Subgroups — C₁₉×#3243 #14561100

Order 2432.

320 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#542	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#500	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#489	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#488	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#485	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#484	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#482	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#480	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#479	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#478	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#477	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#474	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×C₄⋊Q₈	—	2	1	no	—
17	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₉×#126	—	2	1	no	—
21	C₁₉×#125	—	2	1	no	—
22	C₁₉×#125	C₂²	1	1	yes	characteristic
23	C₁₉×#125	C₂²	1	1	yes	characteristic
24	C₁₉×#124	—	2	1	no	—
25	C₁₉×#124	C₂²	1	1	yes	characteristic
26	C₁₉×#123	—	2	1	no	—
27	C₁₉×C₂²⋊Q₈	—	2	1	no	—
28	C₁₉×C₂²⋊Q₈	—	2	1	no	—
29	C₁₉×C₂²⋊Q₈	—	2	1	no	—
30	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₁₉×#121	C₂²	1	1	yes	characteristic
32	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#117	C₂²	1	1	yes	characteristic
35	C₁₉×#117	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#107	C₂²	1	1	yes	characteristic
38	C₁₉×#107	C₂²	1	1	yes	characteristic
39	C₁₉×#107	C₂²	1	1	yes	characteristic
40	C₁₉×#107	C₂²	1	1	yes	characteristic
41	C₁₉×#107	C₂²	1	1	yes	characteristic
42	C₁₉×#107	C₂²	1	1	yes	characteristic
43	C₁₉×#106	C₂²	1	1	yes	characteristic
44	C₁₉×#106	C₂²	1	1	yes	characteristic
45	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₁₉×#103	C₂²	1	1	yes	characteristic
48	C₁₉×#103	C₂²	1	1	yes	characteristic
49	C₁₉×#103	C₂²	1	1	yes	characteristic
50	C₁₉×#103	C₂²	1	1	yes	characteristic
51	C₁₉×#102	C₂²	1	1	yes	characteristic
52	C₁₉×#102	C₂²	1	1	yes	characteristic
53	C₁₉×#102	C₂²	1	1	yes	characteristic
54	C₁₉×#102	C₂²	1	1	yes	characteristic
55	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
56	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₁₉×#97	C₂²	1	1	yes	characteristic
58	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₁₉	—	2	1	no	—
60	C₂×Q₈×C₁₉	—	2	1	no	—
61	C₂×Q₈×C₁₉	—	2	1	no	—
62	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×D₄×C₁₉	—	2	1	no	—
64	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
83	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
84	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂²⋊C₄×C₁₉	—	2	1	no	—
96	C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
97	C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
98	C₄²×C₁₉	—	2	1	no	—
99	C₄²×C₁₉	—	2	1	no	—
100	C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₄²×C₁₉	C₂³	1	1	yes	characteristic
102	C₂³×C₁₉	—	2	1	no	—
103	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
104	Q₈×C₁₉	—	2	1	no	—
105	Q₈×C₁₉	—	2	1	no	—
106	Q₈×C₁₉	—	8	1	no	—
107	Q₈×C₁₉	—	8	1	no	—
108	Q₈×C₁₉	—	8	1	no	—
109	D₄×C₁₉	—	2	1	no	—
110	D₄×C₁₉	—	2	1	no	—
111	D₄×C₁₉	—	8	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	—	2	1	no	—
121	C₂×C₄×C₁₉	—	8	1	no	—
122	C₂×C₄×C₁₉	—	8	1	no	—
123	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
129	C₈×C₁₉	—	2	1	no	—
130	C₈×C₁₉	—	2	1	no	—
131	C₈×C₁₉	—	2	1	no	—
132	C₈×C₁₉	—	2	1	no	—
133	#3243	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂²×C₁₉	—	2	1	no	—
135	C₂²×C₁₉	—	2	1	no	—
136	C₂²×C₁₉	—	2	1	no	—
137	C₂²×C₁₉	—	4	1	no	—
138	C₂²×C₁₉	—	4	1	no	—
139	C₂²×C₁₉	—	4	1	no	—
140	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
141	C₄×C₁₉	—	2	1	no	—
142	C₄×C₁₉	—	2	1	no	—
143	C₄×C₁₉	—	2	1	no	—
144	C₄×C₁₉	—	2	1	no	—
145	C₄×C₁₉	—	2	1	no	—
146	C₄×C₁₉	—	4	1	no	—
147	C₄×C₁₉	—	4	1	no	—
148	C₄×C₁₉	—	4	1	no	—
149	C₄×C₁₉	—	4	1	no	—
150	C₄×C₁₉	—	4	1	no	—
151	C₄×C₁₉	—	4	1	no	—
152	C₄×C₁₉	—	4	1	no	—
153	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
154	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
155	#544	C₂×C₁₉	1	1	yes	characteristic, complemented
156	#542	C₂×C₁₉	1	1	yes	characteristic
157	#501	C₂×C₁₉	1	1	yes	characteristic, complemented
158	#500	C₂×C₁₉	1	1	yes	characteristic, complemented
159	#489	C₂×C₁₉	1	1	yes	characteristic, complemented
160	#488	C₂×C₁₉	1	1	yes	characteristic, complemented
161	#485	C₂×C₁₉	1	1	yes	characteristic, complemented
162	#484	C₂×C₁₉	1	1	yes	characteristic, complemented
163	#482	C₂×C₁₉	1	1	yes	characteristic
164	#480	C₂×C₁₉	1	1	yes	characteristic
165	#479	C₂×C₁₉	1	1	yes	characteristic, complemented
166	#478	C₂×C₁₉	1	1	yes	characteristic, complemented
167	#477	C₂×C₁₉	1	1	yes	characteristic, complemented
168	#474	C₂×C₁₉	1	1	yes	characteristic, complemented
169	#433	C₂×C₁₉	1	1	yes	characteristic, complemented
170	C₂×C₁₉	—	4	1	no	—
171	C₂×C₁₉	—	8	1	no	—
172	C₂×C₁₉	#536	1	1	yes	characteristic
173	C₂×C₁₉	#576	1	1	yes	characteristic
174	C₂×C₁₉	#578	1	1	yes	characteristic
175	C₄⋊Q₈	—	2	1	no	—
176	C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
177	C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
178	C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
179	#126	—	2	1	no	—
180	#125	—	2	1	no	—
181	#125	C₂²×C₁₉	1	1	yes	characteristic
182	#125	C₂²×C₁₉	1	1	yes	characteristic
183	#124	—	2	1	no	—
184	#124	C₂²×C₁₉	1	1	yes	characteristic
185	#123	—	2	1	no	—
186	C₂²⋊Q₈	—	2	1	no	—
187	C₂²⋊Q₈	—	2	1	no	—
188	C₂²⋊Q₈	—	2	1	no	—
189	C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
190	#121	C₂²×C₁₉	1	1	yes	characteristic
191	C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
192	C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
193	#117	C₂²×C₁₉	1	1	yes	characteristic
194	#117	C₂²×C₁₉	1	1	yes	characteristic
195	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
196	#107	C₂²×C₁₉	1	1	yes	characteristic
197	#107	C₂²×C₁₉	1	1	yes	characteristic
198	#107	C₂²×C₁₉	1	1	yes	characteristic
199	#107	C₂²×C₁₉	1	1	yes	characteristic
200	#107	C₂²×C₁₉	1	1	yes	characteristic
201	#107	C₂²×C₁₉	1	1	yes	characteristic
202	#106	C₂²×C₁₉	1	1	yes	characteristic
203	#106	C₂²×C₁₉	1	1	yes	characteristic
204	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
205	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
206	#103	C₂²×C₁₉	1	1	yes	characteristic
207	#103	C₂²×C₁₉	1	1	yes	characteristic
208	#103	C₂²×C₁₉	1	1	yes	characteristic
209	#103	C₂²×C₁₉	1	1	yes	characteristic
210	#102	C₂²×C₁₉	1	1	yes	characteristic
211	#102	C₂²×C₁₉	1	1	yes	characteristic
212	#102	C₂²×C₁₉	1	1	yes	characteristic
213	#102	C₂²×C₁₉	1	1	yes	characteristic
214	C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
215	C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
216	#97	C₂²×C₁₉	1	1	yes	characteristic
217	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
218	C₁₉	#3243	1	1	yes	characteristic, direct product factor, Sylow
219	C₂×Q₈	—	2	1	no	—
220	C₂×Q₈	—	2	1	no	—
221	C₂×Q₈	—	2	1	no	—
222	C₂×Q₈	C₂³×C₁₉	1	1	yes	characteristic
223	C₂×D₄	—	2	1	no	—
224	C₂×D₄	C₂³×C₁₉	1	1	yes	characteristic
225	C₂²×C₄	—	2	1	no	—
226	C₂²×C₄	—	2	1	no	—
227	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
228	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
229	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
230	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
231	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
232	C₄⋊C₄	—	2	1	no	—
233	C₄⋊C₄	—	2	1	no	—
234	C₄⋊C₄	—	2	1	no	—
235	C₄⋊C₄	—	2	1	no	—
236	C₄⋊C₄	—	2	1	no	—
237	C₄⋊C₄	—	2	1	no	—
238	C₄⋊C₄	—	2	1	no	—
239	C₄⋊C₄	—	2	1	no	—
240	C₄⋊C₄	—	2	1	no	—
241	C₄⋊C₄	—	2	1	no	—
242	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
243	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
244	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
245	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
246	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
247	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
248	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
249	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
250	C₂²⋊C₄	—	2	1	no	—
251	C₂²⋊C₄	—	2	1	no	—
252	C₂²⋊C₄	—	2	1	no	—
253	C₂²⋊C₄	—	2	1	no	—
254	C₂²⋊C₄	—	2	1	no	—
255	C₂²⋊C₄	—	2	1	no	—
256	C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
257	C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
258	C₄²	—	2	1	no	—
259	C₄²	—	2	1	no	—
260	C₄²	C₂³×C₁₉	1	1	yes	characteristic
261	C₄²	C₂³×C₁₉	1	1	yes	characteristic
262	C₂³	—	2	1	no	—
263	C₂³	C₂×D₄×C₁₉	1	1	yes	characteristic
264	Q₈	—	2	1	no	—
265	Q₈	—	2	1	no	—
266	Q₈	—	8	1	no	—
267	Q₈	—	8	1	no	—
268	Q₈	—	8	1	no	—
269	D₄	—	2	1	no	—
270	D₄	—	2	1	no	—
271	D₄	—	8	1	no	—
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	—	2	1	no	—
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	—	8	1	no	—
282	C₂×C₄	—	8	1	no	—
283	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
284	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
285	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
286	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
287	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
288	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
289	C₈	—	2	1	no	—
290	C₈	—	2	1	no	—
291	C₈	—	2	1	no	—
292	C₈	—	2	1	no	—
293	C₂²	—	2	1	no	—
294	C₂²	—	2	1	no	—
295	C₂²	—	2	1	no	—
296	C₂²	—	4	1	no	—
297	C₂²	—	4	1	no	—
298	C₂²	—	4	1	no	—
299	C₂²	C₂²×D₄×C₁₉	1	1	yes	characteristic
300	C₄	—	2	1	no	—
301	C₄	—	2	1	no	—
302	C₄	—	2	1	no	—
303	C₄	—	2	1	no	—
304	C₄	—	2	1	no	—
305	C₄	—	4	1	no	—
306	C₄	—	4	1	no	—
307	C₄	—	4	1	no	—
308	C₄	—	4	1	no	—
309	C₄	—	4	1	no	—
310	C₄	—	4	1	no	—
311	C₄	—	4	1	no	—
312	C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
313	C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
314	C₂	—	4	1	no	—
315	C₂	—	8	1	no	—
316	C₂	C₁₉×#536	1	1	yes	characteristic
317	C₂	C₁₉×#576	1	1	yes	characteristic
318	C₂	C₁₉×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#544	C₂	semidirect
3. C₁₉×#501	C₂	semidirect
4. C₁₉×#500	C₂	semidirect
5. C₁₉×#489	C₂	semidirect
6. C₁₉×#488	C₂	semidirect
7. C₁₉×#485	C₂	semidirect
8. C₁₉×#484	C₂	semidirect
11. C₁₉×#479	C₂	semidirect
12. C₁₉×#478	C₂	semidirect
13. C₁₉×#477	C₂	semidirect
14. C₁₉×#474	C₂	semidirect
15. C₁₉×#433	C₂	semidirect
133. #3243	C₁₉	direct (N × H)
155. #544	C₂×C₁₉	semidirect
157. #501	C₂×C₁₉	semidirect
158. #500	C₂×C₁₉	semidirect
159. #489	C₂×C₁₉	semidirect
160. #488	C₂×C₁₉	semidirect
161. #485	C₂×C₁₉	semidirect
162. #484	C₂×C₁₉	semidirect
165. #479	C₂×C₁₉	semidirect
166. #478	C₂×C₁₉	semidirect
167. #477	C₂×C₁₉	semidirect
168. #474	C₂×C₁₉	semidirect
169. #433	C₂×C₁₉	semidirect
218. C₁₉	#3243	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×#544	2
C₁₉×#542	2
C₁₉×#501	2
C₁₉×#500	2
C₁₉×#489	2
C₁₉×#488	2
C₁₉×#485	2
C₁₉×#484	2
C₁₉×#482	2
C₁₉×#480	2
C₁₉×#479	2
C₁₉×#478	2
C₁₉×#477	2
C₁₉×#474	2
C₁₉×#433	2
#3243	19

Subgroups — C19×#3243 #14561100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#3243 #14561100