Subgroups — #18075900

Order 4864.

540 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14566042	C₂	1	1	yes	maximal, characteristic
2	#14563615	C₂	1	1	yes	maximal, characteristic
3	#14561475	C₂	1	4	yes	maximal, complemented
4	C₄×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597372	—	2	1	no	—
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
8	#11926414	C₄	1	1	yes	characteristic
9	#11926414	C₄	1	1	yes	characteristic
10	#11926410	—	2	1	no	—
11	#11926404	—	2	1	no	—
12	#11926404	C₄	1	2	yes	—
13	C₄×C₄⋊Dic₁₉	—	2	1	no	—
14	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
15	#11926299	—	2	1	no	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
19	C₁₉×#336	—	2	1	no	—
20	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	—	2	2	no	—
24	C₂×C₄²×C₁₉	—	2	4	no	—
25	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
30	#10597372	—	4	2	no	—
31	#10597372	—	4	2	no	—
32	C₂×C₄⋊Dic₁₉	—	2	1	no	—
33	C₂×C₄⋊Dic₁₉	—	2	1	no	—
34	C₂×C₄⋊Dic₁₉	—	2	1	no	—
35	C₂×C₄⋊Dic₁₉	—	2	1	no	—
36	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
37	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
38	C₂×C₄×Dic₁₉	—	2	2	no	—
39	C₂²×C₁₉⋊C₈	—	2	2	no	—
40	C₁₉×C₂²⋊C₈	—	2	4	no	—
41	C₄×C₈×C₁₉	—	2	4	no	—
42	C₁₉⋊#95	—	2	2	no	—
43	C₁₉⋊#95	—	2	2	no	—
44	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
46	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	2	2	no	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	—	4	1	no	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	D₈	1	2	yes	—
59	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
60	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×Dic₁₉	—	2	2	no	—
64	C₂²×Dic₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	2	4	no	—
66	C₂×C₈×C₁₉	—	4	2	no	—
67	C₂×C₈×C₁₉	—	4	2	no	—
68	C₄²×C₁₉	—	2	2	no	—
69	C₄²×C₁₉	—	2	2	no	—
70	C₄²×C₁₉	—	2	2	no	—
71	C₄²×C₁₉	#41	1	4	yes	—
72	C₂²⋊Dic₁₉	—	4	4	no	—
73	C₄⋊Dic₁₉	—	2	4	no	—
74	C₄⋊Dic₁₉	—	2	4	no	—
75	C₄⋊Dic₁₉	—	4	2	no	—
76	C₄⋊Dic₁₉	—	4	2	no	—
77	C₄⋊Dic₁₉	—	4	2	no	—
78	C₄⋊Dic₁₉	—	4	2	no	—
79	C₄×Dic₁₉	—	4	2	no	—
80	C₄×Dic₁₉	—	4	2	no	—
81	C₂×C₁₉⋊C₈	—	4	2	no	—
82	C₂×C₁₉⋊C₈	—	4	2	no	—
83	C₂×C₁₉⋊C₈	—	4	2	no	—
84	#8709	—	19	1	no	maximal, Sylow
85	C₂³×C₁₉	—	2	1	no	—
86	C₂³×C₁₉	—	2	1	no	—
87	C₂³×C₁₉	—	2	1	no	—
88	C₂³×C₁₉	—	2	1	no	—
89	C₂³×C₁₉	—	2	1	no	—
90	C₂³×C₁₉	—	2	1	no	—
91	C₂³×C₁₉	#102	1	2	yes	—
92	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	2	4	no	—
100	C₂×C₄×C₁₉	—	2	4	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	—	4	4	no	—
105	C₂×C₄×C₁₉	—	4	4	no	—
106	C₂×C₄×C₁₉	#102	1	2	yes	—
107	C₂×C₄×C₁₉	#104	1	2	yes	—
108	C₂×C₄×C₁₉	#117	1	2	yes	—
109	C₂×C₄×C₁₉	#123	1	2	yes	—
110	C₂×C₄×C₁₉	#123	1	2	yes	—
111	C₂×C₄×C₁₉	#131	1	2	yes	—
112	C₂×C₄×C₁₉	#131	1	2	yes	—
113	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
114	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
115	C₂×C₄×C₁₉	#137	1	2	yes	—
116	C₂×Dic₁₉	—	4	2	no	—
117	C₂×Dic₁₉	—	4	2	no	—
118	C₂×Dic₁₉	—	4	2	no	—
119	C₂×Dic₁₉	—	4	2	no	—
120	C₂×Dic₁₉	—	4	2	no	—
121	C₂×Dic₁₉	—	4	2	no	—
122	C₈×C₁₉	—	4	4	no	—
123	C₁₉⋊C₈	—	8	2	no	—
124	#2285	—	19	1	no	—
125	#1797	—	19	1	no	—
126	C₄×C₂²⋊C₈	D₁₉	1	1	yes	characteristic
127	#1279	—	19	4	no	—
128	C₂²×C₁₉	—	2	2	no	—
129	C₂²×C₁₉	—	2	2	no	—
130	C₂²×C₁₉	—	2	2	no	—
131	C₂²×C₁₉	—	4	1	no	—
132	C₂²×C₁₉	—	4	1	no	—
133	C₂²×C₁₉	—	4	1	no	—
134	C₂²×C₁₉	—	4	1	no	—
135	C₂²×C₁₉	#381	1	1	yes	characteristic
136	C₂²×C₁₉	#408	1	1	yes	characteristic
137	C₂²×C₁₉	#408	1	1	yes	characteristic
138	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
139	C₂²×C₁₉	#419	1	1	yes	characteristic
140	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
141	C₂²×C₁₉	#421	1	1	yes	characteristic
142	C₄×C₁₉	—	2	2	no	—
143	C₄×C₁₉	—	2	2	no	—
144	C₄×C₁₉	—	2	2	no	—
145	C₄×C₁₉	—	4	1	no	—
146	C₄×C₁₉	#433	1	4	yes	—
147	C₄×C₁₉	#480	1	2	yes	—
148	C₄×C₁₉	#483	1	2	yes	—
149	Dic₁₉	—	8	2	no	—
150	Dic₁₉	—	8	2	no	—
151	C₂×#117	—	38	1	no	—
152	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
153	C₂×C₄⋊C₈	—	19	2	no	—
154	C₂×C₂²⋊C₈	—	2	1	no	—
155	C₂×C₂²⋊C₈	—	38	1	no	—
156	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
157	#384	—	19	1	no	—
158	#384	—	19	1	no	—
159	#382	—	38	1	no	—
160	#380	—	19	2	no	—
161	#380	—	38	1	no	—
162	C₄×C₄⋊C₄	—	19	2	no	—
163	C₄×C₄⋊C₄	—	38	1	no	—
164	#336	—	2	1	no	—
165	#336	—	38	1	no	—
166	C₂×C₁₉	—	4	2	no	—
167	C₂×C₁₉	#1480	1	1	yes	characteristic
168	C₂×C₁₉	#1485	1	1	yes	characteristic
169	C₂×C₁₉	#1492	1	1	yes	characteristic
170	C₂×C₁₉	#1497	1	1	yes	characteristic
171	C₂×C₁₉	#1818	1	1	yes	characteristic
172	C₂×C₁₉	#1823	1	1	yes	characteristic
173	C₂×C₁₉	#1826	1	1	yes	characteristic
174	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
175	C₂³×C₄	D₇₆	1	1	yes	characteristic
176	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
177	C₂²×C₈	—	2	2	no	—
178	C₂²×C₈	—	38	2	no	—
179	#117	—	76	2	no	—
180	#117	—	76	2	no	—
181	C₂×C₄⋊C₄	—	19	2	no	—
182	C₂×C₄⋊C₄	—	19	2	no	—
183	C₂×C₄⋊C₄	—	38	1	no	—
184	C₂×C₄⋊C₄	—	38	1	no	—
185	C₂×C₄⋊C₄	—	38	1	no	—
186	C₂×C₄⋊C₄	—	38	1	no	—
187	C₂×C₂²⋊C₄	—	38	2	no	—
188	C₂×C₄²	—	2	4	no	—
189	C₂×C₄²	—	38	2	no	—
190	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
191	C₂×C₄²	D₇₆	1	1	yes	characteristic
192	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
193	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
194	C₄⋊C₈	—	38	4	no	—
195	C₂²⋊C₈	—	2	4	no	—
196	C₂²⋊C₈	—	76	2	no	—
197	C₄×C₈	—	2	4	no	—
198	#95	—	38	2	no	—
199	#95	—	38	2	no	—
200	C₁₉	#8709	1	1	yes	characteristic, complemented, Sylow
201	C₂⁴	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
202	C₂²×C₄	—	2	2	no	—
203	C₂²×C₄	—	2	2	no	—
204	C₂²×C₄	—	2	2	no	—
205	C₂²×C₄	—	2	2	no	—
206	C₂²×C₄	—	2	2	no	—
207	C₂²×C₄	—	2	2	no	—
208	C₂²×C₄	—	2	2	no	—
209	C₂²×C₄	—	4	1	no	—
210	C₂²×C₄	—	38	2	no	—
211	C₂²×C₄	—	38	2	no	—
212	C₂²×C₄	#64516	1	2	yes	—
213	C₂²×C₄	D₁₅₂	1	2	yes	—
214	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
215	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
216	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
217	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
218	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
219	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
220	C₂×C₈	—	2	4	no	—
221	C₂×C₈	—	4	2	no	—
222	C₂×C₈	—	4	2	no	—
223	C₂×C₈	—	76	2	no	—
224	C₂×C₈	—	76	2	no	—
225	C₂×C₈	—	76	2	no	—
226	C₄⋊C₄	—	38	4	no	—
227	C₄⋊C₄	—	38	4	no	—
228	C₄⋊C₄	—	76	2	no	—
229	C₄⋊C₄	—	76	2	no	—
230	C₄⋊C₄	—	76	2	no	—
231	C₄⋊C₄	—	76	2	no	—
232	C₂²⋊C₄	—	76	4	no	—
233	C₄²	—	2	2	no	—
234	C₄²	—	2	2	no	—
235	C₄²	—	2	2	no	—
236	C₄²	—	76	2	no	—
237	C₄²	—	76	2	no	—
238	C₄²	#64543	1	4	yes	—
239	C₂³	—	2	1	no	—
240	C₂³	—	2	1	no	—
241	C₂³	—	2	1	no	—
242	C₂³	—	2	1	no	—
243	C₂³	—	2	1	no	—
244	C₂³	—	2	1	no	—
245	C₂³	#10597278	1	2	yes	—
246	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
247	C₂×C₄	—	2	1	no	—
248	C₂×C₄	—	2	1	no	—
249	C₂×C₄	—	2	1	no	—
250	C₂×C₄	—	2	1	no	—
251	C₂×C₄	—	2	1	no	—
252	C₂×C₄	—	2	1	no	—
253	C₂×C₄	—	2	4	no	—
254	C₂×C₄	—	2	4	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	2	1	no	—
258	C₂×C₄	—	4	4	no	—
259	C₂×C₄	—	4	4	no	—
260	C₂×C₄	—	76	2	no	—
261	C₂×C₄	—	76	2	no	—
262	C₂×C₄	—	76	2	no	—
263	C₂×C₄	—	76	2	no	—
264	C₂×C₄	—	76	2	no	—
265	C₂×C₄	—	76	2	no	—
266	C₂×C₄	#10597262	1	2	yes	—
267	C₂×C₄	#10597278	1	2	yes	—
268	C₂×C₄	#10597323	1	2	yes	—
269	C₂×C₄	#10597332	1	2	yes	—
270	C₂×C₄	#10597347	1	2	yes	—
271	C₂×C₄	C₂×#64516	1	1	yes	characteristic
272	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
273	C₂×C₄	#10597353	1	2	yes	—
274	C₂×C₄	#10597355	1	2	yes	—
275	C₂×C₄	#10597381	1	2	yes	—
276	C₈	—	4	4	no	—
277	C₈	—	152	2	no	—
278	C₂²	—	2	2	no	—
279	C₂²	—	2	2	no	—
280	C₂²	—	2	2	no	—
281	C₂²	—	4	1	no	—
282	C₂²	—	4	1	no	—
283	C₂²	—	4	1	no	—
284	C₂²	—	4	1	no	—
285	C₂²	#11926405	1	1	yes	characteristic
286	C₂²	#11926510	1	1	yes	characteristic
287	C₂²	#11926512	1	1	yes	characteristic
288	C₂²	C₂×#10597278	1	1	yes	characteristic
289	C₂²	#11926554	1	1	yes	characteristic
290	C₂²	C₂×#10597262	1	1	yes	characteristic
291	C₂²	#11926562	1	1	yes	characteristic
292	C₄	—	2	2	no	—
293	C₄	—	2	2	no	—
294	C₄	—	2	2	no	—
295	C₄	—	4	1	no	—
296	C₄	—	152	2	no	—
297	C₄	—	152	2	no	—
298	C₄	#11926602	1	4	yes	—
299	C₄	#11926858	1	2	yes	—
300	C₄	#11926875	1	2	yes	—
301	C₂	—	4	2	no	—
302	C₂	#14562035	1	1	yes	characteristic
303	C₂	#14562057	1	1	yes	characteristic
304	C₂	#14562087	1	1	yes	characteristic
305	C₂	#14562109	1	1	yes	characteristic
306	C₂	#14563704	1	1	yes	characteristic
307	C₂	#14563722	1	1	yes	characteristic
308	C₂	#14563735	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×C₂²⋊C₈	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×C₂²⋊C₈	D₁₉
hypocenter	C₁₉	#8709
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
3. #14561475	C₂	semidirect
200. C₁₉	#8709	semidirect

Maximal subgroups

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

subgroup	index
#14566042	2
#14563615	2
#14561475	2
C₄×C₁₉×C₂²⋊C₈	2
#8709	19