Subgroups — #14569185

Order 2432.

454 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926486	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926472	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926472	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926458	C₂	1	1	yes	maximal, characteristic
5	#11926447	C₂	1	1	yes	maximal, characteristic
6	#11926438	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926437	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926437	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926432	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926431	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926429	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926417	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926395	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂²⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#386	C₂	1	1	yes	maximal, characteristic
16	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
31	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#95	C₂²	1	1	yes	characteristic
40	C₁₉×#95	C₂²	1	1	yes	characteristic
41	C₁₉⋊#95	C₂²	1	1	yes	characteristic
42	C₁₉⋊#95	C₂²	1	1	yes	characteristic
43	C₁₉⋊#95	C₂²	1	1	yes	characteristic
44	C₁₉⋊#95	C₂²	1	1	yes	characteristic
45	C₁₉⋊#95	C₂²	1	1	yes	characteristic
46	C₁₉⋊#95	C₂²	1	1	yes	characteristic
47	C₁₉⋊#95	C₂²	1	1	yes	characteristic
48	C₁₉⋊#95	C₂²	1	1	yes	characteristic
49	C₁₉⋊#95	C₂²	1	1	yes	characteristic
50	C₁₉⋊#95	C₂²	1	1	yes	characteristic
51	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
52	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
53	C₂×D₄×C₁₉	—	2	2	no	—
54	C₂×D₄×C₁₉	—	2	2	no	—
55	C₂×D₄×C₁₉	—	4	1	no	—
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	—	4	1	no	—
58	C₂²×C₄×C₁₉	—	4	1	no	—
59	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
65	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
66	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
67	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
68	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
69	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
70	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
71	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
72	C₂²⋊C₄×C₁₉	—	2	2	no	—
73	C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₂²⋊C₄×C₁₉	—	4	1	no	—
75	C₂²⋊Dic₁₉	—	2	2	no	—
76	C₂²⋊Dic₁₉	—	2	2	no	—
77	C₂²⋊Dic₁₉	—	2	2	no	—
78	C₂²⋊Dic₁₉	—	2	2	no	—
79	C₂²⋊Dic₁₉	—	2	2	no	—
80	C₂²⋊Dic₁₉	—	4	1	no	—
81	C₂²⋊Dic₁₉	—	4	1	no	—
82	C₂²⋊Dic₁₉	—	4	1	no	—
83	C₄⋊Dic₁₉	—	2	2	no	—
84	C₄⋊Dic₁₉	—	4	1	no	—
85	Dic₁₉⋊C₄	—	2	2	no	—
86	Dic₁₉⋊C₄	—	2	2	no	—
87	Dic₁₉⋊C₄	—	2	2	no	—
88	Dic₁₉⋊C₄	—	4	1	no	—
89	C₄×Dic₁₉	—	2	2	no	—
90	C₄×Dic₁₉	—	4	1	no	—
91	C₄×Dic₁₉	—	4	1	no	—
92	C₄×Dic₁₉	—	4	1	no	—
93	C₂³×C₁₉	—	2	1	no	—
94	C₂³×C₁₉	—	2	1	no	—
95	C₂³×C₁₉	—	2	1	no	—
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	—	2	1	no	—
101	C₂³×C₁₉	—	2	1	no	—
102	C₂³×C₁₉	—	2	1	no	—
103	C₂³×C₁₉	—	2	1	no	—
104	C₂³×C₁₉	—	2	1	no	—
105	C₂³×C₁₉	—	2	1	no	—
106	C₂³×C₁₉	#41	1	2	yes	—
107	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
108	D₄×C₁₉	—	4	4	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	—	4	4	no	—
123	C₂×C₄×C₁₉	#41	1	2	yes	—
124	C₂×C₄×C₁₉	#41	1	2	yes	—
125	C₂×Dic₁₉	—	2	1	no	—
126	C₂×Dic₁₉	—	2	1	no	—
127	C₂×Dic₁₉	—	2	1	no	—
128	C₂×Dic₁₉	—	2	1	no	—
129	C₂×Dic₁₉	—	2	1	no	—
130	C₂×Dic₁₉	—	2	1	no	—
131	C₂×Dic₁₉	—	2	1	no	—
132	C₂×Dic₁₉	—	2	1	no	—
133	C₂×Dic₁₉	—	2	1	no	—
134	C₂×Dic₁₉	—	2	1	no	—
135	C₂×Dic₁₉	—	2	1	no	—
136	C₂×Dic₁₉	—	2	1	no	—
137	C₂×Dic₁₉	—	2	1	no	—
138	C₂×Dic₁₉	—	2	1	no	—
139	C₂×Dic₁₉	—	2	1	no	—
140	C₂×Dic₁₉	—	2	1	no	—
141	C₂×Dic₁₉	—	2	1	no	—
142	C₂×Dic₁₉	—	2	1	no	—
143	C₂×Dic₁₉	—	2	1	no	—
144	C₂×Dic₁₉	—	2	1	no	—
145	C₂×Dic₁₉	—	2	1	no	—
146	C₂×Dic₁₉	—	2	1	no	—
147	C₂×Dic₁₉	#41	1	2	yes	—
148	C₂×Dic₁₉	#41	1	2	yes	—
149	#2597	—	19	1	no	maximal, Sylow
150	C₂²×C₁₉	—	2	2	no	—
151	C₂²×C₁₉	—	2	2	no	—
152	C₂²×C₁₉	—	2	2	no	—
153	C₂²×C₁₉	—	4	1	no	—
154	C₂²×C₁₉	—	4	1	no	—
155	C₂²×C₁₉	—	4	1	no	—
156	C₂²×C₁₉	—	4	1	no	—
157	C₂²×C₁₉	—	4	1	no	—
158	C₂²×C₁₉	—	4	1	no	—
159	C₂²×C₁₉	—	4	1	no	—
160	C₂²×C₁₉	—	4	1	no	—
161	C₂²×C₁₉	—	4	1	no	—
162	C₂²×C₁₉	—	4	1	no	—
163	C₂²×C₁₉	—	4	1	no	—
164	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
165	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
166	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
167	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
168	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
169	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
171	C₄×C₁₉	—	2	2	no	—
172	C₄×C₁₉	—	2	2	no	—
173	C₄×C₁₉	—	4	1	no	—
174	C₄×C₁₉	—	4	1	no	—
175	C₄×C₁₉	—	4	1	no	—
176	Dic₁₉	—	2	2	no	—
177	Dic₁₉	—	2	2	no	—
178	Dic₁₉	—	4	1	no	—
179	Dic₁₉	—	4	1	no	—
180	Dic₁₉	—	4	1	no	—
181	Dic₁₉	—	4	1	no	—
182	Dic₁₉	—	4	1	no	—
183	Dic₁₉	—	4	1	no	—
184	#400	—	19	1	no	—
185	#397	—	19	1	no	—
186	#397	—	19	1	no	—
187	#394	—	19	1	no	—
188	#390	—	19	1	no	—
189	#388	—	19	1	no	—
190	#388	—	19	1	no	—
191	#388	—	19	1	no	—
192	#388	—	19	1	no	—
193	#387	—	19	1	no	—
194	#387	—	19	1	no	—
195	#386	D₁₉	1	1	yes	characteristic
196	#385	—	19	1	no	—
197	C₄×C₄⋊C₄	—	19	1	no	—
198	C₄×C₂²⋊C₄	—	19	1	no	—
199	C₂×C₁₉	—	4	2	no	—
200	C₂×C₁₉	—	8	1	no	—
201	C₂×C₁₉	#529	1	1	yes	characteristic
202	C₂×C₁₉	#529	1	1	yes	characteristic
203	C₂×C₁₉	#538	1	1	yes	characteristic
204	C₂×C₁₉	#551	1	1	yes	characteristic
205	C₂×C₁₉	#553	1	1	yes	characteristic
206	C₂×C₁₉	#553	1	1	yes	characteristic
207	C₂×C₁₉	#559	1	1	yes	characteristic
208	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
209	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
210	C₂×C₄⋊C₄	—	19	1	no	—
211	C₂×C₄⋊C₄	—	19	1	no	—
212	C₂×C₄⋊C₄	—	19	1	no	—
213	C₂×C₄⋊C₄	—	19	1	no	—
214	C₂×C₄⋊C₄	—	19	1	no	—
215	C₂×C₄⋊C₄	—	19	1	no	—
216	C₂×C₂²⋊C₄	—	19	1	no	—
217	C₂×C₂²⋊C₄	—	19	1	no	—
218	C₂×C₂²⋊C₄	—	19	1	no	—
219	C₂×C₂²⋊C₄	—	19	1	no	—
220	C₂×C₂²⋊C₄	—	19	1	no	—
221	C₂×C₂²⋊C₄	—	19	1	no	—
222	C₂×C₂²⋊C₄	—	19	1	no	—
223	C₂×C₂²⋊C₄	—	19	1	no	—
224	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
225	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
226	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
227	C₂×C₄²	—	19	1	no	—
228	C₂×C₄²	—	19	1	no	—
229	C₂×C₄²	—	19	1	no	—
230	C₂×C₄²	—	19	1	no	—
231	#95	—	19	1	no	—
232	#95	—	19	1	no	—
233	#95	—	19	1	no	—
234	#95	—	19	1	no	—
235	#95	—	19	1	no	—
236	#95	—	19	1	no	—
237	#95	—	19	1	no	—
238	#95	—	19	1	no	—
239	#95	—	19	1	no	—
240	#95	—	19	1	no	—
241	#95	C₂×D₁₉	1	1	yes	characteristic
242	#95	C₂×D₁₉	1	1	yes	characteristic
243	C₁₉	#2597	1	1	yes	characteristic, complemented, Sylow
244	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
245	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
246	C₂×D₄	—	2	2	no	—
247	C₂×D₄	—	2	2	no	—
248	C₂×D₄	—	4	1	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	4	1	no	—
251	C₂²×C₄	—	4	1	no	—
252	C₂²×C₄	—	19	1	no	—
253	C₂²×C₄	—	19	1	no	—
254	C₂²×C₄	—	19	1	no	—
255	C₂²×C₄	—	19	1	no	—
256	C₂²×C₄	—	19	1	no	—
257	C₂²×C₄	—	19	1	no	—
258	C₂²×C₄	—	19	1	no	—
259	C₂²×C₄	—	19	1	no	—
260	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
261	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
262	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
263	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
264	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
265	C₄⋊C₄	—	38	2	no	—
266	C₄⋊C₄	—	38	2	no	—
267	C₄⋊C₄	—	38	2	no	—
268	C₄⋊C₄	—	38	2	no	—
269	C₄⋊C₄	—	76	1	no	—
270	C₄⋊C₄	—	76	1	no	—
271	C₂²⋊C₄	—	2	2	no	—
272	C₂²⋊C₄	—	2	2	no	—
273	C₂²⋊C₄	—	4	1	no	—
274	C₂²⋊C₄	—	38	2	no	—
275	C₂²⋊C₄	—	38	2	no	—
276	C₂²⋊C₄	—	38	2	no	—
277	C₂²⋊C₄	—	38	2	no	—
278	C₂²⋊C₄	—	38	2	no	—
279	C₂²⋊C₄	—	76	1	no	—
280	C₂²⋊C₄	—	76	1	no	—
281	C₂²⋊C₄	—	76	1	no	—
282	C₄²	—	38	2	no	—
283	C₄²	—	76	1	no	—
284	C₄²	—	76	1	no	—
285	C₄²	—	76	1	no	—
286	C₂³	—	2	1	no	—
287	C₂³	—	2	1	no	—
288	C₂³	—	2	1	no	—
289	C₂³	—	2	1	no	—
290	C₂³	—	2	1	no	—
291	C₂³	—	2	1	no	—
292	C₂³	—	2	1	no	—
293	C₂³	—	2	1	no	—
294	C₂³	—	2	1	no	—
295	C₂³	—	2	1	no	—
296	C₂³	—	2	1	no	—
297	C₂³	—	2	1	no	—
298	C₂³	—	2	1	no	—
299	C₂³	#64543	1	2	yes	—
300	C₂³	C₂³×D₁₉	1	1	yes	characteristic
301	D₄	—	4	4	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	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	—	4	4	no	—
316	C₂×C₄	—	19	2	no	—
317	C₂×C₄	—	19	2	no	—
318	C₂×C₄	—	38	1	no	—
319	C₂×C₄	—	38	1	no	—
320	C₂×C₄	—	38	1	no	—
321	C₂×C₄	—	38	1	no	—
322	C₂×C₄	—	38	1	no	—
323	C₂×C₄	—	38	1	no	—
324	C₂×C₄	—	38	1	no	—
325	C₂×C₄	—	38	1	no	—
326	C₂×C₄	—	38	1	no	—
327	C₂×C₄	—	38	1	no	—
328	C₂×C₄	—	38	1	no	—
329	C₂×C₄	—	38	1	no	—
330	C₂×C₄	—	38	1	no	—
331	C₂×C₄	—	38	1	no	—
332	C₂×C₄	—	38	1	no	—
333	C₂×C₄	—	38	1	no	—
334	C₂×C₄	—	38	1	no	—
335	C₂×C₄	—	38	1	no	—
336	C₂×C₄	—	38	1	no	—
337	C₂×C₄	—	38	1	no	—
338	C₂×C₄	—	38	1	no	—
339	C₂×C₄	—	38	1	no	—
340	C₂×C₄	#64541	1	2	yes	—
341	C₂×C₄	#64543	1	2	yes	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	4	1	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	4	1	no	—
349	C₂²	—	4	1	no	—
350	C₂²	—	4	1	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	C₂×#64541	1	1	yes	characteristic
357	C₂²	C₂×#64543	1	1	yes	characteristic
358	C₂²	C₂×#64543	1	1	yes	characteristic
359	C₂²	#10597430	1	1	yes	characteristic
360	C₂²	#10597430	1	1	yes	characteristic
361	C₂²	#41×D₁₉	1	1	yes	characteristic
362	C₂²	#41×D₁₉	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	4	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	38	2	no	—
369	C₄	—	38	2	no	—
370	C₄	—	76	1	no	—
371	C₄	—	76	1	no	—
372	C₄	—	76	1	no	—
373	C₄	—	76	1	no	—
374	C₄	—	76	1	no	—
375	C₄	—	76	1	no	—
376	C₂	—	4	2	no	—
377	C₂	—	8	1	no	—
378	C₂	#11927075	1	1	yes	characteristic
379	C₂	#11927076	1	1	yes	characteristic
380	C₂	#11927129	1	1	yes	characteristic
381	C₂	#11927220	1	1	yes	characteristic
382	C₂	#11927237	1	1	yes	characteristic
383	C₂	#11927244	1	1	yes	characteristic
384	C₂	#11927278	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#386	C₂
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	#386	D₁₉
hypocenter	C₁₉	#2597
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #386

Complements

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

N	H ≅ G/N	type
1. #11926486	C₂	semidirect
2. #11926472	C₂	semidirect
3. #11926472	C₂	semidirect
6. #11926438	C₂	semidirect
7. #11926437	C₂	semidirect
8. #11926437	C₂	semidirect
9. #11926432	C₂	semidirect
10. #11926431	C₂	semidirect
11. #11926429	C₂	semidirect
12. #11926417	C₂	semidirect
13. #11926395	C₂	semidirect
14. C₄×C₂²⋊Dic₁₉	C₂	semidirect
243. C₁₉	#2597	semidirect

Maximal subgroups

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

subgroup	index
#11926486	2
#11926472	2
#11926458	2
#11926447	2
#11926438	2
#11926437	2
#11926432	2
#11926431	2
#11926429	2
#11926417	2
#11926395	2
C₄×C₂²⋊Dic₁₉	2
C₁₉×#386	2
#2597	19