Subgroups — C₁₉×#3241 #14561098

Order 2432.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 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×#540	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#499	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#490	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#482	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#482	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#481	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#480	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#478	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#478	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#476	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×#127	C₂²	1	1	yes	characteristic
20	C₁₉×#125	—	2	1	no	—
21	C₁₉×#125	C₂²	1	1	yes	characteristic
22	C₁₉×#125	C₂²	1	1	yes	characteristic
23	C₁₉×#125	C₂²	1	1	yes	characteristic
24	C₁₉×#123	—	2	1	no	—
25	C₁₉×#123	—	2	1	no	—
26	C₁₉×C₂²⋊Q₈	—	2	1	no	—
27	C₁₉×C₂²⋊Q₈	—	2	1	no	—
28	C₁₉×#121	—	2	1	no	—
29	C₁₉×#121	—	2	1	no	—
30	C₁₉×#121	C₂²	1	1	yes	characteristic
31	C₁₉×#121	C₂²	1	1	yes	characteristic
32	C₄×D₄×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×#106	C₂²	1	1	yes	characteristic
42	C₁₉×#106	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×#102	C₂²	1	1	yes	characteristic
48	C₁₉×#102	C₂²	1	1	yes	characteristic
49	C₁₉×#102	C₂²	1	1	yes	characteristic
50	C₁₉×#102	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×D₄×C₁₉	—	2	1	no	—
62	C₂×D₄×C₁₉	—	2	1	no	—
63	C₂×D₄×C₁₉	—	2	1	no	—
64	C₂×D₄×C₁₉	—	2	1	no	—
65	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
83	C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
85	C₄⋊C₄×C₁₉	D₄	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	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
97	C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
98	C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
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	—	2	1	no	—
104	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
105	Q₈×C₁₉	—	8	1	no	—
106	Q₈×C₁₉	—	8	1	no	—
107	D₄×C₁₉	—	2	1	no	—
108	D₄×C₁₉	—	2	1	no	—
109	D₄×C₁₉	—	2	1	no	—
110	D₄×C₁₉	—	2	1	no	—
111	D₄×C₁₉	—	8	1	no	—
112	D₄×C₁₉	—	8	1	no	—
113	D₄×C₁₉	—	8	1	no	—
114	D₄×C₁₉	—	8	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	—	2	1	no	—
122	C₂×C₄×C₁₉	—	2	1	no	—
123	C₂×C₄×C₁₉	—	8	1	no	—
124	C₂×C₄×C₁₉	—	8	1	no	—
125	C₂×C₄×C₁₉	—	8	1	no	—
126	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
132	C₈×C₁₉	—	2	1	no	—
133	C₈×C₁₉	—	2	1	no	—
134	C₈×C₁₉	—	2	1	no	—
135	C₈×C₁₉	—	2	1	no	—
136	#3241	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂²×C₁₉	—	2	1	no	—
138	C₂²×C₁₉	—	2	1	no	—
139	C₂²×C₁₉	—	2	1	no	—
140	C₂²×C₁₉	—	4	1	no	—
141	C₂²×C₁₉	—	4	1	no	—
142	C₂²×C₁₉	—	4	1	no	—
143	C₂²×C₁₉	—	4	1	no	—
144	C₂²×C₁₉	—	4	1	no	—
145	C₂²×C₁₉	—	4	1	no	—
146	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
147	C₄×C₁₉	—	2	1	no	—
148	C₄×C₁₉	—	2	1	no	—
149	C₄×C₁₉	—	2	1	no	—
150	C₄×C₁₉	—	2	1	no	—
151	C₄×C₁₉	—	2	1	no	—
152	C₄×C₁₉	—	4	1	no	—
153	C₄×C₁₉	—	4	1	no	—
154	C₄×C₁₉	—	4	1	no	—
155	C₄×C₁₉	—	4	1	no	—
156	C₄×C₁₉	—	4	1	no	—
157	C₄×C₁₉	—	4	1	no	—
158	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
159	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
160	#544	C₂×C₁₉	1	1	yes	characteristic, complemented
161	#540	C₂×C₁₉	1	1	yes	characteristic
162	#501	C₂×C₁₉	1	1	yes	characteristic, complemented
163	#499	C₂×C₁₉	1	1	yes	characteristic, complemented
164	#490	C₂×C₁₉	1	1	yes	characteristic, complemented
165	#486	C₂×C₁₉	1	1	yes	characteristic, complemented
166	#482	C₂×C₁₉	1	1	yes	characteristic, complemented
167	#482	C₂×C₁₉	1	1	yes	characteristic, complemented
168	#481	C₂×C₁₉	1	1	yes	characteristic, complemented
169	#480	C₂×C₁₉	1	1	yes	characteristic, complemented
170	#478	C₂×C₁₉	1	1	yes	characteristic, complemented
171	#478	C₂×C₁₉	1	1	yes	characteristic, complemented
172	#476	C₂×C₁₉	1	1	yes	characteristic, complemented
173	#474	C₂×C₁₉	1	1	yes	characteristic, complemented
174	#433	C₂×C₁₉	1	1	yes	characteristic, complemented
175	C₂×C₁₉	—	4	1	no	—
176	C₂×C₁₉	—	8	1	no	—
177	C₂×C₁₉	—	8	1	no	—
178	C₂×C₁₉	#536	1	1	yes	characteristic
179	C₂×C₁₉	#576	1	1	yes	characteristic
180	C₂×C₁₉	#577	1	1	yes	characteristic
181	C₄⋊Q₈	—	2	1	no	—
182	C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
183	C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
184	#127	C₂²×C₁₉	1	1	yes	characteristic
185	#125	—	2	1	no	—
186	#125	C₂²×C₁₉	1	1	yes	characteristic
187	#125	C₂²×C₁₉	1	1	yes	characteristic
188	#125	C₂²×C₁₉	1	1	yes	characteristic
189	#123	—	2	1	no	—
190	#123	—	2	1	no	—
191	C₂²⋊Q₈	—	2	1	no	—
192	C₂²⋊Q₈	—	2	1	no	—
193	#121	—	2	1	no	—
194	#121	—	2	1	no	—
195	#121	C₂²×C₁₉	1	1	yes	characteristic
196	#121	C₂²×C₁₉	1	1	yes	characteristic
197	C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
198	C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
199	#117	C₂²×C₁₉	1	1	yes	characteristic
200	#117	C₂²×C₁₉	1	1	yes	characteristic
201	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
202	#107	C₂²×C₁₉	1	1	yes	characteristic
203	#107	C₂²×C₁₉	1	1	yes	characteristic
204	#107	C₂²×C₁₉	1	1	yes	characteristic
205	#107	C₂²×C₁₉	1	1	yes	characteristic
206	#106	C₂²×C₁₉	1	1	yes	characteristic
207	#106	C₂²×C₁₉	1	1	yes	characteristic
208	#106	C₂²×C₁₉	1	1	yes	characteristic
209	#106	C₂²×C₁₉	1	1	yes	characteristic
210	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
211	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
212	#102	C₂²×C₁₉	1	1	yes	characteristic
213	#102	C₂²×C₁₉	1	1	yes	characteristic
214	#102	C₂²×C₁₉	1	1	yes	characteristic
215	#102	C₂²×C₁₉	1	1	yes	characteristic
216	#102	C₂²×C₁₉	1	1	yes	characteristic
217	#102	C₂²×C₁₉	1	1	yes	characteristic
218	#102	C₂²×C₁₉	1	1	yes	characteristic
219	#102	C₂²×C₁₉	1	1	yes	characteristic
220	C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
221	C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
222	#97	C₂²×C₁₉	1	1	yes	characteristic
223	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
224	C₁₉	#3241	1	1	yes	characteristic, direct product factor, Sylow
225	C₂×Q₈	—	2	1	no	—
226	C₂×Q₈	—	2	1	no	—
227	C₂×D₄	—	2	1	no	—
228	C₂×D₄	—	2	1	no	—
229	C₂×D₄	—	2	1	no	—
230	C₂×D₄	—	2	1	no	—
231	C₂×D₄	C₂³×C₁₉	1	1	yes	characteristic
232	C₂×D₄	C₂³×C₁₉	1	1	yes	characteristic
233	C₂²×C₄	—	2	1	no	—
234	C₂²×C₄	—	2	1	no	—
235	C₂²×C₄	—	2	1	no	—
236	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
237	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
238	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
239	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
240	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
241	C₄⋊C₄	—	2	1	no	—
242	C₄⋊C₄	—	2	1	no	—
243	C₄⋊C₄	—	2	1	no	—
244	C₄⋊C₄	—	2	1	no	—
245	C₄⋊C₄	—	2	1	no	—
246	C₄⋊C₄	—	2	1	no	—
247	C₄⋊C₄	—	2	1	no	—
248	C₄⋊C₄	—	2	1	no	—
249	C₄⋊C₄	—	2	1	no	—
250	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
251	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
252	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
253	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
254	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
255	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
256	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
257	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
258	C₂²⋊C₄	—	2	1	no	—
259	C₂²⋊C₄	—	2	1	no	—
260	C₂²⋊C₄	—	2	1	no	—
261	C₂²⋊C₄	—	2	1	no	—
262	C₂²⋊C₄	—	2	1	no	—
263	C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
264	C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
265	C₄²	—	2	1	no	—
266	C₄²	C₂³×C₁₉	1	1	yes	characteristic
267	C₄²	C₂³×C₁₉	1	1	yes	characteristic
268	C₂³	—	2	1	no	—
269	C₂³	—	2	1	no	—
270	C₂³	C₂×D₄×C₁₉	1	1	yes	characteristic
271	Q₈	—	8	1	no	—
272	Q₈	—	8	1	no	—
273	D₄	—	2	1	no	—
274	D₄	—	2	1	no	—
275	D₄	—	2	1	no	—
276	D₄	—	2	1	no	—
277	D₄	—	8	1	no	—
278	D₄	—	8	1	no	—
279	D₄	—	8	1	no	—
280	D₄	—	8	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	—	2	1	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	8	1	no	—
290	C₂×C₄	—	8	1	no	—
291	C₂×C₄	—	8	1	no	—
292	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
293	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
294	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
295	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
296	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
297	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
298	C₈	—	2	1	no	—
299	C₈	—	2	1	no	—
300	C₈	—	2	1	no	—
301	C₈	—	2	1	no	—
302	C₂²	—	2	1	no	—
303	C₂²	—	2	1	no	—
304	C₂²	—	2	1	no	—
305	C₂²	—	4	1	no	—
306	C₂²	—	4	1	no	—
307	C₂²	—	4	1	no	—
308	C₂²	—	4	1	no	—
309	C₂²	—	4	1	no	—
310	C₂²	—	4	1	no	—
311	C₂²	C₂²×D₄×C₁₉	1	1	yes	characteristic
312	C₄	—	2	1	no	—
313	C₄	—	2	1	no	—
314	C₄	—	2	1	no	—
315	C₄	—	2	1	no	—
316	C₄	—	2	1	no	—
317	C₄	—	4	1	no	—
318	C₄	—	4	1	no	—
319	C₄	—	4	1	no	—
320	C₄	—	4	1	no	—
321	C₄	—	4	1	no	—
322	C₄	—	4	1	no	—
323	C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
324	C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
325	C₂	—	4	1	no	—
326	C₂	—	8	1	no	—
327	C₂	—	8	1	no	—
328	C₂	C₁₉×#536	1	1	yes	characteristic
329	C₂	C₁₉×#576	1	1	yes	characteristic
330	C₂	C₁₉×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#540	C₂
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×#499	C₂	semidirect
5. C₁₉×#490	C₂	semidirect
6. C₁₉×#486	C₂	semidirect
7. C₁₉×#482	C₂	semidirect
8. C₁₉×#482	C₂	semidirect
9. C₁₉×#481	C₂	semidirect
10. C₁₉×#480	C₂	semidirect
11. C₁₉×#478	C₂	semidirect
12. C₁₉×#478	C₂	semidirect
13. C₁₉×#476	C₂	semidirect
14. C₁₉×#474	C₂	semidirect
15. C₁₉×#433	C₂	semidirect
136. #3241	C₁₉	direct (N × H)
160. #544	C₂×C₁₉	semidirect
162. #501	C₂×C₁₉	semidirect
163. #499	C₂×C₁₉	semidirect
164. #490	C₂×C₁₉	semidirect
165. #486	C₂×C₁₉	semidirect
166. #482	C₂×C₁₉	semidirect
167. #482	C₂×C₁₉	semidirect
168. #481	C₂×C₁₉	semidirect
169. #480	C₂×C₁₉	semidirect
170. #478	C₂×C₁₉	semidirect
171. #478	C₂×C₁₉	semidirect
172. #476	C₂×C₁₉	semidirect
173. #474	C₂×C₁₉	semidirect
174. #433	C₂×C₁₉	semidirect
224. C₁₉	#3241	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×#540	2
C₁₉×#501	2
C₁₉×#499	2
C₁₉×#490	2
C₁₉×#486	2
C₁₉×#482	2
C₁₉×#481	2
C₁₉×#480	2
C₁₉×#478	2
C₁₉×#476	2
C₁₉×#474	2
C₁₉×#433	2
#3241	19

Subgroups — C19×#3241 #14561098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#3241 #14561098