Subgroups — C₁₉×#24501 #18030460

Order 4864.

1208 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#450	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#390	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2065	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2055	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1968	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1934	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1786	C₂	1	1	yes	maximal, characteristic
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
17	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#450	—	2	4	no	—
20	C₁₉×#431	—	2	4	no	—
21	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
23	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
24	C₂×C₁₉×#102	C₂²	1	2	yes	—
25	C₂×C₁₉×#102	C₂²	1	2	yes	—
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	complemented
30	C₁₉×#391	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#391	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#390	—	2	1	no	—
33	C₁₉×#390	—	2	1	no	—
34	C₁₉×#390	C₂²	1	2	yes	—
35	C₁₉×#390	C₂²	1	2	yes	—
36	C₁₉×#389	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#389	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#387	—	2	1	no	—
39	C₁₉×#387	—	2	1	no	—
40	C₁₉×#385	—	2	1	no	—
41	C₁₉×#381	—	2	1	no	—
42	C₁₉×#380	C₂²	1	1	yes	characteristic
43	C₁₉×#340	C₂²	1	2	yes	complemented
44	C₁₉×#340	C₂²	1	2	yes	complemented
45	C₂⁵×C₁₉	—	2	1	no	—
46	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	—	2	4	no	—
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	—	2	2	no	—
50	C₂²×D₄×C₁₉	—	2	2	no	—
51	C₂²×D₄×C₁₉	—	4	2	no	—
52	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₉	—	2	1	no	—
54	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂×SD₁₆×C₁₉	—	2	4	no	—
58	C₂×SD₁₆×C₁₉	—	2	4	no	—
59	C₂×SD₁₆×C₁₉	—	4	2	no	—
60	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
62	C₁₉×C₂²⋊Q₈	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
81	C₂×C₄²×C₁₉	—	2	2	no	—
82	C₂×C₄²×C₁₉	—	2	2	no	—
83	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
87	C₁₉×#106	—	4	2	no	—
88	C₁₉×C₄⋊C₈	—	2	4	no	—
89	C₁₉×#103	—	4	2	no	—
90	C₁₉×#102	—	2	4	no	—
91	C₁₉×#102	—	2	4	no	—
92	C₁₉×#102	—	4	2	no	—
93	C₁₉×C₂²⋊C₈	—	2	2	no	—
94	C₁₉×C₂²⋊C₈	D₄	1	4	yes	—
95	C₄×C₈×C₁₉	—	2	4	no	—
96	C₁₉×#95	—	2	1	no	—
97	C₁₉×#95	—	2	1	no	—
98	C₁₉×#95	—	2	1	no	—
99	C₁₉×#95	—	2	1	no	—
100	C₁₉×#95	—	2	1	no	—
101	C₁₉×#95	—	2	1	no	—
102	C₁₉×#95	—	2	1	no	—
103	C₂⁴×C₁₉	—	2	4	no	—
104	C₂⁴×C₁₉	—	2	2	no	—
105	C₂⁴×C₁₉	—	4	2	no	—
106	C₂⁴×C₁₉	—	4	2	no	—
107	C₂⁴×C₁₉	—	4	2	no	—
108	C₂⁴×C₁₉	—	4	2	no	—
109	C₂⁴×C₁₉	—	4	2	no	—
110	C₂⁴×C₁₉	—	4	2	no	—
111	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	4	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	4	8	no	—
123	C₂×D₄×C₁₉	—	4	8	no	—
124	C₂×D₄×C₁₉	—	4	2	no	—
125	C₂×D₄×C₁₉	—	4	2	no	—
126	C₂×D₄×C₁₉	#41	1	4	yes	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	4	1	no	—
139	C₂²×C₄×C₁₉	—	4	2	no	—
140	C₂²×C₄×C₁₉	—	4	2	no	—
141	C₂²×C₄×C₁₉	—	4	2	no	—
142	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	complemented
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	#41	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
151	SD₁₆×C₁₉	—	4	8	no	—
152	C₂×C₈×C₁₉	—	2	2	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₂×C₈×C₁₉	—	2	2	no	—
156	C₂×C₈×C₁₉	—	2	2	no	—
157	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	4	2	no	—
165	C₄⋊C₄×C₁₉	—	4	2	no	—
166	C₄⋊C₄×C₁₉	—	4	2	no	—
167	C₄⋊C₄×C₁₉	—	4	2	no	—
168	C₂²⋊C₄×C₁₉	—	4	4	no	—
169	C₂²⋊C₄×C₁₉	—	4	2	no	—
170	C₂²⋊C₄×C₁₉	—	4	2	no	—
171	C₂²⋊C₄×C₁₉	—	4	4	no	—
172	C₂²⋊C₄×C₁₉	—	4	4	no	—
173	C₂²⋊C₄×C₁₉	—	4	4	no	—
174	C₄²×C₁₉	—	2	2	no	—
175	C₄²×C₁₉	—	2	2	no	—
176	C₄²×C₁₉	—	2	1	no	—
177	C₄²×C₁₉	—	2	1	no	—
178	C₄²×C₁₉	—	2	1	no	—
179	C₄²×C₁₉	—	2	1	no	—
180	#24501	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	4	no	—
186	C₂³×C₁₉	—	4	8	no	—
187	C₂³×C₁₉	—	4	8	no	—
188	C₂³×C₁₉	—	4	8	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	2	no	—
191	C₂³×C₁₉	—	4	2	no	—
192	C₂³×C₁₉	—	4	2	no	—
193	C₂³×C₁₉	—	4	2	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	8	4	no	—
196	C₂³×C₁₉	—	8	4	no	—
197	C₂³×C₁₉	—	8	4	no	—
198	C₂³×C₁₉	—	8	4	no	—
199	C₂³×C₁₉	#121	1	2	yes	—
200	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
201	C₂³×C₁₉	#135	1	2	yes	—
202	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
203	Q₈×C₁₉	—	4	2	no	—
204	Q₈×C₁₉	—	4	2	no	—
205	D₄×C₁₉	—	2	4	no	—
206	D₄×C₁₉	—	2	4	no	—
207	D₄×C₁₉	—	4	8	no	—
208	D₄×C₁₉	—	4	2	no	—
209	D₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	2	1	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	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	8	no	—
219	C₂×C₄×C₁₉	—	2	4	no	—
220	C₂×C₄×C₁₉	—	2	4	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	4	4	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	8	4	no	—
241	C₂×C₄×C₁₉	#121	1	2	yes	—
242	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
243	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
244	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
245	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
247	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
249	C₈×C₁₉	—	2	4	no	—
250	C₈×C₁₉	—	4	2	no	—
251	C₂×#450	C₂×C₁₉	1	1	yes	characteristic
252	C₂×#431	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#2855	C₂×C₁₉	1	1	yes	characteristic, complemented
254	C₂×#390	C₂×C₁₉	1	1	yes	characteristic
255	#2065	C₂×C₁₉	1	2	yes	complemented
256	#2055	C₂×C₁₉	1	2	yes	complemented
257	#1968	C₂×C₁₉	1	2	yes	complemented
258	#1934	C₂×C₁₉	1	2	yes	complemented
259	#1872	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1853	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1786	C₂×C₁₉	1	1	yes	characteristic
262	C₂²×C₁₉	—	2	2	no	—
263	C₂²×C₁₉	—	2	2	no	—
264	C₂²×C₁₉	—	2	2	no	—
265	C₂²×C₁₉	—	2	2	no	—
266	C₂²×C₁₉	—	2	2	no	—
267	C₂²×C₁₉	—	2	2	no	—
268	C₂²×C₁₉	—	4	4	no	—
269	C₂²×C₁₉	—	4	4	no	—
270	C₂²×C₁₉	—	4	4	no	—
271	C₂²×C₁₉	—	8	16	no	—
272	C₂²×C₁₉	—	8	2	no	—
273	C₂²×C₁₉	—	8	2	no	—
274	C₂²×C₁₉	—	8	2	no	—
275	C₂²×C₁₉	—	8	2	no	—
276	C₂²×C₁₉	#465	1	4	yes	—
277	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
278	C₂²×C₁₉	#525	1	1	yes	characteristic
279	C₂²×C₁₉	#535	1	1	yes	characteristic
280	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
281	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
282	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
283	C₂²×C₁₉	#575	1	1	yes	characteristic
284	C₄×C₁₉	—	2	2	no	—
285	C₄×C₁₉	—	2	2	no	—
286	C₄×C₁₉	—	2	2	no	—
287	C₄×C₁₉	—	2	2	no	—
288	C₄×C₁₉	—	4	1	no	—
289	C₄×C₁₉	—	8	1	no	—
290	C₄×C₁₉	—	8	1	no	—
291	C₄×C₁₉	—	8	2	no	—
292	C₄×C₁₉	—	8	1	no	—
293	C₄×C₁₉	—	8	1	no	—
294	C₄×C₁₉	#546	1	2	yes	—
295	C₄×C₁₉	#551	1	2	yes	—
296	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
297	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
298	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
299	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
300	C₂²×C₂²⋊C₄	—	2	1	no	—
301	C₂²×C₂²⋊C₄	—	2	1	no	—
302	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
303	#450	—	2	4	no	—
304	#431	—	2	4	no	—
305	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
306	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
307	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
308	C₂×#102	C₂²×C₁₉	1	2	yes	—
309	C₂×#102	C₂²×C₁₉	1	2	yes	—
310	C₂×#102	C₂²×C₁₉	1	2	yes	—
311	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
312	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
313	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	complemented
314	#391	C₂²×C₁₉	1	1	yes	characteristic, complemented
315	#391	C₂²×C₁₉	1	1	yes	characteristic, complemented
316	#390	—	2	1	no	—
317	#390	—	2	1	no	—
318	#390	C₂²×C₁₉	1	2	yes	—
319	#390	C₂²×C₁₉	1	2	yes	—
320	#389	C₂²×C₁₉	1	1	yes	characteristic, complemented
321	#389	C₂²×C₁₉	1	1	yes	characteristic, complemented
322	#387	—	2	1	no	—
323	#387	—	2	1	no	—
324	#385	—	2	1	no	—
325	#381	—	2	1	no	—
326	#380	C₂²×C₁₉	1	1	yes	characteristic
327	#340	C₂²×C₁₉	1	2	yes	complemented
328	#340	C₂²×C₁₉	1	2	yes	complemented
329	C₂×C₁₉	—	2	4	no	—
330	C₂×C₁₉	—	8	4	no	—
331	C₂×C₁₉	#2411	1	1	yes	characteristic
332	C₂×C₁₉	C₂×#465	1	1	yes	characteristic
333	C₂×C₁₉	#3055	1	1	yes	characteristic
334	C₂×C₁₉	#3101	1	1	yes	characteristic
335	C₂×C₁₉	#3105	1	1	yes	characteristic
336	C₂×C₁₉	#3208	1	1	yes	characteristic
337	C₂×C₁₉	#3211	1	1	yes	characteristic
338	C₂⁵	—	2	1	no	—
339	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
340	C₂²×D₄	—	2	4	no	—
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	—	2	2	no	—
343	C₂²×D₄	—	2	2	no	—
344	C₂²×D₄	—	4	2	no	—
345	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
346	C₂³×C₄	—	2	1	no	—
347	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
348	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
349	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
350	C₂×SD₁₆	—	2	4	no	—
351	C₂×SD₁₆	—	2	4	no	—
352	C₂×SD₁₆	—	4	2	no	—
353	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
354	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
355	C₂²⋊Q₈	—	2	2	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	4	2	no	—
362	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	—	2	2	no	—
372	C₂×C₂²⋊C₄	—	4	4	no	—
373	C₂×C₂²⋊C₄	—	4	4	no	—
374	C₂×C₄²	—	2	2	no	—
375	C₂×C₄²	—	2	2	no	—
376	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
377	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
378	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
380	#106	—	4	2	no	—
381	C₄⋊C₈	—	2	4	no	—
382	#103	—	4	2	no	—
383	#102	—	2	4	no	—
384	#102	—	2	4	no	—
385	#102	—	4	2	no	—
386	C₂²⋊C₈	—	2	2	no	—
387	C₂²⋊C₈	D₄×C₁₉	1	4	yes	—
388	C₄×C₈	—	2	4	no	—
389	#95	—	2	1	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	C₁₉	#24501	1	1	yes	characteristic, direct product factor, Sylow
397	C₂⁴	—	2	4	no	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	—	4	2	no	—
400	C₂⁴	—	4	2	no	—
401	C₂⁴	—	4	2	no	—
402	C₂⁴	—	4	2	no	—
403	C₂⁴	—	4	2	no	—
404	C₂⁴	—	4	2	no	—
405	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	4	8	no	—
417	C₂×D₄	—	4	8	no	—
418	C₂×D₄	—	4	2	no	—
419	C₂×D₄	—	4	2	no	—
420	C₂×D₄	#41×C₁₉	1	4	yes	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	—	4	2	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	SD₁₆×C₁₉	1	4	yes	complemented
437	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
440	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₂²×C₄	#41×C₁₉	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
445	SD₁₆	—	4	8	no	—
446	C₂×C₈	—	2	2	no	—
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	C₂×D₄×C₁₉	1	4	yes	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	—	4	2	no	—
460	C₄⋊C₄	—	4	2	no	—
461	C₄⋊C₄	—	4	2	no	—
462	C₂²⋊C₄	—	4	4	no	—
463	C₂²⋊C₄	—	4	2	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₂²⋊C₄	—	4	4	no	—
467	C₂²⋊C₄	—	4	4	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	4	8	no	—
480	C₂³	—	4	8	no	—
481	C₂³	—	4	8	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	8	4	no	—
489	C₂³	—	8	4	no	—
490	C₂³	—	8	4	no	—
491	C₂³	—	8	4	no	—
492	C₂³	C₁₉×#121	1	2	yes	—
493	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
494	C₂³	C₁₉×#135	1	2	yes	—
495	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
496	Q₈	—	4	2	no	—
497	Q₈	—	4	2	no	—
498	D₄	—	2	4	no	—
499	D₄	—	2	4	no	—
500	D₄	—	4	8	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	2	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	8	4	no	—
534	C₂×C₄	C₁₉×#121	1	2	yes	—
535	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
536	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
537	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
538	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
539	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
540	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
541	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
542	C₈	—	2	4	no	—
543	C₈	—	4	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	8	16	no	—
554	C₂²	—	8	2	no	—
555	C₂²	—	8	2	no	—
556	C₂²	—	8	2	no	—
557	C₂²	—	8	2	no	—
558	C₂²	C₁₉×#465	1	4	yes	—
559	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
560	C₂²	C₁₉×#525	1	1	yes	characteristic
561	C₂²	C₁₉×#535	1	1	yes	characteristic
562	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
563	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
564	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
565	C₂²	C₁₉×#575	1	1	yes	characteristic
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	4	1	no	—
571	C₄	—	8	1	no	—
572	C₄	—	8	2	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	1	no	—
575	C₄	—	8	1	no	—
576	C₄	C₁₉×#546	1	2	yes	—
577	C₄	C₁₉×#551	1	2	yes	—
578	C₂	—	2	4	no	—
579	C₂	—	8	4	no	—
580	C₂	C₁₉×#2411	1	1	yes	characteristic
581	C₂	C₂×C₁₉×#465	1	1	yes	characteristic
582	C₂	C₁₉×#3055	1	1	yes	characteristic
583	C₂	C₁₉×#3101	1	1	yes	characteristic
584	C₂	C₁₉×#3105	1	1	yes	characteristic
585	C₂	C₁₉×#3208	1	1	yes	characteristic
586	C₂	C₁₉×#3211	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#431	C₂	semidirect
3. C₁₉×#2855	C₂	semidirect
5. C₁₉×#2065	C₂	semidirect
6. C₁₉×#2055	C₂	semidirect
7. C₁₉×#1968	C₂	semidirect
8. C₁₉×#1934	C₂	semidirect
9. C₁₉×#1872	C₂	semidirect
10. C₁₉×#1853	C₂	semidirect
21. C₂×C₁₉×#106	C₂²	semidirect
22. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
23. C₂×C₁₉×#103	C₂²	semidirect
29. C₂×C₄×C₈×C₁₉	C₂²	semidirect
30. C₁₉×#391	C₂²	semidirect
31. C₁₉×#391	C₂²	semidirect
36. C₁₉×#389	C₂²	semidirect
37. C₁₉×#389	C₂²	semidirect
43. C₁₉×#340	C₂²	semidirect
44. C₁₉×#340	C₂²	semidirect
142. C₂²×C₄×C₁₉	SD₁₆	semidirect
180. #24501	C₁₉	direct (N × H)
252. C₂×#431	C₂×C₁₉	semidirect
253. #2855	C₂×C₁₉	semidirect
255. #2065	C₂×C₁₉	semidirect
256. #2055	C₂×C₁₉	semidirect
257. #1968	C₂×C₁₉	semidirect
258. #1934	C₂×C₁₉	semidirect
259. #1872	C₂×C₁₉	semidirect
260. #1853	C₂×C₁₉	semidirect
305. C₂×#106	C₂²×C₁₉	semidirect
306. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
307. C₂×#103	C₂²×C₁₉	semidirect
313. C₂×C₄×C₈	C₂²×C₁₉	semidirect
314. #391	C₂²×C₁₉	semidirect
315. #391	C₂²×C₁₉	semidirect
320. #389	C₂²×C₁₉	semidirect
321. #389	C₂²×C₁₉	semidirect
327. #340	C₂²×C₁₉	semidirect
328. #340	C₂²×C₁₉	semidirect
396. C₁₉	#24501	direct (N × H)
436. C₂²×C₄	SD₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#450	2
C₂×C₁₉×#431	2
C₁₉×#2855	2
C₂×C₁₉×#390	2
C₁₉×#2065	2
C₁₉×#2055	2
C₁₉×#1968	2
C₁₉×#1934	2
C₁₉×#1872	2
C₁₉×#1853	2
C₁₉×#1786	2
#24501	19

Subgroups — C19×#24501 #18030460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24501 #18030460