Subgroups — C₁₉×#62342 #18068301

Order 4864.

1948 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3548	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3357	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3354	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3305	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3303	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3295	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3294	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3274	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3272	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3253	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3198	C₂	1	4	yes	maximal, complemented
14	C₁₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3062	C₂	1	4	yes	maximal, complemented
17	C₁₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
19	C₂×C₁₉×#131	C₂²	1	2	yes	complemented
20	C₁₉×#562	—	2	2	no	—
21	C₁₉×H(3,𝔽₄)	—	2	2	no	—
22	C₁₉×#555	—	2	1	no	—
23	C₁₉×#555	C₂²	1	2	yes	—
24	C₁₉×#555	C₂²	1	2	yes	—
25	C₁₉×#554	—	2	1	no	—
26	C₁₉×#554	C₂²	1	2	yes	complemented
27	C₁₉×#550	—	2	1	no	—
28	C₁₉×#550	C₂²	1	2	yes	complemented
29	C₁₉×#547	C₂²	1	2	yes	complemented
30	C₁₉×#547	C₂²	1	2	yes	complemented
31	D₄²×C₁₉	—	2	1	no	—
32	D₄²×C₁₉	C₂²	1	2	yes	—
33	D₄²×C₁₉	C₂²	1	2	yes	—
34	C₁₉×#540	—	2	2	no	—
35	C₁₉×#537	—	2	2	no	—
36	C₁₉×#537	C₂²	1	4	yes	complemented
37	C₁₉×#535	—	2	2	no	—
38	C₁₉×#535	—	2	2	no	—
39	C₁₉×#535	C₂²	1	4	yes	—
40	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#532	C₂²	1	1	yes	characteristic
42	C₁₉×#532	C₂²	1	1	yes	characteristic
43	C₁₉×#532	C₂²	1	1	yes	characteristic
44	C₁₉×#532	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#493	C₂²	1	1	yes	characteristic
48	C₁₉×#492	C₂²	1	1	yes	characteristic
49	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#486	C₂²	1	1	yes	characteristic
51	C₁₉×#486	C₂²	1	1	yes	characteristic
52	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#485	C₂²	1	4	yes	complemented
54	C₁₉×#482	C₂²	1	4	yes	complemented
55	C₁₉×#481	C₂²	1	4	yes	complemented
56	C₁₉×#480	C₂²	1	4	yes	complemented
57	C₁₉×#477	C₂²	1	2	yes	complemented
58	C₁₉×#476	C₂²	1	2	yes	complemented
59	C₁₉×#476	C₂²	1	2	yes	complemented
60	C₁₉×#474	C₂²	1	2	yes	complemented
61	C₁₉×#469	C₂²	1	4	yes	complemented
62	C₁₉×#469	C₂²	1	4	yes	complemented
63	C₁₉×#468	C₂²	1	4	yes	complemented
64	C₁₉×#468	C₂²	1	4	yes	complemented
65	C₁₉×#466	C₂²	1	2	yes	complemented
66	C₁₉×#466	C₂²	1	2	yes	complemented
67	C₁₉×#466	C₂²	1	4	yes	complemented
68	C₁₉×#465	C₂²	1	2	yes	complemented
69	C₁₉×#465	C₂²	1	2	yes	complemented
70	C₁₉×#465	C₂²	1	4	yes	complemented
71	C₁₉×#461	C₂²	1	2	yes	complemented
72	C₁₉×#460	C₂²	1	2	yes	—
73	C₁₉×#459	C₂²	1	2	yes	—
74	C₁₉×#459	C₂²	1	2	yes	complemented
75	C₁₉×#450	C₂²	1	4	yes	complemented
76	C₁₉×#449	C₂²	1	4	yes	complemented
77	C₁₉×#449	C₂²	1	4	yes	complemented
78	C₁₉×#447	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
80	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
81	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
82	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
83	C₁₉×#436	C₂²	1	2	yes	complemented
84	C₁₉×#436	C₂²	1	2	yes	complemented
85	C₈×D₄×C₁₉	C₂²	1	2	yes	complemented
86	C₈×D₄×C₁₉	C₂²	1	2	yes	complemented
87	C₁₉×#428	C₂²	1	4	yes	complemented
88	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
89	C₁₉×#416	C₂²	1	4	yes	complemented
90	C₂×C₁₉×#102	C₂²	1	4	yes	complemented
91	C₁₉×#408	C₂²	1	2	yes	complemented
92	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
93	C₂×#41×C₁₉	—	2	2	no	—
94	C₂×#41×C₁₉	—	2	1	no	—
95	C₂×#41×C₁₉	—	2	1	no	—
96	C₂×#41×C₁₉	—	2	1	no	—
97	C₂×#41×C₁₉	C₂³	1	4	yes	—
98	C₂×#41×C₁₉	C₂³	1	2	yes	—
99	C₂²×D₄×C₁₉	—	2	2	no	—
100	C₂²×D₄×C₁₉	—	2	2	no	—
101	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
102	C₁₉×AGL(1,ℤ/8)	—	4	8	no	—
103	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
105	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
106	C₂×D₈×C₁₉	C₂³	1	2	yes	—
107	C₂×D₈×C₁₉	C₂³	1	2	yes	—
108	C₂×D₈×C₁₉	C₂³	1	4	yes	—
109	C₁₉×#131	—	4	4	no	—
110	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
111	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
112	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
115	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
116	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₁₉×#127	—	2	4	no	—
122	C₁₉×#127	—	2	2	no	—
123	C₁₉×#127	D₄	1	1	yes	characteristic
124	C₁₉×#127	C₂³	1	1	yes	characteristic
125	C₁₉×#127	C₂³	1	1	yes	characteristic
126	C₁₉×#127	C₂³	1	1	yes	characteristic
127	C₁₉×#125	—	2	2	no	—
128	C₁₉×#125	—	2	1	no	—
129	C₁₉×#124	—	2	4	no	—
130	C₁₉×#124	—	2	4	no	—
131	C₁₉×#124	—	2	4	no	—
132	C₁₉×#124	—	2	1	no	—
133	C₁₉×#124	—	2	1	no	—
134	C₁₉×#124	—	2	1	no	—
135	C₁₉×#124	D₄	1	2	yes	—
136	C₁₉×#123	—	2	4	no	—
137	C₁₉×#123	—	2	4	no	—
138	C₁₉×C₂²⋊Q₈	—	2	4	no	—
139	C₁₉×C₂²⋊Q₈	—	2	1	no	—
140	C₁₉×C₂²⋊Q₈	—	2	2	no	—
141	C₁₉×C₂²⋊Q₈	—	2	4	no	—
142	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
143	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₁₉×#121	—	2	2	no	—
145	C₁₉×#121	—	2	2	no	—
146	C₁₉×#121	—	2	4	no	—
147	C₁₉×#121	—	2	4	no	—
148	C₁₉×#121	—	2	2	no	—
149	C₁₉×#121	—	2	4	no	—
150	C₁₉×#121	—	2	1	no	—
151	C₁₉×#121	—	2	1	no	—
152	C₁₉×#121	—	2	1	no	—
153	C₁₉×#121	—	2	2	no	—
154	C₁₉×#121	—	2	2	no	—
155	C₁₉×#121	—	2	4	no	—
156	C₁₉×#121	D₄	1	2	yes	—
157	C₁₉×#121	D₄	1	2	yes	—
158	C₁₉×#121	C₂³	1	4	yes	—
159	C₁₉×#121	C₂³	1	4	yes	—
160	C₁₉×#121	C₂³	1	4	yes	—
161	C₁₉×#121	C₂³	1	2	yes	—
162	C₁₉×#121	C₂³	1	2	yes	—
163	C₁₉×#121	C₂³	1	2	yes	—
164	C₁₉×#120	—	2	4	no	—
165	C₁₉×#120	—	2	4	no	—
166	C₁₉×#120	—	2	4	no	—
167	C₁₉×#120	—	2	4	no	—
168	C₄×Q₈×C₁₉	—	2	1	no	—
169	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
170	C₄×D₄×C₁₉	—	2	2	no	—
171	C₄×D₄×C₁₉	—	2	2	no	—
172	C₄×D₄×C₁₉	—	2	1	no	—
173	C₄×D₄×C₁₉	—	2	1	no	—
174	C₄×D₄×C₁₉	—	2	1	no	—
175	C₄×D₄×C₁₉	C₂³	1	2	yes	—
176	C₄×D₄×C₁₉	C₂³	1	2	yes	—
177	C₄×D₄×C₁₉	C₂³	1	2	yes	—
178	C₄×D₄×C₁₉	C₂³	1	2	yes	—
179	C₄×D₄×C₁₉	C₂³	1	2	yes	—
180	C₁₉×#117	—	2	1	no	—
181	C₁₉×#117	—	2	2	no	—
182	C₁₉×#117	—	2	2	no	—
183	C₁₉×#117	C₂³	1	4	yes	—
184	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
186	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
187	C₁₉×#107	C₂³	1	2	yes	—
188	C₁₉×#107	C₂³	1	4	yes	—
189	C₁₉×#107	C₂³	1	2	yes	—
190	C₁₉×#106	C₂³	1	2	yes	—
191	C₁₉×#106	C₂³	1	4	yes	—
192	C₁₉×#106	C₂³	1	2	yes	—
193	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
194	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
195	C₁₉×#103	C₂³	1	2	yes	—
196	C₁₉×#103	C₂³	1	4	yes	—
197	C₁₉×#103	C₂³	1	2	yes	—
198	C₁₉×#102	C₂³	1	2	yes	—
199	C₁₉×#102	C₂³	1	2	yes	—
200	C₁₉×#102	C₂³	1	4	yes	—
201	C₁₉×#102	C₂³	1	4	yes	—
202	C₁₉×#102	C₂³	1	2	yes	—
203	C₁₉×#102	C₂³	1	4	yes	—
204	C₁₉×#102	C₂³	1	2	yes	—
205	C₁₉×#102	C₂³	1	2	yes	—
206	C₁₉×#102	C₂³	1	2	yes	—
207	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
208	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
209	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
213	C₂⁴×C₁₉	—	2	4	no	—
214	#41×C₁₉	—	4	2	no	—
215	#41×C₁₉	—	4	2	no	—
216	#41×C₁₉	—	4	4	no	—
217	#41×C₁₉	—	4	4	no	—
218	#41×C₁₉	—	8	2	no	—
219	#41×C₁₉	—	8	2	no	—
220	#41×C₁₉	—	8	2	no	—
221	#41×C₁₉	—	8	4	no	—
222	C₂×Q₈×C₁₉	—	2	1	no	—
223	C₂×Q₈×C₁₉	—	2	1	no	—
224	C₂×Q₈×C₁₉	—	2	1	no	—
225	C₂×Q₈×C₁₉	—	2	1	no	—
226	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
228	C₂×D₄×C₁₉	—	2	4	no	—
229	C₂×D₄×C₁₉	—	2	4	no	—
230	C₂×D₄×C₁₉	—	2	2	no	—
231	C₂×D₄×C₁₉	—	2	2	no	—
232	C₂×D₄×C₁₉	—	2	2	no	—
233	C₂×D₄×C₁₉	—	2	4	no	—
234	C₂×D₄×C₁₉	—	2	4	no	—
235	C₂×D₄×C₁₉	—	2	1	no	—
236	C₂×D₄×C₁₉	—	2	1	no	—
237	C₂×D₄×C₁₉	—	2	1	no	—
238	C₂×D₄×C₁₉	—	2	1	no	—
239	C₂×D₄×C₁₉	—	2	1	no	—
240	C₂×D₄×C₁₉	—	2	4	no	—
241	C₂×D₄×C₁₉	—	2	1	no	—
242	C₂×D₄×C₁₉	—	4	4	no	—
243	C₂×D₄×C₁₉	—	4	4	no	—
244	C₂×D₄×C₁₉	—	8	4	no	—
245	C₂×D₄×C₁₉	—	8	4	no	—
246	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
247	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
248	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
250	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
251	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
252	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₉	—	2	4	no	—
254	C₂²×C₄×C₁₉	—	2	2	no	—
255	C₂²×C₄×C₁₉	—	2	2	no	—
256	C₂²×C₄×C₁₉	—	2	2	no	—
257	C₂²×C₄×C₁₉	—	2	4	no	—
258	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
262	SD₁₆×C₁₉	—	2	4	no	—
263	SD₁₆×C₁₉	—	4	2	no	—
264	SD₁₆×C₁₉	—	4	4	no	—
265	D₈×C₁₉	—	2	4	no	—
266	D₈×C₁₉	—	4	2	no	—
267	D₈×C₁₉	—	4	4	no	—
268	M₁₆×C₁₉	—	2	8	no	—
269	M₁₆×C₁₉	—	4	2	no	—
270	C₂×C₈×C₁₉	—	2	2	no	—
271	C₂×C₈×C₁₉	—	4	1	no	—
272	C₂×C₈×C₁₉	—	4	4	no	—
273	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
274	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
275	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
276	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
277	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
278	C₄⋊C₄×C₁₉	—	2	1	no	—
279	C₄⋊C₄×C₁₉	—	2	4	no	—
280	C₄⋊C₄×C₁₉	—	2	4	no	—
281	C₄⋊C₄×C₁₉	—	2	1	no	—
282	C₄⋊C₄×C₁₉	—	2	1	no	—
283	C₄⋊C₄×C₁₉	—	2	1	no	—
284	C₄⋊C₄×C₁₉	—	2	1	no	—
285	C₄⋊C₄×C₁₉	—	2	1	no	—
286	C₄⋊C₄×C₁₉	—	2	2	no	—
287	C₄⋊C₄×C₁₉	—	2	2	no	—
288	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
289	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
290	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
291	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
292	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
293	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
294	C₂²⋊C₄×C₁₉	—	2	2	no	—
295	C₂²⋊C₄×C₁₉	—	2	4	no	—
296	C₂²⋊C₄×C₁₉	—	2	4	no	—
297	C₂²⋊C₄×C₁₉	—	2	4	no	—
298	C₂²⋊C₄×C₁₉	—	2	4	no	—
299	C₂²⋊C₄×C₁₉	—	2	2	no	—
300	C₂²⋊C₄×C₁₉	—	2	2	no	—
301	C₂²⋊C₄×C₁₉	—	2	4	no	—
302	C₂²⋊C₄×C₁₉	—	2	2	no	—
303	C₂²⋊C₄×C₁₉	—	2	2	no	—
304	C₂²⋊C₄×C₁₉	—	2	2	no	—
305	C₂²⋊C₄×C₁₉	—	2	2	no	—
306	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
307	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
308	C₄²×C₁₉	—	2	4	no	—
309	C₄²×C₁₉	—	2	2	no	—
310	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
313	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
314	#62342	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂³×C₁₉	—	2	2	no	—
316	C₂³×C₁₉	—	2	2	no	—
317	C₂³×C₁₉	—	2	2	no	—
318	C₂³×C₁₉	—	8	4	no	—
319	C₂³×C₁₉	—	8	4	no	—
320	C₂³×C₁₉	—	8	4	no	—
321	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
322	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
323	Q₈×C₁₉	—	2	2	no	—
324	Q₈×C₁₉	—	2	2	no	—
325	Q₈×C₁₉	—	4	2	no	—
326	Q₈×C₁₉	—	4	2	no	—
327	Q₈×C₁₉	—	8	1	no	—
328	Q₈×C₁₉	—	8	1	no	—
329	Q₈×C₁₉	—	8	1	no	—
330	D₄×C₁₉	—	2	4	no	—
331	D₄×C₁₉	—	2	4	no	—
332	D₄×C₁₉	—	2	2	no	—
333	D₄×C₁₉	—	2	2	no	—
334	D₄×C₁₉	—	2	2	no	—
335	D₄×C₁₉	—	2	2	no	—
336	D₄×C₁₉	—	2	2	no	—
337	D₄×C₁₉	—	2	2	no	—
338	D₄×C₁₉	—	4	4	no	—
339	D₄×C₁₉	—	4	2	no	—
340	D₄×C₁₉	—	4	2	no	—
341	D₄×C₁₉	—	4	2	no	—
342	D₄×C₁₉	—	4	2	no	—
343	D₄×C₁₉	—	8	4	no	—
344	D₄×C₁₉	—	8	1	no	—
345	D₄×C₁₉	—	8	1	no	—
346	D₄×C₁₉	—	8	1	no	—
347	D₄×C₁₉	—	8	4	no	—
348	D₄×C₁₉	—	8	4	no	—
349	D₄×C₁₉	—	8	4	no	—
350	D₄×C₁₉	—	8	2	no	—
351	D₄×C₁₉	—	8	2	no	—
352	D₄×C₁₉	—	8	4	no	—
353	D₄×C₁₉	—	8	2	no	—
354	C₂×C₄×C₁₉	—	2	2	no	—
355	C₂×C₄×C₁₉	—	2	2	no	—
356	C₂×C₄×C₁₉	—	2	1	no	—
357	C₂×C₄×C₁₉	—	2	4	no	—
358	C₂×C₄×C₁₉	—	2	1	no	—
359	C₂×C₄×C₁₉	—	2	4	no	—
360	C₂×C₄×C₁₉	—	2	2	no	—
361	C₂×C₄×C₁₉	—	2	2	no	—
362	C₂×C₄×C₁₉	—	2	2	no	—
363	C₂×C₄×C₁₉	—	2	2	no	—
364	C₂×C₄×C₁₉	—	2	2	no	—
365	C₂×C₄×C₁₉	—	4	4	no	—
366	C₂×C₄×C₁₉	—	4	4	no	—
367	C₂×C₄×C₁₉	—	4	4	no	—
368	C₂×C₄×C₁₉	—	8	4	no	—
369	C₂×C₄×C₁₉	—	8	4	no	—
370	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
371	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
377	C₈×C₁₉	—	2	1	no	—
378	C₈×C₁₉	—	2	4	no	—
379	C₈×C₁₉	—	2	1	no	—
380	C₈×C₁₉	—	2	1	no	—
381	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
382	#3549	C₂×C₁₉	1	1	yes	characteristic, complemented
383	#3548	C₂×C₁₉	1	1	yes	characteristic, complemented
384	#3357	C₂×C₁₉	1	2	yes	complemented
385	#3354	C₂×C₁₉	1	2	yes	complemented
386	#3305	C₂×C₁₉	1	2	yes	complemented
387	#3303	C₂×C₁₉	1	2	yes	complemented
388	#3295	C₂×C₁₉	1	2	yes	complemented
389	#3294	C₂×C₁₉	1	2	yes	complemented
390	#3274	C₂×C₁₉	1	2	yes	complemented
391	#3272	C₂×C₁₉	1	2	yes	complemented
392	#3254	C₂×C₁₉	1	1	yes	characteristic, complemented
393	#3253	C₂×C₁₉	1	1	yes	characteristic, complemented
394	#3198	C₂×C₁₉	1	4	yes	complemented
395	#3169	C₂×C₁₉	1	1	yes	characteristic, complemented
396	#3167	C₂×C₁₉	1	1	yes	characteristic, complemented
397	#3062	C₂×C₁₉	1	4	yes	complemented
398	#2931	C₂×C₁₉	1	1	yes	characteristic, complemented
399	C₂²×C₁₉	—	2	1	no	—
400	C₂²×C₁₉	—	2	4	no	—
401	C₂²×C₁₉	—	2	1	no	—
402	C₂²×C₁₉	—	2	4	no	—
403	C₂²×C₁₉	—	2	1	no	—
404	C₂²×C₁₉	—	2	4	no	—
405	C₂²×C₁₉	—	4	2	no	—
406	C₂²×C₁₉	—	4	2	no	—
407	C₂²×C₁₉	—	4	2	no	—
408	C₂²×C₁₉	—	4	2	no	—
409	C₂²×C₁₉	—	4	2	no	—
410	C₂²×C₁₉	—	4	2	no	—
411	C₂²×C₁₉	—	4	2	no	—
412	C₂²×C₁₉	—	4	2	no	—
413	C₂²×C₁₉	—	4	2	no	—
414	C₂²×C₁₉	—	16	8	no	—
415	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
416	C₄×C₁₉	—	2	4	no	—
417	C₄×C₁₉	—	2	1	no	—
418	C₄×C₁₉	—	2	1	no	—
419	C₄×C₁₉	—	2	1	no	—
420	C₄×C₁₉	—	4	2	no	—
421	C₄×C₁₉	—	4	2	no	—
422	C₄×C₁₉	—	4	2	no	—
423	C₄×C₁₉	—	4	2	no	—
424	C₄×C₁₉	—	4	2	no	—
425	C₄×C₁₉	#576	1	2	yes	—
426	C₄×C₁₉	#577	1	2	yes	—
427	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
428	C₄×C₁₉	#585	1	1	yes	characteristic
429	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	complemented
430	C₂×#131	C₂²×C₁₉	1	2	yes	complemented
431	#562	—	2	2	no	—
432	H(3,𝔽₄)	—	2	2	no	—
433	#555	—	2	1	no	—
434	#555	C₂²×C₁₉	1	2	yes	—
435	#555	C₂²×C₁₉	1	2	yes	—
436	#554	—	2	1	no	—
437	#554	C₂²×C₁₉	1	2	yes	complemented
438	#550	—	2	1	no	—
439	#550	C₂²×C₁₉	1	2	yes	complemented
440	#547	C₂²×C₁₉	1	2	yes	complemented
441	#547	C₂²×C₁₉	1	2	yes	complemented
442	D₄²	—	2	1	no	—
443	D₄²	C₂²×C₁₉	1	2	yes	—
444	D₄²	C₂²×C₁₉	1	2	yes	—
445	#540	—	2	2	no	—
446	#537	—	2	2	no	—
447	#537	C₂²×C₁₉	1	4	yes	complemented
448	#535	—	2	2	no	—
449	#535	—	2	2	no	—
450	#535	C₂²×C₁₉	1	4	yes	—
451	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
452	#532	C₂²×C₁₉	1	1	yes	characteristic
453	#532	C₂²×C₁₉	1	1	yes	characteristic
454	#532	C₂²×C₁₉	1	1	yes	characteristic
455	#532	C₂²×C₁₉	1	1	yes	characteristic, complemented
456	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
457	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
458	#493	C₂²×C₁₉	1	1	yes	characteristic
459	#492	C₂²×C₁₉	1	1	yes	characteristic
460	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
461	#486	C₂²×C₁₉	1	1	yes	characteristic
462	#486	C₂²×C₁₉	1	1	yes	characteristic
463	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
464	#485	C₂²×C₁₉	1	4	yes	complemented
465	#482	C₂²×C₁₉	1	4	yes	complemented
466	#481	C₂²×C₁₉	1	4	yes	complemented
467	#480	C₂²×C₁₉	1	4	yes	complemented
468	#477	C₂²×C₁₉	1	2	yes	complemented
469	#476	C₂²×C₁₉	1	2	yes	complemented
470	#476	C₂²×C₁₉	1	2	yes	complemented
471	#474	C₂²×C₁₉	1	2	yes	complemented
472	#469	C₂²×C₁₉	1	4	yes	complemented
473	#469	C₂²×C₁₉	1	4	yes	complemented
474	#468	C₂²×C₁₉	1	4	yes	complemented
475	#468	C₂²×C₁₉	1	4	yes	complemented
476	#466	C₂²×C₁₉	1	2	yes	complemented
477	#466	C₂²×C₁₉	1	2	yes	complemented
478	#466	C₂²×C₁₉	1	4	yes	complemented
479	#465	C₂²×C₁₉	1	2	yes	complemented
480	#465	C₂²×C₁₉	1	2	yes	complemented
481	#465	C₂²×C₁₉	1	4	yes	complemented
482	#461	C₂²×C₁₉	1	2	yes	complemented
483	#460	C₂²×C₁₉	1	2	yes	—
484	#459	C₂²×C₁₉	1	2	yes	—
485	#459	C₂²×C₁₉	1	2	yes	complemented
486	#450	C₂²×C₁₉	1	4	yes	complemented
487	#449	C₂²×C₁₉	1	4	yes	complemented
488	#449	C₂²×C₁₉	1	4	yes	complemented
489	#447	C₂²×C₁₉	1	4	yes	complemented
490	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
491	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
492	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
493	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
494	#436	C₂²×C₁₉	1	2	yes	complemented
495	#436	C₂²×C₁₉	1	2	yes	complemented
496	C₈×D₄	C₂²×C₁₉	1	2	yes	complemented
497	C₈×D₄	C₂²×C₁₉	1	2	yes	complemented
498	#428	C₂²×C₁₉	1	4	yes	complemented
499	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
500	#416	C₂²×C₁₉	1	4	yes	complemented
501	C₂×#102	C₂²×C₁₉	1	4	yes	complemented
502	#408	C₂²×C₁₉	1	2	yes	complemented
503	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
504	C₂×C₁₉	—	4	1	no	—
505	C₂×C₁₉	—	4	4	no	—
506	C₂×C₁₉	—	8	2	no	—
507	C₂×C₁₉	—	8	2	no	—
508	C₂×C₁₉	—	8	2	no	—
509	C₂×C₁₉	#3496	1	1	yes	characteristic
510	C₂×C₁₉	C₂×#576	1	1	yes	characteristic
511	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
512	C₂×#41	—	2	2	no	—
513	C₂×#41	—	2	1	no	—
514	C₂×#41	—	2	1	no	—
515	C₂×#41	—	2	1	no	—
516	C₂×#41	C₂³×C₁₉	1	4	yes	—
517	C₂×#41	C₂³×C₁₉	1	2	yes	—
518	C₂²×D₄	—	2	2	no	—
519	C₂²×D₄	—	2	2	no	—
520	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
521	AGL(1,ℤ/8)	—	4	8	no	—
522	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
523	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
524	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
525	C₂×D₈	C₂³×C₁₉	1	2	yes	—
526	C₂×D₈	C₂³×C₁₉	1	4	yes	—
527	C₂×D₈	C₂³×C₁₉	1	2	yes	—
528	#131	—	4	4	no	—
529	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
530	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
531	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
532	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
533	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
534	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
535	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
536	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
537	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
538	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
539	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
540	#127	—	2	4	no	—
541	#127	—	2	2	no	—
542	#127	D₄×C₁₉	1	1	yes	characteristic
543	#127	C₂³×C₁₉	1	1	yes	characteristic
544	#127	C₂³×C₁₉	1	1	yes	characteristic
545	#127	C₂³×C₁₉	1	1	yes	characteristic
546	#125	—	2	2	no	—
547	#125	—	2	1	no	—
548	#124	—	2	4	no	—
549	#124	—	2	4	no	—
550	#124	—	2	4	no	—
551	#124	—	2	1	no	—
552	#124	—	2	1	no	—
553	#124	—	2	1	no	—
554	#124	D₄×C₁₉	1	2	yes	—
555	#123	—	2	4	no	—
556	#123	—	2	4	no	—
557	C₂²⋊Q₈	—	2	4	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	4	no	—
561	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
562	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
563	#121	—	2	2	no	—
564	#121	—	2	2	no	—
565	#121	—	2	4	no	—
566	#121	—	2	4	no	—
567	#121	—	2	2	no	—
568	#121	—	2	4	no	—
569	#121	—	2	1	no	—
570	#121	—	2	1	no	—
571	#121	—	2	1	no	—
572	#121	—	2	2	no	—
573	#121	—	2	2	no	—
574	#121	—	2	4	no	—
575	#121	D₄×C₁₉	1	2	yes	—
576	#121	D₄×C₁₉	1	2	yes	—
577	#121	C₂³×C₁₉	1	2	yes	—
578	#121	C₂³×C₁₉	1	2	yes	—
579	#121	C₂³×C₁₉	1	2	yes	—
580	#121	C₂³×C₁₉	1	4	yes	—
581	#121	C₂³×C₁₉	1	4	yes	—
582	#121	C₂³×C₁₉	1	4	yes	—
583	#120	—	2	4	no	—
584	#120	—	2	4	no	—
585	#120	—	2	4	no	—
586	#120	—	2	4	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	C₂³×C₁₉	1	2	yes	—
595	C₄×D₄	C₂³×C₁₉	1	2	yes	—
596	C₄×D₄	C₂³×C₁₉	1	2	yes	—
597	C₄×D₄	C₂³×C₁₉	1	2	yes	—
598	C₄×D₄	C₂³×C₁₉	1	2	yes	—
599	#117	—	2	1	no	—
600	#117	—	2	2	no	—
601	#117	—	2	2	no	—
602	#117	C₂³×C₁₉	1	4	yes	—
603	C₂×C₄⋊C₄	—	2	2	no	—
604	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
605	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
606	#107	C₂³×C₁₉	1	2	yes	—
607	#107	C₂³×C₁₉	1	4	yes	—
608	#107	C₂³×C₁₉	1	2	yes	—
609	#106	C₂³×C₁₉	1	2	yes	—
610	#106	C₂³×C₁₉	1	4	yes	—
611	#106	C₂³×C₁₉	1	2	yes	—
612	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
613	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
614	#103	C₂³×C₁₉	1	2	yes	—
615	#103	C₂³×C₁₉	1	4	yes	—
616	#103	C₂³×C₁₉	1	2	yes	—
617	#102	C₂³×C₁₉	1	2	yes	—
618	#102	C₂³×C₁₉	1	2	yes	—
619	#102	C₂³×C₁₉	1	4	yes	—
620	#102	C₂³×C₁₉	1	4	yes	—
621	#102	C₂³×C₁₉	1	2	yes	—
622	#102	C₂³×C₁₉	1	4	yes	—
623	#102	C₂³×C₁₉	1	2	yes	—
624	#102	C₂³×C₁₉	1	2	yes	—
625	#102	C₂³×C₁₉	1	2	yes	—
626	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
627	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
628	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
629	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
630	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
631	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
632	C₁₉	#62342	1	1	yes	characteristic, direct product factor, Sylow
633	C₂⁴	—	2	4	no	—
634	#41	—	4	2	no	—
635	#41	—	4	2	no	—
636	#41	—	4	4	no	—
637	#41	—	4	4	no	—
638	#41	—	8	2	no	—
639	#41	—	8	2	no	—
640	#41	—	8	2	no	—
641	#41	—	8	4	no	—
642	C₂×Q₈	—	2	1	no	—
643	C₂×Q₈	—	2	1	no	—
644	C₂×Q₈	—	2	1	no	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
647	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	4	4	no	—
663	C₂×D₄	—	4	4	no	—
664	C₂×D₄	—	8	4	no	—
665	C₂×D₄	—	8	4	no	—
666	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
667	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
668	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
669	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
670	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
671	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
672	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
681	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
682	SD₁₆	—	2	4	no	—
683	SD₁₆	—	4	2	no	—
684	SD₁₆	—	4	4	no	—
685	D₈	—	2	4	no	—
686	D₈	—	4	2	no	—
687	D₈	—	4	4	no	—
688	M₁₆	—	2	8	no	—
689	M₁₆	—	4	2	no	—
690	C₂×C₈	—	2	2	no	—
691	C₂×C₈	—	4	1	no	—
692	C₂×C₈	—	4	4	no	—
693	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
694	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
695	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
696	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
697	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
709	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
710	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
711	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
712	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
713	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
727	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
728	C₄²	—	2	4	no	—
729	C₄²	—	2	2	no	—
730	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
731	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
732	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
733	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	8	4	no	—
738	C₂³	—	8	4	no	—
739	C₂³	—	8	4	no	—
740	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
741	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
742	Q₈	—	2	2	no	—
743	Q₈	—	2	2	no	—
744	Q₈	—	4	2	no	—
745	Q₈	—	4	2	no	—
746	Q₈	—	8	1	no	—
747	Q₈	—	8	1	no	—
748	Q₈	—	8	1	no	—
749	D₄	—	2	4	no	—
750	D₄	—	2	4	no	—
751	D₄	—	2	2	no	—
752	D₄	—	2	2	no	—
753	D₄	—	2	2	no	—
754	D₄	—	2	2	no	—
755	D₄	—	2	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	4	4	no	—
758	D₄	—	4	2	no	—
759	D₄	—	4	2	no	—
760	D₄	—	4	2	no	—
761	D₄	—	4	2	no	—
762	D₄	—	8	4	no	—
763	D₄	—	8	1	no	—
764	D₄	—	8	1	no	—
765	D₄	—	8	1	no	—
766	D₄	—	8	4	no	—
767	D₄	—	8	4	no	—
768	D₄	—	8	4	no	—
769	D₄	—	8	2	no	—
770	D₄	—	8	2	no	—
771	D₄	—	8	4	no	—
772	D₄	—	8	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	4	4	no	—
787	C₂×C₄	—	8	4	no	—
788	C₂×C₄	—	8	4	no	—
789	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
790	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
795	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
796	C₈	—	2	1	no	—
797	C₈	—	2	4	no	—
798	C₈	—	2	1	no	—
799	C₈	—	2	1	no	—
800	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	4	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	4	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	16	8	no	—
817	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
818	C₄	—	2	4	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	1	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	C₁₉×#576	1	2	yes	—
828	C₄	C₁₉×#577	1	2	yes	—
829	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
830	C₄	C₁₉×#585	1	1	yes	characteristic
831	C₂	—	4	4	no	—
832	C₂	—	4	1	no	—
833	C₂	—	8	2	no	—
834	C₂	—	8	2	no	—
835	C₂	—	8	2	no	—
836	C₂	C₁₉×#3496	1	1	yes	characteristic
837	C₂	C₂×C₁₉×#576	1	1	yes	characteristic
838	C₂	C₂×C₁₉×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3549	C₂	semidirect
2. C₁₉×#3548	C₂	semidirect
3. C₁₉×#3357	C₂	semidirect
4. C₁₉×#3354	C₂	semidirect
5. C₁₉×#3305	C₂	semidirect
6. C₁₉×#3303	C₂	semidirect
7. C₁₉×#3295	C₂	semidirect
8. C₁₉×#3294	C₂	semidirect
9. C₁₉×#3274	C₂	semidirect
10. C₁₉×#3272	C₂	semidirect
11. C₁₉×#3254	C₂	semidirect
12. C₁₉×#3253	C₂	semidirect
13. C₁₉×#3198	C₂	semidirect
14. C₁₉×#3169	C₂	semidirect
15. C₁₉×#3167	C₂	semidirect
16. C₁₉×#3062	C₂	semidirect
17. C₁₉×#2931	C₂	semidirect
18. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
19. C₂×C₁₉×#131	C₂²	semidirect
26. C₁₉×#554	C₂²	semidirect
28. C₁₉×#550	C₂²	semidirect
29. C₁₉×#547	C₂²	semidirect
30. C₁₉×#547	C₂²	semidirect
36. C₁₉×#537	C₂²	semidirect
40. C₁₉×#533	C₂²	semidirect
44. C₁₉×#532	C₂²	semidirect
45. C₁₉×#500	C₂²	semidirect
46. C₁₉×#498	C₂²	semidirect
49. C₁₉×#487	C₂²	semidirect
52. C₁₉×#486	C₂²	semidirect
53. C₁₉×#485	C₂²	semidirect
54. C₁₉×#482	C₂²	semidirect
55. C₁₉×#481	C₂²	semidirect
56. C₁₉×#480	C₂²	semidirect
57. C₁₉×#477	C₂²	semidirect
58. C₁₉×#476	C₂²	semidirect
59. C₁₉×#476	C₂²	semidirect
60. C₁₉×#474	C₂²	semidirect
61. C₁₉×#469	C₂²	semidirect
62. C₁₉×#469	C₂²	semidirect
63. C₁₉×#468	C₂²	semidirect
64. C₁₉×#468	C₂²	semidirect
65. C₁₉×#466	C₂²	semidirect
66. C₁₉×#466	C₂²	semidirect
67. C₁₉×#466	C₂²	semidirect
68. C₁₉×#465	C₂²	semidirect
69. C₁₉×#465	C₂²	semidirect
70. C₁₉×#465	C₂²	semidirect
71. C₁₉×#461	C₂²	semidirect
74. C₁₉×#459	C₂²	semidirect
75. C₁₉×#450	C₂²	semidirect
76. C₁₉×#449	C₂²	semidirect
77. C₁₉×#449	C₂²	semidirect
78. C₁₉×#447	C₂²	semidirect
79. C₄×SD₁₆×C₁₉	C₂²	semidirect
80. C₄×SD₁₆×C₁₉	C₂²	semidirect
81. C₄×D₈×C₁₉	C₂²	semidirect
82. C₄×D₈×C₁₉	C₂²	semidirect
83. C₁₉×#436	C₂²	semidirect
84. C₁₉×#436	C₂²	semidirect
85. C₈×D₄×C₁₉	C₂²	semidirect
86. C₈×D₄×C₁₉	C₂²	semidirect
87. C₁₉×#428	C₂²	semidirect
88. C₁₉×#423	C₂²	semidirect
89. C₁₉×#416	C₂²	semidirect
90. C₂×C₁₉×#102	C₂²	semidirect
91. C₁₉×#408	C₂²	semidirect
92. C₂×C₄×C₈×C₁₉	C₂²	semidirect
314. #62342	C₁₉	direct (N × H)
382. #3549	C₂×C₁₉	semidirect
383. #3548	C₂×C₁₉	semidirect
384. #3357	C₂×C₁₉	semidirect
385. #3354	C₂×C₁₉	semidirect
386. #3305	C₂×C₁₉	semidirect
387. #3303	C₂×C₁₉	semidirect
388. #3295	C₂×C₁₉	semidirect
389. #3294	C₂×C₁₉	semidirect
390. #3274	C₂×C₁₉	semidirect
391. #3272	C₂×C₁₉	semidirect
392. #3254	C₂×C₁₉	semidirect
393. #3253	C₂×C₁₉	semidirect
394. #3198	C₂×C₁₉	semidirect
395. #3169	C₂×C₁₉	semidirect
396. #3167	C₂×C₁₉	semidirect
397. #3062	C₂×C₁₉	semidirect
398. #2931	C₂×C₁₉	semidirect
429. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
430. C₂×#131	C₂²×C₁₉	semidirect
437. #554	C₂²×C₁₉	semidirect
439. #550	C₂²×C₁₉	semidirect
440. #547	C₂²×C₁₉	semidirect
441. #547	C₂²×C₁₉	semidirect
447. #537	C₂²×C₁₉	semidirect
451. #533	C₂²×C₁₉	semidirect
455. #532	C₂²×C₁₉	semidirect
456. #500	C₂²×C₁₉	semidirect
457. #498	C₂²×C₁₉	semidirect
460. #487	C₂²×C₁₉	semidirect
463. #486	C₂²×C₁₉	semidirect
464. #485	C₂²×C₁₉	semidirect
465. #482	C₂²×C₁₉	semidirect
466. #481	C₂²×C₁₉	semidirect
467. #480	C₂²×C₁₉	semidirect
468. #477	C₂²×C₁₉	semidirect
469. #476	C₂²×C₁₉	semidirect
470. #476	C₂²×C₁₉	semidirect
471. #474	C₂²×C₁₉	semidirect
472. #469	C₂²×C₁₉	semidirect
473. #469	C₂²×C₁₉	semidirect
474. #468	C₂²×C₁₉	semidirect
475. #468	C₂²×C₁₉	semidirect
476. #466	C₂²×C₁₉	semidirect
477. #466	C₂²×C₁₉	semidirect
478. #466	C₂²×C₁₉	semidirect
479. #465	C₂²×C₁₉	semidirect
480. #465	C₂²×C₁₉	semidirect
481. #465	C₂²×C₁₉	semidirect
482. #461	C₂²×C₁₉	semidirect
485. #459	C₂²×C₁₉	semidirect
486. #450	C₂²×C₁₉	semidirect
487. #449	C₂²×C₁₉	semidirect
488. #449	C₂²×C₁₉	semidirect
489. #447	C₂²×C₁₉	semidirect
490. C₄×SD₁₆	C₂²×C₁₉	semidirect
491. C₄×SD₁₆	C₂²×C₁₉	semidirect
492. C₄×D₈	C₂²×C₁₉	semidirect
493. C₄×D₈	C₂²×C₁₉	semidirect
494. #436	C₂²×C₁₉	semidirect
495. #436	C₂²×C₁₉	semidirect
496. C₈×D₄	C₂²×C₁₉	semidirect
497. C₈×D₄	C₂²×C₁₉	semidirect
498. #428	C₂²×C₁₉	semidirect
499. #423	C₂²×C₁₉	semidirect
500. #416	C₂²×C₁₉	semidirect
501. C₂×#102	C₂²×C₁₉	semidirect
502. #408	C₂²×C₁₉	semidirect
503. C₂×C₄×C₈	C₂²×C₁₉	semidirect
632. C₁₉	#62342	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3549	2
C₁₉×#3548	2
C₁₉×#3357	2
C₁₉×#3354	2
C₁₉×#3305	2
C₁₉×#3303	2
C₁₉×#3295	2
C₁₉×#3294	2
C₁₉×#3274	2
C₁₉×#3272	2
C₁₉×#3254	2
C₁₉×#3253	2
C₁₉×#3198	2
C₁₉×#3169	2
C₁₉×#3167	2
C₁₉×#3062	2
C₁₉×#2931	2
#62342	19

Subgroups — C19×#62342 #18068301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62342 #18068301