Subgroups — C₁₉×#13303 #18019262

Order 4864.

396 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2565	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1394	C₂	1	2	yes	maximal
5	C₁₉×#1394	C₂	1	2	yes	maximal
6	C₂×C₁₉×#125	C₄	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#423	—	2	1	no	—
9	C₂×C₁₉×#101	C₂²	1	2	yes	—
10	C₂×C₁₉×#101	C₂²	1	2	yes	—
11	C₄×M₁₆×C₁₉	—	2	1	no	—
12	C₁₉×#398	—	2	1	no	—
13	C₁₉×#398	—	2	1	no	—
14	C₁₉×#391	C₂²	1	1	yes	characteristic
15	C₁₉×#391	C₂²	1	1	yes	characteristic
16	C₁₉×#387	—	2	1	no	—
17	C₁₉×#387	—	2	1	no	—
18	C₁₉×#384	C₄	1	1	yes	characteristic
19	C₁₉×#382	C₄	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
21	C₁₉×#343	—	2	1	no	—
22	C₁₉×#343	—	2	1	no	—
23	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×M₁₆×C₁₉	—	2	2	no	—
25	C₂×M₁₆×C₁₉	—	2	2	no	—
26	C₁₉×#125	—	4	1	no	—
27	C₁₉×#125	—	4	1	no	—
28	C₄×Q₈×C₁₉	—	4	1	no	—
29	C₄×Q₈×C₁₉	—	4	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
45	C₁₉×C₄⋊C₈	—	4	1	no	—
46	C₁₉×C₄⋊C₈	—	4	1	no	—
47	C₁₉×#101	—	2	2	no	—
48	C₁₉×#101	—	2	4	no	—
49	C₁₉×#101	Q₈	1	4	yes	—
50	C₁₉×#97	—	4	1	no	—
51	C₄×C₈×C₁₉	—	4	1	no	—
52	C₁₉×#95	—	2	1	no	—
53	C₁₉×#95	—	2	1	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₁₉×#95	—	2	1	no	—
57	C₁₉×#95	—	2	1	no	—
58	C₁₉×#95	—	2	1	no	—
59	C₂×Q₈×C₁₉	—	4	1	no	—
60	C₂×Q₈×C₁₉	—	4	1	no	—
61	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
62	C₂×Q₈×C₁₉	#41	1	2	yes	—
63	C₂²×C₄×C₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂²×C₄	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	M₁₆×C₁₉	—	2	4	no	—
75	M₁₆×C₁₉	—	4	2	no	—
76	M₁₆×C₁₉	—	4	2	no	—
77	M₁₆×C₁₉	—	4	2	no	—
78	C₂×C₈×C₁₉	—	4	2	no	—
79	C₂×C₈×C₁₉	—	4	2	no	—
80	C₄⋊C₄×C₁₉	—	4	1	no	—
81	C₄⋊C₄×C₁₉	—	4	1	no	—
82	C₄⋊C₄×C₁₉	—	4	1	no	—
83	C₄⋊C₄×C₁₉	—	4	1	no	—
84	C₄⋊C₄×C₁₉	—	4	1	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	1	no	—
90	C₄⋊C₄×C₁₉	—	4	1	no	—
91	C₄²×C₁₉	—	2	1	no	—
92	C₄²×C₁₉	—	2	1	no	—
93	C₄²×C₁₉	—	2	1	no	—
94	C₄²×C₁₉	—	2	1	no	—
95	C₄²×C₁₉	—	2	1	no	—
96	C₄²×C₁₉	—	2	1	no	—
97	C₄²×C₁₉	—	4	1	no	—
98	C₄²×C₁₉	—	4	1	no	—
99	#13303	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	Q₈×C₁₉	—	4	2	no	—
102	Q₈×C₁₉	—	4	2	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	2	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	—	4	1	no	—
114	C₂×C₄×C₁₉	—	4	1	no	—
115	C₂×C₄×C₁₉	—	4	1	no	—
116	C₂×C₄×C₁₉	—	4	1	no	—
117	C₂×C₄×C₁₉	—	4	1	no	—
118	C₂×C₄×C₁₉	—	4	1	no	—
119	C₂×C₄×C₁₉	—	4	1	no	—
120	C₂×C₄×C₁₉	—	4	1	no	—
121	C₂×C₄×C₁₉	—	4	1	no	—
122	C₂×C₄×C₁₉	—	4	1	no	—
123	C₂×C₄×C₁₉	—	4	2	no	—
124	C₂×C₄×C₁₉	—	4	1	no	—
125	C₂×C₄×C₁₉	—	4	1	no	—
126	C₂×C₄×C₁₉	—	4	1	no	—
127	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
128	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
129	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
130	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
131	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
132	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
133	C₈×C₁₉	—	4	4	no	—
134	C₈×C₁₉	—	8	2	no	—
135	#2565	C₂×C₁₉	1	1	yes	characteristic
136	#1801	C₂×C₁₉	1	1	yes	characteristic
137	C₄×#101	C₂×C₁₉	1	1	yes	characteristic
138	#1394	C₂×C₁₉	1	2	yes	—
139	#1394	C₂×C₁₉	1	2	yes	—
140	C₂²×C₁₉	—	2	1	no	—
141	C₂²×C₁₉	—	2	1	no	—
142	C₂²×C₁₉	#391	1	1	yes	characteristic
143	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
144	C₂²×C₁₉	#410	1	1	yes	characteristic
145	C₄×C₁₉	—	2	1	no	—
146	C₄×C₁₉	—	2	1	no	—
147	C₄×C₁₉	—	2	2	no	—
148	C₄×C₁₉	—	2	1	no	—
149	C₄×C₁₉	—	2	2	no	—
150	C₄×C₁₉	—	2	1	no	—
151	C₄×C₁₉	—	4	2	no	—
152	C₄×C₁₉	—	4	1	no	—
153	C₄×C₁₉	—	4	1	no	—
154	C₄×C₁₉	—	4	1	no	—
155	C₄×C₁₉	—	8	1	no	—
156	C₄×C₁₉	—	8	1	no	—
157	C₄×C₁₉	—	8	1	no	—
158	C₂×#125	C₄×C₁₉	1	1	yes	characteristic
159	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
160	#423	—	2	1	no	—
161	C₂×#101	C₂²×C₁₉	1	2	yes	—
162	C₂×#101	C₂²×C₁₉	1	2	yes	—
163	C₄×M₁₆	—	2	1	no	—
164	#398	—	2	1	no	—
165	#398	—	2	1	no	—
166	#391	C₂²×C₁₉	1	1	yes	characteristic
167	#391	C₂²×C₁₉	1	1	yes	characteristic
168	#387	—	2	1	no	—
169	#387	—	2	1	no	—
170	#384	C₄×C₁₉	1	1	yes	characteristic
171	#382	C₄×C₁₉	1	1	yes	characteristic
172	C₄×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
173	#343	—	2	1	no	—
174	#343	—	2	1	no	—
175	C₂×C₁₉	—	2	1	no	—
176	C₂×C₁₉	—	2	1	no	—
177	C₂×C₁₉	#1996	1	1	yes	characteristic
178	C₂×C₁₉	#2132	1	1	yes	characteristic
179	C₂×C₁₉	#2133	1	1	yes	characteristic
180	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
181	C₂×M₁₆	—	2	2	no	—
182	C₂×M₁₆	—	2	2	no	—
183	#125	—	4	1	no	—
184	#125	—	4	1	no	—
185	C₄×Q₈	—	4	1	no	—
186	C₄×Q₈	—	4	1	no	—
187	C₂×C₄⋊C₄	—	2	1	no	—
188	C₂×C₄⋊C₄	—	2	1	no	—
189	C₂×C₄⋊C₄	—	2	1	no	—
190	C₂×C₄⋊C₄	—	2	1	no	—
191	C₂×C₄⋊C₄	—	2	1	no	—
192	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
193	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
194	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
195	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
196	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
197	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
198	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
199	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
200	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
201	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
202	C₄⋊C₈	—	4	1	no	—
203	C₄⋊C₈	—	4	1	no	—
204	#101	—	2	2	no	—
205	#101	—	2	4	no	—
206	#101	Q₈×C₁₉	1	4	yes	—
207	#97	—	4	1	no	—
208	C₄×C₈	—	4	1	no	—
209	#95	—	2	1	no	—
210	#95	—	2	1	no	—
211	#95	—	2	1	no	—
212	#95	—	2	1	no	—
213	#95	—	2	1	no	—
214	#95	—	2	1	no	—
215	#95	—	2	1	no	—
216	C₁₉	#13303	1	1	yes	characteristic, direct product factor, Sylow
217	C₂×Q₈	—	4	1	no	—
218	C₂×Q₈	—	4	1	no	—
219	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
220	C₂×Q₈	#41×C₁₉	1	2	yes	—
221	C₂²×C₄	—	2	1	no	—
222	C₂²×C₄	—	2	1	no	—
223	C₂²×C₄	—	2	1	no	—
224	C₂²×C₄	—	2	1	no	—
225	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
226	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
227	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
228	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
229	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
230	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
231	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
232	M₁₆	—	2	4	no	—
233	M₁₆	—	4	2	no	—
234	M₁₆	—	4	2	no	—
235	M₁₆	—	4	2	no	—
236	C₂×C₈	—	4	2	no	—
237	C₂×C₈	—	4	2	no	—
238	C₄⋊C₄	—	4	1	no	—
239	C₄⋊C₄	—	4	1	no	—
240	C₄⋊C₄	—	4	1	no	—
241	C₄⋊C₄	—	4	1	no	—
242	C₄⋊C₄	—	4	1	no	—
243	C₄⋊C₄	—	4	2	no	—
244	C₄⋊C₄	—	4	2	no	—
245	C₄⋊C₄	—	4	2	no	—
246	C₄⋊C₄	—	4	2	no	—
247	C₄⋊C₄	—	4	1	no	—
248	C₄⋊C₄	—	4	1	no	—
249	C₄²	—	2	1	no	—
250	C₄²	—	2	1	no	—
251	C₄²	—	2	1	no	—
252	C₄²	—	2	1	no	—
253	C₄²	—	2	1	no	—
254	C₄²	—	2	1	no	—
255	C₄²	—	4	1	no	—
256	C₄²	—	4	1	no	—
257	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
258	Q₈	—	4	2	no	—
259	Q₈	—	4	2	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	2	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	2	1	no	—
270	C₂×C₄	—	4	1	no	—
271	C₂×C₄	—	4	1	no	—
272	C₂×C₄	—	4	1	no	—
273	C₂×C₄	—	4	1	no	—
274	C₂×C₄	—	4	1	no	—
275	C₂×C₄	—	4	1	no	—
276	C₂×C₄	—	4	1	no	—
277	C₂×C₄	—	4	1	no	—
278	C₂×C₄	—	4	1	no	—
279	C₂×C₄	—	4	1	no	—
280	C₂×C₄	—	4	2	no	—
281	C₂×C₄	—	4	1	no	—
282	C₂×C₄	—	4	1	no	—
283	C₂×C₄	—	4	1	no	—
284	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
285	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
286	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
287	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
288	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
289	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
290	C₈	—	4	4	no	—
291	C₈	—	8	2	no	—
292	C₂²	—	2	1	no	—
293	C₂²	—	2	1	no	—
294	C₂²	C₁₉×#391	1	1	yes	characteristic
295	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
296	C₂²	C₁₉×#410	1	1	yes	characteristic
297	C₄	—	2	2	no	—
298	C₄	—	2	1	no	—
299	C₄	—	2	2	no	—
300	C₄	—	2	1	no	—
301	C₄	—	2	1	no	—
302	C₄	—	2	1	no	—
303	C₄	—	4	2	no	—
304	C₄	—	4	1	no	—
305	C₄	—	4	1	no	—
306	C₄	—	4	1	no	—
307	C₄	—	8	1	no	—
308	C₄	—	8	1	no	—
309	C₄	—	8	1	no	—
310	C₂	—	2	1	no	—
311	C₂	—	2	1	no	—
312	C₂	C₁₉×#1996	1	1	yes	characteristic
313	C₂	C₁₉×#2132	1	1	yes	characteristic
314	C₂	C₁₉×#2133	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×Q₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
99. #13303	C₁₉	direct (N × H)
216. C₁₉	#13303	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×#2565	2
C₁₉×#1801	2
C₄×C₁₉×#101	2
C₁₉×#1394	2
#13303	19

Subgroups — C19×#13303 #18019262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13303 #18019262