Subgroups — C₁₉×#14551 #18020510

Order 4864.

1642 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#399	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#389	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#385	C₂	1	2	yes	maximal
4	C₁₉×#1445	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1441	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1439	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1437	C₂	1	2	yes	maximal
8	C₁₉×#1436	C₂	1	2	yes	maximal, complemented
9	C₁₉×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
10	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
21	C₁₉×#399	C₄	1	8	yes	complemented
22	C₁₉×#389	—	2	8	no	—
23	C₁₉×#385	—	2	8	no	—
24	C₂×C₁₉×#95	C₂²	1	2	yes	—
25	C₂×C₁₉×#95	C₂²	1	2	yes	—
26	C₂×C₁₉×#95	C₂²	1	2	yes	—
27	C₂×C₁₉×#95	C₂²	1	2	yes	—
28	C₂×C₁₉×#95	C₂²	1	2	yes	—
29	C₂×C₁₉×#95	C₂²	1	2	yes	—
30	C₂×C₁₉×#95	C₂²	1	2	yes	—
31	C₂×C₁₉×#95	C₂²	1	2	yes	—
32	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
34	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	—	2	2	no	—
36	C₂³×C₄×C₁₉	—	2	4	no	—
37	C₂³×C₄×C₁₉	—	4	1	no	—
38	C₂³×C₄×C₁₉	—	4	1	no	—
39	C₂³×C₄×C₁₉	—	4	2	no	—
40	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
59	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
60	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
61	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
72	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
73	C₂×C₂²⋊C₄×C₁₉	Q₈	1	4	yes	—
74	C₂×C₄²×C₁₉	—	2	4	no	—
75	C₂×C₄²×C₁₉	—	4	2	no	—
76	C₂×C₄²×C₁₉	—	4	2	no	—
77	C₁₉×#95	—	2	4	no	—
78	C₁₉×#95	—	2	4	no	—
79	C₁₉×#95	—	2	4	no	—
80	C₁₉×#95	—	2	4	no	—
81	C₁₉×#95	—	2	4	no	—
82	C₁₉×#95	—	4	2	no	—
83	C₁₉×#95	—	4	2	no	—
84	C₁₉×#95	—	4	1	no	—
85	C₁₉×#95	—	4	2	no	—
86	C₁₉×#95	C₂×C₄	1	4	yes	complemented
87	C₂⁴×C₁₉	—	2	2	no	—
88	C₂⁴×C₁₉	—	2	2	no	—
89	C₂⁴×C₁₉	—	2	1	no	—
90	C₂⁴×C₁₉	—	2	1	no	—
91	C₂⁴×C₁₉	—	2	1	no	—
92	C₂⁴×C₁₉	—	2	2	no	—
93	C₂⁴×C₁₉	—	2	1	no	—
94	C₂⁴×C₁₉	—	2	2	no	—
95	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
96	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
97	C₂⁴×C₁₉	#41	1	2	yes	—
98	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	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	1	no	—
120	C₂²×C₄×C₁₉	—	2	1	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	2	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
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	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	4	4	no	—
143	C₂²×C₄×C₁₉	—	4	8	no	—
144	C₂²×C₄×C₁₉	—	4	8	no	—
145	C₂²×C₄×C₁₉	—	4	4	no	—
146	C₂²×C₄×C₁₉	—	4	4	no	—
147	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
148	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
155	C₂²×C₄×C₁₉	#41	1	4	yes	—
156	C₄⋊C₄×C₁₉	—	2	16	no	—
157	C₄⋊C₄×C₁₉	—	4	4	no	—
158	C₄⋊C₄×C₁₉	—	4	8	no	—
159	C₄⋊C₄×C₁₉	—	4	4	no	—
160	C₄⋊C₄×C₁₉	—	4	8	no	—
161	C₂²⋊C₄×C₁₉	—	2	16	no	—
162	C₂²⋊C₄×C₁₉	—	4	4	no	—
163	C₂²⋊C₄×C₁₉	—	4	4	no	—
164	C₂²⋊C₄×C₁₉	—	4	8	no	—
165	C₄²×C₁₉	—	4	8	no	—
166	#14551	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₁₉	—	2	4	no	—
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	2	2	no	—
170	C₂³×C₁₉	—	2	4	no	—
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	2	4	no	—
176	C₂³×C₁₉	—	2	4	no	—
177	C₂³×C₁₉	—	2	4	no	—
178	C₂³×C₁₉	—	2	4	no	—
179	C₂³×C₁₉	—	4	2	no	—
180	C₂³×C₁₉	—	4	2	no	—
181	C₂³×C₁₉	—	4	2	no	—
182	C₂³×C₁₉	—	4	2	no	—
183	C₂³×C₁₉	—	4	1	no	—
184	C₂³×C₁₉	—	4	2	no	—
185	C₂³×C₁₉	—	4	1	no	—
186	C₂³×C₁₉	—	4	1	no	—
187	C₂³×C₁₉	—	4	2	no	—
188	C₂³×C₁₉	—	4	1	no	—
189	C₂³×C₁₉	C₄×Q₈	1	4	yes	—
190	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
191	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
192	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
193	C₂³×C₁₉	C₂×#41	1	2	yes	—
194	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
195	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
199	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
200	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	4	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	2	4	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	4	no	—
209	C₂×C₄×C₁₉	—	2	4	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	2	4	no	—
214	C₂×C₄×C₁₉	—	2	4	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	2	4	no	—
217	C₂×C₄×C₁₉	—	2	4	no	—
218	C₂×C₄×C₁₉	—	2	4	no	—
219	C₂×C₄×C₁₉	—	2	4	no	—
220	C₂×C₄×C₁₉	—	2	4	no	—
221	C₂×C₄×C₁₉	—	2	4	no	—
222	C₂×C₄×C₁₉	—	2	4	no	—
223	C₂×C₄×C₁₉	—	4	16	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	2	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	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	4	2	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	4	2	no	—
250	C₂×C₄×C₁₉	—	4	2	no	—
251	C₂×C₄×C₁₉	—	4	2	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
254	C₂×#399	C₂×C₁₉	1	1	yes	characteristic
255	C₂×#389	C₂×C₁₉	1	2	yes	complemented
256	C₂×#385	C₂×C₁₉	1	2	yes	—
257	#1445	C₂×C₁₉	1	2	yes	complemented
258	#1441	C₂×C₁₉	1	2	yes	complemented
259	#1439	C₂×C₁₉	1	1	yes	characteristic
260	#1437	C₂×C₁₉	1	2	yes	—
261	#1436	C₂×C₁₉	1	2	yes	complemented
262	C₂²⋊#95	C₂×C₁₉	1	1	yes	characteristic
263	C₂²×C₁₉	—	2	4	no	—
264	C₂²×C₁₉	—	2	8	no	—
265	C₂²×C₁₉	—	4	4	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	—	4	4	no	—
271	C₂²×C₁₉	—	4	4	no	—
272	C₂²×C₁₉	—	4	2	no	—
273	C₂²×C₁₉	—	4	2	no	—
274	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
275	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
276	C₂²×C₁₉	#518	1	1	yes	characteristic
277	C₂²×C₁₉	#520	1	1	yes	characteristic
278	C₂²×C₁₉	#520	1	2	yes	—
279	C₂²×C₁₉	#534	1	2	yes	—
280	C₂²×C₁₉	#536	1	2	yes	—
281	C₂²×C₁₉	#538	1	1	yes	characteristic
282	C₂²×C₁₉	#539	1	2	yes	—
283	C₂²×C₁₉	#539	1	2	yes	—
284	C₂²×C₁₉	#539	1	1	yes	characteristic
285	C₂²×C₁₉	#543	1	1	yes	characteristic
286	C₂²×C₁₉	#544	1	1	yes	characteristic
287	C₂²×C₁₉	D₄²	1	1	yes	characteristic
288	C₂²×C₁₉	#546	1	2	yes	—
289	C₂²×C₁₉	D₄×Q₈	1	2	yes	—
290	C₂²×C₁₉	#550	1	2	yes	—
291	C₂²×C₁₉	#552	1	2	yes	—
292	C₂²×C₁₉	#554	1	2	yes	—
293	C₂²×C₁₉	#559	1	1	yes	characteristic
294	C₂²×C₁₉	#560	1	1	yes	characteristic
295	C₂²×C₁₉	#562	1	2	yes	—
296	C₂²×C₁₉	#563	1	1	yes	characteristic
297	C₄×C₁₉	—	2	8	no	—
298	C₄×C₁₉	—	4	4	no	—
299	C₄×C₁₉	—	4	2	no	—
300	C₄×C₁₉	—	4	2	no	—
301	C₄×C₁₉	—	4	4	no	—
302	C₄×C₁₉	—	4	4	no	—
303	C₄×C₁₉	—	4	4	no	—
304	C₄×C₁₉	—	8	2	no	—
305	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
306	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
307	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
308	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
309	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
310	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
311	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
312	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
313	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
314	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
315	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
316	#399	C₄×C₁₉	1	8	yes	complemented
317	#389	—	2	8	no	—
318	#385	—	2	8	no	—
319	C₂×#95	C₂²×C₁₉	1	2	yes	—
320	C₂×#95	C₂²×C₁₉	1	2	yes	—
321	C₂×#95	C₂²×C₁₉	1	2	yes	—
322	C₂×#95	C₂²×C₁₉	1	2	yes	—
323	C₂×#95	C₂²×C₁₉	1	2	yes	—
324	C₂×#95	C₂²×C₁₉	1	2	yes	—
325	C₂×#95	C₂²×C₁₉	1	2	yes	—
326	C₂×#95	C₂²×C₁₉	1	2	yes	—
327	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
328	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
329	C₂×C₁₉	—	4	4	no	—
330	C₂×C₁₉	#2322	1	2	yes	—
331	C₂×C₁₉	#2329	1	1	yes	characteristic
332	C₂×C₁₉	#2360	1	2	yes	—
333	C₂×C₁₉	#2366	1	1	yes	characteristic
334	C₂×C₁₉	#2376	1	1	yes	characteristic
335	C₂×C₁₉	#2668	1	1	yes	characteristic
336	C₂×C₁₉	#2677	1	1	yes	characteristic
337	C₂×C₁₉	#2694	1	2	yes	—
338	C₂×C₁₉	#2732	1	2	yes	—
339	C₂×C₁₉	#2771	1	1	yes	characteristic
340	C₂×C₁₉	#2807	1	1	yes	characteristic
341	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
342	C₂³×C₄	—	2	2	no	—
343	C₂³×C₄	—	2	4	no	—
344	C₂³×C₄	—	4	2	no	—
345	C₂³×C₄	—	4	1	no	—
346	C₂³×C₄	—	4	1	no	—
347	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
348	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
349	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
352	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
353	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
354	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
355	C₂×C₄⋊C₄	—	2	4	no	—
356	C₂×C₄⋊C₄	—	2	4	no	—
357	C₂×C₄⋊C₄	—	2	4	no	—
358	C₂×C₄⋊C₄	—	2	4	no	—
359	C₂×C₄⋊C₄	—	2	4	no	—
360	C₂×C₄⋊C₄	—	4	1	no	—
361	C₂×C₄⋊C₄	—	4	1	no	—
362	C₂×C₄⋊C₄	—	4	2	no	—
363	C₂×C₄⋊C₄	—	4	2	no	—
364	C₂×C₄⋊C₄	—	4	1	no	—
365	C₂×C₄⋊C₄	—	4	2	no	—
366	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
367	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
368	C₂×C₄⋊C₄	D₄×C₁₉	1	8	yes	—
369	C₂×C₂²⋊C₄	—	2	4	no	—
370	C₂×C₂²⋊C₄	—	2	4	no	—
371	C₂×C₂²⋊C₄	—	2	4	no	—
372	C₂×C₂²⋊C₄	—	2	4	no	—
373	C₂×C₂²⋊C₄	—	4	1	no	—
374	C₂×C₂²⋊C₄	—	4	1	no	—
375	C₂×C₂²⋊C₄	—	4	1	no	—
376	C₂×C₂²⋊C₄	—	4	1	no	—
377	C₂×C₂²⋊C₄	—	4	2	no	—
378	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
379	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
380	C₂×C₂²⋊C₄	Q₈×C₁₉	1	4	yes	—
381	C₂×C₄²	—	2	4	no	—
382	C₂×C₄²	—	4	2	no	—
383	C₂×C₄²	—	4	2	no	—
384	#95	—	2	4	no	—
385	#95	—	2	4	no	—
386	#95	—	2	4	no	—
387	#95	—	2	4	no	—
388	#95	—	2	4	no	—
389	#95	—	4	2	no	—
390	#95	—	4	2	no	—
391	#95	—	4	2	no	—
392	#95	—	4	1	no	—
393	#95	C₂×C₄×C₁₉	1	4	yes	complemented
394	C₁₉	#14551	1	1	yes	characteristic, direct product factor, Sylow
395	C₂⁴	—	2	2	no	—
396	C₂⁴	—	2	2	no	—
397	C₂⁴	—	2	1	no	—
398	C₂⁴	—	2	1	no	—
399	C₂⁴	—	2	1	no	—
400	C₂⁴	—	2	2	no	—
401	C₂⁴	—	2	1	no	—
402	C₂⁴	—	2	2	no	—
403	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
404	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
405	C₂⁴	#41×C₁₉	1	2	yes	—
406	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
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	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	4	4	no	—
451	C₂²×C₄	—	4	8	no	—
452	C₂²×C₄	—	4	8	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	—	4	4	no	—
455	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
456	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
457	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
458	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
459	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
460	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
461	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
462	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
463	C₂²×C₄	#41×C₁₉	1	4	yes	—
464	C₄⋊C₄	—	2	16	no	—
465	C₄⋊C₄	—	4	4	no	—
466	C₄⋊C₄	—	4	8	no	—
467	C₄⋊C₄	—	4	4	no	—
468	C₄⋊C₄	—	4	8	no	—
469	C₂²⋊C₄	—	2	16	no	—
470	C₂²⋊C₄	—	4	4	no	—
471	C₂²⋊C₄	—	4	4	no	—
472	C₂²⋊C₄	—	4	8	no	—
473	C₄²	—	4	8	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	1	no	—
496	C₂³	C₄×Q₈×C₁₉	1	4	yes	—
497	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
498	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
499	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
500	C₂³	C₂×#41×C₁₉	1	2	yes	—
501	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
502	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
503	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
504	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
505	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
506	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
507	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	4	16	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
561	C₂²	—	2	4	no	—
562	C₂²	—	2	8	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	2	no	—
572	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
573	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
574	C₂²	C₁₉×#518	1	1	yes	characteristic
575	C₂²	C₁₉×#520	1	1	yes	characteristic
576	C₂²	C₁₉×#520	1	2	yes	—
577	C₂²	C₁₉×#534	1	2	yes	—
578	C₂²	C₁₉×#536	1	2	yes	—
579	C₂²	C₁₉×#538	1	1	yes	characteristic
580	C₂²	C₁₉×#539	1	1	yes	characteristic
581	C₂²	C₁₉×#539	1	2	yes	—
582	C₂²	C₁₉×#539	1	2	yes	—
583	C₂²	C₁₉×#543	1	1	yes	characteristic
584	C₂²	C₁₉×#544	1	1	yes	characteristic
585	C₂²	D₄²×C₁₉	1	1	yes	characteristic
586	C₂²	C₁₉×#546	1	2	yes	—
587	C₂²	D₄×Q₈×C₁₉	1	2	yes	—
588	C₂²	C₁₉×#550	1	2	yes	—
589	C₂²	C₁₉×#552	1	2	yes	—
590	C₂²	C₁₉×#554	1	2	yes	—
591	C₂²	C₁₉×#559	1	1	yes	characteristic
592	C₂²	C₁₉×#560	1	1	yes	characteristic
593	C₂²	C₁₉×#562	1	2	yes	—
594	C₂²	C₁₉×#563	1	1	yes	characteristic
595	C₄	—	2	8	no	—
596	C₄	—	4	4	no	—
597	C₄	—	4	4	no	—
598	C₄	—	4	4	no	—
599	C₄	—	4	4	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	8	2	no	—
603	C₂	—	4	4	no	—
604	C₂	C₁₉×#2322	1	2	yes	—
605	C₂	C₁₉×#2329	1	1	yes	characteristic
606	C₂	C₁₉×#2360	1	2	yes	—
607	C₂	C₁₉×#2366	1	1	yes	characteristic
608	C₂	C₁₉×#2376	1	1	yes	characteristic
609	C₂	C₁₉×#2668	1	1	yes	characteristic
610	C₂	C₁₉×#2677	1	1	yes	characteristic
611	C₂	C₁₉×#2694	1	2	yes	—
612	C₂	C₁₉×#2732	1	2	yes	—
613	C₂	C₁₉×#2771	1	1	yes	characteristic
614	C₂	C₁₉×#2807	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#389	C₂	semidirect
4. C₁₉×#1445	C₂	semidirect
5. C₁₉×#1441	C₂	semidirect
8. C₁₉×#1436	C₂	semidirect
21. C₁₉×#399	C₄	semidirect
59. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
60. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
86. C₁₉×#95	C₂×C₄	semidirect
166. #14551	C₁₉	direct (N × H)
255. C₂×#389	C₂×C₁₉	semidirect
257. #1445	C₂×C₁₉	semidirect
258. #1441	C₂×C₁₉	semidirect
261. #1436	C₂×C₁₉	semidirect
316. #399	C₄×C₁₉	semidirect
366. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
367. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
393. #95	C₂×C₄×C₁₉	semidirect
394. C₁₉	#14551	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×#399	2
C₂×C₁₉×#389	2
C₂×C₁₉×#385	2
C₁₉×#1445	2
C₁₉×#1441	2
C₁₉×#1439	2
C₁₉×#1437	2
C₁₉×#1436	2
C₁₉×C₂²⋊#95	2
#14551	19

Subgroups — C19×#14551 #18020510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14551 #18020510