Subgroups — C₁₉×#10284 #18016243

Order 4864.

678 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3226	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3205	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2858	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1276	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#532	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#124	—	2	2	no	—
12	C₁₉×#500	—	2	1	no	—
13	C₁₉×#493	—	2	1	no	—
14	C₁₉×#486	—	2	1	no	—
15	C₁₉×#486	—	2	1	no	—
16	C₁₉×#480	—	2	2	no	—
17	C₁₉×#474	—	2	2	no	—
18	C₁₉×#459	—	2	2	no	—
19	C₁₉×#447	—	2	2	no	—
20	C₁₉×#431	C₂²	1	1	yes	characteristic
21	C₁₉×#431	C₂²	1	1	yes	characteristic
22	C₁₉×#423	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#104	—	2	2	no	—
24	C₁₉×#390	—	2	2	no	—
25	C₁₉×#390	—	2	2	no	—
26	C₄³×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#332	—	2	2	no	—
28	C₁₉×#331	—	2	2	no	—
29	C₂×#41×C₁₉	—	2	1	no	—
30	C₂²×Q₈×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	D₄	1	2	yes	—
34	C₂×D₈×C₁₉	—	2	4	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	—	2	1	no	—
39	C₁₉×C₄⋊Q₈	—	2	1	no	—
40	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
41	C₁₉×#127	—	2	1	no	—
42	C₁₉×#127	—	2	1	no	—
43	C₁₉×#127	—	2	1	no	—
44	C₁₉×#127	—	2	1	no	—
45	C₁₉×#127	D₄	1	1	yes	characteristic
46	C₁₉×#124	—	2	1	no	—
47	C₁₉×#124	—	4	4	no	—
48	C₁₉×#124	—	4	4	no	—
49	C₁₉×#121	—	2	1	no	—
50	C₁₉×#121	—	2	1	no	—
51	C₄×D₄×C₁₉	—	2	1	no	—
52	C₄×D₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
56	C₂×C₄²×C₁₉	—	2	1	no	—
57	C₂×C₄²×C₁₉	—	2	1	no	—
58	C₂×C₄²×C₁₉	D₄	1	2	yes	—
59	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
60	C₁₉×#107	—	2	4	no	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	—	2	1	no	—
63	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
64	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
65	C₁₉×#104	—	4	4	no	—
66	C₁₉×#102	—	2	4	no	—
67	C₁₉×#102	—	2	4	no	—
68	C₁₉×C₂²⋊C₈	—	2	1	no	—
69	C₁₉×C₂²⋊C₈	—	2	1	no	—
70	C₄×C₈×C₁₉	—	2	1	no	—
71	C₄×C₈×C₁₉	—	2	1	no	—
72	C₂⁴×C₁₉	—	2	2	no	—
73	#41×C₁₉	—	4	2	no	—
74	#41×C₁₉	—	4	2	no	—
75	C₂×Q₈×C₁₉	—	2	1	no	—
76	C₂×Q₈×C₁₉	—	4	1	no	—
77	C₂×Q₈×C₁₉	—	4	1	no	—
78	C₂×Q₈×C₁₉	—	4	2	no	—
79	C₂×Q₈×C₁₉	—	4	2	no	—
80	C₂×D₄×C₁₉	—	2	1	no	—
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	2	2	no	—
83	C₂×D₄×C₁₉	—	2	1	no	—
84	C₂×D₄×C₁₉	—	2	2	no	—
85	C₂×D₄×C₁₉	—	4	4	no	—
86	C₂×D₄×C₁₉	—	4	4	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	4	1	no	—
92	C₂×D₄×C₁₉	—	4	2	no	—
93	C₂×D₄×C₁₉	—	4	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	D₈×C₁₉	—	8	4	no	—
101	M₁₆×C₁₉	—	4	2	no	—
102	C₂×C₈×C₁₉	—	2	2	no	—
103	C₂×C₈×C₁₉	—	2	2	no	—
104	C₂×C₈×C₁₉	—	4	1	no	—
105	C₄⋊C₄×C₁₉	—	2	2	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	2	2	no	—
109	C₄⋊C₄×C₁₉	—	4	1	no	—
110	C₄⋊C₄×C₁₉	—	4	1	no	—
111	C₂²⋊C₄×C₁₉	—	4	16	no	—
112	C₂²⋊C₄×C₁₉	—	4	1	no	—
113	C₂²⋊C₄×C₁₉	—	4	1	no	—
114	C₄²×C₁₉	—	2	2	no	—
115	C₄²×C₁₉	—	4	2	no	—
116	C₄²×C₁₉	—	4	2	no	—
117	C₄²×C₁₉	D₈	1	4	yes	complemented
118	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₁₉	#41	1	1	yes	characteristic
122	#10284	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂³×C₁₉	—	4	4	no	—
124	C₂³×C₁₉	—	4	4	no	—
125	C₂³×C₁₉	—	4	1	no	—
126	C₂³×C₁₉	—	4	2	no	—
127	C₂³×C₁₉	—	4	4	no	—
128	C₂³×C₁₉	#120	1	1	yes	characteristic
129	Q₈×C₁₉	—	4	2	no	—
130	Q₈×C₁₉	—	8	2	no	—
131	Q₈×C₁₉	—	8	1	no	—
132	Q₈×C₁₉	—	8	1	no	—
133	D₄×C₁₉	—	4	2	no	—
134	D₄×C₁₉	—	4	2	no	—
135	D₄×C₁₉	—	4	4	no	—
136	D₄×C₁₉	—	4	2	no	—
137	D₄×C₁₉	—	8	2	no	—
138	D₄×C₁₉	—	8	2	no	—
139	D₄×C₁₉	—	8	2	no	—
140	D₄×C₁₉	—	8	2	no	—
141	D₄×C₁₉	—	8	2	no	—
142	D₄×C₁₉	—	8	1	no	—
143	D₄×C₁₉	—	8	1	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	4	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	2	no	—
151	C₂×C₄×C₁₉	—	4	4	no	—
152	C₂×C₄×C₁₉	—	8	1	no	—
153	C₂×C₄×C₁₉	—	8	1	no	—
154	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
161	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
162	C₈×C₁₉	—	4	2	no	—
163	C₈×C₁₉	—	4	2	no	—
164	C₈×C₁₉	—	8	1	no	—
165	#3226	C₂×C₁₉	1	1	yes	characteristic, complemented
166	#3205	C₂×C₁₉	1	1	yes	characteristic
167	#2858	C₂×C₁₉	1	1	yes	characteristic, complemented
168	#1962	C₂×C₁₉	1	1	yes	characteristic, complemented
169	#1546	C₂×C₁₉	1	1	yes	characteristic, complemented
170	#1545	C₂×C₁₉	1	1	yes	characteristic, complemented
171	#1276	C₂×C₁₉	1	1	yes	characteristic, complemented
172	C₂²×C₁₉	—	2	1	no	—
173	C₂²×C₁₉	—	2	1	no	—
174	C₂²×C₁₉	—	8	8	no	—
175	C₂²×C₁₉	—	8	1	no	—
176	C₂²×C₁₉	—	8	2	no	—
177	C₂²×C₁₉	—	8	2	no	—
178	C₂²×C₁₉	—	8	1	no	—
179	C₂²×C₁₉	—	8	1	no	—
180	C₂²×C₁₉	—	8	2	no	—
181	C₂²×C₁₉	#392	1	1	yes	characteristic
182	C₂²×C₁₉	#447	1	2	yes	—
183	C₄×C₁₉	—	2	1	no	—
184	C₄×C₁₉	—	2	1	no	—
185	C₄×C₁₉	—	4	4	no	—
186	C₄×C₁₉	—	8	2	no	—
187	C₄×C₁₉	—	8	1	no	—
188	C₄×C₁₉	#454	1	2	yes	—
189	C₄×C₁₉	#455	1	2	yes	—
190	C₄×C₁₉	#459	1	2	yes	—
191	C₄×C₁₉	#493	1	1	yes	characteristic
192	C₄×C₁₉	#496	1	1	yes	characteristic
193	#532	C₂²×C₁₉	1	1	yes	characteristic
194	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
195	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
196	C₂×#124	—	2	2	no	—
197	#500	—	2	1	no	—
198	#493	—	2	1	no	—
199	#486	—	2	1	no	—
200	#486	—	2	1	no	—
201	#480	—	2	2	no	—
202	#474	—	2	2	no	—
203	#459	—	2	2	no	—
204	#447	—	2	2	no	—
205	#431	C₂²×C₁₉	1	1	yes	characteristic
206	#431	C₂²×C₁₉	1	1	yes	characteristic
207	#423	C₂²×C₁₉	1	1	yes	characteristic
208	C₂×#104	—	2	2	no	—
209	#390	—	2	2	no	—
210	#390	—	2	2	no	—
211	C₄³	C₂²×C₁₉	1	1	yes	characteristic
212	#332	—	2	2	no	—
213	#331	—	2	2	no	—
214	C₂×C₁₉	—	2	2	no	—
215	C₂×C₁₉	—	16	1	no	—
216	C₂×C₁₉	—	16	2	no	—
217	C₂×C₁₉	#2003	1	1	yes	characteristic
218	C₂×C₁₉	#2004	1	1	yes	characteristic
219	C₂×C₁₉	#2011	1	1	yes	characteristic
220	C₂×#41	—	2	1	no	—
221	C₂²×Q₈	—	2	1	no	—
222	C₂²×D₄	—	2	1	no	—
223	C₂²×D₄	—	2	1	no	—
224	C₂²×D₄	D₄×C₁₉	1	2	yes	—
225	C₂×D₈	—	2	4	no	—
226	C₂×M₁₆	—	2	1	no	—
227	C₄⋊Q₈	—	2	1	no	—
228	C₄⋊Q₈	—	2	1	no	—
229	C₄⋊Q₈	—	2	1	no	—
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
232	#127	—	2	1	no	—
233	#127	—	2	1	no	—
234	#127	—	2	1	no	—
235	#127	—	2	1	no	—
236	#127	D₄×C₁₉	1	1	yes	characteristic
237	#124	—	2	1	no	—
238	#124	—	4	4	no	—
239	#124	—	4	4	no	—
240	#121	—	2	1	no	—
241	#121	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
246	C₂×C₂²⋊C₄	—	2	8	no	—
247	C₂×C₄²	—	2	1	no	—
248	C₂×C₄²	—	2	1	no	—
249	C₂×C₄²	D₄×C₁₉	1	2	yes	—
250	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
251	#107	—	2	4	no	—
252	C₄⋊C₈	—	2	1	no	—
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
255	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
256	#104	—	4	4	no	—
257	#102	—	2	4	no	—
258	#102	—	2	4	no	—
259	C₂²⋊C₈	—	2	1	no	—
260	C₂²⋊C₈	—	2	1	no	—
261	C₄×C₈	—	2	1	no	—
262	C₄×C₈	—	2	1	no	—
263	C₁₉	#10284	1	1	yes	characteristic, direct product factor, Sylow
264	C₂⁴	—	2	2	no	—
265	#41	—	4	2	no	—
266	#41	—	4	2	no	—
267	C₂×Q₈	—	2	1	no	—
268	C₂×Q₈	—	4	1	no	—
269	C₂×Q₈	—	4	1	no	—
270	C₂×Q₈	—	4	2	no	—
271	C₂×Q₈	—	4	2	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	4	4	no	—
278	C₂×D₄	—	4	4	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	1	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
292	D₈	—	8	4	no	—
293	M₁₆	—	4	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	4	1	no	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₂²⋊C₄	—	4	16	no	—
304	C₂²⋊C₄	—	4	1	no	—
305	C₂²⋊C₄	—	4	1	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	4	2	no	—
308	C₄²	—	4	2	no	—
309	C₄²	D₈×C₁₉	1	4	yes	complemented
310	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
311	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
312	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
313	C₄²	#41×C₁₉	1	1	yes	characteristic
314	C₂³	—	4	4	no	—
315	C₂³	—	4	4	no	—
316	C₂³	—	4	1	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	4	no	—
319	C₂³	C₁₉×#120	1	1	yes	characteristic
320	Q₈	—	4	2	no	—
321	Q₈	—	8	2	no	—
322	Q₈	—	8	1	no	—
323	Q₈	—	8	1	no	—
324	D₄	—	4	2	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	2	no	—
328	D₄	—	8	2	no	—
329	D₄	—	8	2	no	—
330	D₄	—	8	2	no	—
331	D₄	—	8	2	no	—
332	D₄	—	8	2	no	—
333	D₄	—	8	1	no	—
334	D₄	—	8	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	8	1	no	—
344	C₂×C₄	—	8	1	no	—
345	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
346	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
347	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
348	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
349	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
350	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
351	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
352	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
353	C₈	—	4	2	no	—
354	C₈	—	4	2	no	—
355	C₈	—	8	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	8	8	no	—
359	C₂²	—	8	1	no	—
360	C₂²	—	8	2	no	—
361	C₂²	—	8	2	no	—
362	C₂²	—	8	1	no	—
363	C₂²	—	8	1	no	—
364	C₂²	—	8	2	no	—
365	C₂²	C₁₉×#392	1	1	yes	characteristic
366	C₂²	C₁₉×#447	1	2	yes	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	4	4	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	1	no	—
372	C₄	C₁₉×#454	1	2	yes	—
373	C₄	C₁₉×#455	1	2	yes	—
374	C₄	C₁₉×#459	1	2	yes	—
375	C₄	C₁₉×#493	1	1	yes	characteristic
376	C₄	C₁₉×#496	1	1	yes	characteristic
377	C₂	—	2	2	no	—
378	C₂	—	16	2	no	—
379	C₂	—	16	1	no	—
380	C₂	C₁₉×#2003	1	1	yes	characteristic
381	C₂	C₁₉×#2004	1	1	yes	characteristic
382	C₂	C₁₉×#2011	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3205	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3226	C₂	semidirect
3. C₁₉×#2858	C₂	semidirect
4. C₁₉×#1962	C₂	semidirect
5. C₁₉×#1546	C₂	semidirect
6. C₁₉×#1545	C₂	semidirect
7. C₁₉×#1276	C₂	semidirect
117. C₄²×C₁₉	D₈	semidirect
122. #10284	C₁₉	direct (N × H)
165. #3226	C₂×C₁₉	semidirect
167. #2858	C₂×C₁₉	semidirect
168. #1962	C₂×C₁₉	semidirect
169. #1546	C₂×C₁₉	semidirect
170. #1545	C₂×C₁₉	semidirect
171. #1276	C₂×C₁₉	semidirect
263. C₁₉	#10284	direct (N × H)
309. C₄²	D₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3226	2
C₁₉×#3205	2
C₁₉×#2858	2
C₁₉×#1962	2
C₁₉×#1546	2
C₁₉×#1545	2
C₁₉×#1276	2
#10284	19

Subgroups — C19×#10284 #18016243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10284 #18016243