Subgroups — #18069663

Order 4864.

464 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926313	C₂	1	1	yes	maximal, characteristic
2	#14561888	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#324	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64520	—	2	1	no	—
5	C₂²×C₄⋊Dic₁₉	C₄	1	1	yes	characteristic
6	C₂×C₁₉⋊#95	—	2	1	no	—
7	C₂×C₁₉⋊#95	—	2	1	no	—
8	C₂×C₁₉⋊#95	C₄	1	1	yes	characteristic
9	#11926313	—	2	1	no	—
10	#11926313	C₄	1	2	yes	complemented
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
13	C₁₉×#324	—	2	1	no	—
14	C₁₉×#324	C₄	1	2	yes	complemented
15	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
18	C₂³×Dic₁₉	—	2	1	no	—
19	C₂³×Dic₁₉	—	2	1	no	—
20	C₂²×C₈×C₁₉	—	4	1	no	—
21	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
22	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
23	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₉	—	4	1	no	—
28	C₂×C₄⋊Dic₁₉	—	4	2	no	—
29	C₂×#64520	—	2	2	no	—
30	C₂×#64520	—	2	2	no	—
31	C₂×#64520	—	2	2	no	—
32	C₂×#64520	—	4	1	no	—
33	C₂×#64520	—	4	1	no	—
34	C₂×#64520	—	4	1	no	—
35	C₂²×C₁₉⋊C₈	—	4	1	no	—
36	C₁₉×C₂²⋊C₈	—	2	2	no	—
37	C₁₉×C₂²⋊C₈	—	4	1	no	—
38	C₁₉⋊#95	—	4	2	no	—
39	C₁₉⋊#95	—	4	1	no	—
40	C₁₉⋊#95	—	4	1	no	—
41	C₁₉⋊#95	—	4	1	no	—
42	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	—	2	1	no	—
44	C₂²×C₄×C₁₉	—	2	1	no	—
45	C₂²×C₄×C₁₉	—	2	1	no	—
46	C₂²×C₄×C₁₉	—	2	1	no	—
47	C₂²×C₄×C₁₉	—	2	1	no	—
48	C₂²×C₄×C₁₉	—	2	1	no	—
49	C₂²×C₄×C₁₉	—	2	1	no	—
50	C₂²×C₄×C₁₉	—	2	1	no	—
51	C₂²×C₄×C₁₉	—	4	1	no	—
52	C₂²×C₄×C₁₉	—	4	1	no	—
53	C₂²×C₄×C₁₉	—	4	1	no	—
54	C₂²×C₄×C₁₉	—	4	1	no	—
55	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
65	C₂²×Dic₁₉	—	2	2	no	—
66	C₂²×Dic₁₉	—	2	2	no	—
67	C₂²×Dic₁₉	—	4	1	no	—
68	C₂²×Dic₁₉	—	4	1	no	—
69	C₂²×Dic₁₉	—	4	1	no	—
70	C₂²×Dic₁₉	—	4	1	no	—
71	C₂²×Dic₁₉	—	4	1	no	—
72	C₂²×Dic₁₉	—	4	1	no	—
73	C₂²×Dic₁₉	—	4	1	no	—
74	C₂²×Dic₁₉	—	4	1	no	—
75	C₂²×Dic₁₉	—	4	1	no	—
76	C₂²×Dic₁₉	—	4	1	no	—
77	C₂²×Dic₁₉	—	4	1	no	—
78	C₂²×Dic₁₉	—	4	1	no	—
79	C₂×C₈×C₁₉	—	4	2	no	—
80	C₂×C₈×C₁₉	—	8	1	no	—
81	C₂×C₈×C₁₉	—	8	1	no	—
82	C₄⋊C₄×C₁₉	—	4	1	no	—
83	C₄⋊C₄×C₁₉	—	4	1	no	—
84	C₄⋊C₄×C₁₉	—	4	1	no	—
85	C₄⋊C₄×C₁₉	—	4	1	no	—
86	C₄⋊Dic₁₉	—	4	2	no	—
87	C₄⋊Dic₁₉	—	4	2	no	—
88	#64520	—	2	4	no	—
89	#64520	—	4	2	no	—
90	#64520	—	4	2	no	—
91	#64520	—	4	2	no	—
92	C₂×C₁₉⋊C₈	—	4	2	no	—
93	C₂×C₁₉⋊C₈	—	4	2	no	—
94	C₂×C₁₉⋊C₈	—	4	2	no	—
95	#7251	—	19	1	no	maximal, Sylow
96	C₂³×C₁₉	—	2	1	no	—
97	C₂³×C₁₉	—	2	1	no	—
98	C₂³×C₁₉	—	2	1	no	—
99	C₂³×C₁₉	—	2	1	no	—
100	C₂³×C₁₉	#95	1	1	yes	characteristic
101	C₂³×C₁₉	#99	1	1	yes	characteristic
102	C₂³×C₁₉	#99	1	1	yes	characteristic
103	C₂³×C₁₉	#102	1	1	yes	characteristic
104	C₂³×C₁₉	#103	1	1	yes	characteristic
105	C₂³×C₁₉	#104	1	1	yes	characteristic
106	C₂³×C₁₉	#104	1	1	yes	characteristic
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	2	1	no	—
109	C₂×C₄×C₁₉	—	2	1	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	—	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	—	4	2	no	—
124	C₂×C₄×C₁₉	—	4	1	no	—
125	C₂×C₄×C₁₉	—	4	1	no	—
126	C₂×C₄×C₁₉	—	4	1	no	—
127	C₂×C₄×C₁₉	—	4	1	no	—
128	C₂×C₄×C₁₉	—	4	1	no	—
129	C₂×C₄×C₁₉	—	4	1	no	—
130	C₂×C₄×C₁₉	—	4	1	no	—
131	C₂×C₄×C₁₉	—	4	1	no	—
132	C₂×C₄×C₁₉	—	8	1	no	—
133	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
134	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
135	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
136	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
137	C₂×Dic₁₉	—	4	2	no	—
138	C₂×Dic₁₉	—	4	2	no	—
139	C₂×Dic₁₉	—	4	2	no	—
140	C₂×Dic₁₉	—	4	2	no	—
141	C₂×Dic₁₉	—	4	2	no	—
142	C₂×Dic₁₉	—	4	2	no	—
143	C₂×Dic₁₉	—	8	1	no	—
144	C₂×Dic₁₉	—	8	1	no	—
145	C₂×Dic₁₉	—	8	1	no	—
146	C₂×Dic₁₉	—	8	1	no	—
147	C₂×Dic₁₉	—	8	1	no	—
148	C₂×Dic₁₉	—	8	1	no	—
149	C₂×Dic₁₉	—	8	1	no	—
150	C₂×Dic₁₉	—	8	1	no	—
151	C₈×C₁₉	—	8	2	no	—
152	C₁₉⋊C₈	—	4	4	no	—
153	C₂×#343	—	19	1	no	—
154	C₂×#324	D₁₉	1	1	yes	characteristic
155	#1441	—	19	1	no	—
156	C₂²×C₁₉	—	2	1	no	—
157	C₂²×C₁₉	—	2	1	no	—
158	C₂²×C₁₉	—	2	1	no	—
159	C₂²×C₁₉	—	2	1	no	—
160	C₂²×C₁₉	—	2	1	no	—
161	C₂²×C₁₉	—	2	1	no	—
162	C₂²×C₁₉	—	2	1	no	—
163	C₂²×C₁₉	—	2	1	no	—
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	—	2	1	no	—
166	C₂²×C₁₉	—	2	1	no	—
167	C₂²×C₁₉	—	2	1	no	—
168	C₂²×C₁₉	#327	1	1	yes	characteristic
169	C₂²×C₁₉	#327	1	1	yes	characteristic
170	C₂²×C₁₉	#328	1	1	yes	characteristic
171	C₂²×C₁₉	#328	1	1	yes	characteristic
172	C₂²×C₁₉	#339	1	1	yes	characteristic
173	C₂²×C₁₉	#340	1	1	yes	characteristic
174	C₂²×C₁₉	#342	1	1	yes	characteristic
175	C₂²×C₁₉	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
176	C₂²×C₁₉	#352	1	1	yes	characteristic
177	C₂²×C₁₉	#355	1	1	yes	characteristic
178	C₂²×C₁₉	#356	1	1	yes	characteristic
179	C₄×C₁₉	—	2	1	no	—
180	C₄×C₁₉	—	2	1	no	—
181	C₄×C₁₉	—	2	1	no	—
182	C₄×C₁₉	—	2	1	no	—
183	C₄×C₁₉	—	4	1	no	—
184	C₄×C₁₉	—	4	1	no	—
185	C₄×C₁₉	—	4	1	no	—
186	C₄×C₁₉	—	4	1	no	—
187	Dic₁₉	—	8	2	no	—
188	Dic₁₉	—	8	2	no	—
189	C₂²×M₁₆	—	38	1	no	—
190	C₂²×C₄⋊C₄	—	19	1	no	—
191	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
192	C₂×C₂²⋊C₈	—	2	1	no	—
193	C₂×#95	—	19	1	no	—
194	C₂×#95	—	38	1	no	—
195	C₂×#95	—	38	1	no	—
196	#343	—	19	2	no	—
197	#343	—	38	1	no	—
198	#324	—	2	1	no	—
199	#324	Dic₁₉	1	2	yes	complemented
200	C₂×C₁₉	—	2	1	no	—
201	C₂×C₁₉	—	2	1	no	—
202	C₂×C₁₉	—	2	1	no	—
203	C₂×C₁₉	—	2	1	no	—
204	C₂×C₁₉	#1294	1	1	yes	characteristic
205	C₂×C₁₉	#1345	1	1	yes	characteristic
206	C₂×C₁₉	#1346	1	1	yes	characteristic
207	C₂×C₁₉	#1353	1	1	yes	characteristic
208	C₂×C₁₉	#1354	1	1	yes	characteristic
209	C₂×C₁₉	#1390	1	1	yes	characteristic
210	C₂×C₁₉	#1394	1	1	yes	characteristic
211	C₂³×C₄	—	38	1	no	—
212	C₂³×C₄	—	38	1	no	—
213	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
214	C₂³×C₄	D₇₆	1	1	yes	characteristic
215	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
216	C₂×M₁₆	—	38	2	no	—
217	C₂×M₁₆	—	38	2	no	—
218	C₂×M₁₆	—	38	2	no	—
219	C₂×M₁₆	—	76	1	no	—
220	C₂×M₁₆	—	76	1	no	—
221	C₂×M₁₆	—	76	1	no	—
222	C₂²×C₈	—	4	1	no	—
223	C₂²×C₈	—	76	1	no	—
224	C₂×C₄⋊C₄	—	4	1	no	—
225	C₂×C₄⋊C₄	—	4	1	no	—
226	C₂×C₄⋊C₄	—	76	1	no	—
227	C₂×C₄⋊C₄	—	76	2	no	—
228	C₂×C₄⋊C₄	Dic₃₈	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
232	C₂²⋊C₈	—	2	2	no	—
233	C₂²⋊C₈	—	4	1	no	—
234	#95	—	76	1	no	—
235	#95	—	76	2	no	—
236	#95	—	76	1	no	—
237	#95	—	76	1	no	—
238	C₁₉	#7251	1	1	yes	characteristic, complemented, Sylow
239	C₂⁴	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
240	C₂²×C₄	—	2	1	no	—
241	C₂²×C₄	—	2	1	no	—
242	C₂²×C₄	—	2	1	no	—
243	C₂²×C₄	—	2	1	no	—
244	C₂²×C₄	—	2	1	no	—
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	—	2	1	no	—
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	—	4	1	no	—
249	C₂²×C₄	—	4	1	no	—
250	C₂²×C₄	—	4	1	no	—
251	C₂²×C₄	—	4	1	no	—
252	C₂²×C₄	—	38	2	no	—
253	C₂²×C₄	—	38	2	no	—
254	C₂²×C₄	—	76	1	no	—
255	C₂²×C₄	—	76	1	no	—
256	C₂²×C₄	—	76	1	no	—
257	C₂²×C₄	—	76	1	no	—
258	C₂²×C₄	—	76	1	no	—
259	C₂²×C₄	—	76	1	no	—
260	C₂²×C₄	—	76	1	no	—
261	C₂²×C₄	—	76	1	no	—
262	C₂²×C₄	—	76	1	no	—
263	C₂²×C₄	—	76	1	no	—
264	C₂²×C₄	—	76	1	no	—
265	C₂²×C₄	—	76	1	no	—
266	C₂²×C₄	#64516	1	1	yes	characteristic
267	C₂²×C₄	#64516	1	1	yes	characteristic
268	C₂²×C₄	D₁₅₂	1	1	yes	characteristic
269	C₂²×C₄	Dic₇₆	1	1	yes	characteristic
270	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
271	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
274	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
276	M₁₆	—	38	4	no	—
277	M₁₆	—	76	2	no	—
278	M₁₆	—	76	2	no	—
279	M₁₆	—	76	2	no	—
280	C₂×C₈	—	4	2	no	—
281	C₂×C₈	—	8	1	no	—
282	C₂×C₈	—	8	1	no	—
283	C₂×C₈	—	76	2	no	—
284	C₂×C₈	—	76	2	no	—
285	C₂×C₈	—	76	2	no	—
286	C₄⋊C₄	—	4	1	no	—
287	C₄⋊C₄	—	4	1	no	—
288	C₄⋊C₄	—	4	1	no	—
289	C₄⋊C₄	—	4	1	no	—
290	C₄⋊C₄	—	76	2	no	—
291	C₄⋊C₄	—	76	2	no	—
292	C₂³	—	2	1	no	—
293	C₂³	—	2	1	no	—
294	C₂³	—	2	1	no	—
295	C₂³	—	2	1	no	—
296	C₂³	#10597263	1	1	yes	characteristic
297	C₂³	#10597263	1	1	yes	characteristic
298	C₂³	#10597273	1	1	yes	characteristic
299	C₂³	#10597278	1	1	yes	characteristic
300	C₂³	#10597282	1	1	yes	characteristic
301	C₂³	#10597282	1	1	yes	characteristic
302	C₂³	C₁₉⋊#95	1	1	yes	characteristic
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	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	8	1	no	—
329	C₂×C₄	—	76	2	no	—
330	C₂×C₄	—	76	2	no	—
331	C₂×C₄	—	76	2	no	—
332	C₂×C₄	—	76	2	no	—
333	C₂×C₄	—	76	2	no	—
334	C₂×C₄	—	76	2	no	—
335	C₂×C₄	—	152	1	no	—
336	C₂×C₄	—	152	1	no	—
337	C₂×C₄	—	152	1	no	—
338	C₂×C₄	—	152	1	no	—
339	C₂×C₄	—	152	1	no	—
340	C₂×C₄	—	152	1	no	—
341	C₂×C₄	—	152	1	no	—
342	C₂×C₄	—	152	1	no	—
343	C₂×C₄	#10597273	1	1	yes	characteristic
344	C₂×C₄	#10597274	1	1	yes	characteristic
345	C₂×C₄	#10597275	1	1	yes	characteristic
346	C₂×C₄	#10597278	1	1	yes	characteristic
347	C₈	—	8	2	no	—
348	C₈	—	76	4	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	#11926279	1	1	yes	characteristic
362	C₂²	#11926279	1	1	yes	characteristic
363	C₂²	#11926282	1	1	yes	characteristic
364	C₂²	#11926282	1	1	yes	characteristic
365	C₂²	#11926305	1	1	yes	characteristic
366	C₂²	#11926307	1	1	yes	characteristic
367	C₂²	#11926310	1	1	yes	characteristic
368	C₂²	#11926330	1	1	yes	characteristic
369	C₂²	#11926333	1	1	yes	characteristic
370	C₂²	#11926340	1	1	yes	characteristic
371	C₂²	#11926342	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	1	no	—
377	C₄	—	4	1	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	1	no	—
380	C₄	—	152	2	no	—
381	C₄	—	152	2	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	2	1	no	—
385	C₂	—	2	1	no	—
386	C₂	#14561515	1	1	yes	characteristic
387	C₂	#14561639	1	1	yes	characteristic
388	C₂	#14561642	1	1	yes	characteristic
389	C₂	#14561663	1	1	yes	characteristic
390	C₂	#14561666	1	1	yes	characteristic
391	C₂	#14561752	1	1	yes	characteristic
392	C₂	#14561761	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597263
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₂²×C₄⋊C₄	C₂×D₁₉
Fitting	C₂×C₁₉×#324	C₂
socle	C₂³×C₁₉	#99
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂²×C₄⋊C₄×C₁₉	C₂²
hypercenter	C₂×#324	D₁₉
hypocenter	C₁₉	#7251
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂⁴ ◁ C₂²×C₄⋊C₄ ◁ C₂×#324

Complements

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

N	H ≅ G/N	type
10. #11926313	C₄	semidirect
14. C₁₉×#324	C₄	semidirect
199. #324	Dic₁₉	semidirect
238. C₁₉	#7251	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926313	2
#14561888	2
C₂×C₁₉×#324	2
#7251	19