Subgroups — C₁₉×#34488 #18040447

Order 4864.

1940 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#557	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2382	C₂	1	4	yes	maximal
3	C₁₉×#2370	C₂	1	2	yes	maximal
4	C₁₉×#2365	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2365	C₂	1	2	yes	maximal
6	C₁₉×#2355	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2355	C₂	1	2	yes	maximal
8	C₁₉×#2351	C₂	1	2	yes	maximal
9	Q₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#2336	C₂	1	4	yes	maximal
11	C₁₉×#2330	C₂	1	2	yes	maximal
12	C₁₉×#2327	C₂	1	2	yes	maximal
13	C₁₉×#2320	C₂	1	2	yes	maximal
14	C₁₉×#2320	C₂	1	2	yes	maximal
15	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
16	C₁₉×#2295	C₂	1	1	yes	maximal, characteristic
17	C₁₉×#2295	C₂	1	1	yes	maximal, characteristic
18	C₁₉×#557	C₄	1	16	yes	complemented
19	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₉×#125	C₂²	1	2	yes	—
22	C₂×C₁₉×#125	C₂²	1	4	yes	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
30	C₁₉×#391	C₂²	1	1	yes	characteristic
31	C₁₉×#391	C₂²	1	1	yes	characteristic
32	C₁₉×#391	C₂²	1	1	yes	characteristic
33	C₁₉×#391	C₂²	1	1	yes	characteristic
34	C₁₉×#391	C₂²	1	2	yes	—
35	C₁₉×#391	C₂²	1	2	yes	—
36	C₁₉×#391	C₂²	1	2	yes	—
37	C₁₉×#389	C₂²	1	1	yes	characteristic
38	C₁₉×#389	C₂²	1	1	yes	characteristic
39	C₁₉×#389	C₂²	1	1	yes	characteristic
40	C₁₉×#389	C₂²	1	1	yes	characteristic
41	C₁₉×#389	C₂²	1	2	yes	—
42	C₁₉×#389	C₂²	1	2	yes	—
43	C₁₉×#389	C₂²	1	2	yes	—
44	C₁₉×#389	C₂²	1	2	yes	—
45	C₁₉×#389	C₂²	1	4	yes	—
46	C₁₉×#389	C₂²	1	4	yes	—
47	C₁₉×#389	C₂²	1	4	yes	—
48	C₁₉×#389	C₂²	1	4	yes	—
49	C₁₉×#387	C₂²	1	2	yes	—
50	C₁₉×#387	C₂²	1	2	yes	—
51	C₁₉×#387	C₂²	1	2	yes	—
52	C₁₉×#387	C₂²	1	2	yes	—
53	C₁₉×#387	C₂²	1	4	yes	—
54	C₁₉×#387	C₂²	1	4	yes	—
55	C₁₉×#387	C₂²	1	4	yes	—
56	C₁₉×#387	C₂²	1	4	yes	—
57	C₁₉×#387	C₂²	1	4	yes	—
58	C₁₉×#387	C₂²	1	4	yes	—
59	C₁₉×#387	C₂²	1	4	yes	—
60	C₁₉×#387	C₂²	1	4	yes	—
61	C₁₉×#387	C₂²	1	4	yes	—
62	C₁₉×#387	C₂²	1	4	yes	—
63	C₁₉×#384	C₂²	1	1	yes	characteristic
64	C₁₉×#384	C₂²	1	2	yes	—
65	C₁₉×#383	C₂²	1	4	yes	—
66	C₁₉×#382	C₂²	1	4	yes	—
67	C₁₉×#382	C₂²	1	4	yes	—
68	C₁₉×#382	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
80	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
81	C₁₉×#376	C₂²	1	2	yes	—
82	C₁₉×#376	C₂²	1	2	yes	—
83	C₄³×C₁₉	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
87	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	—
88	C₁₉×C₄⋊Q₈	C₂×C₄	1	16	yes	—
89	C₁₉×#125	C₂×C₄	1	16	yes	—
90	C₁₉×#125	C₂×C₄	1	32	yes	—
91	C₄×Q₈×C₁₉	—	4	4	no	—
92	C₄×Q₈×C₁₉	—	4	4	no	—
93	C₄×Q₈×C₁₉	—	4	4	no	—
94	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	—
95	C₄×Q₈×C₁₉	C₂×C₄	1	8	yes	—
96	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	—
97	C₄×Q₈×C₁₉	C₂×C₄	1	8	yes	—
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
131	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
132	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
133	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
134	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
138	C₁₉×#95	C₂³	1	2	yes	—
139	C₁₉×#95	C₂³	1	2	yes	—
140	C₁₉×#95	C₂³	1	2	yes	—
141	C₁₉×#95	C₂³	1	2	yes	—
142	C₁₉×#95	C₂³	1	2	yes	—
143	C₁₉×#95	C₂³	1	2	yes	—
144	C₁₉×#95	C₂³	1	2	yes	—
145	C₁₉×#95	C₂³	1	2	yes	—
146	C₁₉×#95	C₂³	1	2	yes	—
147	C₁₉×#95	C₂³	1	2	yes	—
148	C₁₉×#95	C₂³	1	2	yes	—
149	C₁₉×#95	C₂³	1	4	yes	—
150	C₁₉×#95	C₂³	1	4	yes	—
151	C₁₉×#95	C₂³	1	4	yes	—
152	C₁₉×#95	C₂³	1	4	yes	—
153	C₁₉×#95	C₂³	1	4	yes	—
154	C₁₉×#95	C₂³	1	4	yes	—
155	C₁₉×#95	C₂³	1	4	yes	—
156	C₁₉×#95	C₂³	1	4	yes	—
157	C₁₉×#95	C₂³	1	2	yes	—
158	C₁₉×#95	C₂³	1	2	yes	—
159	C₁₉×#95	C₂³	1	2	yes	—
160	C₂×Q₈×C₁₉	—	2	4	no	—
161	C₂×Q₈×C₁₉	—	2	2	no	—
162	C₂×Q₈×C₁₉	—	2	2	no	—
163	C₂×Q₈×C₁₉	—	2	2	no	—
164	C₂×Q₈×C₁₉	—	2	2	no	—
165	C₂×Q₈×C₁₉	—	2	4	no	—
166	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
167	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
168	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
169	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	4	no	—
188	C₄⋊C₄×C₁₉	—	2	4	no	—
189	C₄⋊C₄×C₁₉	—	2	4	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	4	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	4	2	no	—
195	C₄⋊C₄×C₁₉	—	4	2	no	—
196	C₄⋊C₄×C₁₉	—	4	2	no	—
197	C₄⋊C₄×C₁₉	—	4	4	no	—
198	C₄⋊C₄×C₁₉	—	4	4	no	—
199	C₄⋊C₄×C₁₉	—	4	4	no	—
200	C₄⋊C₄×C₁₉	—	4	4	no	—
201	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
202	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
203	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
204	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
205	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
206	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
207	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
208	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
209	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
210	C₄²×C₁₉	—	2	2	no	—
211	C₄²×C₁₉	—	2	4	no	—
212	C₄²×C₁₉	—	2	2	no	—
213	C₄²×C₁₉	—	2	2	no	—
214	C₄²×C₁₉	—	2	4	no	—
215	C₄²×C₁₉	—	2	2	no	—
216	C₄²×C₁₉	—	2	2	no	—
217	C₄²×C₁₉	—	4	4	no	—
218	C₄²×C₁₉	—	4	1	no	—
219	C₄²×C₁₉	—	4	4	no	—
220	C₄²×C₁₉	—	4	4	no	—
221	C₄²×C₁₉	—	4	4	no	—
222	C₄²×C₁₉	C₂²×C₄	1	16	yes	—
223	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
224	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
225	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
226	#34488	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
228	Q₈×C₁₉	—	2	8	no	—
229	Q₈×C₁₉	—	2	16	no	—
230	Q₈×C₁₉	—	2	8	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	4	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	4	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	1	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	2	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	2	4	no	—
263	C₂×C₄×C₁₉	—	2	2	no	—
264	C₂×C₄×C₁₉	—	2	2	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	4	no	—
267	C₂×C₄×C₁₉	—	2	1	no	—
268	C₂×C₄×C₁₉	—	2	2	no	—
269	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
270	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
271	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
272	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
273	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
274	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
275	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
276	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
277	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
278	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
279	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
280	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
281	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
282	C₂×#557	C₂×C₁₉	1	1	yes	characteristic
283	#2382	C₂×C₁₉	1	4	yes	—
284	#2370	C₂×C₁₉	1	2	yes	—
285	#2365	C₂×C₁₉	1	2	yes	—
286	#2365	C₂×C₁₉	1	1	yes	characteristic
287	#2355	C₂×C₁₉	1	2	yes	—
288	#2355	C₂×C₁₉	1	1	yes	characteristic
289	#2351	C₂×C₁₉	1	2	yes	—
290	Q₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
291	#2336	C₂×C₁₉	1	4	yes	—
292	#2330	C₂×C₁₉	1	2	yes	—
293	#2327	C₂×C₁₉	1	2	yes	—
294	#2320	C₂×C₁₉	1	2	yes	—
295	#2320	C₂×C₁₉	1	2	yes	—
296	C₄×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
297	#2295	C₂×C₁₉	1	1	yes	characteristic
298	#2295	C₂×C₁₉	1	1	yes	characteristic
299	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
300	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
301	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
302	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
303	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
304	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
305	C₂²×C₁₉	#585	1	1	yes	characteristic
306	C₄×C₁₉	—	2	4	no	—
307	C₄×C₁₉	—	2	8	no	—
308	C₄×C₁₉	—	2	4	no	—
309	C₄×C₁₉	—	2	2	no	—
310	C₄×C₁₉	—	2	4	no	—
311	C₄×C₁₉	—	2	4	no	—
312	C₄×C₁₉	—	2	2	no	—
313	C₄×C₁₉	—	4	2	no	—
314	C₄×C₁₉	—	4	2	no	—
315	C₄×C₁₉	—	4	2	no	—
316	C₄×C₁₉	—	4	1	no	—
317	C₄×C₁₉	—	4	4	no	—
318	C₄×C₁₉	—	4	1	no	—
319	C₄×C₁₉	—	4	2	no	—
320	C₄×C₁₉	—	4	1	no	—
321	C₄×C₁₉	#519	1	4	yes	—
322	C₄×C₁₉	#520	1	4	yes	—
323	#557	C₄×C₁₉	1	16	yes	complemented
324	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
326	C₂×#125	C₂²×C₁₉	1	2	yes	—
327	C₂×#125	C₂²×C₁₉	1	4	yes	—
328	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
329	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
330	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
331	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
332	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
333	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
335	#391	C₂²×C₁₉	1	2	yes	—
336	#391	C₂²×C₁₉	1	1	yes	characteristic
337	#391	C₂²×C₁₉	1	2	yes	—
338	#391	C₂²×C₁₉	1	2	yes	—
339	#391	C₂²×C₁₉	1	1	yes	characteristic
340	#391	C₂²×C₁₉	1	1	yes	characteristic
341	#391	C₂²×C₁₉	1	1	yes	characteristic
342	#389	C₂²×C₁₉	1	2	yes	—
343	#389	C₂²×C₁₉	1	2	yes	—
344	#389	C₂²×C₁₉	1	1	yes	characteristic
345	#389	C₂²×C₁₉	1	2	yes	—
346	#389	C₂²×C₁₉	1	2	yes	—
347	#389	C₂²×C₁₉	1	1	yes	characteristic
348	#389	C₂²×C₁₉	1	4	yes	—
349	#389	C₂²×C₁₉	1	4	yes	—
350	#389	C₂²×C₁₉	1	4	yes	—
351	#389	C₂²×C₁₉	1	4	yes	—
352	#389	C₂²×C₁₉	1	1	yes	characteristic
353	#389	C₂²×C₁₉	1	1	yes	characteristic
354	#387	C₂²×C₁₉	1	4	yes	—
355	#387	C₂²×C₁₉	1	4	yes	—
356	#387	C₂²×C₁₉	1	4	yes	—
357	#387	C₂²×C₁₉	1	4	yes	—
358	#387	C₂²×C₁₉	1	4	yes	—
359	#387	C₂²×C₁₉	1	4	yes	—
360	#387	C₂²×C₁₉	1	4	yes	—
361	#387	C₂²×C₁₉	1	2	yes	—
362	#387	C₂²×C₁₉	1	2	yes	—
363	#387	C₂²×C₁₉	1	4	yes	—
364	#387	C₂²×C₁₉	1	4	yes	—
365	#387	C₂²×C₁₉	1	4	yes	—
366	#387	C₂²×C₁₉	1	2	yes	—
367	#387	C₂²×C₁₉	1	2	yes	—
368	#384	C₂²×C₁₉	1	1	yes	characteristic
369	#384	C₂²×C₁₉	1	2	yes	—
370	#383	C₂²×C₁₉	1	4	yes	—
371	#382	C₂²×C₁₉	1	4	yes	—
372	#382	C₂²×C₁₉	1	4	yes	—
373	#382	C₂²×C₁₉	1	2	yes	—
374	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
375	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
376	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
377	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
378	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
379	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
380	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
381	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
382	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
383	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
384	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
385	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
386	#376	C₂²×C₁₉	1	2	yes	—
387	#376	C₂²×C₁₉	1	2	yes	—
388	C₄³	C₂²×C₁₉	1	1	yes	characteristic
389	C₂×C₁₉	C₂×#519	1	1	yes	characteristic
390	C₂×C₁₉	C₂×#520	1	1	yes	characteristic
391	C₂×C₁₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
392	C₂×C₁₉	#3552	1	1	yes	characteristic
393	C₂×C₁₉	#3554	1	1	yes	characteristic
394	C₂×C₁₉	#3555	1	1	yes	characteristic
395	C₂×C₁₉	#3556	1	1	yes	characteristic
396	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
397	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
398	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
399	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
400	C₄⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
401	#125	C₂×C₄×C₁₉	1	16	yes	—
402	#125	C₂×C₄×C₁₉	1	32	yes	—
403	C₄×Q₈	—	4	4	no	—
404	C₄×Q₈	—	4	4	no	—
405	C₄×Q₈	—	4	4	no	—
406	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	—
407	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	—
408	C₄×Q₈	C₂×C₄×C₁₉	1	8	yes	—
409	C₄×Q₈	C₂×C₄×C₁₉	1	8	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
415	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
419	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
420	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
421	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
423	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
429	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
432	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
433	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
434	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
436	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
437	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
441	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
442	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
443	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
444	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
445	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
446	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
447	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
448	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
450	#95	C₂³×C₁₉	1	2	yes	—
451	#95	C₂³×C₁₉	1	2	yes	—
452	#95	C₂³×C₁₉	1	2	yes	—
453	#95	C₂³×C₁₉	1	2	yes	—
454	#95	C₂³×C₁₉	1	2	yes	—
455	#95	C₂³×C₁₉	1	2	yes	—
456	#95	C₂³×C₁₉	1	2	yes	—
457	#95	C₂³×C₁₉	1	2	yes	—
458	#95	C₂³×C₁₉	1	2	yes	—
459	#95	C₂³×C₁₉	1	2	yes	—
460	#95	C₂³×C₁₉	1	4	yes	—
461	#95	C₂³×C₁₉	1	2	yes	—
462	#95	C₂³×C₁₉	1	4	yes	—
463	#95	C₂³×C₁₉	1	4	yes	—
464	#95	C₂³×C₁₉	1	4	yes	—
465	#95	C₂³×C₁₉	1	4	yes	—
466	#95	C₂³×C₁₉	1	4	yes	—
467	#95	C₂³×C₁₉	1	4	yes	—
468	#95	C₂³×C₁₉	1	4	yes	—
469	#95	C₂³×C₁₉	1	2	yes	—
470	#95	C₂³×C₁₉	1	2	yes	—
471	#95	C₂³×C₁₉	1	2	yes	—
472	C₁₉	#34488	1	1	yes	characteristic, direct product factor, Sylow
473	C₂×Q₈	—	2	4	no	—
474	C₂×Q₈	—	2	2	no	—
475	C₂×Q₈	—	2	2	no	—
476	C₂×Q₈	—	2	2	no	—
477	C₂×Q₈	—	2	4	no	—
478	C₂×Q₈	—	2	2	no	—
479	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
480	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
481	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
482	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
487	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
490	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
492	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
493	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
494	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
495	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
497	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
498	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	4	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	—	4	2	no	—
509	C₄⋊C₄	—	4	2	no	—
510	C₄⋊C₄	—	4	4	no	—
511	C₄⋊C₄	—	4	4	no	—
512	C₄⋊C₄	—	4	4	no	—
513	C₄⋊C₄	—	4	4	no	—
514	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
515	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
516	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
517	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
518	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
519	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
520	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
521	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
522	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
523	C₄²	—	2	2	no	—
524	C₄²	—	2	4	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	2	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	2	2	no	—
529	C₄²	—	2	2	no	—
530	C₄²	—	4	4	no	—
531	C₄²	—	4	1	no	—
532	C₄²	—	4	4	no	—
533	C₄²	—	4	4	no	—
534	C₄²	—	4	4	no	—
535	C₄²	C₂²×C₄×C₁₉	1	16	yes	—
536	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
537	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
538	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
539	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
540	Q₈	—	2	8	no	—
541	Q₈	—	2	16	no	—
542	Q₈	—	2	8	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
582	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
583	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
584	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
585	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
586	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
587	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
588	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
589	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
590	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
591	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
592	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
593	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
594	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
595	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
596	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
597	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
598	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
599	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
600	C₂²	C₁₉×#585	1	1	yes	characteristic
601	C₄	—	2	4	no	—
602	C₄	—	2	8	no	—
603	C₄	—	2	4	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	4	no	—
606	C₄	—	2	4	no	—
607	C₄	—	2	2	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	4	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	2	no	—
615	C₄	—	4	1	no	—
616	C₄	C₁₉×#519	1	4	yes	—
617	C₄	C₁₉×#520	1	4	yes	—
618	C₂	C₂×C₁₉×#519	1	1	yes	characteristic
619	C₂	C₂×C₁₉×#520	1	1	yes	characteristic
620	C₂	C₄×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
621	C₂	C₁₉×#3552	1	1	yes	characteristic
622	C₂	C₁₉×#3554	1	1	yes	characteristic
623	C₂	C₁₉×#3555	1	1	yes	characteristic
624	C₂	C₁₉×#3556	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
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
18. C₁₉×#557	C₄	semidirect
226. #34488	C₁₉	direct (N × H)
323. #557	C₄×C₁₉	semidirect
472. C₁₉	#34488	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×#557	2
C₁₉×#2382	2
C₁₉×#2370	2
C₁₉×#2365	2
C₁₉×#2355	2
C₁₉×#2351	2
Q₈×C₄⋊C₄×C₁₉	2
C₁₉×#2336	2
C₁₉×#2330	2
C₁₉×#2327	2
C₁₉×#2320	2
C₄×C₁₉×C₄⋊Q₈	2
C₁₉×#2295	2
#34488	19

Subgroups — C19×#34488 #18040447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34488 #18040447