Subgroups — C₁₉×#14656 #18020615

Order 4864.

1030 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#401	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1444	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1444	C₂	1	3	yes	maximal
4	C₁₉×#1443	C₂	1	3	yes	maximal
5	C₁₉×#1443	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1442	C₂	1	3	yes	maximal
7	C₁₉×#1436	C₂	1	3	yes	maximal
8	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
9	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
10	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#401	C₄	1	8	yes	complemented
12	C₂×C₁₉×#95	C₂²	1	3	yes	—
13	C₂×C₁₉×#95	C₂²	1	3	yes	—
14	C₂×C₁₉×#95	C₂²	1	3	yes	—
15	C₂×C₁₉×#95	C₂²	1	3	yes	—
16	C₂×C₁₉×#95	C₂²	1	3	yes	—
17	C₂×C₁₉×#95	C₂²	1	3	yes	—
18	C₂×C₁₉×#95	C₂²	1	3	yes	—
19	C₂×C₁₉×#95	C₂²	1	3	yes	—
20	C₂×C₁₉×#95	C₂²	1	3	yes	—
21	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
23	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
24	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
26	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
27	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
30	C₂×C₄⋊C₄×C₁₉	—	4	3	no	—
31	C₂×C₄⋊C₄×C₁₉	—	4	3	no	—
32	C₂×C₄⋊C₄×C₁₉	—	4	3	no	—
33	C₂×C₄⋊C₄×C₁₉	—	4	3	no	—
34	C₂×C₄⋊C₄×C₁₉	—	4	3	no	—
35	C₂×C₄²×C₁₉	—	4	3	no	—
36	C₁₉×#95	—	2	6	no	—
37	C₁₉×#95	—	4	3	no	—
38	C₁₉×#95	—	4	3	no	—
39	C₁₉×#95	—	4	3	no	—
40	C₁₉×#95	—	4	3	no	—
41	C₁₉×#95	—	4	3	no	—
42	C₁₉×#95	—	4	3	no	—
43	C₁₉×#95	C₂×C₄	1	12	yes	—
44	C₁₉×#95	C₂×C₄	1	12	yes	—
45	C₁₉×#95	C₂×C₄	1	4	yes	—
46	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	—	2	3	no	—
48	C₂²×C₄×C₁₉	—	2	3	no	—
49	C₂²×C₄×C₁₉	—	2	3	no	—
50	C₂²×C₄×C₁₉	—	2	3	no	—
51	C₂²×C₄×C₁₉	—	2	3	no	—
52	C₂²×C₄×C₁₉	—	2	3	no	—
53	C₂²×C₄×C₁₉	—	2	3	no	—
54	C₂²×C₄×C₁₉	—	2	3	no	—
55	C₂²×C₄×C₁₉	—	2	3	no	—
56	C₂²×C₄×C₁₉	—	2	3	no	—
57	C₂²×C₄×C₁₉	—	2	3	no	—
58	C₂²×C₄×C₁₉	—	2	3	no	—
59	C₂²×C₄×C₁₉	—	2	3	no	—
60	C₂²×C₄×C₁₉	—	2	3	no	—
61	C₂²×C₄×C₁₉	—	2	3	no	—
62	C₂²×C₄×C₁₉	—	2	3	no	—
63	C₂²×C₄×C₁₉	—	2	3	no	—
64	C₂²×C₄×C₁₉	—	2	3	no	—
65	C₂²×C₄×C₁₉	—	2	3	no	—
66	C₂²×C₄×C₁₉	—	2	3	no	—
67	C₂²×C₄×C₁₉	—	2	3	no	—
68	C₂²×C₄×C₁₉	—	2	3	no	—
69	C₂²×C₄×C₁₉	—	2	3	no	—
70	C₂²×C₄×C₁₉	—	2	3	no	—
71	C₂²×C₄×C₁₉	—	2	3	no	—
72	C₂²×C₄×C₁₉	—	2	3	no	—
73	C₂²×C₄×C₁₉	—	2	3	no	—
74	C₂²×C₄×C₁₉	—	2	3	no	—
75	C₂²×C₄×C₁₉	—	2	3	no	—
76	C₂²×C₄×C₁₉	—	2	3	no	—
77	C₂²×C₄×C₁₉	—	2	3	no	—
78	C₂²×C₄×C₁₉	—	2	3	no	—
79	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
80	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
82	C₂²×C₄×C₁₉	#41	1	2	yes	—
83	C₂²×C₄×C₁₉	#41	1	2	yes	—
84	C₄⋊C₄×C₁₉	—	4	12	no	—
85	C₄⋊C₄×C₁₉	—	4	12	no	—
86	C₄²×C₁₉	—	4	4	no	—
87	#14656	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
89	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
90	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
91	C₂³×C₁₉	H(5,𝔽₂)	1	3	yes	—
92	C₂³×C₁₉	H(5,𝔽₂)	1	3	yes	—
93	C₂³×C₁₉	2₋¹⁺⁴	1	3	yes	—
94	C₂³×C₁₉	2₋¹⁺⁴	1	3	yes	—
95	C₂×C₄×C₁₉	—	2	6	no	—
96	C₂×C₄×C₁₉	—	2	6	no	—
97	C₂×C₄×C₁₉	—	2	6	no	—
98	C₂×C₄×C₁₉	—	2	6	no	—
99	C₂×C₄×C₁₉	—	2	6	no	—
100	C₂×C₄×C₁₉	—	2	6	no	—
101	C₂×C₄×C₁₉	—	2	6	no	—
102	C₂×C₄×C₁₉	—	2	6	no	—
103	C₂×C₄×C₁₉	—	2	6	no	—
104	C₂×C₄×C₁₉	—	4	3	no	—
105	C₂×C₄×C₁₉	—	4	3	no	—
106	C₂×C₄×C₁₉	—	4	3	no	—
107	C₂×C₄×C₁₉	—	4	3	no	—
108	C₂×C₄×C₁₉	—	4	1	no	—
109	C₂×C₄×C₁₉	—	4	1	no	—
110	C₂×C₄×C₁₉	—	4	1	no	—
111	C₂×C₄×C₁₉	—	4	3	no	—
112	C₂×C₄×C₁₉	—	4	3	no	—
113	C₂×C₄×C₁₉	—	4	3	no	—
114	C₂×C₄×C₁₉	—	4	3	no	—
115	C₂×C₄×C₁₉	—	4	3	no	—
116	C₂×C₄×C₁₉	—	4	3	no	—
117	C₂×C₄×C₁₉	—	4	3	no	—
118	C₂×C₄×C₁₉	—	4	3	no	—
119	C₂×C₄×C₁₉	—	4	3	no	—
120	C₂×C₄×C₁₉	—	4	3	no	—
121	C₂×C₄×C₁₉	—	4	3	no	—
122	C₂×C₄×C₁₉	—	4	3	no	—
123	C₂×C₄×C₁₉	—	4	3	no	—
124	C₂×C₄×C₁₉	—	4	3	no	—
125	C₂×C₄×C₁₉	—	4	3	no	—
126	C₂×C₄×C₁₉	—	4	3	no	—
127	C₂×C₄×C₁₉	—	4	3	no	—
128	C₂×C₄×C₁₉	—	4	3	no	—
129	C₂×C₄×C₁₉	—	4	3	no	—
130	C₂×C₄×C₁₉	—	4	3	no	—
131	C₂×C₄×C₁₉	—	4	3	no	—
132	C₂×#401	C₂×C₁₉	1	1	yes	characteristic
133	#1444	C₂×C₁₉	1	3	yes	—
134	#1444	C₂×C₁₉	1	1	yes	characteristic
135	#1443	C₂×C₁₉	1	3	yes	—
136	#1443	C₂×C₁₉	1	1	yes	characteristic
137	#1442	C₂×C₁₉	1	3	yes	—
138	#1436	C₂×C₁₉	1	3	yes	—
139	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
140	C₂²×C₁₉	#520	1	3	yes	—
141	C₂²×C₁₉	#520	1	3	yes	—
142	C₂²×C₁₉	#538	1	3	yes	—
143	C₂²×C₁₉	#539	1	3	yes	—
144	C₂²×C₁₉	#541	1	3	yes	—
145	C₂²×C₁₉	#542	1	3	yes	—
146	C₂²×C₁₉	#560	1	1	yes	characteristic
147	C₂²×C₁₉	#560	1	3	yes	—
148	C₂²×C₁₉	#563	1	3	yes	—
149	C₂²×C₁₉	#563	1	3	yes	—
150	C₂²×C₁₉	#563	1	3	yes	—
151	C₂²×C₁₉	#563	1	3	yes	—
152	C₄×C₁₉	—	4	2	no	—
153	C₄×C₁₉	—	4	2	no	—
154	C₄×C₁₉	—	4	6	no	—
155	C₄×C₁₉	—	4	2	no	—
156	C₄×C₁₉	—	4	6	no	—
157	C₄×C₁₉	—	8	3	no	—
158	C₄×C₁₉	—	8	3	no	—
159	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
160	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
161	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
162	#401	C₄×C₁₉	1	8	yes	complemented
163	C₂×#95	C₂²×C₁₉	1	3	yes	—
164	C₂×#95	C₂²×C₁₉	1	3	yes	—
165	C₂×#95	C₂²×C₁₉	1	3	yes	—
166	C₂×#95	C₂²×C₁₉	1	3	yes	—
167	C₂×#95	C₂²×C₁₉	1	3	yes	—
168	C₂×#95	C₂²×C₁₉	1	3	yes	—
169	C₂×#95	C₂²×C₁₉	1	3	yes	—
170	C₂×#95	C₂²×C₁₉	1	3	yes	—
171	C₂×#95	C₂²×C₁₉	1	3	yes	—
172	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
173	C₂×C₁₉	#2334	1	3	yes	—
174	C₂×C₁₉	#2383	1	1	yes	characteristic
175	C₂×C₁₉	#2383	1	3	yes	—
176	C₂×C₁₉	#2825	1	1	yes	characteristic
177	C₂×C₁₉	#2833	1	3	yes	—
178	C₂×C₁₉	#2834	1	1	yes	characteristic
179	C₂×C₁₉	#2838	1	3	yes	—
180	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
181	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
182	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
183	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
184	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
185	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
186	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
187	C₂×C₄⋊C₄	—	2	6	no	—
188	C₂×C₄⋊C₄	—	4	3	no	—
189	C₂×C₄⋊C₄	—	4	3	no	—
190	C₂×C₄⋊C₄	—	4	3	no	—
191	C₂×C₄⋊C₄	—	4	3	no	—
192	C₂×C₄⋊C₄	—	4	3	no	—
193	C₂×C₄²	—	4	3	no	—
194	#95	—	2	6	no	—
195	#95	—	4	3	no	—
196	#95	—	4	3	no	—
197	#95	—	4	3	no	—
198	#95	—	4	3	no	—
199	#95	—	4	3	no	—
200	#95	—	4	3	no	—
201	#95	C₂×C₄×C₁₉	1	12	yes	—
202	#95	C₂×C₄×C₁₉	1	12	yes	—
203	#95	C₂×C₄×C₁₉	1	4	yes	—
204	C₁₉	#14656	1	1	yes	characteristic, direct product factor, Sylow
205	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
206	C₂²×C₄	—	2	3	no	—
207	C₂²×C₄	—	2	3	no	—
208	C₂²×C₄	—	2	3	no	—
209	C₂²×C₄	—	2	3	no	—
210	C₂²×C₄	—	2	3	no	—
211	C₂²×C₄	—	2	3	no	—
212	C₂²×C₄	—	2	3	no	—
213	C₂²×C₄	—	2	3	no	—
214	C₂²×C₄	—	2	3	no	—
215	C₂²×C₄	—	2	3	no	—
216	C₂²×C₄	—	2	3	no	—
217	C₂²×C₄	—	2	3	no	—
218	C₂²×C₄	—	2	3	no	—
219	C₂²×C₄	—	2	3	no	—
220	C₂²×C₄	—	2	3	no	—
221	C₂²×C₄	—	2	3	no	—
222	C₂²×C₄	—	2	3	no	—
223	C₂²×C₄	—	2	3	no	—
224	C₂²×C₄	—	2	3	no	—
225	C₂²×C₄	—	2	3	no	—
226	C₂²×C₄	—	2	3	no	—
227	C₂²×C₄	—	2	3	no	—
228	C₂²×C₄	—	2	3	no	—
229	C₂²×C₄	—	2	3	no	—
230	C₂²×C₄	—	2	3	no	—
231	C₂²×C₄	—	2	3	no	—
232	C₂²×C₄	—	2	3	no	—
233	C₂²×C₄	—	2	3	no	—
234	C₂²×C₄	—	2	3	no	—
235	C₂²×C₄	—	2	3	no	—
236	C₂²×C₄	—	2	3	no	—
237	C₂²×C₄	—	2	3	no	—
238	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
239	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
240	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
241	C₂²×C₄	#41×C₁₉	1	2	yes	—
242	C₂²×C₄	#41×C₁₉	1	2	yes	—
243	C₄⋊C₄	—	4	12	no	—
244	C₄⋊C₄	—	4	12	no	—
245	C₄²	—	4	4	no	—
246	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
247	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
248	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
249	C₂³	C₁₉×H(5,𝔽₂)	1	3	yes	—
250	C₂³	C₁₉×H(5,𝔽₂)	1	3	yes	—
251	C₂³	C₁₉×2₋¹⁺⁴	1	3	yes	—
252	C₂³	C₁₉×2₋¹⁺⁴	1	3	yes	—
253	C₂×C₄	—	2	6	no	—
254	C₂×C₄	—	2	6	no	—
255	C₂×C₄	—	2	6	no	—
256	C₂×C₄	—	2	6	no	—
257	C₂×C₄	—	2	6	no	—
258	C₂×C₄	—	2	6	no	—
259	C₂×C₄	—	2	6	no	—
260	C₂×C₄	—	2	6	no	—
261	C₂×C₄	—	2	6	no	—
262	C₂×C₄	—	4	3	no	—
263	C₂×C₄	—	4	3	no	—
264	C₂×C₄	—	4	3	no	—
265	C₂×C₄	—	4	3	no	—
266	C₂×C₄	—	4	1	no	—
267	C₂×C₄	—	4	1	no	—
268	C₂×C₄	—	4	1	no	—
269	C₂×C₄	—	4	3	no	—
270	C₂×C₄	—	4	3	no	—
271	C₂×C₄	—	4	3	no	—
272	C₂×C₄	—	4	3	no	—
273	C₂×C₄	—	4	3	no	—
274	C₂×C₄	—	4	3	no	—
275	C₂×C₄	—	4	3	no	—
276	C₂×C₄	—	4	3	no	—
277	C₂×C₄	—	4	3	no	—
278	C₂×C₄	—	4	3	no	—
279	C₂×C₄	—	4	3	no	—
280	C₂×C₄	—	4	3	no	—
281	C₂×C₄	—	4	3	no	—
282	C₂×C₄	—	4	3	no	—
283	C₂×C₄	—	4	3	no	—
284	C₂×C₄	—	4	3	no	—
285	C₂×C₄	—	4	3	no	—
286	C₂×C₄	—	4	3	no	—
287	C₂×C₄	—	4	3	no	—
288	C₂×C₄	—	4	3	no	—
289	C₂×C₄	—	4	3	no	—
290	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
291	C₂²	C₁₉×#520	1	3	yes	—
292	C₂²	C₁₉×#520	1	3	yes	—
293	C₂²	C₁₉×#538	1	3	yes	—
294	C₂²	C₁₉×#539	1	3	yes	—
295	C₂²	C₁₉×#541	1	3	yes	—
296	C₂²	C₁₉×#542	1	3	yes	—
297	C₂²	C₁₉×#560	1	1	yes	characteristic
298	C₂²	C₁₉×#560	1	3	yes	—
299	C₂²	C₁₉×#563	1	3	yes	—
300	C₂²	C₁₉×#563	1	3	yes	—
301	C₂²	C₁₉×#563	1	3	yes	—
302	C₂²	C₁₉×#563	1	3	yes	—
303	C₄	—	4	2	no	—
304	C₄	—	4	2	no	—
305	C₄	—	4	6	no	—
306	C₄	—	4	2	no	—
307	C₄	—	4	6	no	—
308	C₄	—	8	3	no	—
309	C₄	—	8	3	no	—
310	C₂	C₁₉×#2334	1	3	yes	—
311	C₂	C₁₉×#2383	1	1	yes	characteristic
312	C₂	C₁₉×#2383	1	3	yes	—
313	C₂	C₁₉×#2825	1	1	yes	characteristic
314	C₂	C₁₉×#2833	1	3	yes	—
315	C₂	C₁₉×#2834	1	1	yes	characteristic
316	C₂	C₁₉×#2838	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₁₉×#401	C₄	semidirect
87. #14656	C₁₉	direct (N × H)
162. #401	C₄×C₁₉	semidirect
204. C₁₉	#14656	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#401	2
C₁₉×#1444	2
C₁₉×#1443	2
C₁₉×#1442	2
C₁₉×#1436	2
#14656	19

Subgroups — C19×#14656 #18020615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14656 #18020615