Subgroups — C₁₉×#33551 #18039510

Order 4864.

1326 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3026	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×B(4,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3019	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2200	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2199	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2197	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2196	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×AΣL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
13	C₁₉×#575	—	2	1	no	—
14	C₁₉×H(3,𝔽₄)	C₂²	1	1	yes	characteristic, complemented
15	C₁₉×#560	—	2	1	no	—
16	C₁₉×#560	C₂²	1	1	yes	characteristic, complemented
17	C₁₉×#551	—	2	1	no	—
18	C₁₉×#551	C₂²	1	1	yes	characteristic, complemented
19	C₁₉×#546	—	2	1	no	—
20	C₁₉×#546	—	2	1	no	—
21	C₁₉×#546	—	2	1	no	—
22	D₄²×C₁₉	—	2	1	no	—
23	D₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#538	—	2	1	no	—
25	C₁₉×#538	—	2	1	no	—
26	C₁₉×#538	—	2	1	no	—
27	C₁₉×#535	—	2	1	no	—
28	C₁₉×#535	C₂²	1	1	yes	characteristic
29	C₁₉×#534	—	2	1	no	—
30	C₁₉×#534	—	2	1	no	—
31	C₁₉×#534	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#120	—	2	1	no	—
33	C₂×C₁₉×#120	—	2	1	no	—
34	C₂×C₁₉×#120	C₂²	1	1	yes	characteristic
35	C₁₉×#458	—	2	1	no	—
36	C₁₉×#458	C₂²	1	2	yes	complemented
37	C₁₉×B(4,𝔽₂)	—	2	1	no	—
38	C₁₉×B(4,𝔽₂)	—	2	1	no	—
39	C₁₉×B(4,𝔽₂)	—	2	1	no	—
40	C₁₉×B(4,𝔽₂)	C₂²	1	2	yes	—
41	C₁₉×B(4,𝔽₂)	C₂²	1	2	yes	complemented
42	C₁₉×B(4,𝔽₂)	C₂²	1	2	yes	complemented
43	C₁₉×#455	—	2	1	no	—
44	C₁₉×#455	C₂²	1	2	yes	complemented
45	C₁₉×#453	—	2	1	no	—
46	C₁₉×#453	C₂²	1	2	yes	complemented
47	C₁₉×#421	—	2	1	no	—
48	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₉×#99	—	2	1	no	—
50	C₂×C₁₉×#99	—	2	1	no	—
51	C₂×C₁₉×#99	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₁₉×#99	C₂²	1	1	yes	characteristic, complemented
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×AΣL(1,𝔽₁₆)	C₂²	1	2	yes	complemented
57	C₁₉×AΣL(1,𝔽₁₆)	C₂²	1	2	yes	complemented
58	C₁₉×AΣL(1,𝔽₁₆)	C₂²	1	2	yes	complemented
59	C₂⁵×C₁₉	D₄	1	1	yes	characteristic, complemented
60	C₁₉×H(5,𝔽₂)	—	2	1	no	—
61	C₁₉×H(5,𝔽₂)	—	2	1	no	—
62	C₁₉×H(5,𝔽₂)	—	2	1	no	—
63	C₁₉×H(5,𝔽₂)	—	4	2	no	—
64	C₁₉×H(5,𝔽₂)	C₂³	1	2	yes	—
65	C₂×#41×C₁₉	—	2	1	no	—
66	C₂×#41×C₁₉	—	2	1	no	—
67	C₂×#41×C₁₉	—	4	1	no	—
68	C₂×#41×C₁₉	D₄	1	1	yes	characteristic, complemented
69	C₂²×D₄×C₁₉	—	2	1	no	—
70	C₂²×D₄×C₁₉	—	2	1	no	—
71	C₂²×D₄×C₁₉	—	2	1	no	—
72	C₂²×D₄×C₁₉	—	2	1	no	—
73	C₂²×D₄×C₁₉	—	2	1	no	—
74	C₂²×D₄×C₁₉	—	2	1	no	—
75	C₂²×D₄×C₁₉	—	2	1	no	—
76	C₂²×D₄×C₁₉	—	4	1	no	—
77	C₂²×D₄×C₁₉	—	4	1	no	—
78	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic, complemented
79	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×#137	—	2	2	no	—
81	C₁₉×#137	—	4	1	no	—
82	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
83	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
84	C₁₉×#135	—	4	2	no	—
85	C₂×M₁₆×C₁₉	—	2	1	no	—
86	C₁₉×#127	—	2	1	no	—
87	C₁₉×#127	D₄	1	1	yes	characteristic, complemented
88	C₁₉×#127	C₂³	1	1	yes	characteristic
89	C₁₉×#126	—	2	1	no	—
90	C₁₉×#126	—	2	1	no	—
91	C₁₉×#126	—	2	1	no	—
92	C₁₉×#126	—	2	1	no	—
93	C₁₉×#124	—	2	1	no	—
94	C₁₉×#124	—	2	1	no	—
95	C₁₉×#124	—	2	1	no	—
96	C₁₉×#124	—	2	1	no	—
97	C₁₉×#124	—	2	1	no	—
98	C₁₉×#124	D₄	1	1	yes	characteristic, complemented
99	C₁₉×#124	C₂³	1	1	yes	characteristic
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	2	no	—
109	C₁₉×#123	—	4	1	no	—
110	C₁₉×#123	D₄	1	1	yes	characteristic, complemented
111	C₁₉×#123	C₂³	1	1	yes	characteristic
112	C₁₉×C₂²⋊Q₈	—	2	1	no	—
113	C₁₉×C₂²⋊Q₈	—	2	1	no	—
114	C₁₉×C₂²⋊Q₈	—	2	1	no	—
115	C₁₉×#121	—	2	1	no	—
116	C₁₉×#121	—	2	1	no	—
117	C₁₉×#121	—	2	1	no	—
118	C₁₉×#121	—	2	1	no	—
119	C₁₉×#121	—	2	1	no	—
120	C₁₉×#121	—	2	1	no	—
121	C₁₉×#121	—	2	1	no	—
122	C₁₉×#121	—	2	1	no	—
123	C₁₉×#121	—	2	1	no	—
124	C₁₉×#121	—	2	1	no	—
125	C₁₉×#121	—	2	1	no	—
126	C₁₉×#121	—	2	1	no	—
127	C₁₉×#121	—	2	1	no	—
128	C₁₉×#121	—	2	1	no	—
129	C₁₉×#121	—	2	1	no	—
130	C₁₉×#121	—	4	2	no	—
131	C₁₉×#120	—	2	1	no	—
132	C₁₉×#120	—	2	1	no	—
133	C₁₉×#120	—	2	1	no	—
134	C₁₉×#120	—	2	1	no	—
135	C₁₉×#120	—	2	1	no	—
136	C₁₉×#120	—	2	1	no	—
137	C₁₉×#120	—	2	1	no	—
138	C₁₉×#120	—	2	1	no	—
139	C₁₉×#120	—	2	1	no	—
140	C₁₉×#120	—	2	1	no	—
141	C₁₉×#120	—	2	1	no	—
142	C₁₉×#120	—	2	1	no	—
143	C₁₉×#120	—	2	1	no	—
144	C₁₉×#120	—	2	1	no	—
145	C₁₉×#120	—	2	2	no	—
146	C₁₉×#120	—	2	2	no	—
147	C₁₉×#120	—	2	2	no	—
148	C₁₉×#120	—	4	2	no	—
149	C₁₉×#120	—	4	1	no	—
150	C₁₉×#120	D₄	1	1	yes	characteristic, complemented
151	C₁₉×#120	D₄	1	1	yes	characteristic, complemented
152	C₁₉×#120	D₄	1	1	yes	characteristic, complemented
153	C₁₉×#120	C₂³	1	1	yes	characteristic
154	C₁₉×#120	C₂³	1	1	yes	characteristic
155	C₁₉×#120	C₂³	1	1	yes	characteristic
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	C₄×D₄×C₁₉	—	2	1	no	—
161	C₄×D₄×C₁₉	—	2	1	no	—
162	C₁₉×#117	—	2	1	no	—
163	C₁₉×#117	D₄	1	1	yes	characteristic, complemented
164	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
165	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
166	C₂×C₂²⋊C₄×C₁₉	—	2	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, complemented
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	—	2	1	no	—
189	C₂⁴×C₁₉	—	2	1	no	—
190	C₂⁴×C₁₉	—	2	1	no	—
191	C₂⁴×C₁₉	—	4	1	no	—
192	C₂⁴×C₁₉	—	4	1	no	—
193	C₂⁴×C₁₉	—	8	2	no	—
194	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic, complemented
199	#41×C₁₉	—	2	2	no	—
200	#41×C₁₉	—	2	2	no	—
201	#41×C₁₉	—	4	2	no	—
202	#41×C₁₉	—	4	1	no	—
203	#41×C₁₉	—	4	2	no	—
204	#41×C₁₉	—	4	2	no	—
205	#41×C₁₉	—	4	1	no	—
206	#41×C₁₉	—	4	1	no	—
207	#41×C₁₉	—	4	2	no	—
208	#41×C₁₉	—	4	1	no	—
209	#41×C₁₉	—	8	2	no	—
210	C₂×Q₈×C₁₉	—	2	1	no	—
211	C₂×Q₈×C₁₉	—	2	1	no	—
212	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic, complemented
213	C₂×D₄×C₁₉	—	2	1	no	—
214	C₂×D₄×C₁₉	—	2	1	no	—
215	C₂×D₄×C₁₉	—	2	1	no	—
216	C₂×D₄×C₁₉	—	2	2	no	—
217	C₂×D₄×C₁₉	—	2	2	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	2	no	—
223	C₂×D₄×C₁₉	—	2	2	no	—
224	C₂×D₄×C₁₉	—	2	1	no	—
225	C₂×D₄×C₁₉	—	2	1	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	1	no	—
230	C₂×D₄×C₁₉	—	2	1	no	—
231	C₂×D₄×C₁₉	—	2	1	no	—
232	C₂×D₄×C₁₉	—	2	1	no	—
233	C₂×D₄×C₁₉	—	2	1	no	—
234	C₂×D₄×C₁₉	—	2	1	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	—	4	1	no	—
239	C₂×D₄×C₁₉	—	4	1	no	—
240	C₂×D₄×C₁₉	—	4	2	no	—
241	C₂×D₄×C₁₉	—	4	2	no	—
242	C₂×D₄×C₁₉	—	4	1	no	—
243	C₂×D₄×C₁₉	—	4	1	no	—
244	C₂×D₄×C₁₉	—	4	1	no	—
245	C₂×D₄×C₁₉	—	4	1	no	—
246	C₂×D₄×C₁₉	—	4	2	no	—
247	C₂×D₄×C₁₉	—	4	2	no	—
248	C₂×D₄×C₁₉	—	4	1	no	—
249	C₂×D₄×C₁₉	—	4	1	no	—
250	C₂×D₄×C₁₉	—	4	1	no	—
251	C₂×D₄×C₁₉	—	4	1	no	—
252	C₂×D₄×C₁₉	—	4	1	no	—
253	C₂×D₄×C₁₉	—	4	2	no	—
254	C₂×D₄×C₁₉	—	4	2	no	—
255	C₂×D₄×C₁₉	—	4	2	no	—
256	C₂×D₄×C₁₉	—	8	2	no	—
257	C₂×D₄×C₁₉	—	8	2	no	—
258	C₂×D₄×C₁₉	—	8	2	no	—
259	C₂×D₄×C₁₉	—	8	2	no	—
260	C₂×D₄×C₁₉	—	8	1	no	—
261	C₂×D₄×C₁₉	—	8	1	no	—
262	C₂×D₄×C₁₉	—	8	4	no	—
263	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
264	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
265	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
266	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic, complemented
267	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₉	—	2	1	no	—
269	C₂²×C₄×C₁₉	—	2	1	no	—
270	C₂²×C₄×C₁₉	—	2	1	no	—
271	C₂²×C₄×C₁₉	—	2	1	no	—
272	C₂²×C₄×C₁₉	—	2	1	no	—
273	C₂²×C₄×C₁₉	—	2	1	no	—
274	C₂²×C₄×C₁₉	—	2	1	no	—
275	C₂²×C₄×C₁₉	—	2	1	no	—
276	C₂²×C₄×C₁₉	—	2	1	no	—
277	C₂²×C₄×C₁₉	—	2	1	no	—
278	C₂²×C₄×C₁₉	—	4	1	no	—
279	C₂²×C₄×C₁₉	—	4	1	no	—
280	C₂²×C₄×C₁₉	—	4	1	no	—
281	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic, complemented
283	Q₁₆×C₁₉	—	4	2	no	—
284	SD₁₆×C₁₉	—	4	2	no	—
285	SD₁₆×C₁₉	—	4	2	no	—
286	D₈×C₁₉	—	4	2	no	—
287	M₁₆×C₁₉	—	2	2	no	—
288	M₁₆×C₁₉	—	4	1	no	—
289	C₂×C₈×C₁₉	—	4	1	no	—
290	C₄⋊C₄×C₁₉	—	2	1	no	—
291	C₄⋊C₄×C₁₉	—	2	1	no	—
292	C₄⋊C₄×C₁₉	—	2	1	no	—
293	C₄⋊C₄×C₁₉	—	2	1	no	—
294	C₄⋊C₄×C₁₉	—	2	1	no	—
295	C₄⋊C₄×C₁₉	—	2	1	no	—
296	C₄⋊C₄×C₁₉	—	2	1	no	—
297	C₄⋊C₄×C₁₉	—	2	1	no	—
298	C₄⋊C₄×C₁₉	—	2	1	no	—
299	C₄⋊C₄×C₁₉	—	4	2	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	1	no	—
317	C₂²⋊C₄×C₁₉	—	2	1	no	—
318	C₂²⋊C₄×C₁₉	—	2	1	no	—
319	C₂²⋊C₄×C₁₉	—	2	1	no	—
320	C₂²⋊C₄×C₁₉	—	2	1	no	—
321	C₂²⋊C₄×C₁₉	—	2	1	no	—
322	C₂²⋊C₄×C₁₉	—	2	1	no	—
323	C₂²⋊C₄×C₁₉	—	2	1	no	—
324	C₂²⋊C₄×C₁₉	—	2	1	no	—
325	C₂²⋊C₄×C₁₉	—	2	2	no	—
326	C₂²⋊C₄×C₁₉	—	2	2	no	—
327	C₂²⋊C₄×C₁₉	—	4	2	no	—
328	C₂²⋊C₄×C₁₉	—	4	2	no	—
329	C₂²⋊C₄×C₁₉	—	4	2	no	—
330	C₂²⋊C₄×C₁₉	—	4	1	no	—
331	C₂²⋊C₄×C₁₉	—	4	1	no	—
332	C₂²⋊C₄×C₁₉	—	4	2	no	—
333	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
334	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
335	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic, complemented
336	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic, complemented
337	C₄²×C₁₉	—	2	1	no	—
338	C₄²×C₁₉	—	2	1	no	—
339	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic, complemented
340	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic, complemented
341	#33551	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
342	C₂³×C₁₉	—	2	1	no	—
343	C₂³×C₁₉	—	2	1	no	—
344	C₂³×C₁₉	—	2	1	no	—
345	C₂³×C₁₉	—	2	1	no	—
346	C₂³×C₁₉	—	2	1	no	—
347	C₂³×C₁₉	—	2	2	no	—
348	C₂³×C₁₉	—	2	2	no	—
349	C₂³×C₁₉	—	2	1	no	—
350	C₂³×C₁₉	—	2	1	no	—
351	C₂³×C₁₉	—	2	1	no	—
352	C₂³×C₁₉	—	4	1	no	—
353	C₂³×C₁₉	—	4	1	no	—
354	C₂³×C₁₉	—	4	2	no	—
355	C₂³×C₁₉	—	4	2	no	—
356	C₂³×C₁₉	—	4	2	no	—
357	C₂³×C₁₉	—	4	1	no	—
358	C₂³×C₁₉	—	4	1	no	—
359	C₂³×C₁₉	—	4	2	no	—
360	C₂³×C₁₉	—	4	1	no	—
361	C₂³×C₁₉	—	4	4	no	—
362	C₂³×C₁₉	—	4	1	no	—
363	C₂³×C₁₉	—	4	1	no	—
364	C₂³×C₁₉	—	4	1	no	—
365	C₂³×C₁₉	—	8	1	no	—
366	C₂³×C₁₉	—	8	1	no	—
367	C₂³×C₁₉	—	8	1	no	—
368	C₂³×C₁₉	—	8	1	no	—
369	C₂³×C₁₉	—	8	1	no	—
370	C₂³×C₁₉	—	8	1	no	—
371	C₂³×C₁₉	—	8	1	no	—
372	C₂³×C₁₉	—	8	1	no	—
373	C₂³×C₁₉	—	8	1	no	—
374	C₂³×C₁₉	—	8	2	no	—
375	C₂³×C₁₉	—	8	2	no	—
376	C₂³×C₁₉	—	8	2	no	—
377	C₂³×C₁₉	—	8	2	no	—
378	C₂³×C₁₉	—	16	1	no	—
379	C₂³×C₁₉	#120	1	1	yes	characteristic
380	C₂³×C₁₉	#120	1	1	yes	characteristic
381	C₂³×C₁₉	#120	1	1	yes	characteristic
382	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
383	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
384	Q₈×C₁₉	—	2	2	no	—
385	Q₈×C₁₉	—	4	1	no	—
386	Q₈×C₁₉	—	4	1	no	—
387	Q₈×C₁₉	—	8	1	no	—
388	D₄×C₁₉	—	2	2	no	—
389	D₄×C₁₉	—	4	1	no	—
390	D₄×C₁₉	—	4	1	no	—
391	D₄×C₁₉	—	4	1	no	—
392	D₄×C₁₉	—	4	1	no	—
393	D₄×C₁₉	—	4	1	no	—
394	D₄×C₁₉	—	4	1	no	—
395	D₄×C₁₉	—	4	2	no	—
396	D₄×C₁₉	—	4	2	no	—
397	D₄×C₁₉	—	4	2	no	—
398	D₄×C₁₉	—	4	2	no	—
399	D₄×C₁₉	—	4	2	no	—
400	D₄×C₁₉	—	4	2	no	—
401	D₄×C₁₉	—	4	2	no	—
402	D₄×C₁₉	—	4	2	no	—
403	D₄×C₁₉	—	4	2	no	—
404	D₄×C₁₉	—	4	2	no	—
405	D₄×C₁₉	—	4	1	no	—
406	D₄×C₁₉	—	4	1	no	—
407	D₄×C₁₉	—	4	1	no	—
408	D₄×C₁₉	—	4	1	no	—
409	D₄×C₁₉	—	8	1	no	—
410	D₄×C₁₉	—	8	1	no	—
411	D₄×C₁₉	—	8	1	no	—
412	D₄×C₁₉	—	8	1	no	—
413	D₄×C₁₉	—	8	1	no	—
414	D₄×C₁₉	—	8	1	no	—
415	D₄×C₁₉	—	8	1	no	—
416	D₄×C₁₉	—	8	1	no	—
417	D₄×C₁₉	—	8	1	no	—
418	D₄×C₁₉	—	8	1	no	—
419	D₄×C₁₉	—	8	1	no	—
420	D₄×C₁₉	—	8	1	no	—
421	D₄×C₁₉	—	8	1	no	—
422	D₄×C₁₉	—	8	1	no	—
423	D₄×C₁₉	—	8	4	no	—
424	D₄×C₁₉	—	8	4	no	—
425	D₄×C₁₉	—	16	2	no	—
426	C₂×C₄×C₁₉	—	2	1	no	—
427	C₂×C₄×C₁₉	—	2	1	no	—
428	C₂×C₄×C₁₉	—	2	2	no	—
429	C₂×C₄×C₁₉	—	2	2	no	—
430	C₂×C₄×C₁₉	—	2	1	no	—
431	C₂×C₄×C₁₉	—	2	1	no	—
432	C₂×C₄×C₁₉	—	2	1	no	—
433	C₂×C₄×C₁₉	—	2	1	no	—
434	C₂×C₄×C₁₉	—	2	1	no	—
435	C₂×C₄×C₁₉	—	2	1	no	—
436	C₂×C₄×C₁₉	—	2	1	no	—
437	C₂×C₄×C₁₉	—	2	1	no	—
438	C₂×C₄×C₁₉	—	4	2	no	—
439	C₂×C₄×C₁₉	—	4	2	no	—
440	C₂×C₄×C₁₉	—	4	1	no	—
441	C₂×C₄×C₁₉	—	4	1	no	—
442	C₂×C₄×C₁₉	—	4	2	no	—
443	C₂×C₄×C₁₉	—	4	1	no	—
444	C₂×C₄×C₁₉	—	4	1	no	—
445	C₂×C₄×C₁₉	—	4	2	no	—
446	C₂×C₄×C₁₉	—	4	2	no	—
447	C₂×C₄×C₁₉	—	8	1	no	—
448	C₂×C₄×C₁₉	—	8	1	no	—
449	C₂×C₄×C₁₉	—	8	1	no	—
450	C₂×C₄×C₁₉	—	8	1	no	—
451	C₂×C₄×C₁₉	—	8	1	no	—
452	C₂×C₄×C₁₉	—	8	1	no	—
453	C₂×C₄×C₁₉	—	8	1	no	—
454	C₂×C₄×C₁₉	—	8	2	no	—
455	C₂×C₄×C₁₉	—	16	1	no	—
456	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
457	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
458	C₈×C₁₉	—	4	2	no	—
459	#3532	C₂×C₁₉	1	1	yes	characteristic, complemented
460	#3026	C₂×C₁₉	1	1	yes	characteristic, complemented
461	C₂×B(4,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic, complemented
462	#3019	C₂×C₁₉	1	1	yes	characteristic, complemented
463	#2200	C₂×C₁₉	1	2	yes	complemented
464	#2199	C₂×C₁₉	1	2	yes	complemented
465	#2197	C₂×C₁₉	1	2	yes	complemented
466	#2196	C₂×C₁₉	1	2	yes	complemented
467	#2127	C₂×C₁₉	1	1	yes	characteristic, complemented
468	#2121	C₂×C₁₉	1	1	yes	characteristic, complemented
469	C₂×AΣL(1,𝔽₁₆)	C₂×C₁₉	1	1	yes	characteristic, complemented
470	C₂²×C₁₉	—	2	2	no	—
471	C₂²×C₁₉	—	2	1	no	—
472	C₂²×C₁₉	—	2	1	no	—
473	C₂²×C₁₉	—	2	1	no	—
474	C₂²×C₁₉	—	2	1	no	—
475	C₂²×C₁₉	—	4	1	no	—
476	C₂²×C₁₉	—	4	1	no	—
477	C₂²×C₁₉	—	4	1	no	—
478	C₂²×C₁₉	—	4	1	no	—
479	C₂²×C₁₉	—	4	1	no	—
480	C₂²×C₁₉	—	4	1	no	—
481	C₂²×C₁₉	—	4	2	no	—
482	C₂²×C₁₉	—	4	1	no	—
483	C₂²×C₁₉	—	4	1	no	—
484	C₂²×C₁₉	—	4	1	no	—
485	C₂²×C₁₉	—	4	1	no	—
486	C₂²×C₁₉	—	4	1	no	—
487	C₂²×C₁₉	—	4	1	no	—
488	C₂²×C₁₉	—	4	2	no	—
489	C₂²×C₁₉	—	4	1	no	—
490	C₂²×C₁₉	—	4	2	no	—
491	C₂²×C₁₉	—	4	2	no	—
492	C₂²×C₁₉	—	4	1	no	—
493	C₂²×C₁₉	—	4	1	no	—
494	C₂²×C₁₉	—	4	1	no	—
495	C₂²×C₁₉	—	8	1	no	—
496	C₂²×C₁₉	—	8	1	no	—
497	C₂²×C₁₉	—	8	1	no	—
498	C₂²×C₁₉	—	8	2	no	—
499	C₂²×C₁₉	—	8	2	no	—
500	C₂²×C₁₉	—	8	2	no	—
501	C₂²×C₁₉	—	8	1	no	—
502	C₂²×C₁₉	—	8	4	no	—
503	C₂²×C₁₉	—	8	2	no	—
504	C₂²×C₁₉	—	8	2	no	—
505	C₂²×C₁₉	—	8	2	no	—
506	C₂²×C₁₉	—	8	1	no	—
507	C₂²×C₁₉	—	16	2	no	—
508	C₂²×C₁₉	—	16	1	no	—
509	C₂²×C₁₉	—	16	1	no	—
510	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
511	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
512	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
513	C₄×C₁₉	—	2	1	no	—
514	C₄×C₁₉	—	2	1	no	—
515	C₄×C₁₉	—	4	1	no	—
516	C₄×C₁₉	—	4	1	no	—
517	C₄×C₁₉	—	4	1	no	—
518	C₄×C₁₉	—	4	1	no	—
519	C₄×C₁₉	—	4	1	no	—
520	C₄×C₁₉	—	4	1	no	—
521	C₄×C₁₉	—	4	2	no	—
522	C₄×C₁₉	—	4	1	no	—
523	C₄×C₁₉	—	4	1	no	—
524	C₄×C₁₉	—	8	2	no	—
525	C₄×C₁₉	—	8	2	no	—
526	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic, complemented
527	#575	—	2	1	no	—
528	H(3,𝔽₄)	C₂²×C₁₉	1	1	yes	characteristic, complemented
529	#560	—	2	1	no	—
530	#560	C₂²×C₁₉	1	1	yes	characteristic, complemented
531	#551	—	2	1	no	—
532	#551	C₂²×C₁₉	1	1	yes	characteristic, complemented
533	#546	—	2	1	no	—
534	#546	—	2	1	no	—
535	#546	—	2	1	no	—
536	D₄²	—	2	1	no	—
537	D₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
538	#538	—	2	1	no	—
539	#538	—	2	1	no	—
540	#538	—	2	1	no	—
541	#535	—	2	1	no	—
542	#535	C₂²×C₁₉	1	1	yes	characteristic
543	#534	—	2	1	no	—
544	#534	—	2	1	no	—
545	#534	C₂²×C₁₉	1	1	yes	characteristic
546	C₂×#120	—	2	1	no	—
547	C₂×#120	—	2	1	no	—
548	C₂×#120	C₂²×C₁₉	1	1	yes	characteristic
549	#458	—	2	1	no	—
550	#458	C₂²×C₁₉	1	2	yes	complemented
551	B(4,𝔽₂)	—	2	1	no	—
552	B(4,𝔽₂)	—	2	1	no	—
553	B(4,𝔽₂)	—	2	1	no	—
554	B(4,𝔽₂)	C₂²×C₁₉	1	2	yes	—
555	B(4,𝔽₂)	C₂²×C₁₉	1	2	yes	complemented
556	B(4,𝔽₂)	C₂²×C₁₉	1	2	yes	complemented
557	#455	—	2	1	no	—
558	#455	C₂²×C₁₉	1	2	yes	complemented
559	#453	—	2	1	no	—
560	#453	C₂²×C₁₉	1	2	yes	complemented
561	#421	—	2	1	no	—
562	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic, complemented
563	C₂×#99	—	2	1	no	—
564	C₂×#99	—	2	1	no	—
565	C₂×#99	C₂²×C₁₉	1	1	yes	characteristic, complemented
566	C₂×#99	C₂²×C₁₉	1	1	yes	characteristic, complemented
567	#354	C₂²×C₁₉	1	2	yes	complemented
568	#353	C₂²×C₁₉	1	2	yes	complemented
569	#352	C₂²×C₁₉	1	2	yes	complemented
570	AΣL(1,𝔽₁₆)	C₂²×C₁₉	1	2	yes	complemented
571	AΣL(1,𝔽₁₆)	C₂²×C₁₉	1	2	yes	complemented
572	AΣL(1,𝔽₁₆)	C₂²×C₁₉	1	2	yes	complemented
573	C₂×C₁₉	—	2	1	no	—
574	C₂×C₁₉	—	2	1	no	—
575	C₂×C₁₉	—	2	1	no	—
576	C₂×C₁₉	—	4	1	no	—
577	C₂×C₁₉	—	4	1	no	—
578	C₂×C₁₉	—	4	2	no	—
579	C₂×C₁₉	—	4	1	no	—
580	C₂×C₁₉	—	4	1	no	—
581	C₂×C₁₉	—	8	1	no	—
582	C₂×C₁₉	—	8	1	no	—
583	C₂×C₁₉	—	8	1	no	—
584	C₂×C₁₉	—	8	2	no	—
585	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
586	C₂⁵	D₄×C₁₉	1	1	yes	characteristic, complemented
587	H(5,𝔽₂)	—	2	1	no	—
588	H(5,𝔽₂)	—	2	1	no	—
589	H(5,𝔽₂)	—	2	1	no	—
590	H(5,𝔽₂)	—	4	2	no	—
591	H(5,𝔽₂)	C₂³×C₁₉	1	2	yes	—
592	C₂×#41	—	2	1	no	—
593	C₂×#41	—	2	1	no	—
594	C₂×#41	—	4	1	no	—
595	C₂×#41	D₄×C₁₉	1	1	yes	characteristic, complemented
596	C₂²×D₄	—	2	1	no	—
597	C₂²×D₄	—	2	1	no	—
598	C₂²×D₄	—	2	1	no	—
599	C₂²×D₄	—	2	1	no	—
600	C₂²×D₄	—	2	1	no	—
601	C₂²×D₄	—	2	1	no	—
602	C₂²×D₄	—	2	1	no	—
603	C₂²×D₄	—	4	1	no	—
604	C₂²×D₄	—	4	1	no	—
605	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic, complemented
606	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
607	#137	—	2	2	no	—
608	#137	—	4	1	no	—
609	AGL(1,ℤ/8)	—	2	2	no	—
610	AGL(1,ℤ/8)	—	4	1	no	—
611	#135	—	4	2	no	—
612	C₂×M₁₆	—	2	1	no	—
613	#127	—	2	1	no	—
614	#127	D₄×C₁₉	1	1	yes	characteristic, complemented
615	#127	C₂³×C₁₉	1	1	yes	characteristic
616	#126	—	2	1	no	—
617	#126	—	2	1	no	—
618	#126	—	2	1	no	—
619	#126	—	2	1	no	—
620	#124	—	2	1	no	—
621	#124	—	2	1	no	—
622	#124	—	2	1	no	—
623	#124	—	2	1	no	—
624	#124	—	2	1	no	—
625	#124	D₄×C₁₉	1	1	yes	characteristic, complemented
626	#124	C₂³×C₁₉	1	1	yes	characteristic
627	#123	—	2	1	no	—
628	#123	—	2	1	no	—
629	#123	—	2	1	no	—
630	#123	—	2	1	no	—
631	#123	—	2	1	no	—
632	#123	—	2	1	no	—
633	#123	—	2	1	no	—
634	#123	—	2	1	no	—
635	#123	—	2	2	no	—
636	#123	—	4	1	no	—
637	#123	D₄×C₁₉	1	1	yes	characteristic, complemented
638	#123	C₂³×C₁₉	1	1	yes	characteristic
639	C₂²⋊Q₈	—	2	1	no	—
640	C₂²⋊Q₈	—	2	1	no	—
641	C₂²⋊Q₈	—	2	1	no	—
642	#121	—	2	1	no	—
643	#121	—	2	1	no	—
644	#121	—	2	1	no	—
645	#121	—	2	1	no	—
646	#121	—	2	1	no	—
647	#121	—	2	1	no	—
648	#121	—	2	1	no	—
649	#121	—	2	1	no	—
650	#121	—	2	1	no	—
651	#121	—	2	1	no	—
652	#121	—	2	1	no	—
653	#121	—	2	1	no	—
654	#121	—	2	1	no	—
655	#121	—	2	1	no	—
656	#121	—	2	1	no	—
657	#121	—	4	2	no	—
658	#120	—	2	1	no	—
659	#120	—	2	1	no	—
660	#120	—	2	1	no	—
661	#120	—	2	1	no	—
662	#120	—	2	1	no	—
663	#120	—	2	1	no	—
664	#120	—	2	1	no	—
665	#120	—	2	1	no	—
666	#120	—	2	1	no	—
667	#120	—	2	1	no	—
668	#120	—	2	1	no	—
669	#120	—	2	1	no	—
670	#120	—	2	1	no	—
671	#120	—	2	1	no	—
672	#120	—	2	2	no	—
673	#120	—	2	2	no	—
674	#120	—	2	2	no	—
675	#120	—	4	2	no	—
676	#120	—	4	1	no	—
677	#120	D₄×C₁₉	1	1	yes	characteristic, complemented
678	#120	D₄×C₁₉	1	1	yes	characteristic, complemented
679	#120	D₄×C₁₉	1	1	yes	characteristic, complemented
680	#120	C₂³×C₁₉	1	1	yes	characteristic
681	#120	C₂³×C₁₉	1	1	yes	characteristic
682	#120	C₂³×C₁₉	1	1	yes	characteristic
683	C₄×D₄	—	2	1	no	—
684	C₄×D₄	—	2	1	no	—
685	C₄×D₄	—	2	1	no	—
686	C₄×D₄	—	2	1	no	—
687	C₄×D₄	—	2	1	no	—
688	C₄×D₄	—	2	1	no	—
689	#117	—	2	1	no	—
690	#117	D₄×C₁₉	1	1	yes	characteristic, complemented
691	C₂×C₂²⋊C₄	—	2	1	no	—
692	C₂×C₂²⋊C₄	—	2	1	no	—
693	C₂×C₂²⋊C₄	—	2	1	no	—
694	C₂×C₂²⋊C₄	—	2	1	no	—
695	C₂×C₂²⋊C₄	—	2	1	no	—
696	C₂×C₂²⋊C₄	—	2	1	no	—
697	C₂×C₂²⋊C₄	—	2	1	no	—
698	C₂×C₂²⋊C₄	—	4	1	no	—
699	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic, complemented
700	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic, complemented
701	#104	—	2	2	no	—
702	#104	—	2	2	no	—
703	#100	—	2	1	no	—
704	#100	C₂³×C₁₉	1	2	yes	—
705	#99	—	2	1	no	—
706	#99	—	2	1	no	—
707	#99	—	2	2	no	—
708	#99	—	2	2	no	—
709	#99	—	2	2	no	—
710	#99	—	2	2	no	—
711	#99	C₂³×C₁₉	1	2	yes	—
712	#99	C₂³×C₁₉	1	2	yes	—
713	C₁₉	#33551	1	1	yes	characteristic, direct product factor, Sylow
714	C₂⁴	—	2	1	no	—
715	C₂⁴	—	2	1	no	—
716	C₂⁴	—	2	1	no	—
717	C₂⁴	—	2	1	no	—
718	C₂⁴	—	2	1	no	—
719	C₂⁴	—	4	1	no	—
720	C₂⁴	—	4	1	no	—
721	C₂⁴	—	8	2	no	—
722	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
723	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
724	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
725	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
726	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic, complemented
727	#41	—	2	2	no	—
728	#41	—	2	2	no	—
729	#41	—	4	2	no	—
730	#41	—	4	1	no	—
731	#41	—	4	2	no	—
732	#41	—	4	2	no	—
733	#41	—	4	1	no	—
734	#41	—	4	1	no	—
735	#41	—	4	2	no	—
736	#41	—	4	1	no	—
737	#41	—	8	2	no	—
738	C₂×Q₈	—	2	1	no	—
739	C₂×Q₈	—	2	1	no	—
740	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic, complemented
741	C₂×D₄	—	2	1	no	—
742	C₂×D₄	—	2	1	no	—
743	C₂×D₄	—	2	1	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	1	no	—
747	C₂×D₄	—	2	1	no	—
748	C₂×D₄	—	2	1	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	1	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	1	no	—
754	C₂×D₄	—	2	1	no	—
755	C₂×D₄	—	2	1	no	—
756	C₂×D₄	—	2	1	no	—
757	C₂×D₄	—	2	1	no	—
758	C₂×D₄	—	2	1	no	—
759	C₂×D₄	—	2	1	no	—
760	C₂×D₄	—	2	1	no	—
761	C₂×D₄	—	2	1	no	—
762	C₂×D₄	—	2	1	no	—
763	C₂×D₄	—	2	1	no	—
764	C₂×D₄	—	2	1	no	—
765	C₂×D₄	—	2	1	no	—
766	C₂×D₄	—	4	1	no	—
767	C₂×D₄	—	4	1	no	—
768	C₂×D₄	—	4	2	no	—
769	C₂×D₄	—	4	2	no	—
770	C₂×D₄	—	4	1	no	—
771	C₂×D₄	—	4	1	no	—
772	C₂×D₄	—	4	1	no	—
773	C₂×D₄	—	4	1	no	—
774	C₂×D₄	—	4	2	no	—
775	C₂×D₄	—	4	2	no	—
776	C₂×D₄	—	4	1	no	—
777	C₂×D₄	—	4	1	no	—
778	C₂×D₄	—	4	1	no	—
779	C₂×D₄	—	4	1	no	—
780	C₂×D₄	—	4	1	no	—
781	C₂×D₄	—	4	2	no	—
782	C₂×D₄	—	4	2	no	—
783	C₂×D₄	—	4	2	no	—
784	C₂×D₄	—	8	2	no	—
785	C₂×D₄	—	8	2	no	—
786	C₂×D₄	—	8	2	no	—
787	C₂×D₄	—	8	2	no	—
788	C₂×D₄	—	8	1	no	—
789	C₂×D₄	—	8	1	no	—
790	C₂×D₄	—	8	4	no	—
791	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
792	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
793	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
794	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic, complemented
795	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
796	C₂²×C₄	—	2	1	no	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	2	1	no	—
799	C₂²×C₄	—	2	1	no	—
800	C₂²×C₄	—	2	1	no	—
801	C₂²×C₄	—	2	1	no	—
802	C₂²×C₄	—	2	1	no	—
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	4	1	no	—
807	C₂²×C₄	—	4	1	no	—
808	C₂²×C₄	—	4	1	no	—
809	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
810	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic, complemented
811	Q₁₆	—	4	2	no	—
812	SD₁₆	—	4	2	no	—
813	SD₁₆	—	4	2	no	—
814	D₈	—	4	2	no	—
815	M₁₆	—	2	2	no	—
816	M₁₆	—	4	1	no	—
817	C₂×C₈	—	4	1	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	1	no	—
820	C₄⋊C₄	—	2	1	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	1	no	—
824	C₄⋊C₄	—	2	1	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	2	1	no	—
829	C₂²⋊C₄	—	2	1	no	—
830	C₂²⋊C₄	—	2	1	no	—
831	C₂²⋊C₄	—	2	1	no	—
832	C₂²⋊C₄	—	2	1	no	—
833	C₂²⋊C₄	—	2	1	no	—
834	C₂²⋊C₄	—	2	1	no	—
835	C₂²⋊C₄	—	2	1	no	—
836	C₂²⋊C₄	—	2	1	no	—
837	C₂²⋊C₄	—	2	1	no	—
838	C₂²⋊C₄	—	2	1	no	—
839	C₂²⋊C₄	—	2	1	no	—
840	C₂²⋊C₄	—	2	1	no	—
841	C₂²⋊C₄	—	2	1	no	—
842	C₂²⋊C₄	—	2	1	no	—
843	C₂²⋊C₄	—	2	1	no	—
844	C₂²⋊C₄	—	2	1	no	—
845	C₂²⋊C₄	—	2	1	no	—
846	C₂²⋊C₄	—	2	1	no	—
847	C₂²⋊C₄	—	2	1	no	—
848	C₂²⋊C₄	—	2	1	no	—
849	C₂²⋊C₄	—	2	1	no	—
850	C₂²⋊C₄	—	2	1	no	—
851	C₂²⋊C₄	—	2	1	no	—
852	C₂²⋊C₄	—	2	1	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	4	2	no	—
856	C₂²⋊C₄	—	4	2	no	—
857	C₂²⋊C₄	—	4	2	no	—
858	C₂²⋊C₄	—	4	1	no	—
859	C₂²⋊C₄	—	4	1	no	—
860	C₂²⋊C₄	—	4	2	no	—
861	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
862	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
863	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic, complemented
864	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic, complemented
865	C₄²	—	2	1	no	—
866	C₄²	—	2	1	no	—
867	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic, complemented
868	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic, complemented
869	C₂³	—	2	1	no	—
870	C₂³	—	2	1	no	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	1	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	2	no	—
875	C₂³	—	2	2	no	—
876	C₂³	—	2	1	no	—
877	C₂³	—	2	1	no	—
878	C₂³	—	2	1	no	—
879	C₂³	—	4	1	no	—
880	C₂³	—	4	1	no	—
881	C₂³	—	4	2	no	—
882	C₂³	—	4	2	no	—
883	C₂³	—	4	2	no	—
884	C₂³	—	4	1	no	—
885	C₂³	—	4	1	no	—
886	C₂³	—	4	2	no	—
887	C₂³	—	4	1	no	—
888	C₂³	—	4	4	no	—
889	C₂³	—	4	1	no	—
890	C₂³	—	4	1	no	—
891	C₂³	—	4	1	no	—
892	C₂³	—	8	1	no	—
893	C₂³	—	8	1	no	—
894	C₂³	—	8	1	no	—
895	C₂³	—	8	1	no	—
896	C₂³	—	8	1	no	—
897	C₂³	—	8	1	no	—
898	C₂³	—	8	1	no	—
899	C₂³	—	8	1	no	—
900	C₂³	—	8	1	no	—
901	C₂³	—	8	2	no	—
902	C₂³	—	8	2	no	—
903	C₂³	—	8	2	no	—
904	C₂³	—	8	2	no	—
905	C₂³	—	16	1	no	—
906	C₂³	C₁₉×#120	1	1	yes	characteristic
907	C₂³	C₁₉×#120	1	1	yes	characteristic
908	C₂³	C₁₉×#120	1	1	yes	characteristic
909	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
910	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
911	Q₈	—	2	2	no	—
912	Q₈	—	4	1	no	—
913	Q₈	—	4	1	no	—
914	Q₈	—	8	1	no	—
915	D₄	—	2	2	no	—
916	D₄	—	4	1	no	—
917	D₄	—	4	1	no	—
918	D₄	—	4	1	no	—
919	D₄	—	4	1	no	—
920	D₄	—	4	1	no	—
921	D₄	—	4	1	no	—
922	D₄	—	4	2	no	—
923	D₄	—	4	2	no	—
924	D₄	—	4	2	no	—
925	D₄	—	4	2	no	—
926	D₄	—	4	2	no	—
927	D₄	—	4	2	no	—
928	D₄	—	4	2	no	—
929	D₄	—	4	2	no	—
930	D₄	—	4	2	no	—
931	D₄	—	4	1	no	—
932	D₄	—	4	1	no	—
933	D₄	—	4	1	no	—
934	D₄	—	4	1	no	—
935	D₄	—	4	2	no	—
936	D₄	—	8	1	no	—
937	D₄	—	8	1	no	—
938	D₄	—	8	1	no	—
939	D₄	—	8	1	no	—
940	D₄	—	8	1	no	—
941	D₄	—	8	1	no	—
942	D₄	—	8	1	no	—
943	D₄	—	8	1	no	—
944	D₄	—	8	1	no	—
945	D₄	—	8	1	no	—
946	D₄	—	8	1	no	—
947	D₄	—	8	1	no	—
948	D₄	—	8	1	no	—
949	D₄	—	8	1	no	—
950	D₄	—	8	4	no	—
951	D₄	—	8	4	no	—
952	D₄	—	16	2	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	4	2	no	—
966	C₂×C₄	—	4	2	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	4	2	no	—
970	C₂×C₄	—	4	1	no	—
971	C₂×C₄	—	4	1	no	—
972	C₂×C₄	—	4	2	no	—
973	C₂×C₄	—	4	2	no	—
974	C₂×C₄	—	8	1	no	—
975	C₂×C₄	—	8	1	no	—
976	C₂×C₄	—	8	1	no	—
977	C₂×C₄	—	8	1	no	—
978	C₂×C₄	—	8	1	no	—
979	C₂×C₄	—	8	1	no	—
980	C₂×C₄	—	8	1	no	—
981	C₂×C₄	—	8	2	no	—
982	C₂×C₄	—	16	1	no	—
983	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
984	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
985	C₈	—	4	2	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	1	no	—
988	C₂²	—	2	1	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	4	1	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	1	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	1	no	—
1000	C₂²	—	4	1	no	—
1001	C₂²	—	4	1	no	—
1002	C₂²	—	4	1	no	—
1003	C₂²	—	4	1	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	—	4	1	no	—
1010	C₂²	—	4	1	no	—
1011	C₂²	—	8	1	no	—
1012	C₂²	—	8	1	no	—
1013	C₂²	—	8	1	no	—
1014	C₂²	—	8	2	no	—
1015	C₂²	—	8	2	no	—
1016	C₂²	—	8	2	no	—
1017	C₂²	—	8	1	no	—
1018	C₂²	—	8	4	no	—
1019	C₂²	—	8	2	no	—
1020	C₂²	—	8	2	no	—
1021	C₂²	—	8	2	no	—
1022	C₂²	—	8	1	no	—
1023	C₂²	—	16	2	no	—
1024	C₂²	—	16	1	no	—
1025	C₂²	—	16	1	no	—
1026	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
1027	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
1028	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
1029	C₄	—	2	1	no	—
1030	C₄	—	2	1	no	—
1031	C₄	—	4	1	no	—
1032	C₄	—	4	1	no	—
1033	C₄	—	4	1	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	8	2	no	—
1041	C₄	—	8	2	no	—
1042	C₂	—	2	1	no	—
1043	C₂	—	2	1	no	—
1044	C₂	—	2	1	no	—
1045	C₂	—	4	1	no	—
1046	C₂	—	4	1	no	—
1047	C₂	—	4	2	no	—
1048	C₂	—	4	1	no	—
1049	C₂	—	4	1	no	—
1050	C₂	—	8	1	no	—
1051	C₂	—	8	1	no	—
1052	C₂	—	8	1	no	—
1053	C₂	—	8	2	no	—
1054	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×#3532	C₂	semidirect
2. C₁₉×#3026	C₂	semidirect
3. C₂×C₁₉×B(4,𝔽₂)	C₂	semidirect
4. C₁₉×#3019	C₂	semidirect
5. C₁₉×#2200	C₂	semidirect
6. C₁₉×#2199	C₂	semidirect
7. C₁₉×#2197	C₂	semidirect
8. C₁₉×#2196	C₂	semidirect
9. C₁₉×#2127	C₂	semidirect
10. C₁₉×#2121	C₂	semidirect
11. C₂×C₁₉×AΣL(1,𝔽₁₆)	C₂	semidirect
12. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
14. C₁₉×H(3,𝔽₄)	C₂²	semidirect
16. C₁₉×#560	C₂²	semidirect
18. C₁₉×#551	C₂²	semidirect
23. D₄²×C₁₉	C₂²	semidirect
36. C₁₉×#458	C₂²	semidirect
41. C₁₉×B(4,𝔽₂)	C₂²	semidirect
42. C₁₉×B(4,𝔽₂)	C₂²	semidirect
44. C₁₉×#455	C₂²	semidirect
46. C₁₉×#453	C₂²	semidirect
48. C₂×C₁₉×#100	C₂²	semidirect
51. C₂×C₁₉×#99	C₂²	semidirect
52. C₂×C₁₉×#99	C₂²	semidirect
53. C₁₉×#354	C₂²	semidirect
54. C₁₉×#353	C₂²	semidirect
55. C₁₉×#352	C₂²	semidirect
56. C₁₉×AΣL(1,𝔽₁₆)	C₂²	semidirect
57. C₁₉×AΣL(1,𝔽₁₆)	C₂²	semidirect
58. C₁₉×AΣL(1,𝔽₁₆)	C₂²	semidirect
59. C₂⁵×C₁₉	D₄	semidirect
68. C₂×#41×C₁₉	D₄	semidirect
78. C₂²×D₄×C₁₉	D₄	semidirect
87. C₁₉×#127	D₄	semidirect
98. C₁₉×#124	D₄	semidirect
110. C₁₉×#123	D₄	semidirect
150. C₁₉×#120	D₄	semidirect
151. C₁₉×#120	D₄	semidirect
152. C₁₉×#120	D₄	semidirect
163. C₁₉×#117	D₄	semidirect
172. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
173. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
198. C₂⁴×C₁₉	C₂×D₄	semidirect
212. C₂×Q₈×C₁₉	C₂×D₄	semidirect
266. C₂×D₄×C₁₉	C₂×D₄	semidirect
282. C₂²×C₄×C₁₉	C₂×D₄	semidirect
335. C₂²⋊C₄×C₁₉	C₂×D₄	semidirect
336. C₂²⋊C₄×C₁₉	C₂×D₄	semidirect
339. C₄²×C₁₉	C₂×D₄	semidirect
340. C₄²×C₁₉	C₂×D₄	semidirect
341. #33551	C₁₉	direct (N × H)
459. #3532	C₂×C₁₉	semidirect
460. #3026	C₂×C₁₉	semidirect
461. C₂×B(4,𝔽₂)	C₂×C₁₉	semidirect
462. #3019	C₂×C₁₉	semidirect
463. #2200	C₂×C₁₉	semidirect
464. #2199	C₂×C₁₉	semidirect
465. #2197	C₂×C₁₉	semidirect
466. #2196	C₂×C₁₉	semidirect
467. #2127	C₂×C₁₉	semidirect
468. #2121	C₂×C₁₉	semidirect
469. C₂×AΣL(1,𝔽₁₆)	C₂×C₁₉	semidirect
526. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
528. H(3,𝔽₄)	C₂²×C₁₉	semidirect
530. #560	C₂²×C₁₉	semidirect
532. #551	C₂²×C₁₉	semidirect
537. D₄²	C₂²×C₁₉	semidirect
550. #458	C₂²×C₁₉	semidirect
555. B(4,𝔽₂)	C₂²×C₁₉	semidirect
556. B(4,𝔽₂)	C₂²×C₁₉	semidirect
558. #455	C₂²×C₁₉	semidirect
560. #453	C₂²×C₁₉	semidirect
562. C₂×#100	C₂²×C₁₉	semidirect
565. C₂×#99	C₂²×C₁₉	semidirect
566. C₂×#99	C₂²×C₁₉	semidirect
567. #354	C₂²×C₁₉	semidirect
568. #353	C₂²×C₁₉	semidirect
569. #352	C₂²×C₁₉	semidirect
570. AΣL(1,𝔽₁₆)	C₂²×C₁₉	semidirect
571. AΣL(1,𝔽₁₆)	C₂²×C₁₉	semidirect
572. AΣL(1,𝔽₁₆)	C₂²×C₁₉	semidirect
586. C₂⁵	D₄×C₁₉	semidirect
595. C₂×#41	D₄×C₁₉	semidirect
605. C₂²×D₄	D₄×C₁₉	semidirect
614. #127	D₄×C₁₉	semidirect
625. #124	D₄×C₁₉	semidirect
637. #123	D₄×C₁₉	semidirect
677. #120	D₄×C₁₉	semidirect
678. #120	D₄×C₁₉	semidirect
679. #120	D₄×C₁₉	semidirect
690. #117	D₄×C₁₉	semidirect
699. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
700. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
713. C₁₉	#33551	direct (N × H)
726. C₂⁴	C₂×D₄×C₁₉	semidirect
740. C₂×Q₈	C₂×D₄×C₁₉	semidirect
794. C₂×D₄	C₂×D₄×C₁₉	semidirect
810. C₂²×C₄	C₂×D₄×C₁₉	semidirect
863. C₂²⋊C₄	C₂×D₄×C₁₉	semidirect
864. C₂²⋊C₄	C₂×D₄×C₁₉	semidirect
867. C₄²	C₂×D₄×C₁₉	semidirect
868. C₄²	C₂×D₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3532	2
C₁₉×#3026	2
C₂×C₁₉×B(4,𝔽₂)	2
C₁₉×#3019	2
C₁₉×#2200	2
C₁₉×#2199	2
C₁₉×#2197	2
C₁₉×#2196	2
C₁₉×#2127	2
C₁₉×#2121	2
C₂×C₁₉×AΣL(1,𝔽₁₆)	2
#33551	19

Subgroups — C19×#33551 #18039510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33551 #18039510