Subgroups — C₁₉×#34187 #18040146

Order 4864.

2250 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2356	C₂	1	8	yes	maximal, complemented
3	C₁₉×#2355	C₂	1	8	yes	maximal, complemented
4	C₁₉×#2313	C₂	1	4	yes	maximal
5	C₁₉×#2310	C₂	1	2	yes	maximal
6	C₁₉×#2285	C₂	1	2	yes	maximal
7	C₁₉×#2283	C₂	1	4	yes	maximal
8	C₁₉×#2274	C₂	1	2	yes	maximal
9	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₉	C₄	1	16	yes	complemented
11	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
12	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
13	C₂×C₁₉×#117	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#391	C₂²	1	16	yes	—
19	C₁₉×#387	C₂²	1	32	yes	—
20	C₁₉×#384	C₂²	1	4	yes	—
21	C₁₉×#383	C₂²	1	8	yes	—
22	C₁₉×#382	C₂²	1	8	yes	—
23	C₁₉×#382	C₂²	1	4	yes	—
24	C₁₉×#381	C₂²	1	8	yes	—
25	C₁₉×#380	C₂²	1	4	yes	—
26	C₁₉×#380	C₂²	1	4	yes	—
27	C₄×C₄⋊C₄×C₁₉	C₂²	1	16	yes	—
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
29	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
31	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
32	C₁₉×#376	C₂²	1	8	yes	—
33	C₂²×Q₈×C₁₉	—	2	8	no	—
34	C₂²×Q₈×C₁₉	C₂×C₄	1	8	yes	—
35	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
36	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₄×Q₈×C₁₉	C₂×C₄	1	32	yes	—
42	C₄×Q₈×C₁₉	C₂×C₄	1	32	yes	—
43	C₁₉×#117	—	2	16	no	—
44	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	16	yes	—
45	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
46	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
47	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
48	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
49	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
50	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
51	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
52	C₂×C₄²×C₁₉	C₂×C₄	1	16	yes	—
53	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	—
54	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
55	C₂×C₄²×C₁₉	C₂³	1	16	yes	—
56	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
57	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
58	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
59	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
60	C₁₉×#95	C₂³	1	8	yes	—
61	C₁₉×#95	C₂³	1	16	yes	—
62	C₁₉×#95	C₂³	1	16	yes	—
63	C₁₉×#95	C₂³	1	8	yes	—
64	C₁₉×#95	C₂³	1	16	yes	—
65	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
66	C₂×Q₈×C₁₉	—	2	32	no	—
67	C₂×Q₈×C₁₉	—	2	8	no	—
68	C₂×Q₈×C₁₉	—	2	8	no	—
69	C₂×Q₈×C₁₉	C₂²×C₄	1	16	yes	—
70	C₂²×C₄×C₁₉	—	2	8	no	—
71	C₂²×C₄×C₁₉	—	2	4	no	—
72	C₂²×C₄×C₁₉	—	4	4	no	—
73	C₂²×C₄×C₁₉	—	4	2	no	—
74	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
75	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
76	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
77	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
78	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₁₉	#41	1	8	yes	—
80	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
81	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
82	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
84	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
85	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
86	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
87	C₄⋊C₄×C₁₉	—	2	16	no	—
88	C₄⋊C₄×C₁₉	—	2	16	no	—
89	C₄⋊C₄×C₁₉	—	4	8	no	—
90	C₄⋊C₄×C₁₉	C₂²×C₄	1	32	yes	—
91	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
92	C₂²⋊C₄×C₁₉	—	2	16	no	—
93	C₄²×C₁₉	—	2	16	no	—
94	C₄²×C₁₉	—	4	16	no	—
95	C₄²×C₁₉	C₂²×C₄	1	16	yes	—
96	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
97	C₄²×C₁₉	C₂²×C₄	1	16	yes	—
98	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
99	#34187	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂³×C₁₉	—	2	2	no	—
101	C₂³×C₁₉	—	2	2	no	—
102	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
103	C₂³×C₁₉	C₂×#41	1	4	yes	—
104	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
105	Q₈×C₁₉	—	2	32	no	—
106	C₂×C₄×C₁₉	—	2	16	no	—
107	C₂×C₄×C₁₉	—	2	8	no	—
108	C₂×C₄×C₁₉	—	2	2	no	—
109	C₂×C₄×C₁₉	—	2	8	no	—
110	C₂×C₄×C₁₉	—	2	4	no	—
111	C₂×C₄×C₁₉	—	2	8	no	—
112	C₂×C₄×C₁₉	—	2	16	no	—
113	C₂×C₄×C₁₉	—	2	16	no	—
114	C₂×C₄×C₁₉	—	2	16	no	—
115	C₂×C₄×C₁₉	—	4	8	no	—
116	C₂×C₄×C₁₉	—	4	4	no	—
117	C₂×C₄×C₁₉	#117	1	16	yes	—
118	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
119	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
120	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
121	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
122	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
123	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
124	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
125	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
126	C₂×C₄×C₁₉	2₋¹⁺⁴	1	4	yes	—
127	C₂²×C₄×Q₈	C₂×C₁₉	1	1	yes	characteristic
128	#2356	C₂×C₁₉	1	8	yes	complemented
129	#2355	C₂×C₁₉	1	8	yes	complemented
130	#2313	C₂×C₁₉	1	4	yes	—
131	#2310	C₂×C₁₉	1	2	yes	—
132	#2285	C₂×C₁₉	1	2	yes	—
133	#2283	C₂×C₁₉	1	4	yes	—
134	#2274	C₂×C₁₉	1	2	yes	—
135	C₂²×C₁₉	—	2	2	no	—
136	C₂²×C₁₉	—	2	2	no	—
137	C₂²×C₁₉	—	2	8	no	—
138	C₂²×C₁₉	C₂×#117	1	4	yes	—
139	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
140	C₂²×C₁₉	C₂²×#41	1	2	yes	—
141	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
142	C₂²×C₁₉	#585	1	2	yes	—
143	C₄×C₁₉	—	2	8	no	—
144	C₄×C₁₉	—	2	2	no	—
145	C₄×C₁₉	—	2	8	no	—
146	C₄×C₁₉	—	2	4	no	—
147	C₄×C₁₉	—	4	16	no	—
148	C₄×C₁₉	C₂×#117	1	8	yes	—
149	C₄×C₁₉	#519	1	4	yes	—
150	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
151	C₂×C₄×Q₈	C₄×C₁₉	1	16	yes	complemented
152	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
153	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
154	C₂×#117	C₂²×C₁₉	1	4	yes	—
155	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
156	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
157	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
158	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
159	#391	C₂²×C₁₉	1	16	yes	—
160	#387	C₂²×C₁₉	1	32	yes	—
161	#384	C₂²×C₁₉	1	4	yes	—
162	#383	C₂²×C₁₉	1	8	yes	—
163	#382	C₂²×C₁₉	1	8	yes	—
164	#382	C₂²×C₁₉	1	4	yes	—
165	#381	C₂²×C₁₉	1	8	yes	—
166	#380	C₂²×C₁₉	1	4	yes	—
167	#380	C₂²×C₁₉	1	4	yes	—
168	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
169	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
170	C₄×C₄⋊C₄	C₂²×C₁₉	1	16	yes	—
171	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
172	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
173	#376	C₂²×C₁₉	1	8	yes	—
174	C₂×C₁₉	—	2	4	no	—
175	C₂×C₁₉	C₂²×#117	1	1	yes	characteristic
176	C₂×C₁₉	C₂×#519	1	1	yes	characteristic
177	C₂×C₁₉	#3428	1	1	yes	characteristic
178	C₂×C₁₉	#3507	1	4	yes	—
179	C₂²×Q₈	—	2	8	no	—
180	C₂²×Q₈	C₂×C₄×C₁₉	1	8	yes	—
181	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
182	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
183	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
184	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
185	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
186	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
187	C₄×Q₈	C₂×C₄×C₁₉	1	32	yes	—
188	C₄×Q₈	C₂×C₄×C₁₉	1	32	yes	—
189	#117	—	2	16	no	—
190	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	16	yes	—
191	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
192	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
193	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
194	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
195	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
196	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
197	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
198	C₂×C₄²	C₂×C₄×C₁₉	1	16	yes	—
199	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	—
200	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
201	C₂×C₄²	C₂³×C₁₉	1	16	yes	—
202	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
203	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
204	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
205	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
206	#95	C₂³×C₁₉	1	8	yes	—
207	#95	C₂³×C₁₉	1	16	yes	—
208	#95	C₂³×C₁₉	1	16	yes	—
209	#95	C₂³×C₁₉	1	8	yes	—
210	#95	C₂³×C₁₉	1	16	yes	—
211	C₁₉	#34187	1	1	yes	characteristic, direct product factor, Sylow
212	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
213	C₂×Q₈	—	2	32	no	—
214	C₂×Q₈	—	2	8	no	—
215	C₂×Q₈	—	2	8	no	—
216	C₂×Q₈	C₂²×C₄×C₁₉	1	16	yes	—
217	C₂²×C₄	—	2	8	no	—
218	C₂²×C₄	—	2	4	no	—
219	C₂²×C₄	—	4	4	no	—
220	C₂²×C₄	—	4	2	no	—
221	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
222	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
223	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
224	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
225	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
226	C₂²×C₄	#41×C₁₉	1	8	yes	—
227	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
228	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
229	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
230	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
231	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
232	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
233	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
234	C₄⋊C₄	—	2	16	no	—
235	C₄⋊C₄	—	2	16	no	—
236	C₄⋊C₄	—	4	8	no	—
237	C₄⋊C₄	C₂²×C₄×C₁₉	1	32	yes	—
238	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
239	C₂²⋊C₄	—	2	16	no	—
240	C₄²	—	2	16	no	—
241	C₄²	—	4	16	no	—
242	C₄²	C₂²×C₄×C₁₉	1	16	yes	—
243	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
244	C₄²	C₂²×C₄×C₁₉	1	16	yes	—
245	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
246	C₂³	—	2	2	no	—
247	C₂³	—	2	2	no	—
248	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
249	C₂³	C₂×#41×C₁₉	1	4	yes	—
250	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
251	Q₈	—	2	32	no	—
252	C₂×C₄	—	2	16	no	—
253	C₂×C₄	—	2	8	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	8	no	—
256	C₂×C₄	—	2	4	no	—
257	C₂×C₄	—	2	8	no	—
258	C₂×C₄	—	2	16	no	—
259	C₂×C₄	—	2	16	no	—
260	C₂×C₄	—	2	16	no	—
261	C₂×C₄	—	4	8	no	—
262	C₂×C₄	—	4	4	no	—
263	C₂×C₄	C₁₉×#117	1	16	yes	—
264	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
265	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
266	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
267	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
268	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
269	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
270	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
271	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
272	C₂×C₄	C₁₉×2₋¹⁺⁴	1	4	yes	—
273	C₂²	—	2	2	no	—
274	C₂²	—	2	2	no	—
275	C₂²	—	2	8	no	—
276	C₂²	C₂×C₁₉×#117	1	4	yes	—
277	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
278	C₂²	C₂²×#41×C₁₉	1	2	yes	—
279	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
280	C₂²	C₁₉×#585	1	2	yes	—
281	C₄	—	2	2	no	—
282	C₄	—	2	8	no	—
283	C₄	—	2	4	no	—
284	C₄	—	2	8	no	—
285	C₄	—	4	16	no	—
286	C₄	C₂×C₁₉×#117	1	8	yes	—
287	C₄	C₁₉×#519	1	4	yes	—
288	C₂	—	2	4	no	—
289	C₂	C₂²×C₁₉×#117	1	1	yes	characteristic
290	C₂	C₂×C₁₉×#519	1	1	yes	characteristic
291	C₂	C₁₉×#3428	1	1	yes	characteristic
292	C₂	C₁₉×#3507	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂⁴×C₁₉	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2356	C₂	semidirect
3. C₁₉×#2355	C₂	semidirect
10. C₂×C₄×Q₈×C₁₉	C₄	semidirect
99. #34187	C₁₉	direct (N × H)
128. #2356	C₂×C₁₉	semidirect
129. #2355	C₂×C₁₉	semidirect
151. C₂×C₄×Q₈	C₄×C₁₉	semidirect
211. C₁₉	#34187	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₁₉	2
C₁₉×#2356	2
C₁₉×#2355	2
C₁₉×#2313	2
C₁₉×#2310	2
C₁₉×#2285	2
C₁₉×#2283	2
C₁₉×#2274	2
#34187	19

Subgroups — C19×#34187 #18040146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34187 #18040146