Subgroups — C₁₉×#2776 #14560633

Order 2432.

344 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#401	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#400	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#400	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#400	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#398	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#398	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#389	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#389	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#389	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#387	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#387	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#387	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#387	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#387	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#383	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄⋊C₄×C₁₉	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×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#95	C₂²	1	1	yes	characteristic
32	C₁₉×#95	C₂²	1	1	yes	characteristic
33	C₁₉×#95	C₂²	1	1	yes	characteristic
34	C₁₉×#95	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	C₂²×C₄×C₁₉	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×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×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₄⋊C₄×C₁₉	—	4	1	no	—
75	C₄⋊C₄×C₁₉	—	4	1	no	—
76	C₄⋊C₄×C₁₉	—	4	1	no	—
77	C₄⋊C₄×C₁₉	—	4	1	no	—
78	C₄²×C₁₉	—	2	2	no	—
79	C₄²×C₁₉	—	4	1	no	—
80	C₄²×C₁₉	—	4	1	no	—
81	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
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	—	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	#41	1	2	yes	—
125	C₂×C₄×C₁₉	#41	1	2	yes	—
126	C₂×C₄×C₁₉	#41	1	2	yes	—
127	#2776	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
129	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
130	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
131	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
132	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
133	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
134	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
135	C₄×C₁₉	—	2	2	no	—
136	C₄×C₁₉	—	2	2	no	—
137	C₄×C₁₉	—	2	2	no	—
138	C₄×C₁₉	—	4	1	no	—
139	C₄×C₁₉	—	4	1	no	—
140	C₄×C₁₉	—	4	1	no	—
141	C₄×C₁₉	—	4	1	no	—
142	C₄×C₁₉	—	4	1	no	—
143	C₄×C₁₉	—	4	1	no	—
144	C₄×C₁₉	—	4	1	no	—
145	C₄×C₁₉	—	4	1	no	—
146	C₄×C₁₉	—	4	1	no	—
147	C₄×C₁₉	—	4	1	no	—
148	C₄×C₁₉	—	4	1	no	—
149	C₄×C₁₉	—	4	1	no	—
150	#401	C₂×C₁₉	1	1	yes	characteristic
151	#400	C₂×C₁₉	1	1	yes	characteristic
152	#400	C₂×C₁₉	1	1	yes	characteristic
153	#400	C₂×C₁₉	1	1	yes	characteristic
154	#398	C₂×C₁₉	1	1	yes	characteristic
155	#398	C₂×C₁₉	1	1	yes	characteristic
156	#389	C₂×C₁₉	1	1	yes	characteristic
157	#389	C₂×C₁₉	1	1	yes	characteristic
158	#389	C₂×C₁₉	1	1	yes	characteristic
159	#387	C₂×C₁₉	1	1	yes	characteristic
160	#387	C₂×C₁₉	1	1	yes	characteristic
161	#387	C₂×C₁₉	1	1	yes	characteristic
162	#387	C₂×C₁₉	1	1	yes	characteristic
163	#387	C₂×C₁₉	1	1	yes	characteristic
164	#383	C₂×C₁₉	1	1	yes	characteristic
165	C₂×C₁₉	#539	1	1	yes	characteristic
166	C₂×C₁₉	#541	1	1	yes	characteristic
167	C₂×C₁₉	#541	1	1	yes	characteristic
168	C₂×C₁₉	#552	1	1	yes	characteristic
169	C₂×C₁₉	#553	1	1	yes	characteristic
170	C₂×C₁₉	#556	1	1	yes	characteristic
171	C₂×C₁₉	#563	1	1	yes	characteristic
172	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
173	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
174	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
175	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
176	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
177	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
178	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
179	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
180	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
181	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
182	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
183	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
184	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
185	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
186	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
187	#95	C₂²×C₁₉	1	1	yes	characteristic
188	#95	C₂²×C₁₉	1	1	yes	characteristic
189	#95	C₂²×C₁₉	1	1	yes	characteristic
190	#95	C₂²×C₁₉	1	1	yes	characteristic
191	#95	C₂²×C₁₉	1	1	yes	characteristic
192	#95	C₂²×C₁₉	1	1	yes	characteristic
193	#95	C₂²×C₁₉	1	1	yes	characteristic
194	#95	C₂²×C₁₉	1	1	yes	characteristic
195	#95	C₂²×C₁₉	1	1	yes	characteristic
196	#95	C₂²×C₁₉	1	1	yes	characteristic
197	#95	C₂²×C₁₉	1	1	yes	characteristic
198	#95	C₂²×C₁₉	1	1	yes	characteristic
199	#95	C₂²×C₁₉	1	1	yes	characteristic
200	#95	C₂²×C₁₉	1	1	yes	characteristic
201	#95	C₂²×C₁₉	1	1	yes	characteristic
202	#95	C₂²×C₁₉	1	1	yes	characteristic
203	#95	C₂²×C₁₉	1	1	yes	characteristic
204	#95	C₂²×C₁₉	1	1	yes	characteristic
205	#95	C₂²×C₁₉	1	1	yes	characteristic
206	#95	C₂²×C₁₉	1	1	yes	characteristic
207	C₁₉	#2776	1	1	yes	characteristic, direct product factor, Sylow
208	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
209	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
210	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
211	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
212	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
213	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
214	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
215	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
216	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
217	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
218	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
219	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
220	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
221	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
222	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
223	C₄⋊C₄	—	2	2	no	—
224	C₄⋊C₄	—	2	2	no	—
225	C₄⋊C₄	—	2	2	no	—
226	C₄⋊C₄	—	2	2	no	—
227	C₄⋊C₄	—	2	2	no	—
228	C₄⋊C₄	—	2	2	no	—
229	C₄⋊C₄	—	2	2	no	—
230	C₄⋊C₄	—	2	2	no	—
231	C₄⋊C₄	—	4	1	no	—
232	C₄⋊C₄	—	4	1	no	—
233	C₄⋊C₄	—	4	1	no	—
234	C₄⋊C₄	—	4	1	no	—
235	C₄²	—	2	2	no	—
236	C₄²	—	4	1	no	—
237	C₄²	—	4	1	no	—
238	C₂³	C₂⁴×C₁₉	1	1	yes	characteristic
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	2	1	no	—
244	C₂×C₄	—	2	1	no	—
245	C₂×C₄	—	2	1	no	—
246	C₂×C₄	—	2	1	no	—
247	C₂×C₄	—	2	1	no	—
248	C₂×C₄	—	2	1	no	—
249	C₂×C₄	—	2	1	no	—
250	C₂×C₄	—	2	1	no	—
251	C₂×C₄	—	2	1	no	—
252	C₂×C₄	—	2	1	no	—
253	C₂×C₄	—	2	1	no	—
254	C₂×C₄	—	2	1	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	2	1	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	2	1	no	—
260	C₂×C₄	—	2	1	no	—
261	C₂×C₄	—	2	1	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	2	1	no	—
264	C₂×C₄	—	2	1	no	—
265	C₂×C₄	—	2	1	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	2	1	no	—
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	#41×C₁₉	1	2	yes	—
282	C₂×C₄	#41×C₁₉	1	2	yes	—
283	C₂×C₄	#41×C₁₉	1	2	yes	—
284	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
285	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
286	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
287	C₂²	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
288	C₂²	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
289	C₂²	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
290	C₂²	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
291	C₄	—	2	2	no	—
292	C₄	—	2	2	no	—
293	C₄	—	2	2	no	—
294	C₄	—	4	1	no	—
295	C₄	—	4	1	no	—
296	C₄	—	4	1	no	—
297	C₄	—	4	1	no	—
298	C₄	—	4	1	no	—
299	C₄	—	4	1	no	—
300	C₄	—	4	1	no	—
301	C₄	—	4	1	no	—
302	C₄	—	4	1	no	—
303	C₄	—	4	1	no	—
304	C₄	—	4	1	no	—
305	C₄	—	4	1	no	—
306	C₂	C₁₉×#539	1	1	yes	characteristic
307	C₂	C₁₉×#541	1	1	yes	characteristic
308	C₂	C₁₉×#541	1	1	yes	characteristic
309	C₂	C₁₉×#552	1	1	yes	characteristic
310	C₂	C₁₉×#553	1	1	yes	characteristic
311	C₂	C₁₉×#556	1	1	yes	characteristic
312	C₂	C₁₉×#563	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
127. #2776	C₁₉	direct (N × H)
207. C₁₉	#2776	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#401	2
C₁₉×#400	2
C₁₉×#398	2
C₁₉×#389	2
C₁₉×#387	2
C₁₉×#383	2
#2776	19

Subgroups — C19×#2776 #14560633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2776 #14560633