Subgroups — #18069091

Order 4864.

622 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926299	C₂	1	1	yes	maximal, characteristic
2	#14561865	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₁₉⋊C₈	—	2	1	no	—
5	C₂²×C₄⋊Dic₁₉	C₄	1	2	yes	—
6	C₂×C₁₉⋊#95	—	2	1	no	—
7	C₂×C₁₉⋊#95	—	2	1	no	—
8	#11926299	—	2	1	no	—
9	#11926299	C₄	1	2	yes	complemented
10	C₂³×C₈×C₁₉	—	2	1	no	—
11	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#336	—	2	1	no	—
13	C₁₉×#336	C₄	1	2	yes	complemented
14	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₂³×Dic₁₉	—	2	2	no	—
18	C₂²×C₈×C₁₉	—	2	4	no	—
19	C₂²×C₈×C₁₉	—	2	2	no	—
20	C₂²×C₈×C₁₉	—	4	2	no	—
21	C₂²×C₈×C₁₉	—	4	1	no	—
22	C₂²×C₈×C₁₉	—	4	1	no	—
23	C₂×C₄²×C₁₉	—	4	2	no	—
24	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	—	2	2	no	—
29	C₂×C₄⋊Dic₁₉	—	4	2	no	—
30	C₂×C₄⋊Dic₁₉	—	4	2	no	—
31	C₂×C₄⋊Dic₁₉	C₈	1	4	yes	complemented
32	C₂²×C₁₉⋊C₈	—	2	4	no	—
33	C₂²×C₁₉⋊C₈	—	2	2	no	—
34	C₂²×C₁₉⋊C₈	—	4	2	no	—
35	C₂²×C₁₉⋊C₈	—	4	1	no	—
36	C₂²×C₁₉⋊C₈	—	4	1	no	—
37	C₁₉⋊#95	—	4	1	no	—
38	C₁₉⋊#95	—	4	1	no	—
39	C₁₉⋊#95	—	4	1	no	—
40	C₁₉⋊#95	—	4	1	no	—
41	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	—	2	2	no	—
43	C₂²×C₄×C₁₉	—	2	2	no	—
44	C₂²×C₄×C₁₉	—	2	2	no	—
45	C₂²×C₄×C₁₉	—	2	1	no	—
46	C₂²×C₄×C₁₉	—	2	1	no	—
47	C₂²×C₄×C₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
56	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
57	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
65	C₂²×Dic₁₉	—	2	4	no	—
66	C₂²×Dic₁₉	—	4	2	no	—
67	C₂²×Dic₁₉	—	4	2	no	—
68	C₂²×Dic₁₉	—	4	2	no	—
69	C₂²×Dic₁₉	—	4	2	no	—
70	C₂²×Dic₁₉	—	4	2	no	—
71	C₂²×Dic₁₉	—	4	2	no	—
72	C₂×C₈×C₁₉	—	2	4	no	—
73	C₂×C₈×C₁₉	—	4	4	no	—
74	C₂×C₈×C₁₉	—	4	4	no	—
75	C₂×C₈×C₁₉	—	4	2	no	—
76	C₂×C₈×C₁₉	—	4	2	no	—
77	C₄²×C₁₉	—	4	1	no	—
78	C₄²×C₁₉	—	4	1	no	—
79	C₄²×C₁₉	—	4	1	no	—
80	C₄²×C₁₉	—	4	1	no	—
81	C₄⋊Dic₁₉	—	4	4	no	—
82	C₄⋊Dic₁₉	—	4	4	no	—
83	C₂×C₁₉⋊C₈	—	2	4	no	—
84	C₂×C₁₉⋊C₈	—	4	4	no	—
85	C₂×C₁₉⋊C₈	—	4	4	no	—
86	C₂×C₁₉⋊C₈	—	4	2	no	—
87	C₂×C₁₉⋊C₈	—	4	2	no	—
88	#7025	—	19	1	no	maximal, Sylow
89	C₂³×C₁₉	#95	1	1	yes	characteristic
90	C₂³×C₁₉	C₂²⋊C₈	1	2	yes	—
91	C₂³×C₁₉	#99	1	2	yes	—
92	C₂³×C₁₉	#100	1	1	yes	characteristic
93	C₂³×C₁₉	#101	1	1	yes	characteristic
94	C₂³×C₁₉	#102	1	1	yes	characteristic
95	C₂³×C₁₉	#102	1	1	yes	characteristic
96	C₂³×C₁₉	#103	1	1	yes	characteristic
97	C₂³×C₁₉	#103	1	1	yes	characteristic
98	C₂³×C₁₉	#104	1	2	yes	—
99	C₂³×C₁₉	#104	1	2	yes	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	2	2	no	—
102	C₂×C₄×C₁₉	—	2	2	no	—
103	C₂×C₄×C₁₉	—	2	2	no	—
104	C₂×C₄×C₁₉	—	2	2	no	—
105	C₂×C₄×C₁₉	—	2	2	no	—
106	C₂×C₄×C₁₉	—	2	2	no	—
107	C₂×C₄×C₁₉	—	2	2	no	—
108	C₂×C₄×C₁₉	—	2	2	no	—
109	C₂×C₄×C₁₉	—	2	2	no	—
110	C₂×C₄×C₁₉	—	2	2	no	—
111	C₂×C₄×C₁₉	—	2	2	no	—
112	C₂×C₄×C₁₉	—	2	1	no	—
113	C₂×C₄×C₁₉	—	2	1	no	—
114	C₂×C₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	—	2	1	no	—
116	C₂×C₄×C₁₉	—	2	1	no	—
117	C₂×C₄×C₁₉	—	2	1	no	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	2	1	no	—
120	C₂×C₄×C₁₉	—	2	1	no	—
121	C₂×C₄×C₁₉	—	2	1	no	—
122	C₂×C₄×C₁₉	—	2	1	no	—
123	C₂×C₄×C₁₉	—	2	1	no	—
124	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
125	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
126	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
127	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
128	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
129	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
130	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
131	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
132	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
133	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
134	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
135	C₂×Dic₁₉	—	4	4	no	—
136	C₂×Dic₁₉	—	4	4	no	—
137	C₂×Dic₁₉	—	4	4	no	—
138	C₂×Dic₁₉	—	8	2	no	—
139	C₂×Dic₁₉	—	8	2	no	—
140	C₂×Dic₁₉	—	8	2	no	—
141	C₂×Dic₁₉	—	8	2	no	—
142	C₈×C₁₉	—	4	4	no	—
143	C₁₉⋊C₈	—	4	4	no	—
144	C₂×#336	—	19	1	no	—
145	C₂×#336	D₁₉	1	1	yes	characteristic
146	C₄⋊#95	—	19	1	no	—
147	C₂²×C₁₉	#323	1	2	yes	—
148	C₂²×C₁₉	#324	1	2	yes	—
149	C₂²×C₁₉	D₄⋊C₈	1	2	yes	—
150	C₂²×C₁₉	D₄⋊C₈	1	2	yes	—
151	C₂²×C₁₉	Q₈⋊C₈	1	2	yes	—
152	C₂²×C₁₉	Q₈⋊C₈	1	2	yes	—
153	C₂²×C₁₉	#327	1	2	yes	—
154	C₂²×C₁₉	#327	1	2	yes	—
155	C₂²×C₁₉	#328	1	2	yes	—
156	C₂²×C₁₉	#328	1	2	yes	—
157	C₂²×C₁₉	#329	1	2	yes	—
158	C₂²×C₁₉	#330	1	2	yes	—
159	C₂²×C₁₉	#331	1	1	yes	characteristic
160	C₂²×C₁₉	#332	1	1	yes	characteristic
161	C₂²×C₁₉	#332	1	1	yes	characteristic
162	C₂²×C₁₉	#333	1	1	yes	characteristic
163	C₂²×C₁₉	#336	1	1	yes	characteristic
164	C₂²×C₁₉	#339	1	1	yes	characteristic
165	C₂²×C₁₉	#339	1	1	yes	characteristic
166	C₂²×C₁₉	#340	1	1	yes	characteristic
167	C₂²×C₁₉	#340	1	1	yes	characteristic
168	C₂²×C₁₉	#342	1	1	yes	characteristic
169	C₂²×C₁₉	#343	1	1	yes	characteristic
170	C₄×C₁₉	—	2	1	no	—
171	C₄×C₁₉	—	2	1	no	—
172	C₄×C₁₉	—	2	2	no	—
173	C₄×C₁₉	—	2	1	no	—
174	C₄×C₁₉	—	2	1	no	—
175	C₄×C₁₉	—	2	1	no	—
176	C₄×C₁₉	—	2	1	no	—
177	C₄×C₁₉	—	2	1	no	—
178	C₄×C₁₉	—	2	1	no	—
179	C₄×C₁₉	—	2	1	no	—
180	C₄×C₁₉	—	2	1	no	—
181	Dic₁₉	—	8	4	no	—
182	C₂³×C₈	—	2	1	no	—
183	C₂³×C₈	—	38	1	no	—
184	C₂²×C₄⋊C₄	—	19	2	no	—
185	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
186	C₂×#95	—	38	1	no	—
187	C₂×#95	—	38	1	no	—
188	#336	—	2	1	no	—
189	#336	—	19	2	no	—
190	#336	—	38	1	no	—
191	#336	Dic₁₉	1	2	yes	complemented
192	C₂×C₁₉	#1270	1	2	yes	—
193	C₂×C₁₉	#1271	1	2	yes	—
194	C₂×C₁₉	#1271	1	2	yes	—
195	C₂×C₁₉	#1272	1	2	yes	—
196	C₂×C₁₉	#1279	1	1	yes	characteristic
197	C₂×C₁₉	#1279	1	1	yes	characteristic
198	C₂×C₁₉	#1280	1	1	yes	characteristic
199	C₂×C₁₉	#1294	1	1	yes	characteristic
200	C₂×C₁₉	#1294	1	1	yes	characteristic
201	C₂×C₁₉	#1295	1	1	yes	characteristic
202	C₂×C₁₉	#1296	1	1	yes	characteristic
203	C₂³×C₄	—	38	2	no	—
204	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
205	C₂³×C₄	D₇₆	1	1	yes	characteristic
206	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
207	C₂²×C₈	—	2	4	no	—
208	C₂²×C₈	—	2	2	no	—
209	C₂²×C₈	—	4	2	no	—
210	C₂²×C₈	—	4	1	no	—
211	C₂²×C₈	—	4	1	no	—
212	C₂²×C₈	—	38	4	no	—
213	C₂²×C₈	—	38	2	no	—
214	C₂²×C₈	—	76	2	no	—
215	C₂²×C₈	—	76	1	no	—
216	C₂²×C₈	—	76	1	no	—
217	C₂×C₄⋊C₄	—	19	4	no	—
218	C₂×C₄⋊C₄	—	38	2	no	—
219	C₂×C₄⋊C₄	—	76	2	no	—
220	C₂×C₄⋊C₄	—	76	2	no	—
221	C₂×C₄²	—	4	2	no	—
222	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
223	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
224	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
225	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
226	#95	—	76	1	no	—
227	#95	—	76	1	no	—
228	#95	—	76	1	no	—
229	#95	—	76	1	no	—
230	C₁₉	#7025	1	1	yes	characteristic, complemented, Sylow
231	C₂⁴	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	—	2	1	no	—
237	C₂²×C₄	—	2	1	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	38	4	no	—
240	C₂²×C₄	—	76	2	no	—
241	C₂²×C₄	—	76	2	no	—
242	C₂²×C₄	—	76	2	no	—
243	C₂²×C₄	—	76	2	no	—
244	C₂²×C₄	—	76	2	no	—
245	C₂²×C₄	—	76	2	no	—
246	C₂²×C₄	C₈×D₁₉	1	2	yes	—
247	C₂²×C₄	#64515	1	2	yes	—
248	C₂²×C₄	#64516	1	1	yes	characteristic
249	C₂²×C₄	#64516	1	1	yes	characteristic
250	C₂²×C₄	D₁₅₂	1	1	yes	characteristic
251	C₂²×C₄	Dic₇₆	1	1	yes	characteristic
252	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
253	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
254	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
255	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
256	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
257	C₂²×C₄	#64525	1	1	yes	characteristic
258	C₂²×C₄	#64526	1	1	yes	characteristic
259	C₂²×C₄	#64527	1	1	yes	characteristic
260	C₂²×C₄	#64528	1	1	yes	characteristic
261	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	4	4	no	—
264	C₂×C₈	—	4	4	no	—
265	C₂×C₈	—	4	2	no	—
266	C₂×C₈	—	4	2	no	—
267	C₂×C₈	—	38	4	no	—
268	C₂×C₈	—	76	4	no	—
269	C₂×C₈	—	76	4	no	—
270	C₂×C₈	—	76	2	no	—
271	C₂×C₈	—	76	2	no	—
272	C₄⋊C₄	—	76	4	no	—
273	C₄⋊C₄	—	76	4	no	—
274	C₄²	—	4	1	no	—
275	C₄²	—	4	1	no	—
276	C₄²	—	4	1	no	—
277	C₄²	—	4	1	no	—
278	C₂³	#10597262	1	2	yes	—
279	C₂³	#10597263	1	2	yes	—
280	C₂³	#10597266	1	1	yes	characteristic
281	C₂³	#10597267	1	1	yes	characteristic
282	C₂³	#10597273	1	1	yes	characteristic
283	C₂³	(C₂×D₁₉)⋊C₈	1	2	yes	—
284	C₂³	#10597278	1	1	yes	characteristic
285	C₂³	#10597280	1	1	yes	characteristic
286	C₂³	#10597281	1	1	yes	characteristic
287	C₂³	#10597282	1	2	yes	—
288	C₂³	C₁₉⋊#95	1	1	yes	characteristic
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	76	4	no	—
314	C₂×C₄	—	76	4	no	—
315	C₂×C₄	—	76	4	no	—
316	C₂×C₄	—	152	2	no	—
317	C₂×C₄	—	152	2	no	—
318	C₂×C₄	—	152	2	no	—
319	C₂×C₄	—	152	2	no	—
320	C₂×C₄	#10597264	1	1	yes	characteristic
321	C₂×C₄	#10597265	1	1	yes	characteristic
322	C₂×C₄	C₈×Dic₁₉	1	1	yes	characteristic
323	C₂×C₄	Dic₁₉⋊C₈	1	2	yes	—
324	C₂×C₄	#10597272	1	1	yes	characteristic
325	C₂×C₄	#10597273	1	1	yes	characteristic
326	C₂×C₄	#10597274	1	1	yes	characteristic
327	C₂×C₄	#10597275	1	1	yes	characteristic
328	C₂×C₄	#10597278	1	1	yes	characteristic
329	C₂×C₄	#10597289	1	1	yes	characteristic
330	C₂×C₄	#10597292	1	1	yes	characteristic
331	C₈	—	4	4	no	—
332	C₈	—	76	4	no	—
333	C₂²	#11926267	1	2	yes	—
334	C₂²	#11926269	1	2	yes	—
335	C₂²	#11926271	1	2	yes	—
336	C₂²	#11926273	1	2	yes	—
337	C₂²	#11926274	1	2	yes	—
338	C₂²	#11926276	1	2	yes	—
339	C₂²	#11926277	1	2	yes	—
340	C₂²	#11926279	1	2	yes	—
341	C₂²	#11926280	1	2	yes	—
342	C₂²	#11926282	1	2	yes	—
343	C₂²	#11926283	1	2	yes	—
344	C₂²	#11926285	1	2	yes	—
345	C₂²	#11926287	1	1	yes	characteristic
346	C₂²	#11926289	1	1	yes	characteristic
347	C₂²	#11926291	1	1	yes	characteristic
348	C₂²	#11926292	1	1	yes	characteristic
349	C₂²	#11926298	1	1	yes	characteristic
350	C₂²	#11926304	1	1	yes	characteristic
351	C₂²	#11926305	1	1	yes	characteristic
352	C₂²	#11926306	1	1	yes	characteristic
353	C₂²	#11926307	1	1	yes	characteristic
354	C₂²	#11926310	1	1	yes	characteristic
355	C₂²	#11926312	1	1	yes	characteristic
356	C₄	—	2	1	no	—
357	C₄	—	2	2	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	152	4	no	—
368	C₂	#14561455	1	2	yes	—
369	C₂	#14561457	1	2	yes	—
370	C₂	#14561459	1	2	yes	—
371	C₂	#14561460	1	2	yes	—
372	C₂	#14561474	1	1	yes	characteristic
373	C₂	#14561475	1	1	yes	characteristic
374	C₂	#14561477	1	1	yes	characteristic
375	C₂	#14561514	1	1	yes	characteristic
376	C₂	#14561515	1	1	yes	characteristic
377	C₂	#14561517	1	1	yes	characteristic
378	C₂	#14561519	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₄×C₈
Frattini	C₂²×C₄²	C₂×D₁₉
Fitting	C₂×C₁₉×#336	C₂
socle, prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂²×C₄²×C₁₉	C₂²
hypercenter	C₂×#336	D₁₉
hypocenter	C₁₉	#7025
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
9. #11926299	C₄	semidirect
13. C₁₉×#336	C₄	semidirect
31. C₂×C₄⋊Dic₁₉	C₈	semidirect
191. #336	Dic₁₉	semidirect
230. C₁₉	#7025	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926299	2
#14561865	2
C₂×C₁₉×#336	2
#7025	19