—	2	1	no	—
222	C₁₉×#121	—	2	1	no	—
223	C₁₉×#121	—	2	2	no	—
224	C₁₉×#121	—	2	1	no	—
225	C₁₉×#121	C₂³	1	2	yes	—
226	C₁₉×#121	C₂³	1	2	yes	—
227	C₁₉×#121	C₂³	1	2	yes	—
228	C₁₉×#121	C₂³	1	2	yes	—
229	C₁₉×#121	C₂³	1	2	yes	—
230	C₁₉×#121	C₂³	1	1	yes	characteristic
231	C₁₉×#121	C₂³	1	1	yes	characteristic
232	C₁₉×#121	C₂³	1	2	yes	—
233	C₁₉×#121	C₂³	1	1	yes	characteristic
234	C₁₉×#120	—	2	2	no	—
235	C₁₉×#120	—	2	2	no	—
236	C₁₉×#120	—	2	2	no	—
237	C₁₉×#120	—	2	2	no	—
238	C₁₉×#120	—	2	2	no	—
239	C₄×Q₈×C₁₉	—	2	1	no	—
240	C₄×Q₈×C₁₉	—	2	1	no	—
241	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
243	C₄×D₄×C₁₉	—	2	1	no	—
244	C₄×D₄×C₁₉	—	2	2	no	—
245	C₄×D₄×C₁₉	—	2	2	no	—
246	C₄×D₄×C₁₉	—	2	1	no	—
247	C₄×D₄×C₁₉	—	2	2	no	—
248	C₄×D₄×C₁₉	—	2	1	no	—
249	C₄×D₄×C₁₉	—	2	1	no	—
250	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
251	C₄×D₄×C₁₉	D₄	1	2	yes	—
252	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
253	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₁₉	C₂³	1	2	yes	—
257	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₁₉	C₂³	1	2	yes	—
259	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
260	C₁₉×#117	—	2	1	no	—
261	C₁₉×#117	—	2	2	no	—
262	C₁₉×#117	—	2	1	no	—
263	C₁₉×#117	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
265	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
266	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
270	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
272	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
273	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
274	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
275	C₁₉×#107	C₂³	1	1	yes	characteristic
276	C₁₉×#107	C₂³	1	2	yes	—
277	C₁₉×#107	C₂³	1	2	yes	—
278	C₁₉×#107	C₂³	1	2	yes	—
279	C₁₉×#107	C₂³	1	2	yes	—
280	C₁₉×#107	C₂³	1	1	yes	characteristic
281	C₁₉×#107	C₂³	1	2	yes	—
282	C₁₉×#106	C₂³	1	1	yes	characteristic
283	C₁₉×#106	C₂³	1	2	yes	—
284	C₁₉×#106	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	2	yes	—
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	2	yes	—
293	C₁₉×#103	C₂³	1	1	yes	characteristic
294	C₁₉×#103	C₂³	1	2	yes	—
295	C₁₉×#102	C₂³	1	1	yes	characteristic
296	C₁₉×#102	C₂³	1	2	yes	—
297	C₁₉×#102	C₂³	1	2	yes	—
298	C₁₉×#102	C₂³	1	2	yes	—
299	C₁₉×#102	C₂³	1	1	yes	characteristic
300	C₁₉×#102	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	1	yes	characteristic
305	C₁₉×#102	C₂³	1	1	yes	characteristic
306	C₁₉×#102	C₂³	1	1	yes	characteristic
307	C₁₉×#102	C₂³	1	2	yes	—
308	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
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×#97	C₂³	1	1	yes	characteristic
313	C₁₉×#97	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
315	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
316	C₂⁴×C₁₉	—	2	2	no	—
317	C₂⁴×C₁₉	—	2	2	no	—
318	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
319	#41×C₁₉	—	4	4	no	—
320	#41×C₁₉	—	4	4	no	—
321	#41×C₁₉	—	4	2	no	—
322	#41×C₁₉	—	4	2	no	—
323	#41×C₁₉	—	4	8	no	—
324	#41×C₁₉	—	4	4	no	—
325	#41×C₁₉	—	4	4	no	—
326	#41×C₁₉	—	4	4	no	—
327	C₂×Q₈×C₁₉	—	2	1	no	—
328	C₂×Q₈×C₁₉	—	2	1	no	—
329	C₂×Q₈×C₁₉	—	2	1	no	—
330	C₂×Q₈×C₁₉	—	2	2	no	—
331	C₂×Q₈×C₁₉	—	4	2	no	—
332	C₂×Q₈×C₁₉	—	4	2	no	—
333	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
335	C₂×D₄×C₁₉	—	2	4	no	—
336	C₂×D₄×C₁₉	—	2	1	no	—
337	C₂×D₄×C₁₉	—	2	2	no	—
338	C₂×D₄×C₁₉	—	2	2	no	—
339	C₂×D₄×C₁₉	—	2	2	no	—
340	C₂×D₄×C₁₉	—	2	2	no	—
341	C₂×D₄×C₁₉	—	2	2	no	—
342	C₂×D₄×C₁₉	—	2	1	no	—
343	C₂×D₄×C₁₉	—	2	2	no	—
344	C₂×D₄×C₁₉	—	2	1	no	—
345	C₂×D₄×C₁₉	—	2	2	no	—
346	C₂×D₄×C₁₉	—	2	1	no	—
347	C₂×D₄×C₁₉	—	2	1	no	—
348	C₂×D₄×C₁₉	—	2	1	no	—
349	C₂×D₄×C₁₉	—	2	1	no	—
350	C₂×D₄×C₁₉	—	2	2	no	—
351	C₂×D₄×C₁₉	—	2	2	no	—
352	C₂×D₄×C₁₉	—	4	2	no	—
353	C₂×D₄×C₁₉	—	4	2	no	—
354	C₂×D₄×C₁₉	—	4	2	no	—
355	C₂×D₄×C₁₉	—	4	2	no	—
356	C₂×D₄×C₁₉	—	4	8	no	—
357	C₂×D₄×C₁₉	—	4	4	no	—
358	C₂×D₄×C₁₉	—	4	8	no	—
359	C₂×D₄×C₁₉	—	4	8	no	—
360	C₂×D₄×C₁₉	—	4	4	no	—
361	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
362	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
363	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
364	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
365	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
366	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
367	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	1	no	—
373	C₂²×C₄×C₁₉	—	2	2	no	—
374	C₂²×C₄×C₁₉	—	2	1	no	—
375	C₂²×C₄×C₁₉	—	2	1	no	—
376	C₂²×C₄×C₁₉	—	2	2	no	—
377	C₂²×C₄×C₁₉	—	4	2	no	—
378	C₂²×C₄×C₁₉	—	4	2	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	SD₁₆×C₁₉	—	2	2	no	—
388	SD₁₆×C₁₉	—	2	4	no	—
389	SD₁₆×C₁₉	—	4	2	no	—
390	SD₁₆×C₁₉	—	4	2	no	—
391	SD₁₆×C₁₉	—	4	1	no	—
392	SD₁₆×C₁₉	—	4	2	no	—
393	SD₁₆×C₁₉	—	4	2	no	—
394	D₈×C₁₉	—	2	2	no	—
395	D₈×C₁₉	—	4	1	no	—
396	D₈×C₁₉	—	4	2	no	—
397	M₁₆×C₁₉	—	2	2	no	—
398	M₁₆×C₁₉	—	2	4	no	—
399	M₁₆×C₁₉	—	4	2	no	—
400	M₁₆×C₁₉	—	4	2	no	—
401	M₁₆×C₁₉	—	4	1	no	—
402	C₂×C₈×C₁₉	—	2	4	no	—
403	C₂×C₈×C₁₉	—	4	2	no	—
404	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
406	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
407	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₁₉	—	2	1	no	—
411	C₄⋊C₄×C₁₉	—	2	2	no	—
412	C₄⋊C₄×C₁₉	—	2	1	no	—
413	C₄⋊C₄×C₁₉	—	2	2	no	—
414	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
419	C₄⋊C₄×C₁₉	—	2	1	no	—
420	C₄⋊C₄×C₁₉	—	2	1	no	—
421	C₄⋊C₄×C₁₉	—	2	1	no	—
422	C₄⋊C₄×C₁₉	—	2	1	no	—
423	C₄⋊C₄×C₁₉	—	2	2	no	—
424	C₄⋊C₄×C₁₉	—	2	1	no	—
425	C₄⋊C₄×C₁₉	—	2	2	no	—
426	C₄⋊C₄×C₁₉	—	2	1	no	—
427	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
428	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
429	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
430	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
431	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
432	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
433	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
434	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
435	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
436	C₂²⋊C₄×C₁₉	—	2	1	no	—
437	C₂²⋊C₄×C₁₉	—	2	2	no	—
438	C₂²⋊C₄×C₁₉	—	2	2	no	—
439	C₂²⋊C₄×C₁₉	—	2	2	no	—
440	C₂²⋊C₄×C₁₉	—	2	2	no	—
441	C₂²⋊C₄×C₁₉	—	2	2	no	—
442	C₂²⋊C₄×C₁₉	—	2	1	no	—
443	C₂²⋊C₄×C₁₉	—	2	2	no	—
444	C₂²⋊C₄×C₁₉	—	2	1	no	—
445	C₂²⋊C₄×C₁₉	—	2	2	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	1	no	—
450	C₂²⋊C₄×C₁₉	—	2	1	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	1	no	—
455	C₂²⋊C₄×C₁₉	—	2	1	no	—
456	C₂²⋊C₄×C₁₉	—	2	1	no	—
457	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
458	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
459	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
460	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
461	C₄²×C₁₉	—	2	2	no	—
462	C₄²×C₁₉	—	2	2	no	—
463	C₄²×C₁₉	—	2	1	no	—
464	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
465	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
466	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
467	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
468	#62295	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
469	C₂³×C₁₉	—	2	4	no	—
470	C₂³×C₁₉	—	2	1	no	—
471	C₂³×C₁₉	—	2	1	no	—
472	C₂³×C₁₉	—	2	2	no	—
473	C₂³×C₁₉	—	2	1	no	—
474	C₂³×C₁₉	—	4	2	no	—
475	C₂³×C₁₉	—	4	2	no	—
476	C₂³×C₁₉	—	4	4	no	—
477	C₂³×C₁₉	—	4	4	no	—
478	C₂³×C₁₉	—	8	2	no	—
479	C₂³×C₁₉	—	8	2	no	—
480	C₂³×C₁₉	—	8	2	no	—
481	C₂³×C₁₉	—	8	2	no	—
482	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
483	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
484	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
485	Q₈×C₁₉	—	2	1	no	—
486	Q₈×C₁₉	—	2	2	no	—
487	Q₈×C₁₉	—	2	1	no	—
488	Q₈×C₁₉	—	2	2	no	—
489	Q₈×C₁₉	—	4	2	no	—
490	Q₈×C₁₉	—	4	2	no	—
491	Q₈×C₁₉	—	4	2	no	—
492	Q₈×C₁₉	—	8	2	no	—
493	D₄×C₁₉	—	2	4	no	—
494	D₄×C₁₉	—	2	2	no	—
495	D₄×C₁₉	—	2	1	no	—
496	D₄×C₁₉	—	2	1	no	—
497	D₄×C₁₉	—	2	2	no	—
498	D₄×C₁₉	—	2	1	no	—
499	D₄×C₁₉	—	2	1	no	—
500	D₄×C₁₉	—	2	1	no	—
501	D₄×C₁₉	—	2	1	no	—
502	D₄×C₁₉	—	2	2	no	—
503	D₄×C₁₉	—	4	2	no	—
504	D₄×C₁₉	—	4	2	no	—
505	D₄×C₁₉	—	4	4	no	—
506	D₄×C₁₉	—	4	2	no	—
507	D₄×C₁₉	—	4	2	no	—
508	D₄×C₁₉	—	4	4	no	—
509	D₄×C₁₉	—	4	4	no	—
510	D₄×C₁₉	—	4	4	no	—
511	D₄×C₁₉	—	4	4	no	—
512	D₄×C₁₉	—	4	4	no	—
513	D₄×C₁₉	—	4	2	no	—
514	D₄×C₁₉	—	8	1	no	—
515	D₄×C₁₉	—	8	1	no	—
516	D₄×C₁₉	—	8	2	no	—
517	D₄×C₁₉	—	8	2	no	—
518	D₄×C₁₉	—	8	2	no	—
519	D₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	complemented
520	C₂×C₄×C₁₉	—	2	2	no	—
521	C₂×C₄×C₁₉	—	2	2	no	—
522	C₂×C₄×C₁₉	—	2	1	no	—
523	C₂×C₄×C₁₉	—	2	2	no	—
524	C₂×C₄×C₁₉	—	2	1	no	—
525	C₂×C₄×C₁₉	—	2	2	no	—
526	C₂×C₄×C₁₉	—	2	2	no	—
527	C₂×C₄×C₁₉	—	2	1	no	—
528	C₂×C₄×C₁₉	—	2	2	no	—
529	C₂×C₄×C₁₉	—	2	1	no	—
530	C₂×C₄×C₁₉	—	2	2	no	—
531	C₂×C₄×C₁₉	—	2	1	no	—
532	C₂×C₄×C₁₉	—	2	2	no	—
533	C₂×C₄×C₁₉	—	2	1	no	—
534	C₂×C₄×C₁₉	—	2	1	no	—
535	C₂×C₄×C₁₉	—	4	2	no	—
536	C₂×C₄×C₁₉	—	4	2	no	—
537	C₂×C₄×C₁₉	—	4	2	no	—
538	C₂×C₄×C₁₉	—	4	1	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	4	no	—
543	C₂×C₄×C₁₉	—	4	2	no	—
544	C₂×C₄×C₁₉	—	4	2	no	—
545	C₂×C₄×C₁₉	—	4	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	2	yes	—
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	1	yes	characteristic
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	2	no	—
557	C₈×C₁₉	—	2	1	no	—
558	C₈×C₁₉	—	2	2	no	—
559	C₈×C₁₉	—	2	1	no	—
560	C₈×C₁₉	—	2	1	no	—
561	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	complemented
562	#3520	C₂×C₁₉	1	1	yes	characteristic, complemented
563	#3496	C₂×C₁₉	1	1	yes	characteristic, complemented
564	#3353	C₂×C₁₉	1	1	yes	characteristic, complemented
565	#3343	C₂×C₁₉	1	2	yes	complemented
566	#3334	C₂×C₁₉	1	1	yes	characteristic, complemented
567	#3330	C₂×C₁₉	1	1	yes	characteristic, complemented
568	#3324	C₂×C₁₉	1	1	yes	characteristic, complemented
569	#3310	C₂×C₁₉	1	2	yes	complemented
570	#3308	C₂×C₁₉	1	2	yes	complemented
571	#3298	C₂×C₁₉	1	1	yes	characteristic, complemented
572	#3294	C₂×C₁₉	1	1	yes	characteristic, complemented
573	D₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
574	#3272	C₂×C₁₉	1	1	yes	characteristic, complemented
575	#3265	C₂×C₁₉	1	2	yes	complemented
576	#3254	C₂×C₁₉	1	1	yes	characteristic, complemented
577	#3251	C₂×C₁₉	1	1	yes	characteristic, complemented
578	#3194	C₂×C₁₉	1	2	yes	complemented
579	#3193	C₂×C₁₉	1	2	yes	complemented
580	#3182	C₂×C₁₉	1	1	yes	characteristic, complemented
581	#3171	C₂×C₁₉	1	1	yes	characteristic, complemented
582	#3055	C₂×C₁₉	1	2	yes	complemented
583	C₂×#468	C₂×C₁₉	1	2	yes	complemented
584	D₄×M₁₆	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	1	no	—
592	C₂²×C₁₉	—	2	2	no	—
593	C₂²×C₁₉	—	4	1	no	—
594	C₂²×C₁₉	—	4	1	no	—
595	C₂²×C₁₉	—	4	2	no	—
596	C₂²×C₁₉	—	4	1	no	—
597	C₂²×C₁₉	—	4	1	no	—
598	C₂²×C₁₉	—	4	1	no	—
599	C₂²×C₁₉	—	4	2	no	—
600	C₂²×C₁₉	—	4	1	no	—
601	C₂²×C₁₉	—	4	2	no	—
602	C₂²×C₁₉	—	4	1	no	—
603	C₂²×C₁₉	—	4	1	no	—
604	C₂²×C₁₉	—	4	1	no	—
605	C₂²×C₁₉	—	8	4	no	—
606	C₂²×C₁₉	—	16	4	no	—
607	C₂²×C₁₉	—	16	4	no	—
608	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	4	yes	—
609	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
610	C₄×C₁₉	—	2	1	no	—
611	C₄×C₁₉	—	2	1	no	—
612	C₄×C₁₉	—	2	1	no	—
613	C₄×C₁₉	—	2	2	no	—
614	C₄×C₁₉	—	2	2	no	—
615	C₄×C₁₉	—	2	1	no	—
616	C₄×C₁₉	—	4	1	no	—
617	C₄×C₁₉	—	4	2	no	—
618	C₄×C₁₉	—	4	1	no	—
619	C₄×C₁₉	—	4	1	no	—
620	C₄×C₁₉	—	4	2	no	—
621	C₄×C₁₉	—	4	1	no	—
622	C₄×C₁₉	—	4	1	no	—
623	C₄×C₁₉	—	4	2	no	—
624	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
625	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
626	C₄×C₁₉	#585	1	1	yes	characteristic
627	C₂×H(5,𝔽₂)	—	2	1	no	—
628	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	complemented
629	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
630	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	complemented
631	#556	C₂²×C₁₉	1	1	yes	characteristic, complemented
632	#554	—	2	1	no	—
633	#552	C₂²×C₁₉	1	2	yes	complemented
634	#551	—	2	2	no	—
635	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
636	#548	C₂²×C₁₉	1	2	yes	complemented
637	#547	C₂²×C₁₉	1	1	yes	characteristic
638	#547	C₂²×C₁₉	1	1	yes	characteristic
639	#547	C₂²×C₁₉	1	2	yes	—
640	#547	C₂²×C₁₉	1	1	yes	characteristic, complemented
641	#547	C₂²×C₁₉	1	1	yes	characteristic, complemented
642	#546	—	2	1	no	—
643	#546	—	2	1	no	—
644	#546	—	2	2	no	—
645	#546	—	2	1	no	—
646	D₄²	C₂²×C₁₉	1	2	yes	—
647	D₄²	C₂²×C₁₉	1	1	yes	characteristic
648	D₄²	C₂²×C₁₉	1	1	yes	characteristic
649	#542	—	2	1	no	—
650	#539	—	2	2	no	—
651	#537	—	2	1	no	—
652	#534	—	2	2	no	—
653	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
654	#532	C₂²×C₁₉	1	1	yes	characteristic
655	#532	C₂²×C₁₉	1	1	yes	characteristic
656	#529	C₂²×C₁₉	1	1	yes	characteristic, complemented
657	#525	C₂²×C₁₉	1	2	yes	complemented
658	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	complemented
659	C₂×#121	C₂²×C₁₉	1	2	yes	—
660	C₂×#121	C₂²×C₁₉	1	2	yes	—
661	#520	—	2	1	no	—
662	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
663	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
664	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
665	#496	C₂²×C₁₉	1	1	yes	characteristic, complemented
666	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
667	#490	C₂²×C₁₉	1	1	yes	characteristic, complemented
668	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
669	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
670	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
671	#484	C₂²×C₁₉	1	2	yes	complemented
672	#484	C₂²×C₁₉	1	2	yes	complemented
673	#483	C₂²×C₁₉	1	2	yes	complemented
674	#482	C₂²×C₁₉	1	2	yes	complemented
675	#482	C₂²×C₁₉	1	2	yes	complemented
676	#480	C₂²×C₁₉	1	2	yes	complemented
677	#480	C₂²×C₁₉	1	2	yes	complemented
678	#480	C₂²×C₁₉	1	2	yes	complemented
679	#478	C₂²×C₁₉	1	2	yes	complemented
680	#477	C₂²×C₁₉	1	2	yes	complemented
681	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
682	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
683	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
684	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
685	#469	C₂²×C₁₉	1	1	yes	characteristic, complemented
686	#469	C₂²×C₁₉	1	1	yes	characteristic, complemented
687	#469	C₂²×C₁₉	1	2	yes	complemented
688	#468	C₂²×C₁₉	1	2	yes	complemented
689	#468	C₂²×C₁₉	1	2	yes	complemented
690	#468	C₂²×C₁₉	1	2	yes	complemented
691	#468	C₂²×C₁₉	1	1	yes	characteristic, complemented
692	#468	C₂²×C₁₉	1	1	yes	characteristic, complemented
693	#468	C₂²×C₁₉	1	2	yes	complemented
694	#468	C₂²×C₁₉	1	2	yes	complemented
695	#468	C₂²×C₁₉	1	2	yes	complemented
696	#468	C₂²×C₁₉	1	2	yes	complemented
697	#468	C₂²×C₁₉	1	2	yes	complemented
698	#468	C₂²×C₁₉	1	2	yes	complemented
699	#466	C₂²×C₁₉	1	2	yes	complemented
700	#466	C₂²×C₁₉	1	2	yes	complemented
701	#465	C₂²×C₁₉	1	2	yes	complemented
702	#465	C₂²×C₁₉	1	2	yes	complemented
703	#463	C₂²×C₁₉	1	2	yes	complemented
704	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
705	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
706	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
707	#460	C₂²×C₁₉	1	2	yes	complemented
708	#459	C₂²×C₁₉	1	1	yes	characteristic, complemented
709	#450	C₂²×C₁₉	1	2	yes	complemented
710	#450	C₂²×C₁₉	1	2	yes	complemented
711	#450	C₂²×C₁₉	1	2	yes	complemented
712	#449	C₂²×C₁₉	1	2	yes	complemented
713	#449	C₂²×C₁₉	1	2	yes	complemented
714	#448	C₂²×C₁₉	1	2	yes	complemented
715	#448	C₂²×C₁₉	1	2	yes	complemented
716	#447	C₂²×C₁₉	1	2	yes	complemented
717	#440	C₂²×C₁₉	1	2	yes	complemented
718	#440	C₂²×C₁₉	1	2	yes	complemented
719	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
720	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
721	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
722	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
723	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
724	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
725	#435	C₂²×C₁₉	1	2	yes	complemented
726	#435	C₂²×C₁₉	1	2	yes	complemented
727	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
728	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
729	#428	C₂²×C₁₉	1	2	yes	complemented
730	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
731	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
732	#418	C₂²×C₁₉	1	2	yes	complemented
733	#417	C₂²×C₁₉	1	2	yes	complemented
734	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
735	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
736	#407	C₂²×C₁₉	1	2	yes	complemented
737	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
738	C₂×C₁₉	—	2	4	no	—
739	C₂×C₁₉	—	4	1	no	—
740	C₂×C₁₉	—	4	2	no	—
741	C₂×C₁₉	—	8	1	no	—
742	C₂×C₁₉	—	8	1	no	—
743	C₂×C₁₉	—	8	2	no	—
744	C₂×C₁₉	—	8	1	no	—
745	C₂×C₁₉	#3496	1	1	yes	characteristic
746	C₂×C₁₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
747	C₂×C₁₉	#3586	1	1	yes	characteristic
748	H(5,𝔽₂)	—	4	8	no	—
749	C₂×#41	—	2	1	no	—
750	C₂×#41	—	2	2	no	—
751	C₂×#41	—	2	1	no	—
752	C₂×#41	—	2	1	no	—
753	C₂×#41	—	2	1	no	—
754	C₂×#41	—	2	1	no	—
755	C₂×#41	C₂³×C₁₉	1	2	yes	—
756	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
757	C₂²×D₄	—	2	2	no	—
758	C₂²×D₄	—	2	2	no	—
759	C₂²×D₄	—	2	2	no	—
760	C₂²×D₄	—	2	1	no	—
761	C₂²×D₄	—	2	1	no	—
762	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
763	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
764	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
765	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
766	AGL(1,ℤ/8)	—	4	4	no	—
767	C₂×SD₁₆	—	4	4	no	—
768	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
769	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
770	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
771	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
772	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
773	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
774	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
775	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
776	C₂×D₈	C₂³×C₁₉	1	2	yes	—
777	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
778	C₂×M₁₆	—	4	4	no	—
779	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
780	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
781	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
782	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
783	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
784	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
785	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
786	C₄⋊Q₈	—	2	1	no	—
787	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
788	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
789	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
790	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
791	#127	C₂³×C₁₉	1	1	yes	characteristic
792	#127	C₂³×C₁₉	1	1	yes	characteristic
793	#126	—	2	2	no	—
794	#126	—	2	2	no	—
795	#126	—	2	1	no	—
796	#125	—	2	2	no	—
797	#125	—	2	1	no	—
798	#125	C₂³×C₁₉	1	1	yes	characteristic
799	#124	—	2	1	no	—
800	#124	—	2	2	no	—
801	#124	—	2	1	no	—
802	#124	—	2	1	no	—
803	#124	C₂³×C₁₉	1	1	yes	characteristic
804	#123	—	2	2	no	—
805	#123	—	2	2	no	—
806	#123	—	2	1	no	—
807	#123	—	2	2	no	—
808	#123	—	2	2	no	—
809	#123	—	2	2	no	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	C₂²⋊Q₈	—	2	2	no	—
814	C₂²⋊Q₈	—	2	2	no	—
815	C₂²⋊Q₈	—	2	1	no	—
816	C₂²⋊Q₈	—	2	1	no	—
817	C₂²⋊Q₈	—	2	2	no	—
818	C₂²⋊Q₈	—	2	1	no	—
819	C₂²⋊Q₈	—	2	2	no	—
820	C₂²⋊Q₈	—	2	1	no	—
821	C₂²⋊Q₈	—	2	2	no	—
822	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
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	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
827	#121	—	2	2	no	—
828	#121	—	2	1	no	—
829	#121	—	2	2	no	—
830	#121	—	2	2	no	—
831	#121	—	2	2	no	—
832	#121	—	2	2	no	—
833	#121	—	2	1	no	—
834	#121	—	2	1	no	—
835	#121	—	2	1	no	—
836	#121	—	2	2	no	—
837	#121	—	2	1	no	—
838	#121	C₂³×C₁₉	1	1	yes	characteristic
839	#121	C₂³×C₁₉	1	2	yes	—
840	#121	C₂³×C₁₉	1	1	yes	characteristic
841	#121	C₂³×C₁₉	1	2	yes	—
842	#121	C₂³×C₁₉	1	2	yes	—
843	#121	C₂³×C₁₉	1	2	yes	—
844	#121	C₂³×C₁₉	1	2	yes	—
845	#121	C₂³×C₁₉	1	1	yes	characteristic
846	#121	C₂³×C₁₉	1	2	yes	—
847	#120	—	2	2	no	—
848	#120	—	2	2	no	—
849	#120	—	2	2	no	—
850	#120	—	2	2	no	—
851	#120	—	2	2	no	—
852	C₄×Q₈	—	2	1	no	—
853	C₄×Q₈	—	2	1	no	—
854	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
855	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	—	2	2	no	—
858	C₄×D₄	—	2	2	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	2	no	—
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	—	2	1	no	—
863	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
864	C₄×D₄	D₄×C₁₉	1	2	yes	—
865	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
866	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
867	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
868	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
869	C₄×D₄	C₂³×C₁₉	1	2	yes	—
870	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
871	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
872	C₄×D₄	C₂³×C₁₉	1	2	yes	—
873	#117	—	2	1	no	—
874	#117	—	2	2	no	—
875	#117	—	2	1	no	—
876	#117	C₂³×C₁₉	1	2	yes	—
877	C₂×C₄⋊C₄	—	2	2	no	—
878	C₂×C₄⋊C₄	—	2	1	no	—
879	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
880	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
881	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
882	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
883	C₂×C₂²⋊C₄	—	2	2	no	—
884	C₂×C₂²⋊C₄	—	2	2	no	—
885	C₂×C₂²⋊C₄	—	2	2	no	—
886	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
887	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
888	#107	C₂³×C₁₉	1	1	yes	characteristic
889	#107	C₂³×C₁₉	1	2	yes	—
890	#107	C₂³×C₁₉	1	2	yes	—
891	#107	C₂³×C₁₉	1	2	yes	—
892	#107	C₂³×C₁₉	1	2	yes	—
893	#107	C₂³×C₁₉	1	1	yes	characteristic
894	#107	C₂³×C₁₉	1	2	yes	—
895	#106	C₂³×C₁₉	1	1	yes	characteristic
896	#106	C₂³×C₁₉	1	2	yes	—
897	#106	C₂³×C₁₉	1	1	yes	characteristic
898	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
899	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
900	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
901	#103	C₂³×C₁₉	1	1	yes	characteristic
902	#103	C₂³×C₁₉	1	2	yes	—
903	#103	C₂³×C₁₉	1	2	yes	—
904	#103	C₂³×C₁₉	1	2	yes	—
905	#103	C₂³×C₁₉	1	2	yes	—
906	#103	C₂³×C₁₉	1	1	yes	characteristic
907	#103	C₂³×C₁₉	1	2	yes	—
908	#102	C₂³×C₁₉	1	1	yes	characteristic
909	#102	C₂³×C₁₉	1	2	yes	—
910	#102	C₂³×C₁₉	1	2	yes	—
911	#102	C₂³×C₁₉	1	2	yes	—
912	#102	C₂³×C₁₉	1	1	yes	characteristic
913	#102	C₂³×C₁₉	1	2	yes	—
914	#102	C₂³×C₁₉	1	1	yes	characteristic
915	#102	C₂³×C₁₉	1	2	yes	—
916	#102	C₂³×C₁₉	1	2	yes	—
917	#102	C₂³×C₁₉	1	1	yes	characteristic
918	#102	C₂³×C₁₉	1	1	yes	characteristic
919	#102	C₂³×C₁₉	1	1	yes	characteristic
920	#102	C₂³×C₁₉	1	2	yes	—
921	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
922	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
923	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
924	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
925	#97	C₂³×C₁₉	1	1	yes	characteristic
926	#97	C₂³×C₁₉	1	1	yes	characteristic
927	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
928	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
929	C₁₉	#62295	1	1	yes	characteristic, direct product factor, Sylow
930	C₂⁴	—	2	2	no	—
931	C₂⁴	—	2	2	no	—
932	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
933	#41	—	4	4	no	—
934	#41	—	4	4	no	—
935	#41	—	4	2	no	—
936	#41	—	4	2	no	—
937	#41	—	4	8	no	—
938	#41	—	4	4	no	—
939	#41	—	4	4	no	—
940	#41	—	4	4	no	—
941	C₂×Q₈	—	2	1	no	—
942	C₂×Q₈	—	2	1	no	—
943	C₂×Q₈	—	2	1	no	—
944	C₂×Q₈	—	2	2	no	—
945	C₂×Q₈	—	4	2	no	—
946	C₂×Q₈	—	4	2	no	—
947	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
948	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
949	C₂×D₄	—	2	4	no	—
950	C₂×D₄	—	2	1	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	1	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	1	no	—
959	C₂×D₄	—	2	2	no	—
960	C₂×D₄	—	2	1	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	1	no	—
963	C₂×D₄	—	2	1	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	4	2	no	—
967	C₂×D₄	—	4	2	no	—
968	C₂×D₄	—	4	2	no	—
969	C₂×D₄	—	4	2	no	—
970	C₂×D₄	—	4	8	no	—
971	C₂×D₄	—	4	4	no	—
972	C₂×D₄	—	4	8	no	—
973	C₂×D₄	—	4	8	no	—
974	C₂×D₄	—	4	4	no	—
975	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
976	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
977	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
978	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
979	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
980	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
981	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	2	2	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	—	2	1	no	—
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	4	2	no	—
992	C₂²×C₄	—	4	2	no	—
993	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
994	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
995	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
996	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
997	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
998	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
999	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
1000	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1001	SD₁₆	—	2	2	no	—
1002	SD₁₆	—	2	4	no	—
1003	SD₁₆	—	4	2	no	—
1004	SD₁₆	—	4	2	no	—
1005	SD₁₆	—	4	1	no	—
1006	SD₁₆	—	4	2	no	—
1007	SD₁₆	—	4	2	no	—
1008	D₈	—	2	2	no	—
1009	D₈	—	4	1	no	—
1010	D₈	—	4	2	no	—
1011	M₁₆	—	2	2	no	—
1012	M₁₆	—	2	4	no	—
1013	M₁₆	—	4	2	no	—
1014	M₁₆	—	4	2	no	—
1015	M₁₆	—	4	1	no	—
1016	C₂×C₈	—	2	4	no	—
1017	C₂×C₈	—	4	2	no	—
1018	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1019	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1020	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1021	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
1022	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
1023	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	2	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	1	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1042	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1043	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1044	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
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	2	yes	—
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	2	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	1	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	2	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1072	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1073	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1074	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1075	C₄²	—	2	2	no	—
1076	C₄²	—	2	2	no	—
1077	C₄²	—	2	1	no	—
1078	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1079	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1080	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1081	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1082	C₂³	—	2	4	no	—
1083	C₂³	—	2	1	no	—
1084	C₂³	—	2	1	no	—
1085	C₂³	—	2	2	no	—
1086	C₂³	—	2	1	no	—
1087	C₂³	—	4	2	no	—
1088	C₂³	—	4	2	no	—
1089	C₂³	—	4	4	no	—
1090	C₂³	—	4	4	no	—
1091	C₂³	—	8	2	no	—
1092	C₂³	—	8	2	no	—
1093	C₂³	—	8	2	no	—
1094	C₂³	—	8	2	no	—
1095	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1096	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1097	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1098	Q₈	—	2	1	no	—
1099	Q₈	—	2	2	no	—
1100	Q₈	—	2	1	no	—
1101	Q₈	—	2	2	no	—
1102	Q₈	—	4	2	no	—
1103	Q₈	—	4	2	no	—
1104	Q₈	—	4	2	no	—
1105	Q₈	—	8	2	no	—
1106	D₄	—	2	4	no	—
1107	D₄	—	2	2	no	—
1108	D₄	—	2	1	no	—
1109	D₄	—	2	1	no	—
1110	D₄	—	2	2	no	—
1111	D₄	—	2	1	no	—
1112	D₄	—	2	1	no	—
1113	D₄	—	2	1	no	—
1114	D₄	—	2	1	no	—
1115	D₄	—	2	2	no	—
1116	D₄	—	4	2	no	—
1117	D₄	—	4	4	no	—
1118	D₄	—	4	2	no	—
1119	D₄	—	4	2	no	—
1120	D₄	—	4	4	no	—
1121	D₄	—	4	4	no	—
1122	D₄	—	4	2	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	4	no	—
1125	D₄	—	4	4	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	8	2	no	—
1128	D₄	—	8	2	no	—
1129	D₄	—	8	1	no	—
1130	D₄	—	8	1	no	—
1131	D₄	—	8	2	no	—
1132	D₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	complemented
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	4	2	no	—
1150	C₂×C₄	—	4	2	no	—
1151	C₂×C₄	—	4	1	no	—
1152	C₂×C₄	—	4	4	no	—
1153	C₂×C₄	—	4	4	no	—
1154	C₂×C₄	—	4	4	no	—
1155	C₂×C₄	—	4	4	no	—
1156	C₂×C₄	—	4	2	no	—
1157	C₂×C₄	—	4	2	no	—
1158	C₂×C₄	—	4	2	no	—
1159	C₂×C₄	—	8	2	no	—
1160	C₂×C₄	—	8	2	no	—
1161	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1162	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1163	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1164	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1165	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1166	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1167	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1168	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1169	C₈	—	2	2	no	—
1170	C₈	—	2	1	no	—
1171	C₈	—	2	2	no	—
1172	C₈	—	2	1	no	—
1173	C₈	—	2	1	no	—
1174	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	complemented
1175	C₂²	—	2	2	no	—
1176	C₂²	—	2	2	no	—
1177	C₂²	—	2	1	no	—
1178	C₂²	—	2	2	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	4	1	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	2	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	8	4	no	—
1196	C₂²	—	16	4	no	—
1197	C₂²	—	16	4	no	—
1198	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	4	yes	—
1199	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1200	C₄	—	2	1	no	—
1201	C₄	—	2	2	no	—
1202	C₄	—	2	2	no	—
1203	C₄	—	2	1	no	—
1204	C₄	—	2	1	no	—
1205	C₄	—	2	1	no	—
1206	C₄	—	4	2	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	2	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	2	no	—
1213	C₄	—	4	1	no	—
1214	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
1215	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1216	C₄	C₁₉×#585	1	1	yes	characteristic
1217	C₂	—	2	4	no	—
1218	C₂	—	4	1	no	—
1219	C₂	—	4	2	no	—
1220	C₂	—	8	1	no	—
1221	C₂	—	8	2	no	—
1222	C₂	—	8	1	no	—
1223	C₂	—	8	1	no	—
1224	C₂	C₁₉×#3496	1	1	yes	characteristic
1225	C₂	C₂²×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
1226	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 ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3520	C₂	semidirect
2. C₁₉×#3496	C₂	semidirect
3. C₁₉×#3353	C₂	semidirect
4. C₁₉×#3343	C₂	semidirect
5. C₁₉×#3334	C₂	semidirect
6. C₁₉×#3330	C₂	semidirect
7. C₁₉×#3324	C₂	semidirect
8. C₁₉×#3310	C₂	semidirect
9. C₁₉×#3308	C₂	semidirect
10. C₁₉×#3298	C₂	semidirect
11. C₁₉×#3294	C₂	semidirect
12. D₄×SD₁₆×C₁₉	C₂	semidirect
13. C₁₉×#3272	C₂	semidirect
14. C₁₉×#3265	C₂	semidirect
15. C₁₉×#3254	C₂	semidirect
16. C₁₉×#3251	C₂	semidirect
17. C₁₉×#3194	C₂	semidirect
18. C₁₉×#3193	C₂	semidirect
19. C₁₉×#3182	C₂	semidirect
20. C₁₉×#3171	C₂	semidirect
21. C₁₉×#3055	C₂	semidirect
22. C₂×C₁₉×#468	C₂	semidirect
23. D₄×M₁₆×C₁₉	C₂	semidirect
25. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂²×SD₁₆×C₁₉	C₂²	semidirect
27. C₂²×M₁₆×C₁₉	C₂²	semidirect
28. C₁₉×#556	C₂²	semidirect
30. C₁₉×#552	C₂²	semidirect
32. D₄×Q₈×C₁₉	C₂²	semidirect
33. C₁₉×#548	C₂²	semidirect
37. C₁₉×#547	C₂²	semidirect
38. C₁₉×#547	C₂²	semidirect
50. C₁₉×#533	C₂²	semidirect
53. C₁₉×#529	C₂²	semidirect
54. C₁₉×#525	C₂²	semidirect
55. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
60. C₁₉×#501	C₂²	semidirect
61. C₁₉×#500	C₂²	semidirect
62. C₁₉×#496	C₂²	semidirect
63. C₁₉×#492	C₂²	semidirect
64. C₁₉×#490	C₂²	semidirect
65. C₁₉×#489	C₂²	semidirect
66. C₁₉×#487	C₂²	semidirect
67. C₁₉×#486	C₂²	semidirect
68. C₁₉×#484	C₂²	semidirect
69. C₁₉×#484	C₂²	semidirect
70. C₁₉×#483	C₂²	semidirect
71. C₁₉×#482	C₂²	semidirect
72. C₁₉×#482	C₂²	semidirect
73. C₁₉×#480	C₂²	semidirect
74. C₁₉×#480	C₂²	semidirect
75. C₁₉×#480	C₂²	semidirect
76. C₁₉×#478	C₂²	semidirect
77. C₁₉×#477	C₂²	semidirect
78. C₁₉×#475	C₂²	semidirect
79. C₁₉×#474	C₂²	semidirect
80. C₁₉×#474	C₂²	semidirect
81. C₁₉×#474	C₂²	semidirect
82. C₁₉×#469	C₂²	semidirect
83. C₁₉×#469	C₂²	semidirect
84. C₁₉×#469	C₂²	semidirect
85. C₁₉×#468	C₂²	semidirect
86. C₁₉×#468	C₂²	semidirect
87. C₁₉×#468	C₂²	semidirect
88. C₁₉×#468	C₂²	semidirect
89. C₁₉×#468	C₂²	semidirect
90. C₁₉×#468	C₂²	semidirect
91. C₁₉×#468	C₂²	semidirect
92. C₁₉×#468	C₂²	semidirect
93. C₁₉×#468	C₂²	semidirect
94. C₁₉×#468	C₂²	semidirect
95. C₁₉×#468	C₂²	semidirect
96. C₁₉×#466	C₂²	semidirect
97. C₁₉×#466	C₂²	semidirect
98. C₁₉×#465	C₂²	semidirect
99. C₁₉×#465	C₂²	semidirect
100. C₁₉×#463	C₂²	semidirect
101. C₁₉×#461	C₂²	semidirect
102. C₁₉×#461	C₂²	semidirect
103. C₁₉×#460	C₂²	semidirect
104. C₁₉×#460	C₂²	semidirect
105. C₁₉×#459	C₂²	semidirect
106. C₁₉×#450	C₂²	semidirect
107. C₁₉×#450	C₂²	semidirect
108. C₁₉×#450	C₂²	semidirect
109. C₁₉×#449	C₂²	semidirect
110. C₁₉×#449	C₂²	semidirect
111. C₁₉×#448	C₂²	semidirect
112. C₁₉×#448	C₂²	semidirect
113. C₁₉×#447	C₂²	semidirect
114. C₁₉×#440	C₂²	semidirect
115. C₁₉×#440	C₂²	semidirect
116. C₄×SD₁₆×C₁₉	C₂²	semidirect
117. C₄×SD₁₆×C₁₉	C₂²	semidirect
118. C₄×D₈×C₁₉	C₂²	semidirect
119. C₄×D₈×C₁₉	C₂²	semidirect
120. C₁₉×#436	C₂²	semidirect
121. C₁₉×#436	C₂²	semidirect
122. C₁₉×#435	C₂²	semidirect
123. C₁₉×#435	C₂²	semidirect
124. C₈×D₄×C₁₉	C₂²	semidirect
125. C₈×D₄×C₁₉	C₂²	semidirect
126. C₁₉×#428	C₂²	semidirect
127. C₂×C₁₉×#107	C₂²	semidirect
128. C₁₉×#423	C₂²	semidirect
129. C₁₉×#418	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. C₄×M₁₆×C₁₉	C₂²	semidirect
468. #62295	C₁₉	direct (N × H)
519. D₄×C₁₉	AGL(1,ℤ/8)	semidirect
561. C₈×C₁₉	H(5,𝔽₂)	semidirect
562. #3520	C₂×C₁₉	semidirect
563. #3496	C₂×C₁₉	semidirect
564. #3353	C₂×C₁₉	semidirect
565. #3343	C₂×C₁₉	semidirect
566. #3334	C₂×C₁₉	semidirect
567. #3330	C₂×C₁₉	semidirect
568. #3324	C₂×C₁₉	semidirect
569. #3310	C₂×C₁₉	semidirect
570. #3308	C₂×C₁₉	semidirect
571. #3298	C₂×C₁₉	semidirect
572. #3294	C₂×C₁₉	semidirect
573. D₄×SD₁₆	C₂×C₁₉	semidirect
574. #3272	C₂×C₁₉	semidirect
575. #3265	C₂×C₁₉	semidirect
576. #3254	C₂×C₁₉	semidirect
577. #3251	C₂×C₁₉	semidirect
578. #3194	C₂×C₁₉	semidirect
579. #3193	C₂×C₁₉	semidirect
580. #3182	C₂×C₁₉	semidirect
581. #3171	C₂×C₁₉	semidirect
582. #3055	C₂×C₁₉	semidirect
583. C₂×#468	C₂×C₁₉	semidirect
584. D₄×M₁₆	C₂×C₁₉	semidirect
628. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
629. C₂²×SD₁₆	C₂²×C₁₉	semidirect
630. C₂²×M₁₆	C₂²×C₁₉	semidirect
631. #556	C₂²×C₁₉	semidirect
633. #552	C₂²×C₁₉	semidirect
635. D₄×Q₈	C₂²×C₁₉	semidirect
636. #548	C₂²×C₁₉	semidirect
640. #547	C₂²×C₁₉	semidirect
641. #547	C₂²×C₁₉	semidirect
653. #533	C₂²×C₁₉	semidirect
656. #529	C₂²×C₁₉	semidirect
657. #525	C₂²×C₁₉	semidirect
658. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
663. #501	C₂²×C₁₉	semidirect
664. #500	C₂²×C₁₉	semidirect
665. #496	C₂²×C₁₉	semidirect
666. #492	C₂²×C₁₉	semidirect
667. #490	C₂²×C₁₉	semidirect
668. #489	C₂²×C₁₉	semidirect
669. #487	C₂²×C₁₉	semidirect
670. #486	C₂²×C₁₉	semidirect
671. #484	C₂²×C₁₉	semidirect
672. #484	C₂²×C₁₉	semidirect
673. #483	C₂²×C₁₉	semidirect
674. #482	C₂²×C₁₉	semidirect
675. #482	C₂²×C₁₉	semidirect
676. #480	C₂²×C₁₉	semidirect
677. #480	C₂²×C₁₉	semidirect
678. #480	C₂²×C₁₉	semidirect
679. #478	C₂²×C₁₉	semidirect
680. #477	C₂²×C₁₉	semidirect
681. #475	C₂²×C₁₉	semidirect
682. #474	C₂²×C₁₉	semidirect
683. #474	C₂²×C₁₉	semidirect
684. #474	C₂²×C₁₉	semidirect
685. #469	C₂²×C₁₉	semidirect
686. #469	C₂²×C₁₉	semidirect
687. #469	C₂²×C₁₉	semidirect
688. #468	C₂²×C₁₉	semidirect
689. #468	C₂²×C₁₉	semidirect
690. #468	C₂²×C₁₉	semidirect
691. #468	C₂²×C₁₉	semidirect
692. #468	C₂²×C₁₉	semidirect
693. #468	C₂²×C₁₉	semidirect
694. #468	C₂²×C₁₉	semidirect
695. #468	C₂²×C₁₉	semidirect
696. #468	C₂²×C₁₉	semidirect
697. #468	C₂²×C₁₉	semidirect
698. #468	C₂²×C₁₉	semidirect
699. #466	C₂²×C₁₉	semidirect
700. #466	C₂²×C₁₉	semidirect
701. #465	C₂²×C₁₉	semidirect
702. #465	C₂²×C₁₉	semidirect
703. #463	C₂²×C₁₉	semidirect
704. #461	C₂²×C₁₉	semidirect
705. #461	C₂²×C₁₉	semidirect
706. #460	C₂²×C₁₉	semidirect
707. #460	C₂²×C₁₉	semidirect
708. #459	C₂²×C₁₉	semidirect
709. #450	C₂²×C₁₉	semidirect
710. #450	C₂²×C₁₉	semidirect
711. #450	C₂²×C₁₉	semidirect
712. #449	C₂²×C₁₉	semidirect
713. #449	C₂²×C₁₉	semidirect
714. #448	C₂²×C₁₉	semidirect
715. #448	C₂²×C₁₉	semidirect
716. #447	C₂²×C₁₉	semidirect
717. #440	C₂²×C₁₉	semidirect
718. #440	C₂²×C₁₉	semidirect
719. C₄×SD₁₆	C₂²×C₁₉	semidirect
720. C₄×SD₁₆	C₂²×C₁₉	semidirect
721. C₄×D₈	C₂²×C₁₉	semidirect
722. C₄×D₈	C₂²×C₁₉	semidirect
723. #436	C₂²×C₁₉	semidirect
724. #436	C₂²×C₁₉	semidirect
725. #435	C₂²×C₁₉	semidirect
726. #435	C₂²×C₁₉	semidirect
727. C₈×D₄	C₂²×C₁₉	semidirect
728. C₈×D₄	C₂²×C₁₉	semidirect
729. #428	C₂²×C₁₉	semidirect
730. C₂×#107	C₂²×C₁₉	semidirect
731. #423	C₂²×C₁₉	semidirect
732. #418	C₂²×C₁₉	semidirect
733. #417	C₂²×C₁₉	semidirect
734. C₂×#103	C₂²×C₁₉	semidirect
735. C₂×#102	C₂²×C₁₉	semidirect
736. #407	C₂²×C₁₉	semidirect
737. C₄×M₁₆	C₂²×C₁₉	semidirect
929. C₁₉	#62295	direct (N × H)
1132. D₄	C₁₉×AGL(1,ℤ/8)	semidirect
1174. C₈	C₁₉×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3520	2
C₁₉×#3496	2
C₁₉×#3353	2
C₁₉×#3343	2
C₁₉×#3334	2
C₁₉×#3330	2
C₁₉×#3324	2
C₁₉×#3310	2
C₁₉×#3308	2
C₁₉×#3298	2
C₁₉×#3294	2
D₄×SD₁₆×C₁₉	2
C₁₉×#3272	2
C₁₉×#3265	2
C₁₉×#3254	2
C₁₉×#3251	2
C₁₉×#3194	2
C₁₉×#3193	2
C₁₉×#3182	2
C₁₉×#3171	2
C₁₉×#3055	2
C₂×C₁₉×#468	2
D₄×M₁₆×C₁₉	2
#62295	19

Subgroups — C19×#62295 #18068254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62295 #18068254