Subgroups — C₁₉×#60366 #18066325

Order 4864.

4782 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#575	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3449	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3013	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3012	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3011	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3010	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3009	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3008	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3002	C₂	1	8	yes	maximal, complemented
12	C₁₉×#2896	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₉×#416	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₉×#408	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#585	—	2	8	no	—
16	C₁₉×#585	—	2	8	no	—
17	C₂×C₁₉×2₋¹⁺⁴	—	2	1	no	—
18	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	2	yes	—
19	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	2	yes	complemented
20	C₂×C₁₉×H(5,𝔽₂)	—	2	2	no	—
21	C₂×C₁₉×H(5,𝔽₂)	—	2	1	no	—
22	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	2	yes	—
23	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	2	yes	complemented
24	C₂²×#41×C₁₉	—	2	2	no	—
25	C₂²×#41×C₁₉	—	2	2	no	—
26	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
30	C₂²×#41×C₁₉	C₂²	1	4	yes	complemented
31	C₁₉×#575	—	2	8	no	—
32	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
33	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
34	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
35	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
36	C₂×C₁₉×#135	—	2	8	no	—
37	C₂×C₁₉×#135	C₂²	1	4	yes	complemented
38	C₂×C₁₉×#135	C₂²	1	4	yes	complemented
39	C₂×C₁₉×#135	C₂²	1	4	yes	complemented
40	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
41	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
42	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
43	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
44	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
45	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#537	C₂²	1	4	yes	complemented
47	C₁₉×#536	—	2	1	no	—
48	C₁₉×#536	C₂²	1	2	yes	complemented
49	C₁₉×#535	—	2	1	no	—
50	C₁₉×#535	C₂²	1	2	yes	complemented
51	C₁₉×#534	—	2	2	no	—
52	C₁₉×#532	—	2	2	no	—
53	C₁₉×#525	—	2	2	no	—
54	C₁₉×#525	C₂²	1	4	yes	complemented
55	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
56	C₁₉×#452	C₂²	1	8	yes	complemented
57	C₁₉×#452	C₂²	1	8	yes	complemented
58	C₁₉×#451	C₂²	1	8	yes	complemented
59	C₁₉×#450	C₂²	1	8	yes	complemented
60	C₁₉×#449	C₂²	1	8	yes	complemented
61	C₁₉×#449	C₂²	1	8	yes	complemented
62	C₁₉×#448	C₂²	1	8	yes	complemented
63	C₁₉×#447	C₂²	1	8	yes	complemented
64	C₁₉×#419	C₂²	1	2	yes	complemented
65	C₁₉×#418	C₂²	1	2	yes	complemented
66	C₁₉×#417	C₂²	1	4	yes	complemented
67	C₁₉×#416	C₂²	1	4	yes	complemented
68	C₁₉×#416	C₂²	1	4	yes	complemented
69	C₁₉×#416	C₂²	1	2	yes	complemented
70	C₁₉×#416	C₂²	1	2	yes	complemented
71	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
72	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
73	C₁₉×#408	C₂²	1	2	yes	complemented
74	C₁₉×#408	C₂²	1	2	yes	complemented
75	C₁₉×#408	C₂²	1	4	yes	complemented
76	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	complemented
77	C₁₉×2₋¹⁺⁴	—	2	16	no	—
78	C₁₉×2₋¹⁺⁴	—	2	8	no	—
79	C₁₉×2₋¹⁺⁴	—	2	8	no	—
80	C₁₉×2₋¹⁺⁴	—	2	8	no	—
81	C₁₉×2₋¹⁺⁴	—	2	8	no	—
82	C₁₉×H(5,𝔽₂)	—	2	16	no	—
83	C₁₉×H(5,𝔽₂)	—	2	32	no	—
84	C₁₉×H(5,𝔽₂)	—	2	8	no	—
85	C₁₉×H(5,𝔽₂)	—	2	8	no	—
86	C₁₉×H(5,𝔽₂)	—	2	8	no	—
87	C₁₉×H(5,𝔽₂)	—	2	8	no	—
88	C₂×#41×C₁₉	—	2	32	no	—
89	C₂×#41×C₁₉	—	2	32	no	—
90	C₂×#41×C₁₉	—	2	16	no	—
91	C₂×#41×C₁₉	—	2	16	no	—
92	C₂×#41×C₁₉	—	2	2	no	—
93	C₂×#41×C₁₉	—	2	2	no	—
94	C₂×#41×C₁₉	—	2	4	no	—
95	C₂×#41×C₁₉	—	2	2	no	—
96	C₂×#41×C₁₉	—	2	2	no	—
97	C₂×#41×C₁₉	—	2	4	no	—
98	C₂×#41×C₁₉	—	2	1	no	—
99	C₂×#41×C₁₉	—	2	1	no	—
100	C₂×#41×C₁₉	—	2	4	no	—
101	C₂×#41×C₁₉	—	2	1	no	—
102	C₂×#41×C₁₉	—	2	1	no	—
103	C₂×#41×C₁₉	—	2	4	no	—
104	C₂×#41×C₁₉	—	2	4	no	—
105	C₂×#41×C₁₉	—	2	4	no	—
106	C₂×#41×C₁₉	—	2	4	no	—
107	C₂×#41×C₁₉	—	2	4	no	—
108	C₂×#41×C₁₉	—	2	1	no	—
109	C₂×#41×C₁₉	—	2	1	no	—
110	C₂×#41×C₁₉	—	2	4	no	—
111	C₂×#41×C₁₉	—	2	4	no	—
112	C₂×#41×C₁₉	D₄	1	2	yes	—
113	C₂×#41×C₁₉	D₄	1	2	yes	—
114	C₂×#41×C₁₉	D₄	1	8	yes	complemented
115	C₂×#41×C₁₉	D₄	1	8	yes	complemented
116	C₂×#41×C₁₉	C₂³	1	4	yes	—
117	C₂×#41×C₁₉	C₂³	1	4	yes	—
118	C₂×#41×C₁₉	C₂³	1	2	yes	—
119	C₂×#41×C₁₉	C₂³	1	2	yes	—
120	C₂×#41×C₁₉	C₂³	1	2	yes	—
121	C₂×#41×C₁₉	C₂³	1	2	yes	—
122	C₂×#41×C₁₉	C₂³	1	2	yes	—
123	C₂×#41×C₁₉	C₂³	1	2	yes	—
124	C₂×#41×C₁₉	C₂³	1	2	yes	—
125	C₂×#41×C₁₉	C₂³	1	2	yes	—
126	C₂²×Q₈×C₁₉	—	2	2	no	—
127	C₂²×Q₈×C₁₉	—	2	2	no	—
128	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
129	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
130	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₁₉	—	2	1	no	—
134	C₂²×D₄×C₁₉	—	2	1	no	—
135	C₂²×D₄×C₁₉	—	2	4	no	—
136	C₂²×D₄×C₁₉	—	2	4	no	—
137	C₂²×D₄×C₁₉	—	2	2	no	—
138	C₂²×D₄×C₁₉	—	2	4	no	—
139	C₂²×D₄×C₁₉	—	2	2	no	—
140	C₂²×D₄×C₁₉	—	2	1	no	—
141	C₂²×D₄×C₁₉	D₄	1	2	yes	—
142	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
143	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
144	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₁₉	—	2	1	no	—
148	C₂³×C₄×C₁₉	—	2	1	no	—
149	C₂³×C₄×C₁₉	—	2	4	no	—
150	C₂³×C₄×C₁₉	—	2	1	no	—
151	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
152	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
153	C₁₉×#137	—	2	8	no	—
154	C₁₉×#137	—	2	8	no	—
155	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
156	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
157	C₁₉×#135	—	2	16	no	—
158	C₁₉×#135	—	2	16	no	—
159	C₁₉×#135	—	2	16	no	—
160	C₂×Q₁₆×C₁₉	—	2	4	no	—
161	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
162	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
163	C₂×SD₁₆×C₁₉	—	2	4	no	—
164	C₂×SD₁₆×C₁₉	—	2	4	no	—
165	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
166	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
167	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
168	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
169	C₂×D₈×C₁₉	—	2	4	no	—
170	C₂×D₈×C₁₉	C₂³	1	4	yes	—
171	C₂×D₈×C₁₉	C₂³	1	4	yes	—
172	C₂×M₁₆×C₁₉	—	2	4	no	—
173	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
174	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
175	C₂²×C₈×C₁₉	—	2	4	no	—
176	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
177	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
178	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
179	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
181	C₁₉×C₄⋊Q₈	—	2	2	no	—
182	C₁₉×#127	—	2	2	no	—
183	C₁₉×#124	—	2	2	no	—
184	C₁₉×#124	—	2	2	no	—
185	C₁₉×#123	—	2	4	no	—
186	C₁₉×#123	—	2	4	no	—
187	C₁₉×C₂²⋊Q₈	—	2	4	no	—
188	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
189	C₁₉×#121	—	2	4	no	—
190	C₁₉×#121	—	2	8	no	—
191	C₁₉×#121	C₂³	1	8	yes	—
192	C₁₉×#120	—	2	4	no	—
193	C₁₉×#120	—	2	4	no	—
194	C₄×D₄×C₁₉	—	2	8	no	—
195	C₁₉×#117	—	2	1	no	—
196	C₁₉×#117	—	2	1	no	—
197	C₁₉×#117	C₂³	1	2	yes	—
198	C₁₉×#117	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
201	C₂×C₄²×C₁₉	—	2	1	no	—
202	C₁₉×#103	C₂³	1	4	yes	—
203	C₁₉×#103	C₂³	1	4	yes	—
204	C₁₉×#103	C₂³	1	8	yes	—
205	C₁₉×#102	C₂³	1	4	yes	—
206	C₁₉×#102	C₂³	1	4	yes	—
207	C₁₉×#102	C₂³	1	8	yes	—
208	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
209	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
210	C₂⁴×C₁₉	—	2	4	no	—
211	C₂⁴×C₁₉	—	2	1	no	—
212	C₂⁴×C₁₉	—	2	1	no	—
213	C₂⁴×C₁₉	—	2	1	no	—
214	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
215	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
216	#41×C₁₉	—	2	32	no	—
217	#41×C₁₉	—	2	32	no	—
218	#41×C₁₉	—	2	32	no	—
219	#41×C₁₉	—	2	32	no	—
220	#41×C₁₉	—	2	16	no	—
221	#41×C₁₉	—	2	16	no	—
222	#41×C₁₉	—	2	16	no	—
223	#41×C₁₉	—	2	16	no	—
224	#41×C₁₉	—	2	8	no	—
225	#41×C₁₉	—	2	8	no	—
226	#41×C₁₉	—	2	8	no	—
227	#41×C₁₉	—	2	8	no	—
228	#41×C₁₉	—	2	8	no	—
229	#41×C₁₉	—	2	8	no	—
230	#41×C₁₉	—	2	8	no	—
231	#41×C₁₉	—	2	8	no	—
232	#41×C₁₉	—	2	8	no	—
233	#41×C₁₉	—	2	8	no	—
234	#41×C₁₉	—	2	4	no	—
235	#41×C₁₉	—	2	4	no	—
236	#41×C₁₉	—	2	4	no	—
237	#41×C₁₉	—	2	4	no	—
238	#41×C₁₉	—	2	4	no	—
239	#41×C₁₉	—	2	4	no	—
240	#41×C₁₉	—	2	4	no	—
241	#41×C₁₉	—	2	4	no	—
242	#41×C₁₉	—	2	4	no	—
243	#41×C₁₉	—	2	4	no	—
244	#41×C₁₉	—	2	4	no	—
245	#41×C₁₉	—	2	4	no	—
246	#41×C₁₉	—	4	4	no	—
247	#41×C₁₉	—	4	4	no	—
248	#41×C₁₉	C₂×D₄	1	8	yes	—
249	#41×C₁₉	C₂×D₄	1	8	yes	—
250	#41×C₁₉	C₂×D₄	1	8	yes	—
251	#41×C₁₉	C₂×D₄	1	8	yes	—
252	C₂×Q₈×C₁₉	—	2	16	no	—
253	C₂×Q₈×C₁₉	—	2	16	no	—
254	C₂×Q₈×C₁₉	—	2	8	no	—
255	C₂×Q₈×C₁₉	—	2	8	no	—
256	C₂×Q₈×C₁₉	—	2	4	no	—
257	C₂×Q₈×C₁₉	—	2	4	no	—
258	C₂×Q₈×C₁₉	—	2	1	no	—
259	C₂×Q₈×C₁₉	—	2	1	no	—
260	C₂×Q₈×C₁₉	—	2	2	no	—
261	C₂×Q₈×C₁₉	—	2	2	no	—
262	C₂×Q₈×C₁₉	—	2	1	no	—
263	C₂×Q₈×C₁₉	—	2	2	no	—
264	C₂×Q₈×C₁₉	—	2	2	no	—
265	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
266	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
267	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
268	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
269	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
270	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
271	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
272	C₂×D₄×C₁₉	—	2	32	no	—
273	C₂×D₄×C₁₉	—	2	32	no	—
274	C₂×D₄×C₁₉	—	2	32	no	—
275	C₂×D₄×C₁₉	—	2	16	no	—
276	C₂×D₄×C₁₉	—	2	16	no	—
277	C₂×D₄×C₁₉	—	2	8	no	—
278	C₂×D₄×C₁₉	—	2	8	no	—
279	C₂×D₄×C₁₉	—	2	8	no	—
280	C₂×D₄×C₁₉	—	2	4	no	—
281	C₂×D₄×C₁₉	—	2	4	no	—
282	C₂×D₄×C₁₉	—	2	2	no	—
283	C₂×D₄×C₁₉	—	2	2	no	—
284	C₂×D₄×C₁₉	—	2	2	no	—
285	C₂×D₄×C₁₉	—	2	2	no	—
286	C₂×D₄×C₁₉	—	2	8	no	—
287	C₂×D₄×C₁₉	—	2	8	no	—
288	C₂×D₄×C₁₉	—	2	2	no	—
289	C₂×D₄×C₁₉	—	2	2	no	—
290	C₂×D₄×C₁₉	—	2	8	no	—
291	C₂×D₄×C₁₉	—	2	4	no	—
292	C₂×D₄×C₁₉	—	2	4	no	—
293	C₂×D₄×C₁₉	—	2	1	no	—
294	C₂×D₄×C₁₉	—	2	1	no	—
295	C₂×D₄×C₁₉	—	2	2	no	—
296	C₂×D₄×C₁₉	—	2	2	no	—
297	C₂×D₄×C₁₉	—	2	2	no	—
298	C₂×D₄×C₁₉	—	2	2	no	—
299	C₂×D₄×C₁₉	—	2	1	no	—
300	C₂×D₄×C₁₉	—	4	4	no	—
301	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
302	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
303	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
304	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
305	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
306	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
307	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
308	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
309	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₁₉	—	2	32	no	—
311	C₂²×C₄×C₁₉	—	2	4	no	—
312	C₂²×C₄×C₁₉	—	2	1	no	—
313	C₂²×C₄×C₁₉	—	2	1	no	—
314	C₂²×C₄×C₁₉	—	2	8	no	—
315	C₂²×C₄×C₁₉	—	2	8	no	—
316	C₂²×C₄×C₁₉	—	2	4	no	—
317	C₂²×C₄×C₁₉	—	2	4	no	—
318	C₂²×C₄×C₁₉	—	2	2	no	—
319	C₂²×C₄×C₁₉	—	2	2	no	—
320	C₂²×C₄×C₁₉	—	2	4	no	—
321	C₂²×C₄×C₁₉	—	2	4	no	—
322	C₂²×C₄×C₁₉	—	2	2	no	—
323	C₂²×C₄×C₁₉	—	2	2	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	—	2	2	no	—
328	C₂²×C₄×C₁₉	—	4	4	no	—
329	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
330	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
331	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
335	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
336	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
337	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
340	Q₁₆×C₁₉	—	2	8	no	—
341	Q₁₆×C₁₉	—	2	8	no	—
342	SD₁₆×C₁₉	—	2	8	no	—
343	SD₁₆×C₁₉	—	2	8	no	—
344	SD₁₆×C₁₉	—	2	8	no	—
345	SD₁₆×C₁₉	—	2	8	no	—
346	D₈×C₁₉	—	2	8	no	—
347	D₈×C₁₉	—	2	8	no	—
348	M₁₆×C₁₉	—	2	4	no	—
349	M₁₆×C₁₉	—	2	4	no	—
350	C₂×C₈×C₁₉	—	2	2	no	—
351	C₂×C₈×C₁₉	—	2	2	no	—
352	C₂×C₈×C₁₉	—	2	4	no	—
353	C₂×C₈×C₁₉	—	2	4	no	—
354	C₂×C₈×C₁₉	—	2	4	no	—
355	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
356	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
357	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
358	C₄⋊C₄×C₁₉	—	2	2	no	—
359	C₄⋊C₄×C₁₉	—	2	8	no	—
360	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
361	C₂²⋊C₄×C₁₉	—	2	2	no	—
362	C₂²⋊C₄×C₁₉	—	2	2	no	—
363	C₂²⋊C₄×C₁₉	—	2	8	no	—
364	C₂²⋊C₄×C₁₉	—	2	8	no	—
365	C₄²×C₁₉	—	2	2	no	—
366	C₄²×C₁₉	—	2	2	no	—
367	#60366	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
368	C₂³×C₁₉	—	2	16	no	—
369	C₂³×C₁₉	—	2	2	no	—
370	C₂³×C₁₉	—	2	2	no	—
371	C₂³×C₁₉	—	2	4	no	—
372	C₂³×C₁₉	—	2	4	no	—
373	C₂³×C₁₉	—	2	4	no	—
374	C₂³×C₁₉	—	2	2	no	—
375	C₂³×C₁₉	—	4	2	no	—
376	C₂³×C₁₉	—	4	4	no	—
377	C₂³×C₁₉	—	4	2	no	—
378	C₂³×C₁₉	—	8	2	no	—
379	C₂³×C₁₉	—	8	2	no	—
380	C₂³×C₁₉	—	8	2	no	—
381	C₂³×C₁₉	—	8	8	no	—
382	C₂³×C₁₉	#120	1	4	yes	—
383	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
384	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
385	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
386	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
387	Q₈×C₁₉	—	2	16	no	—
388	Q₈×C₁₉	—	2	4	no	—
389	Q₈×C₁₉	—	2	4	no	—
390	Q₈×C₁₉	—	2	4	no	—
391	Q₈×C₁₉	—	2	4	no	—
392	Q₈×C₁₉	—	2	2	no	—
393	Q₈×C₁₉	—	2	2	no	—
394	Q₈×C₁₉	—	2	2	no	—
395	Q₈×C₁₉	—	2	2	no	—
396	Q₈×C₁₉	—	4	2	no	—
397	Q₈×C₁₉	C₂²×D₄	1	4	yes	—
398	Q₈×C₁₉	C₂²×D₄	1	4	yes	—
399	D₄×C₁₉	—	2	16	no	—
400	D₄×C₁₉	—	2	16	no	—
401	D₄×C₁₉	—	2	16	no	—
402	D₄×C₁₉	—	2	8	no	—
403	D₄×C₁₉	—	2	8	no	—
404	D₄×C₁₉	—	2	8	no	—
405	D₄×C₁₉	—	2	8	no	—
406	D₄×C₁₉	—	2	8	no	—
407	D₄×C₁₉	—	2	8	no	—
408	D₄×C₁₉	—	2	4	no	—
409	D₄×C₁₉	—	2	4	no	—
410	D₄×C₁₉	—	2	4	no	—
411	D₄×C₁₉	—	2	4	no	—
412	D₄×C₁₉	—	2	2	no	—
413	D₄×C₁₉	—	2	2	no	—
414	D₄×C₁₉	—	2	2	no	—
415	D₄×C₁₉	—	2	2	no	—
416	D₄×C₁₉	—	4	4	no	—
417	D₄×C₁₉	—	4	4	no	—
418	D₄×C₁₉	—	4	2	no	—
419	D₄×C₁₉	—	8	8	no	—
420	D₄×C₁₉	C₂²×D₄	1	4	yes	—
421	D₄×C₁₉	C₂²×D₄	1	4	yes	—
422	C₂×C₄×C₁₉	—	2	16	no	—
423	C₂×C₄×C₁₉	—	2	16	no	—
424	C₂×C₄×C₁₉	—	2	16	no	—
425	C₂×C₄×C₁₉	—	2	4	no	—
426	C₂×C₄×C₁₉	—	2	4	no	—
427	C₂×C₄×C₁₉	—	2	4	no	—
428	C₂×C₄×C₁₉	—	2	2	no	—
429	C₂×C₄×C₁₉	—	2	2	no	—
430	C₂×C₄×C₁₉	—	2	8	no	—
431	C₂×C₄×C₁₉	—	2	8	no	—
432	C₂×C₄×C₁₉	—	2	8	no	—
433	C₂×C₄×C₁₉	—	2	8	no	—
434	C₂×C₄×C₁₉	—	2	8	no	—
435	C₂×C₄×C₁₉	—	2	4	no	—
436	C₂×C₄×C₁₉	—	2	4	no	—
437	C₂×C₄×C₁₉	—	2	4	no	—
438	C₂×C₄×C₁₉	—	2	2	no	—
439	C₂×C₄×C₁₉	—	4	2	no	—
440	C₂×C₄×C₁₉	—	4	4	no	—
441	C₂×C₄×C₁₉	—	4	4	no	—
442	C₂×C₄×C₁₉	—	8	2	no	—
443	C₂×C₄×C₁₉	#120	1	4	yes	—
444	C₂×C₄×C₁₉	#120	1	4	yes	—
445	C₂×C₄×C₁₉	#120	1	4	yes	—
446	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
447	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
450	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
451	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
457	C₈×C₁₉	—	2	2	no	—
458	C₈×C₁₉	—	2	2	no	—
459	C₈×C₁₉	—	2	4	no	—
460	C₂×#585	C₂×C₁₉	1	1	yes	characteristic, complemented
461	C₂×#575	C₂×C₁₉	1	1	yes	characteristic, complemented
462	C₂²×#135	C₂×C₁₉	1	1	yes	characteristic, complemented
463	#3449	C₂×C₁₉	1	1	yes	characteristic, complemented
464	#3013	C₂×C₁₉	1	4	yes	complemented
465	#3012	C₂×C₁₉	1	4	yes	complemented
466	#3011	C₂×C₁₉	1	2	yes	complemented
467	#3010	C₂×C₁₉	1	2	yes	complemented
468	#3009	C₂×C₁₉	1	2	yes	complemented
469	#3008	C₂×C₁₉	1	2	yes	complemented
470	#3002	C₂×C₁₉	1	8	yes	complemented
471	#2896	C₂×C₁₉	1	1	yes	characteristic, complemented
472	C₂×#416	C₂×C₁₉	1	1	yes	characteristic, complemented
473	C₂×#408	C₂×C₁₉	1	1	yes	characteristic, complemented
474	C₂²×C₁₉	—	2	2	no	—
475	C₂²×C₁₉	—	2	2	no	—
476	C₂²×C₁₉	—	2	2	no	—
477	C₂²×C₁₉	—	2	8	no	—
478	C₂²×C₁₉	—	2	4	no	—
479	C₂²×C₁₉	—	2	4	no	—
480	C₂²×C₁₉	—	2	4	no	—
481	C₂²×C₁₉	—	4	4	no	—
482	C₂²×C₁₉	—	4	4	no	—
483	C₂²×C₁₉	—	4	4	no	—
484	C₂²×C₁₉	—	4	4	no	—
485	C₂²×C₁₉	—	4	2	no	—
486	C₂²×C₁₉	—	8	4	no	—
487	C₂²×C₁₉	—	8	4	no	—
488	C₂²×C₁₉	—	8	4	no	—
489	C₂²×C₁₉	—	8	4	no	—
490	C₂²×C₁₉	—	8	16	no	—
491	C₂²×C₁₉	C₂×#120	1	2	yes	—
492	C₂²×C₁₉	C₂×#120	1	2	yes	—
493	C₂²×C₁₉	C₂×#120	1	2	yes	—
494	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
495	C₄×C₁₉	—	2	4	no	—
496	C₄×C₁₉	—	2	4	no	—
497	C₄×C₁₉	—	2	4	no	—
498	C₄×C₁₉	—	4	4	no	—
499	C₄×C₁₉	—	4	2	no	—
500	C₄×C₁₉	C₂×#120	1	2	yes	—
501	C₄×C₁₉	C₂×#120	1	2	yes	—
502	C₄×C₁₉	C₂×#120	1	2	yes	—
503	C₄×C₁₉	C₂³×D₄	1	1	yes	characteristic
504	C₄×C₁₉	C₂³×D₄	1	1	yes	characteristic
505	#585	—	2	8	no	—
506	#585	—	2	8	no	—
507	C₂×2₋¹⁺⁴	—	2	1	no	—
508	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	2	yes	—
509	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	2	yes	complemented
510	C₂×H(5,𝔽₂)	—	2	2	no	—
511	C₂×H(5,𝔽₂)	—	2	1	no	—
512	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	2	yes	—
513	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	2	yes	complemented
514	C₂²×#41	—	2	2	no	—
515	C₂²×#41	—	2	2	no	—
516	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
517	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
518	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
519	C₂²×#41	C₂²×C₁₉	1	4	yes	complemented
520	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic, complemented
521	#575	—	2	8	no	—
522	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
523	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
524	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	complemented
525	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	complemented
526	C₂×#135	—	2	8	no	—
527	C₂×#135	C₂²×C₁₉	1	4	yes	complemented
528	C₂×#135	C₂²×C₁₉	1	4	yes	complemented
529	C₂×#135	C₂²×C₁₉	1	4	yes	complemented
530	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
531	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
532	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
533	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
534	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
535	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
536	#537	C₂²×C₁₉	1	4	yes	complemented
537	#536	—	2	1	no	—
538	#536	C₂²×C₁₉	1	2	yes	complemented
539	#535	—	2	1	no	—
540	#535	C₂²×C₁₉	1	2	yes	complemented
541	#534	—	2	2	no	—
542	#532	—	2	2	no	—
543	#525	—	2	2	no	—
544	#525	C₂²×C₁₉	1	4	yes	complemented
545	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
546	#452	C₂²×C₁₉	1	8	yes	complemented
547	#452	C₂²×C₁₉	1	8	yes	complemented
548	#451	C₂²×C₁₉	1	8	yes	complemented
549	#450	C₂²×C₁₉	1	8	yes	complemented
550	#449	C₂²×C₁₉	1	8	yes	complemented
551	#449	C₂²×C₁₉	1	8	yes	complemented
552	#448	C₂²×C₁₉	1	8	yes	complemented
553	#447	C₂²×C₁₉	1	8	yes	complemented
554	#419	C₂²×C₁₉	1	2	yes	complemented
555	#418	C₂²×C₁₉	1	2	yes	complemented
556	#417	C₂²×C₁₉	1	4	yes	complemented
557	#416	C₂²×C₁₉	1	4	yes	complemented
558	#416	C₂²×C₁₉	1	2	yes	complemented
559	#416	C₂²×C₁₉	1	2	yes	complemented
560	#416	C₂²×C₁₉	1	4	yes	complemented
561	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
562	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
563	#408	C₂²×C₁₉	1	2	yes	complemented
564	#408	C₂²×C₁₉	1	2	yes	complemented
565	#408	C₂²×C₁₉	1	4	yes	complemented
566	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	complemented
567	C₂×C₁₉	—	2	2	no	—
568	C₂×C₁₉	—	2	2	no	—
569	C₂×C₁₉	—	2	2	no	—
570	C₂×C₁₉	—	4	4	no	—
571	C₂×C₁₉	—	4	4	no	—
572	C₂×C₁₉	—	4	4	no	—
573	C₂×C₁₉	—	8	2	no	—
574	C₂×C₁₉	C₂²×#120	1	1	yes	characteristic
575	C₂×C₁₉	#3584	1	2	yes	—
576	2₋¹⁺⁴	—	2	16	no	—
577	2₋¹⁺⁴	—	2	8	no	—
578	2₋¹⁺⁴	—	2	8	no	—
579	2₋¹⁺⁴	—	2	8	no	—
580	2₋¹⁺⁴	—	2	8	no	—
581	H(5,𝔽₂)	—	2	16	no	—
582	H(5,𝔽₂)	—	2	32	no	—
583	H(5,𝔽₂)	—	2	8	no	—
584	H(5,𝔽₂)	—	2	8	no	—
585	H(5,𝔽₂)	—	2	8	no	—
586	H(5,𝔽₂)	—	2	8	no	—
587	C₂×#41	—	2	32	no	—
588	C₂×#41	—	2	32	no	—
589	C₂×#41	—	2	16	no	—
590	C₂×#41	—	2	16	no	—
591	C₂×#41	—	2	2	no	—
592	C₂×#41	—	2	2	no	—
593	C₂×#41	—	2	4	no	—
594	C₂×#41	—	2	2	no	—
595	C₂×#41	—	2	2	no	—
596	C₂×#41	—	2	4	no	—
597	C₂×#41	—	2	1	no	—
598	C₂×#41	—	2	1	no	—
599	C₂×#41	—	2	4	no	—
600	C₂×#41	—	2	1	no	—
601	C₂×#41	—	2	1	no	—
602	C₂×#41	—	2	4	no	—
603	C₂×#41	—	2	4	no	—
604	C₂×#41	—	2	4	no	—
605	C₂×#41	—	2	4	no	—
606	C₂×#41	—	2	4	no	—
607	C₂×#41	—	2	1	no	—
608	C₂×#41	—	2	1	no	—
609	C₂×#41	—	2	4	no	—
610	C₂×#41	—	2	4	no	—
611	C₂×#41	D₄×C₁₉	1	2	yes	—
612	C₂×#41	D₄×C₁₉	1	2	yes	—
613	C₂×#41	D₄×C₁₉	1	8	yes	complemented
614	C₂×#41	D₄×C₁₉	1	8	yes	complemented
615	C₂×#41	C₂³×C₁₉	1	2	yes	—
616	C₂×#41	C₂³×C₁₉	1	2	yes	—
617	C₂×#41	C₂³×C₁₉	1	4	yes	—
618	C₂×#41	C₂³×C₁₉	1	4	yes	—
619	C₂×#41	C₂³×C₁₉	1	2	yes	—
620	C₂×#41	C₂³×C₁₉	1	2	yes	—
621	C₂×#41	C₂³×C₁₉	1	2	yes	—
622	C₂×#41	C₂³×C₁₉	1	2	yes	—
623	C₂×#41	C₂³×C₁₉	1	2	yes	—
624	C₂×#41	C₂³×C₁₉	1	2	yes	—
625	C₂²×Q₈	—	2	2	no	—
626	C₂²×Q₈	—	2	2	no	—
627	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
628	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
629	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
630	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
631	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
632	C₂²×D₄	—	2	1	no	—
633	C₂²×D₄	—	2	1	no	—
634	C₂²×D₄	—	2	4	no	—
635	C₂²×D₄	—	2	4	no	—
636	C₂²×D₄	—	2	2	no	—
637	C₂²×D₄	—	2	4	no	—
638	C₂²×D₄	—	2	2	no	—
639	C₂²×D₄	—	2	1	no	—
640	C₂²×D₄	D₄×C₁₉	1	2	yes	—
641	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
642	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
643	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
644	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
645	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
646	C₂³×C₄	—	2	1	no	—
647	C₂³×C₄	—	2	1	no	—
648	C₂³×C₄	—	2	4	no	—
649	C₂³×C₄	—	2	1	no	—
650	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
651	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
652	#137	—	2	8	no	—
653	#137	—	2	8	no	—
654	AGL(1,ℤ/8)	—	2	8	no	—
655	AGL(1,ℤ/8)	—	2	8	no	—
656	#135	—	2	16	no	—
657	#135	—	2	16	no	—
658	#135	—	2	16	no	—
659	C₂×Q₁₆	—	2	4	no	—
660	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
661	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
662	C₂×SD₁₆	—	2	4	no	—
663	C₂×SD₁₆	—	2	4	no	—
664	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
665	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
666	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
667	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
668	C₂×D₈	—	2	4	no	—
669	C₂×D₈	C₂³×C₁₉	1	4	yes	—
670	C₂×D₈	C₂³×C₁₉	1	4	yes	—
671	C₂×M₁₆	—	2	4	no	—
672	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
673	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
674	C₂²×C₈	—	2	4	no	—
675	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
676	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
677	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
678	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
679	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
680	C₄⋊Q₈	—	2	2	no	—
681	#127	—	2	2	no	—
682	#124	—	2	2	no	—
683	#124	—	2	2	no	—
684	#123	—	2	4	no	—
685	#123	—	2	4	no	—
686	C₂²⋊Q₈	—	2	4	no	—
687	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
688	#121	—	2	4	no	—
689	#121	—	2	8	no	—
690	#121	C₂³×C₁₉	1	8	yes	—
691	#120	—	2	4	no	—
692	#120	—	2	4	no	—
693	C₄×D₄	—	2	8	no	—
694	#117	—	2	1	no	—
695	#117	—	2	1	no	—
696	#117	C₂³×C₁₉	1	2	yes	—
697	#117	C₂³×C₁₉	1	2	yes	—
698	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
699	C₂×C₂²⋊C₄	—	2	1	no	—
700	C₂×C₄²	—	2	1	no	—
701	#103	C₂³×C₁₉	1	4	yes	—
702	#103	C₂³×C₁₉	1	4	yes	—
703	#103	C₂³×C₁₉	1	8	yes	—
704	#102	C₂³×C₁₉	1	4	yes	—
705	#102	C₂³×C₁₉	1	4	yes	—
706	#102	C₂³×C₁₉	1	8	yes	—
707	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
708	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
709	C₁₉	#60366	1	1	yes	characteristic, direct product factor, Sylow
710	C₂⁴	—	2	4	no	—
711	C₂⁴	—	2	1	no	—
712	C₂⁴	—	2	1	no	—
713	C₂⁴	—	2	1	no	—
714	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
715	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
716	#41	—	2	32	no	—
717	#41	—	2	32	no	—
718	#41	—	2	32	no	—
719	#41	—	2	32	no	—
720	#41	—	2	16	no	—
721	#41	—	2	16	no	—
722	#41	—	2	16	no	—
723	#41	—	2	16	no	—
724	#41	—	2	8	no	—
725	#41	—	2	8	no	—
726	#41	—	2	8	no	—
727	#41	—	2	8	no	—
728	#41	—	2	8	no	—
729	#41	—	2	8	no	—
730	#41	—	2	8	no	—
731	#41	—	2	8	no	—
732	#41	—	2	8	no	—
733	#41	—	2	8	no	—
734	#41	—	2	4	no	—
735	#41	—	2	4	no	—
736	#41	—	2	4	no	—
737	#41	—	2	4	no	—
738	#41	—	2	4	no	—
739	#41	—	2	4	no	—
740	#41	—	2	4	no	—
741	#41	—	2	4	no	—
742	#41	—	2	4	no	—
743	#41	—	2	4	no	—
744	#41	—	2	4	no	—
745	#41	—	2	4	no	—
746	#41	—	4	4	no	—
747	#41	—	4	4	no	—
748	#41	C₂×D₄×C₁₉	1	8	yes	—
749	#41	C₂×D₄×C₁₉	1	8	yes	—
750	#41	C₂×D₄×C₁₉	1	8	yes	—
751	#41	C₂×D₄×C₁₉	1	8	yes	—
752	C₂×Q₈	—	2	16	no	—
753	C₂×Q₈	—	2	16	no	—
754	C₂×Q₈	—	2	8	no	—
755	C₂×Q₈	—	2	8	no	—
756	C₂×Q₈	—	2	4	no	—
757	C₂×Q₈	—	2	4	no	—
758	C₂×Q₈	—	2	1	no	—
759	C₂×Q₈	—	2	1	no	—
760	C₂×Q₈	—	2	2	no	—
761	C₂×Q₈	—	2	2	no	—
762	C₂×Q₈	—	2	1	no	—
763	C₂×Q₈	—	2	2	no	—
764	C₂×Q₈	—	2	2	no	—
765	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
766	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
767	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
768	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
769	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
770	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
771	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
772	C₂×D₄	—	2	32	no	—
773	C₂×D₄	—	2	32	no	—
774	C₂×D₄	—	2	32	no	—
775	C₂×D₄	—	2	16	no	—
776	C₂×D₄	—	2	16	no	—
777	C₂×D₄	—	2	8	no	—
778	C₂×D₄	—	2	8	no	—
779	C₂×D₄	—	2	8	no	—
780	C₂×D₄	—	2	4	no	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	2	8	no	—
787	C₂×D₄	—	2	8	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	8	no	—
791	C₂×D₄	—	2	4	no	—
792	C₂×D₄	—	2	4	no	—
793	C₂×D₄	—	2	1	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	4	4	no	—
801	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
802	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
803	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
804	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
805	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
806	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
807	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
808	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
809	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
810	C₂²×C₄	—	2	32	no	—
811	C₂²×C₄	—	2	4	no	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	8	no	—
815	C₂²×C₄	—	2	8	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	4	no	—
819	C₂²×C₄	—	2	4	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	4	no	—
823	C₂²×C₄	—	2	4	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	4	4	no	—
829	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
830	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
831	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
832	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
833	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
834	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
835	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
836	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
837	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
840	Q₁₆	—	2	8	no	—
841	Q₁₆	—	2	8	no	—
842	SD₁₆	—	2	8	no	—
843	SD₁₆	—	2	8	no	—
844	SD₁₆	—	2	8	no	—
845	SD₁₆	—	2	8	no	—
846	D₈	—	2	8	no	—
847	D₈	—	2	8	no	—
848	M₁₆	—	2	4	no	—
849	M₁₆	—	2	4	no	—
850	C₂×C₈	—	2	2	no	—
851	C₂×C₈	—	2	2	no	—
852	C₂×C₈	—	2	4	no	—
853	C₂×C₈	—	2	4	no	—
854	C₂×C₈	—	2	4	no	—
855	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
856	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
857	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	8	no	—
860	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	8	no	—
864	C₂²⋊C₄	—	2	8	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	2	no	—
867	C₂³	—	2	16	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	4	no	—
871	C₂³	—	2	4	no	—
872	C₂³	—	2	4	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	4	2	no	—
875	C₂³	—	4	4	no	—
876	C₂³	—	4	2	no	—
877	C₂³	—	8	2	no	—
878	C₂³	—	8	2	no	—
879	C₂³	—	8	2	no	—
880	C₂³	—	8	8	no	—
881	C₂³	C₁₉×#120	1	4	yes	—
882	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
883	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
884	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
885	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
886	Q₈	—	2	16	no	—
887	Q₈	—	2	4	no	—
888	Q₈	—	2	4	no	—
889	Q₈	—	2	4	no	—
890	Q₈	—	2	4	no	—
891	Q₈	—	2	2	no	—
892	Q₈	—	2	2	no	—
893	Q₈	—	2	2	no	—
894	Q₈	—	2	2	no	—
895	Q₈	—	4	2	no	—
896	Q₈	C₂²×D₄×C₁₉	1	4	yes	—
897	Q₈	C₂²×D₄×C₁₉	1	4	yes	—
898	D₄	—	2	16	no	—
899	D₄	—	2	16	no	—
900	D₄	—	2	16	no	—
901	D₄	—	2	8	no	—
902	D₄	—	2	8	no	—
903	D₄	—	2	8	no	—
904	D₄	—	2	8	no	—
905	D₄	—	2	8	no	—
906	D₄	—	2	8	no	—
907	D₄	—	2	4	no	—
908	D₄	—	2	4	no	—
909	D₄	—	2	4	no	—
910	D₄	—	2	4	no	—
911	D₄	—	2	2	no	—
912	D₄	—	2	2	no	—
913	D₄	—	2	2	no	—
914	D₄	—	2	2	no	—
915	D₄	—	4	4	no	—
916	D₄	—	4	4	no	—
917	D₄	—	4	2	no	—
918	D₄	—	8	8	no	—
919	D₄	C₂²×D₄×C₁₉	1	4	yes	—
920	D₄	C₂²×D₄×C₁₉	1	4	yes	—
921	C₂×C₄	—	2	16	no	—
922	C₂×C₄	—	2	16	no	—
923	C₂×C₄	—	2	16	no	—
924	C₂×C₄	—	2	4	no	—
925	C₂×C₄	—	2	4	no	—
926	C₂×C₄	—	2	4	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	8	no	—
930	C₂×C₄	—	2	8	no	—
931	C₂×C₄	—	2	8	no	—
932	C₂×C₄	—	2	8	no	—
933	C₂×C₄	—	2	8	no	—
934	C₂×C₄	—	2	4	no	—
935	C₂×C₄	—	2	4	no	—
936	C₂×C₄	—	2	4	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	4	2	no	—
939	C₂×C₄	—	4	4	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	8	2	no	—
942	C₂×C₄	C₁₉×#120	1	4	yes	—
943	C₂×C₄	C₁₉×#120	1	4	yes	—
944	C₂×C₄	C₁₉×#120	1	4	yes	—
945	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
946	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
947	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
948	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
949	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
950	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
951	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
952	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
953	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
954	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
955	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
956	C₈	—	2	2	no	—
957	C₈	—	2	2	no	—
958	C₈	—	2	4	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	2	4	no	—
963	C₂²	—	2	4	no	—
964	C₂²	—	2	4	no	—
965	C₂²	—	2	8	no	—
966	C₂²	—	4	4	no	—
967	C₂²	—	4	4	no	—
968	C₂²	—	4	4	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	4	no	—
971	C₂²	—	8	4	no	—
972	C₂²	—	8	4	no	—
973	C₂²	—	8	4	no	—
974	C₂²	—	8	4	no	—
975	C₂²	—	8	16	no	—
976	C₂²	C₂×C₁₉×#120	1	2	yes	—
977	C₂²	C₂×C₁₉×#120	1	2	yes	—
978	C₂²	C₂×C₁₉×#120	1	2	yes	—
979	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
980	C₄	—	2	4	no	—
981	C₄	—	2	4	no	—
982	C₄	—	2	4	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	4	no	—
985	C₄	C₂×C₁₉×#120	1	2	yes	—
986	C₄	C₂×C₁₉×#120	1	2	yes	—
987	C₄	C₂×C₁₉×#120	1	2	yes	—
988	C₄	C₂³×D₄×C₁₉	1	1	yes	characteristic
989	C₄	C₂³×D₄×C₁₉	1	1	yes	characteristic
990	C₂	—	2	2	no	—
991	C₂	—	2	2	no	—
992	C₂	—	2	2	no	—
993	C₂	—	4	4	no	—
994	C₂	—	4	4	no	—
995	C₂	—	4	4	no	—
996	C₂	—	8	2	no	—
997	C₂	C₂²×C₁₉×#120	1	1	yes	characteristic
998	C₂	C₁₉×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#585	C₂	semidirect
2. C₂×C₁₉×#575	C₂	semidirect
3. C₂²×C₁₉×#135	C₂	semidirect
4. C₁₉×#3449	C₂	semidirect
5. C₁₉×#3013	C₂	semidirect
6. C₁₉×#3012	C₂	semidirect
7. C₁₉×#3011	C₂	semidirect
8. C₁₉×#3010	C₂	semidirect
9. C₁₉×#3009	C₂	semidirect
10. C₁₉×#3008	C₂	semidirect
11. C₁₉×#3002	C₂	semidirect
12. C₁₉×#2896	C₂	semidirect
13. C₂×C₁₉×#416	C₂	semidirect
14. C₂×C₁₉×#408	C₂	semidirect
19. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
23. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
29. C₂²×#41×C₁₉	C₂²	semidirect
30. C₂²×#41×C₁₉	C₂²	semidirect
32. C₂×C₁₉×#137	C₂²	semidirect
33. C₂×C₁₉×#137	C₂²	semidirect
34. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
35. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
37. C₂×C₁₉×#135	C₂²	semidirect
38. C₂×C₁₉×#135	C₂²	semidirect
39. C₂×C₁₉×#135	C₂²	semidirect
40. C₂²×Q₁₆×C₁₉	C₂²	semidirect
41. C₂²×SD₁₆×C₁₉	C₂²	semidirect
42. C₂²×SD₁₆×C₁₉	C₂²	semidirect
43. C₂²×D₈×C₁₉	C₂²	semidirect
44. C₂²×M₁₆×C₁₉	C₂²	semidirect
45. C₂³×C₈×C₁₉	C₂²	semidirect
46. C₁₉×#537	C₂²	semidirect
48. C₁₉×#536	C₂²	semidirect
50. C₁₉×#535	C₂²	semidirect
54. C₁₉×#525	C₂²	semidirect
55. C₂×C₁₉×#117	C₂²	semidirect
56. C₁₉×#452	C₂²	semidirect
57. C₁₉×#452	C₂²	semidirect
58. C₁₉×#451	C₂²	semidirect
59. C₁₉×#450	C₂²	semidirect
60. C₁₉×#449	C₂²	semidirect
61. C₁₉×#449	C₂²	semidirect
62. C₁₉×#448	C₂²	semidirect
63. C₁₉×#447	C₂²	semidirect
64. C₁₉×#419	C₂²	semidirect
65. C₁₉×#418	C₂²	semidirect
66. C₁₉×#417	C₂²	semidirect
67. C₁₉×#416	C₂²	semidirect
68. C₁₉×#416	C₂²	semidirect
69. C₁₉×#416	C₂²	semidirect
70. C₁₉×#416	C₂²	semidirect
71. C₂×C₁₉×#103	C₂²	semidirect
72. C₂×C₁₉×#102	C₂²	semidirect
73. C₁₉×#408	C₂²	semidirect
74. C₁₉×#408	C₂²	semidirect
75. C₁₉×#408	C₂²	semidirect
76. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
114. C₂×#41×C₁₉	D₄	semidirect
115. C₂×#41×C₁₉	D₄	semidirect
367. #60366	C₁₉	direct (N × H)
460. C₂×#585	C₂×C₁₉	semidirect
461. C₂×#575	C₂×C₁₉	semidirect
462. C₂²×#135	C₂×C₁₉	semidirect
463. #3449	C₂×C₁₉	semidirect
464. #3013	C₂×C₁₉	semidirect
465. #3012	C₂×C₁₉	semidirect
466. #3011	C₂×C₁₉	semidirect
467. #3010	C₂×C₁₉	semidirect
468. #3009	C₂×C₁₉	semidirect
469. #3008	C₂×C₁₉	semidirect
470. #3002	C₂×C₁₉	semidirect
471. #2896	C₂×C₁₉	semidirect
472. C₂×#416	C₂×C₁₉	semidirect
473. C₂×#408	C₂×C₁₉	semidirect
509. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
513. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
519. C₂²×#41	C₂²×C₁₉	semidirect
520. C₂²×#41	C₂²×C₁₉	semidirect
522. C₂×#137	C₂²×C₁₉	semidirect
523. C₂×#137	C₂²×C₁₉	semidirect
524. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
525. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
527. C₂×#135	C₂²×C₁₉	semidirect
528. C₂×#135	C₂²×C₁₉	semidirect
529. C₂×#135	C₂²×C₁₉	semidirect
530. C₂²×Q₁₆	C₂²×C₁₉	semidirect
531. C₂²×SD₁₆	C₂²×C₁₉	semidirect
532. C₂²×SD₁₆	C₂²×C₁₉	semidirect
533. C₂²×D₈	C₂²×C₁₉	semidirect
534. C₂²×M₁₆	C₂²×C₁₉	semidirect
535. C₂³×C₈	C₂²×C₁₉	semidirect
536. #537	C₂²×C₁₉	semidirect
538. #536	C₂²×C₁₉	semidirect
540. #535	C₂²×C₁₉	semidirect
544. #525	C₂²×C₁₉	semidirect
545. C₂×#117	C₂²×C₁₉	semidirect
546. #452	C₂²×C₁₉	semidirect
547. #452	C₂²×C₁₉	semidirect
548. #451	C₂²×C₁₉	semidirect
549. #450	C₂²×C₁₉	semidirect
550. #449	C₂²×C₁₉	semidirect
551. #449	C₂²×C₁₉	semidirect
552. #448	C₂²×C₁₉	semidirect
553. #447	C₂²×C₁₉	semidirect
554. #419	C₂²×C₁₉	semidirect
555. #418	C₂²×C₁₉	semidirect
556. #417	C₂²×C₁₉	semidirect
557. #416	C₂²×C₁₉	semidirect
558. #416	C₂²×C₁₉	semidirect
559. #416	C₂²×C₁₉	semidirect
560. #416	C₂²×C₁₉	semidirect
561. C₂×#103	C₂²×C₁₉	semidirect
562. C₂×#102	C₂²×C₁₉	semidirect
563. #408	C₂²×C₁₉	semidirect
564. #408	C₂²×C₁₉	semidirect
565. #408	C₂²×C₁₉	semidirect
566. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
613. C₂×#41	D₄×C₁₉	semidirect
614. C₂×#41	D₄×C₁₉	semidirect
709. C₁₉	#60366	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#585	2
C₂×C₁₉×#575	2
C₂²×C₁₉×#135	2
C₁₉×#3449	2
C₁₉×#3013	2
C₁₉×#3012	2
C₁₉×#3011	2
C₁₉×#3010	2
C₁₉×#3009	2
C₁₉×#3008	2
C₁₉×#3002	2
C₁₉×#2896	2
C₂×C₁₉×#416	2
C₂×C₁₉×#408	2
#60366	19

Subgroups — C19×#60366 #18066325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60366 #18066325