Subgroups — #14568888

Order 2432.

412 conjugacy classes of subgroups.

The subgroup lattice has 350 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	#11926483	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926471	C₂	1	1	yes	maximal, characteristic
4	#11926466	C₂	1	1	yes	maximal, characteristic
5	#11926442	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926435	C₂	1	1	yes	maximal, characteristic
7	#11926435	C₂	1	1	yes	maximal, characteristic
8	#11926428	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926428	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926425	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926415	C₂	1	1	yes	maximal, characteristic
12	#11926411	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926406	C₂	1	1	yes	maximal, characteristic
14	C₄×(C₂×D₁₉)⋊C₄	C₂	1	1	yes	maximal, characteristic
15	C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
30	C₂×Dic₁₉⋊C₄	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×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
35	C₁₉×#95	C₂²	1	1	yes	characteristic
36	C₁₉×#95	C₂²	1	1	yes	characteristic
37	C₁₉⋊#95	C₂²	1	1	yes	characteristic
38	C₁₉⋊#95	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	C₂³×D₁₉	C₂³	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
60	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
61	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
62	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
63	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
64	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
65	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
66	C₂×C₄×D₁₉	—	2	2	no	—
67	C₂×C₄×D₁₉	—	2	2	no	—
68	C₂×C₄×D₁₉	—	4	1	no	—
69	C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₄²×C₁₉	—	2	2	no	—
72	C₄²×C₁₉	—	4	1	no	—
73	C₄²×C₁₉	—	4	1	no	—
74	(C₂×D₁₉)⋊C₄	—	2	2	no	—
75	(C₂×D₁₉)⋊C₄	—	2	2	no	—
76	(C₂×D₁₉)⋊C₄	—	2	2	no	—
77	(C₂×D₁₉)⋊C₄	—	2	2	no	—
78	(C₂×D₁₉)⋊C₄	—	2	2	no	—
79	(C₂×D₁₉)⋊C₄	—	4	1	no	—
80	C₄⋊Dic₁₉	—	2	2	no	—
81	C₄⋊Dic₁₉	—	4	1	no	—
82	Dic₁₉⋊C₄	—	2	2	no	—
83	Dic₁₉⋊C₄	—	2	2	no	—
84	Dic₁₉⋊C₄	—	2	2	no	—
85	Dic₁₉⋊C₄	—	4	1	no	—
86	C₄×Dic₁₉	—	2	2	no	—
87	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
88	C₂²×D₁₉	—	2	1	no	—
89	C₂²×D₁₉	—	2	1	no	—
90	C₂²×D₁₉	—	2	1	no	—
91	C₂²×D₁₉	—	2	1	no	—
92	C₂²×D₁₉	—	2	1	no	—
93	C₂²×D₁₉	—	2	1	no	—
94	C₂²×D₁₉	#41	1	2	yes	—
95	C₂×C₄×C₁₉	—	2	1	no	—
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	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	#41	1	2	yes	—
113	C₂×C₄×C₁₉	#41	1	2	yes	—
114	C₂×C₄×C₁₉	#41	1	2	yes	—
115	C₂×C₄×C₁₉	#41	1	2	yes	—
116	C₂×Dic₁₉	—	2	1	no	—
117	C₂×Dic₁₉	—	2	1	no	—
118	C₂×Dic₁₉	—	2	1	no	—
119	C₂×Dic₁₉	—	2	1	no	—
120	C₂×Dic₁₉	—	2	1	no	—
121	C₂×Dic₁₉	—	2	1	no	—
122	C₂×Dic₁₉	—	2	1	no	—
123	C₂×Dic₁₉	—	2	1	no	—
124	C₂×Dic₁₉	—	2	1	no	—
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	C₄×D₁₉	—	4	4	no	—
138	#2573	—	19	1	no	maximal, Sylow
139	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
140	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
141	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
142	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
143	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
144	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
145	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
146	C₂×D₁₉	—	2	2	no	—
147	C₂×D₁₉	—	2	2	no	—
148	C₂×D₁₉	—	2	2	no	—
149	C₂×D₁₉	—	4	1	no	—
150	C₂×D₁₉	—	4	1	no	—
151	C₂×D₁₉	—	4	1	no	—
152	C₂×D₁₉	—	4	1	no	—
153	C₄×C₁₉	—	2	2	no	—
154	C₄×C₁₉	—	2	2	no	—
155	C₄×C₁₉	—	2	2	no	—
156	C₄×C₁₉	—	2	2	no	—
157	C₄×C₁₉	—	4	1	no	—
158	C₄×C₁₉	—	4	1	no	—
159	C₄×C₁₉	—	4	1	no	—
160	Dic₁₉	—	4	1	no	—
161	Dic₁₉	—	4	1	no	—
162	Dic₁₉	—	4	1	no	—
163	Dic₁₉	—	4	1	no	—
164	Dic₁₉	—	4	1	no	—
165	Dic₁₉	—	4	1	no	—
166	Dic₁₉	—	4	1	no	—
167	#400	—	19	1	no	—
168	#400	—	19	1	no	—
169	#397	—	19	1	no	—
170	#396	—	19	1	no	—
171	#389	—	19	1	no	—
172	#388	—	19	1	no	—
173	#388	—	19	1	no	—
174	#387	—	19	1	no	—
175	#387	—	19	1	no	—
176	#387	—	19	1	no	—
177	#385	—	19	1	no	—
178	#383	—	19	1	no	—
179	#381	—	19	1	no	—
180	C₄×C₄⋊C₄	D₁₉	1	1	yes	characteristic, complemented
181	C₄×C₂²⋊C₄	—	19	1	no	—
182	C₂×C₁₉	#529	1	1	yes	characteristic
183	C₂×C₁₉	#529	1	1	yes	characteristic
184	C₂×C₁₉	#539	1	1	yes	characteristic
185	C₂×C₁₉	#551	1	1	yes	characteristic
186	C₂×C₁₉	#552	1	1	yes	characteristic
187	C₂×C₁₉	#553	1	1	yes	characteristic
188	C₂×C₁₉	#556	1	1	yes	characteristic
189	D₁₉	—	4	2	no	—
190	C₂³×C₄	—	19	1	no	—
191	C₂×C₄⋊C₄	—	19	1	no	—
192	C₂×C₄⋊C₄	—	19	1	no	—
193	C₂×C₄⋊C₄	—	19	1	no	—
194	C₂×C₄⋊C₄	—	19	1	no	—
195	C₂×C₄⋊C₄	—	19	1	no	—
196	C₂×C₄⋊C₄	—	19	1	no	—
197	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
198	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
199	C₂×C₂²⋊C₄	—	19	1	no	—
200	C₂×C₂²⋊C₄	—	19	1	no	—
201	C₂×C₂²⋊C₄	—	19	1	no	—
202	C₂×C₂²⋊C₄	—	19	1	no	—
203	C₂×C₂²⋊C₄	—	19	1	no	—
204	C₂×C₂²⋊C₄	—	19	1	no	—
205	C₂×C₄²	—	19	1	no	—
206	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
207	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
208	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
209	#95	—	19	1	no	—
210	#95	—	19	1	no	—
211	#95	—	19	1	no	—
212	#95	—	19	1	no	—
213	#95	—	19	1	no	—
214	#95	—	19	1	no	—
215	#95	—	19	1	no	—
216	#95	—	19	1	no	—
217	#95	—	19	1	no	—
218	#95	—	19	1	no	—
219	#95	—	19	1	no	—
220	#95	—	19	1	no	—
221	#95	—	19	1	no	—
222	#95	—	19	1	no	—
223	#95	C₂×D₁₉	1	1	yes	characteristic
224	#95	C₂×D₁₉	1	1	yes	characteristic
225	C₁₉	#2573	1	1	yes	characteristic, complemented, Sylow
226	C₂⁴	—	19	1	no	—
227	C₂²×C₄	—	19	1	no	—
228	C₂²×C₄	—	19	1	no	—
229	C₂²×C₄	—	19	1	no	—
230	C₂²×C₄	—	19	1	no	—
231	C₂²×C₄	—	19	1	no	—
232	C₂²×C₄	—	19	1	no	—
233	C₂²×C₄	—	19	1	no	—
234	C₂²×C₄	—	38	2	no	—
235	C₂²×C₄	—	38	2	no	—
236	C₂²×C₄	—	76	1	no	—
237	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
238	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
239	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
240	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
241	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
242	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
243	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
244	C₄⋊C₄	—	2	2	no	—
245	C₄⋊C₄	—	2	2	no	—
246	C₄⋊C₄	—	38	2	no	—
247	C₄⋊C₄	—	38	2	no	—
248	C₄⋊C₄	—	38	2	no	—
249	C₄⋊C₄	—	38	2	no	—
250	C₄⋊C₄	—	76	1	no	—
251	C₄⋊C₄	—	76	1	no	—
252	C₂²⋊C₄	—	38	2	no	—
253	C₂²⋊C₄	—	38	2	no	—
254	C₂²⋊C₄	—	38	2	no	—
255	C₂²⋊C₄	—	38	2	no	—
256	C₂²⋊C₄	—	38	2	no	—
257	C₂²⋊C₄	—	76	1	no	—
258	C₄²	—	2	2	no	—
259	C₄²	—	4	1	no	—
260	C₄²	—	4	1	no	—
261	C₄²	—	38	2	no	—
262	C₂³	—	19	2	no	—
263	C₂³	—	38	1	no	—
264	C₂³	—	38	1	no	—
265	C₂³	—	38	1	no	—
266	C₂³	—	38	1	no	—
267	C₂³	—	38	1	no	—
268	C₂³	—	38	1	no	—
269	C₂³	C₂³×D₁₉	1	1	yes	characteristic
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	2	1	no	—
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	—	2	1	no	—
274	C₂×C₄	—	2	1	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	1	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	38	1	no	—
288	C₂×C₄	—	38	1	no	—
289	C₂×C₄	—	38	1	no	—
290	C₂×C₄	—	38	1	no	—
291	C₂×C₄	—	38	1	no	—
292	C₂×C₄	—	38	1	no	—
293	C₂×C₄	—	38	1	no	—
294	C₂×C₄	—	38	1	no	—
295	C₂×C₄	—	38	1	no	—
296	C₂×C₄	—	38	1	no	—
297	C₂×C₄	—	38	1	no	—
298	C₂×C₄	—	38	1	no	—
299	C₂×C₄	—	38	1	no	—
300	C₂×C₄	—	38	1	no	—
301	C₂×C₄	—	38	1	no	—
302	C₂×C₄	—	38	1	no	—
303	C₂×C₄	—	38	1	no	—
304	C₂×C₄	—	38	1	no	—
305	C₂×C₄	—	38	1	no	—
306	C₂×C₄	—	38	1	no	—
307	C₂×C₄	—	38	1	no	—
308	C₂×C₄	—	76	4	no	—
309	C₂×C₄	#64541	1	2	yes	—
310	C₂×C₄	#64541	1	2	yes	—
311	C₂×C₄	#64541	1	2	yes	—
312	C₂×C₄	#64545	1	2	yes	—
313	C₂²	—	38	2	no	—
314	C₂²	—	38	2	no	—
315	C₂²	—	38	2	no	—
316	C₂²	—	76	1	no	—
317	C₂²	—	76	1	no	—
318	C₂²	—	76	1	no	—
319	C₂²	—	76	1	no	—
320	C₂²	C₂×#64541	1	1	yes	characteristic
321	C₂²	C₂×#64541	1	1	yes	characteristic
322	C₂²	C₂×#64541	1	1	yes	characteristic
323	C₂²	#10597430	1	1	yes	characteristic
324	C₂²	C₂×#64545	1	1	yes	characteristic
325	C₂²	#41×D₁₉	1	1	yes	characteristic
326	C₂²	#10597436	1	1	yes	characteristic
327	C₄	—	2	2	no	—
328	C₄	—	2	2	no	—
329	C₄	—	2	2	no	—
330	C₄	—	2	2	no	—
331	C₄	—	4	1	no	—
332	C₄	—	4	1	no	—
333	C₄	—	4	1	no	—
334	C₄	—	76	1	no	—
335	C₄	—	76	1	no	—
336	C₄	—	76	1	no	—
337	C₄	—	76	1	no	—
338	C₄	—	76	1	no	—
339	C₄	—	76	1	no	—
340	C₄	—	76	1	no	—
341	C₂	—	76	2	no	—
342	C₂	#11927078	1	1	yes	characteristic
343	C₂	#11927081	1	1	yes	characteristic
344	C₂	#11927136	1	1	yes	characteristic
345	C₂	#11927223	1	1	yes	characteristic
346	C₂	#11927233	1	1	yes	characteristic
347	C₂	#11927242	1	1	yes	characteristic
348	C₂	#11927267	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₄×C₄⋊C₄×C₁₉	C₂
prime radical	C₂³×D₁₉	C₂³
hypercenter	C₄×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#2573
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. #11926486	C₂	semidirect
2. #11926483	C₂	semidirect
5. #11926442	C₂	semidirect
8. #11926428	C₂	semidirect
9. #11926428	C₂	semidirect
10. #11926425	C₂	semidirect
12. #11926411	C₂	semidirect
15. C₄×C₄⋊C₄×C₁₉	C₂	semidirect
180. C₄×C₄⋊C₄	D₁₉	semidirect
225. C₁₉	#2573	semidirect

Maximal subgroups

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

subgroup	index
#11926486	2
#11926483	2
#11926471	2
#11926466	2
#11926442	2
#11926435	2
#11926428	2
#11926425	2
#11926415	2
#11926411	2
#11926406	2
C₄×(C₂×D₁₉)⋊C₄	2
C₄×C₄⋊C₄×C₁₉	2
#2573	19