Subgroups — C₁₉×#33552 #18039511

Order 4864.

1156 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3026	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#458	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3019	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2201	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2200	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2198	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2197	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2127	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2121	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#352	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
13	C₁₉×#575	—	2	1	no	—
14	C₁₉×#563	C₂²	1	1	yes	characteristic, complemented
15	C₁₉×#562	—	2	1	no	—
16	C₁₉×#560	C₂²	1	1	yes	characteristic, complemented
17	C₁₉×#559	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#553	—	2	1	no	—
19	C₁₉×#552	—	2	1	no	—
20	C₁₉×#551	—	2	1	no	—
21	C₁₉×#551	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×#547	—	2	1	no	—
23	C₁₉×#546	—	2	1	no	—
24	C₁₉×#542	—	2	1	no	—
25	C₁₉×#540	—	2	1	no	—
26	C₁₉×#539	—	2	1	no	—
27	C₁₉×#538	—	2	1	no	—
28	C₁₉×#538	—	2	1	no	—
29	C₁₉×#535	C₂²	1	1	yes	characteristic
30	C₁₉×#534	—	2	1	no	—
31	C₁₉×#534	C₂²	1	1	yes	characteristic
32	C₁₉×#525	—	2	1	no	—
33	C₂×C₁₉×#123	—	2	1	no	—
34	C₂×C₁₉×#123	C₂²	1	1	yes	characteristic
35	C₁₉×#458	—	2	1	no	—
36	C₁₉×#458	—	2	1	no	—
37	C₁₉×#458	—	2	1	no	—
38	C₁₉×#458	C₂²	1	2	yes	—
39	C₁₉×#458	C₂²	1	2	yes	—
40	C₁₉×#458	C₂²	1	2	yes	—
41	C₁₉×B(4,𝔽₂)	—	2	1	no	—
42	C₁₉×B(4,𝔽₂)	C₂²	1	2	yes	—
43	C₁₉×#455	—	2	1	no	—
44	C₁₉×#455	C₂²	1	2	yes	—
45	C₁₉×#453	—	2	1	no	—
46	C₁₉×#453	C₂²	1	2	yes	—
47	C₁₉×#421	—	2	1	no	—
48	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
49	C₂×C₁₉×#99	—	2	1	no	—
50	C₂×C₁₉×#99	—	2	1	no	—
51	C₂×C₁₉×#99	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×#99	C₂²	1	1	yes	characteristic
53	C₁₉×#354	C₂²	1	2	yes	complemented
54	C₁₉×#353	C₂²	1	2	yes	complemented
55	C₁₉×#352	C₂²	1	2	yes	complemented
56	C₁₉×#352	C₂²	1	2	yes	complemented
57	C₁₉×#352	C₂²	1	2	yes	complemented
58	C₁₉×AΣL(1,𝔽₁₆)	C₂²	1	2	yes	complemented
59	C₁₉×H(5,𝔽₂)	—	2	1	no	—
60	C₁₉×H(5,𝔽₂)	—	2	1	no	—
61	C₁₉×H(5,𝔽₂)	—	2	1	no	—
62	C₁₉×H(5,𝔽₂)	—	4	2	no	—
63	C₁₉×H(5,𝔽₂)	C₂³	1	2	yes	—
64	C₂×#41×C₁₉	—	2	1	no	—
65	C₂×#41×C₁₉	—	2	1	no	—
66	C₂×#41×C₁₉	—	4	1	no	—
67	C₂×#41×C₁₉	D₄	1	1	yes	characteristic, complemented
68	C₂²×D₄×C₁₉	—	2	1	no	—
69	C₂²×D₄×C₁₉	—	2	1	no	—
70	C₂²×D₄×C₁₉	—	4	1	no	—
71	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
72	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic, complemented
74	C₁₉×#137	—	2	2	no	—
75	C₁₉×#137	—	4	1	no	—
76	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
77	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
78	C₁₉×#135	—	4	2	no	—
79	C₂×M₁₆×C₁₉	—	2	1	no	—
80	C₁₉×C₄⋊Q₈	—	2	1	no	—
81	C₁₉×#127	D₄	1	1	yes	characteristic, complemented
82	C₁₉×#127	C₂³	1	1	yes	characteristic
83	C₁₉×#126	—	2	1	no	—
84	C₁₉×#126	—	2	1	no	—
85	C₁₉×#126	—	2	1	no	—
86	C₁₉×#126	—	2	1	no	—
87	C₁₉×#126	—	2	1	no	—
88	C₁₉×#126	—	2	1	no	—
89	C₁₉×#125	—	2	1	no	—
90	C₁₉×#125	—	2	1	no	—
91	C₁₉×#125	—	2	1	no	—
92	C₁₉×#124	—	2	1	no	—
93	C₁₉×#124	—	2	1	no	—
94	C₁₉×#124	—	2	1	no	—
95	C₁₉×#124	—	2	1	no	—
96	C₁₉×#124	D₄	1	1	yes	characteristic, complemented
97	C₁₉×#124	C₂³	1	1	yes	characteristic
98	C₁₉×#123	—	2	1	no	—
99	C₁₉×#123	—	2	1	no	—
100	C₁₉×#123	—	2	1	no	—
101	C₁₉×#123	—	2	1	no	—
102	C₁₉×#123	—	2	1	no	—
103	C₁₉×#123	—	2	1	no	—
104	C₁₉×#123	—	2	1	no	—
105	C₁₉×#123	—	2	1	no	—
106	C₁₉×#123	—	2	1	no	—
107	C₁₉×#123	—	2	1	no	—
108	C₁₉×#123	—	2	1	no	—
109	C₁₉×#123	—	2	1	no	—
110	C₁₉×#123	—	2	2	no	—
111	C₁₉×#123	—	2	2	no	—
112	C₁₉×#123	—	2	2	no	—
113	C₁₉×#123	—	4	1	no	—
114	C₁₉×#123	—	4	2	no	—
115	C₁₉×#123	D₄	1	1	yes	characteristic
116	C₁₉×#123	D₄	1	1	yes	characteristic, complemented
117	C₁₉×#123	D₄	1	1	yes	characteristic, complemented
118	C₁₉×#123	C₂³	1	1	yes	characteristic
119	C₁₉×#123	C₂³	1	1	yes	characteristic
120	C₁₉×#123	C₂³	1	1	yes	characteristic
121	C₁₉×C₂²⋊Q₈	—	2	1	no	—
122	C₁₉×C₂²⋊Q₈	—	2	1	no	—
123	C₁₉×C₂²⋊Q₈	—	2	1	no	—
124	C₁₉×C₂²⋊Q₈	—	2	1	no	—
125	C₁₉×C₂²⋊Q₈	—	2	1	no	—
126	C₁₉×C₂²⋊Q₈	—	2	1	no	—
127	C₁₉×C₂²⋊Q₈	—	2	1	no	—
128	C₁₉×C₂²⋊Q₈	—	2	1	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	1	no	—
136	C₁₉×#121	—	2	1	no	—
137	C₁₉×#121	—	2	1	no	—
138	C₁₉×#121	—	2	1	no	—
139	C₁₉×#121	—	2	1	no	—
140	C₁₉×#121	—	2	1	no	—
141	C₁₉×#121	—	4	2	no	—
142	C₁₉×#120	—	2	1	no	—
143	C₁₉×#120	—	2	1	no	—
144	C₁₉×#120	—	2	1	no	—
145	C₁₉×#120	—	2	1	no	—
146	C₁₉×#120	—	2	2	no	—
147	C₁₉×#120	—	4	1	no	—
148	C₁₉×#120	D₄	1	1	yes	characteristic
149	C₁₉×#120	C₂³	1	1	yes	characteristic
150	C₄×Q₈×C₁₉	—	2	1	no	—
151	C₄×D₄×C₁₉	—	2	1	no	—
152	C₄×D₄×C₁₉	—	2	1	no	—
153	C₄×D₄×C₁₉	—	2	1	no	—
154	C₄×D₄×C₁₉	—	2	1	no	—
155	C₄×D₄×C₁₉	—	2	1	no	—
156	C₄×D₄×C₁₉	—	2	1	no	—
157	C₄×D₄×C₁₉	—	2	1	no	—
158	C₄×D₄×C₁₉	—	2	1	no	—
159	C₄×D₄×C₁₉	—	2	1	no	—
160	C₁₉×#117	—	2	1	no	—
161	C₁₉×#117	—	2	1	no	—
162	C₁₉×#117	—	2	1	no	—
163	C₁₉×#117	D₄	1	1	yes	characteristic, complemented
164	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
167	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
168	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
169	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
170	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
171	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
172	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic, complemented
174	C₁₉×#104	—	2	2	no	—
175	C₁₉×#104	—	2	2	no	—
176	C₁₉×#100	—	2	1	no	—
177	C₁₉×#100	C₂³	1	2	yes	—
178	C₁₉×#99	—	2	1	no	—
179	C₁₉×#99	—	2	1	no	—
180	C₁₉×#99	—	2	2	no	—
181	C₁₉×#99	—	2	2	no	—
182	C₁₉×#99	—	2	2	no	—
183	C₁₉×#99	—	2	2	no	—
184	C₁₉×#99	C₂³	1	2	yes	—
185	C₁₉×#99	C₂³	1	2	yes	—
186	C₂⁴×C₁₉	—	2	1	no	—
187	C₂⁴×C₁₉	—	2	1	no	—
188	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
191	#41×C₁₉	—	2	2	no	—
192	#41×C₁₉	—	2	2	no	—
193	#41×C₁₉	—	4	2	no	—
194	#41×C₁₉	—	4	1	no	—
195	#41×C₁₉	—	4	2	no	—
196	#41×C₁₉	—	4	2	no	—
197	#41×C₁₉	—	4	1	no	—
198	#41×C₁₉	—	4	1	no	—
199	#41×C₁₉	—	4	2	no	—
200	#41×C₁₉	—	4	1	no	—
201	#41×C₁₉	—	8	1	no	—
202	#41×C₁₉	—	8	1	no	—
203	C₂×Q₈×C₁₉	—	2	1	no	—
204	C₂×Q₈×C₁₉	—	2	1	no	—
205	C₂×Q₈×C₁₉	—	2	1	no	—
206	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₂×D₄×C₁₉	—	2	1	no	—
208	C₂×D₄×C₁₉	—	2	2	no	—
209	C₂×D₄×C₁₉	—	2	2	no	—
210	C₂×D₄×C₁₉	—	2	1	no	—
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	1	no	—
215	C₂×D₄×C₁₉	—	2	1	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	1	no	—
222	C₂×D₄×C₁₉	—	2	1	no	—
223	C₂×D₄×C₁₉	—	4	1	no	—
224	C₂×D₄×C₁₉	—	4	1	no	—
225	C₂×D₄×C₁₉	—	4	2	no	—
226	C₂×D₄×C₁₉	—	4	2	no	—
227	C₂×D₄×C₁₉	—	4	1	no	—
228	C₂×D₄×C₁₉	—	4	1	no	—
229	C₂×D₄×C₁₉	—	4	1	no	—
230	C₂×D₄×C₁₉	—	4	1	no	—
231	C₂×D₄×C₁₉	—	4	2	no	—
232	C₂×D₄×C₁₉	—	4	2	no	—
233	C₂×D₄×C₁₉	—	4	1	no	—
234	C₂×D₄×C₁₉	—	4	1	no	—
235	C₂×D₄×C₁₉	—	4	1	no	—
236	C₂×D₄×C₁₉	—	4	1	no	—
237	C₂×D₄×C₁₉	—	4	1	no	—
238	C₂×D₄×C₁₉	—	4	2	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	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
243	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₉	—	2	1	no	—
245	C₂²×C₄×C₁₉	—	2	1	no	—
246	C₂²×C₄×C₁₉	—	2	1	no	—
247	C₂²×C₄×C₁₉	—	2	1	no	—
248	C₂²×C₄×C₁₉	—	2	1	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	1	no	—
254	C₂²×C₄×C₁₉	—	2	1	no	—
255	C₂²×C₄×C₁₉	—	4	1	no	—
256	C₂²×C₄×C₁₉	—	4	1	no	—
257	C₂²×C₄×C₁₉	—	4	1	no	—
258	C₂²×C₄×C₁₉	—	4	1	no	—
259	C₂²×C₄×C₁₉	—	4	1	no	—
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	1	yes	characteristic
264	Q₁₆×C₁₉	—	4	2	no	—
265	SD₁₆×C₁₉	—	4	2	no	—
266	SD₁₆×C₁₉	—	4	2	no	—
267	D₈×C₁₉	—	4	2	no	—
268	M₁₆×C₁₉	—	2	2	no	—
269	M₁₆×C₁₉	—	4	1	no	—
270	C₂×C₈×C₁₉	—	4	1	no	—
271	C₄⋊C₄×C₁₉	—	2	1	no	—
272	C₄⋊C₄×C₁₉	—	2	1	no	—
273	C₄⋊C₄×C₁₉	—	2	1	no	—
274	C₄⋊C₄×C₁₉	—	2	1	no	—
275	C₄⋊C₄×C₁₉	—	2	1	no	—
276	C₄⋊C₄×C₁₉	—	2	1	no	—
277	C₄⋊C₄×C₁₉	—	2	1	no	—
278	C₄⋊C₄×C₁₉	—	2	1	no	—
279	C₄⋊C₄×C₁₉	—	2	1	no	—
280	C₄⋊C₄×C₁₉	—	2	1	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	1	no	—
287	C₄⋊C₄×C₁₉	—	2	1	no	—
288	C₄⋊C₄×C₁₉	—	2	1	no	—
289	C₄⋊C₄×C₁₉	—	2	1	no	—
290	C₄⋊C₄×C₁₉	—	4	2	no	—
291	C₄⋊C₄×C₁₉	—	4	2	no	—
292	C₄⋊C₄×C₁₉	—	4	2	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	1	no	—
297	C₂²⋊C₄×C₁₉	—	2	1	no	—
298	C₂²⋊C₄×C₁₉	—	2	1	no	—
299	C₂²⋊C₄×C₁₉	—	2	1	no	—
300	C₂²⋊C₄×C₁₉	—	2	1	no	—
301	C₂²⋊C₄×C₁₉	—	2	1	no	—
302	C₂²⋊C₄×C₁₉	—	2	1	no	—
303	C₂²⋊C₄×C₁₉	—	2	1	no	—
304	C₂²⋊C₄×C₁₉	—	2	1	no	—
305	C₂²⋊C₄×C₁₉	—	2	1	no	—
306	C₂²⋊C₄×C₁₉	—	2	1	no	—
307	C₂²⋊C₄×C₁₉	—	2	1	no	—
308	C₂²⋊C₄×C₁₉	—	2	1	no	—
309	C₂²⋊C₄×C₁₉	—	2	1	no	—
310	C₂²⋊C₄×C₁₉	—	2	1	no	—
311	C₂²⋊C₄×C₁₉	—	2	1	no	—
312	C₂²⋊C₄×C₁₉	—	2	1	no	—
313	C₂²⋊C₄×C₁₉	—	2	1	no	—
314	C₂²⋊C₄×C₁₉	—	2	1	no	—
315	C₂²⋊C₄×C₁₉	—	2	1	no	—
316	C₂²⋊C₄×C₁₉	—	2	2	no	—
317	C₂²⋊C₄×C₁₉	—	2	2	no	—
318	C₂²⋊C₄×C₁₉	—	4	2	no	—
319	C₂²⋊C₄×C₁₉	—	4	1	no	—
320	C₂²⋊C₄×C₁₉	—	4	1	no	—
321	C₂²⋊C₄×C₁₉	—	4	2	no	—
322	C₂²⋊C₄×C₁₉	—	4	2	no	—
323	C₂²⋊C₄×C₁₉	—	4	2	no	—
324	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
325	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
326	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
327	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₁₉	—	2	1	no	—
329	C₄²×C₁₉	—	2	1	no	—
330	C₄²×C₁₉	—	2	1	no	—
331	C₄²×C₁₉	—	2	1	no	—
332	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
334	#33552	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₂³×C₁₉	—	2	1	no	—
336	C₂³×C₁₉	—	2	1	no	—
337	C₂³×C₁₉	—	2	1	no	—
338	C₂³×C₁₉	—	2	1	no	—
339	C₂³×C₁₉	—	2	2	no	—
340	C₂³×C₁₉	—	2	2	no	—
341	C₂³×C₁₉	—	2	1	no	—
342	C₂³×C₁₉	—	2	1	no	—
343	C₂³×C₁₉	—	4	1	no	—
344	C₂³×C₁₉	—	4	1	no	—
345	C₂³×C₁₉	—	4	1	no	—
346	C₂³×C₁₉	—	4	1	no	—
347	C₂³×C₁₉	—	8	1	no	—
348	C₂³×C₁₉	—	8	1	no	—
349	C₂³×C₁₉	—	8	1	no	—
350	C₂³×C₁₉	—	8	2	no	—
351	C₂³×C₁₉	—	16	1	no	—
352	C₂³×C₁₉	#120	1	1	yes	characteristic
353	C₂³×C₁₉	#120	1	1	yes	characteristic
354	C₂³×C₁₉	#120	1	1	yes	characteristic
355	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
356	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
357	Q₈×C₁₉	—	2	2	no	—
358	Q₈×C₁₉	—	4	1	no	—
359	Q₈×C₁₉	—	4	1	no	—
360	Q₈×C₁₉	—	8	1	no	—
361	Q₈×C₁₉	—	8	1	no	—
362	D₄×C₁₉	—	2	2	no	—
363	D₄×C₁₉	—	4	1	no	—
364	D₄×C₁₉	—	4	1	no	—
365	D₄×C₁₉	—	4	1	no	—
366	D₄×C₁₉	—	4	1	no	—
367	D₄×C₁₉	—	4	1	no	—
368	D₄×C₁₉	—	4	1	no	—
369	D₄×C₁₉	—	4	2	no	—
370	D₄×C₁₉	—	4	2	no	—
371	D₄×C₁₉	—	4	2	no	—
372	D₄×C₁₉	—	4	2	no	—
373	D₄×C₁₉	—	4	2	no	—
374	D₄×C₁₉	—	4	2	no	—
375	D₄×C₁₉	—	4	1	no	—
376	D₄×C₁₉	—	4	1	no	—
377	D₄×C₁₉	—	4	1	no	—
378	D₄×C₁₉	—	4	1	no	—
379	D₄×C₁₉	—	8	1	no	—
380	D₄×C₁₉	—	8	1	no	—
381	D₄×C₁₉	—	8	1	no	—
382	D₄×C₁₉	—	8	1	no	—
383	D₄×C₁₉	—	8	1	no	—
384	D₄×C₁₉	—	8	1	no	—
385	D₄×C₁₉	—	8	1	no	—
386	D₄×C₁₉	—	8	1	no	—
387	D₄×C₁₉	—	8	1	no	—
388	D₄×C₁₉	—	16	2	no	—
389	C₂×C₄×C₁₉	—	2	1	no	—
390	C₂×C₄×C₁₉	—	2	1	no	—
391	C₂×C₄×C₁₉	—	2	2	no	—
392	C₂×C₄×C₁₉	—	2	2	no	—
393	C₂×C₄×C₁₉	—	2	1	no	—
394	C₂×C₄×C₁₉	—	2	1	no	—
395	C₂×C₄×C₁₉	—	2	1	no	—
396	C₂×C₄×C₁₉	—	2	1	no	—
397	C₂×C₄×C₁₉	—	2	1	no	—
398	C₂×C₄×C₁₉	—	2	1	no	—
399	C₂×C₄×C₁₉	—	2	1	no	—
400	C₂×C₄×C₁₉	—	2	1	no	—
401	C₂×C₄×C₁₉	—	2	1	no	—
402	C₂×C₄×C₁₉	—	2	1	no	—
403	C₂×C₄×C₁₉	—	4	2	no	—
404	C₂×C₄×C₁₉	—	4	2	no	—
405	C₂×C₄×C₁₉	—	4	1	no	—
406	C₂×C₄×C₁₉	—	4	1	no	—
407	C₂×C₄×C₁₉	—	4	1	no	—
408	C₂×C₄×C₁₉	—	4	1	no	—
409	C₂×C₄×C₁₉	—	4	1	no	—
410	C₂×C₄×C₁₉	—	4	1	no	—
411	C₂×C₄×C₁₉	—	4	1	no	—
412	C₂×C₄×C₁₉	—	4	1	no	—
413	C₂×C₄×C₁₉	—	4	2	no	—
414	C₂×C₄×C₁₉	—	4	2	no	—
415	C₂×C₄×C₁₉	—	8	1	no	—
416	C₂×C₄×C₁₉	—	8	1	no	—
417	C₂×C₄×C₁₉	—	8	1	no	—
418	C₂×C₄×C₁₉	—	8	1	no	—
419	C₂×C₄×C₁₉	—	8	1	no	—
420	C₂×C₄×C₁₉	—	8	1	no	—
421	C₂×C₄×C₁₉	—	8	1	no	—
422	C₂×C₄×C₁₉	—	8	1	no	—
423	C₂×C₄×C₁₉	—	8	2	no	—
424	C₂×C₄×C₁₉	—	16	1	no	—
425	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
426	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
427	C₈×C₁₉	—	4	2	no	—
428	#3533	C₂×C₁₉	1	1	yes	characteristic, complemented
429	#3026	C₂×C₁₉	1	1	yes	characteristic, complemented
430	C₂×#458	C₂×C₁₉	1	1	yes	characteristic, complemented
431	#3019	C₂×C₁₉	1	1	yes	characteristic, complemented
432	#2201	C₂×C₁₉	1	2	yes	complemented
433	#2200	C₂×C₁₉	1	2	yes	complemented
434	#2198	C₂×C₁₉	1	2	yes	complemented
435	#2197	C₂×C₁₉	1	2	yes	complemented
436	#2127	C₂×C₁₉	1	1	yes	characteristic, complemented
437	#2121	C₂×C₁₉	1	1	yes	characteristic, complemented
438	C₂×#352	C₂×C₁₉	1	1	yes	characteristic, complemented
439	C₂²×C₁₉	—	2	1	no	—
440	C₂²×C₁₉	—	2	1	no	—
441	C₂²×C₁₉	—	2	1	no	—
442	C₂²×C₁₉	—	2	1	no	—
443	C₂²×C₁₉	—	4	1	no	—
444	C₂²×C₁₉	—	4	1	no	—
445	C₂²×C₁₉	—	4	1	no	—
446	C₂²×C₁₉	—	4	1	no	—
447	C₂²×C₁₉	—	4	1	no	—
448	C₂²×C₁₉	—	4	2	no	—
449	C₂²×C₁₉	—	4	1	no	—
450	C₂²×C₁₉	—	4	1	no	—
451	C₂²×C₁₉	—	4	1	no	—
452	C₂²×C₁₉	—	4	1	no	—
453	C₂²×C₁₉	—	4	2	no	—
454	C₂²×C₁₉	—	4	1	no	—
455	C₂²×C₁₉	—	4	1	no	—
456	C₂²×C₁₉	—	8	1	no	—
457	C₂²×C₁₉	—	8	1	no	—
458	C₂²×C₁₉	—	8	1	no	—
459	C₂²×C₁₉	—	8	2	no	—
460	C₂²×C₁₉	—	8	2	no	—
461	C₂²×C₁₉	—	8	2	no	—
462	C₂²×C₁₉	—	8	2	no	—
463	C₂²×C₁₉	—	16	1	no	—
464	C₂²×C₁₉	—	16	1	no	—
465	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
466	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
467	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
468	C₄×C₁₉	—	2	1	no	—
469	C₄×C₁₉	—	2	1	no	—
470	C₄×C₁₉	—	4	1	no	—
471	C₄×C₁₉	—	4	1	no	—
472	C₄×C₁₉	—	4	1	no	—
473	C₄×C₁₉	—	4	1	no	—
474	C₄×C₁₉	—	4	1	no	—
475	C₄×C₁₉	—	4	1	no	—
476	C₄×C₁₉	—	4	2	no	—
477	C₄×C₁₉	—	4	1	no	—
478	C₄×C₁₉	—	4	1	no	—
479	C₄×C₁₉	—	4	1	no	—
480	C₄×C₁₉	—	4	1	no	—
481	C₄×C₁₉	—	8	2	no	—
482	C₄×C₁₉	—	8	2	no	—
483	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
484	#575	—	2	1	no	—
485	#563	C₂²×C₁₉	1	1	yes	characteristic, complemented
486	#562	—	2	1	no	—
487	#560	C₂²×C₁₉	1	1	yes	characteristic, complemented
488	#559	C₂²×C₁₉	1	1	yes	characteristic, complemented
489	#553	—	2	1	no	—
490	#552	—	2	1	no	—
491	#551	—	2	1	no	—
492	#551	C₂²×C₁₉	1	1	yes	characteristic, complemented
493	#547	—	2	1	no	—
494	#546	—	2	1	no	—
495	#542	—	2	1	no	—
496	#540	—	2	1	no	—
497	#539	—	2	1	no	—
498	#538	—	2	1	no	—
499	#538	—	2	1	no	—
500	#535	C₂²×C₁₉	1	1	yes	characteristic
501	#534	—	2	1	no	—
502	#534	C₂²×C₁₉	1	1	yes	characteristic
503	#525	—	2	1	no	—
504	C₂×#123	—	2	1	no	—
505	C₂×#123	C₂²×C₁₉	1	1	yes	characteristic
506	#458	—	2	1	no	—
507	#458	—	2	1	no	—
508	#458	—	2	1	no	—
509	#458	C₂²×C₁₉	1	2	yes	—
510	#458	C₂²×C₁₉	1	2	yes	—
511	#458	C₂²×C₁₉	1	2	yes	—
512	B(4,𝔽₂)	—	2	1	no	—
513	B(4,𝔽₂)	C₂²×C₁₉	1	2	yes	—
514	#455	—	2	1	no	—
515	#455	C₂²×C₁₉	1	2	yes	—
516	#453	—	2	1	no	—
517	#453	C₂²×C₁₉	1	2	yes	—
518	#421	—	2	1	no	—
519	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
520	C₂×#99	—	2	1	no	—
521	C₂×#99	—	2	1	no	—
522	C₂×#99	C₂²×C₁₉	1	1	yes	characteristic
523	C₂×#99	C₂²×C₁₉	1	1	yes	characteristic
524	#354	C₂²×C₁₉	1	2	yes	complemented
525	#353	C₂²×C₁₉	1	2	yes	complemented
526	#352	C₂²×C₁₉	1	2	yes	complemented
527	#352	C₂²×C₁₉	1	2	yes	complemented
528	#352	C₂²×C₁₉	1	2	yes	complemented
529	AΣL(1,𝔽₁₆)	C₂²×C₁₉	1	2	yes	complemented
530	C₂×C₁₉	—	2	1	no	—
531	C₂×C₁₉	—	2	1	no	—
532	C₂×C₁₉	—	2	1	no	—
533	C₂×C₁₉	—	4	1	no	—
534	C₂×C₁₉	—	4	1	no	—
535	C₂×C₁₉	—	4	1	no	—
536	C₂×C₁₉	—	4	1	no	—
537	C₂×C₁₉	—	8	1	no	—
538	C₂×C₁₉	—	8	1	no	—
539	C₂×C₁₉	—	8	2	no	—
540	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
541	H(5,𝔽₂)	—	2	1	no	—
542	H(5,𝔽₂)	—	2	1	no	—
543	H(5,𝔽₂)	—	2	1	no	—
544	H(5,𝔽₂)	—	4	2	no	—
545	H(5,𝔽₂)	C₂³×C₁₉	1	2	yes	—
546	C₂×#41	—	2	1	no	—
547	C₂×#41	—	2	1	no	—
548	C₂×#41	—	4	1	no	—
549	C₂×#41	D₄×C₁₉	1	1	yes	characteristic, complemented
550	C₂²×D₄	—	2	1	no	—
551	C₂²×D₄	—	2	1	no	—
552	C₂²×D₄	—	4	1	no	—
553	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
554	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
555	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic, complemented
556	#137	—	2	2	no	—
557	#137	—	4	1	no	—
558	AGL(1,ℤ/8)	—	2	2	no	—
559	AGL(1,ℤ/8)	—	4	1	no	—
560	#135	—	4	2	no	—
561	C₂×M₁₆	—	2	1	no	—
562	C₄⋊Q₈	—	2	1	no	—
563	#127	D₄×C₁₉	1	1	yes	characteristic, complemented
564	#127	C₂³×C₁₉	1	1	yes	characteristic
565	#126	—	2	1	no	—
566	#126	—	2	1	no	—
567	#126	—	2	1	no	—
568	#126	—	2	1	no	—
569	#126	—	2	1	no	—
570	#126	—	2	1	no	—
571	#125	—	2	1	no	—
572	#125	—	2	1	no	—
573	#125	—	2	1	no	—
574	#124	—	2	1	no	—
575	#124	—	2	1	no	—
576	#124	—	2	1	no	—
577	#124	—	2	1	no	—
578	#124	D₄×C₁₉	1	1	yes	characteristic, complemented
579	#124	C₂³×C₁₉	1	1	yes	characteristic
580	#123	—	2	1	no	—
581	#123	—	2	1	no	—
582	#123	—	2	1	no	—
583	#123	—	2	1	no	—
584	#123	—	2	1	no	—
585	#123	—	2	1	no	—
586	#123	—	2	1	no	—
587	#123	—	2	1	no	—
588	#123	—	2	1	no	—
589	#123	—	2	1	no	—
590	#123	—	2	1	no	—
591	#123	—	2	1	no	—
592	#123	—	2	2	no	—
593	#123	—	2	2	no	—
594	#123	—	2	2	no	—
595	#123	—	4	1	no	—
596	#123	—	4	2	no	—
597	#123	D₄×C₁₉	1	1	yes	characteristic
598	#123	D₄×C₁₉	1	1	yes	characteristic, complemented
599	#123	D₄×C₁₉	1	1	yes	characteristic, complemented
600	#123	C₂³×C₁₉	1	1	yes	characteristic
601	#123	C₂³×C₁₉	1	1	yes	characteristic
602	#123	C₂³×C₁₉	1	1	yes	characteristic
603	C₂²⋊Q₈	—	2	1	no	—
604	C₂²⋊Q₈	—	2	1	no	—
605	C₂²⋊Q₈	—	2	1	no	—
606	C₂²⋊Q₈	—	2	1	no	—
607	C₂²⋊Q₈	—	2	1	no	—
608	C₂²⋊Q₈	—	2	1	no	—
609	C₂²⋊Q₈	—	2	1	no	—
610	C₂²⋊Q₈	—	2	1	no	—
611	#121	—	2	1	no	—
612	#121	—	2	1	no	—
613	#121	—	2	1	no	—
614	#121	—	2	1	no	—
615	#121	—	2	1	no	—
616	#121	—	2	1	no	—
617	#121	—	2	1	no	—
618	#121	—	2	1	no	—
619	#121	—	2	1	no	—
620	#121	—	2	1	no	—
621	#121	—	2	1	no	—
622	#121	—	2	1	no	—
623	#121	—	4	2	no	—
624	#120	—	2	1	no	—
625	#120	—	2	1	no	—
626	#120	—	2	1	no	—
627	#120	—	2	1	no	—
628	#120	—	2	2	no	—
629	#120	—	4	1	no	—
630	#120	D₄×C₁₉	1	1	yes	characteristic
631	#120	C₂³×C₁₉	1	1	yes	characteristic
632	C₄×Q₈	—	2	1	no	—
633	C₄×D₄	—	2	1	no	—
634	C₄×D₄	—	2	1	no	—
635	C₄×D₄	—	2	1	no	—
636	C₄×D₄	—	2	1	no	—
637	C₄×D₄	—	2	1	no	—
638	C₄×D₄	—	2	1	no	—
639	C₄×D₄	—	2	1	no	—
640	C₄×D₄	—	2	1	no	—
641	C₄×D₄	—	2	1	no	—
642	#117	—	2	1	no	—
643	#117	—	2	1	no	—
644	#117	—	2	1	no	—
645	#117	D₄×C₁₉	1	1	yes	characteristic, complemented
646	C₂×C₄⋊C₄	—	2	1	no	—
647	C₂×C₄⋊C₄	—	2	1	no	—
648	C₂×C₄⋊C₄	—	4	1	no	—
649	C₂×C₂²⋊C₄	—	2	1	no	—
650	C₂×C₂²⋊C₄	—	2	1	no	—
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	4	1	no	—
654	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic, complemented
656	#104	—	2	2	no	—
657	#104	—	2	2	no	—
658	#100	—	2	1	no	—
659	#100	C₂³×C₁₉	1	2	yes	—
660	#99	—	2	1	no	—
661	#99	—	2	1	no	—
662	#99	—	2	2	no	—
663	#99	—	2	2	no	—
664	#99	—	2	2	no	—
665	#99	—	2	2	no	—
666	#99	C₂³×C₁₉	1	2	yes	—
667	#99	C₂³×C₁₉	1	2	yes	—
668	C₁₉	#33552	1	1	yes	characteristic, direct product factor, Sylow
669	C₂⁴	—	2	1	no	—
670	C₂⁴	—	2	1	no	—
671	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
672	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
673	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
674	#41	—	2	2	no	—
675	#41	—	2	2	no	—
676	#41	—	4	2	no	—
677	#41	—	4	1	no	—
678	#41	—	4	2	no	—
679	#41	—	4	2	no	—
680	#41	—	4	1	no	—
681	#41	—	4	1	no	—
682	#41	—	4	2	no	—
683	#41	—	4	1	no	—
684	#41	—	8	1	no	—
685	#41	—	8	1	no	—
686	C₂×Q₈	—	2	1	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	2	1	no	—
706	C₂×D₄	—	4	1	no	—
707	C₂×D₄	—	4	1	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	1	no	—
711	C₂×D₄	—	4	1	no	—
712	C₂×D₄	—	4	1	no	—
713	C₂×D₄	—	4	1	no	—
714	C₂×D₄	—	4	2	no	—
715	C₂×D₄	—	4	2	no	—
716	C₂×D₄	—	4	1	no	—
717	C₂×D₄	—	4	1	no	—
718	C₂×D₄	—	4	1	no	—
719	C₂×D₄	—	4	1	no	—
720	C₂×D₄	—	4	1	no	—
721	C₂×D₄	—	4	2	no	—
722	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
723	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
724	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
725	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
726	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	—	4	1	no	—
739	C₂²×C₄	—	4	1	no	—
740	C₂²×C₄	—	4	1	no	—
741	C₂²×C₄	—	4	1	no	—
742	C₂²×C₄	—	4	1	no	—
743	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
744	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
745	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
746	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
747	Q₁₆	—	4	2	no	—
748	SD₁₆	—	4	2	no	—
749	SD₁₆	—	4	2	no	—
750	D₈	—	4	2	no	—
751	M₁₆	—	2	2	no	—
752	M₁₆	—	4	1	no	—
753	C₂×C₈	—	4	1	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	1	no	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	1	no	—
769	C₄⋊C₄	—	2	1	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	1	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	2	1	no	—
777	C₂²⋊C₄	—	2	1	no	—
778	C₂²⋊C₄	—	2	1	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	1	no	—
781	C₂²⋊C₄	—	2	1	no	—
782	C₂²⋊C₄	—	2	1	no	—
783	C₂²⋊C₄	—	2	1	no	—
784	C₂²⋊C₄	—	2	1	no	—
785	C₂²⋊C₄	—	2	1	no	—
786	C₂²⋊C₄	—	2	1	no	—
787	C₂²⋊C₄	—	2	1	no	—
788	C₂²⋊C₄	—	2	1	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	1	no	—
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	—	2	1	no	—
796	C₂²⋊C₄	—	2	1	no	—
797	C₂²⋊C₄	—	2	1	no	—
798	C₂²⋊C₄	—	2	1	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	4	1	no	—
803	C₂²⋊C₄	—	4	1	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
808	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
809	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
810	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
811	C₄²	—	2	1	no	—
812	C₄²	—	2	1	no	—
813	C₄²	—	2	1	no	—
814	C₄²	—	2	1	no	—
815	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
816	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
817	C₂³	—	2	1	no	—
818	C₂³	—	2	1	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	1	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	4	1	no	—
826	C₂³	—	4	1	no	—
827	C₂³	—	4	1	no	—
828	C₂³	—	4	1	no	—
829	C₂³	—	8	1	no	—
830	C₂³	—	8	1	no	—
831	C₂³	—	8	1	no	—
832	C₂³	—	8	2	no	—
833	C₂³	—	16	1	no	—
834	C₂³	C₁₉×#120	1	1	yes	characteristic
835	C₂³	C₁₉×#120	1	1	yes	characteristic
836	C₂³	C₁₉×#120	1	1	yes	characteristic
837	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
838	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
839	Q₈	—	2	2	no	—
840	Q₈	—	4	1	no	—
841	Q₈	—	4	1	no	—
842	Q₈	—	8	1	no	—
843	Q₈	—	8	1	no	—
844	D₄	—	2	2	no	—
845	D₄	—	4	1	no	—
846	D₄	—	4	1	no	—
847	D₄	—	4	1	no	—
848	D₄	—	4	1	no	—
849	D₄	—	4	1	no	—
850	D₄	—	4	1	no	—
851	D₄	—	4	2	no	—
852	D₄	—	4	2	no	—
853	D₄	—	4	2	no	—
854	D₄	—	4	2	no	—
855	D₄	—	4	2	no	—
856	D₄	—	4	1	no	—
857	D₄	—	4	1	no	—
858	D₄	—	4	1	no	—
859	D₄	—	4	1	no	—
860	D₄	—	4	2	no	—
861	D₄	—	8	1	no	—
862	D₄	—	8	1	no	—
863	D₄	—	8	1	no	—
864	D₄	—	8	1	no	—
865	D₄	—	8	1	no	—
866	D₄	—	8	1	no	—
867	D₄	—	8	1	no	—
868	D₄	—	8	1	no	—
869	D₄	—	8	1	no	—
870	D₄	—	16	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	4	2	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	4	1	no	—
888	C₂×C₄	—	4	1	no	—
889	C₂×C₄	—	4	1	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	—	4	1	no	—
892	C₂×C₄	—	4	1	no	—
893	C₂×C₄	—	4	1	no	—
894	C₂×C₄	—	4	1	no	—
895	C₂×C₄	—	4	2	no	—
896	C₂×C₄	—	4	2	no	—
897	C₂×C₄	—	8	1	no	—
898	C₂×C₄	—	8	1	no	—
899	C₂×C₄	—	8	1	no	—
900	C₂×C₄	—	8	1	no	—
901	C₂×C₄	—	8	1	no	—
902	C₂×C₄	—	8	1	no	—
903	C₂×C₄	—	8	1	no	—
904	C₂×C₄	—	8	1	no	—
905	C₂×C₄	—	8	2	no	—
906	C₂×C₄	—	16	1	no	—
907	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
908	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
909	C₈	—	4	2	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	1	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	8	1	no	—
928	C₂²	—	8	1	no	—
929	C₂²	—	8	1	no	—
930	C₂²	—	8	2	no	—
931	C₂²	—	8	2	no	—
932	C₂²	—	8	2	no	—
933	C₂²	—	8	2	no	—
934	C₂²	—	16	1	no	—
935	C₂²	—	16	1	no	—
936	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
937	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
938	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	1	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	1	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	1	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	1	no	—
951	C₄	—	4	1	no	—
952	C₄	—	8	2	no	—
953	C₄	—	8	2	no	—
954	C₂	—	2	1	no	—
955	C₂	—	2	1	no	—
956	C₂	—	2	1	no	—
957	C₂	—	4	1	no	—
958	C₂	—	4	1	no	—
959	C₂	—	4	1	no	—
960	C₂	—	4	1	no	—
961	C₂	—	8	1	no	—
962	C₂	—	8	1	no	—
963	C₂	—	8	2	no	—
964	C₂	C₂×C₁₉×B(4,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×D₄	C₂⁴×C₁₉
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3533	C₂	semidirect
2. C₁₉×#3026	C₂	semidirect
3. C₂×C₁₉×#458	C₂	semidirect
4. C₁₉×#3019	C₂	semidirect
5. C₁₉×#2201	C₂	semidirect
6. C₁₉×#2200	C₂	semidirect
7. C₁₉×#2198	C₂	semidirect
8. C₁₉×#2197	C₂	semidirect
9. C₁₉×#2127	C₂	semidirect
10. C₁₉×#2121	C₂	semidirect
11. C₂×C₁₉×#352	C₂	semidirect
14. C₁₉×#563	C₂²	semidirect
16. C₁₉×#560	C₂²	semidirect
17. C₁₉×#559	C₂²	semidirect
21. C₁₉×#551	C₂²	semidirect
53. C₁₉×#354	C₂²	semidirect
54. C₁₉×#353	C₂²	semidirect
55. C₁₉×#352	C₂²	semidirect
56. C₁₉×#352	C₂²	semidirect
57. C₁₉×#352	C₂²	semidirect
58. C₁₉×AΣL(1,𝔽₁₆)	C₂²	semidirect
67. C₂×#41×C₁₉	D₄	semidirect
73. C₂³×C₄×C₁₉	D₄	semidirect
81. C₁₉×#127	D₄	semidirect
96. C₁₉×#124	D₄	semidirect
116. C₁₉×#123	D₄	semidirect
117. C₁₉×#123	D₄	semidirect
163. C₁₉×#117	D₄	semidirect
173. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
334. #33552	C₁₉	direct (N × H)
428. #3533	C₂×C₁₉	semidirect
429. #3026	C₂×C₁₉	semidirect
430. C₂×#458	C₂×C₁₉	semidirect
431. #3019	C₂×C₁₉	semidirect
432. #2201	C₂×C₁₉	semidirect
433. #2200	C₂×C₁₉	semidirect
434. #2198	C₂×C₁₉	semidirect
435. #2197	C₂×C₁₉	semidirect
436. #2127	C₂×C₁₉	semidirect
437. #2121	C₂×C₁₉	semidirect
438. C₂×#352	C₂×C₁₉	semidirect
485. #563	C₂²×C₁₉	semidirect
487. #560	C₂²×C₁₉	semidirect
488. #559	C₂²×C₁₉	semidirect
492. #551	C₂²×C₁₉	semidirect
524. #354	C₂²×C₁₉	semidirect
525. #353	C₂²×C₁₉	semidirect
526. #352	C₂²×C₁₉	semidirect
527. #352	C₂²×C₁₉	semidirect
528. #352	C₂²×C₁₉	semidirect
529. AΣL(1,𝔽₁₆)	C₂²×C₁₉	semidirect
549. C₂×#41	D₄×C₁₉	semidirect
555. C₂³×C₄	D₄×C₁₉	semidirect
563. #127	D₄×C₁₉	semidirect
578. #124	D₄×C₁₉	semidirect
598. #123	D₄×C₁₉	semidirect
599. #123	D₄×C₁₉	semidirect
645. #117	D₄×C₁₉	semidirect
655. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
668. C₁₉	#33552	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×#3533	2
C₁₉×#3026	2
C₂×C₁₉×#458	2
C₁₉×#3019	2
C₁₉×#2201	2
C₁₉×#2200	2
C₁₉×#2198	2
C₁₉×#2197	2
C₁₉×#2127	2
C₁₉×#2121	2
C₂×C₁₉×#352	2
#33552	19

Subgroups — C19×#33552 #18039511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33552 #18039511