Subgroups — C₁₉×#24805 #18030764

Order 4864.

870 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#471	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3056	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3055	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#468	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#430	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2063	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2052	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2051	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1977	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1952	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1901	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1900	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1816	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#525	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
26	C₁₉×#471	—	2	4	no	—
27	C₁₉×#470	—	2	1	no	—
28	C₁₉×#469	—	2	1	no	—
29	C₁₉×#468	—	2	1	no	—
30	C₁₉×#468	—	2	1	no	—
31	C₁₉×#468	—	2	1	no	—
32	C₁₉×#468	—	2	1	no	—
33	C₁₉×#468	—	2	1	no	—
34	C₁₉×#468	—	2	1	no	—
35	C₁₉×#467	—	2	1	no	—
36	C₁₉×#466	—	2	1	no	—
37	C₁₉×#465	—	2	1	no	—
38	C₁₉×#465	—	2	1	no	—
39	C₁₉×#436	—	2	1	no	—
40	C₁₉×#436	—	2	1	no	—
41	C₁₉×#435	—	2	1	no	—
42	C₁₉×#435	—	2	1	no	—
43	C₁₉×#430	—	2	4	no	—
44	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
48	C₁₉×#428	C₂²	1	1	yes	characteristic
49	C₁₉×#428	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
51	C₁₉×#424	C₂²	1	1	yes	characteristic
52	C₁₉×#419	C₂²	1	1	yes	characteristic
53	C₁₉×#418	C₂²	1	1	yes	characteristic
54	C₁₉×#417	C₂²	1	1	yes	characteristic
55	C₁₉×#417	C₂²	1	1	yes	characteristic
56	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
57	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
58	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
59	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
60	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
61	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
62	C₁₉×#408	C₂²	1	1	yes	characteristic
63	C₁₉×#407	C₂²	1	1	yes	characteristic
64	C₁₉×#405	C₂²	1	1	yes	characteristic
65	C₁₉×#343	C₂²	1	1	yes	characteristic
66	C₁₉×#343	C₂²	1	1	yes	characteristic
67	C₁₉×#343	C₂²	1	1	yes	characteristic
68	C₁₉×#343	C₂²	1	1	yes	characteristic
69	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₉	—	2	1	no	—
72	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
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	C₂×Q₁₆×C₁₉	—	2	1	no	—
79	C₂×SD₁₆×C₁₉	—	2	1	no	—
80	C₂×SD₁₆×C₁₉	—	2	1	no	—
81	C₂×SD₁₆×C₁₉	—	2	1	no	—
82	C₂×SD₁₆×C₁₉	—	2	1	no	—
83	C₂×SD₁₆×C₁₉	—	2	2	no	—
84	C₂×SD₁₆×C₁₉	—	2	2	no	—
85	C₂×D₈×C₁₉	—	2	1	no	—
86	C₁₉×#131	—	2	2	no	—
87	C₁₉×#131	—	2	2	no	—
88	C₂×M₁₆×C₁₉	—	2	1	no	—
89	C₂×M₁₆×C₁₉	—	2	1	no	—
90	C₂×M₁₆×C₁₉	—	2	2	no	—
91	C₂×M₁₆×C₁₉	—	2	1	no	—
92	C₂×M₁₆×C₁₉	—	2	2	no	—
93	C₂×M₁₆×C₁₉	—	2	2	no	—
94	C₂×M₁₆×C₁₉	—	2	2	no	—
95	C₂×M₁₆×C₁₉	—	4	1	no	—
96	C₂×M₁₆×C₁₉	—	4	1	no	—
97	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
98	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
99	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
100	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
101	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₁₉	—	2	1	no	—
108	C₂²×C₈×C₁₉	—	2	1	no	—
109	C₂²×C₈×C₁₉	—	2	1	no	—
110	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
112	C₁₉×#123	—	2	1	no	—
113	C₁₉×C₂²⋊Q₈	—	2	1	no	—
114	C₁₉×C₂²⋊Q₈	—	2	1	no	—
115	C₁₉×C₂²⋊Q₈	—	2	1	no	—
116	C₁₉×C₂²⋊Q₈	—	2	1	no	—
117	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
118	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
124	C₁₉×#121	D₄	1	1	yes	characteristic
125	C₁₉×#120	—	2	1	no	—
126	C₄×D₄×C₁₉	—	2	1	no	—
127	C₄×D₄×C₁₉	—	2	1	no	—
128	C₁₉×#117	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
134	C₁₉×#108	—	2	2	no	—
135	C₁₉×#108	—	2	2	no	—
136	C₁₉×#108	—	2	2	no	—
137	C₁₉×#108	D₄	1	4	yes	complemented
138	C₁₉×#107	—	2	1	no	—
139	C₁₉×#107	—	2	1	no	—
140	C₁₉×#107	—	2	1	no	—
141	C₁₉×#107	—	2	1	no	—
142	C₁₉×#106	—	2	1	no	—
143	C₁₉×#106	—	2	1	no	—
144	C₁₉×C₄⋊C₈	—	2	1	no	—
145	C₁₉×C₄⋊C₈	—	2	1	no	—
146	C₁₉×#103	—	2	1	no	—
147	C₁₉×#103	—	2	1	no	—
148	C₁₉×#103	—	2	1	no	—
149	C₁₉×#103	—	2	1	no	—
150	C₁₉×#103	—	2	1	no	—
151	C₁₉×#103	—	2	1	no	—
152	C₁₉×#102	—	2	1	no	—
153	C₁₉×#102	—	2	1	no	—
154	C₁₉×#102	—	2	1	no	—
155	C₁₉×#102	—	2	1	no	—
156	C₁₉×#102	—	2	1	no	—
157	C₁₉×#102	—	2	1	no	—
158	C₁₉×#101	—	2	2	no	—
159	C₁₉×#101	—	4	1	no	—
160	C₁₉×#100	—	2	2	no	—
161	C₁₉×#100	—	4	1	no	—
162	C₁₉×C₂²⋊C₈	—	2	1	no	—
163	C₁₉×C₂²⋊C₈	—	2	1	no	—
164	C₁₉×C₂²⋊C₈	—	2	1	no	—
165	C₁₉×C₂²⋊C₈	—	2	1	no	—
166	C₁₉×#97	—	2	1	no	—
167	C₄×C₈×C₁₉	—	2	1	no	—
168	C₂⁴×C₁₉	—	2	1	no	—
169	C₂⁴×C₁₉	#41	1	1	yes	characteristic
170	#41×C₁₉	—	2	1	no	—
171	#41×C₁₉	—	2	1	no	—
172	#41×C₁₉	—	2	1	no	—
173	#41×C₁₉	—	2	1	no	—
174	C₂×Q₈×C₁₉	—	2	1	no	—
175	C₂×Q₈×C₁₉	—	2	1	no	—
176	C₂×Q₈×C₁₉	—	2	1	no	—
177	C₂×Q₈×C₁₉	—	2	1	no	—
178	C₂×Q₈×C₁₉	—	2	1	no	—
179	C₂×Q₈×C₁₉	—	2	1	no	—
180	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₂×D₄×C₁₉	—	2	1	no	—
182	C₂×D₄×C₁₉	—	2	1	no	—
183	C₂×D₄×C₁₉	—	2	1	no	—
184	C₂×D₄×C₁₉	—	2	1	no	—
185	C₂×D₄×C₁₉	—	2	1	no	—
186	C₂×D₄×C₁₉	—	2	1	no	—
187	C₂×D₄×C₁₉	—	2	1	no	—
188	C₂×D₄×C₁₉	—	2	1	no	—
189	C₂×D₄×C₁₉	—	2	1	no	—
190	C₂×D₄×C₁₉	—	4	1	no	—
191	C₂×D₄×C₁₉	—	4	1	no	—
192	C₂×D₄×C₁₉	—	8	2	no	—
193	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₉	—	2	1	no	—
195	C₂²×C₄×C₁₉	—	2	1	no	—
196	C₂²×C₄×C₁₉	—	2	1	no	—
197	C₂²×C₄×C₁₉	—	2	1	no	—
198	C₂²×C₄×C₁₉	—	2	1	no	—
199	C₂²×C₄×C₁₉	—	2	1	no	—
200	C₂²×C₄×C₁₉	—	2	1	no	—
201	C₂²×C₄×C₁₉	—	2	1	no	—
202	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
207	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
208	Q₁₆×C₁₉	—	4	2	no	—
209	SD₁₆×C₁₉	—	4	2	no	—
210	SD₁₆×C₁₉	—	4	2	no	—
211	SD₁₆×C₁₉	—	4	2	no	—
212	SD₁₆×C₁₉	—	4	2	no	—
213	D₈×C₁₉	—	4	2	no	—
214	M₁₆×C₁₉	—	2	1	no	—
215	M₁₆×C₁₉	—	2	1	no	—
216	M₁₆×C₁₉	—	2	2	no	—
217	M₁₆×C₁₉	—	2	2	no	—
218	M₁₆×C₁₉	—	2	2	no	—
219	M₁₆×C₁₉	—	2	2	no	—
220	M₁₆×C₁₉	—	2	1	no	—
221	M₁₆×C₁₉	—	2	1	no	—
222	M₁₆×C₁₉	—	2	1	no	—
223	M₁₆×C₁₉	—	2	1	no	—
224	M₁₆×C₁₉	—	2	1	no	—
225	M₁₆×C₁₉	—	2	1	no	—
226	M₁₆×C₁₉	—	2	1	no	—
227	M₁₆×C₁₉	—	2	1	no	—
228	M₁₆×C₁₉	—	4	2	no	—
229	M₁₆×C₁₉	—	4	2	no	—
230	M₁₆×C₁₉	—	4	2	no	—
231	M₁₆×C₁₉	C₂×D₄	1	2	yes	—
232	M₁₆×C₁₉	C₂×D₄	1	2	yes	—
233	C₂×C₈×C₁₉	—	2	1	no	—
234	C₂×C₈×C₁₉	—	2	1	no	—
235	C₂×C₈×C₁₉	—	2	1	no	—
236	C₂×C₈×C₁₉	—	2	1	no	—
237	C₂×C₈×C₁₉	—	2	1	no	—
238	C₂×C₈×C₁₉	—	2	1	no	—
239	C₂×C₈×C₁₉	—	2	1	no	—
240	C₂×C₈×C₁₉	—	2	1	no	—
241	C₂×C₈×C₁₉	—	4	2	no	—
242	C₂×C₈×C₁₉	—	4	2	no	—
243	C₂×C₈×C₁₉	—	4	2	no	—
244	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
245	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
246	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
247	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
248	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
249	C₂×C₈×C₁₉	#41	1	2	yes	—
250	C₄⋊C₄×C₁₉	—	2	1	no	—
251	C₄⋊C₄×C₁₉	—	2	1	no	—
252	C₄⋊C₄×C₁₉	—	2	1	no	—
253	C₄⋊C₄×C₁₉	—	2	1	no	—
254	C₄⋊C₄×C₁₉	—	2	1	no	—
255	C₄⋊C₄×C₁₉	—	2	1	no	—
256	C₄⋊C₄×C₁₉	—	4	1	no	—
257	C₄⋊C₄×C₁₉	—	4	1	no	—
258	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
259	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
260	C₂²⋊C₄×C₁₉	—	2	1	no	—
261	C₂²⋊C₄×C₁₉	—	2	1	no	—
262	C₂²⋊C₄×C₁₉	—	2	1	no	—
263	C₂²⋊C₄×C₁₉	—	2	1	no	—
264	C₂²⋊C₄×C₁₉	—	2	1	no	—
265	C₂²⋊C₄×C₁₉	—	4	1	no	—
266	C₂²⋊C₄×C₁₉	—	4	1	no	—
267	C₂²⋊C₄×C₁₉	—	4	1	no	—
268	C₂²⋊C₄×C₁₉	—	4	1	no	—
269	C₄²×C₁₉	—	2	1	no	—
270	#24805	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂³×C₁₉	—	2	1	no	—
272	C₂³×C₁₉	—	2	1	no	—
273	C₂³×C₁₉	—	2	1	no	—
274	C₂³×C₁₉	—	4	1	no	—
275	C₂³×C₁₉	—	4	1	no	—
276	C₂³×C₁₉	—	4	1	no	—
277	C₂³×C₁₉	—	4	1	no	—
278	C₂³×C₁₉	—	4	1	no	—
279	C₂³×C₁₉	—	8	1	no	—
280	C₂³×C₁₉	—	8	1	no	—
281	C₂³×C₁₉	#121	1	1	yes	characteristic
282	C₂³×C₁₉	#121	1	1	yes	characteristic
283	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
284	Q₈×C₁₉	—	2	1	no	—
285	Q₈×C₁₉	—	2	1	no	—
286	Q₈×C₁₉	—	4	1	no	—
287	Q₈×C₁₉	—	4	1	no	—
288	Q₈×C₁₉	—	4	1	no	—
289	Q₈×C₁₉	—	4	1	no	—
290	D₄×C₁₉	—	2	1	no	—
291	D₄×C₁₉	—	2	1	no	—
292	D₄×C₁₉	—	4	1	no	—
293	D₄×C₁₉	—	4	1	no	—
294	D₄×C₁₉	—	4	1	no	—
295	D₄×C₁₉	—	4	1	no	—
296	D₄×C₁₉	—	4	1	no	—
297	D₄×C₁₉	—	4	1	no	—
298	D₄×C₁₉	—	8	1	no	—
299	D₄×C₁₉	—	8	1	no	—
300	D₄×C₁₉	—	8	2	no	—
301	D₄×C₁₉	—	8	2	no	—
302	C₂×C₄×C₁₉	—	2	1	no	—
303	C₂×C₄×C₁₉	—	2	1	no	—
304	C₂×C₄×C₁₉	—	2	1	no	—
305	C₂×C₄×C₁₉	—	2	1	no	—
306	C₂×C₄×C₁₉	—	2	1	no	—
307	C₂×C₄×C₁₉	—	2	1	no	—
308	C₂×C₄×C₁₉	—	2	1	no	—
309	C₂×C₄×C₁₉	—	2	1	no	—
310	C₂×C₄×C₁₉	—	2	1	no	—
311	C₂×C₄×C₁₉	—	2	1	no	—
312	C₂×C₄×C₁₉	—	2	1	no	—
313	C₂×C₄×C₁₉	—	2	1	no	—
314	C₂×C₄×C₁₉	—	2	1	no	—
315	C₂×C₄×C₁₉	—	4	1	no	—
316	C₂×C₄×C₁₉	—	4	1	no	—
317	C₂×C₄×C₁₉	—	4	1	no	—
318	C₂×C₄×C₁₉	—	4	1	no	—
319	C₂×C₄×C₁₉	—	4	1	no	—
320	C₂×C₄×C₁₉	—	4	1	no	—
321	C₂×C₄×C₁₉	—	4	1	no	—
322	C₂×C₄×C₁₉	—	8	1	no	—
323	C₂×C₄×C₁₉	—	8	1	no	—
324	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
325	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
326	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
330	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
331	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
332	C₈×C₁₉	—	2	1	no	—
333	C₈×C₁₉	—	2	1	no	—
334	C₈×C₁₉	—	2	2	no	—
335	C₈×C₁₉	—	2	2	no	—
336	C₈×C₁₉	—	4	1	no	—
337	C₈×C₁₉	—	4	1	no	—
338	C₈×C₁₉	—	4	1	no	—
339	C₈×C₁₉	—	4	1	no	—
340	C₈×C₁₉	#121	1	2	yes	—
341	C₈×C₁₉	#121	1	2	yes	—
342	C₂×#471	C₂×C₁₉	1	1	yes	characteristic, complemented
343	#3056	C₂×C₁₉	1	1	yes	characteristic, complemented
344	#3055	C₂×C₁₉	1	1	yes	characteristic
345	C₂×#468	C₂×C₁₉	1	1	yes	characteristic, complemented
346	#2930	C₂×C₁₉	1	1	yes	characteristic, complemented
347	C₂×#430	C₂×C₁₉	1	1	yes	characteristic, complemented
348	#2064	C₂×C₁₉	1	1	yes	characteristic, complemented
349	#2063	C₂×C₁₉	1	1	yes	characteristic, complemented
350	#2052	C₂×C₁₉	1	1	yes	characteristic, complemented
351	#2051	C₂×C₁₉	1	1	yes	characteristic, complemented
352	#1977	C₂×C₁₉	1	1	yes	characteristic, complemented
353	#1952	C₂×C₁₉	1	1	yes	characteristic, complemented
354	#1901	C₂×C₁₉	1	1	yes	characteristic, complemented
355	#1900	C₂×C₁₉	1	1	yes	characteristic, complemented
356	#1816	C₂×C₁₉	1	1	yes	characteristic, complemented
357	C₂²×C₁₉	—	2	1	no	—
358	C₂²×C₁₉	—	2	1	no	—
359	C₂²×C₁₉	—	2	1	no	—
360	C₂²×C₁₉	—	2	1	no	—
361	C₂²×C₁₉	—	2	1	no	—
362	C₂²×C₁₉	—	2	1	no	—
363	C₂²×C₁₉	—	2	1	no	—
364	C₂²×C₁₉	—	2	1	no	—
365	C₂²×C₁₉	—	4	1	no	—
366	C₂²×C₁₉	—	4	1	no	—
367	C₂²×C₁₉	—	4	1	no	—
368	C₂²×C₁₉	—	8	1	no	—
369	C₂²×C₁₉	—	8	1	no	—
370	C₂²×C₁₉	—	8	1	no	—
371	C₂²×C₁₉	—	8	1	no	—
372	C₂²×C₁₉	—	8	1	no	—
373	C₂²×C₁₉	—	16	1	no	—
374	C₂²×C₁₉	—	16	1	no	—
375	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
376	C₂²×C₁₉	#548	1	1	yes	characteristic
377	C₂²×C₁₉	#553	1	1	yes	characteristic
378	C₄×C₁₉	—	2	1	no	—
379	C₄×C₁₉	—	2	1	no	—
380	C₄×C₁₉	—	4	1	no	—
381	C₄×C₁₉	—	4	1	no	—
382	C₄×C₁₉	—	4	1	no	—
383	C₄×C₁₉	—	8	1	no	—
384	C₄×C₁₉	—	8	1	no	—
385	C₄×C₁₉	—	8	1	no	—
386	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
387	C₄×C₁₉	#537	1	1	yes	characteristic
388	C₄×C₁₉	D₄²	1	1	yes	characteristic
389	C₄×C₁₉	#547	1	1	yes	characteristic
390	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
391	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
392	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
393	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
394	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
395	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
396	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
397	#525	C₂²×C₁₉	1	1	yes	characteristic
398	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
399	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
400	#471	—	2	4	no	—
401	#470	—	2	1	no	—
402	#469	—	2	1	no	—
403	#468	—	2	1	no	—
404	#468	—	2	1	no	—
405	#468	—	2	1	no	—
406	#468	—	2	1	no	—
407	#468	—	2	1	no	—
408	#468	—	2	1	no	—
409	#467	—	2	1	no	—
410	#466	—	2	1	no	—
411	#465	—	2	1	no	—
412	#465	—	2	1	no	—
413	#436	—	2	1	no	—
414	#436	—	2	1	no	—
415	#435	—	2	1	no	—
416	#435	—	2	1	no	—
417	#430	—	2	4	no	—
418	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
419	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
420	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
421	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
422	#428	C₂²×C₁₉	1	1	yes	characteristic
423	#428	C₂²×C₁₉	1	1	yes	characteristic
424	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
425	#424	C₂²×C₁₉	1	1	yes	characteristic
426	#419	C₂²×C₁₉	1	1	yes	characteristic
427	#418	C₂²×C₁₉	1	1	yes	characteristic
428	#417	C₂²×C₁₉	1	1	yes	characteristic
429	#417	C₂²×C₁₉	1	1	yes	characteristic
430	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
431	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
432	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
433	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
434	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
435	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
436	#408	C₂²×C₁₉	1	1	yes	characteristic
437	#407	C₂²×C₁₉	1	1	yes	characteristic
438	#405	C₂²×C₁₉	1	1	yes	characteristic
439	#343	C₂²×C₁₉	1	1	yes	characteristic
440	#343	C₂²×C₁₉	1	1	yes	characteristic
441	#343	C₂²×C₁₉	1	1	yes	characteristic
442	#343	C₂²×C₁₉	1	1	yes	characteristic
443	C₂×C₁₉	—	2	1	no	—
444	C₂×C₁₉	—	2	1	no	—
445	C₂×C₁₉	—	4	1	no	—
446	C₂×C₁₉	—	4	1	no	—
447	C₂×C₁₉	—	8	1	no	—
448	C₂×C₁₉	—	16	1	no	—
449	C₂×C₁₉	#2416	1	1	yes	characteristic
450	C₂×C₁₉	#3068	1	1	yes	characteristic
451	C₂×C₁₉	#3069	1	1	yes	characteristic
452	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
453	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
454	C₂²×D₄	—	2	1	no	—
455	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
457	#137	—	2	2	no	—
458	#137	—	4	1	no	—
459	AGL(1,ℤ/8)	—	2	2	no	—
460	AGL(1,ℤ/8)	—	4	1	no	—
461	C₂×Q₁₆	—	2	1	no	—
462	C₂×SD₁₆	—	2	1	no	—
463	C₂×SD₁₆	—	2	1	no	—
464	C₂×SD₁₆	—	2	1	no	—
465	C₂×SD₁₆	—	2	1	no	—
466	C₂×SD₁₆	—	2	2	no	—
467	C₂×SD₁₆	—	2	2	no	—
468	C₂×D₈	—	2	1	no	—
469	#131	—	2	2	no	—
470	#131	—	2	2	no	—
471	C₂×M₁₆	—	2	1	no	—
472	C₂×M₁₆	—	2	1	no	—
473	C₂×M₁₆	—	2	2	no	—
474	C₂×M₁₆	—	2	1	no	—
475	C₂×M₁₆	—	2	2	no	—
476	C₂×M₁₆	—	2	2	no	—
477	C₂×M₁₆	—	2	2	no	—
478	C₂×M₁₆	—	4	1	no	—
479	C₂×M₁₆	—	4	1	no	—
480	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
481	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
482	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
483	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
484	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
485	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
486	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
487	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
488	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
489	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
490	C₂²×C₈	—	2	1	no	—
491	C₂²×C₈	—	2	1	no	—
492	C₂²×C₈	—	2	1	no	—
493	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
495	#123	—	2	1	no	—
496	C₂²⋊Q₈	—	2	1	no	—
497	C₂²⋊Q₈	—	2	1	no	—
498	C₂²⋊Q₈	—	2	1	no	—
499	C₂²⋊Q₈	—	2	1	no	—
500	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
501	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
502	#121	—	2	1	no	—
503	#121	—	2	1	no	—
504	#121	—	2	1	no	—
505	#121	—	2	1	no	—
506	#121	D₄×C₁₉	1	1	yes	characteristic
507	#121	D₄×C₁₉	1	1	yes	characteristic
508	#120	—	2	1	no	—
509	C₄×D₄	—	2	1	no	—
510	C₄×D₄	—	2	1	no	—
511	#117	C₂³×C₁₉	1	1	yes	characteristic
512	C₂×C₄⋊C₄	—	2	1	no	—
513	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	#108	—	2	2	no	—
518	#108	—	2	2	no	—
519	#108	—	2	2	no	—
520	#108	D₄×C₁₉	1	4	yes	complemented
521	#107	—	2	1	no	—
522	#107	—	2	1	no	—
523	#107	—	2	1	no	—
524	#107	—	2	1	no	—
525	#106	—	2	1	no	—
526	#106	—	2	1	no	—
527	C₄⋊C₈	—	2	1	no	—
528	C₄⋊C₈	—	2	1	no	—
529	#103	—	2	1	no	—
530	#103	—	2	1	no	—
531	#103	—	2	1	no	—
532	#103	—	2	1	no	—
533	#103	—	2	1	no	—
534	#103	—	2	1	no	—
535	#102	—	2	1	no	—
536	#102	—	2	1	no	—
537	#102	—	2	1	no	—
538	#102	—	2	1	no	—
539	#102	—	2	1	no	—
540	#102	—	2	1	no	—
541	#101	—	2	2	no	—
542	#101	—	4	1	no	—
543	#100	—	2	2	no	—
544	#100	—	4	1	no	—
545	C₂²⋊C₈	—	2	1	no	—
546	C₂²⋊C₈	—	2	1	no	—
547	C₂²⋊C₈	—	2	1	no	—
548	C₂²⋊C₈	—	2	1	no	—
549	#97	—	2	1	no	—
550	C₄×C₈	—	2	1	no	—
551	C₁₉	#24805	1	1	yes	characteristic, direct product factor, Sylow
552	C₂⁴	—	2	1	no	—
553	C₂⁴	#41×C₁₉	1	1	yes	characteristic
554	#41	—	2	1	no	—
555	#41	—	2	1	no	—
556	#41	—	2	1	no	—
557	#41	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	4	1	no	—
575	C₂×D₄	—	4	1	no	—
576	C₂×D₄	—	8	2	no	—
577	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
590	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
592	Q₁₆	—	4	2	no	—
593	SD₁₆	—	4	2	no	—
594	SD₁₆	—	4	2	no	—
595	SD₁₆	—	4	2	no	—
596	SD₁₆	—	4	2	no	—
597	D₈	—	4	2	no	—
598	M₁₆	—	2	1	no	—
599	M₁₆	—	2	1	no	—
600	M₁₆	—	2	2	no	—
601	M₁₆	—	2	2	no	—
602	M₁₆	—	2	2	no	—
603	M₁₆	—	2	2	no	—
604	M₁₆	—	2	1	no	—
605	M₁₆	—	2	1	no	—
606	M₁₆	—	2	1	no	—
607	M₁₆	—	2	1	no	—
608	M₁₆	—	2	1	no	—
609	M₁₆	—	2	1	no	—
610	M₁₆	—	2	1	no	—
611	M₁₆	—	2	1	no	—
612	M₁₆	—	4	2	no	—
613	M₁₆	—	4	2	no	—
614	M₁₆	—	4	2	no	—
615	M₁₆	C₂×D₄×C₁₉	1	2	yes	—
616	M₁₆	C₂×D₄×C₁₉	1	2	yes	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	4	2	no	—
626	C₂×C₈	—	4	2	no	—
627	C₂×C₈	—	4	2	no	—
628	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
629	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
630	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
631	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
632	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
633	C₂×C₈	#41×C₁₉	1	2	yes	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	4	1	no	—
641	C₄⋊C₄	—	4	1	no	—
642	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
643	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	4	1	no	—
650	C₂²⋊C₄	—	4	1	no	—
651	C₂²⋊C₄	—	4	1	no	—
652	C₂²⋊C₄	—	4	1	no	—
653	C₄²	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	8	1	no	—
663	C₂³	—	8	1	no	—
664	C₂³	C₁₉×#121	1	1	yes	characteristic
665	C₂³	C₁₉×#121	1	1	yes	characteristic
666	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
667	Q₈	—	2	1	no	—
668	Q₈	—	2	1	no	—
669	Q₈	—	4	1	no	—
670	Q₈	—	4	1	no	—
671	Q₈	—	4	1	no	—
672	Q₈	—	4	1	no	—
673	D₄	—	2	1	no	—
674	D₄	—	2	1	no	—
675	D₄	—	4	1	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	4	1	no	—
680	D₄	—	4	1	no	—
681	D₄	—	8	1	no	—
682	D₄	—	8	1	no	—
683	D₄	—	8	2	no	—
684	D₄	—	8	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	8	1	no	—
706	C₂×C₄	—	8	1	no	—
707	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
708	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
711	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
712	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
713	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
714	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
715	C₈	—	2	1	no	—
716	C₈	—	2	1	no	—
717	C₈	—	2	2	no	—
718	C₈	—	2	2	no	—
719	C₈	—	4	1	no	—
720	C₈	—	4	1	no	—
721	C₈	—	4	1	no	—
722	C₈	—	4	1	no	—
723	C₈	C₁₉×#121	1	2	yes	—
724	C₈	C₁₉×#121	1	2	yes	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	8	1	no	—
737	C₂²	—	8	1	no	—
738	C₂²	—	8	1	no	—
739	C₂²	—	8	1	no	—
740	C₂²	—	8	1	no	—
741	C₂²	—	16	1	no	—
742	C₂²	—	16	1	no	—
743	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
744	C₂²	C₁₉×#548	1	1	yes	characteristic
745	C₂²	C₁₉×#553	1	1	yes	characteristic
746	C₄	—	2	1	no	—
747	C₄	—	2	1	no	—
748	C₄	—	4	1	no	—
749	C₄	—	4	1	no	—
750	C₄	—	4	1	no	—
751	C₄	—	8	1	no	—
752	C₄	—	8	1	no	—
753	C₄	—	8	1	no	—
754	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
755	C₄	C₁₉×#537	1	1	yes	characteristic
756	C₄	D₄²×C₁₉	1	1	yes	characteristic
757	C₄	C₁₉×#547	1	1	yes	characteristic
758	C₂	—	2	1	no	—
759	C₂	—	2	1	no	—
760	C₂	—	4	1	no	—
761	C₂	—	4	1	no	—
762	C₂	—	8	1	no	—
763	C₂	—	16	1	no	—
764	C₂	C₁₉×#2416	1	1	yes	characteristic
765	C₂	C₁₉×#3068	1	1	yes	characteristic
766	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3055	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. C₂×C₁₉×#471	C₂	semidirect
2. C₁₉×#3056	C₂	semidirect
4. C₂×C₁₉×#468	C₂	semidirect
5. C₁₉×#2930	C₂	semidirect
6. C₂×C₁₉×#430	C₂	semidirect
7. C₁₉×#2064	C₂	semidirect
8. C₁₉×#2063	C₂	semidirect
9. C₁₉×#2052	C₂	semidirect
10. C₁₉×#2051	C₂	semidirect
11. C₁₉×#1977	C₂	semidirect
12. C₁₉×#1952	C₂	semidirect
13. C₁₉×#1901	C₂	semidirect
14. C₁₉×#1900	C₂	semidirect
15. C₁₉×#1816	C₂	semidirect
137. C₁₉×#108	D₄	semidirect
270. #24805	C₁₉	direct (N × H)
342. C₂×#471	C₂×C₁₉	semidirect
343. #3056	C₂×C₁₉	semidirect
345. C₂×#468	C₂×C₁₉	semidirect
346. #2930	C₂×C₁₉	semidirect
347. C₂×#430	C₂×C₁₉	semidirect
348. #2064	C₂×C₁₉	semidirect
349. #2063	C₂×C₁₉	semidirect
350. #2052	C₂×C₁₉	semidirect
351. #2051	C₂×C₁₉	semidirect
352. #1977	C₂×C₁₉	semidirect
353. #1952	C₂×C₁₉	semidirect
354. #1901	C₂×C₁₉	semidirect
355. #1900	C₂×C₁₉	semidirect
356. #1816	C₂×C₁₉	semidirect
520. #108	D₄×C₁₉	semidirect
551. C₁₉	#24805	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×#471	2
C₁₉×#3056	2
C₁₉×#3055	2
C₂×C₁₉×#468	2
C₁₉×#2930	2
C₂×C₁₉×#430	2
C₁₉×#2064	2
C₁₉×#2063	2
C₁₉×#2052	2
C₁₉×#2051	2
C₁₉×#1977	2
C₁₉×#1952	2
C₁₉×#1901	2
C₁₉×#1900	2
C₁₉×#1816	2
#24805	19

Subgroups — C19×#24805 #18030764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24805 #18030764