Subgroups — #14575072

Order 2432.

370 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927148	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927145	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926846	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926845	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926844	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926842	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926796	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926794	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926779	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926777	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926737	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926737	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926736	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926569	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#127	C₂²	1	1	yes	characteristic
19	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	#10597386	C₂²	1	1	yes	characteristic
21	#10597385	—	2	1	no	—
22	#10597385	—	2	1	no	—
23	#10597384	C₂²	1	1	yes	characteristic
24	#10597384	C₂²	1	1	yes	characteristic
25	#10597384	C₂²	1	1	yes	characteristic
26	#10597381	—	2	1	no	—
27	#10597381	—	2	1	no	—
28	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
29	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
30	C₂×#64525	C₂²	1	1	yes	characteristic
31	C₂×#64525	C₂²	1	1	yes	characteristic
32	#10597376	—	2	1	no	—
33	#10597375	—	2	1	no	—
34	C₂×#64515	C₂²	1	1	yes	characteristic
35	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
36	#10597341	C₂²	1	1	yes	characteristic
37	#10597336	C₂²	1	1	yes	characteristic
38	#10597330	—	2	1	no	—
39	#10597329	—	2	1	no	—
40	C₄×D₇₆	C₂²	1	1	yes	characteristic
41	#10597318	C₂²	1	1	yes	characteristic
42	#10597316	C₂²	1	1	yes	characteristic
43	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₁₉×#102	C₂²	1	1	yes	characteristic
45	C₁₉×#102	C₂²	1	1	yes	characteristic
46	#10597289	C₂²	1	1	yes	characteristic
47	#10597289	C₂²	1	1	yes	characteristic
48	#10597289	C₂²	1	1	yes	characteristic
49	#10597289	C₂²	1	1	yes	characteristic
50	#10597278	C₂²	1	1	yes	characteristic
51	#10597278	C₂²	1	1	yes	characteristic
52	#10597275	C₂²	1	1	yes	characteristic
53	#10597274	C₂²	1	1	yes	characteristic
54	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
55	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
56	#10597265	C₂²	1	1	yes	characteristic
57	#10597264	C₂²	1	1	yes	characteristic
58	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
59	C₂×D₄×C₁₉	—	2	1	no	—
60	C₂×D₄×C₁₉	—	2	1	no	—
61	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊D₁₉	—	2	1	no	—
66	C₂×C₂²⋊D₁₉	—	2	1	no	—
67	C₂×C₂²⋊D₁₉	—	2	1	no	—
68	C₂×C₂²⋊D₁₉	—	2	1	no	—
69	C₂×C₂²⋊D₁₉	—	2	1	no	—
70	C₂²×Dic₁₉	—	2	1	no	—
71	C₂²×Dic₁₉	—	2	1	no	—
72	C₂×D₇₆	—	2	1	no	—
73	C₂×D₇₆	C₂³	1	1	yes	characteristic
74	C₂×C₄×D₁₉	—	2	1	no	—
75	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
76	D₈×C₁₉	—	4	1	no	—
77	D₈×C₁₉	—	4	1	no	—
78	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂²⋊C₄×C₁₉	—	2	1	no	—
82	C₄²×C₁₉	C₂³	1	1	yes	characteristic
83	C₂²⋊Dic₁₉	—	2	1	no	—
84	C₂²⋊Dic₁₉	—	2	1	no	—
85	C₂²⋊Dic₁₉	—	2	1	no	—
86	C₂²⋊Dic₁₉	—	2	1	no	—
87	C₂²⋊Dic₁₉	—	2	1	no	—
88	#64525	—	4	1	no	—
89	#64525	—	4	1	no	—
90	(C₂×D₁₉)⋊C₄	—	2	1	no	—
91	(C₂×D₁₉)⋊C₄	—	2	1	no	—
92	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
93	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
94	C₄⋊Dic₁₉	—	2	1	no	—
95	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
96	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
97	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
98	Dic₁₉⋊C₄	—	2	1	no	—
99	Dic₁₉⋊C₄	—	2	1	no	—
100	Dic₁₉⋊C₄	—	2	1	no	—
101	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
102	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
103	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
105	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
106	#64515	—	4	1	no	—
107	C₈×D₁₉	—	4	1	no	—
108	C₂³×C₁₉	—	2	1	no	—
109	C₂³×C₁₉	—	2	1	no	—
110	C₂³×C₁₉	—	2	1	no	—
111	C₂²×D₁₉	—	2	1	no	—
112	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
113	D₄×C₁₉	—	2	1	no	—
114	D₄×C₁₉	—	2	1	no	—
115	D₄×C₁₉	—	2	1	no	—
116	D₄×C₁₉	—	2	1	no	—
117	D₄×C₁₉	—	2	1	no	—
118	D₄×C₁₉	—	2	1	no	—
119	D₄×C₁₉	—	8	1	no	—
120	D₄×C₁₉	—	8	1	no	—
121	C₂×C₄×C₁₉	—	2	1	no	—
122	C₂×C₄×C₁₉	—	8	1	no	—
123	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
126	C₂²⋊D₁₉	—	8	1	no	—
127	C₂²⋊D₁₉	—	8	1	no	—
128	C₂²⋊D₁₉	—	8	1	no	—
129	C₂²⋊D₁₉	—	8	1	no	—
130	C₂²⋊D₁₉	—	8	1	no	—
131	C₂×Dic₁₉	—	2	1	no	—
132	C₂×Dic₁₉	—	2	1	no	—
133	C₂×Dic₁₉	—	2	1	no	—
134	C₂×Dic₁₉	—	8	1	no	—
135	C₂×Dic₁₉	—	8	1	no	—
136	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
139	D₇₆	—	2	1	no	—
140	D₇₆	—	2	1	no	—
141	D₇₆	—	8	1	no	—
142	C₄×D₁₉	—	2	1	no	—
143	C₄×D₁₉	—	2	1	no	—
144	C₄×D₁₉	—	8	1	no	—
145	C₈×C₁₉	—	2	1	no	—
146	C₈×C₁₉	—	2	1	no	—
147	C₁₉⋊C₈	—	2	1	no	—
148	C₁₉⋊C₈	—	2	1	no	—
149	#3259	—	19	1	no	maximal, Sylow
150	C₂²×C₁₉	—	4	1	no	—
151	C₂²×C₁₉	—	4	1	no	—
152	C₂²×C₁₉	—	4	1	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	C₂²×D₄	1	1	yes	characteristic
160	C₂×D₁₉	—	2	1	no	—
161	C₂×D₁₉	—	2	1	no	—
162	C₂×D₁₉	—	2	1	no	—
163	C₂×D₁₉	—	4	1	no	—
164	C₂×D₁₉	—	4	1	no	—
165	C₂×D₁₉	—	4	1	no	—
166	C₄×C₁₉	—	2	1	no	—
167	C₄×C₁₉	—	2	1	no	—
168	C₄×C₁₉	—	4	1	no	—
169	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
170	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
171	Dic₁₉	—	2	1	no	—
172	Dic₁₉	—	2	1	no	—
173	Dic₁₉	—	2	1	no	—
174	Dic₁₉	—	4	1	no	—
175	Dic₁₉	—	4	1	no	—
176	Dic₁₉	—	4	1	no	—
177	#540	—	19	1	no	—
178	#540	—	19	1	no	—
179	#478	—	19	1	no	—
180	#478	—	19	1	no	—
181	#478	—	19	1	no	—
182	#478	—	19	1	no	—
183	#469	—	19	1	no	—
184	#469	—	19	1	no	—
185	#466	—	19	1	no	—
186	#466	—	19	1	no	—
187	#459	—	19	1	no	—
188	#459	—	19	1	no	—
189	#459	—	19	1	no	—
190	#459	D₁₉	1	1	yes	characteristic, complemented
191	#424	—	19	1	no	—
192	C₂×C₁₉	—	8	1	no	—
193	C₂×C₁₉	—	8	1	no	—
194	C₂×C₁₉	—	8	1	no	—
195	C₂×C₁₉	#537	1	1	yes	characteristic
196	C₂×C₁₉	#576	1	1	yes	characteristic
197	C₂×C₁₉	#576	1	1	yes	characteristic
198	D₁₉	—	4	1	no	—
199	D₁₉	—	8	1	no	—
200	C₂×D₈	—	19	1	no	—
201	C₂×D₈	—	19	1	no	—
202	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
203	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
204	C₂×M₁₆	—	19	1	no	—
205	C₂²×C₈	—	19	1	no	—
206	#127	—	19	1	no	—
207	#127	C₂×D₁₉	1	1	yes	characteristic
208	#125	—	19	1	no	—
209	#125	—	19	1	no	—
210	#123	—	38	1	no	—
211	#123	—	38	1	no	—
212	#123	—	38	1	no	—
213	#123	—	38	1	no	—
214	#121	—	19	1	no	—
215	#121	—	19	1	no	—
216	#121	—	19	1	no	—
217	#121	—	19	1	no	—
218	#121	—	38	1	no	—
219	#121	—	38	1	no	—
220	#121	—	38	1	no	—
221	#121	—	38	1	no	—
222	C₄×D₄	—	19	1	no	—
223	C₄×D₄	—	19	1	no	—
224	C₄×D₄	—	19	1	no	—
225	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
226	#117	—	19	1	no	—
227	#107	—	19	1	no	—
228	#107	—	19	1	no	—
229	#106	—	19	1	no	—
230	#106	—	19	1	no	—
231	C₄⋊C₈	—	19	1	no	—
232	C₄⋊C₈	—	19	1	no	—
233	C₄⋊C₈	—	19	1	no	—
234	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
235	#102	—	19	1	no	—
236	#102	—	19	1	no	—
237	#102	—	19	1	no	—
238	#102	—	19	1	no	—
239	#102	—	19	1	no	—
240	#102	—	19	1	no	—
241	#102	C₂×D₁₉	1	1	yes	characteristic
242	#102	C₂×D₁₉	1	1	yes	characteristic
243	C₁₉	#3259	1	1	yes	characteristic, complemented, Sylow
244	C₂×D₄	—	2	1	no	—
245	C₂×D₄	—	2	1	no	—
246	C₂×D₄	—	19	1	no	—
247	C₂×D₄	—	38	1	no	—
248	C₂×D₄	—	38	1	no	—
249	C₂×D₄	—	38	1	no	—
250	C₂×D₄	—	38	1	no	—
251	C₂×D₄	—	38	1	no	—
252	C₂×D₄	—	38	1	no	—
253	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
254	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
255	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	19	1	no	—
258	C₂²×C₄	—	38	1	no	—
259	C₂²×C₄	—	38	1	no	—
260	C₂²×C₄	—	38	1	no	—
261	D₈	—	4	1	no	—
262	D₈	—	4	1	no	—
263	D₈	—	76	1	no	—
264	D₈	—	76	1	no	—
265	M₁₆	—	76	1	no	—
266	C₂×C₈	—	19	1	no	—
267	C₂×C₈	—	19	1	no	—
268	C₂×C₈	—	76	1	no	—
269	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
270	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
271	C₄⋊C₄	—	19	1	no	—
272	C₄⋊C₄	—	19	1	no	—
273	C₄⋊C₄	—	19	1	no	—
274	C₄⋊C₄	—	19	1	no	—
275	C₄⋊C₄	—	19	1	no	—
276	C₄⋊C₄	—	38	1	no	—
277	C₄⋊C₄	—	38	1	no	—
278	C₄⋊C₄	—	38	1	no	—
279	C₄⋊C₄	—	38	1	no	—
280	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
281	C₂²⋊C₄	—	2	1	no	—
282	C₂²⋊C₄	—	19	1	no	—
283	C₂²⋊C₄	—	19	1	no	—
284	C₂²⋊C₄	—	38	1	no	—
285	C₂²⋊C₄	—	38	1	no	—
286	C₂²⋊C₄	—	38	1	no	—
287	C₂²⋊C₄	—	38	1	no	—
288	C₂²⋊C₄	—	38	1	no	—
289	C₂²⋊C₄	—	38	1	no	—
290	C₂²⋊C₄	—	38	1	no	—
291	C₄²	—	19	1	no	—
292	C₄²	C₂²×D₁₉	1	1	yes	characteristic
293	C₂³	—	2	1	no	—
294	C₂³	—	2	1	no	—
295	C₂³	—	2	1	no	—
296	C₂³	—	19	1	no	—
297	C₂³	—	38	1	no	—
298	D₄	—	2	1	no	—
299	D₄	—	2	1	no	—
300	D₄	—	2	1	no	—
301	D₄	—	2	1	no	—
302	D₄	—	2	1	no	—
303	D₄	—	2	1	no	—
304	D₄	—	8	1	no	—
305	D₄	—	8	1	no	—
306	D₄	—	38	1	no	—
307	D₄	—	38	1	no	—
308	D₄	—	152	1	no	—
309	D₄	—	152	1	no	—
310	D₄	—	152	1	no	—
311	D₄	—	152	1	no	—
312	D₄	—	152	1	no	—
313	D₄	—	152	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	8	1	no	—
316	C₂×C₄	—	19	1	no	—
317	C₂×C₄	—	19	1	no	—
318	C₂×C₄	—	19	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	—	152	1	no	—
325	C₂×C₄	—	152	1	no	—
326	C₂×C₄	—	152	1	no	—
327	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
328	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
329	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
330	C₈	—	2	1	no	—
331	C₈	—	2	1	no	—
332	C₈	—	38	1	no	—
333	C₈	—	38	1	no	—
334	C₂²	—	4	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	4	1	no	—
339	C₂²	—	4	1	no	—
340	C₂²	—	4	1	no	—
341	C₂²	—	4	1	no	—
342	C₂²	—	4	1	no	—
343	C₂²	—	38	1	no	—
344	C₂²	—	38	1	no	—
345	C₂²	—	38	1	no	—
346	C₂²	—	76	1	no	—
347	C₂²	—	76	1	no	—
348	C₂²	—	76	1	no	—
349	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	4	1	no	—
353	C₄	—	38	1	no	—
354	C₄	—	38	1	no	—
355	C₄	—	38	1	no	—
356	C₄	—	76	1	no	—
357	C₄	—	76	1	no	—
358	C₄	—	76	1	no	—
359	C₄	#10597430	1	1	yes	characteristic
360	C₄	#10597436	1	1	yes	characteristic
361	C₂	—	8	1	no	—
362	C₂	—	8	1	no	—
363	C₂	—	8	1	no	—
364	C₂	—	76	1	no	—
365	C₂	—	152	1	no	—
366	C₂	#11927123	1	1	yes	characteristic
367	C₂	#11927345	1	1	yes	characteristic
368	C₂	#11927348	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#459	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#459	D₁₉
hypocenter	C₁₉	#3259
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #459

Complements

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

N	H ≅ G/N	type
1. #11927148	C₂	semidirect
2. #11927145	C₂	semidirect
3. #11926846	C₂	semidirect
4. #11926845	C₂	semidirect
5. #11926844	C₂	semidirect
6. #11926842	C₂	semidirect
7. #11926796	C₂	semidirect
8. #11926794	C₂	semidirect
9. #11926779	C₂	semidirect
10. #11926777	C₂	semidirect
11. #11926737	C₂	semidirect
12. #11926737	C₂	semidirect
13. #11926736	C₂	semidirect
14. #11926569	C₂	semidirect
15. C₁₉×#459	C₂	semidirect
190. #459	D₁₉	semidirect
243. C₁₉	#3259	semidirect

Maximal subgroups

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

subgroup	index
#11927148	2
#11927145	2
#11926846	2
#11926845	2
#11926844	2
#11926842	2
#11926796	2
#11926794	2
#11926779	2
#11926777	2
#11926737	2
#11926736	2
#11926569	2
C₁₉×#459	2
#3259	19