Subgroups — C₂×C₁₉×#1814 #18026633

Order 4864.

1330 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#131	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#108	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#427	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#421	C₂	1	2	yes	maximal
5	C₁₉×#1814	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#344	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₁₉×#131	—	2	1	no	—
9	C₂×C₁₉×#131	—	2	1	no	—
10	C₂×C₁₉×#131	—	2	2	no	—
11	C₂×C₁₉×#131	—	2	2	no	—
12	C₂×C₁₉×#131	C₄	1	2	yes	complemented
13	C₂×C₁₉×#131	C₄	1	2	yes	complemented
14	C₂×C₁₉×#131	C₄	1	4	yes	complemented
15	C₂×C₁₉×#131	C₂²	1	4	yes	—
16	C₂²×M₁₆×C₁₉	—	2	1	no	—
17	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
18	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₉	—	2	1	no	—
20	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	2	yes	—
22	C₂×C₁₉×#108	—	2	1	no	—
23	C₂×C₁₉×#108	—	2	1	no	—
24	C₂×C₁₉×#108	—	2	2	no	—
25	C₂×C₁₉×#108	C₂²	1	4	yes	complemented
26	C₁₉×#427	—	2	2	no	—
27	C₁₉×#427	C₂²	1	4	yes	complemented
28	C₂×C₁₉×#107	—	2	1	no	—
29	C₂×C₁₉×#106	—	2	1	no	—
30	C₁₉×#421	—	2	4	no	—
31	C₁₉×#421	C₂²	1	8	yes	—
32	C₂×C₁₉×#104	—	2	4	no	—
33	C₁₉×#344	C₂²	1	8	yes	complemented
34	C₂×#41×C₁₉	—	2	1	no	—
35	C₂×#41×C₁₉	—	2	1	no	—
36	C₂×#41×C₁₉	—	2	1	no	—
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
41	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
42	C₂×#41×C₁₉	D₄	1	2	yes	—
43	C₂×#41×C₁₉	D₄	1	2	yes	—
44	C₂×#41×C₁₉	Q₈	1	2	yes	—
45	C₂×#41×C₁₉	C₂³	1	2	yes	—
46	C₂²×Q₈×C₁₉	Q₈	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	Q₈	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	—	2	1	no	—
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₁₉×#131	—	2	4	no	—
52	C₁₉×#131	—	2	4	no	—
53	C₁₉×#131	—	2	4	no	—
54	C₁₉×#131	—	2	4	no	—
55	C₁₉×#131	—	2	4	no	—
56	C₁₉×#131	—	2	4	no	—
57	C₁₉×#131	C₂×C₄	1	8	yes	complemented
58	C₁₉×#131	C₂×C₄	1	8	yes	complemented
59	C₂×M₁₆×C₁₉	—	2	1	no	—
60	C₂×M₁₆×C₁₉	—	2	1	no	—
61	C₂×M₁₆×C₁₉	—	2	1	no	—
62	C₂×M₁₆×C₁₉	—	2	2	no	—
63	C₂×M₁₆×C₁₉	—	2	2	no	—
64	C₂×M₁₆×C₁₉	—	2	2	no	—
65	C₂×M₁₆×C₁₉	—	2	4	no	—
66	C₂×M₁₆×C₁₉	—	2	4	no	—
67	C₂×M₁₆×C₁₉	—	2	2	no	—
68	C₂×M₁₆×C₁₉	—	2	2	no	—
69	C₂×M₁₆×C₁₉	—	2	2	no	—
70	C₂×M₁₆×C₁₉	—	2	2	no	—
71	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
72	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
73	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
74	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
75	C₂²×C₈×C₁₉	—	2	1	no	—
76	C₂²×C₈×C₁₉	—	2	2	no	—
77	C₂²×C₈×C₁₉	—	2	2	no	—
78	C₂²×C₈×C₁₉	—	2	4	no	—
79	C₂²×C₈×C₁₉	—	2	4	no	—
80	C₂²×C₈×C₁₉	—	2	2	no	—
81	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
84	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
86	C₂²×C₈×C₁₉	D₄	1	2	yes	—
87	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
88	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
89	C₂²×C₈×C₁₉	D₄	1	2	yes	—
90	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
91	C₁₉×#117	—	2	2	no	—
92	C₁₉×#117	—	2	2	no	—
93	C₁₉×#117	—	2	2	no	—
94	C₁₉×#117	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
97	C₂×C₄²×C₁₉	—	2	2	no	—
98	C₁₉×#108	—	2	4	no	—
99	C₁₉×#108	—	2	4	no	—
100	C₁₉×#107	—	2	4	no	—
101	C₁₉×#106	—	2	4	no	—
102	C₁₉×#104	—	2	16	no	—
103	C₂⁴×C₁₉	—	2	1	no	—
104	C₂⁴×C₁₉	#41	1	1	yes	characteristic
105	#41×C₁₉	—	2	2	no	—
106	#41×C₁₉	—	2	2	no	—
107	#41×C₁₉	—	2	2	no	—
108	#41×C₁₉	—	2	2	no	—
109	#41×C₁₉	—	2	2	no	—
110	#41×C₁₉	—	2	2	no	—
111	#41×C₁₉	—	2	2	no	—
112	#41×C₁₉	—	2	2	no	—
113	#41×C₁₉	—	2	2	no	—
114	#41×C₁₉	—	2	2	no	—
115	#41×C₁₉	—	2	2	no	—
116	#41×C₁₉	—	2	2	no	—
117	#41×C₁₉	C₄⋊C₄	1	4	yes	—
118	#41×C₁₉	C₄⋊C₄	1	4	yes	—
119	#41×C₁₉	C₂²×C₄	1	4	yes	—
120	#41×C₁₉	C₂×D₄	1	4	yes	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
125	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
126	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
137	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
138	C₂×D₄×C₁₉	C₂×Q₈	1	2	yes	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	4	2	no	—
147	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
161	M₁₆×C₁₉	—	2	2	no	—
162	M₁₆×C₁₉	—	2	2	no	—
163	M₁₆×C₁₉	—	2	2	no	—
164	M₁₆×C₁₉	—	2	8	no	—
165	M₁₆×C₁₉	—	2	8	no	—
166	M₁₆×C₁₉	—	2	4	no	—
167	M₁₆×C₁₉	—	2	4	no	—
168	M₁₆×C₁₉	—	4	2	no	—
169	M₁₆×C₁₉	—	4	2	no	—
170	M₁₆×C₁₉	C₂²×C₄	1	4	yes	—
171	C₂×C₈×C₁₉	—	2	2	no	—
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	2	8	no	—
175	C₂×C₈×C₁₉	—	2	8	no	—
176	C₂×C₈×C₁₉	—	2	4	no	—
177	C₂×C₈×C₁₉	—	4	2	no	—
178	C₂×C₈×C₁₉	—	4	2	no	—
179	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
182	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
185	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
186	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
187	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
188	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
189	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
190	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
191	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
192	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
193	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
194	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
195	C₄⋊C₄×C₁₉	—	2	4	no	—
196	C₄⋊C₄×C₁₉	—	4	2	no	—
197	C₂²⋊C₄×C₁₉	—	2	4	no	—
198	C₂²⋊C₄×C₁₉	—	4	2	no	—
199	C₄²×C₁₉	—	2	4	no	—
200	C₄²×C₁₉	—	4	2	no	—
201	C₂×#1814	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂³×C₁₉	—	2	2	no	—
203	C₂³×C₁₉	—	2	2	no	—
204	C₂³×C₁₉	—	2	2	no	—
205	C₂³×C₁₉	—	4	2	no	—
206	C₂³×C₁₉	—	4	4	no	—
207	C₂³×C₁₉	#117	1	1	yes	characteristic
208	C₂³×C₁₉	#117	1	1	yes	characteristic
209	C₂³×C₁₉	#121	1	1	yes	characteristic
210	C₂³×C₁₉	#121	1	1	yes	characteristic
211	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
212	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
213	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
214	Q₈×C₁₉	—	2	2	no	—
215	Q₈×C₁₉	—	2	2	no	—
216	Q₈×C₁₉	—	2	2	no	—
217	Q₈×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
218	D₄×C₁₉	—	2	4	no	—
219	D₄×C₁₉	—	2	4	no	—
220	D₄×C₁₉	—	2	4	no	—
221	D₄×C₁₉	—	2	4	no	—
222	D₄×C₁₉	—	2	2	no	—
223	D₄×C₁₉	—	2	2	no	—
224	D₄×C₁₉	—	2	2	no	—
225	D₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	4	no	—
230	C₂×C₄×C₁₉	—	2	4	no	—
231	C₂×C₄×C₁₉	—	2	4	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	4	4	no	—
234	C₂×C₄×C₁₉	—	8	4	no	—
235	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
249	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
250	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
263	C₈×C₁₉	—	2	4	no	—
264	C₈×C₁₉	—	4	4	no	—
265	C₈×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
266	C₈×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
267	C₈×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
268	C₈×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
269	C₂²×#131	C₂×C₁₉	1	1	yes	characteristic
270	C₂²×#108	C₂×C₁₉	1	1	yes	characteristic, complemented
271	C₂×#427	C₂×C₁₉	1	1	yes	characteristic, complemented
272	C₂×#421	C₂×C₁₉	1	2	yes	—
273	#1814	C₂×C₁₉	1	8	yes	direct product factor
274	C₂×#344	C₂×C₁₉	1	2	yes	complemented
275	C₂²×C₁₉	—	2	2	no	—
276	C₂²×C₁₉	—	2	2	no	—
277	C₂²×C₁₉	—	2	2	no	—
278	C₂²×C₁₉	—	2	4	no	—
279	C₂²×C₁₉	—	4	1	no	—
280	C₂²×C₁₉	—	4	1	no	—
281	C₂²×C₁₉	—	4	1	no	—
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	4	no	—
284	C₂²×C₁₉	—	4	4	no	—
285	C₂²×C₁₉	—	4	4	no	—
286	C₂²×C₁₉	#380	1	1	yes	characteristic
287	C₂²×C₁₉	#380	1	1	yes	characteristic
288	C₂²×C₁₉	#380	1	1	yes	characteristic
289	C₂²×C₁₉	#380	1	1	yes	characteristic
290	C₂²×C₁₉	C₂×#117	1	1	yes	characteristic
291	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
292	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
293	C₄×C₁₉	—	2	4	no	—
294	C₄×C₁₉	—	8	4	no	—
295	C₄×C₁₉	#380	1	1	yes	characteristic
296	C₄×C₁₉	#380	1	1	yes	characteristic
297	C₄×C₁₉	#380	1	1	yes	characteristic
298	C₄×C₁₉	#380	1	1	yes	characteristic
299	C₄×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
300	C₄×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
301	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
302	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
303	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
304	C₂×#131	—	2	1	no	—
305	C₂×#131	—	2	1	no	—
306	C₂×#131	—	2	2	no	—
307	C₂×#131	—	2	2	no	—
308	C₂×#131	C₄×C₁₉	1	2	yes	complemented
309	C₂×#131	C₄×C₁₉	1	2	yes	complemented
310	C₂×#131	C₄×C₁₉	1	4	yes	complemented
311	C₂×#131	C₂²×C₁₉	1	4	yes	—
312	C₂²×M₁₆	—	2	1	no	—
313	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
314	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
315	C₂³×C₈	—	2	1	no	—
316	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
317	C₂×#117	C₂²×C₁₉	1	2	yes	—
318	C₂×#108	—	2	1	no	—
319	C₂×#108	—	2	1	no	—
320	C₂×#108	—	2	2	no	—
321	C₂×#108	C₂²×C₁₉	1	4	yes	complemented
322	#427	—	2	2	no	—
323	#427	C₂²×C₁₉	1	4	yes	complemented
324	C₂×#107	—	2	1	no	—
325	C₂×#106	—	2	1	no	—
326	#421	—	2	4	no	—
327	#421	C₂²×C₁₉	1	8	yes	—
328	C₂×#104	—	2	4	no	—
329	#344	C₂²×C₁₉	1	8	yes	complemented
330	C₂×C₁₉	—	2	1	no	—
331	C₂×C₁₉	—	2	1	no	—
332	C₂×C₁₉	—	2	1	no	—
333	C₂×C₁₉	—	2	1	no	—
334	C₂×C₁₉	—	2	1	no	—
335	C₂×C₁₉	—	2	1	no	—
336	C₂×C₁₉	—	4	4	no	—
337	C₂×C₁₉	#1814	1	2	yes	direct product factor
338	C₂×C₁₉	C₂×#380	1	1	yes	characteristic
339	C₂×#41	—	2	1	no	—
340	C₂×#41	—	2	1	no	—
341	C₂×#41	—	2	1	no	—
342	C₂×#41	—	2	1	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	—	2	1	no	—
345	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
346	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
347	C₂×#41	D₄×C₁₉	1	2	yes	—
348	C₂×#41	D₄×C₁₉	1	2	yes	—
349	C₂×#41	Q₈×C₁₉	1	2	yes	—
350	C₂×#41	C₂³×C₁₉	1	2	yes	—
351	C₂²×Q₈	Q₈×C₁₉	1	1	yes	characteristic
352	C₂²×D₄	—	2	1	no	—
353	C₂²×D₄	Q₈×C₁₉	1	1	yes	characteristic
354	C₂³×C₄	—	2	1	no	—
355	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
356	#131	—	2	4	no	—
357	#131	—	2	4	no	—
358	#131	—	2	4	no	—
359	#131	—	2	4	no	—
360	#131	—	2	4	no	—
361	#131	—	2	4	no	—
362	#131	C₂×C₄×C₁₉	1	8	yes	complemented
363	#131	C₂×C₄×C₁₉	1	8	yes	complemented
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	2	no	—
368	C₂×M₁₆	—	2	2	no	—
369	C₂×M₁₆	—	2	2	no	—
370	C₂×M₁₆	—	2	4	no	—
371	C₂×M₁₆	—	2	4	no	—
372	C₂×M₁₆	—	2	2	no	—
373	C₂×M₁₆	—	2	2	no	—
374	C₂×M₁₆	—	2	2	no	—
375	C₂×M₁₆	—	2	2	no	—
376	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
377	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
378	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
379	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	2	2	no	—
382	C₂²×C₈	—	2	2	no	—
383	C₂²×C₈	—	2	4	no	—
384	C₂²×C₈	—	2	4	no	—
385	C₂²×C₈	—	2	2	no	—
386	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
387	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
388	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
389	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
390	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
391	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
392	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
393	C₂²×C₈	D₄×C₁₉	1	2	yes	—
394	C₂²×C₈	D₄×C₁₉	1	2	yes	—
395	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
396	#117	—	2	2	no	—
397	#117	—	2	2	no	—
398	#117	—	2	2	no	—
399	#117	C₂³×C₁₉	1	4	yes	—
400	C₂×C₄⋊C₄	—	2	2	no	—
401	C₂×C₂²⋊C₄	—	2	2	no	—
402	C₂×C₄²	—	2	2	no	—
403	#108	—	2	4	no	—
404	#108	—	2	4	no	—
405	#107	—	2	4	no	—
406	#106	—	2	4	no	—
407	#104	—	2	16	no	—
408	C₁₉	C₂×#1814	1	1	yes	characteristic, direct product factor, Sylow
409	C₂⁴	—	2	1	no	—
410	C₂⁴	#41×C₁₉	1	1	yes	characteristic
411	#41	—	2	2	no	—
412	#41	—	2	2	no	—
413	#41	—	2	2	no	—
414	#41	—	2	2	no	—
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	C₄⋊C₄×C₁₉	1	4	yes	—
424	#41	C₄⋊C₄×C₁₉	1	4	yes	—
425	#41	C₂²×C₄×C₁₉	1	4	yes	—
426	#41	C₂×D₄×C₁₉	1	4	yes	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	C₄⋊C₄×C₁₉	1	2	yes	—
431	C₂×Q₈	C₄⋊C₄×C₁₉	1	2	yes	—
432	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	—
443	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	—
444	C₂×D₄	C₂×Q₈×C₁₉	1	2	yes	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	4	2	no	—
453	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
454	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
462	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
463	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
464	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
465	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
466	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
467	M₁₆	—	2	2	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	2	2	no	—
470	M₁₆	—	2	8	no	—
471	M₁₆	—	2	8	no	—
472	M₁₆	—	2	4	no	—
473	M₁₆	—	2	4	no	—
474	M₁₆	—	4	2	no	—
475	M₁₆	—	4	2	no	—
476	M₁₆	C₂²×C₄×C₁₉	1	4	yes	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	8	no	—
481	C₂×C₈	—	2	8	no	—
482	C₂×C₈	—	2	4	no	—
483	C₂×C₈	—	4	2	no	—
484	C₂×C₈	—	4	2	no	—
485	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
486	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
487	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
488	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
489	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
490	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
491	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
492	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
493	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
494	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
495	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
496	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
497	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
498	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
499	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
500	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	4	2	no	—
503	C₂²⋊C₄	—	2	4	no	—
504	C₂²⋊C₄	—	4	2	no	—
505	C₄²	—	2	4	no	—
506	C₄²	—	4	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	4	no	—
512	C₂³	C₁₉×#117	1	1	yes	characteristic
513	C₂³	C₁₉×#117	1	1	yes	characteristic
514	C₂³	C₁₉×#121	1	1	yes	characteristic
515	C₂³	C₁₉×#121	1	1	yes	characteristic
516	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
517	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
518	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
519	Q₈	—	2	2	no	—
520	Q₈	—	2	2	no	—
521	Q₈	—	2	2	no	—
522	Q₈	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
523	D₄	—	2	4	no	—
524	D₄	—	2	4	no	—
525	D₄	—	2	4	no	—
526	D₄	—	2	4	no	—
527	D₄	—	2	2	no	—
528	D₄	—	2	2	no	—
529	D₄	—	2	2	no	—
530	D₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	8	4	no	—
540	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
541	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
542	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
543	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
544	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
545	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
546	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
547	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
548	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
549	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
550	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
551	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
552	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
553	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
554	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
555	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
556	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
557	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
558	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
559	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
560	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
561	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
562	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
563	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
564	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
565	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
566	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
567	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
568	C₈	—	2	4	no	—
569	C₈	—	4	4	no	—
570	C₈	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
571	C₈	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
572	C₈	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
573	C₈	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	4	no	—
585	C₂²	C₁₉×#380	1	1	yes	characteristic
586	C₂²	C₁₉×#380	1	1	yes	characteristic
587	C₂²	C₁₉×#380	1	1	yes	characteristic
588	C₂²	C₁₉×#380	1	1	yes	characteristic
589	C₂²	C₂×C₁₉×#117	1	1	yes	characteristic
590	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
591	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
592	C₄	—	2	4	no	—
593	C₄	—	8	4	no	—
594	C₄	C₁₉×#380	1	1	yes	characteristic
595	C₄	C₁₉×#380	1	1	yes	characteristic
596	C₄	C₁₉×#380	1	1	yes	characteristic
597	C₄	C₁₉×#380	1	1	yes	characteristic
598	C₄	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
599	C₄	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
600	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
601	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
602	C₂	—	2	1	no	—
603	C₂	—	2	1	no	—
604	C₂	—	2	1	no	—
605	C₂	—	2	1	no	—
606	C₂	—	2	1	no	—
607	C₂	—	2	1	no	—
608	C₂	—	4	4	no	—
609	C₂	C₁₉×#1814	1	2	yes	direct product factor
610	C₂	C₂×C₁₉×#380	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#121
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	#380
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#108	C₂	semidirect
3. C₂×C₁₉×#427	C₂	semidirect
5. C₁₉×#1814	C₂	direct (N × H)
6. C₂×C₁₉×#344	C₂	semidirect
12. C₂×C₁₉×#131	C₄	semidirect
13. C₂×C₁₉×#131	C₄	semidirect
14. C₂×C₁₉×#131	C₄	semidirect
25. C₂×C₁₉×#108	C₂²	semidirect
27. C₁₉×#427	C₂²	semidirect
33. C₁₉×#344	C₂²	semidirect
57. C₁₉×#131	C₂×C₄	semidirect
58. C₁₉×#131	C₂×C₄	semidirect
201. C₂×#1814	C₁₉	direct (N × H)
270. C₂²×#108	C₂×C₁₉	semidirect
271. C₂×#427	C₂×C₁₉	semidirect
273. #1814	C₂×C₁₉	direct (N × H)
274. C₂×#344	C₂×C₁₉	semidirect
308. C₂×#131	C₄×C₁₉	semidirect
309. C₂×#131	C₄×C₁₉	semidirect
310. C₂×#131	C₄×C₁₉	semidirect
321. C₂×#108	C₂²×C₁₉	semidirect
323. #427	C₂²×C₁₉	semidirect
329. #344	C₂²×C₁₉	semidirect
337. C₂×C₁₉	#1814	direct (N × H)
362. #131	C₂×C₄×C₁₉	semidirect
363. #131	C₂×C₄×C₁₉	semidirect
408. C₁₉	C₂×#1814	direct (N × H)
609. C₂	C₁₉×#1814	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×C₁₉×#131	2
C₂²×C₁₉×#108	2
C₂×C₁₉×#427	2
C₂×C₁₉×#421	2
C₁₉×#1814	2
C₂×C₁₉×#344	2
C₂×#1814	19

Subgroups — C2×C19×#1814 #18026633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1814 #18026633