Subgroups — C₁₉×#22531 #18028490

Order 4864.

1136 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1955	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1954	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1954	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1798	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1750	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#529	—	2	4	no	—
13	C₁₉×#529	—	2	4	no	—
14	C₂×C₁₉×#126	C₄	1	2	yes	—
15	C₂×C₁₉×#125	C₄	1	1	yes	characteristic
16	C₂×C₁₉×#124	C₄	1	1	yes	characteristic
17	C₂×C₁₉×#123	C₄	1	2	yes	—
18	C₂×C₁₉×C₂²⋊Q₈	C₄	1	1	yes	characteristic
19	C₂×C₁₉×#121	C₄	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×C₄×D₄×C₁₉	C₂²	1	2	yes	—
23	C₂×C₁₉×#117	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#446	—	2	4	no	—
26	C₈×Q₈×C₁₉	—	2	4	no	—
27	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
29	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
31	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
37	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₂×C₁₉×#97	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
42	C₁₉×#336	C₂²	1	1	yes	characteristic
43	C₁₉×#336	C₂²	1	1	yes	characteristic
44	C₁₉×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
48	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×#126	—	2	8	no	—
59	C₁₉×#125	—	2	4	no	—
60	C₁₉×#124	—	2	4	no	—
61	C₁₉×#123	—	2	8	no	—
62	C₁₉×C₂²⋊Q₈	—	2	4	no	—
63	C₁₉×#121	—	2	4	no	—
64	C₄×Q₈×C₁₉	D₄	1	4	yes	—
65	C₄×Q₈×C₁₉	D₄	1	4	yes	—
66	C₄×D₄×C₁₉	—	2	2	no	—
67	C₄×D₄×C₁₉	—	2	2	no	—
68	C₄×D₄×C₁₉	—	2	4	no	—
69	C₄×D₄×C₁₉	—	2	4	no	—
70	C₁₉×#117	—	2	4	no	—
71	C₁₉×#117	—	2	4	no	—
72	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
79	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
81	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₁₉	—	2	2	no	—
84	C₂×C₄²×C₁₉	—	2	2	no	—
85	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
90	C₁₉×C₄⋊C₈	—	2	2	no	—
91	C₁₉×C₄⋊C₈	—	2	4	no	—
92	C₁₉×C₄⋊C₈	—	2	2	no	—
93	C₁₉×C₄⋊C₈	—	2	4	no	—
94	C₁₉×C₂²⋊C₈	—	2	2	no	—
95	C₁₉×C₂²⋊C₈	—	2	4	no	—
96	C₁₉×C₂²⋊C₈	—	2	4	no	—
97	C₁₉×C₂²⋊C₈	—	2	2	no	—
98	C₁₉×C₂²⋊C₈	—	4	2	no	—
99	C₁₉×C₂²⋊C₈	—	4	2	no	—
100	C₁₉×C₂²⋊C₈	—	4	2	no	—
101	C₁₉×#97	—	2	4	no	—
102	C₄×C₈×C₁₉	—	2	2	no	—
103	C₄×C₈×C₁₉	—	2	4	no	—
104	C₄×C₈×C₁₉	—	2	2	no	—
105	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
106	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
110	C₂×D₄×C₁₉	—	2	4	no	—
111	C₂×D₄×C₁₉	—	2	4	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	4	2	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	4	1	no	—
134	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	—	2	1	no	—
145	C₂×C₈×C₁₉	—	2	1	no	—
146	C₂×C₈×C₁₉	—	2	1	no	—
147	C₂×C₈×C₁₉	—	2	1	no	—
148	C₂×C₈×C₁₉	—	2	2	no	—
149	C₂×C₈×C₁₉	—	2	1	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	2	1	no	—
152	C₂×C₈×C₁₉	—	2	2	no	—
153	C₂×C₈×C₁₉	—	2	1	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₂×C₈×C₁₉	—	2	1	no	—
156	C₂×C₈×C₁₉	—	2	2	no	—
157	C₂×C₈×C₁₉	—	2	1	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₂×C₈×C₁₉	#41	1	2	yes	—
160	C₂×C₈×C₁₉	#41	1	2	yes	—
161	C₄⋊C₄×C₁₉	—	2	4	no	—
162	C₄⋊C₄×C₁₉	—	2	4	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	4	no	—
165	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
166	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
167	C₂²⋊C₄×C₁₉	—	2	4	no	—
168	C₂²⋊C₄×C₁₉	—	2	4	no	—
169	C₂²⋊C₄×C₁₉	—	2	4	no	—
170	C₂²⋊C₄×C₁₉	—	2	4	no	—
171	C₂²⋊C₄×C₁₉	—	2	4	no	—
172	C₄²×C₁₉	—	2	2	no	—
173	C₄²×C₁₉	—	2	2	no	—
174	C₄²×C₁₉	—	2	1	no	—
175	C₄²×C₁₉	—	2	1	no	—
176	C₄²×C₁₉	C₂×D₄	1	2	yes	—
177	C₄²×C₁₉	C₂×D₄	1	2	yes	—
178	C₄²×C₁₉	C₂×D₄	1	4	yes	—
179	C₄²×C₁₉	C₂×D₄	1	4	yes	—
180	#22531	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂³×C₁₉	—	2	1	no	—
182	C₂³×C₁₉	—	2	1	no	—
183	C₂³×C₁₉	—	2	1	no	—
184	C₂³×C₁₉	—	2	1	no	—
185	C₂³×C₁₉	—	2	1	no	—
186	C₂³×C₁₉	—	2	1	no	—
187	C₂³×C₁₉	—	2	2	no	—
188	C₂³×C₁₉	—	2	2	no	—
189	C₂³×C₁₉	—	2	2	no	—
190	C₂³×C₁₉	—	2	2	no	—
191	C₂³×C₁₉	—	2	2	no	—
192	C₂³×C₁₉	—	2	2	no	—
193	C₂³×C₁₉	—	2	2	no	—
194	C₂³×C₁₉	#131	1	2	yes	—
195	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
196	Q₈×C₁₉	—	2	8	no	—
197	D₄×C₁₉	—	4	8	no	—
198	D₄×C₁₉	—	4	4	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	4	4	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	4	no	—
227	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
228	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
229	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
230	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
231	C₂×C₄×C₁₉	#131	1	2	yes	—
232	C₂×C₄×C₁₉	#131	1	2	yes	—
233	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
239	C₈×C₁₉	—	2	2	no	—
240	C₈×C₁₉	—	2	2	no	—
241	C₈×C₁₉	—	4	1	no	—
242	C₈×C₁₉	—	4	2	no	—
243	C₈×C₁₉	—	4	1	no	—
244	C₈×C₁₉	—	4	2	no	—
245	C₂×#529	C₂×C₁₉	1	1	yes	characteristic
246	C₂×#446	C₂×C₁₉	1	1	yes	characteristic, complemented
247	C₂×C₈×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
248	#1955	C₂×C₁₉	1	2	yes	complemented
249	#1954	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#1954	C₂×C₁₉	1	1	yes	characteristic, complemented
251	#1954	C₂×C₁₉	1	2	yes	complemented
252	#1798	C₂×C₁₉	1	2	yes	complemented
253	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#1750	C₂×C₁₉	1	2	yes	complemented
255	C₄×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
256	C₂²×C₁₉	—	2	2	no	—
257	C₂²×C₁₉	—	2	2	no	—
258	C₂²×C₁₉	—	2	2	no	—
259	C₂²×C₁₉	—	4	1	no	—
260	C₂²×C₁₉	—	4	1	no	—
261	C₂²×C₁₉	—	4	1	no	—
262	C₂²×C₁₉	—	4	1	no	—
263	C₂²×C₁₉	—	4	2	no	—
264	C₂²×C₁₉	—	4	2	no	—
265	C₂²×C₁₉	—	4	2	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	4	2	no	—
268	C₂²×C₁₉	—	4	2	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
271	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
272	C₂²×C₁₉	#520	1	1	yes	characteristic
273	C₂²×C₁₉	C₂×#131	1	1	yes	characteristic
274	C₂²×C₁₉	C₂×#131	1	1	yes	characteristic
275	C₂²×C₁₉	C₂×#131	1	1	yes	characteristic
276	C₂²×C₁₉	#568	1	1	yes	characteristic
277	C₄×C₁₉	—	2	4	no	—
278	C₄×C₁₉	—	2	2	no	—
279	C₄×C₁₉	—	2	4	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	4	2	no	—
282	C₄×C₁₉	—	4	1	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	#408	1	4	yes	—
285	C₄×C₁₉	#548	1	1	yes	characteristic
286	C₄×C₁₉	#548	1	1	yes	characteristic
287	C₄×C₁₉	#550	1	1	yes	characteristic
288	C₄×C₁₉	#550	1	1	yes	characteristic
289	#529	—	2	4	no	—
290	#529	—	2	4	no	—
291	C₂×#126	C₄×C₁₉	1	2	yes	—
292	C₂×#125	C₄×C₁₉	1	1	yes	characteristic
293	C₂×#124	C₄×C₁₉	1	1	yes	characteristic
294	C₂×#123	C₄×C₁₉	1	2	yes	—
295	C₂×C₂²⋊Q₈	C₄×C₁₉	1	1	yes	characteristic
296	C₂×#121	C₄×C₁₉	1	1	yes	characteristic
297	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
298	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
299	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
300	C₂×#117	C₂²×C₁₉	1	2	yes	—
301	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
302	#446	—	2	4	no	—
303	C₈×Q₈	—	2	4	no	—
304	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
305	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
306	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
307	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
308	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
309	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
310	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
311	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
312	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
313	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
314	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
315	C₂×#97	C₂²×C₁₉	1	2	yes	—
316	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
317	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
318	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
319	#336	C₂²×C₁₉	1	2	yes	—
320	#336	C₂²×C₁₉	1	1	yes	characteristic
321	#336	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×C₁₉	—	4	2	no	—
323	C₂×C₁₉	—	8	2	no	—
324	C₂×C₁₉	#2341	1	1	yes	characteristic
325	C₂×C₁₉	C₂×#408	1	1	yes	characteristic
326	C₂×C₁₉	#2880	1	1	yes	characteristic
327	C₂×C₁₉	#2966	1	1	yes	characteristic
328	C₂×C₁₉	#2969	1	1	yes	characteristic
329	C₂×C₁₉	#2993	1	1	yes	characteristic
330	C₂×C₁₉	#2994	1	1	yes	characteristic
331	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
332	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
333	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
334	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
335	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
336	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
337	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
339	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
342	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
344	#126	—	2	8	no	—
345	#125	—	2	4	no	—
346	#124	—	2	4	no	—
347	#123	—	2	8	no	—
348	C₂²⋊Q₈	—	2	4	no	—
349	#121	—	2	4	no	—
350	C₄×Q₈	D₄×C₁₉	1	4	yes	—
351	C₄×Q₈	D₄×C₁₉	1	4	yes	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	4	no	—
355	C₄×D₄	—	2	4	no	—
356	#117	—	2	4	no	—
357	#117	—	2	4	no	—
358	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
359	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
360	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
362	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
364	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
365	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
366	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
367	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
368	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
369	C₂×C₄²	—	2	2	no	—
370	C₂×C₄²	—	2	2	no	—
371	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
372	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
375	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
376	C₄⋊C₈	—	2	2	no	—
377	C₄⋊C₈	—	2	4	no	—
378	C₄⋊C₈	—	2	2	no	—
379	C₄⋊C₈	—	2	4	no	—
380	C₂²⋊C₈	—	2	2	no	—
381	C₂²⋊C₈	—	2	4	no	—
382	C₂²⋊C₈	—	2	4	no	—
383	C₂²⋊C₈	—	2	2	no	—
384	C₂²⋊C₈	—	4	2	no	—
385	C₂²⋊C₈	—	4	2	no	—
386	C₂²⋊C₈	—	4	2	no	—
387	#97	—	2	4	no	—
388	C₄×C₈	—	2	2	no	—
389	C₄×C₈	—	2	4	no	—
390	C₄×C₈	—	2	2	no	—
391	C₁₉	#22531	1	1	yes	characteristic, direct product factor, Sylow
392	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
393	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	4	1	no	—
421	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
422	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
423	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
424	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
425	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
426	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
427	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
428	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	#41×C₁₉	1	2	yes	—
447	C₂×C₈	#41×C₁₉	1	2	yes	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
453	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	4	no	—
458	C₂²⋊C₄	—	2	4	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	2	1	no	—
463	C₄²	C₂×D₄×C₁₉	1	2	yes	—
464	C₄²	C₂×D₄×C₁₉	1	2	yes	—
465	C₄²	C₂×D₄×C₁₉	1	4	yes	—
466	C₄²	C₂×D₄×C₁₉	1	4	yes	—
467	C₂³	—	2	1	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	1	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	2	no	—
480	C₂³	C₁₉×#131	1	2	yes	—
481	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
482	Q₈	—	2	8	no	—
483	D₄	—	4	8	no	—
484	D₄	—	4	4	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	—	4	4	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
514	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
515	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
516	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
517	C₂×C₄	C₁₉×#131	1	2	yes	—
518	C₂×C₄	C₁₉×#131	1	2	yes	—
519	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
521	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
522	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
523	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
525	C₈	—	2	2	no	—
526	C₈	—	2	2	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	2	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
546	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
547	C₂²	C₁₉×#520	1	1	yes	characteristic
548	C₂²	C₂×C₁₉×#131	1	1	yes	characteristic
549	C₂²	C₂×C₁₉×#131	1	1	yes	characteristic
550	C₂²	C₂×C₁₉×#131	1	1	yes	characteristic
551	C₂²	C₁₉×#568	1	1	yes	characteristic
552	C₄	—	2	4	no	—
553	C₄	—	2	2	no	—
554	C₄	—	2	4	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	C₁₉×#408	1	4	yes	—
560	C₄	C₁₉×#548	1	1	yes	characteristic
561	C₄	C₁₉×#548	1	1	yes	characteristic
562	C₄	C₁₉×#550	1	1	yes	characteristic
563	C₄	C₁₉×#550	1	1	yes	characteristic
564	C₂	—	4	2	no	—
565	C₂	—	8	2	no	—
566	C₂	C₁₉×#2341	1	1	yes	characteristic
567	C₂	C₂×C₁₉×#408	1	1	yes	characteristic
568	C₂	C₁₉×#2880	1	1	yes	characteristic
569	C₂	C₁₉×#2966	1	1	yes	characteristic
570	C₂	C₁₉×#2969	1	1	yes	characteristic
571	C₂	C₁₉×#2993	1	1	yes	characteristic
572	C₂	C₁₉×#2994	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#446	C₂	semidirect
3. C₂×C₈×Q₈×C₁₉	C₂	semidirect
4. C₁₉×#1955	C₂	semidirect
5. C₁₉×#1954	C₂	semidirect
6. C₁₉×#1954	C₂	semidirect
7. C₁₉×#1954	C₂	semidirect
8. C₁₉×#1798	C₂	semidirect
9. C₁₉×#1797	C₂	semidirect
10. C₁₉×#1750	C₂	semidirect
11. C₄×C₁₉×C₂²⋊C₈	C₂	semidirect
180. #22531	C₁₉	direct (N × H)
246. C₂×#446	C₂×C₁₉	semidirect
247. C₂×C₈×Q₈	C₂×C₁₉	semidirect
248. #1955	C₂×C₁₉	semidirect
249. #1954	C₂×C₁₉	semidirect
250. #1954	C₂×C₁₉	semidirect
251. #1954	C₂×C₁₉	semidirect
252. #1798	C₂×C₁₉	semidirect
253. #1797	C₂×C₁₉	semidirect
254. #1750	C₂×C₁₉	semidirect
255. C₄×C₂²⋊C₈	C₂×C₁₉	semidirect
391. C₁₉	#22531	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×#529	2
C₂×C₁₉×#446	2
C₂×C₈×Q₈×C₁₉	2
C₁₉×#1955	2
C₁₉×#1954	2
C₁₉×#1798	2
C₁₉×#1797	2
C₁₉×#1750	2
C₄×C₁₉×C₂²⋊C₈	2
#22531	19

Subgroups — C19×#22531 #18028490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22531 #18028490