Subgroups — C₁₉×#32791 #18038750

Order 4864.

628 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2851	C₂	1	2	yes	maximal
2	C₁₉×#2101	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2101	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2077	C₂	1	2	yes	maximal
5	C₁₉×#2076	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2075	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2059	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2059	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1817	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₉×#125	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#106	C₂²	1	2	yes	—
15	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
17	C₁₉×#389	C₂²	1	2	yes	—
18	C₁₉×#389	C₂²	1	2	yes	—
19	C₁₉×#387	—	2	2	no	—
20	C₁₉×#387	—	2	2	no	—
21	C₁₉×#385	—	2	2	no	—
22	C₁₉×#385	—	2	2	no	—
23	C₁₉×#382	C₂²	1	2	yes	—
24	C₁₉×#380	C₂²	1	2	yes	—
25	C₁₉×#380	C₂²	1	2	yes	—
26	C₁₉×#340	C₂²	1	2	yes	—
27	C₁₉×#340	C₂²	1	2	yes	—
28	C₁₉×#340	C₂²	1	2	yes	—
29	C₁₉×#340	C₂²	1	2	yes	—
30	C₁₉×#340	C₂²	1	1	yes	characteristic
31	C₁₉×#340	C₂²	1	1	yes	characteristic
32	C₁₉×#340	C₂²	1	2	yes	—
33	C₁₉×#336	C₂²	1	2	yes	—
34	C₁₉×#336	C₂²	1	2	yes	—
35	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
41	C₁₉×#125	—	4	2	no	—
42	C₁₉×#125	—	4	2	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	2	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	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄²×C₁₉	—	4	1	no	—
54	C₂×C₄²×C₁₉	—	4	1	no	—
55	C₂×C₄²×C₁₉	D₄	1	2	yes	—
56	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
57	C₁₉×#107	—	4	1	no	—
58	C₁₉×#107	—	4	1	no	—
59	C₁₉×#106	—	4	2	no	—
60	C₁₉×C₂²⋊C₈	—	4	1	no	—
61	C₁₉×C₂²⋊C₈	—	4	1	no	—
62	C₁₉×#95	—	2	2	no	—
63	C₁₉×#95	—	2	2	no	—
64	C₁₉×#95	—	2	2	no	—
65	C₁₉×#95	—	2	2	no	—
66	C₁₉×#95	—	2	2	no	—
67	C₁₉×#95	—	2	2	no	—
68	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	1	no	—
80	C₂²×C₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	—	4	2	no	—
82	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
86	C₂×C₈×C₁₉	—	2	2	no	—
87	C₂×C₈×C₁₉	—	2	1	no	—
88	C₂×C₈×C₁₉	—	2	1	no	—
89	C₂×C₈×C₁₉	—	2	2	no	—
90	C₂×C₈×C₁₉	—	2	2	no	—
91	C₂×C₈×C₁₉	—	2	2	no	—
92	C₂×C₈×C₁₉	—	2	2	no	—
93	C₄⋊C₄×C₁₉	—	2	2	no	—
94	C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₄⋊C₄×C₁₉	—	2	2	no	—
97	C₄⋊C₄×C₁₉	—	2	2	no	—
98	C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₄⋊C₄×C₁₉	—	2	2	no	—
101	C₄⋊C₄×C₁₉	—	4	4	no	—
102	C₄⋊C₄×C₁₉	—	4	4	no	—
103	C₄⋊C₄×C₁₉	—	4	4	no	—
104	C₄⋊C₄×C₁₉	—	4	4	no	—
105	C₂²⋊C₄×C₁₉	—	4	4	no	—
106	C₂²⋊C₄×C₁₉	—	4	4	no	—
107	C₄²×C₁₉	—	2	2	no	—
108	C₄²×C₁₉	—	2	2	no	—
109	C₄²×C₁₉	—	4	2	no	—
110	#32791	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂³×C₁₉	—	2	1	no	—
112	C₂³×C₁₉	—	2	2	no	—
113	C₂³×C₁₉	—	2	2	no	—
114	C₂³×C₁₉	—	2	1	no	—
115	C₂³×C₁₉	#135	1	2	yes	—
116	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
117	C₂×C₄×C₁₉	—	2	2	no	—
118	C₂×C₄×C₁₉	—	2	2	no	—
119	C₂×C₄×C₁₉	—	2	1	no	—
120	C₂×C₄×C₁₉	—	2	2	no	—
121	C₂×C₄×C₁₉	—	2	2	no	—
122	C₂×C₄×C₁₉	—	2	2	no	—
123	C₂×C₄×C₁₉	—	2	2	no	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	4	4	no	—
126	C₂×C₄×C₁₉	—	4	4	no	—
127	C₂×C₄×C₁₉	—	4	2	no	—
128	C₂×C₄×C₁₉	—	4	1	no	—
129	C₂×C₄×C₁₉	—	4	1	no	—
130	C₂×C₄×C₁₉	—	4	2	no	—
131	C₂×C₄×C₁₉	—	4	2	no	—
132	C₂×C₄×C₁₉	—	4	2	no	—
133	C₂×C₄×C₁₉	—	4	2	no	—
134	C₂×C₄×C₁₉	—	4	2	no	—
135	C₂×C₄×C₁₉	—	4	2	no	—
136	C₂×C₄×C₁₉	—	4	2	no	—
137	C₂×C₄×C₁₉	—	4	2	no	—
138	C₂×C₄×C₁₉	—	4	2	no	—
139	C₂×C₄×C₁₉	—	4	2	no	—
140	C₂×C₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
143	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
144	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
145	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
146	C₈×C₁₉	—	4	2	no	—
147	C₈×C₁₉	—	4	1	no	—
148	C₈×C₁₉	—	4	1	no	—
149	#2851	C₂×C₁₉	1	2	yes	—
150	#2101	C₂×C₁₉	1	2	yes	complemented
151	#2101	C₂×C₁₉	1	2	yes	complemented
152	#2077	C₂×C₁₉	1	2	yes	—
153	#2076	C₂×C₁₉	1	1	yes	characteristic
154	#2075	C₂×C₁₉	1	1	yes	characteristic
155	#2059	C₂×C₁₉	1	2	yes	complemented
156	#2059	C₂×C₁₉	1	2	yes	complemented
157	#1817	C₂×C₁₉	1	1	yes	characteristic
158	C₂²×C₁₉	—	2	2	no	—
159	C₂²×C₁₉	—	2	4	no	—
160	C₂²×C₁₉	—	4	1	no	—
161	C₂²×C₁₉	—	4	1	no	—
162	C₂²×C₁₉	—	4	2	no	—
163	C₂²×C₁₉	#534	1	1	yes	characteristic
164	C₂²×C₁₉	#536	1	2	yes	—
165	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
166	C₂²×C₁₉	#575	1	1	yes	characteristic
167	C₂²×C₁₉	#575	1	2	yes	—
168	C₄×C₁₉	—	4	1	no	—
169	C₄×C₁₉	—	4	2	no	—
170	C₄×C₁₉	—	4	2	no	—
171	C₄×C₁₉	—	8	2	no	—
172	C₄×C₁₉	—	8	2	no	—
173	C₄×C₁₉	—	8	2	no	—
174	C₄×C₁₉	—	8	2	no	—
175	C₄×C₁₉	#563	1	2	yes	—
176	C₄×C₁₉	#563	1	1	yes	characteristic
177	C₄×C₁₉	#563	1	1	yes	characteristic
178	C₂×#125	C₂²×C₁₉	1	2	yes	—
179	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
180	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
181	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
182	C₂×#106	C₂²×C₁₉	1	2	yes	—
183	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
184	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
185	#389	C₂²×C₁₉	1	2	yes	—
186	#389	C₂²×C₁₉	1	2	yes	—
187	#387	—	2	2	no	—
188	#387	—	2	2	no	—
189	#385	—	2	2	no	—
190	#385	—	2	2	no	—
191	#382	C₂²×C₁₉	1	2	yes	—
192	#380	C₂²×C₁₉	1	2	yes	—
193	#380	C₂²×C₁₉	1	2	yes	—
194	#340	C₂²×C₁₉	1	2	yes	—
195	#340	C₂²×C₁₉	1	2	yes	—
196	#340	C₂²×C₁₉	1	2	yes	—
197	#340	C₂²×C₁₉	1	2	yes	—
198	#340	C₂²×C₁₉	1	1	yes	characteristic
199	#340	C₂²×C₁₉	1	1	yes	characteristic
200	#340	C₂²×C₁₉	1	2	yes	—
201	#336	C₂²×C₁₉	1	2	yes	—
202	#336	C₂²×C₁₉	1	2	yes	—
203	C₂×C₁₉	—	4	2	no	—
204	C₂×C₁₉	#2817	1	1	yes	characteristic
205	C₂×C₁₉	#3191	1	1	yes	characteristic
206	C₂×C₁₉	#3197	1	1	yes	characteristic
207	C₂×C₁₉	#3232	1	2	yes	—
208	C₂×C₁₉	#3240	1	2	yes	—
209	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
210	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
211	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
212	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
213	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
214	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
215	#125	—	4	2	no	—
216	#125	—	4	2	no	—
217	C₂×C₄⋊C₄	—	2	2	no	—
218	C₂×C₄⋊C₄	—	2	2	no	—
219	C₂×C₄⋊C₄	—	2	2	no	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
222	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
223	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
224	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
225	C₂×C₂²⋊C₄	—	2	2	no	—
226	C₂×C₂²⋊C₄	—	2	2	no	—
227	C₂×C₄²	—	4	1	no	—
228	C₂×C₄²	—	4	1	no	—
229	C₂×C₄²	D₄×C₁₉	1	2	yes	—
230	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
231	#107	—	4	1	no	—
232	#107	—	4	1	no	—
233	#106	—	4	2	no	—
234	C₂²⋊C₈	—	4	1	no	—
235	C₂²⋊C₈	—	4	1	no	—
236	#95	—	2	2	no	—
237	#95	—	2	2	no	—
238	#95	—	2	2	no	—
239	#95	—	2	2	no	—
240	#95	—	2	2	no	—
241	#95	—	2	2	no	—
242	C₁₉	#32791	1	1	yes	characteristic, direct product factor, Sylow
243	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	—	2	1	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	4	1	no	—
254	C₂²×C₄	—	4	1	no	—
255	C₂²×C₄	—	4	1	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
259	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
260	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	1	no	—
263	C₂×C₈	—	2	1	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₄⋊C₄	—	2	2	no	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	2	2	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	4	4	no	—
277	C₄⋊C₄	—	4	4	no	—
278	C₄⋊C₄	—	4	4	no	—
279	C₄⋊C₄	—	4	4	no	—
280	C₂²⋊C₄	—	4	4	no	—
281	C₂²⋊C₄	—	4	4	no	—
282	C₄²	—	2	2	no	—
283	C₄²	—	2	2	no	—
284	C₄²	—	4	2	no	—
285	C₂³	—	2	1	no	—
286	C₂³	—	2	2	no	—
287	C₂³	—	2	2	no	—
288	C₂³	—	2	1	no	—
289	C₂³	C₁₉×#135	1	2	yes	—
290	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	4	4	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	—	4	1	no	—
303	C₂×C₄	—	4	1	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
317	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
318	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
319	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
320	C₈	—	4	2	no	—
321	C₈	—	4	1	no	—
322	C₈	—	4	1	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	4	1	no	—
326	C₂²	—	4	2	no	—
327	C₂²	—	4	1	no	—
328	C₂²	C₁₉×#534	1	1	yes	characteristic
329	C₂²	C₁₉×#536	1	2	yes	—
330	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
331	C₂²	C₁₉×#575	1	1	yes	characteristic
332	C₂²	C₁₉×#575	1	2	yes	—
333	C₄	—	4	2	no	—
334	C₄	—	4	2	no	—
335	C₄	—	4	1	no	—
336	C₄	—	8	2	no	—
337	C₄	—	8	2	no	—
338	C₄	—	8	2	no	—
339	C₄	—	8	2	no	—
340	C₄	C₁₉×#563	1	2	yes	—
341	C₄	C₁₉×#563	1	1	yes	characteristic
342	C₄	C₁₉×#563	1	1	yes	characteristic
343	C₂	—	4	2	no	—
344	C₂	C₁₉×#2817	1	1	yes	characteristic
345	C₂	C₁₉×#3191	1	1	yes	characteristic
346	C₂	C₁₉×#3197	1	1	yes	characteristic
347	C₂	C₁₉×#3232	1	2	yes	—
348	C₂	C₁₉×#3240	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2101	C₂	semidirect
3. C₁₉×#2101	C₂	semidirect
7. C₁₉×#2059	C₂	semidirect
8. C₁₉×#2059	C₂	semidirect
110. #32791	C₁₉	direct (N × H)
150. #2101	C₂×C₁₉	semidirect
151. #2101	C₂×C₁₉	semidirect
155. #2059	C₂×C₁₉	semidirect
156. #2059	C₂×C₁₉	semidirect
242. C₁₉	#32791	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×#2851	2
C₁₉×#2101	2
C₁₉×#2077	2
C₁₉×#2076	2
C₁₉×#2075	2
C₁₉×#2059	2
C₁₉×#1817	2
#32791	19

Subgroups — C19×#32791 #18038750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32791 #18038750