Subgroups — C₁₉×#23426 #18029385

Order 4864.

2178 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#535	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#417	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2015	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2014	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2012	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2011	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
16	C₂×C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
17	C₂×C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
18	C₂×C₁₉×#135	—	2	4	no	—
19	C₂×C₁₉×#135	—	2	4	no	—
20	C₂×C₁₉×#135	—	2	4	no	—
21	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
22	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
23	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
24	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
25	C₂²×D₈×C₁₉	C₂²	1	2	yes	—
26	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
27	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#535	—	2	4	no	—
30	C₁₉×#535	—	2	4	no	—
31	C₂×C₁₉×#127	C₂²	1	2	yes	—
32	C₂×C₁₉×#124	C₂²	1	2	yes	—
33	C₂×C₁₉×#121	—	2	2	no	—
34	C₂×C₁₉×#120	—	2	2	no	—
35	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#417	—	2	4	no	—
38	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
39	C₂×C₁₉×#102	—	2	4	no	—
40	C₂×C₁₉×#102	C₂²	1	2	yes	—
41	C₂×C₁₉×#102	C₂²	1	2	yes	—
42	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
43	C₁₉×#391	C₂²	1	2	yes	complemented
44	C₁₉×#390	C₂²	1	2	yes	complemented
45	C₁₉×#386	—	2	2	no	—
46	C₁₉×#380	—	2	2	no	—
47	C₁₉×#336	C₂²	1	2	yes	complemented
48	C₁₉×#336	C₂²	1	2	yes	complemented
49	C₂⁵×C₁₉	—	2	1	no	—
50	C₂×#41×C₁₉	—	2	2	no	—
51	C₂×#41×C₁₉	—	2	2	no	—
52	C₂×#41×C₁₉	—	2	2	no	—
53	C₂×#41×C₁₉	—	2	2	no	—
54	C₂×#41×C₁₉	—	2	2	no	—
55	C₂×#41×C₁₉	—	2	2	no	—
56	C₂×#41×C₁₉	—	2	2	no	—
57	C₂×#41×C₁₉	—	2	2	no	—
58	C₂×#41×C₁₉	—	2	2	no	—
59	C₂×#41×C₁₉	—	2	2	no	—
60	C₂×#41×C₁₉	D₄	1	4	yes	—
61	C₂×#41×C₁₉	D₄	1	4	yes	complemented
62	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₉	—	2	1	no	—
65	C₂²×D₄×C₁₉	—	2	1	no	—
66	C₂²×D₄×C₁₉	—	2	2	no	—
67	C₂²×D₄×C₁₉	—	2	2	no	—
68	C₂²×D₄×C₁₉	—	2	2	no	—
69	C₂²×D₄×C₁₉	—	2	1	no	—
70	C₂²×D₄×C₁₉	—	2	2	no	—
71	C₂²×D₄×C₁₉	—	2	4	no	—
72	C₂²×D₄×C₁₉	—	2	2	no	—
73	C₂²×D₄×C₁₉	D₄	1	4	yes	—
74	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
76	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₉	—	2	1	no	—
78	C₂³×C₄×C₁₉	—	2	1	no	—
79	C₂³×C₄×C₁₉	—	2	1	no	—
80	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₁₉×AGL(1,ℤ/8)	—	2	32	no	—
82	C₁₉×#135	—	2	32	no	—
83	C₂×Q₁₆×C₁₉	—	2	2	no	—
84	C₂×Q₁₆×C₁₉	—	2	2	no	—
85	C₂×Q₁₆×C₁₉	—	2	2	no	—
86	C₂×SD₁₆×C₁₉	—	2	4	no	—
87	C₂×SD₁₆×C₁₉	—	2	2	no	—
88	C₂×SD₁₆×C₁₉	—	2	2	no	—
89	C₂×SD₁₆×C₁₉	—	2	4	no	—
90	C₂×SD₁₆×C₁₉	—	2	2	no	—
91	C₂×SD₁₆×C₁₉	—	2	2	no	—
92	C₂×SD₁₆×C₁₉	—	2	4	no	—
93	C₂×SD₁₆×C₁₉	—	2	2	no	—
94	C₂×SD₁₆×C₁₉	—	2	2	no	—
95	C₂×D₈×C₁₉	—	2	4	no	—
96	C₂×D₈×C₁₉	—	2	4	no	—
97	C₂×D₈×C₁₉	—	2	2	no	—
98	C₂×D₈×C₁₉	—	2	2	no	—
99	C₂×D₈×C₁₉	—	2	4	no	—
100	C₂×D₈×C₁₉	—	2	2	no	—
101	C₂×M₁₆×C₁₉	—	2	2	no	—
102	C₂×M₁₆×C₁₉	—	2	2	no	—
103	C₂×M₁₆×C₁₉	D₄	1	4	yes	complemented
104	C₂²×C₈×C₁₉	—	2	2	no	—
105	C₂²×C₈×C₁₉	—	2	2	no	—
106	C₂²×C₈×C₁₉	D₄	1	4	yes	complemented
107	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
110	C₁₉×#127	—	2	4	no	—
111	C₁₉×#127	—	2	4	no	—
112	C₁₉×#124	—	2	4	no	—
113	C₁₉×#124	—	2	4	no	—
114	C₁₉×#121	—	2	16	no	—
115	C₁₉×#120	—	2	16	no	—
116	C₁₉×#117	—	2	2	no	—
117	C₁₉×#117	—	2	2	no	—
118	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
124	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
125	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
126	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
127	C₁₉×#103	—	2	4	no	—
128	C₁₉×#102	—	2	4	no	—
129	C₁₉×#102	—	2	4	no	—
130	C₁₉×#102	—	2	4	no	—
131	C₁₉×#95	—	2	4	no	—
132	C₂⁴×C₁₉	—	2	1	no	—
133	C₂⁴×C₁₉	—	2	2	no	—
134	C₂⁴×C₁₉	—	2	1	no	—
135	C₂⁴×C₁₉	—	2	4	no	—
136	C₂⁴×C₁₉	—	4	2	no	—
137	C₂⁴×C₁₉	—	4	2	no	—
138	C₂⁴×C₁₉	—	8	2	no	—
139	C₂⁴×C₁₉	—	8	2	no	—
140	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
141	#41×C₁₉	—	2	8	no	—
142	#41×C₁₉	—	2	8	no	—
143	#41×C₁₉	—	2	8	no	—
144	#41×C₁₉	—	2	8	no	—
145	#41×C₁₉	—	4	4	no	—
146	#41×C₁₉	—	4	4	no	—
147	#41×C₁₉	—	4	4	no	—
148	#41×C₁₉	—	4	4	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	—	2	1	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	2	1	no	—
156	C₂×Q₈×C₁₉	—	2	1	no	—
157	C₂×Q₈×C₁₉	—	2	1	no	—
158	C₂×Q₈×C₁₉	—	2	1	no	—
159	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
160	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
161	C₂×D₄×C₁₉	—	2	4	no	—
162	C₂×D₄×C₁₉	—	2	4	no	—
163	C₂×D₄×C₁₉	—	2	16	no	—
164	C₂×D₄×C₁₉	—	2	8	no	—
165	C₂×D₄×C₁₉	—	2	4	no	—
166	C₂×D₄×C₁₉	—	2	8	no	—
167	C₂×D₄×C₁₉	—	2	1	no	—
168	C₂×D₄×C₁₉	—	2	1	no	—
169	C₂×D₄×C₁₉	—	2	2	no	—
170	C₂×D₄×C₁₉	—	2	2	no	—
171	C₂×D₄×C₁₉	—	2	1	no	—
172	C₂×D₄×C₁₉	—	2	1	no	—
173	C₂×D₄×C₁₉	—	2	1	no	—
174	C₂×D₄×C₁₉	—	2	1	no	—
175	C₂×D₄×C₁₉	—	2	2	no	—
176	C₂×D₄×C₁₉	—	2	1	no	—
177	C₂×D₄×C₁₉	—	2	2	no	—
178	C₂×D₄×C₁₉	—	2	1	no	—
179	C₂×D₄×C₁₉	—	2	2	no	—
180	C₂×D₄×C₁₉	—	2	1	no	—
181	C₂×D₄×C₁₉	—	2	1	no	—
182	C₂×D₄×C₁₉	—	4	2	no	—
183	C₂×D₄×C₁₉	—	4	2	no	—
184	C₂×D₄×C₁₉	—	4	2	no	—
185	C₂×D₄×C₁₉	—	4	2	no	—
186	C₂×D₄×C₁₉	—	4	4	no	—
187	C₂×D₄×C₁₉	—	4	4	no	—
188	C₂×D₄×C₁₉	—	4	2	no	—
189	C₂×D₄×C₁₉	—	4	2	no	—
190	C₂×D₄×C₁₉	—	8	4	no	—
191	C₂×D₄×C₁₉	—	8	4	no	—
192	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
193	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
194	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₁₉	—	2	1	no	—
196	C₂²×C₄×C₁₉	—	2	1	no	—
197	C₂²×C₄×C₁₉	—	2	4	no	—
198	C₂²×C₄×C₁₉	—	2	4	no	—
199	C₂²×C₄×C₁₉	—	2	2	no	—
200	C₂²×C₄×C₁₉	—	4	2	no	—
201	C₂²×C₄×C₁₉	—	4	2	no	—
202	C₂²×C₄×C₁₉	—	4	2	no	—
203	C₂²×C₄×C₁₉	—	4	2	no	—
204	C₂²×C₄×C₁₉	—	4	2	no	—
205	C₂²×C₄×C₁₉	—	8	2	no	—
206	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
207	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
208	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
209	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
213	C₂²×C₄×C₁₉	#41	1	2	yes	—
214	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
215	Q₁₆×C₁₉	—	2	8	no	—
216	SD₁₆×C₁₉	—	2	8	no	—
217	SD₁₆×C₁₉	—	2	8	no	—
218	SD₁₆×C₁₉	—	2	16	no	—
219	D₈×C₁₉	—	2	8	no	—
220	D₈×C₁₉	—	2	16	no	—
221	M₁₆×C₁₉	—	2	8	no	—
222	C₂×C₈×C₁₉	—	2	8	no	—
223	C₂×C₈×C₁₉	—	2	1	no	—
224	C₂×C₈×C₁₉	—	2	1	no	—
225	C₂×C₈×C₁₉	—	2	1	no	—
226	C₂×C₈×C₁₉	—	2	1	no	—
227	C₂×C₈×C₁₉	—	2	2	no	—
228	C₂×C₈×C₁₉	—	2	2	no	—
229	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
230	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
231	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
232	C₄⋊C₄×C₁₉	—	2	4	no	—
233	C₄⋊C₄×C₁₉	—	2	2	no	—
234	C₄⋊C₄×C₁₉	—	2	2	no	—
235	C₄⋊C₄×C₁₉	—	4	2	no	—
236	C₂²⋊C₄×C₁₉	—	2	16	no	—
237	C₂²⋊C₄×C₁₉	—	2	4	no	—
238	C₂²⋊C₄×C₁₉	—	8	4	no	—
239	C₄²×C₁₉	—	2	2	no	—
240	C₄²×C₁₉	—	2	2	no	—
241	#23426	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂³×C₁₉	—	2	2	no	—
243	C₂³×C₁₉	—	2	2	no	—
244	C₂³×C₁₉	—	2	4	no	—
245	C₂³×C₁₉	—	2	2	no	—
246	C₂³×C₁₉	—	2	2	no	—
247	C₂³×C₁₉	—	4	1	no	—
248	C₂³×C₁₉	—	4	1	no	—
249	C₂³×C₁₉	—	4	2	no	—
250	C₂³×C₁₉	—	4	1	no	—
251	C₂³×C₁₉	—	4	1	no	—
252	C₂³×C₁₉	—	4	2	no	—
253	C₂³×C₁₉	—	4	2	no	—
254	C₂³×C₁₉	—	4	2	no	—
255	C₂³×C₁₉	—	4	4	no	—
256	C₂³×C₁₉	—	4	2	no	—
257	C₂³×C₁₉	—	4	4	no	—
258	C₂³×C₁₉	—	4	2	no	—
259	C₂³×C₁₉	—	4	8	no	—
260	C₂³×C₁₉	—	8	8	no	—
261	C₂³×C₁₉	—	8	4	no	—
262	C₂³×C₁₉	—	8	4	no	—
263	C₂³×C₁₉	—	8	8	no	—
264	C₂³×C₁₉	#120	1	2	yes	—
265	C₂³×C₁₉	#121	1	2	yes	—
266	C₂³×C₁₉	#127	1	2	yes	—
267	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
268	Q₈×C₁₉	—	2	2	no	—
269	Q₈×C₁₉	—	2	2	no	—
270	Q₈×C₁₉	—	2	2	no	—
271	Q₈×C₁₉	—	2	2	no	—
272	Q₈×C₁₉	—	4	1	no	—
273	Q₈×C₁₉	—	4	1	no	—
274	Q₈×C₁₉	—	4	1	no	—
275	Q₈×C₁₉	—	4	1	no	—
276	D₄×C₁₉	—	2	2	no	—
277	D₄×C₁₉	—	2	4	no	—
278	D₄×C₁₉	—	2	2	no	—
279	D₄×C₁₉	—	2	2	no	—
280	D₄×C₁₉	—	2	4	no	—
281	D₄×C₁₉	—	2	2	no	—
282	D₄×C₁₉	—	4	8	no	—
283	D₄×C₁₉	—	4	8	no	—
284	D₄×C₁₉	—	4	2	no	—
285	D₄×C₁₉	—	4	1	no	—
286	D₄×C₁₉	—	4	2	no	—
287	D₄×C₁₉	—	4	1	no	—
288	D₄×C₁₉	—	4	1	no	—
289	D₄×C₁₉	—	4	1	no	—
290	D₄×C₁₉	—	4	8	no	—
291	D₄×C₁₉	—	8	16	no	—
292	C₂×C₄×C₁₉	—	2	4	no	—
293	C₂×C₄×C₁₉	—	2	2	no	—
294	C₂×C₄×C₁₉	—	2	2	no	—
295	C₂×C₄×C₁₉	—	2	4	no	—
296	C₂×C₄×C₁₉	—	2	4	no	—
297	C₂×C₄×C₁₉	—	4	1	no	—
298	C₂×C₄×C₁₉	—	4	1	no	—
299	C₂×C₄×C₁₉	—	4	1	no	—
300	C₂×C₄×C₁₉	—	4	1	no	—
301	C₂×C₄×C₁₉	—	4	8	no	—
302	C₂×C₄×C₁₉	—	4	8	no	—
303	C₂×C₄×C₁₉	—	4	2	no	—
304	C₂×C₄×C₁₉	—	4	4	no	—
305	C₂×C₄×C₁₉	—	8	4	no	—
306	C₂×C₄×C₁₉	#120	1	4	yes	—
307	C₂×C₄×C₁₉	#120	1	4	yes	—
308	C₂×C₄×C₁₉	#120	1	2	yes	—
309	C₂×C₄×C₁₉	#121	1	4	yes	—
310	C₂×C₄×C₁₉	#121	1	4	yes	—
311	C₂×C₄×C₁₉	#121	1	2	yes	—
312	C₂×C₄×C₁₉	#127	1	2	yes	—
313	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
319	C₈×C₁₉	—	2	2	no	—
320	C₈×C₁₉	—	2	2	no	—
321	C₈×C₁₉	—	2	4	no	—
322	C₂²×AGL(1,ℤ/8)	C₂×C₁₉	1	1	yes	characteristic, complemented
323	C₂²×#135	C₂×C₁₉	1	1	yes	characteristic, complemented
324	C₂×#535	C₂×C₁₉	1	1	yes	characteristic, complemented
325	C₂×#417	C₂×C₁₉	1	1	yes	characteristic, complemented
326	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#2311	C₂×C₁₉	1	1	yes	characteristic, complemented
328	#2015	C₂×C₁₉	1	2	yes	complemented
329	#2014	C₂×C₁₉	1	2	yes	complemented
330	#2012	C₂×C₁₉	1	2	yes	complemented
331	#2011	C₂×C₁₉	1	2	yes	complemented
332	#1729	C₂×C₁₉	1	1	yes	characteristic, complemented
333	C₂²×C₁₉	—	2	2	no	—
334	C₂²×C₁₉	—	2	2	no	—
335	C₂²×C₁₉	—	2	4	no	—
336	C₂²×C₁₉	—	2	4	no	—
337	C₂²×C₁₉	—	4	2	no	—
338	C₂²×C₁₉	—	4	2	no	—
339	C₂²×C₁₉	—	4	4	no	—
340	C₂²×C₁₉	—	4	4	no	—
341	C₂²×C₁₉	—	4	8	no	—
342	C₂²×C₁₉	—	4	4	no	—
343	C₂²×C₁₉	—	8	16	no	—
344	C₂²×C₁₉	—	8	1	no	—
345	C₂²×C₁₉	—	8	1	no	—
346	C₂²×C₁₉	—	8	2	no	—
347	C₂²×C₁₉	—	8	1	no	—
348	C₂²×C₁₉	—	8	1	no	—
349	C₂²×C₁₉	—	8	2	no	—
350	C₂²×C₁₉	—	8	2	no	—
351	C₂²×C₁₉	—	8	2	no	—
352	C₂²×C₁₉	—	8	4	no	—
353	C₂²×C₁₉	#392	1	4	yes	—
354	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
355	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
356	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
357	C₂²×C₁₉	#576	1	2	yes	—
358	C₂²×C₁₉	#577	1	2	yes	—
359	C₄×C₁₉	—	4	2	no	—
360	C₄×C₁₉	—	4	2	no	—
361	C₄×C₁₉	—	4	4	no	—
362	C₄×C₁₉	—	8	2	no	—
363	C₄×C₁₉	#392	1	4	yes	—
364	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
365	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
366	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
367	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
368	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
369	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
370	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
371	C₂×AGL(1,ℤ/8)	—	2	4	no	—
372	C₂×AGL(1,ℤ/8)	—	2	4	no	—
373	C₂×AGL(1,ℤ/8)	—	2	4	no	—
374	C₂×#135	—	2	4	no	—
375	C₂×#135	—	2	4	no	—
376	C₂×#135	—	2	4	no	—
377	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
378	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
379	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
380	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
381	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
382	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
383	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
384	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
385	#535	—	2	4	no	—
386	#535	—	2	4	no	—
387	C₂×#127	C₂²×C₁₉	1	2	yes	—
388	C₂×#124	C₂²×C₁₉	1	2	yes	—
389	C₂×#121	—	2	2	no	—
390	C₂×#120	—	2	2	no	—
391	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
392	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
393	#417	—	2	4	no	—
394	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
395	C₂×#102	—	2	4	no	—
396	C₂×#102	C₂²×C₁₉	1	2	yes	—
397	C₂×#102	C₂²×C₁₉	1	2	yes	—
398	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
399	#391	C₂²×C₁₉	1	2	yes	complemented
400	#390	C₂²×C₁₉	1	2	yes	complemented
401	#386	—	2	2	no	—
402	#380	—	2	2	no	—
403	#336	C₂²×C₁₉	1	2	yes	complemented
404	#336	C₂²×C₁₉	1	2	yes	complemented
405	C₂×C₁₉	—	2	4	no	—
406	C₂×C₁₉	—	8	2	no	—
407	C₂×C₁₉	—	8	2	no	—
408	C₂×C₁₉	—	8	4	no	—
409	C₂×C₁₉	C₂×#392	1	1	yes	characteristic
410	C₂×C₁₉	#3012	1	2	yes	—
411	C₂×C₁₉	#3045	1	2	yes	—
412	C₂×C₁₉	#3154	1	1	yes	characteristic
413	C₂×C₁₉	#3155	1	1	yes	characteristic
414	C₂⁵	—	2	1	no	—
415	C₂×#41	—	2	2	no	—
416	C₂×#41	—	2	2	no	—
417	C₂×#41	—	2	2	no	—
418	C₂×#41	—	2	2	no	—
419	C₂×#41	—	2	2	no	—
420	C₂×#41	—	2	2	no	—
421	C₂×#41	—	2	2	no	—
422	C₂×#41	—	2	2	no	—
423	C₂×#41	—	2	2	no	—
424	C₂×#41	—	2	2	no	—
425	C₂×#41	D₄×C₁₉	1	4	yes	—
426	C₂×#41	D₄×C₁₉	1	4	yes	complemented
427	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
428	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
429	C₂²×D₄	—	2	1	no	—
430	C₂²×D₄	—	2	1	no	—
431	C₂²×D₄	—	2	2	no	—
432	C₂²×D₄	—	2	2	no	—
433	C₂²×D₄	—	2	2	no	—
434	C₂²×D₄	—	2	1	no	—
435	C₂²×D₄	—	2	2	no	—
436	C₂²×D₄	—	2	4	no	—
437	C₂²×D₄	—	2	2	no	—
438	C₂²×D₄	D₄×C₁₉	1	4	yes	—
439	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
440	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
441	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
442	C₂³×C₄	—	2	1	no	—
443	C₂³×C₄	—	2	1	no	—
444	C₂³×C₄	—	2	1	no	—
445	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
446	AGL(1,ℤ/8)	—	2	32	no	—
447	#135	—	2	32	no	—
448	C₂×Q₁₆	—	2	2	no	—
449	C₂×Q₁₆	—	2	2	no	—
450	C₂×Q₁₆	—	2	2	no	—
451	C₂×SD₁₆	—	2	4	no	—
452	C₂×SD₁₆	—	2	2	no	—
453	C₂×SD₁₆	—	2	2	no	—
454	C₂×SD₁₆	—	2	4	no	—
455	C₂×SD₁₆	—	2	2	no	—
456	C₂×SD₁₆	—	2	2	no	—
457	C₂×SD₁₆	—	2	4	no	—
458	C₂×SD₁₆	—	2	2	no	—
459	C₂×SD₁₆	—	2	2	no	—
460	C₂×D₈	—	2	4	no	—
461	C₂×D₈	—	2	4	no	—
462	C₂×D₈	—	2	2	no	—
463	C₂×D₈	—	2	2	no	—
464	C₂×D₈	—	2	4	no	—
465	C₂×D₈	—	2	2	no	—
466	C₂×M₁₆	—	2	2	no	—
467	C₂×M₁₆	—	2	2	no	—
468	C₂×M₁₆	D₄×C₁₉	1	4	yes	complemented
469	C₂²×C₈	—	2	2	no	—
470	C₂²×C₈	—	2	2	no	—
471	C₂²×C₈	D₄×C₁₉	1	4	yes	complemented
472	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
475	#127	—	2	4	no	—
476	#127	—	2	4	no	—
477	#124	—	2	4	no	—
478	#124	—	2	4	no	—
479	#121	—	2	16	no	—
480	#120	—	2	16	no	—
481	#117	—	2	2	no	—
482	#117	—	2	2	no	—
483	C₂×C₄⋊C₄	—	2	2	no	—
484	C₂×C₄⋊C₄	—	2	2	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
488	C₂×C₂²⋊C₄	—	2	4	no	—
489	C₂×C₂²⋊C₄	—	2	4	no	—
490	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
491	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
492	#103	—	2	4	no	—
493	#102	—	2	4	no	—
494	#102	—	2	4	no	—
495	#102	—	2	4	no	—
496	#95	—	2	4	no	—
497	C₁₉	#23426	1	1	yes	characteristic, direct product factor, Sylow
498	C₂⁴	—	2	1	no	—
499	C₂⁴	—	2	2	no	—
500	C₂⁴	—	2	1	no	—
501	C₂⁴	—	2	4	no	—
502	C₂⁴	—	4	2	no	—
503	C₂⁴	—	4	2	no	—
504	C₂⁴	—	8	2	no	—
505	C₂⁴	—	8	2	no	—
506	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
507	#41	—	2	8	no	—
508	#41	—	2	8	no	—
509	#41	—	2	8	no	—
510	#41	—	2	8	no	—
511	#41	—	4	4	no	—
512	#41	—	4	4	no	—
513	#41	—	4	4	no	—
514	#41	—	4	4	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
526	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	16	no	—
530	C₂×D₄	—	2	8	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	4	2	no	—
549	C₂×D₄	—	4	2	no	—
550	C₂×D₄	—	4	2	no	—
551	C₂×D₄	—	4	2	no	—
552	C₂×D₄	—	4	4	no	—
553	C₂×D₄	—	4	2	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	—	4	2	no	—
556	C₂×D₄	—	8	4	no	—
557	C₂×D₄	—	8	4	no	—
558	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
559	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
560	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	—	8	2	no	—
572	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
573	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
574	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
575	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
576	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
578	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
579	C₂²×C₄	#41×C₁₉	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
581	Q₁₆	—	2	8	no	—
582	SD₁₆	—	2	8	no	—
583	SD₁₆	—	2	8	no	—
584	SD₁₆	—	2	16	no	—
585	D₈	—	2	8	no	—
586	D₈	—	2	16	no	—
587	M₁₆	—	2	8	no	—
588	C₂×C₈	—	2	8	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	2	no	—
594	C₂×C₈	—	2	2	no	—
595	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
596	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
597	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	4	2	no	—
602	C₂²⋊C₄	—	2	16	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	8	4	no	—
605	C₄²	—	2	2	no	—
606	C₄²	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	4	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	4	8	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	2	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	2	no	—
619	C₂³	—	4	2	no	—
620	C₂³	—	4	2	no	—
621	C₂³	—	4	4	no	—
622	C₂³	—	4	2	no	—
623	C₂³	—	4	4	no	—
624	C₂³	—	4	2	no	—
625	C₂³	—	8	8	no	—
626	C₂³	—	8	8	no	—
627	C₂³	—	8	4	no	—
628	C₂³	—	8	4	no	—
629	C₂³	C₁₉×#120	1	2	yes	—
630	C₂³	C₁₉×#121	1	2	yes	—
631	C₂³	C₁₉×#127	1	2	yes	—
632	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
633	Q₈	—	2	2	no	—
634	Q₈	—	2	2	no	—
635	Q₈	—	2	2	no	—
636	Q₈	—	2	2	no	—
637	Q₈	—	4	1	no	—
638	Q₈	—	4	1	no	—
639	Q₈	—	4	1	no	—
640	Q₈	—	4	1	no	—
641	D₄	—	2	2	no	—
642	D₄	—	2	4	no	—
643	D₄	—	2	2	no	—
644	D₄	—	2	2	no	—
645	D₄	—	2	4	no	—
646	D₄	—	2	2	no	—
647	D₄	—	4	8	no	—
648	D₄	—	4	8	no	—
649	D₄	—	4	8	no	—
650	D₄	—	4	2	no	—
651	D₄	—	4	1	no	—
652	D₄	—	4	2	no	—
653	D₄	—	4	1	no	—
654	D₄	—	4	1	no	—
655	D₄	—	4	1	no	—
656	D₄	—	8	16	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	8	no	—
667	C₂×C₄	—	4	8	no	—
668	C₂×C₄	—	4	2	no	—
669	C₂×C₄	—	4	4	no	—
670	C₂×C₄	—	8	4	no	—
671	C₂×C₄	C₁₉×#120	1	2	yes	—
672	C₂×C₄	C₁₉×#120	1	4	yes	—
673	C₂×C₄	C₁₉×#120	1	4	yes	—
674	C₂×C₄	C₁₉×#121	1	2	yes	—
675	C₂×C₄	C₁₉×#121	1	4	yes	—
676	C₂×C₄	C₁₉×#121	1	4	yes	—
677	C₂×C₄	C₁₉×#127	1	2	yes	—
678	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
679	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
680	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
681	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
682	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
683	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
684	C₈	—	2	2	no	—
685	C₈	—	2	2	no	—
686	C₈	—	2	4	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	4	4	no	—
692	C₂²	—	4	8	no	—
693	C₂²	—	4	4	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	4	no	—
697	C₂²	—	8	16	no	—
698	C₂²	—	8	2	no	—
699	C₂²	—	8	4	no	—
700	C₂²	—	8	2	no	—
701	C₂²	—	8	2	no	—
702	C₂²	—	8	1	no	—
703	C₂²	—	8	1	no	—
704	C₂²	—	8	2	no	—
705	C₂²	—	8	1	no	—
706	C₂²	—	8	1	no	—
707	C₂²	C₁₉×#392	1	4	yes	—
708	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
709	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
710	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
711	C₂²	C₁₉×#576	1	2	yes	—
712	C₂²	C₁₉×#577	1	2	yes	—
713	C₄	—	4	4	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	8	2	no	—
717	C₄	C₁₉×#392	1	4	yes	—
718	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
719	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
720	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
721	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
722	C₂	—	2	4	no	—
723	C₂	—	8	4	no	—
724	C₂	—	8	2	no	—
725	C₂	—	8	2	no	—
726	C₂	C₂×C₁₉×#392	1	1	yes	characteristic
727	C₂	C₁₉×#3012	1	2	yes	—
728	C₂	C₁₉×#3045	1	2	yes	—
729	C₂	C₁₉×#3154	1	1	yes	characteristic
730	C₂	C₁₉×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
2. C₂²×C₁₉×#135	C₂	semidirect
3. C₂×C₁₉×#535	C₂	semidirect
4. C₂×C₁₉×#417	C₂	semidirect
5. C₂²×C₁₉×#102	C₂	semidirect
6. C₁₉×#2311	C₂	semidirect
7. C₁₉×#2015	C₂	semidirect
8. C₁₉×#2014	C₂	semidirect
9. C₁₉×#2012	C₂	semidirect
10. C₁₉×#2011	C₂	semidirect
11. C₁₉×#1729	C₂	semidirect
21. C₂²×Q₁₆×C₁₉	C₂²	semidirect
23. C₂²×SD₁₆×C₁₉	C₂²	semidirect
24. C₂²×SD₁₆×C₁₉	C₂²	semidirect
26. C₂²×D₈×C₁₉	C₂²	semidirect
38. C₂×C₁₉×#103	C₂²	semidirect
42. C₂×C₁₉×#102	C₂²	semidirect
43. C₁₉×#391	C₂²	semidirect
44. C₁₉×#390	C₂²	semidirect
47. C₁₉×#336	C₂²	semidirect
48. C₁₉×#336	C₂²	semidirect
61. C₂×#41×C₁₉	D₄	semidirect
103. C₂×M₁₆×C₁₉	D₄	semidirect
106. C₂²×C₈×C₁₉	D₄	semidirect
241. #23426	C₁₉	direct (N × H)
322. C₂²×AGL(1,ℤ/8)	C₂×C₁₉	semidirect
323. C₂²×#135	C₂×C₁₉	semidirect
324. C₂×#535	C₂×C₁₉	semidirect
325. C₂×#417	C₂×C₁₉	semidirect
326. C₂²×#102	C₂×C₁₉	semidirect
327. #2311	C₂×C₁₉	semidirect
328. #2015	C₂×C₁₉	semidirect
329. #2014	C₂×C₁₉	semidirect
330. #2012	C₂×C₁₉	semidirect
331. #2011	C₂×C₁₉	semidirect
332. #1729	C₂×C₁₉	semidirect
377. C₂²×Q₁₆	C₂²×C₁₉	semidirect
379. C₂²×SD₁₆	C₂²×C₁₉	semidirect
380. C₂²×SD₁₆	C₂²×C₁₉	semidirect
382. C₂²×D₈	C₂²×C₁₉	semidirect
394. C₂×#103	C₂²×C₁₉	semidirect
398. C₂×#102	C₂²×C₁₉	semidirect
399. #391	C₂²×C₁₉	semidirect
400. #390	C₂²×C₁₉	semidirect
403. #336	C₂²×C₁₉	semidirect
404. #336	C₂²×C₁₉	semidirect
426. C₂×#41	D₄×C₁₉	semidirect
468. C₂×M₁₆	D₄×C₁₉	semidirect
471. C₂²×C₈	D₄×C₁₉	semidirect
497. C₁₉	#23426	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×AGL(1,ℤ/8)	2
C₂²×C₁₉×#135	2
C₂×C₁₉×#535	2
C₂×C₁₉×#417	2
C₂²×C₁₉×#102	2
C₁₉×#2311	2
C₁₉×#2015	2
C₁₉×#2014	2
C₁₉×#2012	2
C₁₉×#2011	2
C₁₉×#1729	2
#23426	19

Subgroups — C19×#23426 #18029385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23426 #18029385