Subgroups — C₁₉×#23721 #18029680

Order 4864.

776 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2923	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2089	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2078	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
11	C₁₉×#2046	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2019	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1778	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₉×#100	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	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#442	—	2	1	no	—
23	C₁₉×#441	—	2	1	no	—
24	C₁₉×#440	—	2	2	no	—
25	C₁₉×#440	—	2	2	no	—
26	C₁₉×#440	—	2	1	no	—
27	C₁₉×#440	—	2	1	no	—
28	C₄×Q₁₆×C₁₉	—	2	1	no	—
29	C₄×SD₁₆×C₁₉	—	2	1	no	—
30	C₄×SD₁₆×C₁₉	—	2	1	no	—
31	C₄×D₈×C₁₉	—	2	1	no	—
32	C₁₉×#433	—	2	2	no	—
33	C₁₉×#432	—	2	2	no	—
34	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
36	C₁₉×#428	C₂²	1	1	yes	characteristic
37	C₁₉×#428	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
39	C₁₉×#424	C₂²	1	1	yes	characteristic
40	C₁₉×#424	C₂²	1	1	yes	characteristic
41	C₁₉×#419	C₂²	1	1	yes	characteristic
42	C₁₉×#418	C₂²	1	1	yes	characteristic
43	C₁₉×#417	C₂²	1	1	yes	characteristic
44	C₁₉×#417	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
49	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
51	C₁₉×#408	C₂²	1	1	yes	characteristic
52	C₁₉×#408	C₂²	1	1	yes	characteristic
53	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
54	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
55	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
56	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
57	C₁₉×#343	C₂²	1	1	yes	characteristic
58	C₁₉×#343	C₂²	1	1	yes	characteristic
59	C₁₉×#343	C₂²	1	1	yes	characteristic
60	C₁₉×#343	C₂²	1	1	yes	characteristic
61	C₁₉×#341	C₂²	1	1	yes	characteristic
62	C₁₉×#341	C₂²	1	1	yes	characteristic
63	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	—	2	1	no	—
67	C₁₉×#137	—	2	2	no	—
68	C₁₉×#137	—	2	2	no	—
69	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
70	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
71	C₂×Q₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	2	no	—
74	C₂×SD₁₆×C₁₉	—	2	1	no	—
75	C₂×SD₁₆×C₁₉	—	2	2	no	—
76	C₂×SD₁₆×C₁₉	—	2	2	no	—
77	C₂×D₈×C₁₉	—	2	1	no	—
78	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×Q₈×C₁₉	—	2	1	no	—
88	C₄×Q₈×C₁₉	—	2	1	no	—
89	C₄×Q₈×C₁₉	—	2	1	no	—
90	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
92	C₄×D₄×C₁₉	—	2	1	no	—
93	C₄×D₄×C₁₉	—	2	1	no	—
94	C₄×D₄×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	—	2	1	no	—
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	—	2	1	no	—
98	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
99	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
100	C₁₉×#117	—	2	1	no	—
101	C₁₉×#117	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₄²×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
109	C₁₉×#108	—	2	2	no	—
110	C₁₉×#108	—	2	2	no	—
111	C₁₉×#107	—	2	2	no	—
112	C₁₉×#107	—	2	1	no	—
113	C₁₉×#107	—	2	1	no	—
114	C₁₉×#106	—	2	1	no	—
115	C₁₉×#106	—	2	1	no	—
116	C₁₉×C₄⋊C₈	—	2	2	no	—
117	C₁₉×C₄⋊C₈	—	2	2	no	—
118	C₁₉×#103	—	2	1	no	—
119	C₁₉×#103	—	2	1	no	—
120	C₁₉×#103	—	2	2	no	—
121	C₁₉×#103	—	2	1	no	—
122	C₁₉×#103	—	2	1	no	—
123	C₁₉×#102	—	2	1	no	—
124	C₁₉×#102	—	2	1	no	—
125	C₁₉×#102	—	2	2	no	—
126	C₁₉×#102	—	2	1	no	—
127	C₁₉×#102	—	2	1	no	—
128	C₁₉×#101	—	2	2	no	—
129	C₁₉×#101	—	2	2	no	—
130	C₁₉×#100	—	2	2	no	—
131	C₁₉×#100	—	2	2	no	—
132	C₁₉×C₂²⋊C₈	—	2	2	no	—
133	C₁₉×C₂²⋊C₈	—	2	2	no	—
134	C₁₉×#97	—	2	1	no	—
135	C₁₉×#97	—	2	1	no	—
136	C₁₉×#97	—	2	1	no	—
137	C₁₉×#97	D₄	1	2	yes	—
138	C₁₉×#97	D₄	1	2	yes	—
139	C₄×C₈×C₁₉	—	2	1	no	—
140	C₄×C₈×C₁₉	—	2	1	no	—
141	C₄×C₈×C₁₉	—	2	1	no	—
142	C₂⁴×C₁₉	—	2	1	no	—
143	#41×C₁₉	—	2	1	no	—
144	#41×C₁₉	—	2	1	no	—
145	#41×C₁₉	—	2	1	no	—
146	#41×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂×Q₈×C₁₉	#41	1	2	yes	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂×D₄×C₁₉	#41	1	2	yes	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	4	1	no	—
169	C₂²×C₄×C₁₉	—	4	1	no	—
170	C₂²×C₄×C₁₉	—	8	2	no	—
171	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
174	Q₁₆×C₁₉	—	2	4	no	—
175	SD₁₆×C₁₉	—	2	8	no	—
176	SD₁₆×C₁₉	—	2	4	no	—
177	SD₁₆×C₁₉	—	2	4	no	—
178	D₈×C₁₉	—	2	4	no	—
179	M₁₆×C₁₉	—	2	1	no	—
180	M₁₆×C₁₉	—	2	1	no	—
181	M₁₆×C₁₉	—	2	1	no	—
182	M₁₆×C₁₉	—	2	1	no	—
183	M₁₆×C₁₉	—	2	1	no	—
184	M₁₆×C₁₉	—	2	1	no	—
185	M₁₆×C₁₉	—	2	1	no	—
186	M₁₆×C₁₉	—	2	1	no	—
187	M₁₆×C₁₉	—	2	1	no	—
188	M₁₆×C₁₉	—	2	1	no	—
189	M₁₆×C₁₉	#41	1	2	yes	—
190	M₁₆×C₁₉	#41	1	2	yes	—
191	C₂×C₈×C₁₉	—	2	1	no	—
192	C₂×C₈×C₁₉	—	2	1	no	—
193	C₂×C₈×C₁₉	—	2	1	no	—
194	C₂×C₈×C₁₉	—	2	1	no	—
195	C₂×C₈×C₁₉	—	2	1	no	—
196	C₂×C₈×C₁₉	—	2	1	no	—
197	C₂×C₈×C₁₉	—	2	1	no	—
198	C₂×C₈×C₁₉	—	2	1	no	—
199	C₂×C₈×C₁₉	—	2	1	no	—
200	C₂×C₈×C₁₉	—	2	1	no	—
201	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
202	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	2	1	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	—	4	1	no	—
210	C₄⋊C₄×C₁₉	—	4	1	no	—
211	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₂²⋊C₄×C₁₉	—	2	1	no	—
215	C₂²⋊C₄×C₁₉	—	2	1	no	—
216	C₂²⋊C₄×C₁₉	—	4	1	no	—
217	C₂²⋊C₄×C₁₉	—	4	1	no	—
218	C₄²×C₁₉	—	2	1	no	—
219	C₄²×C₁₉	—	2	1	no	—
220	C₄²×C₁₉	—	2	1	no	—
221	C₄²×C₁₉	—	4	1	no	—
222	C₄²×C₁₉	—	4	1	no	—
223	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
224	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
225	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
227	#23721	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂³×C₁₉	—	2	1	no	—
229	C₂³×C₁₉	—	2	2	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	—	4	1	no	—
232	C₂³×C₁₉	—	8	1	no	—
233	C₂³×C₁₉	—	8	1	no	—
234	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
235	Q₈×C₁₉	—	2	2	no	—
236	Q₈×C₁₉	—	2	1	no	—
237	Q₈×C₁₉	—	2	2	no	—
238	Q₈×C₁₉	—	2	1	no	—
239	Q₈×C₁₉	—	4	1	no	—
240	Q₈×C₁₉	—	4	1	no	—
241	D₄×C₁₉	—	2	1	no	—
242	D₄×C₁₉	—	2	2	no	—
243	D₄×C₁₉	—	2	2	no	—
244	D₄×C₁₉	—	2	1	no	—
245	D₄×C₁₉	—	4	1	no	—
246	D₄×C₁₉	—	4	1	no	—
247	D₄×C₁₉	—	4	1	no	—
248	D₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	8	1	no	—
262	C₂×C₄×C₁₉	—	8	1	no	—
263	C₂×C₄×C₁₉	—	8	2	no	—
264	C₂×C₄×C₁₉	—	8	2	no	—
265	C₂×C₄×C₁₉	—	8	1	no	—
266	C₂×C₄×C₁₉	—	8	1	no	—
267	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
268	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
269	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
270	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
271	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
277	C₈×C₁₉	—	2	2	no	—
278	C₈×C₁₉	—	2	2	no	—
279	C₈×C₁₉	—	2	2	no	—
280	C₈×C₁₉	—	2	2	no	—
281	C₈×C₁₉	—	4	1	no	—
282	C₈×C₁₉	—	4	1	no	—
283	C₈×C₁₉	—	4	1	no	—
284	C₈×C₁₉	—	4	1	no	—
285	C₄×#137	C₂×C₁₉	1	1	yes	characteristic, complemented
286	C₄×AGL(1,ℤ/8)	C₂×C₁₉	1	1	yes	characteristic
287	C₂×#440	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#2923	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#2089	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#2078	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#2064	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#2063	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#2052	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#2051	C₂×C₁₉	1	1	yes	characteristic
295	#2046	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#2019	C₂×C₁₉	1	1	yes	characteristic
297	#1778	C₂×C₁₉	1	1	yes	characteristic, complemented
298	C₄×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
299	C₄×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
300	C₂²×C₁₉	—	2	1	no	—
301	C₂²×C₁₉	—	2	1	no	—
302	C₂²×C₁₉	—	4	1	no	—
303	C₂²×C₁₉	—	4	2	no	—
304	C₂²×C₁₉	—	4	1	no	—
305	C₂²×C₁₉	—	4	1	no	—
306	C₂²×C₁₉	—	8	2	no	—
307	C₂²×C₁₉	—	8	2	no	—
308	C₂²×C₁₉	—	8	1	no	—
309	C₂²×C₁₉	—	8	1	no	—
310	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
311	C₂²×C₁₉	#529	1	1	yes	characteristic
312	C₂²×C₁₉	#529	1	1	yes	characteristic
313	C₄×C₁₉	—	2	1	no	—
314	C₄×C₁₉	—	2	1	no	—
315	C₄×C₁₉	—	2	1	no	—
316	C₄×C₁₉	—	2	1	no	—
317	C₄×C₁₉	—	4	1	no	—
318	C₄×C₁₉	—	4	2	no	—
319	C₄×C₁₉	—	4	1	no	—
320	C₄×C₁₉	—	4	1	no	—
321	C₄×C₁₉	—	8	1	no	—
322	C₄×C₁₉	—	8	1	no	—
323	C₄×C₁₉	#525	1	1	yes	characteristic
324	C₄×C₁₉	#525	1	1	yes	characteristic
325	C₄×C₁₉	#525	1	1	yes	characteristic
326	C₄×C₁₉	#532	1	1	yes	characteristic
327	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
328	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
329	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
330	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
331	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
333	#442	—	2	1	no	—
334	#441	—	2	1	no	—
335	#440	—	2	1	no	—
336	#440	—	2	1	no	—
337	#440	—	2	2	no	—
338	#440	—	2	2	no	—
339	C₄×Q₁₆	—	2	1	no	—
340	C₄×SD₁₆	—	2	1	no	—
341	C₄×SD₁₆	—	2	1	no	—
342	C₄×D₈	—	2	1	no	—
343	#433	—	2	2	no	—
344	#432	—	2	2	no	—
345	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
346	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
347	#428	C₂²×C₁₉	1	1	yes	characteristic
348	#428	C₂²×C₁₉	1	1	yes	characteristic
349	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
350	#424	C₂²×C₁₉	1	1	yes	characteristic
351	#424	C₂²×C₁₉	1	1	yes	characteristic
352	#419	C₂²×C₁₉	1	1	yes	characteristic
353	#418	C₂²×C₁₉	1	1	yes	characteristic
354	#417	C₂²×C₁₉	1	1	yes	characteristic
355	#417	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
361	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
362	#408	C₂²×C₁₉	1	1	yes	characteristic
363	#408	C₂²×C₁₉	1	1	yes	characteristic
364	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
365	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
366	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
368	#343	C₂²×C₁₉	1	1	yes	characteristic
369	#343	C₂²×C₁₉	1	1	yes	characteristic
370	#343	C₂²×C₁₉	1	1	yes	characteristic
371	#343	C₂²×C₁₉	1	1	yes	characteristic
372	#341	C₂²×C₁₉	1	1	yes	characteristic
373	#341	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×C₁₉	—	2	1	no	—
375	C₂×C₁₉	—	2	1	no	—
376	C₂×C₁₉	—	8	1	no	—
377	C₂×C₁₉	—	8	2	no	—
378	C₂×C₁₉	#2392	1	1	yes	characteristic
379	C₂×C₁₉	#3068	1	1	yes	characteristic
380	C₂×C₁₉	#3069	1	1	yes	characteristic
381	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
382	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
383	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
384	C₂³×C₄	—	2	1	no	—
385	#137	—	2	2	no	—
386	#137	—	2	2	no	—
387	AGL(1,ℤ/8)	—	2	2	no	—
388	AGL(1,ℤ/8)	—	2	2	no	—
389	C₂×Q₁₆	—	2	1	no	—
390	C₂×SD₁₆	—	2	1	no	—
391	C₂×SD₁₆	—	2	2	no	—
392	C₂×SD₁₆	—	2	1	no	—
393	C₂×SD₁₆	—	2	2	no	—
394	C₂×SD₁₆	—	2	2	no	—
395	C₂×D₈	—	2	1	no	—
396	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
397	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
398	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
399	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
400	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
401	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
403	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
404	C₄×Q₈	—	2	1	no	—
405	C₄×Q₈	—	2	1	no	—
406	C₄×Q₈	—	2	1	no	—
407	C₄×Q₈	—	2	1	no	—
408	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
409	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	—	2	1	no	—
415	C₄×D₄	—	2	1	no	—
416	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
417	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
418	#117	—	2	1	no	—
419	#117	C₂³×C₁₉	1	1	yes	characteristic
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
427	#108	—	2	2	no	—
428	#108	—	2	2	no	—
429	#107	—	2	2	no	—
430	#107	—	2	1	no	—
431	#107	—	2	1	no	—
432	#106	—	2	1	no	—
433	#106	—	2	1	no	—
434	C₄⋊C₈	—	2	2	no	—
435	C₄⋊C₈	—	2	2	no	—
436	#103	—	2	1	no	—
437	#103	—	2	1	no	—
438	#103	—	2	2	no	—
439	#103	—	2	1	no	—
440	#103	—	2	1	no	—
441	#102	—	2	1	no	—
442	#102	—	2	1	no	—
443	#102	—	2	2	no	—
444	#102	—	2	1	no	—
445	#102	—	2	1	no	—
446	#101	—	2	2	no	—
447	#101	—	2	2	no	—
448	#100	—	2	2	no	—
449	#100	—	2	2	no	—
450	C₂²⋊C₈	—	2	2	no	—
451	C₂²⋊C₈	—	2	2	no	—
452	#97	—	2	1	no	—
453	#97	—	2	1	no	—
454	#97	—	2	1	no	—
455	#97	D₄×C₁₉	1	2	yes	—
456	#97	D₄×C₁₉	1	2	yes	—
457	C₄×C₈	—	2	1	no	—
458	C₄×C₈	—	2	1	no	—
459	C₄×C₈	—	2	1	no	—
460	C₁₉	#23721	1	1	yes	characteristic, direct product factor, Sylow
461	C₂⁴	—	2	1	no	—
462	#41	—	2	1	no	—
463	#41	—	2	1	no	—
464	#41	—	2	1	no	—
465	#41	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
472	C₂×Q₈	#41×C₁₉	1	2	yes	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₂×D₄	#41×C₁₉	1	2	yes	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	4	1	no	—
488	C₂²×C₄	—	4	1	no	—
489	C₂²×C₄	—	8	2	no	—
490	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
491	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
492	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
493	Q₁₆	—	2	4	no	—
494	SD₁₆	—	2	8	no	—
495	SD₁₆	—	2	4	no	—
496	SD₁₆	—	2	4	no	—
497	D₈	—	2	4	no	—
498	M₁₆	—	2	1	no	—
499	M₁₆	—	2	1	no	—
500	M₁₆	—	2	1	no	—
501	M₁₆	—	2	1	no	—
502	M₁₆	—	2	1	no	—
503	M₁₆	—	2	1	no	—
504	M₁₆	—	2	1	no	—
505	M₁₆	—	2	1	no	—
506	M₁₆	—	2	1	no	—
507	M₁₆	—	2	1	no	—
508	M₁₆	#41×C₁₉	1	2	yes	—
509	M₁₆	#41×C₁₉	1	2	yes	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
521	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	4	1	no	—
529	C₄⋊C₄	—	4	1	no	—
530	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
532	C₂²⋊C₄	—	2	1	no	—
533	C₂²⋊C₄	—	2	1	no	—
534	C₂²⋊C₄	—	2	1	no	—
535	C₂²⋊C₄	—	4	1	no	—
536	C₂²⋊C₄	—	4	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	4	1	no	—
541	C₄²	—	4	1	no	—
542	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
543	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
544	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
545	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
546	C₂³	—	2	1	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	8	1	no	—
551	C₂³	—	8	1	no	—
552	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
553	Q₈	—	2	2	no	—
554	Q₈	—	2	1	no	—
555	Q₈	—	2	2	no	—
556	Q₈	—	2	1	no	—
557	Q₈	—	4	1	no	—
558	Q₈	—	4	1	no	—
559	D₄	—	2	1	no	—
560	D₄	—	2	2	no	—
561	D₄	—	2	2	no	—
562	D₄	—	2	1	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	1	no	—
566	D₄	—	4	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	8	1	no	—
580	C₂×C₄	—	8	1	no	—
581	C₂×C₄	—	8	2	no	—
582	C₂×C₄	—	8	2	no	—
583	C₂×C₄	—	8	1	no	—
584	C₂×C₄	—	8	1	no	—
585	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
586	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
587	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
588	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
589	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
590	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
591	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
592	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
593	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
594	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
595	C₈	—	2	2	no	—
596	C₈	—	2	2	no	—
597	C₈	—	2	2	no	—
598	C₈	—	2	2	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₈	—	4	1	no	—
602	C₈	—	4	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	8	2	no	—
610	C₂²	—	8	2	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
614	C₂²	C₁₉×#529	1	1	yes	characteristic
615	C₂²	C₁₉×#529	1	1	yes	characteristic
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	2	no	—
624	C₄	—	8	1	no	—
625	C₄	—	8	1	no	—
626	C₄	C₁₉×#525	1	1	yes	characteristic
627	C₄	C₁₉×#525	1	1	yes	characteristic
628	C₄	C₁₉×#525	1	1	yes	characteristic
629	C₄	C₁₉×#532	1	1	yes	characteristic
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	8	1	no	—
633	C₂	—	8	2	no	—
634	C₂	C₁₉×#2392	1	1	yes	characteristic
635	C₂	C₁₉×#3068	1	1	yes	characteristic
636	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	C₂×C₁₉×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×C₁₉×#137	C₂	semidirect
3. C₂×C₁₉×#440	C₂	semidirect
4. C₁₉×#2923	C₂	semidirect
5. C₁₉×#2089	C₂	semidirect
6. C₁₉×#2078	C₂	semidirect
7. C₁₉×#2064	C₂	semidirect
8. C₁₉×#2063	C₂	semidirect
9. C₁₉×#2052	C₂	semidirect
11. C₁₉×#2046	C₂	semidirect
13. C₁₉×#1778	C₂	semidirect
14. C₄×C₁₉×#101	C₂	semidirect
15. C₄×C₁₉×#100	C₂	semidirect
227. #23721	C₁₉	direct (N × H)
285. C₄×#137	C₂×C₁₉	semidirect
287. C₂×#440	C₂×C₁₉	semidirect
288. #2923	C₂×C₁₉	semidirect
289. #2089	C₂×C₁₉	semidirect
290. #2078	C₂×C₁₉	semidirect
291. #2064	C₂×C₁₉	semidirect
292. #2063	C₂×C₁₉	semidirect
293. #2052	C₂×C₁₉	semidirect
295. #2046	C₂×C₁₉	semidirect
297. #1778	C₂×C₁₉	semidirect
298. C₄×#101	C₂×C₁₉	semidirect
299. C₄×#100	C₂×C₁₉	semidirect
460. C₁₉	#23721	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₉×#137	2
C₄×C₁₉×AGL(1,ℤ/8)	2
C₂×C₁₉×#440	2
C₁₉×#2923	2
C₁₉×#2089	2
C₁₉×#2078	2
C₁₉×#2064	2
C₁₉×#2063	2
C₁₉×#2052	2
C₁₉×#2051	2
C₁₉×#2046	2
C₁₉×#2019	2
C₁₉×#1778	2
C₄×C₁₉×#101	2
C₄×C₁₉×#100	2
#23721	19

Subgroups — C19×#23721 #18029680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23721 #18029680