Subgroups — #18075388

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 330 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×#11926297	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561469	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#335	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	#11926297	—	2	2	no	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#335	—	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	1	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	1	no	—
66	C₂×C₄×D₁₉	—	2	2	no	—
67	C₂×C₄×D₁₉	—	2	2	no	—
68	C₂×C₄×D₁₉	—	4	2	no	—
69	C₂×C₄×D₁₉	D₈	1	2	yes	—
70	C₂×C₄×D₁₉	Q₁₆	1	2	yes	—
71	C₂×C₈×C₁₉	—	2	2	no	—
72	C₂×C₈×C₁₉	—	2	2	no	—
73	C₂×C₈×C₁₉	—	4	2	no	—
74	C₂×C₈×C₁₉	—	4	2	no	—
75	C₂×C₈×C₁₉	—	4	2	no	—
76	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
77	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
78	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₁₉	#41	1	1	yes	characteristic
81	C₄²×C₁₉	#41	1	1	yes	characteristic
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	C₄×Dic₁₉	—	2	1	no	—
87	C₄×Dic₁₉	—	2	1	no	—
88	C₂×C₁₉⋊C₈	—	2	1	no	—
89	C₂×C₁₉⋊C₈	—	2	1	no	—
90	C₂×C₁₉⋊C₈	—	2	2	no	—
91	C₂×C₁₉⋊C₈	—	2	2	no	—
92	C₂×C₁₉⋊C₈	—	4	2	no	—
93	C₂×C₁₉⋊C₈	—	4	2	no	—
94	C₂×C₁₉⋊C₈	—	4	2	no	—
95	#8599	—	19	1	no	maximal, Sylow
96	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
97	C₂²×D₁₉	—	2	1	no	—
98	C₂²×D₁₉	—	2	2	no	—
99	C₂²×D₁₉	—	2	1	no	—
100	C₂²×D₁₉	—	2	2	no	—
101	C₂²×D₁₉	#107	1	2	yes	—
102	C₂×C₄×C₁₉	—	2	2	no	—
103	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
105	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
107	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
108	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#131	1	2	yes	—
110	C₂×C₄×C₁₉	#131	1	2	yes	—
111	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
112	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
113	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
114	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
115	C₂×Dic₁₉	—	2	1	no	—
116	C₂×Dic₁₉	—	2	1	no	—
117	C₂×Dic₁₉	—	2	1	no	—
118	C₂×Dic₁₉	—	2	1	no	—
119	C₂×Dic₁₉	—	2	2	no	—
120	C₂×Dic₁₉	—	2	2	no	—
121	C₂×Dic₁₉	#107	1	2	yes	—
122	C₄×D₁₉	—	2	2	no	—
123	C₄×D₁₉	—	2	2	no	—
124	C₄×D₁₉	—	2	2	no	—
125	C₄×D₁₉	—	2	2	no	—
126	C₄×D₁₉	—	4	2	no	—
127	C₄×D₁₉	—	4	2	no	—
128	C₄×D₁₉	—	4	1	no	—
129	C₄×D₁₉	—	4	1	no	—
130	C₄×D₁₉	—	4	2	no	—
131	C₈×C₁₉	—	2	2	no	—
132	C₈×C₁₉	—	2	2	no	—
133	C₈×C₁₉	—	8	2	no	—
134	C₁₉⋊C₈	—	4	1	no	—
135	C₁₉⋊C₈	—	4	1	no	—
136	C₁₉⋊C₈	—	8	2	no	—
137	C₂×#431	—	19	1	no	—
138	#1797	—	19	2	no	—
139	C₂×#335	—	19	1	no	—
140	C₂×#335	D₁₉	1	1	yes	characteristic, complemented
141	#1277	—	19	2	no	—
142	C₂²×C₁₉	#380	1	1	yes	characteristic
143	C₂²×C₁₉	#424	1	2	yes	—
144	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
145	C₂²×C₁₉	#427	1	1	yes	characteristic
146	C₂²×C₁₉	#430	1	2	yes	—
147	C₂×D₁₉	—	2	2	no	—
148	C₂×D₁₉	—	2	4	no	—
149	C₂×D₁₉	—	4	1	no	—
150	C₂×D₁₉	—	4	1	no	—
151	C₂×D₁₉	—	4	2	no	—
152	C₄×C₁₉	—	2	1	no	—
153	C₄×C₁₉	—	2	1	no	—
154	C₄×C₁₉	#408	1	1	yes	characteristic
155	C₄×C₁₉	#408	1	1	yes	characteristic
156	C₄×C₁₉	#433	1	2	yes	—
157	C₄×C₁₉	#466	1	1	yes	characteristic
158	C₄×C₁₉	#466	1	1	yes	characteristic
159	C₄×C₁₉	#467	1	1	yes	characteristic
160	C₄×C₁₉	#467	1	1	yes	characteristic
161	Dic₁₉	—	2	2	no	—
162	Dic₁₉	—	4	1	no	—
163	Dic₁₉	—	4	1	no	—
164	C₂²×C₄²	—	19	1	no	—
165	#431	—	38	2	no	—
166	#431	—	38	2	no	—
167	C₂×C₄⋊C₈	—	19	1	no	—
168	C₂×C₄⋊C₈	—	19	1	no	—
169	C₂×C₄⋊C₈	—	19	2	no	—
170	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
171	C₂×C₂²⋊C₈	—	19	1	no	—
172	C₂×C₂²⋊C₈	—	19	1	no	—
173	C₂×C₂²⋊C₈	—	38	2	no	—
174	C₂×C₄×C₈	—	19	1	no	—
175	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
176	#336	—	38	2	no	—
177	#335	—	2	2	no	—
178	#335	—	38	2	no	—
179	C₂×C₁₉	#1571	1	2	yes	—
180	C₂×C₁₉	#1572	1	2	yes	—
181	C₂×C₁₉	#1798	1	1	yes	characteristic
182	C₂×C₁₉	#1808	1	1	yes	characteristic
183	C₂×C₁₉	#1811	1	1	yes	characteristic
184	D₁₉	—	4	2	no	—
185	C₂³×C₄	—	19	1	no	—
186	C₂³×C₄	—	19	1	no	—
187	C₂³×C₄	—	19	1	no	—
188	C₂²×C₈	—	2	2	no	—
189	C₂²×C₈	—	19	1	no	—
190	C₂²×C₈	—	19	1	no	—
191	C₂²×C₈	—	38	2	no	—
192	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
193	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
194	C₂×C₄²	—	19	1	no	—
195	C₂×C₄²	—	19	1	no	—
196	C₂×C₄²	—	19	1	no	—
197	C₂×C₄²	—	38	1	no	—
198	C₂×C₄²	—	38	1	no	—
199	C₂×C₄²	—	38	1	no	—
200	C₂×C₄²	—	38	1	no	—
201	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
202	C₄⋊C₈	—	2	2	no	—
203	C₄⋊C₈	—	2	2	no	—
204	C₄⋊C₈	—	38	2	no	—
205	C₄⋊C₈	—	38	2	no	—
206	C₄⋊C₈	—	38	2	no	—
207	C₄⋊C₈	—	38	2	no	—
208	C₂²⋊C₈	—	38	2	no	—
209	C₂²⋊C₈	—	38	2	no	—
210	C₂²⋊C₈	—	76	4	no	—
211	C₄×C₈	—	38	1	no	—
212	C₄×C₈	—	38	1	no	—
213	C₄×C₈	D₇₆	1	2	yes	—
214	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
215	C₁₉	#8599	1	1	yes	characteristic, complemented, Sylow
216	C₂⁴	—	19	1	no	—
217	C₂²×C₄	—	19	1	no	—
218	C₂²×C₄	—	19	2	no	—
219	C₂²×C₄	—	19	2	no	—
220	C₂²×C₄	—	19	1	no	—
221	C₂²×C₄	—	19	1	no	—
222	C₂²×C₄	—	38	1	no	—
223	C₂²×C₄	—	38	1	no	—
224	C₂²×C₄	—	38	1	no	—
225	C₂²×C₄	—	38	1	no	—
226	C₂²×C₄	—	38	1	no	—
227	C₂²×C₄	—	38	1	no	—
228	C₂²×C₄	—	38	1	no	—
229	C₂²×C₄	—	38	2	no	—
230	C₂²×C₄	—	38	2	no	—
231	C₂²×C₄	—	38	1	no	—
232	C₂²×C₄	—	76	2	no	—
233	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
234	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
235	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
236	C₂×C₈	—	2	2	no	—
237	C₂×C₈	—	2	2	no	—
238	C₂×C₈	—	4	2	no	—
239	C₂×C₈	—	4	2	no	—
240	C₂×C₈	—	4	2	no	—
241	C₂×C₈	—	38	2	no	—
242	C₂×C₈	—	38	2	no	—
243	C₂×C₈	—	38	1	no	—
244	C₂×C₈	—	38	1	no	—
245	C₂×C₈	—	76	2	no	—
246	C₂×C₈	—	76	2	no	—
247	C₂×C₈	—	76	2	no	—
248	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
249	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
250	C₄²	—	38	1	no	—
251	C₄²	—	38	1	no	—
252	C₄²	—	38	1	no	—
253	C₄²	—	38	1	no	—
254	C₄²	—	38	1	no	—
255	C₄²	—	38	1	no	—
256	C₄²	C₂×D₇₆	1	1	yes	characteristic
257	C₄²	#64543	1	1	yes	characteristic
258	C₄²	#64545	1	1	yes	characteristic
259	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
260	C₂³	—	19	2	no	—
261	C₂³	—	38	2	no	—
262	C₂³	—	38	1	no	—
263	C₂³	—	38	2	no	—
264	C₂³	—	38	1	no	—
265	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
266	C₂×C₄	—	2	2	no	—
267	C₂×C₄	—	19	2	no	—
268	C₂×C₄	—	38	1	no	—
269	C₂×C₄	—	38	1	no	—
270	C₂×C₄	—	38	2	no	—
271	C₂×C₄	—	38	2	no	—
272	C₂×C₄	—	38	2	no	—
273	C₂×C₄	—	38	2	no	—
274	C₂×C₄	—	38	2	no	—
275	C₂×C₄	—	38	2	no	—
276	C₂×C₄	—	38	1	no	—
277	C₂×C₄	—	38	1	no	—
278	C₂×C₄	—	76	2	no	—
279	C₂×C₄	—	76	2	no	—
280	C₂×C₄	—	76	2	no	—
281	C₂×C₄	—	76	1	no	—
282	C₂×C₄	—	76	1	no	—
283	C₂×C₄	#10597338	1	1	yes	characteristic
284	C₂×C₄	#10597341	1	1	yes	characteristic
285	C₂×C₄	#10597343	1	1	yes	characteristic
286	C₂×C₄	#10597347	1	2	yes	—
287	C₂×C₄	#10597353	1	2	yes	—
288	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
289	C₂×C₄	#10597358	1	1	yes	characteristic
290	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
291	C₂×C₄	#10597365	1	1	yes	characteristic
292	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
293	C₂×C₄	#10597384	1	1	yes	characteristic
294	C₂×C₄	#10597392	1	1	yes	characteristic
295	C₈	—	2	2	no	—
296	C₈	—	2	2	no	—
297	C₈	—	8	2	no	—
298	C₈	—	76	1	no	—
299	C₈	—	76	1	no	—
300	C₈	—	152	2	no	—
301	C₂²	—	38	2	no	—
302	C₂²	—	38	4	no	—
303	C₂²	—	76	1	no	—
304	C₂²	—	76	1	no	—
305	C₂²	—	76	2	no	—
306	C₂²	#11926401	1	1	yes	characteristic
307	C₂²	#11926569	1	2	yes	—
308	C₂²	#107×D₁₉	1	1	yes	characteristic
309	C₂²	#11926581	1	1	yes	characteristic
310	C₂²	#11926591	1	2	yes	—
311	C₄	—	2	1	no	—
312	C₄	—	2	1	no	—
313	C₄	—	38	2	no	—
314	C₄	—	76	1	no	—
315	C₄	—	76	1	no	—
316	C₄	#11926510	1	1	yes	characteristic
317	C₄	#11926512	1	1	yes	characteristic
318	C₄	#11926604	1	2	yes	—
319	C₄	#11926777	1	1	yes	characteristic
320	C₄	#11926781	1	1	yes	characteristic
321	C₄	#11926782	1	1	yes	characteristic
322	C₄	#11926786	1	1	yes	characteristic
323	C₂	—	76	2	no	—
324	C₂	#14562408	1	2	yes	—
325	C₂	#14562414	1	2	yes	—
326	C₂	#14563616	1	1	yes	characteristic
327	C₂	#14563661	1	1	yes	characteristic
328	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×#335	C₂
socle	C₂³×C₁₉	C₂×C₄⋊C₄
prime radical	C₂³×D₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#335	D₁₉
hypocenter	C₁₉	#8599
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
3. C₂×#11926297	C₂	semidirect
4. #14561469	C₂	semidirect
5. C₂×C₁₉×#335	C₂	semidirect
140. C₂×#335	D₁₉	semidirect
215. C₁₉	#8599	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×#11926297	2
#14561469	2
C₂×C₁₉×#335	2
#8599	19