Subgroups — #18082056

Order 4864.

522 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564621	C₂	1	2	yes	maximal
2	#14563664	C₂	1	1	yes	maximal, characteristic
3	C₈×C₂²⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic
4	#14562207	C₂	1	2	yes	maximal
5	C₂×C₁₉×#467	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597275	—	2	1	no	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
8	C₂×C₈×Dic₁₉	—	2	1	no	—
9	#11926404	C₂²	1	2	yes	—
10	C₄×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	#11926311	—	2	4	no	—
12	#11926307	—	2	1	no	—
13	#11926298	—	2	1	no	—
14	#11926281	—	2	4	no	—
15	C₂²×Q₁₆×C₁₉	C₄	1	1	yes	characteristic, complemented
16	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₁₉×#467	—	2	1	no	—
19	C₁₉×#467	—	2	1	no	—
20	C₁₉×#467	—	2	1	no	—
21	C₁₉×#467	—	2	1	no	—
22	C₂×C₁₉×#107	C₄	1	1	yes	characteristic, complemented
23	C₂×C₁₉×#103	C₄	1	2	yes	complemented
24	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×Q₁₆×C₁₉	—	2	1	no	—
27	C₂×Q₁₆×C₁₉	—	2	1	no	—
28	C₂×Q₁₆×C₁₉	—	4	2	no	—
29	C₂²×C₈×C₁₉	—	4	2	no	—
30	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
36	C₁₉×C₂²⋊Q₈	—	2	2	no	—
37	C₁₉×C₂²⋊Q₈	—	2	2	no	—
38	C₁₉×C₂²⋊Q₈	—	2	2	no	—
39	C₁₉×C₂²⋊Q₈	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
44	C₂×C₂²⋊Dic₁₉	D₄	1	2	yes	—
45	C₂×C₄⋊Dic₁₉	—	2	2	no	—
46	C₂×C₄×Dic₁₉	—	2	1	no	—
47	C₂²×C₁₉⋊C₈	—	2	1	no	—
48	C₁₉×#107	—	2	1	no	—
49	C₁₉×#107	—	2	1	no	—
50	C₁₉×#103	—	2	2	no	—
51	C₁₉×#103	—	2	2	no	—
52	C₁₉⋊#95	—	2	1	no	—
53	C₁₉⋊#95	—	2	2	no	—
54	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
55	C₂²⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
56	#10597275	—	4	2	no	—
57	C₈×Dic₁₉	—	4	2	no	—
58	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂×Q₈×C₁₉	—	2	2	no	—
60	C₂×Q₈×C₁₉	—	2	2	no	—
61	C₂×Q₈×C₁₉	—	4	2	no	—
62	C₂×Q₈×C₁₉	—	4	2	no	—
63	C₂²×C₄×C₁₉	—	2	2	no	—
64	C₂²×C₄×C₁₉	—	2	2	no	—
65	C₂²×C₄×C₁₉	—	4	1	no	—
66	C₂²×C₄×C₁₉	—	4	1	no	—
67	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
73	C₂²×Dic₁₉	—	2	2	no	—
74	C₂²×Dic₁₉	—	4	2	no	—
75	Q₁₆×C₁₉	—	4	2	no	—
76	Q₁₆×C₁₉	—	4	2	no	—
77	C₂×C₈×C₁₉	—	2	2	no	—
78	C₂×C₈×C₁₉	—	2	2	no	—
79	C₂×C₈×C₁₉	—	2	2	no	—
80	C₂×C₈×C₁₉	—	4	1	no	—
81	C₂×C₈×C₁₉	—	4	1	no	—
82	C₂×C₈×C₁₉	—	4	1	no	—
83	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₄⋊C₄×C₁₉	—	2	2	no	—
88	C₄⋊C₄×C₁₉	—	2	2	no	—
89	C₄⋊C₄×C₁₉	—	4	2	no	—
90	C₄⋊C₄×C₁₉	—	4	2	no	—
91	C₂²⋊C₄×C₁₉	—	4	2	no	—
92	C₂²⋊C₄×C₁₉	—	4	2	no	—
93	C₂²⋊Dic₁₉	—	2	2	no	—
94	C₂²⋊Dic₁₉	—	4	4	no	—
95	C₂²⋊Dic₁₉	Q₁₆	1	4	yes	complemented
96	C₄⋊Dic₁₉	—	4	2	no	—
97	C₄⋊Dic₁₉	—	4	2	no	—
98	C₄×Dic₁₉	—	4	1	no	—
99	C₄×Dic₁₉	—	4	1	no	—
100	C₂×C₁₉⋊C₈	—	2	2	no	—
101	C₂×C₁₉⋊C₈	—	4	1	no	—
102	C₂×C₁₉⋊C₈	—	4	1	no	—
103	#9782	—	19	1	no	maximal, Sylow
104	C₂³×C₁₉	—	4	1	no	—
105	C₂³×C₁₉	—	4	1	no	—
106	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
107	C₂³×C₁₉	#121	1	1	yes	characteristic
108	C₂³×C₁₉	#127	1	1	yes	characteristic
109	C₂³×C₁₉	C₂×Q₁₆	1	2	yes	—
110	C₂³×C₁₉	#135	1	2	yes	—
111	Q₈×C₁₉	—	4	2	no	—
112	Q₈×C₁₉	—	4	2	no	—
113	Q₈×C₁₉	—	8	2	no	—
114	C₂×C₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	—	2	1	no	—
116	C₂×C₄×C₁₉	—	2	1	no	—
117	C₂×C₄×C₁₉	—	2	1	no	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	2	1	no	—
120	C₂×C₄×C₁₉	—	4	1	no	—
121	C₂×C₄×C₁₉	—	4	1	no	—
122	C₂×C₄×C₁₉	—	4	1	no	—
123	C₂×C₄×C₁₉	—	4	2	no	—
124	C₂×C₄×C₁₉	—	4	2	no	—
125	C₂×C₄×C₁₉	—	8	2	no	—
126	C₂×C₄×C₁₉	—	8	2	no	—
127	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
129	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
130	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
131	C₂×Dic₁₉	—	2	4	no	—
132	C₂×Dic₁₉	—	4	2	no	—
133	C₂×Dic₁₉	—	4	2	no	—
134	C₂×Dic₁₉	—	8	2	no	—
135	C₂×Dic₁₉	—	8	2	no	—
136	C₂×Dic₁₉	—	8	2	no	—
137	C₈×C₁₉	—	2	1	no	—
138	C₈×C₁₉	—	2	1	no	—
139	C₈×C₁₉	—	2	1	no	—
140	C₈×C₁₉	#99	1	2	yes	—
141	C₁₉⋊C₈	—	4	2	no	—
142	C₂×#467	D₁₉	1	1	yes	characteristic
143	#1996	—	19	2	no	—
144	#1808	—	19	1	no	—
145	C₈×C₂²⋊C₄	—	19	1	no	—
146	#1520	—	19	2	no	—
147	C₂²×C₁₉	—	2	1	no	—
148	C₂²×C₁₉	—	2	1	no	—
149	C₂²×C₁₉	—	2	1	no	—
150	C₂²×C₁₉	—	2	1	no	—
151	C₂²×C₁₉	—	2	1	no	—
152	C₂²×C₁₉	—	2	1	no	—
153	C₂²×C₁₉	—	4	2	no	—
154	C₂²×C₁₉	—	4	2	no	—
155	C₂²×C₁₉	#390	1	1	yes	characteristic
156	C₂²×C₁₉	C₄×Q₁₆	1	2	yes	—
157	C₂²×C₁₉	#467	1	2	yes	—
158	C₂²×C₁₉	#494	1	1	yes	characteristic
159	C₂²×C₁₉	#495	1	1	yes	characteristic
160	C₄×C₁₉	—	2	1	no	—
161	C₄×C₁₉	—	2	1	no	—
162	C₄×C₁₉	—	2	1	no	—
163	C₄×C₁₉	—	8	2	no	—
164	C₄×C₁₉	—	8	2	no	—
165	C₄×C₁₉	C₂×#99	1	1	yes	characteristic
166	C₄×C₁₉	#410	1	1	yes	characteristic
167	Dic₁₉	—	4	4	no	—
168	Dic₁₉	—	16	2	no	—
169	C₂²×Q₁₆	Dic₁₉	1	1	yes	characteristic, complemented
170	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
171	C₂×C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
172	#467	—	2	1	no	—
173	#467	—	2	1	no	—
174	#467	—	2	1	no	—
175	#467	—	2	1	no	—
176	C₂×#107	—	38	1	no	—
177	C₂×#107	Dic₁₉	1	1	yes	characteristic, complemented
178	C₂×#103	Dic₁₉	1	2	yes	complemented
179	C₂×C₂²⋊C₈	—	19	1	no	—
180	C₂×C₄×C₈	—	38	1	no	—
181	#380	—	19	2	no	—
182	C₄×C₂²⋊C₄	—	19	1	no	—
183	#342	—	38	4	no	—
184	#340	—	38	1	no	—
185	#336	—	38	1	no	—
186	#328	—	38	4	no	—
187	C₂×C₁₉	—	2	2	no	—
188	C₂×C₁₉	—	2	1	no	—
189	C₂×C₁₉	—	2	2	no	—
190	C₂×C₁₉	—	2	1	no	—
191	C₂×C₁₉	#1964	1	1	yes	characteristic
192	C₂×C₁₉	#1969	1	1	yes	characteristic
193	C₂×C₁₉	#1976	1	1	yes	characteristic
194	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
195	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
196	C₂×Q₁₆	—	2	1	no	—
197	C₂×Q₁₆	—	2	1	no	—
198	C₂×Q₁₆	—	4	2	no	—
199	C₂²×C₈	—	4	2	no	—
200	C₂²×C₈	—	38	1	no	—
201	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
202	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
203	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
204	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
205	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
206	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	—	2	2	no	—
210	C₂²⋊Q₈	—	2	2	no	—
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	—	38	2	no	—
213	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
214	C₂×C₂²⋊C₄	—	2	2	no	—
215	C₂×C₂²⋊C₄	—	19	2	no	—
216	C₂×C₂²⋊C₄	—	38	2	no	—
217	C₂×C₄²	—	38	1	no	—
218	#107	—	2	1	no	—
219	#107	—	2	1	no	—
220	#107	—	76	2	no	—
221	#103	—	2	2	no	—
222	#103	—	2	2	no	—
223	C₂²⋊C₈	—	19	2	no	—
224	C₂²⋊C₈	—	38	1	no	—
225	C₄×C₈	—	76	2	no	—
226	#95	—	38	1	no	—
227	#95	—	38	2	no	—
228	C₁₉	#9782	1	1	yes	characteristic, complemented, Sylow
229	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
230	C₂×Q₈	—	2	2	no	—
231	C₂×Q₈	—	2	2	no	—
232	C₂×Q₈	—	4	2	no	—
233	C₂×Q₈	—	4	2	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	—	4	1	no	—
237	C₂²×C₄	—	4	1	no	—
238	C₂²×C₄	—	38	2	no	—
239	C₂²×C₄	—	76	2	no	—
240	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
241	C₂²×C₄	#64543	1	1	yes	characteristic
242	C₂²×C₄	#64543	1	1	yes	characteristic
243	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
244	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
245	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
246	Q₁₆	—	4	2	no	—
247	Q₁₆	—	4	2	no	—
248	C₂×C₈	—	2	2	no	—
249	C₂×C₈	—	2	2	no	—
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	—	4	1	no	—
252	C₂×C₈	—	4	1	no	—
253	C₂×C₈	—	4	1	no	—
254	C₂×C₈	—	38	2	no	—
255	C₂×C₈	—	76	1	no	—
256	C₂×C₈	—	76	1	no	—
257	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
258	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
259	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
260	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
261	C₄⋊C₄	—	2	2	no	—
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	4	2	no	—
264	C₄⋊C₄	—	4	2	no	—
265	C₄⋊C₄	—	76	2	no	—
266	C₄⋊C₄	—	76	2	no	—
267	C₂²⋊C₄	—	4	2	no	—
268	C₂²⋊C₄	—	4	2	no	—
269	C₂²⋊C₄	—	19	4	no	—
270	C₂²⋊C₄	—	38	2	no	—
271	C₂²⋊C₄	—	76	4	no	—
272	C₄²	—	76	1	no	—
273	C₄²	—	76	1	no	—
274	C₂³	—	4	1	no	—
275	C₂³	—	4	1	no	—
276	C₂³	Q₁₆×D₁₉	1	2	yes	—
277	C₂³	#10597365	1	2	yes	—
278	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
279	C₂³	#10597384	1	1	yes	characteristic
280	C₂³	#10597386	1	1	yes	characteristic
281	Q₈	—	4	2	no	—
282	Q₈	—	4	2	no	—
283	Q₈	—	8	2	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	4	1	no	—
291	C₂×C₄	—	4	1	no	—
292	C₂×C₄	—	4	1	no	—
293	C₂×C₄	—	4	2	no	—
294	C₂×C₄	—	4	2	no	—
295	C₂×C₄	—	8	2	no	—
296	C₂×C₄	—	8	2	no	—
297	C₂×C₄	—	38	4	no	—
298	C₂×C₄	—	76	2	no	—
299	C₂×C₄	—	76	2	no	—
300	C₂×C₄	—	152	2	no	—
301	C₂×C₄	—	152	2	no	—
302	C₂×C₄	—	152	2	no	—
303	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
304	C₂×C₄	#10597382	1	1	yes	characteristic
305	C₂×C₄	#10597384	1	1	yes	characteristic
306	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
307	C₈	—	2	1	no	—
308	C₈	—	2	1	no	—
309	C₈	—	2	1	no	—
310	C₈	—	76	2	no	—
311	C₈	#10597291	1	2	yes	—
312	C₂²	—	2	1	no	—
313	C₂²	—	2	1	no	—
314	C₂²	—	2	1	no	—
315	C₂²	—	2	1	no	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	1	no	—
318	C₂²	—	4	2	no	—
319	C₂²	—	4	2	no	—
320	C₂²	#11926447	1	1	yes	characteristic
321	C₂²	Q₁₆×Dic₁₉	1	2	yes	—
322	C₂²	#11926782	1	2	yes	—
323	C₂²	#11926922	1	1	yes	characteristic
324	C₂²	#11926929	1	1	yes	characteristic
325	C₄	—	2	1	no	—
326	C₄	—	2	1	no	—
327	C₄	—	2	1	no	—
328	C₄	—	8	2	no	—
329	C₄	—	8	2	no	—
330	C₄	—	304	2	no	—
331	C₄	—	76	4	no	—
332	C₄	C₂×#10597291	1	1	yes	characteristic
333	C₄	#11926518	1	1	yes	characteristic
334	C₂	—	2	1	no	—
335	C₂	—	2	2	no	—
336	C₂	—	2	2	no	—
337	C₂	—	2	1	no	—
338	C₂	#14564472	1	1	yes	characteristic
339	C₂	#14564497	1	1	yes	characteristic
340	C₂	#14564534	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926447
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#467	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#467	D₁₉
hypocenter	C₁₉	#9782
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#467

Complements

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

N	H ≅ G/N	type
15. C₂²×Q₁₆×C₁₉	C₄	semidirect
22. C₂×C₁₉×#107	C₄	semidirect
23. C₂×C₁₉×#103	C₄	semidirect
95. C₂²⋊Dic₁₉	Q₁₆	semidirect
169. C₂²×Q₁₆	Dic₁₉	semidirect
177. C₂×#107	Dic₁₉	semidirect
178. C₂×#103	Dic₁₉	semidirect
228. C₁₉	#9782	semidirect

Maximal subgroups

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

subgroup	index
#14564621	2
#14563664	2
C₈×C₂²⋊Dic₁₉	2
#14562207	2
C₂×C₁₉×#467	2
#9782	19