Subgroups — C₁₉×#62252 #18068211

Order 4864.

1886 conjugacy classes of subgroups.

The subgroup lattice has 766 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	2	yes	maximal, complemented
2	C₁₉×#3342	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3336	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3334	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3302	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3300	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3298	C₂	1	2	yes	maximal, complemented
8	D₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#3285	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3283	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3248	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3190	C₂	1	4	yes	maximal, complemented
13	C₁₉×#3170	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3050	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₉×#467	C₂	1	2	yes	maximal, complemented
17	C₂×C₈×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₉×#135	C₂²	1	2	yes	complemented
19	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
20	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
21	C₁₉×#556	C₂²	1	2	yes	—
22	C₁₉×#554	—	2	2	no	—
23	C₁₉×#552	C₂²	1	4	yes	—
24	C₁₉×#551	—	2	4	no	—
25	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
26	C₁₉×#548	C₂²	1	4	yes	—
27	C₁₉×#547	C₂²	1	2	yes	—
28	C₁₉×#547	C₂²	1	2	yes	—
29	C₁₉×#546	—	2	2	no	—
30	C₁₉×#542	—	2	2	no	—
31	C₁₉×#539	—	2	4	no	—
32	C₁₉×#533	C₂²	1	2	yes	—
33	C₁₉×#529	C₂²	1	2	yes	—
34	C₁₉×#525	C₂²	1	4	yes	—
35	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
36	C₁₉×#520	—	2	2	no	—
37	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#499	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#495	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#488	C₂²	1	2	yes	complemented
43	C₁₉×#487	C₂²	1	2	yes	complemented
44	C₁₉×#485	C₂²	1	4	yes	complemented
45	C₁₉×#485	C₂²	1	4	yes	complemented
46	C₁₉×#483	C₂²	1	4	yes	complemented
47	C₁₉×#480	C₂²	1	4	yes	complemented
48	C₁₉×#479	C₂²	1	4	yes	complemented
49	C₁₉×#475	C₂²	1	2	yes	complemented
50	C₁₉×#474	C₂²	1	2	yes	complemented
51	C₁₉×#467	C₂²	1	1	yes	characteristic
52	C₁₉×#467	C₂²	1	2	yes	—
53	C₁₉×#467	C₂²	1	2	yes	—
54	C₁₉×#467	C₂²	1	4	yes	—
55	C₁₉×#467	C₂²	1	2	yes	complemented
56	C₁₉×#467	C₂²	1	2	yes	complemented
57	C₁₉×#467	C₂²	1	2	yes	complemented
58	C₁₉×#467	C₂²	1	4	yes	complemented
59	C₁₉×#466	C₂²	1	1	yes	characteristic
60	C₁₉×#466	C₂²	1	2	yes	complemented
61	C₁₉×#465	C₂²	1	2	yes	—
62	C₁₉×#465	C₂²	1	4	yes	—
63	C₁₉×#465	C₂²	1	4	yes	complemented
64	C₁₉×#464	C₂²	1	4	yes	complemented
65	C₁₉×#462	C₂²	1	2	yes	complemented
66	C₁₉×#461	C₂²	1	2	yes	complemented
67	C₁₉×#452	C₂²	1	4	yes	complemented
68	C₁₉×#452	C₂²	1	4	yes	complemented
69	C₁₉×#451	C₂²	1	4	yes	complemented
70	C₁₉×#448	C₂²	1	4	yes	complemented
71	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
72	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
73	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
74	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
75	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
76	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
77	C₈×D₄×C₁₉	C₂²	1	2	yes	—
78	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
79	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₁₉	C₂²	1	2	yes	—
81	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
82	C₁₉×#427	C₂²	1	2	yes	complemented
83	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
84	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
85	C₁₉×#416	C₂²	1	4	yes	complemented
86	C₂×C₁₉×#103	C₂²	1	4	yes	complemented
87	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
89	C₂×#41×C₁₉	—	2	2	no	—
90	C₂×#41×C₁₉	C₂³	1	4	yes	—
91	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
92	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
93	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
94	C₁₉×#135	—	4	4	no	—
95	C₂×Q₁₆×C₁₉	—	4	4	no	—
96	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
97	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
99	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
101	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
102	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₁₉	—	4	4	no	—
104	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
106	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
107	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
109	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
110	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
111	C₁₉×C₄⋊Q₈	—	2	2	no	—
112	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₉×#126	—	2	4	no	—
115	C₁₉×#126	—	2	4	no	—
116	C₁₉×#126	—	2	2	no	—
117	C₁₉×#125	—	2	4	no	—
118	C₁₉×#125	—	2	2	no	—
119	C₁₉×#125	C₂³	1	2	yes	—
120	C₁₉×#124	—	2	2	no	—
121	C₁₉×#124	—	2	4	no	—
122	C₁₉×#124	C₂³	1	2	yes	—
123	C₁₉×#123	—	2	4	no	—
124	C₁₉×#123	—	2	4	no	—
125	C₁₉×#123	—	2	2	no	—
126	C₁₉×#123	—	2	4	no	—
127	C₁₉×#123	—	2	4	no	—
128	C₁₉×C₂²⋊Q₈	—	2	4	no	—
129	C₁₉×C₂²⋊Q₈	—	2	4	no	—
130	C₁₉×C₂²⋊Q₈	—	2	2	no	—
131	C₁₉×C₂²⋊Q₈	—	2	4	no	—
132	C₁₉×C₂²⋊Q₈	—	2	2	no	—
133	C₁₉×C₂²⋊Q₈	—	2	4	no	—
134	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
137	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
138	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₁₉×#121	—	2	4	no	—
140	C₁₉×#121	—	2	2	no	—
141	C₁₉×#121	C₂³	1	4	yes	—
142	C₁₉×#121	C₂³	1	2	yes	—
143	C₁₉×#120	—	2	4	no	—
144	C₄×Q₈×C₁₉	—	2	2	no	—
145	C₄×Q₈×C₁₉	—	2	2	no	—
146	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
147	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
148	C₄×D₄×C₁₉	—	2	2	no	—
149	C₄×D₄×C₁₉	—	2	4	no	—
150	C₄×D₄×C₁₉	—	2	4	no	—
151	C₄×D₄×C₁₉	—	2	2	no	—
152	C₄×D₄×C₁₉	—	2	4	no	—
153	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
154	C₄×D₄×C₁₉	D₄	1	2	yes	—
155	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
156	C₄×D₄×C₁₉	C₂³	1	2	yes	—
157	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
158	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
159	C₄×D₄×C₁₉	C₂³	1	2	yes	—
160	C₁₉×#117	—	2	2	no	—
161	C₁₉×#117	—	2	4	no	—
162	C₁₉×#117	—	2	2	no	—
163	C₁₉×#117	C₂³	1	4	yes	—
164	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
165	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
168	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
169	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
170	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
171	C₁₉×#107	C₂³	1	1	yes	characteristic
172	C₁₉×#107	C₂³	1	2	yes	—
173	C₁₉×#107	C₂³	1	4	yes	—
174	C₁₉×#107	C₂³	1	1	yes	characteristic
175	C₁₉×#107	C₂³	1	2	yes	—
176	C₁₉×#106	C₂³	1	4	yes	—
177	C₁₉×#106	C₂³	1	2	yes	—
178	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
179	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
180	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
181	C₁₉×#103	C₂³	1	2	yes	—
182	C₁₉×#103	C₂³	1	4	yes	—
183	C₁₉×#103	C₂³	1	4	yes	—
184	C₁₉×#103	C₂³	1	4	yes	—
185	C₁₉×#103	C₂³	1	4	yes	—
186	C₁₉×#103	C₂³	1	4	yes	—
187	C₁₉×#103	C₂³	1	2	yes	—
188	C₁₉×#102	C₂³	1	2	yes	—
189	C₁₉×#102	C₂³	1	4	yes	—
190	C₁₉×#102	C₂³	1	2	yes	—
191	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
193	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
199	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
200	#41×C₁₉	—	4	4	no	—
201	#41×C₁₉	—	4	4	no	—
202	#41×C₁₉	—	4	8	no	—
203	C₂×Q₈×C₁₉	—	2	2	no	—
204	C₂×Q₈×C₁₉	—	2	4	no	—
205	C₂×Q₈×C₁₉	—	4	4	no	—
206	C₂×Q₈×C₁₉	—	4	4	no	—
207	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
208	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
209	C₂×D₄×C₁₉	—	2	4	no	—
210	C₂×D₄×C₁₉	—	2	2	no	—
211	C₂×D₄×C₁₉	—	2	4	no	—
212	C₂×D₄×C₁₉	—	2	4	no	—
213	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
214	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₉	—	2	4	no	—
218	C₂²×C₄×C₁₉	—	2	4	no	—
219	C₂²×C₄×C₁₉	—	2	2	no	—
220	C₂²×C₄×C₁₉	—	2	4	no	—
221	C₂²×C₄×C₁₉	—	4	2	no	—
222	C₂²×C₄×C₁₉	—	4	2	no	—
223	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
231	Q₁₆×C₁₉	—	2	2	no	—
232	Q₁₆×C₁₉	—	2	4	no	—
233	Q₁₆×C₁₉	—	4	4	no	—
234	Q₁₆×C₁₉	—	4	2	no	—
235	SD₁₆×C₁₉	—	4	2	no	—
236	SD₁₆×C₁₉	—	4	4	no	—
237	D₈×C₁₉	—	2	2	no	—
238	C₂×C₈×C₁₉	—	2	2	no	—
239	C₂×C₈×C₁₉	—	2	4	no	—
240	C₂×C₈×C₁₉	—	2	4	no	—
241	C₂×C₈×C₁₉	—	4	2	no	—
242	C₂×C₈×C₁₉	—	4	2	no	—
243	C₂×C₈×C₁₉	—	4	2	no	—
244	C₂×C₈×C₁₉	—	4	1	no	—
245	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
247	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
248	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
251	C₄⋊C₄×C₁₉	—	2	2	no	—
252	C₄⋊C₄×C₁₉	—	2	4	no	—
253	C₄⋊C₄×C₁₉	—	2	2	no	—
254	C₄⋊C₄×C₁₉	—	2	4	no	—
255	C₄⋊C₄×C₁₉	—	2	4	no	—
256	C₄⋊C₄×C₁₉	—	2	4	no	—
257	C₄⋊C₄×C₁₉	—	2	2	no	—
258	C₄⋊C₄×C₁₉	—	2	2	no	—
259	C₄⋊C₄×C₁₉	—	2	2	no	—
260	C₄⋊C₄×C₁₉	—	2	4	no	—
261	C₄⋊C₄×C₁₉	—	2	2	no	—
262	C₄⋊C₄×C₁₉	—	2	4	no	—
263	C₄⋊C₄×C₁₉	—	2	2	no	—
264	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
265	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
266	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
267	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
268	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
269	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
270	C₂²⋊C₄×C₁₉	—	2	2	no	—
271	C₂²⋊C₄×C₁₉	—	2	4	no	—
272	C₂²⋊C₄×C₁₉	—	2	4	no	—
273	C₂²⋊C₄×C₁₉	—	2	4	no	—
274	C₂²⋊C₄×C₁₉	—	2	4	no	—
275	C₂²⋊C₄×C₁₉	—	2	4	no	—
276	C₂²⋊C₄×C₁₉	—	2	2	no	—
277	C₂²⋊C₄×C₁₉	—	2	2	no	—
278	C₂²⋊C₄×C₁₉	—	2	2	no	—
279	C₂²⋊C₄×C₁₉	—	2	4	no	—
280	C₂²⋊C₄×C₁₉	—	2	2	no	—
281	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
282	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
283	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
284	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
285	C₄²×C₁₉	—	2	4	no	—
286	C₄²×C₁₉	—	2	4	no	—
287	C₄²×C₁₉	—	2	2	no	—
288	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
289	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
290	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
291	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
292	#62252	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
293	C₂³×C₁₉	—	2	4	no	—
294	C₂³×C₁₉	—	2	4	no	—
295	C₂³×C₁₉	—	2	2	no	—
296	C₂³×C₁₉	—	4	2	no	—
297	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
298	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
299	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
300	Q₈×C₁₉	—	2	4	no	—
301	Q₈×C₁₉	—	2	2	no	—
302	Q₈×C₁₉	—	2	2	no	—
303	Q₈×C₁₉	—	2	4	no	—
304	Q₈×C₁₉	—	4	4	no	—
305	Q₈×C₁₉	—	8	4	no	—
306	D₄×C₁₉	—	2	4	no	—
307	D₄×C₁₉	—	2	2	no	—
308	D₄×C₁₉	—	2	2	no	—
309	D₄×C₁₉	—	2	2	no	—
310	D₄×C₁₉	—	4	8	no	—
311	D₄×C₁₉	—	4	4	no	—
312	D₄×C₁₉	—	8	4	no	—
313	D₄×C₁₉	#135	1	4	yes	complemented
314	C₂×C₄×C₁₉	—	2	2	no	—
315	C₂×C₄×C₁₉	—	2	2	no	—
316	C₂×C₄×C₁₉	—	2	1	no	—
317	C₂×C₄×C₁₉	—	2	2	no	—
318	C₂×C₄×C₁₉	—	2	2	no	—
319	C₂×C₄×C₁₉	—	2	1	no	—
320	C₂×C₄×C₁₉	—	2	2	no	—
321	C₂×C₄×C₁₉	—	2	2	no	—
322	C₂×C₄×C₁₉	—	2	2	no	—
323	C₂×C₄×C₁₉	—	2	4	no	—
324	C₂×C₄×C₁₉	—	2	2	no	—
325	C₂×C₄×C₁₉	—	2	4	no	—
326	C₂×C₄×C₁₉	—	2	2	no	—
327	C₂×C₄×C₁₉	—	4	2	no	—
328	C₂×C₄×C₁₉	—	4	2	no	—
329	C₂×C₄×C₁₉	—	4	2	no	—
330	C₂×C₄×C₁₉	—	4	8	no	—
331	C₂×C₄×C₁₉	—	4	4	no	—
332	C₂×C₄×C₁₉	—	8	4	no	—
333	C₂×C₄×C₁₉	—	8	4	no	—
334	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
342	C₈×C₁₉	—	2	1	no	—
343	C₈×C₁₉	—	2	2	no	—
344	C₈×C₁₉	—	2	2	no	—
345	C₈×C₁₉	—	2	1	no	—
346	C₈×C₁₉	—	2	1	no	—
347	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
348	#3520	C₂×C₁₉	1	2	yes	complemented
349	#3342	C₂×C₁₉	1	1	yes	characteristic, complemented
350	#3336	C₂×C₁₉	1	2	yes	complemented
351	#3334	C₂×C₁₉	1	1	yes	characteristic, complemented
352	#3302	C₂×C₁₉	1	2	yes	complemented
353	#3300	C₂×C₁₉	1	4	yes	complemented
354	#3298	C₂×C₁₉	1	2	yes	complemented
355	D₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
356	#3285	C₂×C₁₉	1	2	yes	complemented
357	#3283	C₂×C₁₉	1	1	yes	characteristic, complemented
358	#3248	C₂×C₁₉	1	2	yes	complemented
359	#3190	C₂×C₁₉	1	4	yes	complemented
360	#3170	C₂×C₁₉	1	1	yes	characteristic, complemented
361	#3168	C₂×C₁₉	1	1	yes	characteristic, complemented
362	#3050	C₂×C₁₉	1	2	yes	complemented
363	C₂×#467	C₂×C₁₉	1	2	yes	complemented
364	C₂×C₈×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
365	C₂²×C₁₉	—	2	1	no	—
366	C₂²×C₁₉	—	2	2	no	—
367	C₂²×C₁₉	—	2	1	no	—
368	C₂²×C₁₉	—	2	2	no	—
369	C₂²×C₁₉	—	2	2	no	—
370	C₂²×C₁₉	—	2	2	no	—
371	C₂²×C₁₉	—	2	2	no	—
372	C₂²×C₁₉	—	4	8	no	—
373	C₂²×C₁₉	—	4	2	no	—
374	C₂²×C₁₉	—	4	2	no	—
375	C₂²×C₁₉	—	4	2	no	—
376	C₂²×C₁₉	C₂×#135	1	4	yes	—
377	C₂²×C₁₉	#578	1	2	yes	—
378	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
379	C₄×C₁₉	—	2	1	no	—
380	C₄×C₁₉	—	2	2	no	—
381	C₄×C₁₉	—	2	2	no	—
382	C₄×C₁₉	—	2	1	no	—
383	C₄×C₁₉	—	2	1	no	—
384	C₄×C₁₉	—	2	1	no	—
385	C₄×C₁₉	—	4	4	no	—
386	C₄×C₁₉	—	4	2	no	—
387	C₄×C₁₉	—	4	2	no	—
388	C₄×C₁₉	—	4	4	no	—
389	C₄×C₁₉	—	4	2	no	—
390	C₄×C₁₉	C₂×#135	1	2	yes	—
391	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
392	C₄×C₁₉	#585	1	1	yes	characteristic
393	C₂×#135	C₂²×C₁₉	1	2	yes	complemented
394	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
395	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
396	#556	C₂²×C₁₉	1	2	yes	—
397	#554	—	2	2	no	—
398	#552	C₂²×C₁₉	1	4	yes	—
399	#551	—	2	4	no	—
400	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
401	#548	C₂²×C₁₉	1	4	yes	—
402	#547	C₂²×C₁₉	1	2	yes	—
403	#547	C₂²×C₁₉	1	2	yes	—
404	#546	—	2	2	no	—
405	#542	—	2	2	no	—
406	#539	—	2	4	no	—
407	#533	C₂²×C₁₉	1	2	yes	—
408	#529	C₂²×C₁₉	1	2	yes	—
409	#525	C₂²×C₁₉	1	4	yes	—
410	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
411	#520	—	2	2	no	—
412	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
413	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
414	#499	C₂²×C₁₉	1	1	yes	characteristic, complemented
415	#495	C₂²×C₁₉	1	1	yes	characteristic, complemented
416	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
417	#488	C₂²×C₁₉	1	2	yes	complemented
418	#487	C₂²×C₁₉	1	2	yes	complemented
419	#485	C₂²×C₁₉	1	4	yes	complemented
420	#485	C₂²×C₁₉	1	4	yes	complemented
421	#483	C₂²×C₁₉	1	4	yes	complemented
422	#480	C₂²×C₁₉	1	4	yes	complemented
423	#479	C₂²×C₁₉	1	4	yes	complemented
424	#475	C₂²×C₁₉	1	2	yes	complemented
425	#474	C₂²×C₁₉	1	2	yes	complemented
426	#467	C₂²×C₁₉	1	1	yes	characteristic
427	#467	C₂²×C₁₉	1	2	yes	—
428	#467	C₂²×C₁₉	1	2	yes	—
429	#467	C₂²×C₁₉	1	4	yes	—
430	#467	C₂²×C₁₉	1	2	yes	complemented
431	#467	C₂²×C₁₉	1	2	yes	complemented
432	#467	C₂²×C₁₉	1	2	yes	complemented
433	#467	C₂²×C₁₉	1	4	yes	complemented
434	#466	C₂²×C₁₉	1	1	yes	characteristic
435	#466	C₂²×C₁₉	1	2	yes	complemented
436	#465	C₂²×C₁₉	1	2	yes	—
437	#465	C₂²×C₁₉	1	4	yes	—
438	#465	C₂²×C₁₉	1	4	yes	complemented
439	#464	C₂²×C₁₉	1	4	yes	complemented
440	#462	C₂²×C₁₉	1	2	yes	complemented
441	#461	C₂²×C₁₉	1	2	yes	complemented
442	#452	C₂²×C₁₉	1	4	yes	complemented
443	#452	C₂²×C₁₉	1	4	yes	complemented
444	#451	C₂²×C₁₉	1	4	yes	complemented
445	#448	C₂²×C₁₉	1	4	yes	complemented
446	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
447	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
448	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
449	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
450	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
451	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
452	C₈×D₄	C₂²×C₁₉	1	2	yes	—
453	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
454	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
455	C₈×D₄	C₂²×C₁₉	1	2	yes	—
456	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
457	#427	C₂²×C₁₉	1	2	yes	complemented
458	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
459	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
460	#416	C₂²×C₁₉	1	4	yes	complemented
461	C₂×#103	C₂²×C₁₉	1	4	yes	complemented
462	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
463	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
464	C₂×C₁₉	—	2	2	no	—
465	C₂×C₁₉	—	2	4	no	—
466	C₂×C₁₉	—	4	2	no	—
467	C₂×C₁₉	—	8	2	no	—
468	C₂×C₁₉	#3496	1	1	yes	characteristic
469	C₂×C₁₉	C₂²×#135	1	1	yes	characteristic
470	C₂×C₁₉	C₂×#578	1	1	yes	characteristic
471	C₂×#41	—	2	2	no	—
472	C₂×#41	C₂³×C₁₉	1	4	yes	—
473	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
474	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
476	#135	—	4	4	no	—
477	C₂×Q₁₆	—	4	4	no	—
478	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
479	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
480	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
481	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
482	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
483	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
484	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
485	C₂²×C₈	—	4	4	no	—
486	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
488	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
489	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
490	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
491	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
492	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
493	C₄⋊Q₈	—	2	2	no	—
494	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
495	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
496	#126	—	2	4	no	—
497	#126	—	2	4	no	—
498	#126	—	2	2	no	—
499	#125	—	2	4	no	—
500	#125	—	2	2	no	—
501	#125	C₂³×C₁₉	1	2	yes	—
502	#124	—	2	2	no	—
503	#124	—	2	4	no	—
504	#124	C₂³×C₁₉	1	2	yes	—
505	#123	—	2	4	no	—
506	#123	—	2	4	no	—
507	#123	—	2	2	no	—
508	#123	—	2	4	no	—
509	#123	—	2	4	no	—
510	C₂²⋊Q₈	—	2	4	no	—
511	C₂²⋊Q₈	—	2	4	no	—
512	C₂²⋊Q₈	—	2	2	no	—
513	C₂²⋊Q₈	—	2	4	no	—
514	C₂²⋊Q₈	—	2	2	no	—
515	C₂²⋊Q₈	—	2	4	no	—
516	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
517	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
518	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
519	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
520	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
521	#121	—	2	4	no	—
522	#121	—	2	2	no	—
523	#121	C₂³×C₁₉	1	2	yes	—
524	#121	C₂³×C₁₉	1	4	yes	—
525	#120	—	2	4	no	—
526	C₄×Q₈	—	2	2	no	—
527	C₄×Q₈	—	2	2	no	—
528	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
529	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	4	no	—
532	C₄×D₄	—	2	4	no	—
533	C₄×D₄	—	2	2	no	—
534	C₄×D₄	—	2	4	no	—
535	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
536	C₄×D₄	D₄×C₁₉	1	2	yes	—
537	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
538	C₄×D₄	C₂³×C₁₉	1	2	yes	—
539	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
540	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
541	C₄×D₄	C₂³×C₁₉	1	2	yes	—
542	#117	—	2	2	no	—
543	#117	—	2	4	no	—
544	#117	—	2	2	no	—
545	#117	C₂³×C₁₉	1	4	yes	—
546	C₂×C₄⋊C₄	—	2	4	no	—
547	C₂×C₄⋊C₄	—	2	2	no	—
548	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
550	C₂×C₂²⋊C₄	—	2	4	no	—
551	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
552	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
553	#107	C₂³×C₁₉	1	1	yes	characteristic
554	#107	C₂³×C₁₉	1	2	yes	—
555	#107	C₂³×C₁₉	1	4	yes	—
556	#107	C₂³×C₁₉	1	1	yes	characteristic
557	#107	C₂³×C₁₉	1	2	yes	—
558	#106	C₂³×C₁₉	1	4	yes	—
559	#106	C₂³×C₁₉	1	2	yes	—
560	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
561	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
562	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
563	#103	C₂³×C₁₉	1	2	yes	—
564	#103	C₂³×C₁₉	1	4	yes	—
565	#103	C₂³×C₁₉	1	4	yes	—
566	#103	C₂³×C₁₉	1	4	yes	—
567	#103	C₂³×C₁₉	1	4	yes	—
568	#103	C₂³×C₁₉	1	4	yes	—
569	#103	C₂³×C₁₉	1	2	yes	—
570	#102	C₂³×C₁₉	1	2	yes	—
571	#102	C₂³×C₁₉	1	4	yes	—
572	#102	C₂³×C₁₉	1	2	yes	—
573	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
574	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
575	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
576	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
577	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
578	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
579	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
580	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
581	C₁₉	#62252	1	1	yes	characteristic, direct product factor, Sylow
582	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
583	#41	—	4	4	no	—
584	#41	—	4	4	no	—
585	#41	—	4	8	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	—	4	4	no	—
589	C₂×Q₈	—	4	4	no	—
590	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
591	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
597	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
598	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
599	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	4	2	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
609	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
610	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
614	Q₁₆	—	2	2	no	—
615	Q₁₆	—	2	4	no	—
616	Q₁₆	—	4	4	no	—
617	Q₁₆	—	4	2	no	—
618	SD₁₆	—	4	2	no	—
619	SD₁₆	—	4	4	no	—
620	D₈	—	2	2	no	—
621	C₂×C₈	—	2	2	no	—
622	C₂×C₈	—	2	4	no	—
623	C₂×C₈	—	2	4	no	—
624	C₂×C₈	—	4	2	no	—
625	C₂×C₈	—	4	2	no	—
626	C₂×C₈	—	4	2	no	—
627	C₂×C₈	—	4	1	no	—
628	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
629	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
630	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
631	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
632	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
633	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
648	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
649	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
650	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
651	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
652	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
665	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
666	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
667	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	4	no	—
670	C₄²	—	2	2	no	—
671	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
672	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
673	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
674	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
675	C₂³	—	2	4	no	—
676	C₂³	—	2	4	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
680	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
681	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
682	Q₈	—	2	4	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	2	2	no	—
685	Q₈	—	2	4	no	—
686	Q₈	—	4	4	no	—
687	Q₈	—	8	4	no	—
688	D₄	—	2	4	no	—
689	D₄	—	2	2	no	—
690	D₄	—	2	2	no	—
691	D₄	—	2	2	no	—
692	D₄	—	4	8	no	—
693	D₄	—	4	4	no	—
694	D₄	—	8	4	no	—
695	D₄	C₁₉×#135	1	4	yes	complemented
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	8	no	—
713	C₂×C₄	—	4	4	no	—
714	C₂×C₄	—	8	4	no	—
715	C₂×C₄	—	8	4	no	—
716	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
719	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
720	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
721	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
722	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
723	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
724	C₈	—	2	1	no	—
725	C₈	—	2	2	no	—
726	C₈	—	2	2	no	—
727	C₈	—	2	1	no	—
728	C₈	—	2	1	no	—
729	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	4	8	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	C₂×C₁₉×#135	1	4	yes	—
742	C₂²	C₁₉×#578	1	2	yes	—
743	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
744	C₄	—	2	1	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	1	no	—
748	C₄	—	2	1	no	—
749	C₄	—	2	1	no	—
750	C₄	—	4	4	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	4	no	—
754	C₄	—	4	2	no	—
755	C₄	C₂×C₁₉×#135	1	2	yes	—
756	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
757	C₄	C₁₉×#585	1	1	yes	characteristic
758	C₂	—	2	2	no	—
759	C₂	—	2	4	no	—
760	C₂	—	4	2	no	—
761	C₂	—	8	2	no	—
762	C₂	C₁₉×#3496	1	1	yes	characteristic
763	C₂	C₂²×C₁₉×#135	1	1	yes	characteristic
764	C₂	C₂×C₁₉×#578	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×#3342	C₂	semidirect
3. C₁₉×#3336	C₂	semidirect
4. C₁₉×#3334	C₂	semidirect
5. C₁₉×#3302	C₂	semidirect
6. C₁₉×#3300	C₂	semidirect
7. C₁₉×#3298	C₂	semidirect
8. D₄×Q₁₆×C₁₉	C₂	semidirect
9. C₁₉×#3285	C₂	semidirect
10. C₁₉×#3283	C₂	semidirect
11. C₁₉×#3248	C₂	semidirect
12. C₁₉×#3190	C₂	semidirect
13. C₁₉×#3170	C₂	semidirect
14. C₁₉×#3168	C₂	semidirect
15. C₁₉×#3050	C₂	semidirect
16. C₂×C₁₉×#467	C₂	semidirect
17. C₂×C₈×D₄×C₁₉	C₂	semidirect
18. C₂×C₁₉×#135	C₂²	semidirect
19. C₂²×Q₁₆×C₁₉	C₂²	semidirect
38. C₁₉×#500	C₂²	semidirect
39. C₁₉×#499	C₂²	semidirect
40. C₁₉×#495	C₂²	semidirect
41. C₁₉×#494	C₂²	semidirect
42. C₁₉×#488	C₂²	semidirect
43. C₁₉×#487	C₂²	semidirect
44. C₁₉×#485	C₂²	semidirect
45. C₁₉×#485	C₂²	semidirect
46. C₁₉×#483	C₂²	semidirect
47. C₁₉×#480	C₂²	semidirect
48. C₁₉×#479	C₂²	semidirect
49. C₁₉×#475	C₂²	semidirect
50. C₁₉×#474	C₂²	semidirect
55. C₁₉×#467	C₂²	semidirect
56. C₁₉×#467	C₂²	semidirect
57. C₁₉×#467	C₂²	semidirect
58. C₁₉×#467	C₂²	semidirect
60. C₁₉×#466	C₂²	semidirect
63. C₁₉×#465	C₂²	semidirect
64. C₁₉×#464	C₂²	semidirect
65. C₁₉×#462	C₂²	semidirect
66. C₁₉×#461	C₂²	semidirect
67. C₁₉×#452	C₂²	semidirect
68. C₁₉×#452	C₂²	semidirect
69. C₁₉×#451	C₂²	semidirect
70. C₁₉×#448	C₂²	semidirect
71. C₄×Q₁₆×C₁₉	C₂²	semidirect
72. C₄×Q₁₆×C₁₉	C₂²	semidirect
73. C₄×Q₁₆×C₁₉	C₂²	semidirect
74. C₄×SD₁₆×C₁₉	C₂²	semidirect
75. C₄×D₈×C₁₉	C₂²	semidirect
82. C₁₉×#427	C₂²	semidirect
83. C₂×C₁₉×#107	C₂²	semidirect
85. C₁₉×#416	C₂²	semidirect
86. C₂×C₁₉×#103	C₂²	semidirect
292. #62252	C₁₉	direct (N × H)
313. D₄×C₁₉	#135	semidirect
348. #3520	C₂×C₁₉	semidirect
349. #3342	C₂×C₁₉	semidirect
350. #3336	C₂×C₁₉	semidirect
351. #3334	C₂×C₁₉	semidirect
352. #3302	C₂×C₁₉	semidirect
353. #3300	C₂×C₁₉	semidirect
354. #3298	C₂×C₁₉	semidirect
355. D₄×Q₁₆	C₂×C₁₉	semidirect
356. #3285	C₂×C₁₉	semidirect
357. #3283	C₂×C₁₉	semidirect
358. #3248	C₂×C₁₉	semidirect
359. #3190	C₂×C₁₉	semidirect
360. #3170	C₂×C₁₉	semidirect
361. #3168	C₂×C₁₉	semidirect
362. #3050	C₂×C₁₉	semidirect
363. C₂×#467	C₂×C₁₉	semidirect
364. C₂×C₈×D₄	C₂×C₁₉	semidirect
393. C₂×#135	C₂²×C₁₉	semidirect
394. C₂²×Q₁₆	C₂²×C₁₉	semidirect
413. #500	C₂²×C₁₉	semidirect
414. #499	C₂²×C₁₉	semidirect
415. #495	C₂²×C₁₉	semidirect
416. #494	C₂²×C₁₉	semidirect
417. #488	C₂²×C₁₉	semidirect
418. #487	C₂²×C₁₉	semidirect
419. #485	C₂²×C₁₉	semidirect
420. #485	C₂²×C₁₉	semidirect
421. #483	C₂²×C₁₉	semidirect
422. #480	C₂²×C₁₉	semidirect
423. #479	C₂²×C₁₉	semidirect
424. #475	C₂²×C₁₉	semidirect
425. #474	C₂²×C₁₉	semidirect
430. #467	C₂²×C₁₉	semidirect
431. #467	C₂²×C₁₉	semidirect
432. #467	C₂²×C₁₉	semidirect
433. #467	C₂²×C₁₉	semidirect
435. #466	C₂²×C₁₉	semidirect
438. #465	C₂²×C₁₉	semidirect
439. #464	C₂²×C₁₉	semidirect
440. #462	C₂²×C₁₉	semidirect
441. #461	C₂²×C₁₉	semidirect
442. #452	C₂²×C₁₉	semidirect
443. #452	C₂²×C₁₉	semidirect
444. #451	C₂²×C₁₉	semidirect
445. #448	C₂²×C₁₉	semidirect
446. C₄×Q₁₆	C₂²×C₁₉	semidirect
447. C₄×Q₁₆	C₂²×C₁₉	semidirect
448. C₄×Q₁₆	C₂²×C₁₉	semidirect
449. C₄×SD₁₆	C₂²×C₁₉	semidirect
450. C₄×D₈	C₂²×C₁₉	semidirect
457. #427	C₂²×C₁₉	semidirect
458. C₂×#107	C₂²×C₁₉	semidirect
460. #416	C₂²×C₁₉	semidirect
461. C₂×#103	C₂²×C₁₉	semidirect
581. C₁₉	#62252	direct (N × H)
695. D₄	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×#3520	2
C₁₉×#3342	2
C₁₉×#3336	2
C₁₉×#3334	2
C₁₉×#3302	2
C₁₉×#3300	2
C₁₉×#3298	2
D₄×Q₁₆×C₁₉	2
C₁₉×#3285	2
C₁₉×#3283	2
C₁₉×#3248	2
C₁₉×#3190	2
C₁₉×#3170	2
C₁₉×#3168	2
C₁₉×#3050	2
C₂×C₁₉×#467	2
C₂×C₈×D₄×C₁₉	2
#62252	19

Subgroups — C19×#62252 #18068211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62252 #18068211