Subgroups — C₁₉×#13382 #18019341

Order 4864.

446 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#367	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#358	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#358	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1808	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1380	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
11	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#467	—	2	2	no	—
14	C₁₉×#467	—	2	2	no	—
15	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#103	—	2	1	no	—
19	C₁₉×#380	—	2	1	no	—
20	C₁₉×#367	—	2	2	no	—
21	C₁₉×#358	—	2	2	no	—
22	C₁₉×#358	—	2	2	no	—
23	C₁₉×C₂²⋊C₁₆	—	2	2	no	—
24	C₁₉×#340	—	2	1	no	—
25	C₂²×Q₈×C₁₉	—	2	1	no	—
26	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂×Q₁₆×C₁₉	—	2	1	no	—
28	C₂×Q₁₆×C₁₉	—	2	1	no	—
29	C₂×Q₁₆×C₁₉	—	2	1	no	—
30	C₂×Q₁₆×C₁₉	—	2	1	no	—
31	C₂×Q₁₆×C₁₉	—	2	1	no	—
32	C₂×Q₁₆×C₁₉	D₄	1	2	yes	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
41	C₁₉×C₂²⋊Q₈	—	2	4	no	—
42	C₁₉×C₂²⋊Q₈	—	4	2	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
49	C₂×C₁₆×C₁₉	—	2	1	no	—
50	C₂×C₁₆×C₁₉	—	2	1	no	—
51	C₂×C₁₆×C₁₉	—	2	1	no	—
52	C₂×C₁₆×C₁₉	—	2	1	no	—
53	C₂×C₁₆×C₁₉	—	2	1	no	—
54	C₂×C₁₆×C₁₉	D₄	1	2	yes	—
55	C₁₉×#107	—	2	1	no	—
56	C₁₉×#107	—	2	1	no	—
57	C₁₉×#107	—	2	1	no	—
58	C₁₉×#107	—	2	1	no	—
59	C₁₉×#107	—	2	1	no	—
60	C₁₉×#107	D₄	1	2	yes	—
61	C₁₉×#103	—	2	4	no	—
62	C₁₉×#95	—	4	1	no	—
63	C₂⁴×C₁₉	D₈	1	1	yes	characteristic
64	C₂×Q₈×C₁₉	—	2	2	no	—
65	C₂×Q₈×C₁₉	—	4	1	no	—
66	C₂×Q₈×C₁₉	—	4	1	no	—
67	C₂×Q₈×C₁₉	—	4	1	no	—
68	C₂×Q₈×C₁₉	—	4	1	no	—
69	C₂×Q₈×C₁₉	—	4	1	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	1	no	—
80	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	Q₁₆×C₁₉	—	2	2	no	—
83	Q₁₆×C₁₉	—	2	2	no	—
84	Q₁₆×C₁₉	—	4	1	no	—
85	Q₁₆×C₁₉	—	4	1	no	—
86	C₂×C₈×C₁₉	—	2	1	no	—
87	C₂×C₈×C₁₉	—	2	1	no	—
88	C₂×C₈×C₁₉	—	2	1	no	—
89	C₂×C₈×C₁₉	—	4	1	no	—
90	C₂×C₈×C₁₉	—	4	1	no	—
91	C₂×C₈×C₁₉	—	4	1	no	—
92	C₂×C₈×C₁₉	—	4	1	no	—
93	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
97	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
98	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
99	C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₄⋊C₄×C₁₉	—	4	4	no	—
101	C₄⋊C₄×C₁₉	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	4	1	no	—
103	C₄⋊C₄×C₁₉	—	4	1	no	—
104	C₄⋊C₄×C₁₉	—	4	1	no	—
105	C₄⋊C₄×C₁₉	—	4	1	no	—
106	C₂²⋊C₄×C₁₉	—	4	4	no	—
107	C₂²⋊C₄×C₁₉	—	8	2	no	—
108	C₁₆×C₁₉	—	2	2	no	—
109	C₁₆×C₁₉	—	4	1	no	—
110	#13382	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂³×C₁₉	—	2	1	no	—
112	C₂³×C₁₉	—	2	1	no	—
113	C₂³×C₁₉	—	2	1	no	—
114	C₂³×C₁₉	—	2	1	no	—
115	C₂³×C₁₉	—	2	1	no	—
116	C₂³×C₁₉	—	2	1	no	—
117	C₂³×C₁₉	SD₃₂	1	2	yes	—
118	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
119	Q₈×C₁₉	—	4	2	no	—
120	Q₈×C₁₉	—	4	2	no	—
121	Q₈×C₁₉	—	8	1	no	—
122	Q₈×C₁₉	—	8	1	no	—
123	C₂×C₄×C₁₉	—	2	1	no	—
124	C₂×C₄×C₁₉	—	2	1	no	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	4	1	no	—
127	C₂×C₄×C₁₉	—	4	1	no	—
128	C₂×C₄×C₁₉	—	4	1	no	—
129	C₂×C₄×C₁₉	—	4	1	no	—
130	C₂×C₄×C₁₉	—	4	2	no	—
131	C₂×C₄×C₁₉	—	4	2	no	—
132	C₂×C₄×C₁₉	—	8	1	no	—
133	C₂×C₄×C₁₉	—	8	1	no	—
134	C₂×C₄×C₁₉	—	8	1	no	—
135	C₂×C₄×C₁₉	—	8	1	no	—
136	C₂×C₄×C₁₉	—	8	1	no	—
137	C₂×C₄×C₁₉	—	8	1	no	—
138	C₂×C₄×C₁₉	—	8	1	no	—
139	C₂×C₄×C₁₉	—	8	1	no	—
140	C₂×C₄×C₁₉	—	8	1	no	—
141	C₂×C₄×C₁₉	—	8	1	no	—
142	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
146	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
148	C₈×C₁₉	—	4	1	no	—
149	C₈×C₁₉	#121	1	1	yes	characteristic
150	C₈×C₁₉	#121	1	1	yes	characteristic
151	C₈×C₁₉	#123	1	1	yes	characteristic
152	C₈×C₁₉	#124	1	1	yes	characteristic
153	C₂×#467	C₂×C₁₉	1	1	yes	characteristic
154	C₂×#367	C₂×C₁₉	1	1	yes	characteristic, complemented
155	C₂×#358	C₂×C₁₉	1	1	yes	characteristic, complemented
156	C₂×#358	C₂×C₁₉	1	1	yes	characteristic, complemented
157	C₂×C₂²⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic
158	#1808	C₂×C₁₉	1	1	yes	characteristic
159	#1380	C₂×C₁₉	1	1	yes	characteristic, complemented
160	C₂²×C₁₉	—	2	2	no	—
161	C₂²×C₁₉	—	2	2	no	—
162	C₂²×C₁₉	—	2	2	no	—
163	C₂²×C₁₉	—	4	1	no	—
164	C₂²×C₁₉	—	4	1	no	—
165	C₂²×C₁₉	—	4	1	no	—
166	C₂²×C₁₉	—	4	1	no	—
167	C₂²×C₁₉	#447	1	1	yes	characteristic
168	C₂²×C₁₉	#466	1	1	yes	characteristic
169	C₂²×C₁₉	#480	1	1	yes	characteristic
170	C₂²×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
171	C₂²×C₁₉	#508	1	1	yes	characteristic
172	C₂²×C₁₉	#510	1	1	yes	characteristic
173	C₂²×C₁₉	#510	1	1	yes	characteristic
174	C₄×C₁₉	—	4	1	no	—
175	C₄×C₁₉	—	8	2	no	—
176	C₄×C₁₉	—	8	2	no	—
177	C₄×C₁₉	—	16	1	no	—
178	C₄×C₁₉	—	16	1	no	—
179	C₄×C₁₉	#394	1	1	yes	characteristic
180	C₄×C₁₉	#452	1	1	yes	characteristic
181	C₄×C₁₉	#468	1	1	yes	characteristic
182	C₄×C₁₉	#482	1	1	yes	characteristic
183	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
184	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
185	C₂×C₂²⋊Q₈	—	2	1	no	—
186	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
187	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
188	#467	—	2	2	no	—
189	#467	—	2	2	no	—
190	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
191	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
192	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
193	C₂×#103	—	2	1	no	—
194	#380	—	2	1	no	—
195	#367	—	2	2	no	—
196	#358	—	2	2	no	—
197	#358	—	2	2	no	—
198	C₂²⋊C₁₆	—	2	2	no	—
199	#340	—	2	1	no	—
200	C₂×C₁₉	—	4	2	no	—
201	C₂×C₁₉	#2033	1	1	yes	characteristic
202	C₂×C₁₉	#2185	1	1	yes	characteristic
203	C₂×C₁₉	#2189	1	1	yes	characteristic
204	C₂×C₁₉	#2217	1	1	yes	characteristic
205	C₂×C₁₉	#2219	1	1	yes	characteristic
206	C₂×C₁₉	#2235	1	1	yes	characteristic
207	C₂×C₁₉	#2237	1	1	yes	characteristic
208	C₂²×Q₈	—	2	1	no	—
209	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
210	C₂×Q₁₆	—	2	1	no	—
211	C₂×Q₁₆	—	2	1	no	—
212	C₂×Q₁₆	—	2	1	no	—
213	C₂×Q₁₆	—	2	1	no	—
214	C₂×Q₁₆	—	2	1	no	—
215	C₂×Q₁₆	D₄×C₁₉	1	2	yes	—
216	C₂²×C₈	—	2	1	no	—
217	C₂²×C₈	—	2	1	no	—
218	C₂²×C₈	—	2	1	no	—
219	C₂²×C₈	—	2	1	no	—
220	C₂²×C₈	—	2	1	no	—
221	C₂²×C₈	—	2	1	no	—
222	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
224	C₂²⋊Q₈	—	2	4	no	—
225	C₂²⋊Q₈	—	4	2	no	—
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₄⋊C₄	—	2	1	no	—
228	C₂×C₄⋊C₄	—	2	1	no	—
229	C₂×C₄⋊C₄	—	4	1	no	—
230	C₂×C₂²⋊C₄	—	4	1	no	—
231	C₂×C₂²⋊C₄	—	4	1	no	—
232	C₂×C₁₆	—	2	1	no	—
233	C₂×C₁₆	—	2	1	no	—
234	C₂×C₁₆	—	2	1	no	—
235	C₂×C₁₆	—	2	1	no	—
236	C₂×C₁₆	—	2	1	no	—
237	C₂×C₁₆	D₄×C₁₉	1	2	yes	—
238	#107	—	2	1	no	—
239	#107	—	2	1	no	—
240	#107	—	2	1	no	—
241	#107	—	2	1	no	—
242	#107	—	2	1	no	—
243	#107	D₄×C₁₉	1	2	yes	—
244	#103	—	2	4	no	—
245	#95	—	4	1	no	—
246	C₁₉	#13382	1	1	yes	characteristic, direct product factor, Sylow
247	C₂⁴	D₈×C₁₉	1	1	yes	characteristic
248	C₂×Q₈	—	2	2	no	—
249	C₂×Q₈	—	4	1	no	—
250	C₂×Q₈	—	4	1	no	—
251	C₂×Q₈	—	4	1	no	—
252	C₂×Q₈	—	4	1	no	—
253	C₂×Q₈	—	4	1	no	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	1	no	—
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	4	1	no	—
261	C₂²×C₄	—	4	1	no	—
262	C₂²×C₄	—	4	1	no	—
263	C₂²×C₄	—	4	1	no	—
264	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
266	Q₁₆	—	2	2	no	—
267	Q₁₆	—	2	2	no	—
268	Q₁₆	—	4	1	no	—
269	Q₁₆	—	4	1	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	2	1	no	—
272	C₂×C₈	—	2	1	no	—
273	C₂×C₈	—	4	1	no	—
274	C₂×C₈	—	4	1	no	—
275	C₂×C₈	—	4	1	no	—
276	C₂×C₈	—	4	1	no	—
277	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
278	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
279	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
280	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
281	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
282	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	4	4	no	—
285	C₄⋊C₄	—	4	1	no	—
286	C₄⋊C₄	—	4	1	no	—
287	C₄⋊C₄	—	4	1	no	—
288	C₄⋊C₄	—	4	1	no	—
289	C₄⋊C₄	—	4	1	no	—
290	C₂²⋊C₄	—	4	4	no	—
291	C₂²⋊C₄	—	8	2	no	—
292	C₁₆	—	2	2	no	—
293	C₁₆	—	4	1	no	—
294	C₂³	—	2	1	no	—
295	C₂³	—	2	1	no	—
296	C₂³	—	2	1	no	—
297	C₂³	—	2	1	no	—
298	C₂³	—	2	1	no	—
299	C₂³	—	2	1	no	—
300	C₂³	C₁₉×SD₃₂	1	2	yes	—
301	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
302	Q₈	—	4	2	no	—
303	Q₈	—	4	2	no	—
304	Q₈	—	8	1	no	—
305	Q₈	—	8	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	4	1	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	8	1	no	—
316	C₂×C₄	—	8	1	no	—
317	C₂×C₄	—	8	1	no	—
318	C₂×C₄	—	8	1	no	—
319	C₂×C₄	—	8	1	no	—
320	C₂×C₄	—	8	1	no	—
321	C₂×C₄	—	8	1	no	—
322	C₂×C₄	—	8	1	no	—
323	C₂×C₄	—	8	1	no	—
324	C₂×C₄	—	8	1	no	—
325	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
326	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
327	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
328	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
329	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
330	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
331	C₈	—	4	1	no	—
332	C₈	C₁₉×#121	1	1	yes	characteristic
333	C₈	C₁₉×#121	1	1	yes	characteristic
334	C₈	C₁₉×#123	1	1	yes	characteristic
335	C₈	C₁₉×#124	1	1	yes	characteristic
336	C₂²	—	2	2	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	4	1	no	—
340	C₂²	—	4	1	no	—
341	C₂²	—	4	1	no	—
342	C₂²	—	4	1	no	—
343	C₂²	C₁₉×#447	1	1	yes	characteristic
344	C₂²	C₁₉×#466	1	1	yes	characteristic
345	C₂²	C₁₉×#480	1	1	yes	characteristic
346	C₂²	C₂×C₁₉×SD₃₂	1	1	yes	characteristic
347	C₂²	C₁₉×#508	1	1	yes	characteristic
348	C₂²	C₁₉×#510	1	1	yes	characteristic
349	C₂²	C₁₉×#510	1	1	yes	characteristic
350	C₄	—	4	1	no	—
351	C₄	—	8	2	no	—
352	C₄	—	8	2	no	—
353	C₄	—	16	1	no	—
354	C₄	—	16	1	no	—
355	C₄	C₁₉×#394	1	1	yes	characteristic
356	C₄	C₁₉×#452	1	1	yes	characteristic
357	C₄	C₁₉×#468	1	1	yes	characteristic
358	C₄	C₁₉×#482	1	1	yes	characteristic
359	C₂	—	4	2	no	—
360	C₂	C₁₉×#2033	1	1	yes	characteristic
361	C₂	C₁₉×#2185	1	1	yes	characteristic
362	C₂	C₁₉×#2189	1	1	yes	characteristic
363	C₂	C₁₉×#2217	1	1	yes	characteristic
364	C₂	C₁₉×#2219	1	1	yes	characteristic
365	C₂	C₁₉×#2235	1	1	yes	characteristic
366	C₂	C₁₉×#2237	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	D₈
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ C₂³×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#367	C₂	semidirect
3. C₂×C₁₉×#358	C₂	semidirect
4. C₂×C₁₉×#358	C₂	semidirect
7. C₁₉×#1380	C₂	semidirect
110. #13382	C₁₉	direct (N × H)
154. C₂×#367	C₂×C₁₉	semidirect
155. C₂×#358	C₂×C₁₉	semidirect
156. C₂×#358	C₂×C₁₉	semidirect
159. #1380	C₂×C₁₉	semidirect
246. C₁₉	#13382	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×#467	2
C₂×C₁₉×#367	2
C₂×C₁₉×#358	2
C₂×C₁₉×C₂²⋊C₁₆	2
C₁₉×#1808	2
C₁₉×#1380	2
#13382	19

Subgroups — C19×#13382 #18019341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13382 #18019341