Subgroups — C₁₉×#16245 #18022204

Order 4864.

1230 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#1442	C₂	1	4	yes	maximal, complemented
2	C₁₉×#1440	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1439	C₂	1	4	yes	maximal
4	C₁₉×#1437	C₂	1	2	yes	maximal
5	C₁₉×#1436	C₂	1	4	yes	maximal, complemented
6	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
7	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
8	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
11	C₂×C₁₉×#95	C₂²	1	4	yes	—
12	C₂×C₁₉×#95	C₂²	1	4	yes	—
13	C₂×C₁₉×#95	C₂²	1	4	yes	—
14	C₂×C₁₉×#95	C₂²	1	4	yes	—
15	C₂×C₁₉×#95	C₂²	1	4	yes	—
16	C₂×C₁₉×#95	C₂²	1	2	yes	—
17	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
18	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
19	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
20	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
21	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
22	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
23	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
24	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
25	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
26	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
27	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
28	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
29	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
30	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
31	C₂×C₂²⋊C₄×C₁₉	Q₈	1	4	yes	—
32	C₂×C₄²×C₁₉	—	4	2	no	—
33	C₂×C₄²×C₁₉	—	4	4	no	—
34	C₁₉×#95	—	2	8	no	—
35	C₁₉×#95	—	2	8	no	—
36	C₁₉×#95	—	2	8	no	—
37	C₁₉×#95	—	4	4	no	—
38	C₁₉×#95	—	4	4	no	—
39	C₁₉×#95	—	4	2	no	—
40	C₂⁴×C₁₉	—	2	4	no	—
41	C₂⁴×C₁₉	—	2	4	no	—
42	C₂⁴×C₁₉	—	2	2	no	—
43	C₂⁴×C₁₉	—	2	4	no	—
44	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
45	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	—	2	4	no	—
47	C₂²×C₄×C₁₉	—	2	4	no	—
48	C₂²×C₄×C₁₉	—	2	4	no	—
49	C₂²×C₄×C₁₉	—	2	4	no	—
50	C₂²×C₄×C₁₉	—	2	4	no	—
51	C₂²×C₄×C₁₉	—	2	4	no	—
52	C₂²×C₄×C₁₉	—	2	4	no	—
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	—	2	4	no	—
55	C₂²×C₄×C₁₉	—	2	4	no	—
56	C₂²×C₄×C₁₉	—	2	4	no	—
57	C₂²×C₄×C₁₉	—	2	4	no	—
58	C₂²×C₄×C₁₉	—	2	4	no	—
59	C₂²×C₄×C₁₉	—	2	2	no	—
60	C₂²×C₄×C₁₉	—	2	4	no	—
61	C₂²×C₄×C₁₉	—	2	4	no	—
62	C₂²×C₄×C₁₉	—	2	4	no	—
63	C₂²×C₄×C₁₉	—	2	4	no	—
64	C₂²×C₄×C₁₉	—	2	4	no	—
65	C₂²×C₄×C₁₉	—	2	4	no	—
66	C₂²×C₄×C₁₉	—	2	4	no	—
67	C₂²×C₄×C₁₉	—	2	4	no	—
68	C₂²×C₄×C₁₉	—	2	4	no	—
69	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
70	C₂²×C₄×C₁₉	#41	1	8	yes	—
71	C₂²×C₄×C₁₉	#41	1	8	yes	—
72	C₄⋊C₄×C₁₉	—	4	16	no	—
73	C₂²⋊C₄×C₁₉	—	4	4	no	—
74	C₂²⋊C₄×C₁₉	—	4	16	no	—
75	C₂²⋊C₄×C₁₉	—	4	8	no	—
76	C₄²×C₁₉	—	4	8	no	—
77	#16245	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂³×C₁₉	—	2	4	no	—
79	C₂³×C₁₉	—	2	2	no	—
80	C₂³×C₁₉	—	2	8	no	—
81	C₂³×C₁₉	—	4	4	no	—
82	C₂³×C₁₉	—	4	4	no	—
83	C₂³×C₁₉	—	4	4	no	—
84	C₂³×C₁₉	—	4	4	no	—
85	C₂³×C₁₉	—	4	4	no	—
86	C₂³×C₁₉	—	4	4	no	—
87	C₂³×C₁₉	—	4	2	no	—
88	C₂³×C₁₉	—	4	2	no	—
89	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
90	C₂³×C₁₉	C₂×#41	1	4	yes	—
91	C₂³×C₁₉	C₂×#41	1	4	yes	—
92	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
93	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
94	C₂×C₄×C₁₉	—	2	8	no	—
95	C₂×C₄×C₁₉	—	2	8	no	—
96	C₂×C₄×C₁₉	—	2	4	no	—
97	C₂×C₄×C₁₉	—	2	8	no	—
98	C₂×C₄×C₁₉	—	2	8	no	—
99	C₂×C₄×C₁₉	—	2	8	no	—
100	C₂×C₄×C₁₉	—	2	8	no	—
101	C₂×C₄×C₁₉	—	2	8	no	—
102	C₂×C₄×C₁₉	—	4	4	no	—
103	C₂×C₄×C₁₉	—	4	4	no	—
104	C₂×C₄×C₁₉	—	4	4	no	—
105	C₂×C₄×C₁₉	—	4	4	no	—
106	C₂×C₄×C₁₉	—	4	4	no	—
107	C₂×C₄×C₁₉	—	4	4	no	—
108	C₂×C₄×C₁₉	—	4	4	no	—
109	C₂×C₄×C₁₉	—	4	4	no	—
110	C₂×C₄×C₁₉	—	4	2	no	—
111	C₂×C₄×C₁₉	—	4	4	no	—
112	C₂×C₄×C₁₉	—	4	2	no	—
113	C₂×C₄×C₁₉	—	4	4	no	—
114	C₂×C₄×C₁₉	—	4	4	no	—
115	C₂×C₄×C₁₉	—	4	4	no	—
116	C₂×C₄×C₁₉	—	4	4	no	—
117	C₂×C₄×C₁₉	—	4	4	no	—
118	C₂×C₄×C₁₉	—	4	4	no	—
119	C₂×C₄×C₁₉	—	4	4	no	—
120	#1442	C₂×C₁₉	1	4	yes	complemented
121	#1440	C₂×C₁₉	1	1	yes	characteristic
122	#1439	C₂×C₁₉	1	4	yes	—
123	#1437	C₂×C₁₉	1	2	yes	—
124	#1436	C₂×C₁₉	1	4	yes	complemented
125	C₂²×C₁₉	—	4	2	no	—
126	C₂²×C₁₉	—	4	8	no	—
127	C₂²×C₁₉	—	4	4	no	—
128	C₂²×C₁₉	—	8	4	no	—
129	C₂²×C₁₉	—	8	4	no	—
130	C₂²×C₁₉	#529	1	4	yes	—
131	C₂²×C₁₉	#533	1	2	yes	—
132	C₂²×C₁₉	#538	1	4	yes	—
133	C₂²×C₁₉	#540	1	4	yes	—
134	C₂²×C₁₉	#543	1	1	yes	characteristic
135	C₂²×C₁₉	#551	1	4	yes	—
136	C₂²×C₁₉	#553	1	4	yes	—
137	C₂²×C₁₉	#553	1	4	yes	—
138	C₂²×C₁₉	#554	1	4	yes	—
139	C₂²×C₁₉	#559	1	2	yes	—
140	C₂²×C₁₉	H(3,𝔽₄)	1	2	yes	—
141	C₄×C₁₉	—	4	8	no	—
142	C₄×C₁₉	—	4	8	no	—
143	C₄×C₁₉	—	4	4	no	—
144	C₄×C₁₉	—	8	4	no	—
145	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
146	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
147	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
148	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
149	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
150	C₂×#95	C₂²×C₁₉	1	4	yes	—
151	C₂×#95	C₂²×C₁₉	1	4	yes	—
152	C₂×#95	C₂²×C₁₉	1	4	yes	—
153	C₂×#95	C₂²×C₁₉	1	4	yes	—
154	C₂×#95	C₂²×C₁₉	1	4	yes	—
155	C₂×#95	C₂²×C₁₉	1	2	yes	—
156	C₂×C₁₉	—	8	2	no	—
157	C₂×C₁₉	#2522	1	4	yes	—
158	C₂×C₁₉	#2595	1	4	yes	—
159	C₂×C₁₉	#2608	1	1	yes	characteristic
160	C₂×C₁₉	#2753	1	4	yes	—
161	C₂×C₁₉	#2804	1	2	yes	—
162	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
163	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
164	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
165	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
166	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
167	C₂×C₄⋊C₄	—	2	8	no	—
168	C₂×C₄⋊C₄	—	4	4	no	—
169	C₂×C₄⋊C₄	—	4	4	no	—
170	C₂×C₂²⋊C₄	—	2	8	no	—
171	C₂×C₂²⋊C₄	—	2	8	no	—
172	C₂×C₂²⋊C₄	—	4	2	no	—
173	C₂×C₂²⋊C₄	—	4	4	no	—
174	C₂×C₂²⋊C₄	—	4	4	no	—
175	C₂×C₂²⋊C₄	—	4	2	no	—
176	C₂×C₂²⋊C₄	Q₈×C₁₉	1	4	yes	—
177	C₂×C₄²	—	4	4	no	—
178	C₂×C₄²	—	4	2	no	—
179	#95	—	2	8	no	—
180	#95	—	2	8	no	—
181	#95	—	2	8	no	—
182	#95	—	4	4	no	—
183	#95	—	4	4	no	—
184	#95	—	4	2	no	—
185	C₁₉	#16245	1	1	yes	characteristic, direct product factor, Sylow
186	C₂⁴	—	2	4	no	—
187	C₂⁴	—	2	4	no	—
188	C₂⁴	—	2	2	no	—
189	C₂⁴	—	2	4	no	—
190	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
191	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
192	C₂²×C₄	—	2	4	no	—
193	C₂²×C₄	—	2	4	no	—
194	C₂²×C₄	—	2	4	no	—
195	C₂²×C₄	—	2	4	no	—
196	C₂²×C₄	—	2	4	no	—
197	C₂²×C₄	—	2	4	no	—
198	C₂²×C₄	—	2	4	no	—
199	C₂²×C₄	—	2	4	no	—
200	C₂²×C₄	—	2	4	no	—
201	C₂²×C₄	—	2	2	no	—
202	C₂²×C₄	—	2	4	no	—
203	C₂²×C₄	—	2	4	no	—
204	C₂²×C₄	—	2	2	no	—
205	C₂²×C₄	—	2	4	no	—
206	C₂²×C₄	—	2	4	no	—
207	C₂²×C₄	—	2	4	no	—
208	C₂²×C₄	—	2	4	no	—
209	C₂²×C₄	—	2	4	no	—
210	C₂²×C₄	—	2	4	no	—
211	C₂²×C₄	—	2	4	no	—
212	C₂²×C₄	—	2	4	no	—
213	C₂²×C₄	—	2	4	no	—
214	C₂²×C₄	—	2	4	no	—
215	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
216	C₂²×C₄	#41×C₁₉	1	8	yes	—
217	C₂²×C₄	#41×C₁₉	1	8	yes	—
218	C₄⋊C₄	—	4	16	no	—
219	C₂²⋊C₄	—	4	4	no	—
220	C₂²⋊C₄	—	4	16	no	—
221	C₂²⋊C₄	—	4	8	no	—
222	C₄²	—	4	8	no	—
223	C₂³	—	2	4	no	—
224	C₂³	—	2	2	no	—
225	C₂³	—	2	8	no	—
226	C₂³	—	4	4	no	—
227	C₂³	—	4	4	no	—
228	C₂³	—	4	4	no	—
229	C₂³	—	4	4	no	—
230	C₂³	—	4	4	no	—
231	C₂³	—	4	4	no	—
232	C₂³	—	4	2	no	—
233	C₂³	—	4	2	no	—
234	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
235	C₂³	C₂×#41×C₁₉	1	4	yes	—
236	C₂³	C₂×#41×C₁₉	1	4	yes	—
237	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
238	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
239	C₂×C₄	—	2	8	no	—
240	C₂×C₄	—	2	8	no	—
241	C₂×C₄	—	2	4	no	—
242	C₂×C₄	—	2	8	no	—
243	C₂×C₄	—	2	8	no	—
244	C₂×C₄	—	2	8	no	—
245	C₂×C₄	—	2	8	no	—
246	C₂×C₄	—	2	8	no	—
247	C₂×C₄	—	4	4	no	—
248	C₂×C₄	—	4	4	no	—
249	C₂×C₄	—	4	4	no	—
250	C₂×C₄	—	4	4	no	—
251	C₂×C₄	—	4	4	no	—
252	C₂×C₄	—	4	4	no	—
253	C₂×C₄	—	4	4	no	—
254	C₂×C₄	—	4	2	no	—
255	C₂×C₄	—	4	4	no	—
256	C₂×C₄	—	4	4	no	—
257	C₂×C₄	—	4	2	no	—
258	C₂×C₄	—	4	4	no	—
259	C₂×C₄	—	4	4	no	—
260	C₂×C₄	—	4	4	no	—
261	C₂×C₄	—	4	4	no	—
262	C₂×C₄	—	4	4	no	—
263	C₂×C₄	—	4	4	no	—
264	C₂×C₄	—	4	4	no	—
265	C₂²	—	4	8	no	—
266	C₂²	—	4	4	no	—
267	C₂²	—	4	2	no	—
268	C₂²	—	8	4	no	—
269	C₂²	—	8	4	no	—
270	C₂²	C₁₉×#529	1	4	yes	—
271	C₂²	C₁₉×#533	1	2	yes	—
272	C₂²	C₁₉×#538	1	4	yes	—
273	C₂²	C₁₉×#540	1	4	yes	—
274	C₂²	C₁₉×#543	1	1	yes	characteristic
275	C₂²	C₁₉×#551	1	4	yes	—
276	C₂²	C₁₉×#553	1	4	yes	—
277	C₂²	C₁₉×#553	1	4	yes	—
278	C₂²	C₁₉×#554	1	4	yes	—
279	C₂²	C₁₉×#559	1	2	yes	—
280	C₂²	C₁₉×H(3,𝔽₄)	1	2	yes	—
281	C₄	—	4	8	no	—
282	C₄	—	4	4	no	—
283	C₄	—	4	8	no	—
284	C₄	—	8	4	no	—
285	C₂	—	8	2	no	—
286	C₂	C₁₉×#2522	1	4	yes	—
287	C₂	C₁₉×#2595	1	4	yes	—
288	C₂	C₁₉×#2608	1	1	yes	characteristic
289	C₂	C₁₉×#2753	1	4	yes	—
290	C₂	C₁₉×#2804	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#1442	C₂	semidirect
5. C₁₉×#1436	C₂	semidirect
77. #16245	C₁₉	direct (N × H)
120. #1442	C₂×C₁₉	semidirect
124. #1436	C₂×C₁₉	semidirect
185. C₁₉	#16245	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×#1442	2
C₁₉×#1440	2
C₁₉×#1439	2
C₁₉×#1437	2
C₁₉×#1436	2
#16245	19

Subgroups — C19×#16245 #18022204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#16245 #18022204