Subgroups — C₁₉×#23877 #18029836

Order 4864.

1764 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3488	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#455	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3004	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2436	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2007	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2004	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1900	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1882	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1871	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1789	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₁₉×#137	—	2	1	no	—
16	C₂×C₁₉×#137	—	2	1	no	—
17	C₂×C₁₉×#137	—	2	8	no	—
18	C₂×C₁₉×#137	C₂²	1	2	yes	—
19	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
20	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
21	C₂²×Q₁₆×C₁₉	—	2	1	no	—
22	C₂²×SD₁₆×C₁₉	—	2	1	no	—
23	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#550	—	2	1	no	—
25	C₁₉×#548	—	2	1	no	—
26	C₁₉×#546	—	2	1	no	—
27	C₁₉×#546	—	2	2	no	—
28	D₄²×C₁₉	—	2	2	no	—
29	D₄²×C₁₉	—	2	1	no	—
30	C₁₉×#537	—	2	1	no	—
31	C₁₉×#537	C₂²	1	1	yes	characteristic
32	C₁₉×#535	—	2	1	no	—
33	C₁₉×#535	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#124	C₂²	1	2	yes	complemented
35	C₁₉×#525	—	2	1	no	—
36	C₁₉×#525	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#121	—	2	1	no	—
38	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
39	C₁₉×#520	C₂²	1	1	yes	characteristic
40	C₁₉×#455	—	2	8	no	—
41	C₁₉×#451	—	2	1	no	—
42	C₁₉×#451	—	2	1	no	—
43	C₁₉×#448	—	2	1	no	—
44	C₁₉×#448	—	2	1	no	—
45	C₂×C₁₉×#104	C₂²	1	2	yes	—
46	C₂×C₁₉×#104	C₂²	1	2	yes	complemented
47	C₂×C₁₉×#104	C₂²	1	2	yes	complemented
48	C₁₉×#419	C₂²	1	2	yes	complemented
49	C₂×C₁₉×#100	C₂²	1	2	yes	complemented
50	C₁₉×#407	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×#393	—	2	2	no	—
52	C₁₉×#391	C₂²	1	2	yes	complemented
53	C₁₉×#386	—	2	2	no	—
54	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×#343	C₂²	1	2	yes	complemented
56	C₁₉×#339	C₂²	1	2	yes	complemented
57	C₁₉×H(5,𝔽₂)	—	2	4	no	—
58	C₁₉×H(5,𝔽₂)	—	4	2	no	—
59	C₂×#41×C₁₉	—	2	1	no	—
60	C₂×#41×C₁₉	—	2	1	no	—
61	C₂×#41×C₁₉	—	2	1	no	—
62	C₂×#41×C₁₉	—	2	1	no	—
63	C₂×#41×C₁₉	—	2	4	no	—
64	C₂×#41×C₁₉	—	4	2	no	—
65	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
66	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
67	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₉	—	2	1	no	—
71	C₂²×Q₈×C₁₉	—	2	4	no	—
72	C₂²×Q₈×C₁₉	—	2	1	no	—
73	C₂²×Q₈×C₁₉	—	2	1	no	—
74	C₂²×Q₈×C₁₉	—	2	1	no	—
75	C₂²×Q₈×C₁₉	—	2	1	no	—
76	C₂²×Q₈×C₁₉	—	4	2	no	—
77	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
78	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
79	C₂²×D₄×C₁₉	—	2	1	no	—
80	C₂²×D₄×C₁₉	—	2	2	no	—
81	C₂²×D₄×C₁₉	—	2	2	no	—
82	C₂²×D₄×C₁₉	—	2	1	no	—
83	C₂²×D₄×C₁₉	—	2	1	no	—
84	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
85	C₂²×D₄×C₁₉	D₄	1	2	yes	—
86	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₉	—	2	1	no	—
88	C₂³×C₄×C₁₉	—	2	1	no	—
89	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₁₉×#137	—	2	8	no	—
91	C₁₉×#137	—	2	8	no	—
92	C₁₉×#137	—	2	4	no	—
93	C₁₉×#137	—	2	4	no	—
94	C₁₉×#137	—	2	4	no	—
95	C₁₉×#137	—	2	4	no	—
96	C₁₉×#137	—	4	2	no	—
97	C₁₉×#137	D₄	1	8	yes	complemented
98	C₂×Q₁₆×C₁₉	—	2	8	no	—
99	C₂×Q₁₆×C₁₉	—	2	2	no	—
100	C₂×Q₁₆×C₁₉	—	2	2	no	—
101	C₂×Q₁₆×C₁₉	—	2	2	no	—
102	C₂×SD₁₆×C₁₉	—	2	8	no	—
103	C₂×SD₁₆×C₁₉	—	2	2	no	—
104	C₂×SD₁₆×C₁₉	—	2	2	no	—
105	C₂×SD₁₆×C₁₉	—	2	2	no	—
106	C₂×M₁₆×C₁₉	—	2	1	no	—
107	C₂×M₁₆×C₁₉	—	2	4	no	—
108	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
109	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
110	C₂²×C₈×C₁₉	—	2	1	no	—
111	C₁₉×#127	—	2	2	no	—
112	C₁₉×#127	—	2	1	no	—
113	C₁₉×#124	—	2	2	no	—
114	C₁₉×#124	—	2	1	no	—
115	C₁₉×#124	—	2	4	no	—
116	C₁₉×#124	—	4	2	no	—
117	C₁₉×#123	—	2	2	no	—
118	C₁₉×#123	—	2	1	no	—
119	C₁₉×C₂²⋊Q₈	—	2	2	no	—
120	C₁₉×C₂²⋊Q₈	—	2	1	no	—
121	C₁₉×C₂²⋊Q₈	—	2	1	no	—
122	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
123	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
124	C₁₉×#121	—	2	2	no	—
125	C₁₉×#121	—	2	2	no	—
126	C₁₉×#121	—	2	2	no	—
127	C₁₉×#121	—	2	2	no	—
128	C₁₉×#121	—	2	2	no	—
129	C₁₉×#121	—	2	1	no	—
130	C₁₉×#121	—	2	1	no	—
131	C₁₉×#121	—	2	1	no	—
132	C₁₉×#121	—	2	1	no	—
133	C₁₉×#121	—	2	1	no	—
134	C₁₉×#121	—	2	1	no	—
135	C₁₉×#121	—	2	2	no	—
136	C₁₉×#121	—	2	1	no	—
137	C₁₉×#121	—	2	1	no	—
138	C₁₉×#121	D₄	1	1	yes	characteristic
139	C₁₉×#121	D₄	1	1	yes	characteristic
140	C₁₉×#120	—	2	2	no	—
141	C₁₉×#120	—	2	2	no	—
142	C₁₉×#120	—	2	2	no	—
143	C₁₉×#120	—	2	1	no	—
144	C₁₉×#120	—	2	2	no	—
145	C₄×Q₈×C₁₉	—	2	1	no	—
146	C₄×D₄×C₁₉	—	2	2	no	—
147	C₄×D₄×C₁₉	—	2	2	no	—
148	C₄×D₄×C₁₉	—	2	1	no	—
149	C₄×D₄×C₁₉	—	2	2	no	—
150	C₄×D₄×C₁₉	—	2	1	no	—
151	C₄×D₄×C₁₉	—	2	1	no	—
152	C₁₉×#117	—	2	1	no	—
153	C₁₉×#117	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
157	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
159	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
160	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
161	C₁₉×#104	—	2	4	no	—
162	C₁₉×#104	—	2	4	no	—
163	C₁₉×#104	—	4	2	no	—
164	C₁₉×#103	—	2	2	no	—
165	C₁₉×#103	—	2	2	no	—
166	C₁₉×#100	—	2	4	no	—
167	C₁₉×C₂²⋊C₈	—	2	1	no	—
168	C₁₉×C₂²⋊C₈	—	2	1	no	—
169	C₁₉×#95	—	2	1	no	—
170	C₁₉×#95	—	2	4	no	—
171	C₂⁴×C₁₉	—	2	2	no	—
172	C₂⁴×C₁₉	—	2	1	no	—
173	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
175	#41×C₁₉	—	2	2	no	—
176	#41×C₁₉	—	2	2	no	—
177	#41×C₁₉	—	2	2	no	—
178	#41×C₁₉	—	2	2	no	—
179	#41×C₁₉	—	2	2	no	—
180	#41×C₁₉	—	2	2	no	—
181	#41×C₁₉	—	2	2	no	—
182	#41×C₁₉	—	4	4	no	—
183	#41×C₁₉	—	4	1	no	—
184	#41×C₁₉	—	4	1	no	—
185	#41×C₁₉	—	4	4	no	—
186	#41×C₁₉	—	4	4	no	—
187	#41×C₁₉	—	4	2	no	—
188	#41×C₁₉	—	4	2	no	—
189	#41×C₁₉	C₂×D₄	1	4	yes	—
190	C₂×Q₈×C₁₉	—	2	1	no	—
191	C₂×Q₈×C₁₉	—	2	2	no	—
192	C₂×Q₈×C₁₉	—	2	4	no	—
193	C₂×Q₈×C₁₉	—	2	4	no	—
194	C₂×Q₈×C₁₉	—	2	2	no	—
195	C₂×Q₈×C₁₉	—	2	2	no	—
196	C₂×Q₈×C₁₉	—	2	2	no	—
197	C₂×Q₈×C₁₉	—	2	2	no	—
198	C₂×Q₈×C₁₉	—	2	2	no	—
199	C₂×Q₈×C₁₉	—	4	4	no	—
200	C₂×Q₈×C₁₉	—	4	1	no	—
201	C₂×Q₈×C₁₉	—	4	4	no	—
202	C₂×Q₈×C₁₉	—	4	4	no	—
203	C₂×Q₈×C₁₉	—	4	2	no	—
204	C₂×Q₈×C₁₉	—	4	2	no	—
205	C₂×Q₈×C₁₉	—	4	1	no	—
206	C₂×Q₈×C₁₉	—	4	1	no	—
207	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	complemented
211	C₂×D₄×C₁₉	—	2	1	no	—
212	C₂×D₄×C₁₉	—	2	2	no	—
213	C₂×D₄×C₁₉	—	2	2	no	—
214	C₂×D₄×C₁₉	—	2	2	no	—
215	C₂×D₄×C₁₉	—	2	2	no	—
216	C₂×D₄×C₁₉	—	2	1	no	—
217	C₂×D₄×C₁₉	—	2	1	no	—
218	C₂×D₄×C₁₉	—	2	1	no	—
219	C₂×D₄×C₁₉	—	2	1	no	—
220	C₂×D₄×C₁₉	—	2	1	no	—
221	C₂×D₄×C₁₉	—	2	2	no	—
222	C₂×D₄×C₁₉	—	2	2	no	—
223	C₂×D₄×C₁₉	—	2	2	no	—
224	C₂×D₄×C₁₉	—	2	1	no	—
225	C₂×D₄×C₁₉	—	2	2	no	—
226	C₂×D₄×C₁₉	—	2	1	no	—
227	C₂×D₄×C₁₉	—	2	1	no	—
228	C₂×D₄×C₁₉	—	2	1	no	—
229	C₂×D₄×C₁₉	—	2	2	no	—
230	C₂×D₄×C₁₉	—	2	2	no	—
231	C₂×D₄×C₁₉	—	4	1	no	—
232	C₂×D₄×C₁₉	—	4	4	no	—
233	C₂×D₄×C₁₉	—	4	4	no	—
234	C₂×D₄×C₁₉	—	4	8	no	—
235	C₂×D₄×C₁₉	—	4	2	no	—
236	C₂×D₄×C₁₉	—	4	2	no	—
237	C₂×D₄×C₁₉	—	4	4	no	—
238	C₂×D₄×C₁₉	—	8	4	no	—
239	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
240	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
241	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₁₉	—	2	1	no	—
243	C₂²×C₄×C₁₉	—	2	2	no	—
244	C₂²×C₄×C₁₉	—	2	2	no	—
245	C₂²×C₄×C₁₉	—	2	2	no	—
246	C₂²×C₄×C₁₉	—	2	1	no	—
247	C₂²×C₄×C₁₉	—	2	2	no	—
248	C₂²×C₄×C₁₉	—	2	2	no	—
249	C₂²×C₄×C₁₉	—	2	1	no	—
250	C₂²×C₄×C₁₉	—	2	1	no	—
251	C₂²×C₄×C₁₉	—	2	1	no	—
252	C₂²×C₄×C₁₉	—	2	1	no	—
253	C₂²×C₄×C₁₉	—	2	2	no	—
254	C₂²×C₄×C₁₉	—	4	4	no	—
255	C₂²×C₄×C₁₉	—	4	4	no	—
256	C₂²×C₄×C₁₉	—	4	1	no	—
257	C₂²×C₄×C₁₉	—	4	1	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	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
265	Q₁₆×C₁₉	—	2	8	no	—
266	Q₁₆×C₁₉	—	2	8	no	—
267	Q₁₆×C₁₉	—	4	4	no	—
268	SD₁₆×C₁₉	—	2	8	no	—
269	SD₁₆×C₁₉	—	2	8	no	—
270	SD₁₆×C₁₉	—	4	4	no	—
271	M₁₆×C₁₉	—	2	4	no	—
272	M₁₆×C₁₉	—	2	2	no	—
273	M₁₆×C₁₉	—	2	2	no	—
274	M₁₆×C₁₉	—	2	2	no	—
275	M₁₆×C₁₉	C₂×D₄	1	4	yes	complemented
276	C₂×C₈×C₁₉	—	2	4	no	—
277	C₂×C₈×C₁₉	—	2	2	no	—
278	C₂×C₈×C₁₉	—	2	2	no	—
279	C₄⋊C₄×C₁₉	—	2	2	no	—
280	C₄⋊C₄×C₁₉	—	2	2	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	C₂×D₄	1	1	yes	characteristic
286	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
287	C₂²⋊C₄×C₁₉	—	2	2	no	—
288	C₂²⋊C₄×C₁₉	—	2	2	no	—
289	C₂²⋊C₄×C₁₉	—	2	2	no	—
290	C₂²⋊C₄×C₁₉	—	2	2	no	—
291	C₂²⋊C₄×C₁₉	—	2	2	no	—
292	C₂²⋊C₄×C₁₉	—	2	1	no	—
293	C₂²⋊C₄×C₁₉	—	2	1	no	—
294	C₂²⋊C₄×C₁₉	—	2	1	no	—
295	C₂²⋊C₄×C₁₉	—	2	1	no	—
296	C₂²⋊C₄×C₁₉	—	2	2	no	—
297	C₂²⋊C₄×C₁₉	—	2	2	no	—
298	C₂²⋊C₄×C₁₉	—	2	1	no	—
299	C₂²⋊C₄×C₁₉	—	4	8	no	—
300	C₂²⋊C₄×C₁₉	—	4	2	no	—
301	C₄²×C₁₉	—	2	2	no	—
302	C₄²×C₁₉	—	2	1	no	—
303	C₄²×C₁₉	—	2	2	no	—
304	C₄²×C₁₉	—	2	2	no	—
305	#23877	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
306	C₂³×C₁₉	—	2	1	no	—
307	C₂³×C₁₉	—	2	2	no	—
308	C₂³×C₁₉	—	2	2	no	—
309	C₂³×C₁₉	—	2	2	no	—
310	C₂³×C₁₉	—	2	1	no	—
311	C₂³×C₁₉	—	2	1	no	—
312	C₂³×C₁₉	—	2	4	no	—
313	C₂³×C₁₉	—	4	1	no	—
314	C₂³×C₁₉	—	4	2	no	—
315	C₂³×C₁₉	—	4	4	no	—
316	C₂³×C₁₉	—	4	2	no	—
317	C₂³×C₁₉	—	4	2	no	—
318	C₂³×C₁₉	—	4	2	no	—
319	C₂³×C₁₉	—	8	1	no	—
320	C₂³×C₁₉	—	8	2	no	—
321	C₂³×C₁₉	—	8	2	no	—
322	C₂³×C₁₉	#120	1	1	yes	characteristic
323	C₂³×C₁₉	#120	1	1	yes	characteristic
324	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
325	Q₈×C₁₉	—	2	1	no	—
326	Q₈×C₁₉	—	2	4	no	—
327	Q₈×C₁₉	—	2	1	no	—
328	Q₈×C₁₉	—	2	1	no	—
329	Q₈×C₁₉	—	2	4	no	—
330	Q₈×C₁₉	—	2	2	no	—
331	Q₈×C₁₉	—	4	2	no	—
332	Q₈×C₁₉	—	4	4	no	—
333	Q₈×C₁₉	—	4	4	no	—
334	Q₈×C₁₉	—	4	2	no	—
335	Q₈×C₁₉	—	4	2	no	—
336	Q₈×C₁₉	#120	1	2	yes	—
337	D₄×C₁₉	—	2	4	no	—
338	D₄×C₁₉	—	2	1	no	—
339	D₄×C₁₉	—	2	1	no	—
340	D₄×C₁₉	—	2	1	no	—
341	D₄×C₁₉	—	2	2	no	—
342	D₄×C₁₉	—	4	2	no	—
343	D₄×C₁₉	—	4	2	no	—
344	D₄×C₁₉	—	4	4	no	—
345	D₄×C₁₉	—	4	2	no	—
346	D₄×C₁₉	—	4	4	no	—
347	D₄×C₁₉	—	4	2	no	—
348	D₄×C₁₉	—	4	2	no	—
349	D₄×C₁₉	—	4	4	no	—
350	D₄×C₁₉	—	4	2	no	—
351	D₄×C₁₉	—	4	1	no	—
352	D₄×C₁₉	—	4	1	no	—
353	D₄×C₁₉	—	4	2	no	—
354	D₄×C₁₉	—	8	1	no	—
355	D₄×C₁₉	—	8	2	no	—
356	D₄×C₁₉	—	8	2	no	—
357	D₄×C₁₉	—	8	2	no	—
358	D₄×C₁₉	—	8	2	no	—
359	D₄×C₁₉	#120	1	2	yes	—
360	C₂×C₄×C₁₉	—	2	1	no	—
361	C₂×C₄×C₁₉	—	2	2	no	—
362	C₂×C₄×C₁₉	—	2	1	no	—
363	C₂×C₄×C₁₉	—	2	1	no	—
364	C₂×C₄×C₁₉	—	2	1	no	—
365	C₂×C₄×C₁₉	—	2	1	no	—
366	C₂×C₄×C₁₉	—	2	2	no	—
367	C₂×C₄×C₁₉	—	2	2	no	—
368	C₂×C₄×C₁₉	—	2	4	no	—
369	C₂×C₄×C₁₉	—	2	1	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	1	no	—
374	C₂×C₄×C₁₉	—	2	4	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	4	no	—
379	C₂×C₄×C₁₉	—	4	4	no	—
380	C₂×C₄×C₁₉	—	4	4	no	—
381	C₂×C₄×C₁₉	—	4	2	no	—
382	C₂×C₄×C₁₉	—	4	2	no	—
383	C₂×C₄×C₁₉	—	4	1	no	—
384	C₂×C₄×C₁₉	—	4	1	no	—
385	C₂×C₄×C₁₉	—	4	2	no	—
386	C₂×C₄×C₁₉	—	4	2	no	—
387	C₂×C₄×C₁₉	—	4	2	no	—
388	C₂×C₄×C₁₉	—	4	2	no	—
389	C₂×C₄×C₁₉	—	4	2	no	—
390	C₂×C₄×C₁₉	—	8	2	no	—
391	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
392	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
393	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
397	C₈×C₁₉	—	2	4	no	—
398	C₈×C₁₉	—	4	2	no	—
399	C₂²×#137	C₂×C₁₉	1	1	yes	characteristic, complemented
400	#3488	C₂×C₁₉	1	1	yes	characteristic
401	C₂×#455	C₂×C₁₉	1	2	yes	complemented
402	#3004	C₂×C₁₉	1	1	yes	characteristic, complemented
403	#2436	C₂×C₁₉	1	1	yes	characteristic, complemented
404	#2007	C₂×C₁₉	1	2	yes	complemented
405	#2004	C₂×C₁₉	1	2	yes	complemented
406	#1900	C₂×C₁₉	1	1	yes	characteristic, complemented
407	#1882	C₂×C₁₉	1	2	yes	complemented
408	#1871	C₂×C₁₉	1	1	yes	characteristic, complemented
409	#1789	C₂×C₁₉	1	1	yes	characteristic, complemented
410	C₂²×C₁₉	—	2	1	no	—
411	C₂²×C₁₉	—	2	1	no	—
412	C₂²×C₁₉	—	2	1	no	—
413	C₂²×C₁₉	—	2	1	no	—
414	C₂²×C₁₉	—	2	1	no	—
415	C₂²×C₁₉	—	2	2	no	—
416	C₂²×C₁₉	—	2	1	no	—
417	C₂²×C₁₉	—	2	1	no	—
418	C₂²×C₁₉	—	4	4	no	—
419	C₂²×C₁₉	—	4	1	no	—
420	C₂²×C₁₉	—	4	1	no	—
421	C₂²×C₁₉	—	4	1	no	—
422	C₂²×C₁₉	—	4	1	no	—
423	C₂²×C₁₉	—	4	2	no	—
424	C₂²×C₁₉	—	4	2	no	—
425	C₂²×C₁₉	—	4	1	no	—
426	C₂²×C₁₉	—	4	1	no	—
427	C₂²×C₁₉	—	4	1	no	—
428	C₂²×C₁₉	—	4	2	no	—
429	C₂²×C₁₉	—	4	1	no	—
430	C₂²×C₁₉	—	8	4	no	—
431	C₂²×C₁₉	—	8	4	no	—
432	C₂²×C₁₉	—	16	4	no	—
433	C₂²×C₁₉	#455	1	2	yes	complemented
434	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
435	C₂²×C₁₉	D₄²	1	2	yes	—
436	C₄×C₁₉	—	2	1	no	—
437	C₄×C₁₉	—	2	1	no	—
438	C₄×C₁₉	—	2	2	no	—
439	C₄×C₁₉	—	4	1	no	—
440	C₄×C₁₉	—	4	1	no	—
441	C₄×C₁₉	—	4	4	no	—
442	C₄×C₁₉	—	4	2	no	—
443	C₄×C₁₉	—	4	1	no	—
444	C₄×C₁₉	—	4	1	no	—
445	C₄×C₁₉	—	8	2	no	—
446	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
447	C₄×C₁₉	#534	1	1	yes	characteristic
448	C₄×C₁₉	D₄²	1	2	yes	—
449	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
450	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
451	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
452	C₂×#137	—	2	1	no	—
453	C₂×#137	—	2	1	no	—
454	C₂×#137	—	2	8	no	—
455	C₂×#137	C₂²×C₁₉	1	2	yes	—
456	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
457	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
458	C₂²×Q₁₆	—	2	1	no	—
459	C₂²×SD₁₆	—	2	1	no	—
460	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
461	#550	—	2	1	no	—
462	#548	—	2	1	no	—
463	#546	—	2	1	no	—
464	#546	—	2	2	no	—
465	D₄²	—	2	2	no	—
466	D₄²	—	2	1	no	—
467	#537	—	2	1	no	—
468	#537	C₂²×C₁₉	1	1	yes	characteristic
469	#535	—	2	1	no	—
470	#535	C₂²×C₁₉	1	1	yes	characteristic
471	C₂×#124	C₂²×C₁₉	1	2	yes	complemented
472	#525	—	2	1	no	—
473	#525	C₂²×C₁₉	1	1	yes	characteristic
474	C₂×#121	—	2	1	no	—
475	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
476	#520	C₂²×C₁₉	1	1	yes	characteristic
477	#455	—	2	8	no	—
478	#451	—	2	1	no	—
479	#451	—	2	1	no	—
480	#448	—	2	1	no	—
481	#448	—	2	1	no	—
482	C₂×#104	C₂²×C₁₉	1	2	yes	—
483	C₂×#104	C₂²×C₁₉	1	2	yes	complemented
484	C₂×#104	C₂²×C₁₉	1	2	yes	complemented
485	#419	C₂²×C₁₉	1	2	yes	complemented
486	C₂×#100	C₂²×C₁₉	1	2	yes	complemented
487	#407	C₂²×C₁₉	1	1	yes	characteristic, complemented
488	#393	—	2	2	no	—
489	#391	C₂²×C₁₉	1	2	yes	complemented
490	#386	—	2	2	no	—
491	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
492	#343	C₂²×C₁₉	1	2	yes	complemented
493	#339	C₂²×C₁₉	1	2	yes	complemented
494	C₂×C₁₉	—	2	2	no	—
495	C₂×C₁₉	—	2	2	no	—
496	C₂×C₁₉	—	4	1	no	—
497	C₂×C₁₉	—	4	2	no	—
498	C₂×C₁₉	—	8	1	no	—
499	C₂×C₁₉	—	8	2	no	—
500	C₂×C₁₉	—	8	1	no	—
501	C₂×C₁₉	#2403	1	1	yes	characteristic
502	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
503	C₂×C₁₉	#3022	1	1	yes	characteristic
504	H(5,𝔽₂)	—	2	4	no	—
505	H(5,𝔽₂)	—	4	2	no	—
506	C₂×#41	—	2	1	no	—
507	C₂×#41	—	2	1	no	—
508	C₂×#41	—	2	1	no	—
509	C₂×#41	—	2	1	no	—
510	C₂×#41	—	2	4	no	—
511	C₂×#41	—	4	2	no	—
512	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
513	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
514	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
515	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
516	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
517	C₂²×Q₈	—	2	1	no	—
518	C₂²×Q₈	—	2	4	no	—
519	C₂²×Q₈	—	2	1	no	—
520	C₂²×Q₈	—	2	1	no	—
521	C₂²×Q₈	—	2	1	no	—
522	C₂²×Q₈	—	2	1	no	—
523	C₂²×Q₈	—	4	2	no	—
524	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
525	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
526	C₂²×D₄	—	2	1	no	—
527	C₂²×D₄	—	2	2	no	—
528	C₂²×D₄	—	2	2	no	—
529	C₂²×D₄	—	2	1	no	—
530	C₂²×D₄	—	2	1	no	—
531	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
532	C₂²×D₄	D₄×C₁₉	1	2	yes	—
533	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
534	C₂³×C₄	—	2	1	no	—
535	C₂³×C₄	—	2	1	no	—
536	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
537	#137	—	2	8	no	—
538	#137	—	2	8	no	—
539	#137	—	2	4	no	—
540	#137	—	2	4	no	—
541	#137	—	2	4	no	—
542	#137	—	2	4	no	—
543	#137	—	4	2	no	—
544	#137	D₄×C₁₉	1	8	yes	complemented
545	C₂×Q₁₆	—	2	8	no	—
546	C₂×Q₁₆	—	2	2	no	—
547	C₂×Q₁₆	—	2	2	no	—
548	C₂×Q₁₆	—	2	2	no	—
549	C₂×SD₁₆	—	2	8	no	—
550	C₂×SD₁₆	—	2	2	no	—
551	C₂×SD₁₆	—	2	2	no	—
552	C₂×SD₁₆	—	2	2	no	—
553	C₂×M₁₆	—	2	1	no	—
554	C₂×M₁₆	—	2	4	no	—
555	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
556	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
557	C₂²×C₈	—	2	1	no	—
558	#127	—	2	2	no	—
559	#127	—	2	1	no	—
560	#124	—	2	2	no	—
561	#124	—	2	1	no	—
562	#124	—	2	4	no	—
563	#124	—	4	2	no	—
564	#123	—	2	2	no	—
565	#123	—	2	1	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	1	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
570	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
571	#121	—	2	2	no	—
572	#121	—	2	2	no	—
573	#121	—	2	2	no	—
574	#121	—	2	2	no	—
575	#121	—	2	2	no	—
576	#121	—	2	1	no	—
577	#121	—	2	1	no	—
578	#121	—	2	1	no	—
579	#121	—	2	1	no	—
580	#121	—	2	1	no	—
581	#121	—	2	1	no	—
582	#121	—	2	2	no	—
583	#121	—	2	1	no	—
584	#121	—	2	1	no	—
585	#121	D₄×C₁₉	1	1	yes	characteristic
586	#121	D₄×C₁₉	1	1	yes	characteristic
587	#120	—	2	2	no	—
588	#120	—	2	2	no	—
589	#120	—	2	2	no	—
590	#120	—	2	1	no	—
591	#120	—	2	2	no	—
592	C₄×Q₈	—	2	1	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	1	no	—
599	#117	—	2	1	no	—
600	#117	C₂³×C₁₉	1	1	yes	characteristic
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
603	C₂×C₂²⋊C₄	—	2	2	no	—
604	C₂×C₂²⋊C₄	—	2	4	no	—
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
607	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
608	#104	—	2	4	no	—
609	#104	—	2	4	no	—
610	#104	—	4	2	no	—
611	#103	—	2	2	no	—
612	#103	—	2	2	no	—
613	#100	—	2	4	no	—
614	C₂²⋊C₈	—	2	1	no	—
615	C₂²⋊C₈	—	2	1	no	—
616	#95	—	2	1	no	—
617	#95	—	2	4	no	—
618	C₁₉	#23877	1	1	yes	characteristic, direct product factor, Sylow
619	C₂⁴	—	2	2	no	—
620	C₂⁴	—	2	1	no	—
621	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
622	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
623	#41	—	2	2	no	—
624	#41	—	2	2	no	—
625	#41	—	2	2	no	—
626	#41	—	2	2	no	—
627	#41	—	2	2	no	—
628	#41	—	2	2	no	—
629	#41	—	2	2	no	—
630	#41	—	4	4	no	—
631	#41	—	4	1	no	—
632	#41	—	4	1	no	—
633	#41	—	4	4	no	—
634	#41	—	4	4	no	—
635	#41	—	4	2	no	—
636	#41	—	4	2	no	—
637	#41	C₂×D₄×C₁₉	1	4	yes	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	2	2	no	—
640	C₂×Q₈	—	2	4	no	—
641	C₂×Q₈	—	2	4	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	—	2	2	no	—
645	C₂×Q₈	—	2	2	no	—
646	C₂×Q₈	—	2	2	no	—
647	C₂×Q₈	—	4	4	no	—
648	C₂×Q₈	—	4	1	no	—
649	C₂×Q₈	—	4	4	no	—
650	C₂×Q₈	—	4	4	no	—
651	C₂×Q₈	—	4	2	no	—
652	C₂×Q₈	—	4	2	no	—
653	C₂×Q₈	—	4	1	no	—
654	C₂×Q₈	—	4	1	no	—
655	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
656	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
657	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
658	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	complemented
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	4	1	no	—
680	C₂×D₄	—	4	4	no	—
681	C₂×D₄	—	4	4	no	—
682	C₂×D₄	—	4	8	no	—
683	C₂×D₄	—	4	2	no	—
684	C₂×D₄	—	4	2	no	—
685	C₂×D₄	—	4	4	no	—
686	C₂×D₄	—	8	4	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	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	4	4	no	—
703	C₂²×C₄	—	4	4	no	—
704	C₂²×C₄	—	4	1	no	—
705	C₂²×C₄	—	4	1	no	—
706	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
710	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
713	Q₁₆	—	2	8	no	—
714	Q₁₆	—	2	8	no	—
715	Q₁₆	—	4	4	no	—
716	SD₁₆	—	2	8	no	—
717	SD₁₆	—	2	8	no	—
718	SD₁₆	—	4	4	no	—
719	M₁₆	—	2	4	no	—
720	M₁₆	—	2	2	no	—
721	M₁₆	—	2	2	no	—
722	M₁₆	—	2	2	no	—
723	M₁₆	C₂×D₄×C₁₉	1	4	yes	complemented
724	C₂×C₈	—	2	4	no	—
725	C₂×C₈	—	2	2	no	—
726	C₂×C₈	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
734	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	4	8	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	1	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	4	no	—
760	C₂³	—	4	1	no	—
761	C₂³	—	4	2	no	—
762	C₂³	—	4	4	no	—
763	C₂³	—	4	2	no	—
764	C₂³	—	4	2	no	—
765	C₂³	—	4	2	no	—
766	C₂³	—	8	1	no	—
767	C₂³	—	8	2	no	—
768	C₂³	—	8	2	no	—
769	C₂³	C₁₉×#120	1	1	yes	characteristic
770	C₂³	C₁₉×#120	1	1	yes	characteristic
771	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
772	Q₈	—	2	1	no	—
773	Q₈	—	2	4	no	—
774	Q₈	—	2	1	no	—
775	Q₈	—	2	1	no	—
776	Q₈	—	2	4	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	4	2	no	—
779	Q₈	—	4	4	no	—
780	Q₈	—	4	4	no	—
781	Q₈	—	4	2	no	—
782	Q₈	—	4	2	no	—
783	Q₈	C₁₉×#120	1	2	yes	—
784	D₄	—	2	4	no	—
785	D₄	—	2	1	no	—
786	D₄	—	2	1	no	—
787	D₄	—	2	1	no	—
788	D₄	—	2	2	no	—
789	D₄	—	4	2	no	—
790	D₄	—	4	2	no	—
791	D₄	—	4	4	no	—
792	D₄	—	4	2	no	—
793	D₄	—	4	4	no	—
794	D₄	—	4	4	no	—
795	D₄	—	4	2	no	—
796	D₄	—	4	2	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	1	no	—
799	D₄	—	4	1	no	—
800	D₄	—	4	2	no	—
801	D₄	—	8	2	no	—
802	D₄	—	8	1	no	—
803	D₄	—	8	2	no	—
804	D₄	—	8	2	no	—
805	D₄	—	8	2	no	—
806	D₄	C₁₉×#120	1	2	yes	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	4	2	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	4	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	4	2	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	2	no	—
837	C₂×C₄	—	8	2	no	—
838	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
839	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
842	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
843	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
844	C₈	—	2	4	no	—
845	C₈	—	4	2	no	—
846	C₂²	—	2	1	no	—
847	C₂²	—	2	1	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	4	4	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	8	4	no	—
867	C₂²	—	8	4	no	—
868	C₂²	—	16	4	no	—
869	C₂²	C₁₉×#455	1	2	yes	complemented
870	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
871	C₂²	D₄²×C₁₉	1	2	yes	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	2	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	4	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	1	no	—
881	C₄	—	8	2	no	—
882	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
883	C₄	C₁₉×#534	1	1	yes	characteristic
884	C₄	D₄²×C₁₉	1	2	yes	—
885	C₂	—	2	2	no	—
886	C₂	—	2	2	no	—
887	C₂	—	4	1	no	—
888	C₂	—	4	2	no	—
889	C₂	—	8	1	no	—
890	C₂	—	8	2	no	—
891	C₂	—	8	1	no	—
892	C₂	C₁₉×#2403	1	1	yes	characteristic
893	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
894	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3488	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×#137	C₂	semidirect
3. C₂×C₁₉×#455	C₂	semidirect
4. C₁₉×#3004	C₂	semidirect
5. C₁₉×#2436	C₂	semidirect
6. C₁₉×#2007	C₂	semidirect
7. C₁₉×#2004	C₂	semidirect
8. C₁₉×#1900	C₂	semidirect
9. C₁₉×#1882	C₂	semidirect
10. C₁₉×#1871	C₂	semidirect
11. C₁₉×#1789	C₂	semidirect
14. C₂³×Q₈×C₁₉	C₂²	semidirect
19. C₂×C₁₉×#137	C₂²	semidirect
20. C₂×C₁₉×#137	C₂²	semidirect
23. C₂²×M₁₆×C₁₉	C₂²	semidirect
34. C₂×C₁₉×#124	C₂²	semidirect
46. C₂×C₁₉×#104	C₂²	semidirect
47. C₂×C₁₉×#104	C₂²	semidirect
48. C₁₉×#419	C₂²	semidirect
49. C₂×C₁₉×#100	C₂²	semidirect
50. C₁₉×#407	C₂²	semidirect
52. C₁₉×#391	C₂²	semidirect
54. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
55. C₁₉×#343	C₂²	semidirect
56. C₁₉×#339	C₂²	semidirect
97. C₁₉×#137	D₄	semidirect
210. C₂×Q₈×C₁₉	C₂×D₄	semidirect
275. M₁₆×C₁₉	C₂×D₄	semidirect
305. #23877	C₁₉	direct (N × H)
399. C₂²×#137	C₂×C₁₉	semidirect
401. C₂×#455	C₂×C₁₉	semidirect
402. #3004	C₂×C₁₉	semidirect
403. #2436	C₂×C₁₉	semidirect
404. #2007	C₂×C₁₉	semidirect
405. #2004	C₂×C₁₉	semidirect
406. #1900	C₂×C₁₉	semidirect
407. #1882	C₂×C₁₉	semidirect
408. #1871	C₂×C₁₉	semidirect
409. #1789	C₂×C₁₉	semidirect
433. C₂²×C₁₉	#455	semidirect
451. C₂³×Q₈	C₂²×C₁₉	semidirect
456. C₂×#137	C₂²×C₁₉	semidirect
457. C₂×#137	C₂²×C₁₉	semidirect
460. C₂²×M₁₆	C₂²×C₁₉	semidirect
471. C₂×#124	C₂²×C₁₉	semidirect
483. C₂×#104	C₂²×C₁₉	semidirect
484. C₂×#104	C₂²×C₁₉	semidirect
485. #419	C₂²×C₁₉	semidirect
486. C₂×#100	C₂²×C₁₉	semidirect
487. #407	C₂²×C₁₉	semidirect
489. #391	C₂²×C₁₉	semidirect
491. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
492. #343	C₂²×C₁₉	semidirect
493. #339	C₂²×C₁₉	semidirect
544. #137	D₄×C₁₉	semidirect
618. C₁₉	#23877	direct (N × H)
658. C₂×Q₈	C₂×D₄×C₁₉	semidirect
723. M₁₆	C₂×D₄×C₁₉	semidirect
869. C₂²	C₁₉×#455	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#137	2
C₁₉×#3488	2
C₂×C₁₉×#455	2
C₁₉×#3004	2
C₁₉×#2436	2
C₁₉×#2007	2
C₁₉×#2004	2
C₁₉×#1900	2
C₁₉×#1882	2
C₁₉×#1871	2
C₁₉×#1789	2
#23877	19

Subgroups — C19×#23877 #18029836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23877 #18029836