Subgroups — C₁₉×#24474 #18030433

Order 4864.

1298 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3586	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3069	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3039	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3022	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#456	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2901	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2050	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2049	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2009	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2005	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1906	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1902	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1902	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1861	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1796	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#585	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
18	C₁₉×#578	—	2	2	no	—
19	C₁₉×#578	—	2	2	no	—
20	C₁₉×#577	—	2	2	no	—
21	C₁₉×#577	—	2	2	no	—
22	C₁₉×#575	—	2	2	no	—
23	C₁₉×#575	C₂²	1	1	yes	characteristic
24	C₁₉×#575	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#137	—	2	2	no	—
26	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#568	C₂²	1	1	yes	characteristic
32	C₁₉×#568	C₂²	1	1	yes	characteristic
33	C₁₉×#536	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#473	—	2	2	no	—
37	C₁₉×#471	—	2	2	no	—
38	C₁₉×#462	—	2	2	no	—
39	C₁₉×#461	—	2	2	no	—
40	C₁₉×#456	—	2	2	no	—
41	C₁₉×#456	—	2	2	no	—
42	C₁₉×#456	—	2	2	no	—
43	C₁₉×#455	—	2	2	no	—
44	C₁₉×#430	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#421	—	2	2	no	—
47	C₁₉×#421	C₂²	1	1	yes	characteristic
48	C₁₉×#421	C₂²	1	1	yes	characteristic
49	C₁₉×#421	C₂²	1	1	yes	characteristic
50	C₁₉×#421	C₂²	1	1	yes	characteristic
51	C₂×C₁₉×#104	—	2	2	no	—
52	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×#419	C₂²	1	1	yes	characteristic, complemented
56	C₁₉×#419	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#419	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#413	C₂²	1	1	yes	characteristic
59	C₁₉×#413	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#410	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#344	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#344	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#338	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×2₋¹⁺⁴	—	2	2	no	—
68	C₁₉×2₋¹⁺⁴	—	2	2	no	—
69	C₁₉×2₋¹⁺⁴	—	2	1	no	—
70	C₁₉×2₋¹⁺⁴	—	2	1	no	—
71	C₁₉×2₋¹⁺⁴	—	2	2	no	—
72	C₁₉×2₋¹⁺⁴	—	4	1	no	—
73	C₁₉×2₋¹⁺⁴	D₄	1	2	yes	—
74	C₁₉×H(5,𝔽₂)	—	2	1	no	—
75	C₁₉×H(5,𝔽₂)	—	2	1	no	—
76	C₁₉×H(5,𝔽₂)	—	4	1	no	—
77	C₁₉×H(5,𝔽₂)	D₄	1	2	yes	—
78	C₂×#41×C₁₉	—	2	2	no	—
79	C₂×#41×C₁₉	—	2	2	no	—
80	C₂×#41×C₁₉	—	2	1	no	—
81	C₂×#41×C₁₉	—	2	1	no	—
82	C₂×#41×C₁₉	—	4	1	no	—
83	C₂×#41×C₁₉	—	4	1	no	—
84	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₉	—	2	1	no	—
89	C₂²×Q₈×C₁₉	—	2	1	no	—
90	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₁₉×#137	—	2	4	no	—
93	C₁₉×#137	—	2	4	no	—
94	C₁₉×#137	—	2	4	no	—
95	C₁₉×#137	—	2	2	no	—
96	C₁₉×#137	—	2	2	no	—
97	C₁₉×#137	—	2	1	no	—
98	C₁₉×#137	—	2	2	no	—
99	C₁₉×#137	—	2	1	no	—
100	C₁₉×#137	—	2	1	no	—
101	C₁₉×#137	—	2	2	no	—
102	C₁₉×#137	—	2	2	no	—
103	C₁₉×#137	—	2	2	no	—
104	C₁₉×#137	—	2	2	no	—
105	C₁₉×#137	—	2	2	no	—
106	C₁₉×#137	—	2	2	no	—
107	C₁₉×#137	—	4	1	no	—
108	C₁₉×#137	D₄	1	2	yes	—
109	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
110	C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
111	C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
112	C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
113	C₁₉×AGL(1,ℤ/8)	D₄	1	2	yes	—
114	C₁₉×#135	—	2	4	no	—
115	C₁₉×#135	—	2	4	no	—
116	C₁₉×#135	—	2	2	no	—
117	C₁₉×#135	—	2	2	no	—
118	C₂×Q₁₆×C₁₉	—	2	4	no	—
119	C₂×Q₁₆×C₁₉	—	2	1	no	—
120	C₂×Q₁₆×C₁₉	—	2	1	no	—
121	C₂×Q₁₆×C₁₉	—	2	1	no	—
122	C₂×Q₁₆×C₁₉	—	2	1	no	—
123	C₂×Q₁₆×C₁₉	D₄	1	2	yes	—
124	C₂×SD₁₆×C₁₉	—	2	4	no	—
125	C₂×SD₁₆×C₁₉	—	2	1	no	—
126	C₂×SD₁₆×C₁₉	—	2	1	no	—
127	C₂×SD₁₆×C₁₉	—	2	1	no	—
128	C₂×SD₁₆×C₁₉	—	2	1	no	—
129	C₂×SD₁₆×C₁₉	D₄	1	2	yes	—
130	C₁₉×#131	—	2	2	no	—
131	C₁₉×#131	—	2	2	no	—
132	C₁₉×#131	—	2	2	no	—
133	C₁₉×#131	—	4	1	no	—
134	C₂×M₁₆×C₁₉	—	2	2	no	—
135	C₂×M₁₆×C₁₉	—	2	2	no	—
136	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
142	C₁₉×C₄⋊Q₈	—	2	1	no	—
143	C₁₉×C₄⋊Q₈	—	2	2	no	—
144	C₁₉×C₄⋊Q₈	—	2	1	no	—
145	C₁₉×C₄⋊Q₈	—	2	1	no	—
146	C₁₉×#124	—	2	1	no	—
147	C₁₉×#123	—	4	1	no	—
148	C₁₉×C₂²⋊Q₈	—	4	1	no	—
149	C₄×Q₈×C₁₉	—	2	1	no	—
150	C₄×D₄×C₁₉	—	2	1	no	—
151	C₄×D₄×C₁₉	—	4	1	no	—
152	C₁₉×#117	—	2	1	no	—
153	C₁₉×#117	C₂³	1	1	yes	characteristic
154	C₁₉×#117	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
156	C₂×C₄²×C₁₉	—	2	1	no	—
157	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
158	C₁₉×#108	—	2	2	no	—
159	C₁₉×C₄⋊C₈	—	2	2	no	—
160	C₁₉×#104	—	2	2	no	—
161	C₁₉×#104	—	2	2	no	—
162	C₁₉×#104	—	2	2	no	—
163	C₁₉×#104	—	2	2	no	—
164	C₁₉×#104	—	2	1	no	—
165	C₁₉×#104	—	2	1	no	—
166	C₁₉×#104	—	2	1	no	—
167	C₁₉×#104	—	2	1	no	—
168	C₁₉×#104	D₄	1	2	yes	—
169	C₁₉×#104	D₄	1	2	yes	—
170	C₁₉×#103	—	2	2	no	—
171	C₁₉×#103	—	2	2	no	—
172	C₁₉×#103	—	4	1	no	—
173	C₁₉×#101	—	2	1	no	—
174	C₁₉×#101	—	2	1	no	—
175	C₁₉×#101	—	2	2	no	—
176	C₁₉×#101	—	2	2	no	—
177	C₁₉×#100	—	2	1	no	—
178	C₁₉×#100	—	2	1	no	—
179	C₁₉×#99	—	4	1	no	—
180	#41×C₁₉	—	2	1	no	—
181	#41×C₁₉	—	2	1	no	—
182	#41×C₁₉	—	2	1	no	—
183	#41×C₁₉	—	2	1	no	—
184	#41×C₁₉	—	2	4	no	—
185	#41×C₁₉	—	2	2	no	—
186	#41×C₁₉	—	2	2	no	—
187	#41×C₁₉	—	2	2	no	—
188	#41×C₁₉	—	2	2	no	—
189	#41×C₁₉	—	2	1	no	—
190	#41×C₁₉	—	2	1	no	—
191	#41×C₁₉	—	2	1	no	—
192	#41×C₁₉	—	2	1	no	—
193	#41×C₁₉	—	2	1	no	—
194	#41×C₁₉	—	2	1	no	—
195	#41×C₁₉	—	2	1	no	—
196	#41×C₁₉	—	2	1	no	—
197	#41×C₁₉	—	4	2	no	—
198	#41×C₁₉	—	4	2	no	—
199	#41×C₁₉	—	4	2	no	—
200	#41×C₁₉	—	4	2	no	—
201	#41×C₁₉	—	4	2	no	—
202	#41×C₁₉	—	4	4	no	—
203	#41×C₁₉	—	4	2	no	—
204	#41×C₁₉	—	4	1	no	—
205	#41×C₁₉	—	4	1	no	—
206	#41×C₁₉	—	4	4	no	—
207	#41×C₁₉	—	4	2	no	—
208	#41×C₁₉	C₂×D₄	1	2	yes	—
209	#41×C₁₉	C₂×D₄	1	2	yes	—
210	#41×C₁₉	C₂×D₄	1	2	yes	—
211	#41×C₁₉	C₂×D₄	1	2	yes	—
212	C₂×Q₈×C₁₉	—	2	1	no	—
213	C₂×Q₈×C₁₉	—	2	4	no	—
214	C₂×Q₈×C₁₉	—	2	2	no	—
215	C₂×Q₈×C₁₉	—	2	2	no	—
216	C₂×Q₈×C₁₉	—	2	1	no	—
217	C₂×Q₈×C₁₉	—	2	1	no	—
218	C₂×Q₈×C₁₉	—	2	1	no	—
219	C₂×Q₈×C₁₉	—	2	1	no	—
220	C₂×Q₈×C₁₉	—	2	1	no	—
221	C₂×Q₈×C₁₉	—	2	1	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	—	4	1	no	—
227	C₂×Q₈×C₁₉	—	4	2	no	—
228	C₂×Q₈×C₁₉	—	4	2	no	—
229	C₂×Q₈×C₁₉	—	4	1	no	—
230	C₂×Q₈×C₁₉	—	4	2	no	—
231	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
232	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
233	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
234	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
235	C₂×Q₈×C₁₉	#41	1	1	yes	characteristic
236	C₂×D₄×C₁₉	—	2	1	no	—
237	C₂×D₄×C₁₉	—	2	1	no	—
238	C₂×D₄×C₁₉	—	2	2	no	—
239	C₂×D₄×C₁₉	—	2	2	no	—
240	C₂×D₄×C₁₉	—	2	1	no	—
241	C₂×D₄×C₁₉	—	2	1	no	—
242	C₂×D₄×C₁₉	—	4	2	no	—
243	C₂×D₄×C₁₉	—	4	1	no	—
244	C₂×D₄×C₁₉	—	4	2	no	—
245	C₂×D₄×C₁₉	—	4	2	no	—
246	C₂×D₄×C₁₉	—	4	1	no	—
247	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
248	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
249	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
250	C₂×D₄×C₁₉	#41	1	1	yes	characteristic
251	C₂²×C₄×C₁₉	—	2	1	no	—
252	C₂²×C₄×C₁₉	—	2	1	no	—
253	C₂²×C₄×C₁₉	—	2	1	no	—
254	C₂²×C₄×C₁₉	—	2	1	no	—
255	C₂²×C₄×C₁₉	—	2	1	no	—
256	C₂²×C₄×C₁₉	—	2	1	no	—
257	C₂²×C₄×C₁₉	—	2	1	no	—
258	C₂²×C₄×C₁₉	—	4	2	no	—
259	C₂²×C₄×C₁₉	—	4	1	no	—
260	C₂²×C₄×C₁₉	—	4	1	no	—
261	C₂²×C₄×C₁₉	—	4	1	no	—
262	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
263	Q₁₆×C₁₉	—	2	4	no	—
264	Q₁₆×C₁₉	—	2	2	no	—
265	Q₁₆×C₁₉	—	2	2	no	—
266	Q₁₆×C₁₉	—	2	4	no	—
267	Q₁₆×C₁₉	—	4	2	no	—
268	Q₁₆×C₁₉	—	4	2	no	—
269	Q₁₆×C₁₉	—	4	2	no	—
270	SD₁₆×C₁₉	—	2	4	no	—
271	SD₁₆×C₁₉	—	2	2	no	—
272	SD₁₆×C₁₉	—	2	2	no	—
273	SD₁₆×C₁₉	—	2	2	no	—
274	SD₁₆×C₁₉	—	2	2	no	—
275	SD₁₆×C₁₉	—	2	4	no	—
276	SD₁₆×C₁₉	—	4	2	no	—
277	SD₁₆×C₁₉	—	4	2	no	—
278	SD₁₆×C₁₉	—	4	2	no	—
279	D₈×C₁₉	—	2	2	no	—
280	D₈×C₁₉	—	2	2	no	—
281	M₁₆×C₁₉	—	2	4	no	—
282	M₁₆×C₁₉	—	2	1	no	—
283	M₁₆×C₁₉	—	2	1	no	—
284	M₁₆×C₁₉	—	2	1	no	—
285	M₁₆×C₁₉	—	2	1	no	—
286	M₁₆×C₁₉	—	2	1	no	—
287	M₁₆×C₁₉	—	2	1	no	—
288	M₁₆×C₁₉	—	2	1	no	—
289	M₁₆×C₁₉	—	2	1	no	—
290	M₁₆×C₁₉	—	2	1	no	—
291	M₁₆×C₁₉	—	2	1	no	—
292	M₁₆×C₁₉	—	4	2	no	—
293	M₁₆×C₁₉	C₂×D₄	1	2	yes	—
294	M₁₆×C₁₉	C₂×D₄	1	2	yes	—
295	C₂×C₈×C₁₉	—	2	4	no	—
296	C₂×C₈×C₁₉	—	2	1	no	—
297	C₂×C₈×C₁₉	—	2	1	no	—
298	C₂×C₈×C₁₉	—	2	1	no	—
299	C₂×C₈×C₁₉	—	2	1	no	—
300	C₂×C₈×C₁₉	—	2	1	no	—
301	C₂×C₈×C₁₉	—	4	2	no	—
302	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₁₉	—	2	1	no	—
304	C₄⋊C₄×C₁₉	—	2	1	no	—
305	C₄⋊C₄×C₁₉	—	4	2	no	—
306	C₄⋊C₄×C₁₉	—	4	2	no	—
307	C₄⋊C₄×C₁₉	—	4	1	no	—
308	C₄⋊C₄×C₁₉	—	4	2	no	—
309	C₂²⋊C₄×C₁₉	—	2	1	no	—
310	C₂²⋊C₄×C₁₉	—	2	1	no	—
311	C₂²⋊C₄×C₁₉	—	4	1	no	—
312	C₂²⋊C₄×C₁₉	—	4	2	no	—
313	C₄²×C₁₉	—	2	1	no	—
314	C₄²×C₁₉	—	2	1	no	—
315	C₄²×C₁₉	—	2	1	no	—
316	C₄²×C₁₉	—	4	1	no	—
317	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
319	#24474	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
320	C₂³×C₁₉	—	2	1	no	—
321	C₂³×C₁₉	—	2	1	no	—
322	C₂³×C₁₉	—	2	1	no	—
323	C₂³×C₁₉	—	2	1	no	—
324	C₂³×C₁₉	—	4	2	no	—
325	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
326	Q₈×C₁₉	—	2	1	no	—
327	Q₈×C₁₉	—	2	1	no	—
328	Q₈×C₁₉	—	2	1	no	—
329	Q₈×C₁₉	—	2	2	no	—
330	Q₈×C₁₉	—	2	1	no	—
331	Q₈×C₁₉	—	2	1	no	—
332	Q₈×C₁₉	—	2	1	no	—
333	Q₈×C₁₉	—	2	2	no	—
334	Q₈×C₁₉	—	4	2	no	—
335	Q₈×C₁₉	—	4	4	no	—
336	Q₈×C₁₉	—	4	1	no	—
337	Q₈×C₁₉	—	4	1	no	—
338	Q₈×C₁₉	—	4	1	no	—
339	Q₈×C₁₉	—	4	1	no	—
340	Q₈×C₁₉	—	4	1	no	—
341	Q₈×C₁₉	—	4	1	no	—
342	Q₈×C₁₉	#120	1	2	yes	—
343	Q₈×C₁₉	#121	1	2	yes	—
344	D₄×C₁₉	—	2	2	no	—
345	D₄×C₁₉	—	2	2	no	—
346	D₄×C₁₉	—	2	2	no	—
347	D₄×C₁₉	—	2	2	no	—
348	D₄×C₁₉	—	2	1	no	—
349	D₄×C₁₉	—	2	1	no	—
350	D₄×C₁₉	—	2	1	no	—
351	D₄×C₁₉	—	2	1	no	—
352	D₄×C₁₉	—	2	1	no	—
353	D₄×C₁₉	—	2	1	no	—
354	D₄×C₁₉	—	4	2	no	—
355	D₄×C₁₉	—	4	2	no	—
356	D₄×C₁₉	—	4	2	no	—
357	D₄×C₁₉	—	4	4	no	—
358	D₄×C₁₉	—	4	1	no	—
359	D₄×C₁₉	—	4	1	no	—
360	D₄×C₁₉	—	4	1	no	—
361	D₄×C₁₉	—	4	1	no	—
362	D₄×C₁₉	#120	1	2	yes	—
363	D₄×C₁₉	#121	1	2	yes	—
364	C₂×C₄×C₁₉	—	2	1	no	—
365	C₂×C₄×C₁₉	—	2	1	no	—
366	C₂×C₄×C₁₉	—	2	1	no	—
367	C₂×C₄×C₁₉	—	2	2	no	—
368	C₂×C₄×C₁₉	—	2	2	no	—
369	C₂×C₄×C₁₉	—	2	2	no	—
370	C₂×C₄×C₁₉	—	2	2	no	—
371	C₂×C₄×C₁₉	—	2	1	no	—
372	C₂×C₄×C₁₉	—	2	1	no	—
373	C₂×C₄×C₁₉	—	2	2	no	—
374	C₂×C₄×C₁₉	—	2	1	no	—
375	C₂×C₄×C₁₉	—	4	2	no	—
376	C₂×C₄×C₁₉	—	4	2	no	—
377	C₂×C₄×C₁₉	—	4	2	no	—
378	C₂×C₄×C₁₉	—	4	2	no	—
379	C₂×C₄×C₁₉	—	4	4	no	—
380	C₂×C₄×C₁₉	—	4	4	no	—
381	C₂×C₄×C₁₉	—	4	1	no	—
382	C₂×C₄×C₁₉	—	4	1	no	—
383	C₂×C₄×C₁₉	—	4	1	no	—
384	C₂×C₄×C₁₉	—	4	1	no	—
385	C₂×C₄×C₁₉	—	4	1	no	—
386	C₂×C₄×C₁₉	—	4	1	no	—
387	C₂×C₄×C₁₉	—	4	1	no	—
388	C₂×C₄×C₁₉	—	4	1	no	—
389	C₂×C₄×C₁₉	—	4	1	no	—
390	C₂×C₄×C₁₉	—	4	1	no	—
391	C₂×C₄×C₁₉	—	4	1	no	—
392	C₂×C₄×C₁₉	—	8	2	no	—
393	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
398	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
399	C₈×C₁₉	—	2	2	no	—
400	C₈×C₁₉	—	2	2	no	—
401	C₈×C₁₉	—	2	2	no	—
402	C₈×C₁₉	—	4	1	no	—
403	C₈×C₁₉	—	4	1	no	—
404	C₈×C₁₉	—	4	1	no	—
405	#3586	C₂×C₁₉	1	1	yes	characteristic
406	#3069	C₂×C₁₉	1	1	yes	characteristic, complemented
407	#3039	C₂×C₁₉	1	1	yes	characteristic, complemented
408	#3022	C₂×C₁₉	1	1	yes	characteristic, complemented
409	C₂×#456	C₂×C₁₉	1	1	yes	characteristic, complemented
410	#2901	C₂×C₁₉	1	1	yes	characteristic, complemented
411	#2050	C₂×C₁₉	1	1	yes	characteristic, complemented
412	#2049	C₂×C₁₉	1	1	yes	characteristic, complemented
413	#2009	C₂×C₁₉	1	1	yes	characteristic, complemented
414	#2005	C₂×C₁₉	1	1	yes	characteristic, complemented
415	#1906	C₂×C₁₉	1	1	yes	characteristic, complemented
416	#1902	C₂×C₁₉	1	1	yes	characteristic, complemented
417	#1902	C₂×C₁₉	1	1	yes	characteristic, complemented
418	#1861	C₂×C₁₉	1	1	yes	characteristic, complemented
419	#1796	C₂×C₁₉	1	1	yes	characteristic, complemented
420	C₂²×C₁₉	—	2	2	no	—
421	C₂²×C₁₉	—	2	2	no	—
422	C₂²×C₁₉	—	4	1	no	—
423	C₂²×C₁₉	—	4	1	no	—
424	C₂²×C₁₉	—	4	1	no	—
425	C₂²×C₁₉	—	8	1	no	—
426	C₂²×C₁₉	—	8	1	no	—
427	C₂²×C₁₉	—	8	1	no	—
428	C₂²×C₁₉	—	8	1	no	—
429	C₂²×C₁₉	—	16	2	no	—
430	C₂²×C₁₉	#534	1	1	yes	characteristic
431	C₂²×C₁₉	D₄²	1	1	yes	characteristic
432	C₂²×C₁₉	#546	1	1	yes	characteristic
433	C₄×C₁₉	—	2	2	no	—
434	C₄×C₁₉	—	2	2	no	—
435	C₄×C₁₉	—	2	2	no	—
436	C₄×C₁₉	—	4	1	no	—
437	C₄×C₁₉	—	4	1	no	—
438	C₄×C₁₉	—	4	2	no	—
439	C₄×C₁₉	—	4	1	no	—
440	C₄×C₁₉	—	8	1	no	—
441	C₄×C₁₉	—	8	1	no	—
442	C₄×C₁₉	—	8	1	no	—
443	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
444	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
445	C₄×C₁₉	D₄²	1	1	yes	characteristic
446	C₄×C₁₉	#546	1	1	yes	characteristic
447	#585	C₂²×C₁₉	1	1	yes	characteristic
448	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic
449	#578	—	2	2	no	—
450	#578	—	2	2	no	—
451	#577	—	2	2	no	—
452	#577	—	2	2	no	—
453	#575	—	2	2	no	—
454	#575	C₂²×C₁₉	1	1	yes	characteristic
455	#575	C₂²×C₁₉	1	1	yes	characteristic
456	C₂×#137	—	2	2	no	—
457	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
458	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
459	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
460	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
461	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic, complemented
462	#568	C₂²×C₁₉	1	1	yes	characteristic
463	#568	C₂²×C₁₉	1	1	yes	characteristic
464	#536	C₂²×C₁₉	1	1	yes	characteristic
465	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
466	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
467	#473	—	2	2	no	—
468	#471	—	2	2	no	—
469	#462	—	2	2	no	—
470	#461	—	2	2	no	—
471	#456	—	2	2	no	—
472	#456	—	2	2	no	—
473	#456	—	2	2	no	—
474	#455	—	2	2	no	—
475	#430	C₂²×C₁₉	1	1	yes	characteristic, complemented
476	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
477	#421	—	2	2	no	—
478	#421	C₂²×C₁₉	1	1	yes	characteristic
479	#421	C₂²×C₁₉	1	1	yes	characteristic
480	#421	C₂²×C₁₉	1	1	yes	characteristic
481	#421	C₂²×C₁₉	1	1	yes	characteristic
482	C₂×#104	—	2	2	no	—
483	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
484	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
485	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
486	#419	C₂²×C₁₉	1	1	yes	characteristic, complemented
487	#419	C₂²×C₁₉	1	1	yes	characteristic, complemented
488	#419	C₂²×C₁₉	1	1	yes	characteristic, complemented
489	#413	C₂²×C₁₉	1	1	yes	characteristic
490	#413	C₂²×C₁₉	1	1	yes	characteristic, complemented
491	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic, complemented
492	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic, complemented
493	#410	C₂²×C₁₉	1	1	yes	characteristic, complemented
494	#344	C₂²×C₁₉	1	1	yes	characteristic, complemented
495	#344	C₂²×C₁₉	1	1	yes	characteristic, complemented
496	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
497	#338	C₂²×C₁₉	1	1	yes	characteristic, complemented
498	C₂×C₁₉	—	2	1	no	—
499	C₂×C₁₉	—	2	1	no	—
500	C₂×C₁₉	—	2	1	no	—
501	C₂×C₁₉	—	4	2	no	—
502	C₂×C₁₉	—	4	2	no	—
503	C₂×C₁₉	—	8	1	no	—
504	C₂×C₁₉	—	8	1	no	—
505	C₂×C₁₉	#2410	1	1	yes	characteristic
506	2₋¹⁺⁴	—	2	2	no	—
507	2₋¹⁺⁴	—	2	2	no	—
508	2₋¹⁺⁴	—	2	1	no	—
509	2₋¹⁺⁴	—	2	1	no	—
510	2₋¹⁺⁴	—	2	2	no	—
511	2₋¹⁺⁴	—	4	1	no	—
512	2₋¹⁺⁴	D₄×C₁₉	1	2	yes	—
513	H(5,𝔽₂)	—	2	1	no	—
514	H(5,𝔽₂)	—	2	1	no	—
515	H(5,𝔽₂)	—	4	1	no	—
516	H(5,𝔽₂)	D₄×C₁₉	1	2	yes	—
517	C₂×#41	—	2	2	no	—
518	C₂×#41	—	2	2	no	—
519	C₂×#41	—	2	1	no	—
520	C₂×#41	—	2	1	no	—
521	C₂×#41	—	4	1	no	—
522	C₂×#41	—	4	1	no	—
523	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
524	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
525	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
526	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
527	C₂²×Q₈	—	2	1	no	—
528	C₂²×Q₈	—	2	1	no	—
529	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
530	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
531	#137	—	2	4	no	—
532	#137	—	2	4	no	—
533	#137	—	2	4	no	—
534	#137	—	2	2	no	—
535	#137	—	2	2	no	—
536	#137	—	2	1	no	—
537	#137	—	2	2	no	—
538	#137	—	2	1	no	—
539	#137	—	2	1	no	—
540	#137	—	2	2	no	—
541	#137	—	2	2	no	—
542	#137	—	2	2	no	—
543	#137	—	2	2	no	—
544	#137	—	2	2	no	—
545	#137	—	2	2	no	—
546	#137	—	4	1	no	—
547	#137	D₄×C₁₉	1	2	yes	—
548	AGL(1,ℤ/8)	—	2	4	no	—
549	AGL(1,ℤ/8)	—	2	1	no	—
550	AGL(1,ℤ/8)	—	2	1	no	—
551	AGL(1,ℤ/8)	—	2	1	no	—
552	AGL(1,ℤ/8)	D₄×C₁₉	1	2	yes	—
553	#135	—	2	4	no	—
554	#135	—	2	4	no	—
555	#135	—	2	2	no	—
556	#135	—	2	2	no	—
557	C₂×Q₁₆	—	2	4	no	—
558	C₂×Q₁₆	—	2	1	no	—
559	C₂×Q₁₆	—	2	1	no	—
560	C₂×Q₁₆	—	2	1	no	—
561	C₂×Q₁₆	—	2	1	no	—
562	C₂×Q₁₆	D₄×C₁₉	1	2	yes	—
563	C₂×SD₁₆	—	2	4	no	—
564	C₂×SD₁₆	—	2	1	no	—
565	C₂×SD₁₆	—	2	1	no	—
566	C₂×SD₁₆	—	2	1	no	—
567	C₂×SD₁₆	—	2	1	no	—
568	C₂×SD₁₆	D₄×C₁₉	1	2	yes	—
569	#131	—	2	2	no	—
570	#131	—	2	2	no	—
571	#131	—	2	2	no	—
572	#131	—	4	1	no	—
573	C₂×M₁₆	—	2	2	no	—
574	C₂×M₁₆	—	2	2	no	—
575	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
576	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
577	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
578	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
579	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
580	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
581	C₄⋊Q₈	—	2	2	no	—
582	C₄⋊Q₈	—	2	1	no	—
583	C₄⋊Q₈	—	2	1	no	—
584	C₄⋊Q₈	—	2	1	no	—
585	#124	—	2	1	no	—
586	#123	—	4	1	no	—
587	C₂²⋊Q₈	—	4	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	4	1	no	—
591	#117	—	2	1	no	—
592	#117	C₂³×C₁₉	1	1	yes	characteristic
593	#117	C₂³×C₁₉	1	1	yes	characteristic
594	C₂×C₄⋊C₄	—	4	1	no	—
595	C₂×C₄²	—	2	1	no	—
596	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
597	#108	—	2	2	no	—
598	C₄⋊C₈	—	2	2	no	—
599	#104	—	2	2	no	—
600	#104	—	2	2	no	—
601	#104	—	2	2	no	—
602	#104	—	2	2	no	—
603	#104	—	2	1	no	—
604	#104	—	2	1	no	—
605	#104	—	2	1	no	—
606	#104	—	2	1	no	—
607	#104	D₄×C₁₉	1	2	yes	—
608	#104	D₄×C₁₉	1	2	yes	—
609	#103	—	2	2	no	—
610	#103	—	2	2	no	—
611	#103	—	4	1	no	—
612	#101	—	2	1	no	—
613	#101	—	2	1	no	—
614	#101	—	2	2	no	—
615	#101	—	2	2	no	—
616	#100	—	2	1	no	—
617	#100	—	2	1	no	—
618	#99	—	4	1	no	—
619	C₁₉	#24474	1	1	yes	characteristic, direct product factor, Sylow
620	#41	—	2	1	no	—
621	#41	—	2	1	no	—
622	#41	—	2	1	no	—
623	#41	—	2	1	no	—
624	#41	—	2	4	no	—
625	#41	—	2	2	no	—
626	#41	—	2	2	no	—
627	#41	—	2	2	no	—
628	#41	—	2	2	no	—
629	#41	—	2	1	no	—
630	#41	—	2	1	no	—
631	#41	—	2	1	no	—
632	#41	—	2	1	no	—
633	#41	—	2	1	no	—
634	#41	—	2	1	no	—
635	#41	—	2	1	no	—
636	#41	—	2	1	no	—
637	#41	—	4	2	no	—
638	#41	—	4	2	no	—
639	#41	—	4	2	no	—
640	#41	—	4	2	no	—
641	#41	—	4	2	no	—
642	#41	—	4	4	no	—
643	#41	—	4	2	no	—
644	#41	—	4	1	no	—
645	#41	—	4	1	no	—
646	#41	—	4	4	no	—
647	#41	—	4	2	no	—
648	#41	C₂×D₄×C₁₉	1	2	yes	—
649	#41	C₂×D₄×C₁₉	1	2	yes	—
650	#41	C₂×D₄×C₁₉	1	2	yes	—
651	#41	C₂×D₄×C₁₉	1	2	yes	—
652	C₂×Q₈	—	2	1	no	—
653	C₂×Q₈	—	2	4	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	4	1	no	—
667	C₂×Q₈	—	4	2	no	—
668	C₂×Q₈	—	4	2	no	—
669	C₂×Q₈	—	4	1	no	—
670	C₂×Q₈	—	4	2	no	—
671	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
672	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
673	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
674	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
675	C₂×Q₈	#41×C₁₉	1	1	yes	characteristic
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	4	2	no	—
683	C₂×D₄	—	4	1	no	—
684	C₂×D₄	—	4	2	no	—
685	C₂×D₄	—	4	2	no	—
686	C₂×D₄	—	4	1	no	—
687	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
688	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
689	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
690	C₂×D₄	#41×C₁₉	1	1	yes	characteristic
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	—	4	1	no	—
700	C₂²×C₄	—	4	1	no	—
701	C₂²×C₄	—	4	1	no	—
702	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
703	Q₁₆	—	2	4	no	—
704	Q₁₆	—	2	2	no	—
705	Q₁₆	—	2	2	no	—
706	Q₁₆	—	2	4	no	—
707	Q₁₆	—	4	2	no	—
708	Q₁₆	—	4	2	no	—
709	Q₁₆	—	4	2	no	—
710	SD₁₆	—	2	4	no	—
711	SD₁₆	—	2	2	no	—
712	SD₁₆	—	2	2	no	—
713	SD₁₆	—	2	2	no	—
714	SD₁₆	—	2	2	no	—
715	SD₁₆	—	2	4	no	—
716	SD₁₆	—	4	2	no	—
717	SD₁₆	—	4	2	no	—
718	SD₁₆	—	4	2	no	—
719	D₈	—	2	2	no	—
720	D₈	—	2	2	no	—
721	M₁₆	—	2	4	no	—
722	M₁₆	—	2	1	no	—
723	M₁₆	—	2	1	no	—
724	M₁₆	—	2	1	no	—
725	M₁₆	—	2	1	no	—
726	M₁₆	—	2	1	no	—
727	M₁₆	—	2	1	no	—
728	M₁₆	—	2	1	no	—
729	M₁₆	—	2	1	no	—
730	M₁₆	—	2	1	no	—
731	M₁₆	—	2	1	no	—
732	M₁₆	—	4	2	no	—
733	M₁₆	C₂×D₄×C₁₉	1	2	yes	—
734	M₁₆	C₂×D₄×C₁₉	1	2	yes	—
735	C₂×C₈	—	2	4	no	—
736	C₂×C₈	—	2	1	no	—
737	C₂×C₈	—	2	1	no	—
738	C₂×C₈	—	2	1	no	—
739	C₂×C₈	—	2	1	no	—
740	C₂×C₈	—	2	1	no	—
741	C₂×C₈	—	4	2	no	—
742	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	—	4	1	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	4	1	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₄²	—	2	1	no	—
754	C₄²	—	2	1	no	—
755	C₄²	—	2	1	no	—
756	C₄²	—	4	1	no	—
757	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
758	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	2	1	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	4	2	no	—
764	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
765	Q₈	—	2	1	no	—
766	Q₈	—	2	1	no	—
767	Q₈	—	2	1	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	2	1	no	—
770	Q₈	—	2	1	no	—
771	Q₈	—	2	1	no	—
772	Q₈	—	2	2	no	—
773	Q₈	—	4	2	no	—
774	Q₈	—	4	4	no	—
775	Q₈	—	4	1	no	—
776	Q₈	—	4	1	no	—
777	Q₈	—	4	1	no	—
778	Q₈	—	4	1	no	—
779	Q₈	—	4	1	no	—
780	Q₈	—	4	1	no	—
781	Q₈	C₁₉×#120	1	2	yes	—
782	Q₈	C₁₉×#121	1	2	yes	—
783	D₄	—	2	2	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	1	no	—
788	D₄	—	2	1	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	1	no	—
791	D₄	—	2	1	no	—
792	D₄	—	2	1	no	—
793	D₄	—	4	2	no	—
794	D₄	—	4	2	no	—
795	D₄	—	4	2	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	1	no	—
798	D₄	—	4	1	no	—
799	D₄	—	4	1	no	—
800	D₄	—	4	1	no	—
801	D₄	C₁₉×#120	1	2	yes	—
802	D₄	C₁₉×#121	1	2	yes	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	4	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	8	2	no	—
832	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
833	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
836	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
837	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
838	C₈	—	2	2	no	—
839	C₈	—	2	2	no	—
840	C₈	—	2	2	no	—
841	C₈	—	4	1	no	—
842	C₈	—	4	1	no	—
843	C₈	—	4	1	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	2	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	8	1	no	—
850	C₂²	—	8	1	no	—
851	C₂²	—	8	1	no	—
852	C₂²	—	8	1	no	—
853	C₂²	—	16	2	no	—
854	C₂²	C₁₉×#534	1	1	yes	characteristic
855	C₂²	D₄²×C₁₉	1	1	yes	characteristic
856	C₂²	C₁₉×#546	1	1	yes	characteristic
857	C₄	—	2	2	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	1	no	—
864	C₄	—	8	1	no	—
865	C₄	—	8	1	no	—
866	C₄	—	8	1	no	—
867	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
868	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
869	C₄	D₄²×C₁₉	1	1	yes	characteristic
870	C₄	C₁₉×#546	1	1	yes	characteristic
871	C₂	—	2	1	no	—
872	C₂	—	2	1	no	—
873	C₂	—	2	1	no	—
874	C₂	—	4	2	no	—
875	C₂	—	4	2	no	—
876	C₂	—	8	1	no	—
877	C₂	—	8	1	no	—
878	C₂	C₁₉×#2410	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2410
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3586	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3069	C₂	semidirect
3. C₁₉×#3039	C₂	semidirect
4. C₁₉×#3022	C₂	semidirect
5. C₂×C₁₉×#456	C₂	semidirect
6. C₁₉×#2901	C₂	semidirect
7. C₁₉×#2050	C₂	semidirect
8. C₁₉×#2049	C₂	semidirect
9. C₁₉×#2009	C₂	semidirect
10. C₁₉×#2005	C₂	semidirect
11. C₁₉×#1906	C₂	semidirect
12. C₁₉×#1902	C₂	semidirect
13. C₁₉×#1902	C₂	semidirect
14. C₁₉×#1861	C₂	semidirect
15. C₁₉×#1796	C₂	semidirect
30. C₂×C₁₉×#137	C₂²	semidirect
34. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
44. C₁₉×#430	C₂²	semidirect
45. C₁₉×#423	C₂²	semidirect
54. C₂×C₁₉×#104	C₂²	semidirect
55. C₁₉×#419	C₂²	semidirect
56. C₁₉×#419	C₂²	semidirect
57. C₁₉×#419	C₂²	semidirect
59. C₁₉×#413	C₂²	semidirect
60. C₂×C₁₉×#101	C₂²	semidirect
61. C₂×C₁₉×#101	C₂²	semidirect
62. C₁₉×#410	C₂²	semidirect
63. C₁₉×#344	C₂²	semidirect
64. C₁₉×#344	C₂²	semidirect
65. C₁₉×#339	C₂²	semidirect
66. C₁₉×#338	C₂²	semidirect
319. #24474	C₁₉	direct (N × H)
406. #3069	C₂×C₁₉	semidirect
407. #3039	C₂×C₁₉	semidirect
408. #3022	C₂×C₁₉	semidirect
409. C₂×#456	C₂×C₁₉	semidirect
410. #2901	C₂×C₁₉	semidirect
411. #2050	C₂×C₁₉	semidirect
412. #2049	C₂×C₁₉	semidirect
413. #2009	C₂×C₁₉	semidirect
414. #2005	C₂×C₁₉	semidirect
415. #1906	C₂×C₁₉	semidirect
416. #1902	C₂×C₁₉	semidirect
417. #1902	C₂×C₁₉	semidirect
418. #1861	C₂×C₁₉	semidirect
419. #1796	C₂×C₁₉	semidirect
461. C₂×#137	C₂²×C₁₉	semidirect
465. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
475. #430	C₂²×C₁₉	semidirect
476. #423	C₂²×C₁₉	semidirect
485. C₂×#104	C₂²×C₁₉	semidirect
486. #419	C₂²×C₁₉	semidirect
487. #419	C₂²×C₁₉	semidirect
488. #419	C₂²×C₁₉	semidirect
490. #413	C₂²×C₁₉	semidirect
491. C₂×#101	C₂²×C₁₉	semidirect
492. C₂×#101	C₂²×C₁₉	semidirect
493. #410	C₂²×C₁₉	semidirect
494. #344	C₂²×C₁₉	semidirect
495. #344	C₂²×C₁₉	semidirect
496. #339	C₂²×C₁₉	semidirect
497. #338	C₂²×C₁₉	semidirect
619. C₁₉	#24474	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×#3586	2
C₁₉×#3069	2
C₁₉×#3039	2
C₁₉×#3022	2
C₂×C₁₉×#456	2
C₁₉×#2901	2
C₁₉×#2050	2
C₁₉×#2049	2
C₁₉×#2009	2
C₁₉×#2005	2
C₁₉×#1906	2
C₁₉×#1902	2
C₁₉×#1861	2
C₁₉×#1796	2
#24474	19

Subgroups — C19×#24474 #18030433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24474 #18030433