Subgroups — C₁₉×#60147 #18066106

Order 4864.

2742 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#568	C₂	1	2	yes	maximal, complemented
2	D₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2935	C₂	1	3	yes	maximal, complemented
4	D₄×M₁₆×C₁₉	C₂	1	3	yes	maximal, complemented
5	C₁₉×#2933	C₂	1	6	yes	maximal, complemented
6	C₁₉×#2931	C₂	1	3	yes	maximal, complemented
7	C₁₉×#2930	C₂	1	6	yes	maximal, complemented
8	C₂×C₁₉×#436	C₂	1	3	yes	maximal, complemented
9	C₁₉×#2906	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2880	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₉	C₂²	1	2	yes	—
13	C₁₉×#568	—	2	16	no	—
14	C₂×C₁₉×#131	C₂²	1	2	yes	—
15	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#131	C₂²	1	6	yes	complemented
18	C₂×C₁₉×#131	C₂²	1	6	yes	complemented
19	C₂²×M₁₆×C₁₉	C₂²	1	6	yes	complemented
20	C₂²×M₁₆×C₁₉	C₂²	1	6	yes	complemented
21	C₁₉×#550	C₄	1	1	yes	characteristic
22	D₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
23	C₁₉×#548	C₄	1	2	yes	—
24	C₁₉×#547	C₄	1	3	yes	—
25	C₁₉×#546	C₄	1	6	yes	—
26	D₄²×C₁₉	C₄	1	3	yes	—
27	C₁₉×#532	C₂²	1	3	yes	—
28	C₁₉×#525	C₂²	1	6	yes	—
29	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
31	C₁₉×#436	C₂²	1	1	yes	characteristic
32	C₁₉×#436	C₂²	1	3	yes	—
33	C₁₉×#436	C₂²	1	6	yes	complemented
34	C₁₉×#436	C₂²	1	3	yes	complemented
35	C₁₉×#436	C₂²	1	6	yes	complemented
36	C₁₉×#436	C₂²	1	3	yes	complemented
37	C₁₉×#436	C₂²	1	6	yes	complemented
38	C₁₉×#435	C₂²	1	12	yes	complemented
39	C₁₉×#435	C₂²	1	12	yes	complemented
40	C₈×D₄×C₁₉	C₂²	1	6	yes	complemented
41	C₈×D₄×C₁₉	C₂²	1	6	yes	complemented
42	C₁₉×#424	C₂²	1	6	yes	complemented
43	C₁₉×#423	C₂²	1	3	yes	complemented
44	C₂×C₁₉×C₄⋊C₈	C₂²	1	3	yes	complemented
45	C₁₉×#408	C₂²	1	6	yes	complemented
46	C₁₉×#408	C₂²	1	6	yes	complemented
47	C₁₉×#407	C₂²	1	6	yes	complemented
48	C₂×C₁₉×C₂²⋊C₈	C₂²	1	6	yes	complemented
49	C₁₉×#405	C₂²	1	3	yes	complemented
50	C₁₉×#405	C₂²	1	3	yes	complemented
51	C₄×M₁₆×C₁₉	C₂²	1	3	yes	complemented
52	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	complemented
53	C₂×#41×C₁₉	—	2	8	no	—
54	C₂×#41×C₁₉	—	2	8	no	—
55	C₂×#41×C₁₉	C₂×C₄	1	6	yes	—
56	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
57	C₂×#41×C₁₉	C₂³	1	6	yes	—
58	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
60	C₂²×D₄×C₁₉	C₂×C₄	1	6	yes	—
61	C₂²×D₄×C₁₉	C₂×C₄	1	3	yes	—
62	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
63	C₁₉×#131	—	2	8	no	—
64	C₁₉×#131	—	2	4	no	—
65	C₁₉×#131	—	2	24	no	—
66	C₁₉×#131	—	2	24	no	—
67	C₁₉×#131	D₄	1	8	yes	complemented
68	C₂×M₁₆×C₁₉	—	2	24	no	—
69	C₂×M₁₆×C₁₉	—	2	24	no	—
70	C₂×M₁₆×C₁₉	C₂³	1	3	yes	—
71	C₂×M₁₆×C₁₉	C₂³	1	6	yes	—
72	C₂×M₁₆×C₁₉	C₂³	1	6	yes	—
73	C₂×M₁₆×C₁₉	C₂³	1	6	yes	—
74	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
75	C₂×M₁₆×C₁₉	C₂³	1	6	yes	—
76	C₂×M₁₆×C₁₉	C₂³	1	3	yes	—
77	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
78	C₂²×C₈×C₁₉	C₂³	1	6	yes	—
79	C₂²×C₈×C₁₉	C₂³	1	12	yes	—
80	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
81	C₁₉×C₄⋊Q₈	C₂×C₄	1	3	yes	—
82	C₁₉×#127	C₂×C₄	1	3	yes	—
83	C₁₉×#124	C₂×C₄	1	6	yes	—
84	C₁₉×#123	C₂×C₄	1	12	yes	—
85	C₁₉×C₂²⋊Q₈	C₂×C₄	1	6	yes	—
86	C₁₉×C₂²⋊Q₈	C₂×C₄	1	6	yes	—
87	C₁₉×#121	C₂×C₄	1	6	yes	—
88	C₁₉×#121	C₂×C₄	1	6	yes	—
89	C₁₉×#121	C₂×C₄	1	6	yes	—
90	C₁₉×#121	C₂×C₄	1	6	yes	—
91	C₁₉×#120	C₂×C₄	1	12	yes	—
92	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
93	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
94	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
95	C₄×D₄×C₁₉	C₂×C₄	1	6	yes	—
96	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
97	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
98	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
99	C₄×D₄×C₁₉	C₂³	1	3	yes	—
100	C₄×D₄×C₁₉	C₂³	1	6	yes	—
101	C₄×D₄×C₁₉	C₂³	1	6	yes	—
102	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₁₉×#117	C₂³	1	3	yes	—
104	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	3	yes	—
105	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	6	yes	—
106	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
107	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
108	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
109	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
110	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
111	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
112	C₁₉×C₂²⋊C₈	C₂³	1	6	yes	—
113	C₁₉×C₂²⋊C₈	C₂³	1	6	yes	—
114	C₁₉×C₂²⋊C₈	C₂³	1	6	yes	—
115	C₁₉×C₂²⋊C₈	C₂³	1	12	yes	—
116	C₁₉×#97	C₂³	1	6	yes	—
117	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
118	C₄×C₈×C₁₉	C₂³	1	3	yes	—
119	C₄×C₈×C₁₉	C₂³	1	3	yes	—
120	C₄×C₈×C₁₉	C₂³	1	3	yes	—
121	C₂⁴×C₁₉	C₂²×C₄	1	6	yes	—
122	#41×C₁₉	—	2	8	no	—
123	#41×C₁₉	—	2	24	no	—
124	#41×C₁₉	—	2	12	no	—
125	#41×C₁₉	—	2	12	no	—
126	#41×C₁₉	C₂×D₄	1	4	yes	—
127	#41×C₁₉	#41	1	4	yes	—
128	C₂×Q₈×C₁₉	—	2	8	no	—
129	C₂×Q₈×C₁₉	C₂²×C₄	1	6	yes	—
130	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
131	C₂×D₄×C₁₉	—	2	24	no	—
132	C₂×D₄×C₁₉	—	4	6	no	—
133	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
134	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
135	C₂×D₄×C₁₉	C₂²×C₄	1	12	yes	—
136	C₂×D₄×C₁₉	C₂²×C₄	1	6	yes	—
137	C₂×D₄×C₁₉	C₂²×C₄	1	6	yes	—
138	C₂×D₄×C₁₉	C₂²×C₄	1	6	yes	—
139	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
140	C₂²×C₄×C₁₉	—	2	12	no	—
141	C₂²×C₄×C₁₉	—	2	12	no	—
142	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
143	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
144	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
145	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
146	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
147	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
148	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
150	M₁₆×C₁₉	—	2	12	no	—
151	M₁₆×C₁₉	—	2	6	no	—
152	M₁₆×C₁₉	—	2	12	no	—
153	M₁₆×C₁₉	—	2	4	no	—
154	M₁₆×C₁₉	—	2	12	no	—
155	M₁₆×C₁₉	—	2	12	no	—
156	M₁₆×C₁₉	C₂×D₄	1	12	yes	complemented
157	C₂×C₈×C₁₉	—	2	12	no	—
158	C₂×C₈×C₁₉	—	2	6	no	—
159	C₂×C₈×C₁₉	—	2	24	no	—
160	C₂×C₈×C₁₉	C₂×D₄	1	12	yes	complemented
161	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
162	C₂×C₈×C₁₉	C₂⁴	1	6	yes	—
163	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
164	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
165	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
166	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
167	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
168	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
169	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
170	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
171	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
172	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
173	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
174	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
175	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
176	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
177	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
178	C₂²⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
179	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
180	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
181	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
182	C₄²×C₁₉	C₂⁴	1	3	yes	—
183	#60147	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂³×C₁₉	—	2	12	no	—
185	C₂³×C₁₉	—	4	6	no	—
186	C₂³×C₁₉	—	4	6	no	—
187	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
188	C₂³×C₁₉	C₂³×C₄	1	6	yes	—
189	C₂³×C₁₉	C₂³×C₄	1	3	yes	—
190	Q₈×C₁₉	—	2	12	no	—
191	Q₈×C₁₉	C₄×D₄	1	4	yes	—
192	D₄×C₁₉	—	2	24	no	—
193	D₄×C₁₉	—	2	12	no	—
194	D₄×C₁₉	—	2	2	no	—
195	D₄×C₁₉	—	2	6	no	—
196	D₄×C₁₉	—	4	6	no	—
197	D₄×C₁₉	—	4	6	no	—
198	D₄×C₁₉	C₄×D₄	1	12	yes	—
199	C₂×C₄×C₁₉	—	2	12	no	—
200	C₂×C₄×C₁₉	—	2	12	no	—
201	C₂×C₄×C₁₉	—	2	12	no	—
202	C₂×C₄×C₁₉	—	2	6	no	—
203	C₂×C₄×C₁₉	—	2	6	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	6	no	—
207	C₂×C₄×C₁₉	—	4	3	no	—
208	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
210	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
211	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
212	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
213	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
214	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂²×D₄	1	6	yes	—
216	C₂×C₄×C₁₉	C₂×#41	1	6	yes	—
217	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
218	C₈×C₁₉	—	2	2	no	—
219	C₈×C₁₉	—	2	6	no	—
220	C₈×C₁₉	—	2	1	no	—
221	C₈×C₁₉	—	2	3	no	—
222	C₈×C₁₉	C₂²×D₄	1	6	yes	—
223	C₈×C₁₉	C₂²×D₄	1	2	yes	—
224	C₂×#568	C₂×C₁₉	1	2	yes	complemented
225	D₄×#41	C₂×C₁₉	1	1	yes	characteristic
226	#2935	C₂×C₁₉	1	3	yes	complemented
227	D₄×M₁₆	C₂×C₁₉	1	3	yes	complemented
228	#2933	C₂×C₁₉	1	6	yes	complemented
229	#2931	C₂×C₁₉	1	3	yes	complemented
230	#2930	C₂×C₁₉	1	6	yes	complemented
231	C₂×#436	C₂×C₁₉	1	3	yes	complemented
232	#2906	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#2880	C₂×C₁₉	1	2	yes	complemented
234	C₄×#131	C₂×C₁₉	1	1	yes	characteristic, complemented
235	C₂²×C₁₉	—	2	3	no	—
236	C₂²×C₁₉	—	2	3	no	—
237	C₂²×C₁₉	—	2	2	no	—
238	C₂²×C₁₉	—	2	6	no	—
239	C₂²×C₁₉	—	2	2	no	—
240	C₂²×C₁₉	—	2	6	no	—
241	C₂²×C₁₉	—	2	6	no	—
242	C₂²×C₁₉	—	2	2	no	—
243	C₂²×C₁₉	—	8	12	no	—
244	C₂²×C₁₉	C₂×C₄×D₄	1	6	yes	—
245	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
246	C₄×C₁₉	—	2	2	no	—
247	C₄×C₁₉	—	2	6	no	—
248	C₄×C₁₉	—	2	3	no	—
249	C₄×C₁₉	—	2	1	no	—
250	C₄×C₁₉	—	2	3	no	—
251	C₄×C₁₉	C₂×C₄×D₄	1	6	yes	—
252	C₄×C₁₉	#568	1	2	yes	complemented
253	C₄×C₁₉	C₂³×D₄	1	1	yes	characteristic
254	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
255	C₂²×#41	C₂²×C₁₉	1	2	yes	—
256	#568	—	2	16	no	—
257	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
258	C₂×#131	C₂²×C₁₉	1	2	yes	—
259	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
260	C₂×#131	C₂²×C₁₉	1	6	yes	complemented
261	C₂×#131	C₂²×C₁₉	1	6	yes	complemented
262	C₂²×M₁₆	C₂²×C₁₉	1	6	yes	complemented
263	C₂²×M₁₆	C₂²×C₁₉	1	6	yes	complemented
264	#550	C₄×C₁₉	1	1	yes	characteristic
265	D₄×Q₈	C₄×C₁₉	1	1	yes	characteristic
266	#548	C₄×C₁₉	1	2	yes	—
267	#547	C₄×C₁₉	1	3	yes	—
268	#546	C₄×C₁₉	1	6	yes	—
269	D₄²	C₄×C₁₉	1	3	yes	—
270	#532	C₂²×C₁₉	1	3	yes	—
271	#525	C₂²×C₁₉	1	6	yes	—
272	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
273	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
274	#436	C₂²×C₁₉	1	1	yes	characteristic
275	#436	C₂²×C₁₉	1	3	yes	—
276	#436	C₂²×C₁₉	1	6	yes	complemented
277	#436	C₂²×C₁₉	1	3	yes	complemented
278	#436	C₂²×C₁₉	1	6	yes	complemented
279	#436	C₂²×C₁₉	1	3	yes	complemented
280	#436	C₂²×C₁₉	1	6	yes	complemented
281	#435	C₂²×C₁₉	1	12	yes	complemented
282	#435	C₂²×C₁₉	1	12	yes	complemented
283	C₈×D₄	C₂²×C₁₉	1	6	yes	complemented
284	C₈×D₄	C₂²×C₁₉	1	6	yes	complemented
285	#424	C₂²×C₁₉	1	6	yes	complemented
286	#423	C₂²×C₁₉	1	3	yes	complemented
287	C₂×C₄⋊C₈	C₂²×C₁₉	1	3	yes	complemented
288	#408	C₂²×C₁₉	1	6	yes	complemented
289	#408	C₂²×C₁₉	1	6	yes	complemented
290	#407	C₂²×C₁₉	1	6	yes	complemented
291	C₂×C₂²⋊C₈	C₂²×C₁₉	1	6	yes	complemented
292	#405	C₂²×C₁₉	1	3	yes	complemented
293	#405	C₂²×C₁₉	1	3	yes	complemented
294	C₄×M₁₆	C₂²×C₁₉	1	3	yes	complemented
295	C₂×C₄×C₈	C₂²×C₁₉	1	3	yes	complemented
296	C₂×C₁₉	—	2	6	no	—
297	C₂×C₁₉	—	4	6	no	—
298	C₂×C₁₉	—	4	2	no	—
299	C₂×C₁₉	C₂²×C₄×D₄	1	1	yes	characteristic
300	C₂×C₁₉	C₂×#568	1	1	yes	characteristic
301	C₂×C₁₉	#3573	1	1	yes	characteristic
302	C₂×#41	—	2	8	no	—
303	C₂×#41	—	2	8	no	—
304	C₂×#41	C₂×C₄×C₁₉	1	6	yes	—
305	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
306	C₂×#41	C₂³×C₁₉	1	6	yes	—
307	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
308	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
309	C₂²×D₄	C₂×C₄×C₁₉	1	6	yes	—
310	C₂²×D₄	C₂×C₄×C₁₉	1	3	yes	—
311	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
312	#131	—	2	8	no	—
313	#131	—	2	4	no	—
314	#131	—	2	24	no	—
315	#131	—	2	24	no	—
316	#131	D₄×C₁₉	1	8	yes	complemented
317	C₂×M₁₆	—	2	24	no	—
318	C₂×M₁₆	—	2	24	no	—
319	C₂×M₁₆	C₂³×C₁₉	1	6	yes	—
320	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
321	C₂×M₁₆	C₂³×C₁₉	1	6	yes	—
322	C₂×M₁₆	C₂³×C₁₉	1	6	yes	—
323	C₂×M₁₆	C₂³×C₁₉	1	6	yes	—
324	C₂×M₁₆	C₂³×C₁₉	1	3	yes	—
325	C₂×M₁₆	C₂³×C₁₉	1	3	yes	—
326	C₂²×C₈	C₂³×C₁₉	1	6	yes	—
327	C₂²×C₈	C₂³×C₁₉	1	12	yes	—
328	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
329	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
330	C₄⋊Q₈	C₂×C₄×C₁₉	1	3	yes	—
331	#127	C₂×C₄×C₁₉	1	3	yes	—
332	#124	C₂×C₄×C₁₉	1	6	yes	—
333	#123	C₂×C₄×C₁₉	1	12	yes	—
334	C₂²⋊Q₈	C₂×C₄×C₁₉	1	6	yes	—
335	C₂²⋊Q₈	C₂×C₄×C₁₉	1	6	yes	—
336	#121	C₂×C₄×C₁₉	1	6	yes	—
337	#121	C₂×C₄×C₁₉	1	6	yes	—
338	#121	C₂×C₄×C₁₉	1	6	yes	—
339	#121	C₂×C₄×C₁₉	1	6	yes	—
340	#120	C₂×C₄×C₁₉	1	12	yes	—
341	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
342	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
343	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
344	C₄×D₄	C₂×C₄×C₁₉	1	6	yes	—
345	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
346	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
347	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
348	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
349	C₄×D₄	C₂³×C₁₉	1	6	yes	—
350	C₄×D₄	C₂³×C₁₉	1	3	yes	—
351	C₄×D₄	C₂³×C₁₉	1	6	yes	—
352	#117	C₂³×C₁₉	1	3	yes	—
353	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	3	yes	—
354	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	6	yes	—
355	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
356	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
357	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
358	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
359	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
360	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
361	C₂²⋊C₈	C₂³×C₁₉	1	6	yes	—
362	C₂²⋊C₈	C₂³×C₁₉	1	6	yes	—
363	C₂²⋊C₈	C₂³×C₁₉	1	6	yes	—
364	C₂²⋊C₈	C₂³×C₁₉	1	12	yes	—
365	#97	C₂³×C₁₉	1	6	yes	—
366	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
367	C₄×C₈	C₂³×C₁₉	1	3	yes	—
368	C₄×C₈	C₂³×C₁₉	1	3	yes	—
369	C₄×C₈	C₂³×C₁₉	1	3	yes	—
370	C₁₉	#60147	1	1	yes	characteristic, direct product factor, Sylow
371	C₂⁴	C₂²×C₄×C₁₉	1	6	yes	—
372	#41	—	2	8	no	—
373	#41	—	2	24	no	—
374	#41	—	2	12	no	—
375	#41	—	2	12	no	—
376	#41	C₂×D₄×C₁₉	1	4	yes	—
377	#41	#41×C₁₉	1	4	yes	—
378	C₂×Q₈	—	2	8	no	—
379	C₂×Q₈	C₂²×C₄×C₁₉	1	6	yes	—
380	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
381	C₂×D₄	—	2	24	no	—
382	C₂×D₄	—	4	6	no	—
383	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
384	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
385	C₂×D₄	C₂²×C₄×C₁₉	1	12	yes	—
386	C₂×D₄	C₂²×C₄×C₁₉	1	6	yes	—
387	C₂×D₄	C₂²×C₄×C₁₉	1	6	yes	—
388	C₂×D₄	C₂²×C₄×C₁₉	1	6	yes	—
389	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
390	C₂²×C₄	—	2	12	no	—
391	C₂²×C₄	—	2	12	no	—
392	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
393	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
394	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
395	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
396	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
397	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
398	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
400	M₁₆	—	2	12	no	—
401	M₁₆	—	2	6	no	—
402	M₁₆	—	2	12	no	—
403	M₁₆	—	2	4	no	—
404	M₁₆	—	2	12	no	—
405	M₁₆	—	2	12	no	—
406	M₁₆	C₂×D₄×C₁₉	1	12	yes	complemented
407	C₂×C₈	—	2	12	no	—
408	C₂×C₈	—	2	6	no	—
409	C₂×C₈	—	2	24	no	—
410	C₂×C₈	C₂×D₄×C₁₉	1	12	yes	complemented
411	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
412	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
413	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
414	C₂×C₈	C₂⁴×C₁₉	1	6	yes	—
415	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
416	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
417	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
418	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
419	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
420	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
421	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
422	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
423	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
424	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
425	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
426	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
427	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
428	C₂²⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
429	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
430	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
431	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
432	C₄²	C₂⁴×C₁₉	1	3	yes	—
433	C₂³	—	2	12	no	—
434	C₂³	—	4	6	no	—
435	C₂³	—	4	6	no	—
436	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
437	C₂³	C₂³×C₄×C₁₉	1	6	yes	—
438	C₂³	C₂³×C₄×C₁₉	1	3	yes	—
439	Q₈	—	2	12	no	—
440	Q₈	C₄×D₄×C₁₉	1	4	yes	—
441	D₄	—	2	24	no	—
442	D₄	—	2	12	no	—
443	D₄	—	2	2	no	—
444	D₄	—	2	6	no	—
445	D₄	—	4	6	no	—
446	D₄	—	4	6	no	—
447	D₄	C₄×D₄×C₁₉	1	12	yes	—
448	C₂×C₄	—	2	12	no	—
449	C₂×C₄	—	2	12	no	—
450	C₂×C₄	—	2	12	no	—
451	C₂×C₄	—	2	6	no	—
452	C₂×C₄	—	2	6	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	6	no	—
456	C₂×C₄	—	4	3	no	—
457	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
458	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
459	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
460	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
461	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
462	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
463	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₁₉	1	6	yes	—
465	C₂×C₄	C₂×#41×C₁₉	1	6	yes	—
466	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	6	no	—
469	C₈	—	2	1	no	—
470	C₈	—	2	3	no	—
471	C₈	C₂²×D₄×C₁₉	1	6	yes	—
472	C₈	C₂²×D₄×C₁₉	1	2	yes	—
473	C₂²	—	2	3	no	—
474	C₂²	—	2	3	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	6	no	—
477	C₂²	—	2	6	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	6	no	—
481	C₂²	—	8	12	no	—
482	C₂²	C₂×C₄×D₄×C₁₉	1	6	yes	—
483	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
484	C₄	—	2	3	no	—
485	C₄	—	2	1	no	—
486	C₄	—	2	3	no	—
487	C₄	—	2	2	no	—
488	C₄	—	2	6	no	—
489	C₄	C₂×C₄×D₄×C₁₉	1	6	yes	—
490	C₄	C₁₉×#568	1	2	yes	complemented
491	C₄	C₂³×D₄×C₁₉	1	1	yes	characteristic
492	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
493	C₂	—	2	6	no	—
494	C₂	—	4	2	no	—
495	C₂	—	4	6	no	—
496	C₂	C₂²×C₄×D₄×C₁₉	1	1	yes	characteristic
497	C₂	C₂×C₁₉×#568	1	1	yes	characteristic
498	C₂	C₁₉×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁴×C₄
prime radical	D₄×#41×C₁₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#568	C₂	semidirect
3. C₁₉×#2935	C₂	semidirect
4. D₄×M₁₆×C₁₉	C₂	semidirect
5. C₁₉×#2933	C₂	semidirect
6. C₁₉×#2931	C₂	semidirect
7. C₁₉×#2930	C₂	semidirect
8. C₂×C₁₉×#436	C₂	semidirect
9. C₁₉×#2906	C₂	semidirect
10. C₁₉×#2880	C₂	semidirect
11. C₄×C₁₉×#131	C₂	semidirect
17. C₂×C₁₉×#131	C₂²	semidirect
18. C₂×C₁₉×#131	C₂²	semidirect
19. C₂²×M₁₆×C₁₉	C₂²	semidirect
20. C₂²×M₁₆×C₁₉	C₂²	semidirect
33. C₁₉×#436	C₂²	semidirect
34. C₁₉×#436	C₂²	semidirect
35. C₁₉×#436	C₂²	semidirect
36. C₁₉×#436	C₂²	semidirect
37. C₁₉×#436	C₂²	semidirect
38. C₁₉×#435	C₂²	semidirect
39. C₁₉×#435	C₂²	semidirect
40. C₈×D₄×C₁₉	C₂²	semidirect
41. C₈×D₄×C₁₉	C₂²	semidirect
42. C₁₉×#424	C₂²	semidirect
43. C₁₉×#423	C₂²	semidirect
44. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
45. C₁₉×#408	C₂²	semidirect
46. C₁₉×#408	C₂²	semidirect
47. C₁₉×#407	C₂²	semidirect
48. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
49. C₁₉×#405	C₂²	semidirect
50. C₁₉×#405	C₂²	semidirect
51. C₄×M₁₆×C₁₉	C₂²	semidirect
52. C₂×C₄×C₈×C₁₉	C₂²	semidirect
67. C₁₉×#131	D₄	semidirect
156. M₁₆×C₁₉	C₂×D₄	semidirect
160. C₂×C₈×C₁₉	C₂×D₄	semidirect
183. #60147	C₁₉	direct (N × H)
224. C₂×#568	C₂×C₁₉	semidirect
226. #2935	C₂×C₁₉	semidirect
227. D₄×M₁₆	C₂×C₁₉	semidirect
228. #2933	C₂×C₁₉	semidirect
229. #2931	C₂×C₁₉	semidirect
230. #2930	C₂×C₁₉	semidirect
231. C₂×#436	C₂×C₁₉	semidirect
232. #2906	C₂×C₁₉	semidirect
233. #2880	C₂×C₁₉	semidirect
234. C₄×#131	C₂×C₁₉	semidirect
252. C₄×C₁₉	#568	semidirect
260. C₂×#131	C₂²×C₁₉	semidirect
261. C₂×#131	C₂²×C₁₉	semidirect
262. C₂²×M₁₆	C₂²×C₁₉	semidirect
263. C₂²×M₁₆	C₂²×C₁₉	semidirect
276. #436	C₂²×C₁₉	semidirect
277. #436	C₂²×C₁₉	semidirect
278. #436	C₂²×C₁₉	semidirect
279. #436	C₂²×C₁₉	semidirect
280. #436	C₂²×C₁₉	semidirect
281. #435	C₂²×C₁₉	semidirect
282. #435	C₂²×C₁₉	semidirect
283. C₈×D₄	C₂²×C₁₉	semidirect
284. C₈×D₄	C₂²×C₁₉	semidirect
285. #424	C₂²×C₁₉	semidirect
286. #423	C₂²×C₁₉	semidirect
287. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
288. #408	C₂²×C₁₉	semidirect
289. #408	C₂²×C₁₉	semidirect
290. #407	C₂²×C₁₉	semidirect
291. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
292. #405	C₂²×C₁₉	semidirect
293. #405	C₂²×C₁₉	semidirect
294. C₄×M₁₆	C₂²×C₁₉	semidirect
295. C₂×C₄×C₈	C₂²×C₁₉	semidirect
316. #131	D₄×C₁₉	semidirect
370. C₁₉	#60147	direct (N × H)
406. M₁₆	C₂×D₄×C₁₉	semidirect
410. C₂×C₈	C₂×D₄×C₁₉	semidirect
490. C₄	C₁₉×#568	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#568	2
D₄×#41×C₁₉	2
C₁₉×#2935	2
D₄×M₁₆×C₁₉	2
C₁₉×#2933	2
C₁₉×#2931	2
C₁₉×#2930	2
C₂×C₁₉×#436	2
C₁₉×#2906	2
C₁₉×#2880	2
C₄×C₁₉×#131	2
#60147	19

Subgroups — C19×#60147 #18066106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60147 #18066106