Subgroups — #18073222

Order 4864.

498 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597353	C₂	1	1	yes	maximal, characteristic
2	#14562018	C₂	1	1	yes	maximal, characteristic
3	#14562015	C₂	1	1	yes	maximal, characteristic
4	#14561928	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926266	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561473	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1278	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597353	C₄	1	2	yes	—
9	C₄×#64541	C₂²	1	1	yes	characteristic
10	#11926597	C₂²	1	1	yes	characteristic
11	#11926502	C₄	1	2	yes	—
12	#11926501	—	2	2	no	—
13	C₄×#64515	—	2	1	no	—
14	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₈×D₁₉	—	2	1	no	—
17	#11926276	C₄	1	2	yes	—
18	#11926274	C₄	1	2	yes	—
19	#11926273	C₄	1	2	yes	—
20	#11926271	C₄	1	2	yes	—
21	#11926266	—	2	2	no	—
22	#11926266	—	2	1	no	—
23	#11926265	—	2	1	no	—
24	C₁₉×#431	C₂²	1	1	yes	characteristic
25	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×#64541	C₂×C₄	1	1	yes	characteristic
28	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₉	—	2	1	no	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₄×C₂²⋊D₁₉	—	2	1	no	—
32	C₄×C₂²⋊D₁₉	—	2	1	no	—
33	#10597372	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₁₉⋊C₈	—	2	1	no	—
35	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
36	#10597353	—	2	4	no	—
37	#10597353	—	2	4	no	—
38	C₂×#64515	—	2	2	no	—
39	C₂×C₈×D₁₉	—	2	2	no	—
40	C₄×D₇₆	C₂×C₄	1	1	yes	characteristic
41	C₄×D₇₆	C₂×C₄	1	1	yes	characteristic
42	#10597318	—	2	1	no	—
43	C₄²×D₁₉	—	2	1	no	—
44	C₄×Dic₃₈	C₂×C₄	1	1	yes	characteristic
45	C₄×Dic₃₈	C₂×C₄	1	1	yes	characteristic
46	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
47	C₁₉×C₂²⋊C₈	—	2	1	no	—
48	C₁₉×#97	—	2	1	no	—
49	C₄×C₈×C₁₉	—	2	1	no	—
50	C₄×C₈×C₁₉	—	2	1	no	—
51	C₄×C₈×C₁₉	—	2	1	no	—
52	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
53	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
54	#10597272	—	2	2	no	—
55	C₈×Dic₁₉	—	2	2	no	—
56	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
57	C₄×C₁₉⋊C₈	—	2	1	no	—
58	C₄×C₁₉⋊C₈	—	2	1	no	—
59	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
60	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
61	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
62	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
63	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
66	C₂×C₂²⋊D₁₉	—	2	1	no	—
67	#64541	—	2	2	no	—
68	#64541	M₁₆	1	4	yes	—
69	C₂×D₇₆	C₄²	1	1	yes	characteristic
70	C₂×C₄×D₁₉	—	2	1	no	—
71	C₂×C₄×D₁₉	—	2	1	no	—
72	C₂×C₄×D₁₉	—	2	1	no	—
73	C₂×Dic₃₈	C₄²	1	1	yes	characteristic
74	M₁₆×C₁₉	—	2	2	no	—
75	M₁₆×C₁₉	M₁₆	1	4	yes	—
76	C₂×C₈×C₁₉	—	2	2	no	—
77	C₂×C₈×C₁₉	—	2	2	no	—
78	C₂×C₈×C₁₉	—	2	2	no	—
79	C₂×C₈×C₁₉	—	4	2	no	—
80	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
82	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂²⋊Dic₁₉	—	2	1	no	—
85	(C₂×D₁₉)⋊C₄	—	2	1	no	—
86	(C₂×D₁₉)⋊C₄	—	2	1	no	—
87	C₄⋊Dic₁₉	C₄²	1	1	yes	characteristic
88	C₄⋊Dic₁₉	C₄²	1	1	yes	characteristic
89	Dic₁₉⋊C₄	—	2	1	no	—
90	Dic₁₉⋊C₄	—	2	1	no	—
91	C₄×Dic₁₉	—	2	1	no	—
92	C₄×Dic₁₉	—	2	1	no	—
93	C₄×Dic₁₉	—	2	1	no	—
94	C₂×C₁₉⋊C₈	—	2	4	no	—
95	C₂×C₁₉⋊C₈	—	2	2	no	—
96	C₂×C₁₉⋊C₈	—	2	2	no	—
97	C₂×C₁₉⋊C₈	—	2	2	no	—
98	C₂×C₁₉⋊C₈	—	2	2	no	—
99	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
100	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
101	#64515	—	2	8	no	—
102	C₈×D₁₉	—	2	8	no	—
103	#8186	—	19	1	no	maximal, Sylow
104	C₂³×C₁₉	#117	1	1	yes	characteristic
105	C₂²×D₁₉	—	2	1	no	—
106	C₂×C₄×C₁₉	—	2	2	no	—
107	C₂×C₄×C₁₉	—	2	2	no	—
108	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
109	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
111	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
112	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
114	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
115	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
116	C₂²⋊D₁₉	—	2	4	no	—
117	C₂×Dic₁₉	—	2	1	no	—
118	C₂×Dic₁₉	—	2	1	no	—
119	C₂×Dic₁₉	—	2	1	no	—
120	D₇₆	—	2	1	no	—
121	D₇₆	#97	1	2	yes	—
122	C₄×D₁₉	—	2	4	no	—
123	C₄×D₁₉	—	4	2	no	—
124	C₄×D₁₉	—	4	2	no	—
125	Dic₃₈	—	2	1	no	—
126	Dic₃₈	#97	1	2	yes	—
127	C₈×C₁₉	—	2	4	no	—
128	C₈×C₁₉	—	4	2	no	—
129	C₈×C₁₉	—	4	2	no	—
130	C₁₉⋊C₈	—	2	4	no	—
131	C₁₉⋊C₈	—	2	2	no	—
132	C₁₉⋊C₈	—	2	2	no	—
133	C₁₉⋊C₈	—	4	2	no	—
134	C₄×#131	—	19	1	no	—
135	#1476	—	19	1	no	—
136	#1476	—	19	1	no	—
137	#1452	—	19	1	no	—
138	C₂×#322	—	19	1	no	—
139	#1278	—	19	1	no	—
140	#1278	D₁₉	1	1	yes	characteristic, complemented
141	C₂²×C₁₉	—	2	1	no	—
142	C₂²×C₁₉	—	2	1	no	—
143	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×C₁₉	#432	1	2	yes	—
145	C₂×D₁₉	—	2	2	no	—
146	C₂×D₁₉	—	4	1	no	—
147	C₂×D₁₉	—	4	1	no	—
148	C₄×C₁₉	—	2	1	no	—
149	C₄×C₁₉	—	2	1	no	—
150	C₄×C₁₉	C₂×#97	1	1	yes	characteristic
151	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
152	C₄×C₁₉	#407	1	2	yes	—
153	C₄×C₁₉	#443	1	2	yes	—
154	C₄×C₁₉	#444	1	2	yes	—
155	Dic₁₉	—	2	2	no	—
156	Dic₁₉	—	4	1	no	—
157	Dic₁₉	—	4	1	no	—
158	C₂×#131	—	19	2	no	—
159	C₄×#41	—	19	1	no	—
160	#431	—	19	1	no	—
161	#431	C₂×D₁₉	1	1	yes	characteristic
162	#405	—	19	2	no	—
163	#405	—	38	2	no	—
164	C₄×M₁₆	—	38	1	no	—
165	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
166	C₂×C₄×C₈	—	19	1	no	—
167	C₂×C₄×C₈	—	19	1	no	—
168	C₂×C₄×C₈	—	38	1	no	—
169	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
170	Q₈⋊C₈	—	19	2	no	—
171	Q₈⋊C₈	—	19	2	no	—
172	D₄⋊C₈	—	19	2	no	—
173	D₄⋊C₈	—	19	2	no	—
174	#322	—	38	2	no	—
175	#322	—	38	1	no	—
176	#322	—	38	1	no	—
177	C₂×C₁₉	—	2	2	no	—
178	C₂×C₁₉	#1749	1	1	yes	characteristic
179	C₂×C₁₉	#1764	1	1	yes	characteristic
180	C₂×C₁₉	#1765	1	1	yes	characteristic
181	D₁₉	—	4	2	no	—
182	C₂×#41	—	19	1	no	—
183	#131	—	38	4	no	—
184	#131	—	38	4	no	—
185	C₂×M₁₆	—	38	2	no	—
186	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
187	C₂²×C₈	—	2	1	no	—
188	C₂²×C₈	—	19	2	no	—
189	C₂²×C₈	—	38	2	no	—
190	C₂²×C₈	—	38	1	no	—
191	C₄×Q₈	—	19	1	no	—
192	C₄×Q₈	—	19	1	no	—
193	C₄×D₄	—	19	1	no	—
194	C₄×D₄	—	19	1	no	—
195	C₄×D₄	—	38	1	no	—
196	C₄×D₄	—	38	1	no	—
197	#117	—	19	1	no	—
198	#117	—	38	1	no	—
199	C₂×C₄²	—	38	1	no	—
200	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
201	C₄⋊C₈	—	19	2	no	—
202	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
203	C₂²⋊C₈	—	2	1	no	—
204	C₂²⋊C₈	—	38	1	no	—
205	#97	—	2	1	no	—
206	#97	—	38	2	no	—
207	C₄×C₈	—	2	1	no	—
208	C₄×C₈	—	2	1	no	—
209	C₄×C₈	—	2	1	no	—
210	C₄×C₈	—	19	2	no	—
211	C₄×C₈	—	19	2	no	—
212	C₄×C₈	—	19	1	no	—
213	C₄×C₈	—	19	1	no	—
214	C₄×C₈	—	38	2	no	—
215	C₄×C₈	—	38	1	no	—
216	C₄×C₈	—	38	1	no	—
217	C₄×C₈	C₄×D₁₉	1	2	yes	—
218	C₁₉	#8186	1	1	yes	characteristic, complemented, Sylow
219	#41	—	19	4	no	—
220	#41	—	38	2	no	—
221	C₂×Q₈	—	19	1	no	—
222	C₂×D₄	—	19	1	no	—
223	C₂×D₄	—	38	1	no	—
224	C₂²×C₄	—	38	1	no	—
225	C₂²×C₄	—	38	1	no	—
226	C₂²×C₄	—	38	1	no	—
227	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
228	C₂²×C₄	#64543	1	1	yes	characteristic
229	C₂²×C₄	#64545	1	1	yes	characteristic
230	M₁₆	—	2	2	no	—
231	M₁₆	—	38	8	no	—
232	M₁₆	#64515	1	4	yes	—
233	C₂×C₈	—	2	2	no	—
234	C₂×C₈	—	2	2	no	—
235	C₂×C₈	—	2	2	no	—
236	C₂×C₈	—	4	2	no	—
237	C₂×C₈	—	19	2	no	—
238	C₂×C₈	—	19	2	no	—
239	C₂×C₈	—	38	8	no	—
240	C₂×C₈	—	38	4	no	—
241	C₂×C₈	—	38	2	no	—
242	C₂×C₈	—	38	2	no	—
243	C₂×C₈	—	38	2	no	—
244	C₂×C₈	—	38	2	no	—
245	C₄⋊C₄	—	19	1	no	—
246	C₄⋊C₄	—	19	1	no	—
247	C₄⋊C₄	—	38	1	no	—
248	C₄⋊C₄	—	38	1	no	—
249	C₂²⋊C₄	—	38	1	no	—
250	C₂²⋊C₄	—	38	1	no	—
251	C₂²⋊C₄	—	38	1	no	—
252	C₄²	—	38	1	no	—
253	C₄²	—	38	1	no	—
254	C₄²	—	38	1	no	—
255	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
256	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
257	C₄²	D₄×D₁₉	1	1	yes	characteristic
258	C₄²	D₄×D₁₉	1	1	yes	characteristic
259	C₂³	—	38	1	no	—
260	C₂³	#10597338	1	1	yes	characteristic
261	Q₈	—	19	2	no	—
262	Q₈	—	38	1	no	—
263	D₄	—	19	2	no	—
264	D₄	—	38	4	no	—
265	D₄	—	38	1	no	—
266	C₂×C₄	—	2	2	no	—
267	C₂×C₄	—	2	2	no	—
268	C₂×C₄	—	38	1	no	—
269	C₂×C₄	—	38	4	no	—
270	C₂×C₄	—	38	1	no	—
271	C₂×C₄	—	38	1	no	—
272	C₂×C₄	—	76	2	no	—
273	C₂×C₄	—	76	2	no	—
274	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
275	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
276	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
277	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
278	C₂×C₄	#10597339	1	1	yes	characteristic
279	C₂×C₄	#10597339	1	1	yes	characteristic
280	C₂×C₄	C₂×#64515	1	2	yes	—
281	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
282	C₈	—	2	4	no	—
283	C₈	—	4	2	no	—
284	C₈	—	4	2	no	—
285	C₈	—	38	4	no	—
286	C₈	—	38	2	no	—
287	C₈	—	38	2	no	—
288	C₈	—	76	2	no	—
289	C₂²	—	2	1	no	—
290	C₂²	—	2	1	no	—
291	C₂²	—	38	2	no	—
292	C₂²	—	76	1	no	—
293	C₂²	—	76	1	no	—
294	C₂²	#11926391	1	1	yes	characteristic
295	C₂²	#11926600	1	2	yes	—
296	C₄	—	2	1	no	—
297	C₄	—	2	1	no	—
298	C₄	—	38	2	no	—
299	C₄	—	76	1	no	—
300	C₄	—	76	1	no	—
301	C₄	#97×D₁₉	1	1	yes	characteristic
302	C₄	C₄×#64515	1	1	yes	characteristic
303	C₄	#11926506	1	2	yes	—
304	C₄	#11926660	1	2	yes	—
305	C₄	#11926663	1	2	yes	—
306	C₂	—	2	2	no	—
307	C₂	—	76	2	no	—
308	C₂	#14563396	1	1	yes	characteristic
309	C₂	#14563471	1	1	yes	characteristic
310	C₂	#14563476	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1278	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₂×#64541	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1278	D₁₉
hypocenter	C₁₉	#8186
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ #1278

Complements

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

N	H ≅ G/N	type
4. #14561928	C₂	semidirect
5. C₂×#11926266	C₂	semidirect
6. #14561473	C₂	semidirect
7. C₁₉×#1278	C₂	semidirect
140. #1278	D₁₉	semidirect
218. C₁₉	#8186	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10597353	2
#14562018	2
#14562015	2
#14561928	2
C₂×#11926266	2
#14561473	2
C₁₉×#1278	2
#8186	19