Subgroups — #18075384

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926595	C₂	1	1	yes	maximal, characteristic
2	#14563612	C₂	1	2	yes	maximal
3	C₂×#11926295	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561469	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
7	#11926595	—	2	2	no	—
8	#11926595	—	2	2	no	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
10	C₂×Dic₁₉⋊C₈	C₄	1	1	yes	characteristic
11	C₂×Dic₁₉⋊C₈	C₄	1	1	yes	characteristic
12	C₂×(C₂×D₁₉)⋊C₈	—	2	2	no	—
13	C₂×(C₂×D₁₉)⋊C₈	C₄	1	1	yes	characteristic
14	C₂×(C₂×D₁₉)⋊C₈	C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	#11926298	—	2	2	no	—
17	#11926295	—	2	2	no	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#334	—	2	2	no	—
21	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₄×D₁₉	Q₈	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
30	C₂×C₄×Dic₁₉	Q₈	1	1	yes	characteristic
31	C₂²×C₁₉⋊C₈	—	2	2	no	—
32	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
34	C₄²×D₁₉	—	2	1	no	—
35	C₄²×D₁₉	—	2	1	no	—
36	C₄²×D₁₉	—	2	1	no	—
37	C₄²×D₁₉	—	2	1	no	—
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₄×C₈×C₁₉	D₄	1	2	yes	—
41	C₄×C₈×C₁₉	D₄	1	2	yes	—
42	(C₂×D₁₉)⋊C₈	—	2	2	no	—
43	(C₂×D₁₉)⋊C₈	—	2	2	no	—
44	(C₂×D₁₉)⋊C₈	—	4	4	no	—
45	Dic₁₉⋊C₈	—	2	2	no	—
46	Dic₁₉⋊C₈	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
49	C₄×C₁₉⋊C₈	—	2	1	no	—
50	C₄×C₁₉⋊C₈	—	2	1	no	—
51	C₂³×D₁₉	C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
55	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
57	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₄×D₁₉	—	2	1	no	—
59	C₂×C₄×D₁₉	—	2	1	no	—
60	C₂×C₄×D₁₉	—	2	2	no	—
61	C₂×C₄×D₁₉	—	2	1	no	—
62	C₂×C₄×D₁₉	—	2	1	no	—
63	C₂×C₄×D₁₉	—	2	1	no	—
64	C₂×C₄×D₁₉	—	2	1	no	—
65	C₂×C₄×D₁₉	—	2	2	no	—
66	C₂×C₄×D₁₉	—	2	2	no	—
67	C₂×C₄×D₁₉	—	4	2	no	—
68	C₂×C₄×D₁₉	SD₁₆	1	4	yes	—
69	C₂×C₈×C₁₉	—	2	2	no	—
70	C₂×C₈×C₁₉	—	2	2	no	—
71	C₂×C₈×C₁₉	—	4	2	no	—
72	C₂×C₈×C₁₉	—	4	2	no	—
73	C₂×C₈×C₁₉	—	4	2	no	—
74	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
75	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
76	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₁₉	#41	1	1	yes	characteristic
79	C₄²×C₁₉	#41	1	1	yes	characteristic
80	C₄×Dic₁₉	—	2	1	no	—
81	C₄×Dic₁₉	—	2	1	no	—
82	C₄×Dic₁₉	—	2	1	no	—
83	C₄×Dic₁₉	—	2	1	no	—
84	C₄×Dic₁₉	—	2	1	no	—
85	C₄×Dic₁₉	—	2	1	no	—
86	C₂×C₁₉⋊C₈	—	2	1	no	—
87	C₂×C₁₉⋊C₈	—	2	1	no	—
88	C₂×C₁₉⋊C₈	—	2	2	no	—
89	C₂×C₁₉⋊C₈	—	2	2	no	—
90	C₂×C₁₉⋊C₈	—	4	2	no	—
91	C₂×C₁₉⋊C₈	—	4	2	no	—
92	C₂×C₁₉⋊C₈	—	4	2	no	—
93	#8598	—	19	1	no	maximal, Sylow
94	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
95	C₂²×D₁₉	—	2	1	no	—
96	C₂²×D₁₉	—	2	2	no	—
97	C₂²×D₁₉	—	2	1	no	—
98	C₂²×D₁₉	—	2	2	no	—
99	C₂²×D₁₉	#106	1	2	yes	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
105	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
106	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#131	1	2	yes	—
108	C₂×C₄×C₁₉	#131	1	2	yes	—
109	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
110	C₂×C₄×C₁₉	#135	1	2	yes	—
111	C₂×Dic₁₉	—	2	1	no	—
112	C₂×Dic₁₉	—	2	1	no	—
113	C₂×Dic₁₉	—	2	1	no	—
114	C₂×Dic₁₉	—	2	1	no	—
115	C₂×Dic₁₉	—	2	2	no	—
116	C₂×Dic₁₉	—	2	2	no	—
117	C₂×Dic₁₉	#106	1	2	yes	—
118	C₄×D₁₉	—	2	4	no	—
119	C₄×D₁₉	—	2	4	no	—
120	C₄×D₁₉	—	4	2	no	—
121	C₄×D₁₉	—	4	2	no	—
122	C₄×D₁₉	—	4	1	no	—
123	C₄×D₁₉	—	4	1	no	—
124	C₄×D₁₉	—	4	2	no	—
125	C₈×C₁₉	—	2	2	no	—
126	C₈×C₁₉	—	2	2	no	—
127	C₈×C₁₉	—	8	2	no	—
128	C₁₉⋊C₈	—	4	1	no	—
129	C₁₉⋊C₈	—	4	1	no	—
130	C₁₉⋊C₈	—	8	2	no	—
131	C₂×#431	—	19	1	no	—
132	#1797	—	19	2	no	—
133	C₂×#334	—	19	1	no	—
134	C₂×#334	D₁₉	1	1	yes	characteristic, complemented
135	#1277	—	19	2	no	—
136	C₂²×C₁₉	#380	1	1	yes	characteristic
137	C₂²×C₁₉	#424	1	2	yes	—
138	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
139	C₂²×C₁₉	#427	1	1	yes	characteristic
140	C₂²×C₁₉	#430	1	2	yes	—
141	C₂×D₁₉	—	2	2	no	—
142	C₂×D₁₉	—	2	4	no	—
143	C₂×D₁₉	—	4	1	no	—
144	C₂×D₁₉	—	4	1	no	—
145	C₂×D₁₉	—	4	2	no	—
146	C₄×C₁₉	—	2	1	no	—
147	C₄×C₁₉	—	2	1	no	—
148	C₄×C₁₉	#408	1	1	yes	characteristic
149	C₄×C₁₉	#408	1	1	yes	characteristic
150	C₄×C₁₉	#433	1	2	yes	—
151	C₄×C₁₉	#465	1	2	yes	—
152	C₄×C₁₉	#465	1	2	yes	—
153	Dic₁₉	—	2	2	no	—
154	Dic₁₉	—	4	1	no	—
155	Dic₁₉	—	4	1	no	—
156	C₂²×C₄²	—	19	1	no	—
157	#431	—	38	2	no	—
158	#431	—	38	2	no	—
159	C₂×C₄⋊C₈	—	19	1	no	—
160	C₂×C₄⋊C₈	—	19	1	no	—
161	C₂×C₄⋊C₈	—	19	2	no	—
162	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
163	C₂×C₂²⋊C₈	—	19	1	no	—
164	C₂×C₂²⋊C₈	—	19	1	no	—
165	C₂×C₂²⋊C₈	—	38	2	no	—
166	C₂×C₄×C₈	—	19	1	no	—
167	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
168	#336	—	38	2	no	—
169	#334	—	2	2	no	—
170	#334	—	38	2	no	—
171	C₂×C₁₉	#1570	1	2	yes	—
172	C₂×C₁₉	#1572	1	2	yes	—
173	C₂×C₁₉	#1798	1	1	yes	characteristic
174	C₂×C₁₉	#1807	1	1	yes	characteristic
175	C₂×C₁₉	#1811	1	1	yes	characteristic
176	D₁₉	—	4	2	no	—
177	C₂³×C₄	—	19	1	no	—
178	C₂³×C₄	—	19	1	no	—
179	C₂³×C₄	—	19	1	no	—
180	C₂²×C₈	—	2	2	no	—
181	C₂²×C₈	—	19	1	no	—
182	C₂²×C₈	—	19	1	no	—
183	C₂²×C₈	—	38	2	no	—
184	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
185	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
186	C₂×C₄²	—	19	1	no	—
187	C₂×C₄²	—	19	1	no	—
188	C₂×C₄²	—	19	1	no	—
189	C₂×C₄²	—	38	1	no	—
190	C₂×C₄²	—	38	1	no	—
191	C₂×C₄²	—	38	1	no	—
192	C₂×C₄²	—	38	1	no	—
193	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
194	C₄⋊C₈	—	2	2	no	—
195	C₄⋊C₈	—	2	2	no	—
196	C₄⋊C₈	—	38	2	no	—
197	C₄⋊C₈	—	38	2	no	—
198	C₄⋊C₈	—	38	2	no	—
199	C₄⋊C₈	—	38	2	no	—
200	C₂²⋊C₈	—	38	2	no	—
201	C₂²⋊C₈	—	38	2	no	—
202	C₂²⋊C₈	—	76	4	no	—
203	C₄×C₈	—	38	1	no	—
204	C₄×C₈	—	38	1	no	—
205	C₄×C₈	D₇₆	1	2	yes	—
206	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
207	C₁₉	#8598	1	1	yes	characteristic, complemented, Sylow
208	C₂⁴	—	19	1	no	—
209	C₂²×C₄	—	19	1	no	—
210	C₂²×C₄	—	19	4	no	—
211	C₂²×C₄	—	19	1	no	—
212	C₂²×C₄	—	19	1	no	—
213	C₂²×C₄	—	38	1	no	—
214	C₂²×C₄	—	38	1	no	—
215	C₂²×C₄	—	38	2	no	—
216	C₂²×C₄	—	38	1	no	—
217	C₂²×C₄	—	38	1	no	—
218	C₂²×C₄	—	38	1	no	—
219	C₂²×C₄	—	38	2	no	—
220	C₂²×C₄	—	38	2	no	—
221	C₂²×C₄	—	38	1	no	—
222	C₂²×C₄	—	76	2	no	—
223	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
224	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
225	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
226	C₂×C₈	—	2	2	no	—
227	C₂×C₈	—	2	2	no	—
228	C₂×C₈	—	4	2	no	—
229	C₂×C₈	—	4	2	no	—
230	C₂×C₈	—	4	2	no	—
231	C₂×C₈	—	38	2	no	—
232	C₂×C₈	—	38	2	no	—
233	C₂×C₈	—	38	1	no	—
234	C₂×C₈	—	38	1	no	—
235	C₂×C₈	—	76	2	no	—
236	C₂×C₈	—	76	2	no	—
237	C₂×C₈	—	76	2	no	—
238	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
239	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
240	C₄²	—	38	1	no	—
241	C₄²	—	38	1	no	—
242	C₄²	—	38	1	no	—
243	C₄²	—	38	1	no	—
244	C₄²	—	38	1	no	—
245	C₄²	—	38	1	no	—
246	C₄²	C₂×D₇₆	1	1	yes	characteristic
247	C₄²	#64543	1	1	yes	characteristic
248	C₄²	#64545	1	1	yes	characteristic
249	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
250	C₂³	—	19	2	no	—
251	C₂³	—	38	2	no	—
252	C₂³	—	38	1	no	—
253	C₂³	—	38	2	no	—
254	C₂³	—	38	1	no	—
255	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
256	C₂×C₄	—	2	2	no	—
257	C₂×C₄	—	19	2	no	—
258	C₂×C₄	—	38	1	no	—
259	C₂×C₄	—	38	1	no	—
260	C₂×C₄	—	38	4	no	—
261	C₂×C₄	—	38	4	no	—
262	C₂×C₄	—	38	2	no	—
263	C₂×C₄	—	38	2	no	—
264	C₂×C₄	—	38	1	no	—
265	C₂×C₄	—	38	1	no	—
266	C₂×C₄	—	76	2	no	—
267	C₂×C₄	—	76	2	no	—
268	C₂×C₄	—	76	2	no	—
269	C₂×C₄	—	76	1	no	—
270	C₂×C₄	—	76	1	no	—
271	C₂×C₄	#10597338	1	1	yes	characteristic
272	C₂×C₄	#10597341	1	1	yes	characteristic
273	C₂×C₄	#10597343	1	1	yes	characteristic
274	C₂×C₄	#10597347	1	2	yes	—
275	C₂×C₄	#10597353	1	2	yes	—
276	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
277	C₂×C₄	#10597362	1	2	yes	—
278	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
279	C₂×C₄	#10597384	1	1	yes	characteristic
280	C₂×C₄	#10597392	1	1	yes	characteristic
281	C₈	—	2	2	no	—
282	C₈	—	2	2	no	—
283	C₈	—	8	2	no	—
284	C₈	—	76	1	no	—
285	C₈	—	76	1	no	—
286	C₈	—	152	2	no	—
287	C₂²	—	38	2	no	—
288	C₂²	—	38	4	no	—
289	C₂²	—	76	1	no	—
290	C₂²	—	76	1	no	—
291	C₂²	—	76	2	no	—
292	C₂²	#11926401	1	1	yes	characteristic
293	C₂²	#11926569	1	2	yes	—
294	C₂²	#106×D₁₉	1	1	yes	characteristic
295	C₂²	#11926579	1	1	yes	characteristic
296	C₂²	#11926591	1	2	yes	—
297	C₄	—	2	1	no	—
298	C₄	—	2	1	no	—
299	C₄	—	38	2	no	—
300	C₄	—	76	1	no	—
301	C₄	—	76	1	no	—
302	C₄	#11926510	1	1	yes	characteristic
303	C₄	#11926512	1	1	yes	characteristic
304	C₄	#11926604	1	2	yes	—
305	C₄	#11926770	1	2	yes	—
306	C₄	#11926774	1	2	yes	—
307	C₂	—	76	2	no	—
308	C₂	#14562404	1	2	yes	—
309	C₂	#14562412	1	2	yes	—
310	C₂	#14563616	1	1	yes	characteristic
311	C₂	#14563657	1	1	yes	characteristic
312	C₂	#14563674	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#334	C₂
socle	C₂³×C₁₉	C₂×C₄⋊C₄
prime radical	C₂³×D₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#334	D₁₉
hypocenter	C₁₉	#8598
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
3. C₂×#11926295	C₂	semidirect
4. #14561469	C₂	semidirect
5. C₂×C₁₉×#334	C₂	semidirect
134. C₂×#334	D₁₉	semidirect
207. C₁₉	#8598	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926595	2
#14563612	2
C₂×#11926295	2
#14561469	2
C₂×C₁₉×#334	2
#8598	19