Subgroups — C₁₉×#23131 #18029090

Order 4864.

922 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#465	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2363	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2362	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1934	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1933	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1919	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1875	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1735	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₁₉×#465	C₄	1	8	yes	complemented
25	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
35	C₁₉×#391	C₂²	1	1	yes	characteristic
36	C₁₉×#390	—	2	1	no	—
37	C₁₉×#390	C₂²	1	1	yes	characteristic
38	C₁₉×#389	C₂²	1	1	yes	characteristic
39	C₁₉×#389	C₂²	1	1	yes	characteristic
40	C₁₉×#388	—	2	1	no	—
41	C₁₉×#388	—	2	1	no	—
42	C₁₉×#388	—	2	1	no	—
43	C₁₉×#387	—	2	1	no	—
44	C₁₉×#386	—	2	1	no	—
45	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
49	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
50	C₁₉×#340	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	C₂²	1	1	yes	characteristic
57	C₁₉×#340	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₁₉×#336	C₂²	1	1	yes	characteristic
60	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₁₉	—	2	1	no	—
62	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	—	2	1	no	—
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×SD₁₆×C₁₉	—	4	1	no	—
66	C₂×SD₁₆×C₁₉	—	4	1	no	—
67	C₂×SD₁₆×C₁₉	C₂×C₄	1	4	yes	—
68	C₂²×C₈×C₁₉	—	4	1	no	—
69	C₂²×C₈×C₁₉	—	4	1	no	—
70	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	complemented
71	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	complemented
77	C₁₉×#121	—	2	2	no	—
78	C₁₉×#121	C₂×C₄	1	4	yes	—
79	C₄×Q₈×C₁₉	—	2	2	no	—
80	C₄×Q₈×C₁₉	—	4	1	no	—
81	C₄×D₄×C₁₉	—	2	2	no	—
82	C₄×D₄×C₁₉	—	4	1	no	—
83	C₁₉×#117	—	2	2	no	—
84	C₁₉×#117	—	2	2	no	—
85	C₁₉×#117	—	4	1	no	—
86	C₁₉×#117	—	4	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	—	2	1	no	—
109	C₂×C₄²×C₁₉	—	2	1	no	—
110	C₂×C₄²×C₁₉	—	2	1	no	—
111	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
113	C₁₉×#106	C₂×C₄	1	4	yes	complemented
114	C₁₉×#103	—	2	2	no	—
115	C₁₉×#103	—	4	1	no	—
116	C₁₉×#103	C₂×C₄	1	4	yes	complemented
117	C₁₉×#102	—	2	2	no	—
118	C₁₉×#102	—	4	1	no	—
119	C₁₉×#102	C₂×C₄	1	4	yes	—
120	C₁₉×C₂²⋊C₈	—	2	2	no	—
121	C₄×C₈×C₁₉	—	4	1	no	—
122	C₄×C₈×C₁₉	—	4	1	no	—
123	C₁₉×#95	—	2	1	no	—
124	C₁₉×#95	—	2	1	no	—
125	C₁₉×#95	—	2	1	no	—
126	C₁₉×#95	—	2	1	no	—
127	C₁₉×#95	—	2	1	no	—
128	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	D₄	1	1	yes	characteristic
130	C₁₉×#95	D₄	1	1	yes	characteristic
131	C₂⁴×C₁₉	—	2	1	no	—
132	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂×Q₈×C₁₉	—	2	1	no	—
134	C₂×Q₈×C₁₉	—	2	1	no	—
135	C₂×Q₈×C₁₉	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
139	C₂×D₄×C₁₉	—	2	4	no	—
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	—	2	1	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	8	1	no	—
146	C₂×D₄×C₁₉	—	8	1	no	—
147	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	4	2	no	—
160	C₂²×C₄×C₁₉	—	4	2	no	—
161	C₂²×C₄×C₁₉	—	8	1	no	—
162	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	#41	1	2	yes	—
169	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
170	SD₁₆×C₁₉	—	4	4	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
178	C₂×C₈×C₁₉	—	2	1	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	4	4	no	—
182	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
183	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
184	C₄⋊C₄×C₁₉	—	2	4	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	4	2	no	—
194	C₄⋊C₄×C₁₉	—	4	2	no	—
195	C₄⋊C₄×C₁₉	—	8	1	no	—
196	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
197	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
198	C₄⋊C₄×C₁₉	#41	1	2	yes	—
199	C₄⋊C₄×C₁₉	#41	1	2	yes	—
200	C₂²⋊C₄×C₁₉	—	2	4	no	—
201	C₂²⋊C₄×C₁₉	—	2	4	no	—
202	C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	4	2	no	—
205	C₂²⋊C₄×C₁₉	—	4	2	no	—
206	C₂²⋊C₄×C₁₉	—	4	2	no	—
207	C₂²⋊C₄×C₁₉	—	4	2	no	—
208	C₂²⋊C₄×C₁₉	—	8	1	no	—
209	C₄²×C₁₉	—	2	1	no	—
210	C₄²×C₁₉	—	2	1	no	—
211	C₄²×C₁₉	—	2	1	no	—
212	C₄²×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	—	4	2	no	—
214	C₄²×C₁₉	—	4	2	no	—
215	C₄²×C₁₉	—	4	2	no	—
216	C₄²×C₁₉	—	4	2	no	—
217	C₄²×C₁₉	—	8	1	no	—
218	#23131	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	2	1	no	—
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	2	1	no	—
223	C₂³×C₁₉	—	2	1	no	—
224	C₂³×C₁₉	—	2	1	no	—
225	C₂³×C₁₉	—	2	2	no	—
226	C₂³×C₁₉	—	4	1	no	—
227	C₂³×C₁₉	—	4	1	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	—	4	1	no	—
232	C₂³×C₁₉	C₄×D₄	1	2	yes	—
233	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₁₉	—	2	2	no	—
235	Q₈×C₁₉	—	2	2	no	—
236	Q₈×C₁₉	—	4	1	no	—
237	Q₈×C₁₉	—	4	1	no	—
238	D₄×C₁₉	—	2	2	no	—
239	D₄×C₁₉	—	2	2	no	—
240	D₄×C₁₉	—	4	1	no	—
241	D₄×C₁₉	—	4	1	no	—
242	D₄×C₁₉	—	8	4	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	2	2	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	2	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	8	4	no	—
281	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
282	C₂×C₄×C₁₉	#135	1	2	yes	—
283	C₂×C₄×C₁₉	#135	1	2	yes	—
284	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
285	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
289	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
290	C₈×C₁₉	—	2	2	no	—
291	C₈×C₁₉	—	2	2	no	—
292	C₈×C₁₉	—	4	1	no	—
293	C₈×C₁₉	—	4	1	no	—
294	C₂×#465	C₂×C₁₉	1	1	yes	characteristic
295	#2363	C₂×C₁₉	1	1	yes	characteristic
296	#2362	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#1934	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#1933	C₂×C₁₉	1	1	yes	characteristic, complemented
299	#1920	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#1919	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#1880	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1877	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#1875	C₂×C₁₉	1	1	yes	characteristic
304	#1873	C₂×C₁₉	1	1	yes	characteristic, complemented
305	C₄×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
306	C₄×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
307	C₈×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#1735	C₂×C₁₉	1	1	yes	characteristic, complemented
309	C₂²×C₁₉	—	2	2	no	—
310	C₂²×C₁₉	—	2	2	no	—
311	C₂²×C₁₉	—	2	2	no	—
312	C₂²×C₁₉	—	4	1	no	—
313	C₂²×C₁₉	—	4	1	no	—
314	C₂²×C₁₉	—	4	1	no	—
315	C₂²×C₁₉	—	4	1	no	—
316	C₂²×C₁₉	—	4	2	no	—
317	C₂²×C₁₉	—	4	2	no	—
318	C₂²×C₁₉	—	4	2	no	—
319	C₂²×C₁₉	—	8	1	no	—
320	C₂²×C₁₉	—	8	1	no	—
321	C₂²×C₁₉	—	8	1	no	—
322	C₂²×C₁₉	—	8	1	no	—
323	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
324	C₂²×C₁₉	#546	1	1	yes	characteristic
325	C₂²×C₁₉	#546	1	1	yes	characteristic
326	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
327	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
328	C₂²×C₁₉	#577	1	1	yes	characteristic
329	C₂²×C₁₉	#577	1	1	yes	characteristic
330	C₄×C₁₉	—	2	2	no	—
331	C₄×C₁₉	—	2	2	no	—
332	C₄×C₁₉	—	2	2	no	—
333	C₄×C₁₉	—	4	2	no	—
334	C₄×C₁₉	—	4	2	no	—
335	C₄×C₁₉	—	4	2	no	—
336	C₄×C₁₉	—	4	2	no	—
337	C₄×C₁₉	—	4	1	no	—
338	C₄×C₁₉	—	4	2	no	—
339	C₄×C₁₉	—	4	1	no	—
340	C₄×C₁₉	—	8	1	no	—
341	C₄×C₁₉	—	8	1	no	—
342	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
343	C₄×C₁₉	#518	1	1	yes	characteristic
344	C₄×C₁₉	#553	1	1	yes	characteristic
345	C₄×C₁₉	#553	1	1	yes	characteristic
346	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
347	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
348	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
349	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
350	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
351	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
352	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
353	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
354	#465	C₄×C₁₉	1	8	yes	complemented
355	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
361	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
362	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
363	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
364	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
365	#391	C₂²×C₁₉	1	1	yes	characteristic
366	#390	—	2	1	no	—
367	#390	C₂²×C₁₉	1	1	yes	characteristic
368	#389	C₂²×C₁₉	1	1	yes	characteristic
369	#389	C₂²×C₁₉	1	1	yes	characteristic
370	#388	—	2	1	no	—
371	#388	—	2	1	no	—
372	#388	—	2	1	no	—
373	#387	—	2	1	no	—
374	#386	—	2	1	no	—
375	C₄×C₄⋊C₄	—	2	1	no	—
376	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
377	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
378	C₄×C₂²⋊C₄	—	2	1	no	—
379	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
380	#340	C₂²×C₁₉	1	1	yes	characteristic
381	#340	C₂²×C₁₉	1	1	yes	characteristic
382	#340	C₂²×C₁₉	1	1	yes	characteristic
383	#340	C₂²×C₁₉	1	1	yes	characteristic
384	#340	C₂²×C₁₉	1	1	yes	characteristic
385	#340	C₂²×C₁₉	1	1	yes	characteristic
386	#340	C₂²×C₁₉	1	1	yes	characteristic
387	#340	C₂²×C₁₉	1	1	yes	characteristic
388	#336	C₂²×C₁₉	1	1	yes	characteristic
389	#336	C₂²×C₁₉	1	1	yes	characteristic
390	C₂×C₁₉	—	4	2	no	—
391	C₂×C₁₉	—	8	2	no	—
392	C₂×C₁₉	#2364	1	1	yes	characteristic
393	C₂×C₁₉	C₄×#135	1	1	yes	characteristic
394	C₂×C₁₉	#2949	1	1	yes	characteristic
395	C₂×C₁₉	#3296	1	1	yes	characteristic
396	C₂×C₁₉	#3301	1	1	yes	characteristic
397	C₂×C₁₉	#3303	1	1	yes	characteristic
398	C₂×C₁₉	#3304	1	1	yes	characteristic
399	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
400	C₂²×D₄	—	2	1	no	—
401	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
402	C₂³×C₄	—	2	1	no	—
403	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
404	C₂×SD₁₆	—	4	1	no	—
405	C₂×SD₁₆	—	4	1	no	—
406	C₂×SD₁₆	C₂×C₄×C₁₉	1	4	yes	—
407	C₂²×C₈	—	4	1	no	—
408	C₂²×C₈	—	4	1	no	—
409	C₂²×C₈	C₂×C₄×C₁₉	1	4	yes	complemented
410	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
413	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
414	C₂²⋊Q₈	—	2	2	no	—
415	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
416	#121	—	2	2	no	—
417	#121	C₂×C₄×C₁₉	1	4	yes	—
418	C₄×Q₈	—	2	2	no	—
419	C₄×Q₈	—	4	1	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	—	4	1	no	—
422	#117	—	2	2	no	—
423	#117	—	2	2	no	—
424	#117	—	4	1	no	—
425	#117	—	4	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	—	2	1	no	—
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
445	C₂×C₄²	—	2	1	no	—
446	C₂×C₄²	—	2	1	no	—
447	C₂×C₄²	—	2	1	no	—
448	C₂×C₄²	—	2	1	no	—
449	C₂×C₄²	—	2	1	no	—
450	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
451	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
452	#106	C₂×C₄×C₁₉	1	4	yes	complemented
453	#103	—	2	2	no	—
454	#103	—	4	1	no	—
455	#103	C₂×C₄×C₁₉	1	4	yes	complemented
456	#102	—	2	2	no	—
457	#102	—	4	1	no	—
458	#102	C₂×C₄×C₁₉	1	4	yes	—
459	C₂²⋊C₈	—	2	2	no	—
460	C₄×C₈	—	4	1	no	—
461	C₄×C₈	—	4	1	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	D₄×C₁₉	1	1	yes	characteristic
469	#95	D₄×C₁₉	1	1	yes	characteristic
470	C₁₉	#23131	1	1	yes	characteristic, direct product factor, Sylow
471	C₂⁴	—	2	1	no	—
472	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	8	1	no	—
486	C₂×D₄	—	8	1	no	—
487	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	—	4	2	no	—
501	C₂²×C₄	—	8	1	no	—
502	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
503	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
508	C₂²×C₄	#41×C₁₉	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
510	SD₁₆	—	4	4	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	4	4	no	—
522	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
523	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
524	C₄⋊C₄	—	2	4	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	4	2	no	—
534	C₄⋊C₄	—	4	2	no	—
535	C₄⋊C₄	—	8	1	no	—
536	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
537	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
538	C₄⋊C₄	#41×C₁₉	1	2	yes	—
539	C₄⋊C₄	#41×C₁₉	1	2	yes	—
540	C₂²⋊C₄	—	2	4	no	—
541	C₂²⋊C₄	—	2	4	no	—
542	C₂²⋊C₄	—	2	2	no	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	4	2	no	—
545	C₂²⋊C₄	—	4	2	no	—
546	C₂²⋊C₄	—	4	2	no	—
547	C₂²⋊C₄	—	4	2	no	—
548	C₂²⋊C₄	—	8	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	4	2	no	—
554	C₄²	—	4	2	no	—
555	C₄²	—	4	2	no	—
556	C₄²	—	4	2	no	—
557	C₄²	—	8	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	2	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	1	no	—
570	C₂³	—	4	1	no	—
571	C₂³	C₄×D₄×C₁₉	1	2	yes	—
572	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
573	Q₈	—	2	2	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	4	1	no	—
576	Q₈	—	4	1	no	—
577	D₄	—	2	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	1	no	—
581	D₄	—	8	4	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	8	4	no	—
620	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
621	C₂×C₄	C₁₉×#135	1	2	yes	—
622	C₂×C₄	C₁₉×#135	1	2	yes	—
623	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
624	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
625	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
626	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
627	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
628	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
629	C₈	—	2	2	no	—
630	C₈	—	2	2	no	—
631	C₈	—	4	1	no	—
632	C₈	—	4	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	2	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	8	1	no	—
644	C₂²	—	8	1	no	—
645	C₂²	—	8	1	no	—
646	C₂²	—	8	1	no	—
647	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
648	C₂²	C₁₉×#546	1	1	yes	characteristic
649	C₂²	C₁₉×#546	1	1	yes	characteristic
650	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
651	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
652	C₂²	C₁₉×#577	1	1	yes	characteristic
653	C₂²	C₁₉×#577	1	1	yes	characteristic
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	2	no	—
664	C₄	—	8	1	no	—
665	C₄	—	8	1	no	—
666	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
667	C₄	C₁₉×#518	1	1	yes	characteristic
668	C₄	C₁₉×#553	1	1	yes	characteristic
669	C₄	C₁₉×#553	1	1	yes	characteristic
670	C₂	—	4	2	no	—
671	C₂	—	8	2	no	—
672	C₂	C₁₉×#2364	1	1	yes	characteristic
673	C₂	C₄×C₁₉×#135	1	1	yes	characteristic
674	C₂	C₁₉×#2949	1	1	yes	characteristic
675	C₂	C₁₉×#3296	1	1	yes	characteristic
676	C₂	C₁₉×#3301	1	1	yes	characteristic
677	C₂	C₁₉×#3303	1	1	yes	characteristic
678	C₂	C₁₉×#3304	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₂²⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#2362	C₂	semidirect
4. C₁₉×#1934	C₂	semidirect
5. C₁₉×#1933	C₂	semidirect
6. C₁₉×#1920	C₂	semidirect
7. C₁₉×#1919	C₂	semidirect
8. C₁₉×#1880	C₂	semidirect
9. C₁₉×#1877	C₂	semidirect
11. C₁₉×#1873	C₂	semidirect
12. C₄×C₁₉×#103	C₂	semidirect
13. C₄×C₁₉×#102	C₂	semidirect
14. C₈×C₂²⋊C₄×C₁₉	C₂	semidirect
15. C₁₉×#1735	C₂	semidirect
24. C₁₉×#465	C₄	semidirect
70. C₂²×C₈×C₁₉	C₂×C₄	semidirect
76. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
113. C₁₉×#106	C₂×C₄	semidirect
116. C₁₉×#103	C₂×C₄	semidirect
218. #23131	C₁₉	direct (N × H)
296. #2362	C₂×C₁₉	semidirect
297. #1934	C₂×C₁₉	semidirect
298. #1933	C₂×C₁₉	semidirect
299. #1920	C₂×C₁₉	semidirect
300. #1919	C₂×C₁₉	semidirect
301. #1880	C₂×C₁₉	semidirect
302. #1877	C₂×C₁₉	semidirect
304. #1873	C₂×C₁₉	semidirect
305. C₄×#103	C₂×C₁₉	semidirect
306. C₄×#102	C₂×C₁₉	semidirect
307. C₈×C₂²⋊C₄	C₂×C₁₉	semidirect
308. #1735	C₂×C₁₉	semidirect
354. #465	C₄×C₁₉	semidirect
409. C₂²×C₈	C₂×C₄×C₁₉	semidirect
415. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
452. #106	C₂×C₄×C₁₉	semidirect
455. #103	C₂×C₄×C₁₉	semidirect
470. C₁₉	#23131	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#465	2
C₁₉×#2363	2
C₁₉×#2362	2
C₁₉×#1934	2
C₁₉×#1933	2
C₁₉×#1920	2
C₁₉×#1919	2
C₁₉×#1880	2
C₁₉×#1877	2
C₁₉×#1875	2
C₁₉×#1873	2
C₄×C₁₉×#103	2
C₄×C₁₉×#102	2
C₈×C₂²⋊C₄×C₁₉	2
C₁₉×#1735	2
#23131	19

Subgroups — C19×#23131 #18029090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23131 #18029090