Subgroups — #18073240

Order 4864.

420 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572277	C₂	1	1	yes	maximal, characteristic
2	#14562018	C₂	1	1	yes	maximal, characteristic
3	#14562018	C₂	1	1	yes	maximal, characteristic
4	#14561918	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561472	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561472	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#64541	C₂²	1	1	yes	characteristic
9	#11926603	—	2	2	no	—
10	#11926597	C₂²	1	1	yes	characteristic
11	#11926597	C₂²	1	1	yes	characteristic
12	#11926595	—	2	1	no	—
13	#11926595	—	2	1	no	—
14	#11926570	C₄	1	2	yes	—
15	#11926510	C₄	1	2	yes	—
16	C₄×#64520	C₂²	1	1	yes	characteristic
17	#11926276	C₄	1	2	yes	—
18	#11926276	C₄	1	2	yes	—
19	#11926273	C₄	1	2	yes	—
20	#11926273	C₄	1	2	yes	—
21	#11926265	—	2	1	no	—
22	C₈×C₁₉⋊C₈	—	2	1	no	—
23	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#322	—	2	2	no	—
27	C₂×#64541	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₉	—	2	1	no	—
29	C₂²×C₈×C₁₉	—	2	1	no	—
30	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₄×C₂²⋊D₁₉	—	2	1	no	—
33	C₄×C₂²⋊D₁₉	—	2	1	no	—
34	#10597372	C₂×C₄	1	1	yes	characteristic
35	C₂×#64520	C₂×C₄	1	2	yes	—
36	C₄×D₇₆	C₂×C₄	1	1	yes	characteristic
37	C₄×D₇₆	C₂×C₄	1	1	yes	characteristic
38	#10597318	—	2	1	no	—
39	C₄²×D₁₉	—	2	1	no	—
40	C₄×Dic₃₈	C₂×C₄	1	1	yes	characteristic
41	C₄×Dic₃₈	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₁₉	—	2	1	no	—
43	C₄×C₈×C₁₉	—	2	1	no	—
44	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
45	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
46	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
47	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
48	C₄×C₈×C₁₉	D₄	1	2	yes	—
49	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
50	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
51	(C₂×D₁₉)⋊C₈	—	2	2	no	—
52	(C₂×D₁₉)⋊C₈	—	2	2	no	—
53	Dic₁₉⋊C₈	—	2	2	no	—
54	Dic₁₉⋊C₈	—	2	2	no	—
55	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
56	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
57	#10597260	—	2	1	no	—
58	C₄×C₁₉⋊C₈	—	2	1	no	—
59	C₄×C₁₉⋊C₈	—	2	1	no	—
60	C₄×C₁₉⋊C₈	—	2	1	no	—
61	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
64	C₂×C₂²⋊D₁₉	—	2	1	no	—
65	#64541	—	2	4	no	—
66	C₂×D₇₆	C₄²	1	1	yes	characteristic
67	C₂×C₄×D₁₉	—	2	1	no	—
68	C₂×C₄×D₁₉	—	2	1	no	—
69	C₂×C₄×D₁₉	—	2	1	no	—
70	C₂×Dic₃₈	C₄²	1	1	yes	characteristic
71	C₂×C₈×C₁₉	—	2	4	no	—
72	C₂×C₈×C₁₉	—	2	2	no	—
73	C₂×C₈×C₁₉	—	2	4	no	—
74	C₂×C₈×C₁₉	—	2	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	C₂²×C₄	1	1	yes	characteristic
79	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂²⋊Dic₁₉	—	2	1	no	—
83	(C₂×D₁₉)⋊C₄	—	2	1	no	—
84	(C₂×D₁₉)⋊C₄	—	2	1	no	—
85	C₄⋊Dic₁₉	C₄²	1	1	yes	characteristic
86	C₄⋊Dic₁₉	C₄²	1	1	yes	characteristic
87	Dic₁₉⋊C₄	—	2	1	no	—
88	Dic₁₉⋊C₄	—	2	1	no	—
89	C₄×Dic₁₉	—	2	1	no	—
90	C₄×Dic₁₉	—	2	1	no	—
91	C₄×Dic₁₉	—	2	1	no	—
92	#64520	—	2	4	no	—
93	C₂×C₁₉⋊C₈	—	2	2	no	—
94	C₂×C₁₉⋊C₈	—	2	2	no	—
95	C₂×C₁₉⋊C₈	—	2	2	no	—
96	#8189	—	19	1	no	maximal, Sylow
97	C₂³×C₁₉	#117	1	1	yes	characteristic
98	C₂²×D₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	2	2	no	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
102	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
104	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
105	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
106	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#131	1	4	yes	—
108	C₂²⋊D₁₉	—	4	2	no	—
109	C₂×Dic₁₉	—	2	1	no	—
110	C₂×Dic₁₉	—	2	1	no	—
111	C₂×Dic₁₉	—	2	1	no	—
112	D₇₆	—	2	2	no	—
113	C₄×D₁₉	—	4	2	no	—
114	C₄×D₁₉	—	4	2	no	—
115	C₄×D₁₉	—	4	2	no	—
116	Dic₃₈	—	2	2	no	—
117	C₈×C₁₉	—	2	4	no	—
118	C₈×C₁₉	—	2	2	no	—
119	C₈×C₁₉	—	2	2	no	—
120	C₈×C₁₉	—	4	2	no	—
121	C₁₉⋊C₈	—	4	2	no	—
122	C₁₉⋊C₈	—	4	2	no	—
123	C₁₉⋊C₈	—	4	2	no	—
124	#2922	—	19	1	no	—
125	#1476	—	19	1	no	—
126	#1476	—	19	1	no	—
127	#1450	—	19	1	no	—
128	C₂×#322	D₁₉	1	1	yes	characteristic, complemented
129	#1278	—	19	1	no	—
130	#1278	—	19	1	no	—
131	C₂²×C₁₉	—	2	1	no	—
132	C₂²×C₁₉	—	2	1	no	—
133	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×C₁₉	#433	1	2	yes	—
135	C₂×D₁₉	—	4	1	no	—
136	C₂×D₁₉	—	4	1	no	—
137	C₂×D₁₉	—	4	1	no	—
138	C₄×C₁₉	—	2	1	no	—
139	C₄×C₁₉	—	2	1	no	—
140	C₄×C₁₉	#405	1	2	yes	—
141	C₄×C₁₉	#408	1	2	yes	—
142	C₄×C₁₉	#443	1	2	yes	—
143	C₄×C₁₉	#444	1	2	yes	—
144	Dic₁₉	—	4	1	no	—
145	Dic₁₉	—	4	1	no	—
146	Dic₁₉	—	4	1	no	—
147	C₄×#41	—	19	1	no	—
148	#433	—	38	2	no	—
149	#431	—	19	1	no	—
150	#431	—	19	1	no	—
151	#431	—	38	1	no	—
152	#431	—	38	1	no	—
153	#424	—	19	2	no	—
154	#408	—	19	2	no	—
155	C₄×M₁₆	—	19	1	no	—
156	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
157	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
158	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
159	Q₈⋊C₈	—	19	2	no	—
160	Q₈⋊C₈	—	19	2	no	—
161	D₄⋊C₈	—	19	2	no	—
162	D₄⋊C₈	—	19	2	no	—
163	#322	—	2	2	no	—
164	#322	—	38	1	no	—
165	C₈²	—	38	1	no	—
166	C₂×C₁₉	—	2	2	no	—
167	C₂×C₁₉	#1750	1	1	yes	characteristic
168	C₂×C₁₉	#1764	1	1	yes	characteristic
169	C₂×C₁₉	#1765	1	1	yes	characteristic
170	D₁₉	—	8	1	no	—
171	C₂×#41	—	19	1	no	—
172	C₂×M₁₆	—	19	2	no	—
173	C₂²×C₈	—	2	1	no	—
174	C₂²×C₈	—	2	1	no	—
175	C₂²×C₈	C₄×D₁₉	1	2	yes	—
176	C₄×Q₈	—	19	1	no	—
177	C₄×Q₈	—	19	1	no	—
178	C₄×D₄	—	19	1	no	—
179	C₄×D₄	—	19	1	no	—
180	C₄×D₄	—	38	1	no	—
181	C₄×D₄	—	38	1	no	—
182	#117	—	19	1	no	—
183	#117	—	38	1	no	—
184	C₂×C₄²	—	38	1	no	—
185	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
186	C₄⋊C₈	—	19	2	no	—
187	C₄⋊C₈	—	19	2	no	—
188	C₄⋊C₈	—	38	2	no	—
189	C₄⋊C₈	—	38	2	no	—
190	C₂²⋊C₈	—	38	1	no	—
191	C₂²⋊C₈	—	38	1	no	—
192	C₂²⋊C₈	—	38	2	no	—
193	C₂²⋊C₈	—	38	2	no	—
194	#97	—	38	1	no	—
195	C₄×C₈	—	2	1	no	—
196	C₄×C₈	—	2	1	no	—
197	C₄×C₈	—	38	1	no	—
198	C₄×C₈	—	38	1	no	—
199	C₄×C₈	—	38	1	no	—
200	C₄×C₈	C₄×D₁₉	1	2	yes	—
201	C₄×C₈	C₄×D₁₉	1	2	yes	—
202	C₄×C₈	D₇₆	1	1	yes	characteristic
203	C₄×C₈	D₇₆	1	1	yes	characteristic
204	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
205	C₁₉	#8189	1	1	yes	characteristic, complemented, Sylow
206	#41	—	38	4	no	—
207	C₂×Q₈	—	19	1	no	—
208	C₂×D₄	—	19	1	no	—
209	C₂×D₄	—	38	1	no	—
210	C₂²×C₄	—	38	1	no	—
211	C₂²×C₄	—	38	1	no	—
212	C₂²×C₄	—	38	1	no	—
213	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
214	C₂²×C₄	#64541	1	1	yes	characteristic
215	C₂²×C₄	#64541	1	1	yes	characteristic
216	M₁₆	—	38	4	no	—
217	C₂×C₈	—	2	4	no	—
218	C₂×C₈	—	2	4	no	—
219	C₂×C₈	—	2	2	no	—
220	C₂×C₈	—	2	2	no	—
221	C₂×C₈	—	4	2	no	—
222	C₂×C₈	—	38	2	no	—
223	C₂×C₈	—	38	2	no	—
224	C₂×C₈	—	38	2	no	—
225	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
226	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
227	C₄⋊C₄	—	19	1	no	—
228	C₄⋊C₄	—	19	1	no	—
229	C₄⋊C₄	—	38	1	no	—
230	C₄⋊C₄	—	38	1	no	—
231	C₂²⋊C₄	—	38	1	no	—
232	C₂²⋊C₄	—	38	1	no	—
233	C₂²⋊C₄	—	38	1	no	—
234	C₄²	—	38	1	no	—
235	C₄²	—	38	1	no	—
236	C₄²	—	38	1	no	—
237	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
238	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
239	C₄²	C₂×D₇₆	1	1	yes	characteristic
240	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
241	C₂³	—	38	1	no	—
242	C₂³	#10597318	1	1	yes	characteristic
243	Q₈	—	38	2	no	—
244	D₄	—	38	2	no	—
245	D₄	—	76	2	no	—
246	C₂×C₄	—	2	2	no	—
247	C₂×C₄	—	2	2	no	—
248	C₂×C₄	—	38	1	no	—
249	C₂×C₄	—	38	1	no	—
250	C₂×C₄	—	38	1	no	—
251	C₂×C₄	—	76	2	no	—
252	C₂×C₄	—	76	2	no	—
253	C₂×C₄	—	76	2	no	—
254	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
255	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
256	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
257	C₂×C₄	#10597353	1	4	yes	—
258	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
259	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
260	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
261	C₈	—	2	4	no	—
262	C₈	—	2	2	no	—
263	C₈	—	2	2	no	—
264	C₈	—	4	2	no	—
265	C₈	—	76	2	no	—
266	C₈	—	76	2	no	—
267	C₈	—	76	2	no	—
268	C₂²	—	2	1	no	—
269	C₂²	—	2	1	no	—
270	C₂²	—	76	1	no	—
271	C₂²	—	76	1	no	—
272	C₂²	—	76	1	no	—
273	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
274	C₂²	#11926606	1	2	yes	—
275	C₄	—	2	1	no	—
276	C₄	—	2	1	no	—
277	C₄	—	76	1	no	—
278	C₄	—	76	1	no	—
279	C₄	—	76	1	no	—
280	C₄	#11926501	1	2	yes	—
281	C₄	#11926512	1	2	yes	—
282	C₄	#11926662	1	2	yes	—
283	C₄	#11926667	1	2	yes	—
284	C₂	—	2	2	no	—
285	C₂	—	152	1	no	—
286	C₂	#14563404	1	1	yes	characteristic
287	C₂	#14563472	1	1	yes	characteristic
288	C₂	#14563479	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#322	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₂×#64541	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#8189
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ C₂×#322

Complements

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

N	H ≅ G/N	type
4. #14561918	C₂	semidirect
5. #14561472	C₂	semidirect
6. #14561472	C₂	semidirect
7. C₂×C₁₉×#322	C₂	semidirect
128. C₂×#322	D₁₉	semidirect
205. C₁₉	#8189	semidirect

Maximal subgroups

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

subgroup	index
#14572277	2
#14562018	2
#14561918	2
#14561472	2
C₂×C₁₉×#322	2
#8189	19