Subgroups — C₁₉×#22482 #18028441

Order 4864.

1132 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#553	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₁₉	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1998	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1900	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1900	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×#1800	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₁₉×#100	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×#553	—	2	2	no	—
15	C₁₉×#553	—	2	2	no	—
16	C₁₉×#553	—	2	2	no	—
17	C₁₉×#553	—	2	2	no	—
18	C₂×C₁₉×#126	C₄	1	2	yes	—
19	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#123	C₄	1	2	yes	—
21	C₂×C₁₉×#121	C₄	1	2	yes	—
22	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
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×#100	C₂²	1	2	yes	—
35	C₂×C₁₉×#100	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×D₄×C₁₉	C₂×C₄	1	2	yes	—
48	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
49	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
52	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
53	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₁₉	—	2	2	no	—
56	C₂×M₁₆×C₁₉	—	2	2	no	—
57	C₂×M₁₆×C₁₉	—	2	4	no	—
58	C₂×M₁₆×C₁₉	—	2	4	no	—
59	C₂×M₁₆×C₁₉	—	4	2	no	—
60	C₂×M₁₆×C₁₉	—	4	2	no	—
61	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
62	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
63	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
64	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
65	C₂²×C₈×C₁₉	—	2	2	no	—
66	C₂²×C₈×C₁₉	—	2	2	no	—
67	C₁₉×#126	—	2	4	no	—
68	C₁₉×#126	—	2	4	no	—
69	C₁₉×#125	—	2	2	no	—
70	C₁₉×#125	—	2	2	no	—
71	C₁₉×#123	—	2	4	no	—
72	C₁₉×#123	—	2	4	no	—
73	C₁₉×#121	—	2	4	no	—
74	C₁₉×#121	—	2	4	no	—
75	C₁₉×#121	—	2	2	no	—
76	C₁₉×#121	—	2	2	no	—
77	C₁₉×#121	—	2	2	no	—
78	C₁₉×#121	—	2	2	no	—
79	C₄×D₄×C₁₉	—	2	2	no	—
80	C₄×D₄×C₁₉	—	2	2	no	—
81	C₄×D₄×C₁₉	—	2	2	no	—
82	C₄×D₄×C₁₉	—	2	2	no	—
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	D₄	1	2	yes	—
86	C₄×D₄×C₁₉	D₄	1	2	yes	—
87	C₄×D₄×C₁₉	D₄	1	2	yes	—
88	C₄×D₄×C₁₉	D₄	1	2	yes	—
89	C₁₉×#117	—	2	2	no	—
90	C₁₉×#117	—	2	2	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
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	2	yes	—
104	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
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×#100	—	2	4	no	—
111	C₁₉×#100	—	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	2	yes	—
120	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	4	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	1	no	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	4	2	no	—
129	C₂×D₄×C₁₉	—	4	4	no	—
130	C₂×D₄×C₁₉	—	8	2	no	—
131	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
132	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	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	—	2	1	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	—	8	2	no	—
144	C₂²×C₄×C₁₉	—	8	2	no	—
145	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂²×C₄	1	2	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	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
157	M₁₆×C₁₉	—	2	2	no	—
158	M₁₆×C₁₉	—	2	2	no	—
159	M₁₆×C₁₉	—	2	2	no	—
160	M₁₆×C₁₉	—	2	2	no	—
161	M₁₆×C₁₉	—	2	2	no	—
162	M₁₆×C₁₉	—	2	2	no	—
163	M₁₆×C₁₉	—	2	2	no	—
164	M₁₆×C₁₉	—	4	4	no	—
165	M₁₆×C₁₉	—	4	4	no	—
166	M₁₆×C₁₉	#41	1	4	yes	—
167	C₂×C₈×C₁₉	—	2	2	no	—
168	C₂×C₈×C₁₉	—	2	2	no	—
169	C₂×C₈×C₁₉	—	2	2	no	—
170	C₂×C₈×C₁₉	—	2	2	no	—
171	C₂×C₈×C₁₉	—	4	4	no	—
172	C₂×C₈×C₁₉	—	4	4	no	—
173	C₄⋊C₄×C₁₉	—	2	4	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	4	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
181	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
182	C₂²⋊C₄×C₁₉	—	2	4	no	—
183	C₂²⋊C₄×C₁₉	—	2	4	no	—
184	C₂²⋊C₄×C₁₉	—	2	2	no	—
185	C₂²⋊C₄×C₁₉	—	2	2	no	—
186	C₂²⋊C₄×C₁₉	—	2	4	no	—
187	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
188	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
189	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
190	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
191	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
192	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
193	C₄²×C₁₉	—	2	2	no	—
194	C₄²×C₁₉	—	2	2	no	—
195	C₄²×C₁₉	C₂×D₄	1	2	yes	—
196	C₄²×C₁₉	C₂×D₄	1	2	yes	—
197	#22482	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂³×C₁₉	—	2	1	no	—
199	C₂³×C₁₉	—	2	1	no	—
200	C₂³×C₁₉	—	2	2	no	—
201	C₂³×C₁₉	—	2	1	no	—
202	C₂³×C₁₉	—	2	1	no	—
203	C₂³×C₁₉	—	2	2	no	—
204	C₂³×C₁₉	—	2	2	no	—
205	C₂³×C₁₉	—	2	2	no	—
206	C₂³×C₁₉	—	4	1	no	—
207	C₂³×C₁₉	—	4	1	no	—
208	C₂³×C₁₉	—	4	1	no	—
209	C₂³×C₁₉	—	4	2	no	—
210	C₂³×C₁₉	—	4	2	no	—
211	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
212	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
215	D₄×C₁₉	—	2	4	no	—
216	D₄×C₁₉	—	4	2	no	—
217	D₄×C₁₉	—	4	4	no	—
218	D₄×C₁₉	—	4	4	no	—
219	D₄×C₁₉	—	4	2	no	—
220	D₄×C₁₉	—	4	2	no	—
221	D₄×C₁₉	—	8	4	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	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	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	8	2	no	—
243	C₂×C₄×C₁₉	—	8	2	no	—
244	C₂×C₄×C₁₉	—	8	2	no	—
245	C₂×C₄×C₁₉	—	8	2	no	—
246	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
249	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
252	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
254	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
255	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
256	C₈×C₁₉	—	2	4	no	—
257	C₈×C₁₉	—	4	2	no	—
258	C₈×C₁₉	—	4	2	no	—
259	C₈×C₁₉	—	4	2	no	—
260	C₂×#553	C₂×C₁₉	1	1	yes	characteristic
261	D₄×M₁₆	C₂×C₁₉	1	2	yes	complemented
262	#1998	C₂×C₁₉	1	2	yes	complemented
263	#1900	C₂×C₁₉	1	2	yes	complemented
264	#1900	C₂×C₁₉	1	2	yes	complemented
265	#1822	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1821	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1800	C₂×C₁₉	1	1	yes	characteristic, complemented
268	C₄×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1742	C₂×C₁₉	1	1	yes	characteristic, complemented
270	C₂×#343	C₂×C₁₉	1	1	yes	characteristic, complemented
271	C₂²×C₁₉	—	2	1	no	—
272	C₂²×C₁₉	—	2	1	no	—
273	C₂²×C₁₉	—	2	1	no	—
274	C₂²×C₁₉	—	2	1	no	—
275	C₂²×C₁₉	—	2	1	no	—
276	C₂²×C₁₉	—	2	2	no	—
277	C₂²×C₁₉	—	2	2	no	—
278	C₂²×C₁₉	—	2	1	no	—
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	2	2	no	—
281	C₂²×C₁₉	—	4	2	no	—
282	C₂²×C₁₉	—	4	2	no	—
283	C₂²×C₁₉	—	4	2	no	—
284	C₂²×C₁₉	—	4	2	no	—
285	C₂²×C₁₉	—	4	2	no	—
286	C₂²×C₁₉	—	8	1	no	—
287	C₂²×C₁₉	—	8	1	no	—
288	C₂²×C₁₉	—	8	2	no	—
289	C₂²×C₁₉	—	8	2	no	—
290	C₂²×C₁₉	#413	1	2	yes	—
291	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
292	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
293	C₂²×C₁₉	#520	1	1	yes	characteristic
294	C₄×C₁₉	—	2	1	no	—
295	C₄×C₁₉	—	2	2	no	—
296	C₄×C₁₉	—	2	1	no	—
297	C₄×C₁₉	—	2	2	no	—
298	C₄×C₁₉	—	2	1	no	—
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	4	2	no	—
301	C₄×C₁₉	—	4	2	no	—
302	C₄×C₁₉	—	4	2	no	—
303	C₄×C₁₉	#546	1	2	yes	—
304	C₄×C₁₉	#547	1	2	yes	—
305	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
306	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
307	#553	—	2	2	no	—
308	#553	—	2	2	no	—
309	#553	—	2	2	no	—
310	#553	—	2	2	no	—
311	C₂×#126	C₄×C₁₉	1	2	yes	—
312	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
313	C₂×#123	C₄×C₁₉	1	2	yes	—
314	C₂×#121	C₄×C₁₉	1	2	yes	—
315	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
317	C₂×C₄×D₄	C₄×C₁₉	1	2	yes	—
318	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
321	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
322	#436	—	2	2	no	—
323	#435	—	2	2	no	—
324	#435	—	2	2	no	—
325	C₈×D₄	—	2	2	no	—
326	#423	C₂²×C₁₉	1	2	yes	—
327	C₂×#100	C₂²×C₁₉	1	2	yes	—
328	C₂×#100	C₂²×C₁₉	1	2	yes	—
329	#407	C₂²×C₁₉	1	2	yes	—
330	#407	C₂²×C₁₉	1	2	yes	—
331	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
332	#343	C₂²×C₁₉	1	1	yes	characteristic
333	#343	C₂²×C₁₉	1	1	yes	characteristic
334	#343	C₂²×C₁₉	1	1	yes	characteristic
335	#343	C₂²×C₁₉	1	2	yes	—
336	#343	C₂²×C₁₉	1	2	yes	—
337	#343	C₂²×C₁₉	1	2	yes	—
338	#343	C₂²×C₁₉	1	2	yes	—
339	#343	C₂²×C₁₉	1	1	yes	characteristic
340	C₂×C₁₉	—	2	1	no	—
341	C₂×C₁₉	—	2	1	no	—
342	C₂×C₁₉	—	2	2	no	—
343	C₂×C₁₉	—	4	1	no	—
344	C₂×C₁₉	—	4	2	no	—
345	C₂×C₁₉	—	8	2	no	—
346	C₂×C₁₉	#2339	1	1	yes	characteristic
347	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
348	C₂×C₁₉	#2888	1	1	yes	characteristic
349	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
350	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
351	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
352	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
353	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
354	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
355	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
356	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
357	C₂×M₁₆	—	2	2	no	—
358	C₂×M₁₆	—	2	2	no	—
359	C₂×M₁₆	—	2	4	no	—
360	C₂×M₁₆	—	2	4	no	—
361	C₂×M₁₆	—	4	2	no	—
362	C₂×M₁₆	—	4	2	no	—
363	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
364	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
365	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
366	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
367	C₂²×C₈	—	2	2	no	—
368	C₂²×C₈	—	2	2	no	—
369	#126	—	2	4	no	—
370	#126	—	2	4	no	—
371	#125	—	2	2	no	—
372	#125	—	2	2	no	—
373	#123	—	2	4	no	—
374	#123	—	2	4	no	—
375	#121	—	2	4	no	—
376	#121	—	2	4	no	—
377	#121	—	2	2	no	—
378	#121	—	2	2	no	—
379	#121	—	2	2	no	—
380	#121	—	2	2	no	—
381	C₄×D₄	—	2	2	no	—
382	C₄×D₄	—	2	2	no	—
383	C₄×D₄	—	2	2	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	D₄×C₁₉	1	2	yes	—
388	C₄×D₄	D₄×C₁₉	1	2	yes	—
389	C₄×D₄	D₄×C₁₉	1	2	yes	—
390	C₄×D₄	D₄×C₁₉	1	2	yes	—
391	#117	—	2	2	no	—
392	#117	—	2	2	no	—
393	C₂×C₄⋊C₄	—	2	2	no	—
394	C₂×C₄⋊C₄	—	2	2	no	—
395	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
396	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
397	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
398	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
403	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
404	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
405	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
406	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
407	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
408	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
409	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
410	C₄⋊C₈	—	2	2	no	—
411	C₄⋊C₈	—	2	2	no	—
412	#100	—	2	4	no	—
413	#100	—	4	2	no	—
414	C₂²⋊C₈	—	2	2	no	—
415	C₂²⋊C₈	—	2	2	no	—
416	C₂²⋊C₈	—	2	2	no	—
417	C₂²⋊C₈	—	2	2	no	—
418	#97	—	2	2	no	—
419	C₄×C₈	—	2	2	no	—
420	C₁₉	#22482	1	1	yes	characteristic, direct product factor, Sylow
421	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
422	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
423	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	4	2	no	—
432	C₂×D₄	—	4	4	no	—
433	C₂×D₄	—	8	2	no	—
434	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
435	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	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	—	8	2	no	—
447	C₂²×C₄	—	8	2	no	—
448	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
449	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
450	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
451	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
452	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
453	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
454	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
456	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
457	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
458	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
460	M₁₆	—	2	2	no	—
461	M₁₆	—	2	2	no	—
462	M₁₆	—	2	2	no	—
463	M₁₆	—	2	2	no	—
464	M₁₆	—	2	2	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	2	2	no	—
467	M₁₆	—	4	4	no	—
468	M₁₆	—	4	4	no	—
469	M₁₆	#41×C₁₉	1	4	yes	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	4	4	no	—
475	C₂×C₈	—	4	4	no	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
484	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
485	C₂²⋊C₄	—	2	4	no	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
491	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
492	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
493	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
494	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
495	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	C₂×D₄×C₁₉	1	2	yes	—
499	C₄²	C₂×D₄×C₁₉	1	2	yes	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	1	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	2	2	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	4	1	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
514	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
515	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
516	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
517	D₄	—	2	4	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	4	no	—
520	D₄	—	4	4	no	—
521	D₄	—	4	2	no	—
522	D₄	—	4	2	no	—
523	D₄	—	8	4	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	—	8	2	no	—
546	C₂×C₄	—	8	2	no	—
547	C₂×C₄	—	8	2	no	—
548	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
549	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
550	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
551	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
552	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
553	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
555	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
556	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
557	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
558	C₈	—	2	4	no	—
559	C₈	—	4	2	no	—
560	C₈	—	4	2	no	—
561	C₈	—	4	2	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	4	2	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	8	1	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	2	no	—
580	C₂²	—	8	2	no	—
581	C₂²	C₁₉×#413	1	2	yes	—
582	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
583	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
584	C₂²	C₁₉×#520	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	2	no	—
594	C₄	C₁₉×#546	1	2	yes	—
595	C₄	C₁₉×#547	1	2	yes	—
596	C₂	—	2	1	no	—
597	C₂	—	2	1	no	—
598	C₂	—	2	2	no	—
599	C₂	—	4	1	no	—
600	C₂	—	4	2	no	—
601	C₂	—	8	2	no	—
602	C₂	C₁₉×#2339	1	1	yes	characteristic
603	C₂	C₂×C₁₉×#413	1	1	yes	characteristic
604	C₂	C₁₉×#2888	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	C₂×C₁₉×#553	C₂
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
2. D₄×M₁₆×C₁₉	C₂	semidirect
3. C₁₉×#1998	C₂	semidirect
4. C₁₉×#1900	C₂	semidirect
5. C₁₉×#1900	C₂	semidirect
6. C₁₉×#1822	C₂	semidirect
7. C₁₉×#1821	C₂	semidirect
8. C₁₉×#1800	C₂	semidirect
9. C₄×C₁₉×#100	C₂	semidirect
10. C₁₉×#1742	C₂	semidirect
11. C₂×C₁₉×#343	C₂	semidirect
197. #22482	C₁₉	direct (N × H)
261. D₄×M₁₆	C₂×C₁₉	semidirect
262. #1998	C₂×C₁₉	semidirect
263. #1900	C₂×C₁₉	semidirect
264. #1900	C₂×C₁₉	semidirect
265. #1822	C₂×C₁₉	semidirect
266. #1821	C₂×C₁₉	semidirect
267. #1800	C₂×C₁₉	semidirect
268. C₄×#100	C₂×C₁₉	semidirect
269. #1742	C₂×C₁₉	semidirect
270. C₂×#343	C₂×C₁₉	semidirect
420. C₁₉	#22482	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×#553	2
D₄×M₁₆×C₁₉	2
C₁₉×#1998	2
C₁₉×#1900	2
C₁₉×#1822	2
C₁₉×#1821	2
C₁₉×#1800	2
C₄×C₁₉×#100	2
C₁₉×#1742	2
C₂×C₁₉×#343	2
#22482	19

Subgroups — C19×#22482 #18028441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22482 #18028441