Subgroups — #18075945

Order 4864.

482 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563397	C₂	1	1	yes	maximal, characteristic
2	#14563397	C₂	1	1	yes	maximal, characteristic
3	#14561516	C₂	1	2	yes	maximal, complemented
4	#14561516	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic
6	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
8	C₂×#10597260	C₂²	1	2	yes	—
9	C₂×#10597260	C₂²	1	2	yes	—
10	#11926299	—	2	1	no	—
11	#11926299	—	2	1	no	—
12	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#383	—	2	1	no	—
14	C₁₉×#382	C₂²	1	1	yes	characteristic
15	C₁₉×#382	C₂²	1	1	yes	characteristic
16	C₁₉×#381	—	2	1	no	—
17	C₁₉×#380	C₄	1	1	yes	characteristic
18	C₁₉×#380	C₄	1	1	yes	characteristic
19	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
21	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
22	C₁₉×#376	—	2	1	no	—
23	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄²×C₁₉	—	2	4	no	—
33	C₂×C₄²×C₁₉	—	2	1	no	—
34	C₂×C₄²×C₁₉	—	2	1	no	—
35	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₂²×C₁₉⋊C₈	—	2	2	no	—
40	C₂²×C₁₉⋊C₈	—	2	2	no	—
41	C₁₉×#95	—	2	1	no	—
42	C₁₉×#95	—	2	1	no	—
43	C₁₉×#95	—	2	1	no	—
44	C₁₉×#95	—	2	1	no	—
45	C₁₉×#95	—	2	1	no	—
46	C₁₉×#95	—	2	1	no	—
47	C₁₉×#95	—	2	1	no	—
48	C₁₉×#95	—	2	1	no	—
49	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
50	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
51	#10597260	—	2	4	no	—
52	#10597260	—	2	4	no	—
53	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	—	2	2	no	—
55	C₂²×C₄×C₁₉	—	2	2	no	—
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	—	2	2	no	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	—	2	1	no	—
60	C₂²×C₄×C₁₉	—	2	1	no	—
61	C₂²×C₄×C₁₉	—	2	1	no	—
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂²×C₄×C₁₉	—	4	1	no	—
64	C₂²×C₄×C₁₉	—	4	1	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	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₄⋊C₄×C₁₉	—	4	1	no	—
74	C₄⋊C₄×C₁₉	—	4	1	no	—
75	C₄⋊C₄×C₁₉	—	4	1	no	—
76	C₄⋊C₄×C₁₉	—	4	1	no	—
77	C₂²⋊C₄×C₁₉	—	4	2	no	—
78	C₂²⋊C₄×C₁₉	—	4	2	no	—
79	C₄²×C₁₉	—	2	2	no	—
80	C₄²×C₁₉	—	2	2	no	—
81	C₄²×C₁₉	—	2	2	no	—
82	C₄²×C₁₉	—	4	2	no	—
83	C₄²×C₁₉	—	4	2	no	—
84	C₄²×C₁₉	#41	1	4	yes	—
85	C₂×C₁₉⋊C₈	—	2	4	no	—
86	C₂×C₁₉⋊C₈	—	2	4	no	—
87	C₂×C₁₉⋊C₈	—	4	2	no	—
88	C₂×C₁₉⋊C₈	—	4	2	no	—
89	C₂×C₁₉⋊C₈	—	4	2	no	—
90	C₂×C₁₉⋊C₈	—	4	2	no	—
91	#8720	—	19	1	no	maximal, Sylow
92	C₂³×C₁₉	—	2	1	no	—
93	C₂³×C₁₉	—	2	1	no	—
94	C₂³×C₁₉	—	2	1	no	—
95	C₂³×C₁₉	—	2	1	no	—
96	C₂³×C₁₉	—	2	1	no	—
97	C₂³×C₁₉	—	2	1	no	—
98	C₂³×C₁₉	#104	1	2	yes	—
99	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	2	1	no	—
103	C₂×C₄×C₁₉	—	2	1	no	—
104	C₂×C₄×C₁₉	—	2	1	no	—
105	C₂×C₄×C₁₉	—	2	1	no	—
106	C₂×C₄×C₁₉	—	2	1	no	—
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	2	1	no	—
109	C₂×C₄×C₁₉	—	2	1	no	—
110	C₂×C₄×C₁₉	—	2	1	no	—
111	C₂×C₄×C₁₉	—	2	1	no	—
112	C₂×C₄×C₁₉	—	2	1	no	—
113	C₂×C₄×C₁₉	—	2	1	no	—
114	C₂×C₄×C₁₉	—	4	4	no	—
115	C₂×C₄×C₁₉	—	4	4	no	—
116	C₂×C₄×C₁₉	—	4	4	no	—
117	C₂×C₄×C₁₉	—	4	1	no	—
118	C₂×C₄×C₁₉	—	4	1	no	—
119	C₂×C₄×C₁₉	—	4	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	1	no	—
124	C₂×C₄×C₁₉	—	4	1	no	—
125	C₂×C₄×C₁₉	—	4	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	#104	1	2	yes	—
130	C₂×C₄×C₁₉	#117	1	2	yes	—
131	C₂×C₄×C₁₉	#123	1	2	yes	—
132	C₂×C₄×C₁₉	#123	1	2	yes	—
133	C₁₉⋊C₈	—	4	4	no	—
134	C₁₉⋊C₈	—	4	4	no	—
135	#2283	D₁₉	1	1	yes	characteristic
136	#1749	—	19	1	no	—
137	#1749	—	19	1	no	—
138	#1295	—	19	2	no	—
139	#1295	—	19	2	no	—
140	C₂²×C₁₉	—	2	2	no	—
141	C₂²×C₁₉	—	2	2	no	—
142	C₂²×C₁₉	—	2	2	no	—
143	C₂²×C₁₉	—	4	1	no	—
144	C₂²×C₁₉	—	4	1	no	—
145	C₂²×C₁₉	—	4	1	no	—
146	C₂²×C₁₉	—	4	1	no	—
147	C₂²×C₁₉	#381	1	1	yes	characteristic
148	C₂²×C₁₉	#413	1	1	yes	characteristic
149	C₂²×C₁₉	#413	1	1	yes	characteristic
150	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
151	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
152	C₂²×C₁₉	#421	1	1	yes	characteristic
153	C₂²×C₁₉	#421	1	1	yes	characteristic
154	C₄×C₁₉	—	2	2	no	—
155	C₄×C₁₉	—	2	2	no	—
156	C₄×C₁₉	—	2	2	no	—
157	C₄×C₁₉	—	2	2	no	—
158	C₄×C₁₉	—	4	1	no	—
159	C₄×C₁₉	—	4	1	no	—
160	C₄×C₁₉	—	8	1	no	—
161	C₄×C₁₉	—	8	1	no	—
162	C₄×C₁₉	—	8	1	no	—
163	C₄×C₁₉	—	8	1	no	—
164	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
165	C₂×C₂²⋊C₈	—	38	1	no	—
166	C₂×C₂²⋊C₈	—	38	1	no	—
167	C₂×#97	—	19	2	no	—
168	C₂×#97	—	19	2	no	—
169	#383	—	2	1	no	—
170	#382	C₂×D₁₉	1	1	yes	characteristic
171	#382	C₂×D₁₉	1	1	yes	characteristic
172	#381	—	2	1	no	—
173	#380	Dic₁₉	1	1	yes	characteristic
174	#380	Dic₁₉	1	1	yes	characteristic
175	C₄×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
176	C₄×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
177	C₄×C₂²⋊C₄	—	2	1	no	—
178	#376	—	2	1	no	—
179	#336	—	38	1	no	—
180	#336	—	38	1	no	—
181	C₂×C₁₉	—	4	2	no	—
182	C₂×C₁₉	#1524	1	1	yes	characteristic
183	C₂×C₁₉	#1529	1	1	yes	characteristic
184	C₂×C₁₉	#1532	1	1	yes	characteristic
185	C₂×C₁₉	#1535	1	1	yes	characteristic
186	C₂×C₁₉	#1822	1	1	yes	characteristic
187	C₂×C₁₉	#1826	1	1	yes	characteristic
188	C₂×C₁₉	#1826	1	1	yes	characteristic
189	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
190	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
191	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
192	C₂²×C₈	—	38	2	no	—
193	C₂²×C₈	—	38	2	no	—
194	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
195	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
196	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
197	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
198	C₂×C₂²⋊C₄	—	2	1	no	—
199	C₂×C₂²⋊C₄	—	2	1	no	—
200	C₂×C₄²	—	2	4	no	—
201	C₂×C₄²	—	2	1	no	—
202	C₂×C₄²	—	2	1	no	—
203	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
204	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
205	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
206	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
207	C₂²⋊C₈	—	38	4	no	—
208	C₂²⋊C₈	—	38	4	no	—
209	#97	—	38	4	no	—
210	#97	—	38	4	no	—
211	#95	—	2	1	no	—
212	#95	—	2	1	no	—
213	#95	—	2	1	no	—
214	#95	—	2	1	no	—
215	#95	—	2	1	no	—
216	#95	—	2	1	no	—
217	#95	—	2	1	no	—
218	#95	—	2	1	no	—
219	C₁₉	#8720	1	1	yes	characteristic, complemented, Sylow
220	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
221	C₂²×C₄	—	2	2	no	—
222	C₂²×C₄	—	2	2	no	—
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	2	2	no	—
226	C₂²×C₄	—	2	1	no	—
227	C₂²×C₄	—	2	1	no	—
228	C₂²×C₄	—	2	1	no	—
229	C₂²×C₄	—	2	1	no	—
230	C₂²×C₄	—	4	1	no	—
231	C₂²×C₄	—	4	1	no	—
232	C₂²×C₄	—	4	1	no	—
233	C₂²×C₄	—	4	1	no	—
234	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
235	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
236	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
237	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
238	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
239	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
240	C₂×C₈	—	38	4	no	—
241	C₂×C₈	—	38	4	no	—
242	C₂×C₈	—	76	2	no	—
243	C₂×C₈	—	76	2	no	—
244	C₂×C₈	—	76	2	no	—
245	C₂×C₈	—	76	2	no	—
246	C₄⋊C₄	—	4	1	no	—
247	C₄⋊C₄	—	4	1	no	—
248	C₄⋊C₄	—	4	1	no	—
249	C₄⋊C₄	—	4	1	no	—
250	C₂²⋊C₄	—	4	2	no	—
251	C₂²⋊C₄	—	4	2	no	—
252	C₄²	—	2	2	no	—
253	C₄²	—	2	2	no	—
254	C₄²	—	2	2	no	—
255	C₄²	—	4	2	no	—
256	C₄²	—	4	2	no	—
257	C₄²	#64541	1	4	yes	—
258	C₂³	—	2	1	no	—
259	C₂³	—	2	1	no	—
260	C₂³	—	2	1	no	—
261	C₂³	—	2	1	no	—
262	C₂³	—	2	1	no	—
263	C₂³	—	2	1	no	—
264	C₂³	#10597294	1	2	yes	—
265	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	2	1	no	—
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	2	1	no	—
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	—	2	1	no	—
274	C₂×C₄	—	2	1	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	1	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	4	4	no	—
281	C₂×C₄	—	4	4	no	—
282	C₂×C₄	—	4	4	no	—
283	C₂×C₄	—	4	1	no	—
284	C₂×C₄	—	4	1	no	—
285	C₂×C₄	—	4	1	no	—
286	C₂×C₄	—	4	1	no	—
287	C₂×C₄	—	4	1	no	—
288	C₂×C₄	—	4	1	no	—
289	C₂×C₄	—	4	1	no	—
290	C₂×C₄	—	4	1	no	—
291	C₂×C₄	—	4	1	no	—
292	C₂×C₄	—	4	1	no	—
293	C₂×C₄	—	4	1	no	—
294	C₂×C₄	—	4	1	no	—
295	C₂×C₄	#10597294	1	2	yes	—
296	C₂×C₄	#10597372	1	2	yes	—
297	C₂×C₄	#10597375	1	2	yes	—
298	C₂×C₄	#10597375	1	2	yes	—
299	C₈	—	76	4	no	—
300	C₈	—	76	4	no	—
301	C₂²	—	2	2	no	—
302	C₂²	—	2	2	no	—
303	C₂²	—	2	2	no	—
304	C₂²	—	4	1	no	—
305	C₂²	—	4	1	no	—
306	C₂²	—	4	1	no	—
307	C₂²	—	4	1	no	—
308	C₂²	#11926407	1	1	yes	characteristic
309	C₂²	#11926528	1	1	yes	characteristic
310	C₂²	#11926528	1	1	yes	characteristic
311	C₂²	C₂×#10597294	1	1	yes	characteristic
312	C₂²	C₂×#10597294	1	1	yes	characteristic
313	C₂²	#11926561	1	1	yes	characteristic
314	C₂²	#11926561	1	1	yes	characteristic
315	C₄	—	2	2	no	—
316	C₄	—	2	2	no	—
317	C₄	—	2	2	no	—
318	C₄	—	2	2	no	—
319	C₄	—	4	1	no	—
320	C₄	—	4	1	no	—
321	C₄	—	8	1	no	—
322	C₄	—	8	1	no	—
323	C₄	—	8	1	no	—
324	C₄	—	8	1	no	—
325	C₂	—	4	2	no	—
326	C₂	#14562223	1	1	yes	characteristic
327	C₂	#14562242	1	1	yes	characteristic
328	C₂	#14562255	1	1	yes	characteristic
329	C₂	#14562266	1	1	yes	characteristic
330	C₂	#14563718	1	1	yes	characteristic
331	C₂	#14563734	1	1	yes	characteristic
332	C₂	#14563734	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2283	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2283	D₁₉
hypocenter	C₁₉	#8720
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2283

Complements

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

N	H ≅ G/N	type
3. #14561516	C₂	semidirect
4. #14561516	C₂	semidirect
219. C₁₉	#8720	semidirect

Maximal subgroups

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

subgroup	index
#14563397	2
#14561516	2
C₁₉×#2283	2
#8720	19