Subgroups — C₁₉×#32849 #18038808

Order 4864.

604 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2859	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2859	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2100	C₂	1	2	yes	maximal
4	C₁₉×#2099	C₂	1	2	yes	maximal
5	C₁₉×#2088	C₂	1	4	yes	maximal
6	C₁₉×#2084	C₂	1	2	yes	maximal
7	C₁₉×#2084	C₂	1	2	yes	maximal
8	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₉×#125	—	2	1	no	—
10	C₂×C₁₉×#125	—	2	1	no	—
11	C₂×C₁₉×#106	C₂²	1	4	yes	—
12	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
13	C₁₉×#389	—	2	1	no	—
14	C₁₉×#389	—	2	1	no	—
15	C₁₉×#389	—	2	1	no	—
16	C₁₉×#389	—	2	1	no	—
17	C₁₉×#389	C₂²	1	2	yes	—
18	C₁₉×#389	C₂²	1	2	yes	—
19	C₁₉×#389	C₂²	1	2	yes	—
20	C₁₉×#389	C₂²	1	2	yes	—
21	C₁₉×#384	C₂²	1	1	yes	characteristic
22	C₁₉×#384	C₂²	1	1	yes	characteristic
23	C₁₉×#384	C₂²	1	1	yes	characteristic
24	C₁₉×#384	C₂²	1	1	yes	characteristic
25	C₁₉×#382	—	2	1	no	—
26	C₁₉×#382	—	2	1	no	—
27	C₄³×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#340	C₂²	1	4	yes	—
29	C₁₉×#340	C₂²	1	4	yes	—
30	C₁₉×#340	C₂²	1	4	yes	—
31	C₁₉×#336	C₂²	1	2	yes	—
32	C₁₉×#336	C₂²	1	2	yes	—
33	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
34	C₁₉×#125	—	4	4	no	—
35	C₁₉×#125	—	4	4	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
52	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
59	C₁₉×#106	—	4	4	no	—
60	C₁₉×C₄⋊C₈	—	4	2	no	—
61	C₁₉×#95	—	2	2	no	—
62	C₁₉×#95	—	2	2	no	—
63	C₁₉×#95	—	2	2	no	—
64	C₁₉×#95	—	2	2	no	—
65	C₂²×C₄×C₁₉	—	2	2	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
76	C₂×C₈×C₁₉	—	2	4	no	—
77	C₂×C₈×C₁₉	—	2	4	no	—
78	C₂×C₈×C₁₉	—	2	4	no	—
79	C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₄⋊C₄×C₁₉	—	2	4	no	—
82	C₄⋊C₄×C₁₉	—	2	4	no	—
83	C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₄⋊C₄×C₁₉	—	4	2	no	—
86	C₄⋊C₄×C₁₉	—	4	2	no	—
87	C₄⋊C₄×C₁₉	—	4	2	no	—
88	C₄⋊C₄×C₁₉	—	4	2	no	—
89	C₄⋊C₄×C₁₉	—	4	4	no	—
90	C₄⋊C₄×C₁₉	—	4	2	no	—
91	C₄⋊C₄×C₁₉	—	4	2	no	—
92	C₄⋊C₄×C₁₉	—	4	4	no	—
93	C₄⋊C₄×C₁₉	—	4	4	no	—
94	C₄⋊C₄×C₁₉	—	4	2	no	—
95	C₄⋊C₄×C₁₉	—	4	4	no	—
96	C₄⋊C₄×C₁₉	—	4	2	no	—
97	C₄²×C₁₉	—	2	2	no	—
98	C₄²×C₁₉	—	2	2	no	—
99	C₄²×C₁₉	—	2	1	no	—
100	C₄²×C₁₉	—	2	2	no	—
101	C₄²×C₁₉	—	2	2	no	—
102	C₄²×C₁₉	—	2	1	no	—
103	C₄²×C₁₉	—	4	1	no	—
104	C₄²×C₁₉	SD₁₆	1	4	yes	—
105	#32849	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
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	—	4	2	no	—
121	C₂×C₄×C₁₉	—	4	2	no	—
122	C₂×C₄×C₁₉	—	4	2	no	—
123	C₂×C₄×C₁₉	—	4	2	no	—
124	C₂×C₄×C₁₉	—	4	2	no	—
125	C₂×C₄×C₁₉	—	4	2	no	—
126	C₂×C₄×C₁₉	—	4	2	no	—
127	C₂×C₄×C₁₉	—	4	2	no	—
128	C₂×C₄×C₁₉	—	4	2	no	—
129	C₂×C₄×C₁₉	—	4	2	no	—
130	C₂×C₄×C₁₉	—	4	2	no	—
131	C₂×C₄×C₁₉	—	4	2	no	—
132	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
133	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
134	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
135	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
136	C₂×C₄×C₁₉	#137	1	2	yes	—
137	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
138	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
139	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
140	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
141	C₈×C₁₉	—	4	4	no	—
142	#2859	C₂×C₁₉	1	1	yes	characteristic
143	#2859	C₂×C₁₉	1	1	yes	characteristic
144	#2100	C₂×C₁₉	1	2	yes	—
145	#2099	C₂×C₁₉	1	2	yes	—
146	#2088	C₂×C₁₉	1	4	yes	—
147	#2084	C₂×C₁₉	1	2	yes	—
148	#2084	C₂×C₁₉	1	2	yes	—
149	#1831	C₂×C₁₉	1	1	yes	characteristic
150	C₂²×C₁₉	#536	1	1	yes	characteristic
151	C₂²×C₁₉	#536	1	1	yes	characteristic
152	C₂²×C₁₉	#537	1	1	yes	characteristic
153	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
154	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
156	C₂²×C₁₉	#575	1	1	yes	characteristic
157	C₄×C₁₉	—	2	2	no	—
158	C₄×C₁₉	—	2	2	no	—
159	C₄×C₁₉	—	2	2	no	—
160	C₄×C₁₉	—	2	2	no	—
161	C₄×C₁₉	—	2	2	no	—
162	C₄×C₁₉	—	4	1	no	—
163	C₄×C₁₉	—	8	2	no	—
164	C₄×C₁₉	—	8	2	no	—
165	C₄×C₁₉	—	8	2	no	—
166	C₄×C₁₉	—	8	2	no	—
167	C₄×C₁₉	#563	1	2	yes	—
168	C₄×C₁₉	#564	1	2	yes	—
169	C₂×#125	—	2	1	no	—
170	C₂×#125	—	2	1	no	—
171	C₂×#106	C₂²×C₁₉	1	4	yes	—
172	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
173	#389	—	2	1	no	—
174	#389	—	2	1	no	—
175	#389	—	2	1	no	—
176	#389	—	2	1	no	—
177	#389	C₂²×C₁₉	1	2	yes	—
178	#389	C₂²×C₁₉	1	2	yes	—
179	#389	C₂²×C₁₉	1	2	yes	—
180	#389	C₂²×C₁₉	1	2	yes	—
181	#384	C₂²×C₁₉	1	1	yes	characteristic
182	#384	C₂²×C₁₉	1	1	yes	characteristic
183	#384	C₂²×C₁₉	1	1	yes	characteristic
184	#384	C₂²×C₁₉	1	1	yes	characteristic
185	#382	—	2	1	no	—
186	#382	—	2	1	no	—
187	C₄³	C₂²×C₁₉	1	1	yes	characteristic
188	#340	C₂²×C₁₉	1	4	yes	—
189	#340	C₂²×C₁₉	1	4	yes	—
190	#340	C₂²×C₁₉	1	4	yes	—
191	#336	C₂²×C₁₉	1	2	yes	—
192	#336	C₂²×C₁₉	1	2	yes	—
193	C₂×C₁₉	#2822	1	1	yes	characteristic
194	C₂×C₁₉	#3227	1	1	yes	characteristic
195	C₂×C₁₉	#3229	1	1	yes	characteristic
196	C₂×C₁₉	#3234	1	1	yes	characteristic
197	C₂×C₁₉	#3236	1	1	yes	characteristic
198	C₂×C₁₉	#3246	1	1	yes	characteristic
199	C₂×C₁₉	#3254	1	1	yes	characteristic
200	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
201	#125	—	4	4	no	—
202	#125	—	4	4	no	—
203	C₂×C₄⋊C₄	—	2	1	no	—
204	C₂×C₄⋊C₄	—	2	1	no	—
205	C₂×C₄⋊C₄	—	2	1	no	—
206	C₂×C₄⋊C₄	—	2	1	no	—
207	C₂×C₄⋊C₄	—	2	2	no	—
208	C₂×C₄⋊C₄	—	2	2	no	—
209	C₂×C₄⋊C₄	—	2	2	no	—
210	C₂×C₄⋊C₄	—	2	2	no	—
211	C₂×C₄⋊C₄	—	2	1	no	—
212	C₂×C₄⋊C₄	—	2	1	no	—
213	C₂×C₄⋊C₄	—	2	1	no	—
214	C₂×C₄⋊C₄	—	2	1	no	—
215	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
216	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
217	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
218	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
219	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
220	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
221	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
222	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
223	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
224	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
225	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
226	#106	—	4	4	no	—
227	C₄⋊C₈	—	4	2	no	—
228	#95	—	2	2	no	—
229	#95	—	2	2	no	—
230	#95	—	2	2	no	—
231	#95	—	2	2	no	—
232	C₁₉	#32849	1	1	yes	characteristic, direct product factor, Sylow
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
238	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
239	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
240	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
241	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
242	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
243	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
244	C₂×C₈	—	2	4	no	—
245	C₂×C₈	—	2	4	no	—
246	C₂×C₈	—	2	4	no	—
247	C₄⋊C₄	—	2	2	no	—
248	C₄⋊C₄	—	2	2	no	—
249	C₄⋊C₄	—	2	4	no	—
250	C₄⋊C₄	—	2	4	no	—
251	C₄⋊C₄	—	2	2	no	—
252	C₄⋊C₄	—	2	2	no	—
253	C₄⋊C₄	—	4	2	no	—
254	C₄⋊C₄	—	4	2	no	—
255	C₄⋊C₄	—	4	2	no	—
256	C₄⋊C₄	—	4	2	no	—
257	C₄⋊C₄	—	4	4	no	—
258	C₄⋊C₄	—	4	2	no	—
259	C₄⋊C₄	—	4	2	no	—
260	C₄⋊C₄	—	4	4	no	—
261	C₄⋊C₄	—	4	4	no	—
262	C₄⋊C₄	—	4	2	no	—
263	C₄⋊C₄	—	4	4	no	—
264	C₄⋊C₄	—	4	2	no	—
265	C₄²	—	2	2	no	—
266	C₄²	—	2	2	no	—
267	C₄²	—	2	1	no	—
268	C₄²	—	2	2	no	—
269	C₄²	—	2	2	no	—
270	C₄²	—	2	1	no	—
271	C₄²	—	4	1	no	—
272	C₄²	SD₁₆×C₁₉	1	4	yes	—
273	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
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	—	4	2	no	—
288	C₂×C₄	—	4	2	no	—
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	4	2	no	—
291	C₂×C₄	—	4	2	no	—
292	C₂×C₄	—	4	2	no	—
293	C₂×C₄	—	4	2	no	—
294	C₂×C₄	—	4	2	no	—
295	C₂×C₄	—	4	2	no	—
296	C₂×C₄	—	4	2	no	—
297	C₂×C₄	—	4	2	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
300	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
301	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
302	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
303	C₂×C₄	C₁₉×#137	1	2	yes	—
304	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
305	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
306	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
307	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
308	C₈	—	4	4	no	—
309	C₂²	C₁₉×#536	1	1	yes	characteristic
310	C₂²	C₁₉×#536	1	1	yes	characteristic
311	C₂²	C₁₉×#537	1	1	yes	characteristic
312	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
313	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
314	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
315	C₂²	C₁₉×#575	1	1	yes	characteristic
316	C₄	—	2	2	no	—
317	C₄	—	2	2	no	—
318	C₄	—	2	2	no	—
319	C₄	—	2	2	no	—
320	C₄	—	2	2	no	—
321	C₄	—	4	1	no	—
322	C₄	—	8	2	no	—
323	C₄	—	8	2	no	—
324	C₄	—	8	2	no	—
325	C₄	—	8	2	no	—
326	C₄	C₁₉×#563	1	2	yes	—
327	C₄	C₁₉×#564	1	2	yes	—
328	C₂	C₁₉×#2822	1	1	yes	characteristic
329	C₂	C₁₉×#3227	1	1	yes	characteristic
330	C₂	C₁₉×#3229	1	1	yes	characteristic
331	C₂	C₁₉×#3234	1	1	yes	characteristic
332	C₂	C₁₉×#3236	1	1	yes	characteristic
333	C₂	C₁₉×#3246	1	1	yes	characteristic
334	C₂	C₁₉×#3254	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
105. #32849	C₁₉	direct (N × H)
232. C₁₉	#32849	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×#2859	2
C₁₉×#2100	2
C₁₉×#2099	2
C₁₉×#2088	2
C₁₉×#2084	2
C₁₉×#1831	2
#32849	19

Subgroups — C19×#32849 #18038808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32849 #18038808