Subgroups — #18073474

Order 4864.

488 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563384	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597260	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926286	C₂	1	2	yes	maximal
4	#14561516	C₂	1	2	yes	maximal
5	C₄×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597260	—	2	1	no	—
7	C₂×#10597260	C₂²	1	2	yes	—
8	C₂×#10597260	C₂²	1	2	yes	—
9	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
10	#11926299	—	2	1	no	—
11	#11926299	—	2	1	no	—
12	#11926286	C₄	1	8	yes	complemented
13	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
14	C₁₉×#389	C₄	1	1	yes	characteristic
15	C₁₉×#389	C₄	1	1	yes	characteristic
16	C₁₉×#387	—	2	1	no	—
17	C₁₉×#387	—	2	1	no	—
18	C₁₉×#382	C₂²	1	1	yes	characteristic
19	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
20	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
21	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
23	C₄³×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#125	—	2	2	no	—
25	C₁₉×#125	C₂×C₄	1	4	yes	—
26	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	—	2	1	no	—
35	C₂×C₄²×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×C₁₉⋊C₈	—	2	2	no	—
44	C₂²×C₁₉⋊C₈	—	2	2	no	—
45	C₁₉×#95	—	2	1	no	—
46	C₁₉×#95	—	2	1	no	—
47	C₁₉×#95	—	2	1	no	—
48	C₁₉×#95	—	2	1	no	—
49	C₁₉×#95	—	2	1	no	—
50	C₁₉×#95	—	2	1	no	—
51	#10597260	—	2	4	no	—
52	#10597260	—	2	2	no	—
53	#10597260	—	2	2	no	—
54	#10597260	C₂×C₄	1	4	yes	—
55	#10597260	C₂×C₄	1	4	yes	—
56	C₄×C₁₉⋊C₈	—	2	4	no	—
57	C₂²×C₄×C₁₉	—	2	1	no	—
58	C₂²×C₄×C₁₉	—	2	1	no	—
59	C₂²×C₄×C₁₉	—	2	1	no	—
60	C₂²×C₄×C₁₉	—	2	1	no	—
61	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₄⋊C₄×C₁₉	—	2	4	no	—
71	C₄⋊C₄×C₁₉	—	2	4	no	—
72	C₄⋊C₄×C₁₉	—	4	1	no	—
73	C₄⋊C₄×C₁₉	—	4	1	no	—
74	C₄⋊C₄×C₁₉	—	4	2	no	—
75	C₄⋊C₄×C₁₉	—	4	2	no	—
76	C₄⋊C₄×C₁₉	C₄²	1	2	yes	—
77	C₄⋊C₄×C₁₉	C₄²	1	2	yes	—
78	C₄²×C₁₉	—	2	2	no	—
79	C₄²×C₁₉	—	2	2	no	—
80	C₄²×C₁₉	—	2	2	no	—
81	C₄²×C₁₉	—	4	1	no	—
82	C₄²×C₁₉	—	4	1	no	—
83	C₄²×C₁₉	—	4	1	no	—
84	C₄²×C₁₉	—	4	2	no	—
85	C₄²×C₁₉	—	4	2	no	—
86	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
87	C₄²×C₁₉	#41	1	2	yes	—
88	C₂×C₁₉⋊C₈	—	2	4	no	—
89	C₂×C₁₉⋊C₈	—	2	4	no	—
90	C₂×C₁₉⋊C₈	—	2	4	no	—
91	C₂×C₁₉⋊C₈	—	2	4	no	—
92	C₂×C₁₉⋊C₈	—	4	2	no	—
93	C₂×C₁₉⋊C₈	—	4	2	no	—
94	#8227	—	19	1	no	maximal, Sylow
95	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	1	no	—
100	C₂×C₄×C₁₉	—	2	1	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	—	2	1	no	—
105	C₂×C₄×C₁₉	—	2	1	no	—
106	C₂×C₄×C₁₉	—	2	1	no	—
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	2	2	no	—
109	C₂×C₄×C₁₉	—	2	2	no	—
110	C₂×C₄×C₁₉	—	2	1	no	—
111	C₂×C₄×C₁₉	—	2	1	no	—
112	C₂×C₄×C₁₉	—	2	1	no	—
113	C₂×C₄×C₁₉	—	4	1	no	—
114	C₂×C₄×C₁₉	—	4	1	no	—
115	C₂×C₄×C₁₉	—	4	1	no	—
116	C₂×C₄×C₁₉	—	4	1	no	—
117	C₂×C₄×C₁₉	—	4	1	no	—
118	C₂×C₄×C₁₉	—	4	1	no	—
119	C₂×C₄×C₁₉	—	4	1	no	—
120	C₂×C₄×C₁₉	—	4	1	no	—
121	C₂×C₄×C₁₉	—	4	1	no	—
122	C₂×C₄×C₁₉	—	4	1	no	—
123	C₂×C₄×C₁₉	#101	1	2	yes	—
124	C₂×C₄×C₁₉	#104	1	2	yes	—
125	C₂×C₄×C₁₉	#104	1	2	yes	—
126	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
127	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
128	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
129	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
130	C₁₉⋊C₈	—	2	8	no	—
131	C₁₉⋊C₈	—	4	4	no	—
132	C₄×#125	D₁₉	1	1	yes	characteristic
133	#1745	—	19	1	no	—
134	C₄×#97	—	19	1	no	—
135	C₂×#330	—	19	2	no	—
136	#1295	—	19	2	no	—
137	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
139	C₂²×C₁₉	#413	1	1	yes	characteristic
140	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
141	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
142	C₂²×C₁₉	#421	1	1	yes	characteristic
143	C₂²×C₁₉	#421	1	1	yes	characteristic
144	C₄×C₁₉	—	2	1	no	—
145	C₄×C₁₉	—	2	1	no	—
146	C₄×C₁₉	—	2	2	no	—
147	C₄×C₁₉	—	2	2	no	—
148	C₄×C₁₉	—	2	2	no	—
149	C₄×C₁₉	—	2	2	no	—
150	C₄×C₁₉	—	2	2	no	—
151	C₄×C₁₉	—	4	2	no	—
152	C₄×C₁₉	—	4	2	no	—
153	C₄×C₁₉	—	4	1	no	—
154	C₄×C₁₉	—	8	1	no	—
155	C₄×C₁₉	—	8	1	no	—
156	C₂×#125	C₂×D₁₉	1	1	yes	characteristic
157	C₂×#97	—	19	2	no	—
158	C₂×#97	—	19	2	no	—
159	C₂×#97	—	38	1	no	—
160	C₂×C₄×C₈	—	38	1	no	—
161	#389	Dic₁₉	1	1	yes	characteristic
162	#389	Dic₁₉	1	1	yes	characteristic
163	#387	—	2	1	no	—
164	#387	—	2	1	no	—
165	#382	C₂×D₁₉	1	1	yes	characteristic
166	C₄×C₄⋊C₄	—	2	1	no	—
167	C₄×C₄⋊C₄	—	2	1	no	—
168	C₄×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
169	C₄×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
170	C₄³	C₂×D₁₉	1	1	yes	characteristic
171	#336	—	38	1	no	—
172	#336	—	38	1	no	—
173	#330	—	19	8	no	—
174	C₂×C₁₉	#1528	1	1	yes	characteristic
175	C₂×C₁₉	#1529	1	1	yes	characteristic
176	C₂×C₁₉	#1531	1	1	yes	characteristic
177	C₂×C₁₉	#1532	1	1	yes	characteristic
178	C₂×C₁₉	C₄×#101	1	1	yes	characteristic
179	C₂×C₁₉	C₄×#104	1	1	yes	characteristic
180	C₂×C₁₉	#1759	1	1	yes	characteristic
181	C₂²×C₈	—	38	2	no	—
182	C₂²×C₈	—	38	2	no	—
183	#125	—	2	2	no	—
184	#125	C₄×D₁₉	1	4	yes	—
185	C₂×C₄⋊C₄	—	2	1	no	—
186	C₂×C₄⋊C₄	—	2	1	no	—
187	C₂×C₄⋊C₄	—	2	1	no	—
188	C₂×C₄⋊C₄	—	2	1	no	—
189	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
190	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
191	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
192	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
193	C₂×C₄²	—	2	1	no	—
194	C₂×C₄²	—	2	1	no	—
195	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
196	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
197	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
198	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
199	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
200	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
201	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
202	#97	—	19	4	no	—
203	#97	—	19	4	no	—
204	#97	—	38	4	no	—
205	#97	—	38	2	no	—
206	#97	—	38	2	no	—
207	C₄×C₈	—	38	4	no	—
208	#95	—	2	1	no	—
209	#95	—	2	1	no	—
210	#95	—	2	1	no	—
211	#95	—	2	1	no	—
212	#95	—	2	1	no	—
213	#95	—	2	1	no	—
214	C₁₉	#8227	1	1	yes	characteristic, complemented, Sylow
215	C₂²×C₄	—	2	1	no	—
216	C₂²×C₄	—	2	1	no	—
217	C₂²×C₄	—	2	1	no	—
218	C₂²×C₄	—	2	1	no	—
219	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
220	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
221	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
222	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
223	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
224	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
225	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
226	C₂×C₈	—	38	4	no	—
227	C₂×C₈	—	38	4	no	—
228	C₂×C₈	—	38	4	no	—
229	C₂×C₈	—	38	4	no	—
230	C₂×C₈	—	76	2	no	—
231	C₂×C₈	—	76	2	no	—
232	C₄⋊C₄	—	2	1	no	—
233	C₄⋊C₄	—	2	1	no	—
234	C₄⋊C₄	—	2	4	no	—
235	C₄⋊C₄	—	2	4	no	—
236	C₄⋊C₄	—	4	1	no	—
237	C₄⋊C₄	—	4	1	no	—
238	C₄⋊C₄	—	4	2	no	—
239	C₄⋊C₄	—	4	2	no	—
240	C₄⋊C₄	C₄×Dic₁₉	1	2	yes	—
241	C₄⋊C₄	C₄×Dic₁₉	1	2	yes	—
242	C₄²	—	2	2	no	—
243	C₄²	—	2	2	no	—
244	C₄²	—	2	2	no	—
245	C₄²	—	4	1	no	—
246	C₄²	—	4	1	no	—
247	C₄²	—	4	1	no	—
248	C₄²	—	4	2	no	—
249	C₄²	—	4	2	no	—
250	C₄²	C₂×C₄×D₁₉	1	2	yes	—
251	C₄²	#64541	1	2	yes	—
252	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
253	C₂×C₄	—	2	1	no	—
254	C₂×C₄	—	2	1	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	2	1	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	2	1	no	—
260	C₂×C₄	—	2	1	no	—
261	C₂×C₄	—	2	1	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	2	1	no	—
264	C₂×C₄	—	2	1	no	—
265	C₂×C₄	—	2	1	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	4	1	no	—
271	C₂×C₄	—	4	1	no	—
272	C₂×C₄	—	4	1	no	—
273	C₂×C₄	—	4	1	no	—
274	C₂×C₄	—	4	1	no	—
275	C₂×C₄	—	4	1	no	—
276	C₂×C₄	—	4	1	no	—
277	C₂×C₄	—	4	1	no	—
278	C₂×C₄	—	4	1	no	—
279	C₂×C₄	—	4	1	no	—
280	C₂×C₄	#10597293	1	2	yes	—
281	C₂×C₄	#10597294	1	2	yes	—
282	C₂×C₄	#10597294	1	2	yes	—
283	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
284	C₂×C₄	#10597372	1	1	yes	characteristic
285	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
286	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
287	C₈	—	38	8	no	—
288	C₈	—	76	4	no	—
289	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
290	C₂²	C₂×#10597293	1	1	yes	characteristic
291	C₂²	#11926528	1	1	yes	characteristic
292	C₂²	C₂×#10597294	1	1	yes	characteristic
293	C₂²	C₂×#10597294	1	1	yes	characteristic
294	C₂²	#11926561	1	1	yes	characteristic
295	C₂²	#11926561	1	1	yes	characteristic
296	C₄	—	2	1	no	—
297	C₄	—	2	1	no	—
298	C₄	—	2	2	no	—
299	C₄	—	2	2	no	—
300	C₄	—	2	2	no	—
301	C₄	—	2	2	no	—
302	C₄	—	2	2	no	—
303	C₄	—	4	2	no	—
304	C₄	—	4	2	no	—
305	C₄	—	4	1	no	—
306	C₄	—	8	1	no	—
307	C₄	—	8	1	no	—
308	C₂	#14562237	1	1	yes	characteristic
309	C₂	#14562242	1	1	yes	characteristic
310	C₂	#14562250	1	1	yes	characteristic
311	C₂	#14562255	1	1	yes	characteristic
312	C₂	C₄×#10597293	1	1	yes	characteristic
313	C₂	C₄×#10597294	1	1	yes	characteristic
314	C₂	#14563445	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#125	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#125	D₁₉
hypocenter	C₁₉	#8227
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#125

Complements

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

N	H ≅ G/N	type
12. #11926286	C₄	semidirect
214. C₁₉	#8227	semidirect

Maximal subgroups

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

subgroup	index
#14563384	2
C₄×#10597260	2
C₂×#11926286	2
#14561516	2
C₄×C₁₉×#125	2
#8227	19