Subgroups — C₁₉×#14240 #18020199

Order 4864.

1638 conjugacy classes of subgroups.

The subgroup lattice has 656 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×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1445	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1442	C₂	1	1	yes	maximal, characteristic, 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×#1436	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1434	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×C₂²⋊#95	C₂	1	2	yes	maximal
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
23	C₁₉×#399	C₄	1	8	yes	complemented
24	C₄×C₄⋊C₄×C₁₉	—	2	4	no	—
25	C₄×C₂²⋊C₄×C₁₉	—	2	4	no	—
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	1	yes	characteristic
31	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#95	C₂²	1	2	yes	—
33	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#95	C₂²	1	2	yes	—
35	C₂×C₁₉×#95	C₂²	1	2	yes	—
36	C₂×C₁₉×#95	C₂²	1	2	yes	—
37	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
38	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	—	2	2	no	—
40	C₂³×C₄×C₁₉	—	2	2	no	—
41	C₂³×C₄×C₁₉	—	2	2	no	—
42	C₂³×C₄×C₁₉	—	2	4	no	—
43	C₂³×C₄×C₁₉	—	4	2	no	—
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
60	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
61	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
62	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
72	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
73	C₂×C₂²⋊C₄×C₁₉	Q₈	1	4	yes	—
74	C₂×C₄²×C₁₉	—	2	4	no	—
75	C₂×C₄²×C₁₉	—	2	2	no	—
76	C₂×C₄²×C₁₉	—	2	4	no	—
77	C₂×C₄²×C₁₉	—	4	2	no	—
78	C₂×C₄²×C₁₉	—	4	2	no	—
79	C₂×C₄²×C₁₉	—	4	2	no	—
80	C₂×C₄²×C₁₉	D₄	1	4	yes	—
81	C₁₉×#95	—	2	2	no	—
82	C₁₉×#95	—	2	2	no	—
83	C₁₉×#95	—	2	4	no	—
84	C₁₉×#95	—	2	4	no	—
85	C₁₉×#95	—	2	4	no	—
86	C₁₉×#95	—	2	4	no	—
87	C₁₉×#95	—	2	4	no	—
88	C₁₉×#95	—	2	2	no	—
89	C₁₉×#95	—	4	2	no	—
90	C₁₉×#95	—	4	2	no	—
91	C₁₉×#95	—	4	2	no	—
92	C₁₉×#95	C₂×C₄	1	4	yes	complemented
93	C₂⁴×C₁₉	—	2	1	no	—
94	C₂⁴×C₁₉	—	2	1	no	—
95	C₂⁴×C₁₉	—	2	1	no	—
96	C₂⁴×C₁₉	—	2	2	no	—
97	C₂⁴×C₁₉	—	2	1	no	—
98	C₂⁴×C₁₉	—	2	2	no	—
99	C₂⁴×C₁₉	—	2	2	no	—
100	C₂⁴×C₁₉	—	2	2	no	—
101	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
102	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
103	C₂⁴×C₁₉	#41	1	2	yes	—
104	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
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	1	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	8	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	1	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	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	4	8	no	—
151	C₂²×C₄×C₁₉	—	4	8	no	—
152	C₂²×C₄×C₁₉	—	4	4	no	—
153	C₂²×C₄×C₁₉	—	4	4	no	—
154	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
156	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
157	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
158	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
162	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
163	C₂²×C₄×C₁₉	#41	1	4	yes	—
164	C₂²×C₄×C₁₉	#41	1	2	yes	—
165	C₂²×C₄×C₁₉	#41	1	2	yes	—
166	C₂²×C₄×C₁₉	#41	1	2	yes	—
167	C₂²×C₄×C₁₉	#41	1	4	yes	—
168	C₄⋊C₄×C₁₉	—	2	8	no	—
169	C₄⋊C₄×C₁₉	—	2	8	no	—
170	C₄⋊C₄×C₁₉	—	4	8	no	—
171	C₂²⋊C₄×C₁₉	—	2	8	no	—
172	C₂²⋊C₄×C₁₉	—	2	8	no	—
173	C₂²⋊C₄×C₁₉	—	4	8	no	—
174	C₂²⋊C₄×C₁₉	—	4	8	no	—
175	C₄²×C₁₉	—	2	8	no	—
176	C₄²×C₁₉	—	4	8	no	—
177	C₄²×C₁₉	—	4	4	no	—
178	#14240	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂³×C₁₉	—	2	2	no	—
180	C₂³×C₁₉	—	2	4	no	—
181	C₂³×C₁₉	—	2	2	no	—
182	C₂³×C₁₉	—	2	4	no	—
183	C₂³×C₁₉	—	2	2	no	—
184	C₂³×C₁₉	—	2	2	no	—
185	C₂³×C₁₉	—	2	2	no	—
186	C₂³×C₁₉	—	2	2	no	—
187	C₂³×C₁₉	—	2	4	no	—
188	C₂³×C₁₉	—	2	4	no	—
189	C₂³×C₁₉	—	2	4	no	—
190	C₂³×C₁₉	—	2	4	no	—
191	C₂³×C₁₉	—	4	1	no	—
192	C₂³×C₁₉	—	4	1	no	—
193	C₂³×C₁₉	—	4	2	no	—
194	C₂³×C₁₉	—	4	1	no	—
195	C₂³×C₁₉	—	4	1	no	—
196	C₂³×C₁₉	—	4	2	no	—
197	C₂³×C₁₉	—	4	2	no	—
198	C₂³×C₁₉	—	4	2	no	—
199	C₂³×C₁₉	—	4	2	no	—
200	C₂³×C₁₉	—	4	2	no	—
201	C₂³×C₁₉	C₄×Q₈	1	4	yes	—
202	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
203	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
204	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
205	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
206	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
207	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
208	C₂³×C₁₉	C₂×#41	1	2	yes	—
209	C₂³×C₁₉	C₂×#41	1	2	yes	—
210	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
211	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
212	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
213	C₂×C₄×C₁₉	—	2	4	no	—
214	C₂×C₄×C₁₉	—	2	2	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	4	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	4	no	—
222	C₂×C₄×C₁₉	—	2	4	no	—
223	C₂×C₄×C₁₉	—	2	4	no	—
224	C₂×C₄×C₁₉	—	2	4	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	4	no	—
227	C₂×C₄×C₁₉	—	2	4	no	—
228	C₂×C₄×C₁₉	—	2	4	no	—
229	C₂×C₄×C₁₉	—	2	4	no	—
230	C₂×C₄×C₁₉	—	2	4	no	—
231	C₂×C₄×C₁₉	—	2	4	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	4	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	4	no	—
237	C₂×C₄×C₁₉	—	2	4	no	—
238	C₂×C₄×C₁₉	—	2	4	no	—
239	C₂×C₄×C₁₉	—	2	4	no	—
240	C₂×C₄×C₁₉	—	4	16	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	4	1	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	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	2	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	4	2	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	—	4	2	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	4	2	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	2	no	—
260	C₂×C₄×C₁₉	—	4	2	no	—
261	C₂×C₄×C₁₉	—	4	2	no	—
262	C₂×C₄×C₁₉	—	4	2	no	—
263	C₂×C₄×C₁₉	—	4	2	no	—
264	C₂×C₄×C₁₉	—	4	2	no	—
265	C₂×C₄×C₁₉	—	4	2	no	—
266	C₂×C₄×C₁₉	—	4	2	no	—
267	C₂×C₄×C₁₉	—	4	2	no	—
268	C₂×C₄×C₁₉	—	4	2	no	—
269	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
270	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
271	C₂×C₄×C₁₉	#123	1	4	yes	—
272	C₂×#399	C₂×C₁₉	1	1	yes	characteristic
273	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
274	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
275	#1445	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1442	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1439	C₂×C₁₉	1	1	yes	characteristic
278	#1437	C₂×C₁₉	1	2	yes	—
279	#1436	C₂×C₁₉	1	2	yes	complemented
280	#1436	C₂×C₁₉	1	2	yes	complemented
281	#1434	C₂×C₁₉	1	1	yes	characteristic, complemented
282	C₂²⋊#95	C₂×C₁₉	1	2	yes	—
283	C₂²×C₁₉	—	2	8	no	—
284	C₂²×C₁₉	—	2	4	no	—
285	C₂²×C₁₉	—	4	2	no	—
286	C₂²×C₁₉	—	4	2	no	—
287	C₂²×C₁₉	—	4	2	no	—
288	C₂²×C₁₉	—	4	4	no	—
289	C₂²×C₁₉	—	4	2	no	—
290	C₂²×C₁₉	—	4	2	no	—
291	C₂²×C₁₉	—	4	4	no	—
292	C₂²×C₁₉	—	4	4	no	—
293	C₂²×C₁₉	—	4	2	no	—
294	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
295	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
296	C₂²×C₁₉	C₄×#41	1	2	yes	—
297	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
298	C₂²×C₁₉	#518	1	2	yes	—
299	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
300	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
301	C₂²×C₁₉	#525	1	1	yes	characteristic
302	C₂²×C₁₉	#525	1	1	yes	characteristic
303	C₂²×C₁₉	#529	1	1	yes	characteristic
304	C₂²×C₁₉	#529	1	2	yes	—
305	C₂²×C₁₉	#533	1	1	yes	characteristic
306	C₂²×C₁₉	#535	1	1	yes	characteristic
307	C₂²×C₁₉	#535	1	1	yes	characteristic
308	C₂²×C₁₉	#540	1	2	yes	—
309	C₂²×C₁₉	#551	1	2	yes	—
310	C₂²×C₁₉	#551	1	2	yes	—
311	C₂²×C₁₉	#551	1	2	yes	—
312	C₂²×C₁₉	#553	1	2	yes	—
313	C₂²×C₁₉	#553	1	2	yes	—
314	C₂²×C₁₉	#554	1	2	yes	—
315	C₂²×C₁₉	#554	1	2	yes	—
316	C₂²×C₁₉	#559	1	2	yes	—
317	C₄×C₁₉	—	2	4	no	—
318	C₄×C₁₉	—	2	4	no	—
319	C₄×C₁₉	—	2	4	no	—
320	C₄×C₁₉	—	4	2	no	—
321	C₄×C₁₉	—	4	2	no	—
322	C₄×C₁₉	—	4	4	no	—
323	C₄×C₁₉	—	4	4	no	—
324	C₄×C₁₉	—	4	4	no	—
325	C₄×C₁₉	—	4	2	no	—
326	C₄×C₁₉	—	8	2	no	—
327	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
328	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
329	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
330	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
331	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
332	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
333	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
334	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
335	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
336	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
337	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
338	#399	C₄×C₁₉	1	8	yes	complemented
339	C₄×C₄⋊C₄	—	2	4	no	—
340	C₄×C₂²⋊C₄	—	2	4	no	—
341	C₂×#95	C₂²×C₁₉	1	2	yes	—
342	C₂×#95	C₂²×C₁₉	1	2	yes	—
343	C₂×#95	C₂²×C₁₉	1	2	yes	—
344	C₂×#95	C₂²×C₁₉	1	2	yes	—
345	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
346	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
347	C₂×#95	C₂²×C₁₉	1	2	yes	—
348	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
349	C₂×#95	C₂²×C₁₉	1	2	yes	—
350	C₂×#95	C₂²×C₁₉	1	2	yes	—
351	C₂×#95	C₂²×C₁₉	1	2	yes	—
352	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
353	C₂×C₁₉	—	4	4	no	—
354	C₂×C₁₉	C₄×#123	1	1	yes	characteristic
355	C₂×C₁₉	C₄×C₂²⋊Q₈	1	1	yes	characteristic
356	C₂×C₁₉	#2328	1	1	yes	characteristic
357	C₂×C₁₉	#2368	1	2	yes	—
358	C₂×C₁₉	#2374	1	2	yes	—
359	C₂×C₁₉	#2482	1	1	yes	characteristic
360	C₂×C₁₉	#2487	1	1	yes	characteristic
361	C₂×C₁₉	#2516	1	2	yes	—
362	C₂×C₁₉	#2522	1	2	yes	—
363	C₂×C₁₉	#2580	1	1	yes	characteristic
364	C₂×C₁₉	#2598	1	1	yes	characteristic
365	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
366	C₂³×C₄	—	2	2	no	—
367	C₂³×C₄	—	2	2	no	—
368	C₂³×C₄	—	2	2	no	—
369	C₂³×C₄	—	2	4	no	—
370	C₂³×C₄	—	4	2	no	—
371	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
372	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
373	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
374	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
375	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
377	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
378	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
379	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
380	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
381	C₂×C₄⋊C₄	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	2	no	—
383	C₂×C₄⋊C₄	—	2	4	no	—
384	C₂×C₄⋊C₄	—	2	2	no	—
385	C₂×C₄⋊C₄	—	4	2	no	—
386	C₂×C₄⋊C₄	—	4	2	no	—
387	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
388	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
389	C₂×C₂²⋊C₄	—	2	2	no	—
390	C₂×C₂²⋊C₄	—	2	2	no	—
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₂²⋊C₄	—	2	2	no	—
393	C₂×C₂²⋊C₄	—	2	4	no	—
394	C₂×C₂²⋊C₄	—	2	4	no	—
395	C₂×C₂²⋊C₄	—	4	2	no	—
396	C₂×C₂²⋊C₄	—	4	2	no	—
397	C₂×C₂²⋊C₄	—	4	2	no	—
398	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
400	C₂×C₂²⋊C₄	Q₈×C₁₉	1	4	yes	—
401	C₂×C₄²	—	2	4	no	—
402	C₂×C₄²	—	2	2	no	—
403	C₂×C₄²	—	2	4	no	—
404	C₂×C₄²	—	4	2	no	—
405	C₂×C₄²	—	4	2	no	—
406	C₂×C₄²	—	4	2	no	—
407	C₂×C₄²	D₄×C₁₉	1	4	yes	—
408	#95	—	2	2	no	—
409	#95	—	2	2	no	—
410	#95	—	2	4	no	—
411	#95	—	2	4	no	—
412	#95	—	2	4	no	—
413	#95	—	2	4	no	—
414	#95	—	2	4	no	—
415	#95	—	2	2	no	—
416	#95	—	4	2	no	—
417	#95	—	4	2	no	—
418	#95	—	4	2	no	—
419	#95	C₂×C₄×C₁₉	1	4	yes	complemented
420	C₁₉	#14240	1	1	yes	characteristic, direct product factor, Sylow
421	C₂⁴	—	2	1	no	—
422	C₂⁴	—	2	1	no	—
423	C₂⁴	—	2	1	no	—
424	C₂⁴	—	2	2	no	—
425	C₂⁴	—	2	1	no	—
426	C₂⁴	—	2	2	no	—
427	C₂⁴	—	2	2	no	—
428	C₂⁴	—	2	2	no	—
429	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
430	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
431	C₂⁴	#41×C₁₉	1	2	yes	—
432	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	8	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	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	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	4	8	no	—
479	C₂²×C₄	—	4	8	no	—
480	C₂²×C₄	—	4	4	no	—
481	C₂²×C₄	—	4	4	no	—
482	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
483	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
484	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
485	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
486	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
487	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
488	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
489	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
490	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
491	C₂²×C₄	#41×C₁₉	1	2	yes	—
492	C₂²×C₄	#41×C₁₉	1	4	yes	—
493	C₂²×C₄	#41×C₁₉	1	2	yes	—
494	C₂²×C₄	#41×C₁₉	1	2	yes	—
495	C₂²×C₄	#41×C₁₉	1	4	yes	—
496	C₄⋊C₄	—	2	8	no	—
497	C₄⋊C₄	—	2	8	no	—
498	C₄⋊C₄	—	4	8	no	—
499	C₂²⋊C₄	—	2	8	no	—
500	C₂²⋊C₄	—	2	8	no	—
501	C₂²⋊C₄	—	4	8	no	—
502	C₂²⋊C₄	—	4	8	no	—
503	C₄²	—	2	8	no	—
504	C₄²	—	4	8	no	—
505	C₄²	—	4	4	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	2	4	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	4	1	no	—
519	C₂³	—	4	1	no	—
520	C₂³	—	4	2	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	4	2	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	2	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	2	no	—
528	C₂³	C₄×Q₈×C₁₉	1	4	yes	—
529	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
530	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
531	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
532	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
533	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
534	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
535	C₂³	C₂×#41×C₁₉	1	2	yes	—
536	C₂³	C₂×#41×C₁₉	1	2	yes	—
537	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
538	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
539	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	4	16	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
597	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
598	C₂×C₄	C₁₉×#123	1	4	yes	—
599	C₂²	—	2	4	no	—
600	C₂²	—	2	8	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	4	4	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	4	no	—
610	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
611	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
612	C₂²	C₄×#41×C₁₉	1	2	yes	—
613	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
614	C₂²	C₁₉×#518	1	2	yes	—
615	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
616	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
617	C₂²	C₁₉×#525	1	1	yes	characteristic
618	C₂²	C₁₉×#525	1	1	yes	characteristic
619	C₂²	C₁₉×#529	1	1	yes	characteristic
620	C₂²	C₁₉×#529	1	2	yes	—
621	C₂²	C₁₉×#533	1	1	yes	characteristic
622	C₂²	C₁₉×#535	1	1	yes	characteristic
623	C₂²	C₁₉×#535	1	1	yes	characteristic
624	C₂²	C₁₉×#540	1	2	yes	—
625	C₂²	C₁₉×#551	1	2	yes	—
626	C₂²	C₁₉×#551	1	2	yes	—
627	C₂²	C₁₉×#551	1	2	yes	—
628	C₂²	C₁₉×#553	1	2	yes	—
629	C₂²	C₁₉×#553	1	2	yes	—
630	C₂²	C₁₉×#554	1	2	yes	—
631	C₂²	C₁₉×#554	1	2	yes	—
632	C₂²	C₁₉×#559	1	2	yes	—
633	C₄	—	2	4	no	—
634	C₄	—	2	4	no	—
635	C₄	—	2	4	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	4	no	—
640	C₄	—	4	4	no	—
641	C₄	—	4	4	no	—
642	C₄	—	8	2	no	—
643	C₂	—	4	4	no	—
644	C₂	C₄×C₁₉×#123	1	1	yes	characteristic
645	C₂	C₄×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
646	C₂	C₁₉×#2328	1	1	yes	characteristic
647	C₂	C₁₉×#2368	1	2	yes	—
648	C₂	C₁₉×#2374	1	2	yes	—
649	C₂	C₁₉×#2482	1	1	yes	characteristic
650	C₂	C₁₉×#2487	1	1	yes	characteristic
651	C₂	C₁₉×#2516	1	2	yes	—
652	C₂	C₁₉×#2522	1	2	yes	—
653	C₂	C₁₉×#2580	1	1	yes	characteristic
654	C₂	C₁₉×#2598	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×C₄×C₄⋊C₄×C₁₉	C₂	semidirect
4. C₁₉×#1445	C₂	semidirect
5. C₁₉×#1442	C₂	semidirect
8. C₁₉×#1436	C₂	semidirect
9. C₁₉×#1436	C₂	semidirect
10. C₁₉×#1434	C₂	semidirect
23. C₁₉×#399	C₄	semidirect
60. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
61. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
92. C₁₉×#95	C₂×C₄	semidirect
178. #14240	C₁₉	direct (N × H)
273. C₂×C₄×C₄⋊C₄	C₂×C₁₉	semidirect
275. #1445	C₂×C₁₉	semidirect
276. #1442	C₂×C₁₉	semidirect
279. #1436	C₂×C₁₉	semidirect
280. #1436	C₂×C₁₉	semidirect
281. #1434	C₂×C₁₉	semidirect
338. #399	C₄×C₁₉	semidirect
387. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
388. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
419. #95	C₂×C₄×C₁₉	semidirect
420. C₁₉	#14240	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×C₄×C₄⋊C₄×C₁₉	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₁₉×#1445	2
C₁₉×#1442	2
C₁₉×#1439	2
C₁₉×#1437	2
C₁₉×#1436	2
C₁₉×#1434	2
C₁₉×C₂²⋊#95	2
#14240	19

Subgroups — C19×#14240 #18020199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14240 #18020199