Subgroups — C₁₉×#22480 #18028439

Order 4864.

1068 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#552	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₁₉	C₂	1	2	yes	maximal
3	C₁₉×#1998	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1901	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1901	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1822	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1821	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1742	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
14	C₁₉×#552	—	2	2	no	—
15	C₁₉×#552	—	2	2	no	—
16	C₁₉×#552	—	2	2	no	—
17	C₁₉×#552	—	2	2	no	—
18	C₂×C₁₉×#126	C₄	1	2	yes	—
19	C₂×C₁₉×#125	C₄	1	2	yes	—
20	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#123	C₄	1	2	yes	—
22	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#117	C₄	1	2	yes	—
27	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#436	—	2	2	no	—
30	C₁₉×#435	—	2	2	no	—
31	C₁₉×#435	—	2	2	no	—
32	C₈×D₄×C₁₉	—	2	2	no	—
33	C₁₉×#423	C₂²	1	2	yes	—
34	C₂×C₁₉×#101	C₂²	1	2	yes	—
35	C₂×C₁₉×#101	C₂²	1	2	yes	—
36	C₁₉×#407	C₂²	1	2	yes	—
37	C₁₉×#407	C₂²	1	2	yes	—
38	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
39	C₁₉×#343	C₂²	1	2	yes	—
40	C₁₉×#343	C₂²	1	2	yes	—
41	C₁₉×#343	C₂²	1	2	yes	—
42	C₁₉×#343	C₂²	1	2	yes	—
43	C₁₉×#343	C₂²	1	1	yes	characteristic
44	C₁₉×#343	C₂²	1	1	yes	characteristic
45	C₁₉×#343	C₂²	1	1	yes	characteristic
46	C₁₉×#343	C₂²	1	1	yes	characteristic
47	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₁₉	—	2	2	no	—
53	C₂×M₁₆×C₁₉	—	2	2	no	—
54	C₂×M₁₆×C₁₉	—	2	4	no	—
55	C₂×M₁₆×C₁₉	—	2	4	no	—
56	C₂×M₁₆×C₁₉	—	4	2	no	—
57	C₂×M₁₆×C₁₉	—	4	2	no	—
58	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
59	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
60	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
61	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₉	—	2	2	no	—
63	C₂²×C₈×C₁₉	—	2	2	no	—
64	C₁₉×#126	—	2	4	no	—
65	C₁₉×#126	—	2	4	no	—
66	C₁₉×#125	—	2	4	no	—
67	C₁₉×#125	—	2	4	no	—
68	C₁₉×#125	—	2	2	no	—
69	C₁₉×#125	—	2	2	no	—
70	C₁₉×#123	—	2	4	no	—
71	C₁₉×#123	—	2	4	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	—	2	2	no	—
74	C₁₉×C₂²⋊Q₈	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₄×Q₈×C₁₉	—	2	2	no	—
77	C₄×Q₈×C₁₉	—	2	2	no	—
78	C₄×D₄×C₁₉	D₄	1	2	yes	—
79	C₄×D₄×C₁₉	D₄	1	2	yes	—
80	C₄×D₄×C₁₉	D₄	1	2	yes	—
81	C₄×D₄×C₁₉	D₄	1	2	yes	—
82	C₁₉×#117	—	2	2	no	—
83	C₁₉×#117	—	2	2	no	—
84	C₁₉×#117	—	2	2	no	—
85	C₁₉×#117	—	2	2	no	—
86	C₁₉×#117	—	2	2	no	—
87	C₁₉×#117	—	2	2	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
90	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
92	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
93	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
96	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
101	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
102	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
103	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
106	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
107	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×C₄⋊C₈	—	2	2	no	—
109	C₁₉×C₄⋊C₈	—	2	2	no	—
110	C₁₉×#101	—	2	4	no	—
111	C₁₉×#101	—	4	2	no	—
112	C₁₉×C₂²⋊C₈	—	2	2	no	—
113	C₁₉×C₂²⋊C₈	—	2	2	no	—
114	C₁₉×C₂²⋊C₈	—	2	2	no	—
115	C₁₉×C₂²⋊C₈	—	2	2	no	—
116	C₁₉×#97	—	2	2	no	—
117	C₄×C₈×C₁₉	—	2	2	no	—
118	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
119	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
120	C₂×Q₈×C₁₉	—	2	2	no	—
121	C₂×Q₈×C₁₉	—	2	2	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	—	4	2	no	—
125	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
126	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
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	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	4	4	no	—
136	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
142	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
149	M₁₆×C₁₉	—	2	2	no	—
150	M₁₆×C₁₉	—	2	2	no	—
151	M₁₆×C₁₉	—	2	2	no	—
152	M₁₆×C₁₉	—	2	2	no	—
153	M₁₆×C₁₉	—	2	2	no	—
154	M₁₆×C₁₉	—	2	2	no	—
155	M₁₆×C₁₉	—	2	2	no	—
156	M₁₆×C₁₉	—	4	4	no	—
157	M₁₆×C₁₉	—	4	4	no	—
158	M₁₆×C₁₉	#41	1	4	yes	—
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₂×C₈×C₁₉	—	2	2	no	—
163	C₂×C₈×C₁₉	—	4	4	no	—
164	C₂×C₈×C₁₉	—	4	4	no	—
165	C₄⋊C₄×C₁₉	—	2	4	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	4	no	—
171	C₄⋊C₄×C₁₉	—	2	4	no	—
172	C₄⋊C₄×C₁₉	—	2	4	no	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
177	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₉	—	2	4	no	—
181	C₂²⋊C₄×C₁₉	—	2	4	no	—
182	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
183	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
184	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
185	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
186	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
187	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
188	C₄²×C₁₉	—	2	2	no	—
189	C₄²×C₁₉	—	2	2	no	—
190	C₄²×C₁₉	—	2	2	no	—
191	C₄²×C₁₉	—	2	2	no	—
192	C₄²×C₁₉	C₂×D₄	1	2	yes	—
193	C₄²×C₁₉	C₂×D₄	1	2	yes	—
194	#22480	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂³×C₁₉	—	2	1	no	—
196	C₂³×C₁₉	—	2	1	no	—
197	C₂³×C₁₉	—	2	2	no	—
198	C₂³×C₁₉	—	2	1	no	—
199	C₂³×C₁₉	—	2	1	no	—
200	C₂³×C₁₉	—	4	1	no	—
201	C₂³×C₁₉	—	4	1	no	—
202	C₂³×C₁₉	—	4	1	no	—
203	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
204	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
207	Q₈×C₁₉	—	4	2	no	—
208	Q₈×C₁₉	—	4	2	no	—
209	D₄×C₁₉	—	2	4	no	—
210	D₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
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	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	4	no	—
232	C₂×C₄×C₁₉	—	4	4	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
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×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
241	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
242	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
244	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
245	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
246	C₈×C₁₉	—	2	4	no	—
247	C₈×C₁₉	—	4	2	no	—
248	C₈×C₁₉	—	4	2	no	—
249	C₈×C₁₉	—	4	2	no	—
250	C₂×#552	C₂×C₁₉	1	1	yes	characteristic
251	D₄×M₁₆	C₂×C₁₉	1	2	yes	—
252	#1998	C₂×C₁₉	1	2	yes	complemented
253	#1901	C₂×C₁₉	1	2	yes	complemented
254	#1901	C₂×C₁₉	1	2	yes	complemented
255	#1822	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1821	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1801	C₂×C₁₉	1	1	yes	characteristic, complemented
258	C₄×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1742	C₂×C₁₉	1	1	yes	characteristic, complemented
260	C₂×#343	C₂×C₁₉	1	1	yes	characteristic, complemented
261	C₂²×C₁₉	—	2	1	no	—
262	C₂²×C₁₉	—	2	1	no	—
263	C₂²×C₁₉	—	2	1	no	—
264	C₂²×C₁₉	—	2	1	no	—
265	C₂²×C₁₉	—	2	1	no	—
266	C₂²×C₁₉	—	2	2	no	—
267	C₂²×C₁₉	—	2	1	no	—
268	C₂²×C₁₉	—	2	2	no	—
269	C₂²×C₁₉	—	2	1	no	—
270	C₂²×C₁₉	—	2	2	no	—
271	C₂²×C₁₉	—	4	2	no	—
272	C₂²×C₁₉	—	4	2	no	—
273	C₂²×C₁₉	—	8	1	no	—
274	C₂²×C₁₉	—	8	1	no	—
275	C₂²×C₁₉	#413	1	2	yes	—
276	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
277	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
278	C₂²×C₁₉	#520	1	1	yes	characteristic
279	C₄×C₁₉	—	2	1	no	—
280	C₄×C₁₉	—	2	2	no	—
281	C₄×C₁₉	—	2	1	no	—
282	C₄×C₁₉	—	2	2	no	—
283	C₄×C₁₉	—	2	1	no	—
284	C₄×C₁₉	—	2	1	no	—
285	C₄×C₁₉	—	4	2	no	—
286	C₄×C₁₉	—	4	2	no	—
287	C₄×C₁₉	—	4	2	no	—
288	C₄×C₁₉	—	4	2	no	—
289	C₄×C₁₉	#546	1	2	yes	—
290	C₄×C₁₉	#547	1	2	yes	—
291	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
292	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
293	#552	—	2	2	no	—
294	#552	—	2	2	no	—
295	#552	—	2	2	no	—
296	#552	—	2	2	no	—
297	C₂×#126	C₄×C₁₉	1	2	yes	—
298	C₂×#125	C₄×C₁₉	1	2	yes	—
299	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
300	C₂×#123	C₄×C₁₉	1	2	yes	—
301	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
303	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
304	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
305	C₂×#117	C₄×C₁₉	1	2	yes	—
306	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
307	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
308	#436	—	2	2	no	—
309	#435	—	2	2	no	—
310	#435	—	2	2	no	—
311	C₈×D₄	—	2	2	no	—
312	#423	C₂²×C₁₉	1	2	yes	—
313	C₂×#101	C₂²×C₁₉	1	2	yes	—
314	C₂×#101	C₂²×C₁₉	1	2	yes	—
315	#407	C₂²×C₁₉	1	2	yes	—
316	#407	C₂²×C₁₉	1	2	yes	—
317	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
318	#343	C₂²×C₁₉	1	1	yes	characteristic
319	#343	C₂²×C₁₉	1	1	yes	characteristic
320	#343	C₂²×C₁₉	1	1	yes	characteristic
321	#343	C₂²×C₁₉	1	2	yes	—
322	#343	C₂²×C₁₉	1	2	yes	—
323	#343	C₂²×C₁₉	1	2	yes	—
324	#343	C₂²×C₁₉	1	2	yes	—
325	#343	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×C₁₉	—	2	1	no	—
327	C₂×C₁₉	—	2	1	no	—
328	C₂×C₁₉	—	2	2	no	—
329	C₂×C₁₉	—	4	1	no	—
330	C₂×C₁₉	—	4	2	no	—
331	C₂×C₁₉	#2339	1	1	yes	characteristic
332	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
333	C₂×C₁₉	#2889	1	1	yes	characteristic
334	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
335	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
336	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
337	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
338	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
339	C₂×M₁₆	—	2	2	no	—
340	C₂×M₁₆	—	2	2	no	—
341	C₂×M₁₆	—	2	4	no	—
342	C₂×M₁₆	—	2	4	no	—
343	C₂×M₁₆	—	4	2	no	—
344	C₂×M₁₆	—	4	2	no	—
345	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
346	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
347	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
348	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
349	C₂²×C₈	—	2	2	no	—
350	C₂²×C₈	—	2	2	no	—
351	#126	—	2	4	no	—
352	#126	—	2	4	no	—
353	#125	—	2	4	no	—
354	#125	—	2	4	no	—
355	#125	—	2	2	no	—
356	#125	—	2	2	no	—
357	#123	—	2	4	no	—
358	#123	—	2	4	no	—
359	C₂²⋊Q₈	—	2	2	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₂²⋊Q₈	—	2	2	no	—
362	C₂²⋊Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	—	2	2	no	—
365	C₄×D₄	D₄×C₁₉	1	2	yes	—
366	C₄×D₄	D₄×C₁₉	1	2	yes	—
367	C₄×D₄	D₄×C₁₉	1	2	yes	—
368	C₄×D₄	D₄×C₁₉	1	2	yes	—
369	#117	—	2	2	no	—
370	#117	—	2	2	no	—
371	#117	—	2	2	no	—
372	#117	—	2	2	no	—
373	#117	—	2	2	no	—
374	#117	—	2	2	no	—
375	C₂×C₄⋊C₄	—	2	2	no	—
376	C₂×C₄⋊C₄	—	2	2	no	—
377	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
378	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
379	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
380	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
381	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
382	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
383	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
388	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
389	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
390	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
392	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
393	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
394	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
395	C₄⋊C₈	—	2	2	no	—
396	C₄⋊C₈	—	2	2	no	—
397	#101	—	2	4	no	—
398	#101	—	4	2	no	—
399	C₂²⋊C₈	—	2	2	no	—
400	C₂²⋊C₈	—	2	2	no	—
401	C₂²⋊C₈	—	2	2	no	—
402	C₂²⋊C₈	—	2	2	no	—
403	#97	—	2	2	no	—
404	C₄×C₈	—	2	2	no	—
405	C₁₉	#22480	1	1	yes	characteristic, direct product factor, Sylow
406	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
407	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×D₄	—	4	2	no	—
413	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
414	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	4	4	no	—
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	1	yes	characteristic
427	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
428	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
429	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
430	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
431	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
433	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
434	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
435	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
437	M₁₆	—	2	2	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	2	2	no	—
443	M₁₆	—	2	2	no	—
444	M₁₆	—	4	4	no	—
445	M₁₆	—	4	4	no	—
446	M₁₆	#41×C₁₉	1	4	yes	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	4	4	no	—
452	C₂×C₈	—	4	4	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
465	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
471	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
472	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
473	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
474	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
475	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
476	C₄²	—	2	2	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	2	no	—
480	C₄²	C₂×D₄×C₁₉	1	2	yes	—
481	C₄²	C₂×D₄×C₁₉	1	2	yes	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	1	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	—	4	1	no	—
490	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
491	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
492	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
493	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
494	Q₈	—	4	2	no	—
495	Q₈	—	4	2	no	—
496	D₄	—	2	4	no	—
497	D₄	—	4	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	4	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
524	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
525	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
526	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
527	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
528	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
529	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
530	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
531	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
533	C₈	—	2	4	no	—
534	C₈	—	4	2	no	—
535	C₈	—	4	2	no	—
536	C₈	—	4	2	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	8	1	no	—
551	C₂²	C₁₉×#413	1	2	yes	—
552	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
553	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
554	C₂²	C₁₉×#520	1	1	yes	characteristic
555	C₄	—	2	1	no	—
556	C₄	—	2	2	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	2	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	C₁₉×#546	1	2	yes	—
566	C₄	C₁₉×#547	1	2	yes	—
567	C₂	—	2	1	no	—
568	C₂	—	2	1	no	—
569	C₂	—	2	2	no	—
570	C₂	—	4	1	no	—
571	C₂	—	4	2	no	—
572	C₂	C₁₉×#2339	1	1	yes	characteristic
573	C₂	C₂×C₁₉×#413	1	1	yes	characteristic
574	C₂	C₁₉×#2889	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1998	C₂	semidirect
4. C₁₉×#1901	C₂	semidirect
5. C₁₉×#1901	C₂	semidirect
6. C₁₉×#1822	C₂	semidirect
7. C₁₉×#1821	C₂	semidirect
8. C₁₉×#1801	C₂	semidirect
9. C₄×C₁₉×#101	C₂	semidirect
10. C₁₉×#1742	C₂	semidirect
11. C₂×C₁₉×#343	C₂	semidirect
194. #22480	C₁₉	direct (N × H)
252. #1998	C₂×C₁₉	semidirect
253. #1901	C₂×C₁₉	semidirect
254. #1901	C₂×C₁₉	semidirect
255. #1822	C₂×C₁₉	semidirect
256. #1821	C₂×C₁₉	semidirect
257. #1801	C₂×C₁₉	semidirect
258. C₄×#101	C₂×C₁₉	semidirect
259. #1742	C₂×C₁₉	semidirect
260. C₂×#343	C₂×C₁₉	semidirect
405. C₁₉	#22480	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×#552	2
D₄×M₁₆×C₁₉	2
C₁₉×#1998	2
C₁₉×#1901	2
C₁₉×#1822	2
C₁₉×#1821	2
C₁₉×#1801	2
C₄×C₁₉×#101	2
C₁₉×#1742	2
C₂×C₁₉×#343	2
#22480	19

Subgroups — C19×#22480 #18028439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22480 #18028439