Subgroups — C₁₉×#21473 #18027432

Order 4864.

1486 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#453	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2328	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1887	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1883	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1860	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1856	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1792	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1759	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
14	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
15	C₁₉×#520	—	2	2	no	—
16	C₁₉×#520	C₂²	1	2	yes	—
17	C₁₉×#518	—	2	2	no	—
18	C₁₉×#518	—	2	2	no	—
19	C₁₉×#518	C₂²	1	1	yes	characteristic
20	C₄×#41×C₁₉	—	2	2	no	—
21	C₄×#41×C₁₉	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₉	—	2	2	no	—
23	C₂×C₄×D₄×C₁₉	—	2	2	no	—
24	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#453	C₄	1	8	yes	complemented
27	C₁₉×#442	—	2	2	no	—
28	C₁₉×#440	—	2	2	no	—
29	C₄×SD₁₆×C₁₉	—	2	2	no	—
30	C₄×D₈×C₁₉	—	2	2	no	—
31	C₁₉×#428	C₂²	1	2	yes	complemented
32	C₂×C₁₉×#104	C₂²	1	2	yes	—
33	C₂×C₁₉×#104	C₂²	1	2	yes	—
34	C₁₉×#418	C₂²	1	2	yes	complemented
35	C₁₉×#417	C₂²	1	2	yes	—
36	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₁₉	C₂²	1	2	yes	complemented
39	C₁₉×#390	C₂²	1	1	yes	characteristic
40	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#386	—	2	2	no	—
42	C₁₉×#386	—	2	2	no	—
43	C₁₉×#382	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#376	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#343	C₂²	1	2	yes	complemented
46	C₁₉×#339	C₂²	1	2	yes	complemented
47	C₁₉×#339	C₂²	1	2	yes	complemented
48	C₁₉×H(5,𝔽₂)	—	2	4	no	—
49	C₁₉×H(5,𝔽₂)	—	2	2	no	—
50	C₁₉×H(5,𝔽₂)	C₂×C₄	1	4	yes	complemented
51	C₂×#41×C₁₉	—	2	2	no	—
52	C₂×#41×C₁₉	C₂³	1	2	yes	—
53	C₂²×D₄×C₁₉	—	2	2	no	—
54	C₂²×D₄×C₁₉	—	2	2	no	—
55	C₂²×D₄×C₁₉	—	2	2	no	—
56	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₉	—	2	2	no	—
59	C₂³×C₄×C₁₉	—	2	1	no	—
60	C₂³×C₄×C₁₉	D₄	1	2	yes	—
61	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
62	C₁₉×AGL(1,ℤ/8)	C₂×C₄	1	8	yes	complemented
63	C₂×SD₁₆×C₁₉	—	2	2	no	—
64	C₂×D₈×C₁₉	—	2	2	no	—
65	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
66	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
67	C₁₉×#127	—	2	2	no	—
68	C₁₉×#127	C₂×C₄	1	4	yes	complemented
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₄×Q₈×C₁₉	D₄	1	2	yes	complemented
71	C₄×Q₈×C₁₉	D₄	1	2	yes	complemented
72	C₄×D₄×C₁₉	—	2	4	no	—
73	C₄×D₄×C₁₉	—	2	4	no	—
74	C₄×D₄×C₁₉	—	2	4	no	—
75	C₄×D₄×C₁₉	—	2	4	no	—
76	C₄×D₄×C₁₉	—	2	2	no	—
77	C₄×D₄×C₁₉	—	2	2	no	—
78	C₄×D₄×C₁₉	—	2	4	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	—	2	2	no	—
86	C₄×D₄×C₁₉	D₄	1	2	yes	complemented
87	C₄×D₄×C₁₉	D₄	1	2	yes	complemented
88	C₁₉×#117	—	2	4	no	—
89	C₁₉×#117	—	2	2	no	—
90	C₁₉×#117	—	2	2	no	—
91	C₁₉×#117	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
103	C₂×C₄²×C₁₉	—	2	2	no	—
104	C₂×C₄²×C₁₉	—	2	2	no	—
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×#107	—	2	2	no	—
109	C₁₉×#106	—	2	2	no	—
110	C₁₉×#104	—	2	4	no	—
111	C₁₉×#104	C₂×C₄	1	8	yes	complemented
112	C₁₉×#103	—	2	2	no	—
113	C₁₉×#102	—	2	2	no	—
114	C₁₉×#102	—	2	2	no	—
115	C₁₉×#102	—	2	2	no	—
116	C₁₉×#100	—	2	2	no	—
117	C₁₉×#100	C₂×C₄	1	4	yes	complemented
118	C₁₉×#97	—	2	2	no	—
119	C₄×C₈×C₁₉	—	2	2	no	—
120	C₁₉×#95	—	2	1	no	—
121	C₁₉×#95	—	2	1	no	—
122	C₁₉×#95	—	2	2	no	—
123	C₂⁴×C₁₉	—	2	2	no	—
124	C₂⁴×C₁₉	—	2	1	no	—
125	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
126	#41×C₁₉	—	2	8	no	—
127	#41×C₁₉	—	2	8	no	—
128	#41×C₁₉	—	2	2	no	—
129	#41×C₁₉	—	2	2	no	—
130	#41×C₁₉	C₂²×C₄	1	4	yes	—
131	#41×C₁₉	#41	1	4	yes	—
132	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
133	C₂×D₄×C₁₉	—	2	4	no	—
134	C₂×D₄×C₁₉	—	2	8	no	—
135	C₂×D₄×C₁₉	—	2	8	no	—
136	C₂×D₄×C₁₉	—	2	8	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	2	8	no	—
139	C₂×D₄×C₁₉	—	2	8	no	—
140	C₂×D₄×C₁₉	—	2	2	no	—
141	C₂×D₄×C₁₉	—	2	2	no	—
142	C₂×D₄×C₁₉	—	2	2	no	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	8	2	no	—
146	C₂×D₄×C₁₉	—	8	2	no	—
147	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
148	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	complemented
149	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂×D₄×C₁₉	#41	1	2	yes	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	4	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	4	2	no	—
164	C₂²×C₄×C₁₉	—	8	2	no	—
165	C₂²×C₄×C₁₉	—	8	4	no	—
166	C₂²×C₄×C₁₉	—	8	2	no	—
167	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
171	SD₁₆×C₁₉	—	2	8	no	—
172	D₈×C₁₉	—	2	8	no	—
173	M₁₆×C₁₉	—	2	2	no	—
174	M₁₆×C₁₉	—	2	2	no	—
175	M₁₆×C₁₉	—	2	2	no	—
176	M₁₆×C₁₉	C₂²×C₄	1	4	yes	complemented
177	C₂×C₈×C₁₉	—	2	2	no	—
178	C₂×C₈×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	4	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
185	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
186	C₂²⋊C₄×C₁₉	—	2	4	no	—
187	C₂²⋊C₄×C₁₉	—	2	4	no	—
188	C₂²⋊C₄×C₁₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₉	—	2	4	no	—
192	C₂²⋊C₄×C₁₉	—	4	1	no	—
193	C₂²⋊C₄×C₁₉	—	4	1	no	—
194	C₂²⋊C₄×C₁₉	—	8	2	no	—
195	C₂²⋊C₄×C₁₉	—	8	2	no	—
196	C₄²×C₁₉	—	2	4	no	—
197	C₄²×C₁₉	—	2	2	no	—
198	C₄²×C₁₉	—	2	2	no	—
199	C₄²×C₁₉	—	2	2	no	—
200	C₄²×C₁₉	—	2	1	no	—
201	C₄²×C₁₉	—	2	2	no	—
202	C₄²×C₁₉	C₂²×C₄	1	2	yes	complemented
203	C₄²×C₁₉	C₂×D₄	1	2	yes	—
204	C₄²×C₁₉	C₂×D₄	1	2	yes	—
205	#21473	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂³×C₁₉	—	2	8	no	—
207	C₂³×C₁₉	—	2	2	no	—
208	C₂³×C₁₉	—	2	2	no	—
209	C₂³×C₁₉	—	2	2	no	—
210	C₂³×C₁₉	—	2	2	no	—
211	C₂³×C₁₉	—	4	2	no	—
212	C₂³×C₁₉	—	4	2	no	—
213	C₂³×C₁₉	—	4	2	no	—
214	C₂³×C₁₉	—	4	2	no	—
215	C₂³×C₁₉	—	4	1	no	—
216	C₂³×C₁₉	—	4	1	no	—
217	C₂³×C₁₉	—	8	2	no	—
218	C₂³×C₁₉	—	8	2	no	—
219	C₂³×C₁₉	C₄×D₄	1	4	yes	—
220	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
221	Q₈×C₁₉	—	2	2	no	—
222	Q₈×C₁₉	C₄×D₄	1	4	yes	—
223	D₄×C₁₉	—	2	16	no	—
224	D₄×C₁₉	—	2	4	no	—
225	D₄×C₁₉	—	2	4	no	—
226	D₄×C₁₉	—	2	4	no	—
227	D₄×C₁₉	—	2	4	no	—
228	D₄×C₁₉	—	2	2	no	—
229	D₄×C₁₉	—	2	4	no	—
230	D₄×C₁₉	—	4	2	no	—
231	D₄×C₁₉	—	8	8	no	—
232	D₄×C₁₉	C₄×D₄	1	4	yes	—
233	C₂×C₄×C₁₉	—	2	8	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	4	no	—
236	C₂×C₄×C₁₉	—	2	4	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	4	no	—
244	C₂×C₄×C₁₉	—	4	4	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	2	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	8	2	no	—
254	C₂×C₄×C₁₉	—	8	2	no	—
255	C₂×C₄×C₁₉	—	8	4	no	—
256	C₂×C₄×C₁₉	—	8	2	no	—
257	C₂×C₄×C₁₉	—	8	4	no	—
258	C₂×C₄×C₁₉	—	8	2	no	—
259	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
260	C₂×C₄×C₁₉	#120	1	2	yes	—
261	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
265	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
266	C₈×C₁₉	—	2	4	no	—
267	C₈×C₁₉	—	4	2	no	—
268	C₄×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic, complemented
269	C₂×#453	C₂×C₁₉	1	1	yes	characteristic
270	C₄×AGL(1,ℤ/8)	C₂×C₁₉	1	2	yes	complemented
271	#2328	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1887	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1883	C₂×C₁₉	1	2	yes	complemented
274	#1860	C₂×C₁₉	1	2	yes	complemented
275	#1856	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1792	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1759	C₂×C₁₉	1	2	yes	complemented
278	C₄×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	2	1	no	—
281	C₂²×C₁₉	—	2	4	no	—
282	C₂²×C₁₉	—	2	4	no	—
283	C₂²×C₁₉	—	4	4	no	—
284	C₂²×C₁₉	—	4	4	no	—
285	C₂²×C₁₉	—	4	2	no	—
286	C₂²×C₁₉	—	4	2	no	—
287	C₂²×C₁₉	—	4	2	no	—
288	C₂²×C₁₉	—	4	2	no	—
289	C₂²×C₁₉	—	4	2	no	—
290	C₂²×C₁₉	—	8	2	no	—
291	C₂²×C₁₉	—	8	2	no	—
292	C₂²×C₁₉	—	8	8	no	—
293	C₂²×C₁₉	—	8	1	no	—
294	C₂²×C₁₉	—	8	1	no	—
295	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
296	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
297	C₂²×C₁₉	#525	1	1	yes	characteristic
298	C₄×C₁₉	—	2	1	no	—
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	2	2	no	—
301	C₄×C₁₉	—	2	4	no	—
302	C₄×C₁₉	—	4	2	no	—
303	C₄×C₁₉	—	4	2	no	—
304	C₄×C₁₉	—	4	2	no	—
305	C₄×C₁₉	—	4	2	no	—
306	C₄×C₁₉	—	8	1	no	—
307	C₄×C₁₉	—	8	1	no	—
308	C₄×C₁₉	C₂×C₄×D₄	1	2	yes	—
309	C₄×C₁₉	#525	1	2	yes	—
310	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
311	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	—
312	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
313	#520	—	2	2	no	—
314	#520	C₂²×C₁₉	1	2	yes	—
315	#518	—	2	2	no	—
316	#518	—	2	2	no	—
317	#518	C₂²×C₁₉	1	1	yes	characteristic
318	C₄×#41	—	2	2	no	—
319	C₄×#41	C₂²×C₁₉	1	2	yes	—
320	C₂×C₄×D₄	—	2	2	no	—
321	C₂×C₄×D₄	—	2	2	no	—
322	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
324	#453	C₄×C₁₉	1	8	yes	complemented
325	#442	—	2	2	no	—
326	#440	—	2	2	no	—
327	C₄×SD₁₆	—	2	2	no	—
328	C₄×D₈	—	2	2	no	—
329	#428	C₂²×C₁₉	1	2	yes	complemented
330	C₂×#104	C₂²×C₁₉	1	2	yes	—
331	C₂×#104	C₂²×C₁₉	1	2	yes	—
332	#418	C₂²×C₁₉	1	2	yes	complemented
333	#417	C₂²×C₁₉	1	2	yes	—
334	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
336	C₄×M₁₆	C₂²×C₁₉	1	2	yes	complemented
337	#390	C₂²×C₁₉	1	1	yes	characteristic
338	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	#386	—	2	2	no	—
340	#386	—	2	2	no	—
341	#382	C₂²×C₁₉	1	1	yes	characteristic, complemented
342	#376	C₂²×C₁₉	1	1	yes	characteristic, complemented
343	#343	C₂²×C₁₉	1	2	yes	complemented
344	#339	C₂²×C₁₉	1	2	yes	complemented
345	#339	C₂²×C₁₉	1	2	yes	complemented
346	C₂×C₁₉	—	2	1	no	—
347	C₂×C₁₉	—	2	1	no	—
348	C₂×C₁₉	—	4	4	no	—
349	C₂×C₁₉	—	4	4	no	—
350	C₂×C₁₉	—	8	2	no	—
351	C₂×C₁₉	C₄×#120	1	1	yes	characteristic
352	C₂×C₁₉	#3019	1	1	yes	characteristic
353	C₂×C₁₉	#3021	1	1	yes	characteristic
354	H(5,𝔽₂)	—	2	4	no	—
355	H(5,𝔽₂)	—	2	2	no	—
356	H(5,𝔽₂)	C₂×C₄×C₁₉	1	4	yes	complemented
357	C₂×#41	—	2	2	no	—
358	C₂×#41	C₂³×C₁₉	1	2	yes	—
359	C₂²×D₄	—	2	2	no	—
360	C₂²×D₄	—	2	2	no	—
361	C₂²×D₄	—	2	2	no	—
362	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
363	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
364	C₂³×C₄	—	2	2	no	—
365	C₂³×C₄	—	2	1	no	—
366	C₂³×C₄	D₄×C₁₉	1	2	yes	—
367	AGL(1,ℤ/8)	—	2	4	no	—
368	AGL(1,ℤ/8)	C₂×C₄×C₁₉	1	8	yes	complemented
369	C₂×SD₁₆	—	2	2	no	—
370	C₂×D₈	—	2	2	no	—
371	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
372	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
373	#127	—	2	2	no	—
374	#127	C₂×C₄×C₁₉	1	4	yes	complemented
375	C₄×Q₈	—	2	2	no	—
376	C₄×Q₈	D₄×C₁₉	1	2	yes	complemented
377	C₄×Q₈	D₄×C₁₉	1	2	yes	complemented
378	C₄×D₄	—	2	4	no	—
379	C₄×D₄	—	2	4	no	—
380	C₄×D₄	—	2	4	no	—
381	C₄×D₄	—	2	4	no	—
382	C₄×D₄	—	2	2	no	—
383	C₄×D₄	—	2	2	no	—
384	C₄×D₄	—	2	4	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	2	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
393	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
394	#117	—	2	4	no	—
395	#117	—	2	2	no	—
396	#117	—	2	2	no	—
397	#117	C₂³×C₁₉	1	2	yes	—
398	C₂×C₄⋊C₄	—	2	2	no	—
399	C₂×C₄⋊C₄	—	2	2	no	—
400	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	—	2	2	no	—
403	C₂×C₂²⋊C₄	—	2	4	no	—
404	C₂×C₂²⋊C₄	—	2	2	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	2	no	—
407	C₂×C₂²⋊C₄	—	2	2	no	—
408	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
409	C₂×C₄²	—	2	2	no	—
410	C₂×C₄²	—	2	2	no	—
411	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
414	#107	—	2	2	no	—
415	#106	—	2	2	no	—
416	#104	—	2	4	no	—
417	#104	C₂×C₄×C₁₉	1	8	yes	complemented
418	#103	—	2	2	no	—
419	#102	—	2	2	no	—
420	#102	—	2	2	no	—
421	#102	—	2	2	no	—
422	#100	—	2	2	no	—
423	#100	C₂×C₄×C₁₉	1	4	yes	complemented
424	#97	—	2	2	no	—
425	C₄×C₈	—	2	2	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	2	no	—
429	C₁₉	#21473	1	1	yes	characteristic, direct product factor, Sylow
430	C₂⁴	—	2	2	no	—
431	C₂⁴	—	2	1	no	—
432	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
433	#41	—	2	8	no	—
434	#41	—	2	8	no	—
435	#41	—	2	2	no	—
436	#41	—	2	2	no	—
437	#41	C₂²×C₄×C₁₉	1	4	yes	—
438	#41	#41×C₁₉	1	4	yes	—
439	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	8	no	—
442	C₂×D₄	—	2	8	no	—
443	C₂×D₄	—	2	8	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	8	no	—
446	C₂×D₄	—	2	8	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	8	2	no	—
453	C₂×D₄	—	8	2	no	—
454	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
455	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	complemented
456	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
457	C₂×D₄	#41×C₁₉	1	2	yes	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	4	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	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	8	2	no	—
472	C₂²×C₄	—	8	4	no	—
473	C₂²×C₄	—	8	2	no	—
474	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
475	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
478	SD₁₆	—	2	8	no	—
479	D₈	—	2	8	no	—
480	M₁₆	—	2	2	no	—
481	M₁₆	—	2	2	no	—
482	M₁₆	—	2	2	no	—
483	M₁₆	C₂²×C₄×C₁₉	1	4	yes	complemented
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
492	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₂²⋊C₄	—	8	2	no	—
502	C₂²⋊C₄	—	8	2	no	—
503	C₄²	—	2	4	no	—
504	C₄²	—	2	2	no	—
505	C₄²	—	2	2	no	—
506	C₄²	—	2	2	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	2	no	—
509	C₄²	C₂²×C₄×C₁₉	1	2	yes	complemented
510	C₄²	C₂×D₄×C₁₉	1	2	yes	—
511	C₄²	C₂×D₄×C₁₉	1	2	yes	—
512	C₂³	—	2	8	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	2	no	—
520	C₂³	—	4	2	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	8	2	no	—
524	C₂³	—	8	2	no	—
525	C₂³	C₄×D₄×C₁₉	1	4	yes	—
526	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
527	Q₈	—	2	2	no	—
528	Q₈	C₄×D₄×C₁₉	1	4	yes	—
529	D₄	—	2	16	no	—
530	D₄	—	2	4	no	—
531	D₄	—	2	4	no	—
532	D₄	—	2	4	no	—
533	D₄	—	2	4	no	—
534	D₄	—	2	2	no	—
535	D₄	—	2	4	no	—
536	D₄	—	4	2	no	—
537	D₄	—	8	8	no	—
538	D₄	C₄×D₄×C₁₉	1	4	yes	—
539	C₂×C₄	—	2	8	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	4	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	8	2	no	—
560	C₂×C₄	—	8	2	no	—
561	C₂×C₄	—	8	4	no	—
562	C₂×C₄	—	8	4	no	—
563	C₂×C₄	—	8	2	no	—
564	C₂×C₄	—	8	2	no	—
565	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
566	C₂×C₄	C₁₉×#120	1	2	yes	—
567	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
568	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
570	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
571	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
572	C₈	—	2	4	no	—
573	C₈	—	4	2	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	4	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	4	4	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	8	2	no	—
586	C₂²	—	8	2	no	—
587	C₂²	—	8	8	no	—
588	C₂²	—	8	1	no	—
589	C₂²	—	8	1	no	—
590	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
591	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
592	C₂²	C₁₉×#525	1	1	yes	characteristic
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	4	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	2	no	—
601	C₄	—	8	1	no	—
602	C₄	—	8	1	no	—
603	C₄	C₂×C₄×D₄×C₁₉	1	2	yes	—
604	C₄	C₁₉×#525	1	2	yes	—
605	C₂	—	2	1	no	—
606	C₂	—	2	1	no	—
607	C₂	—	4	4	no	—
608	C₂	—	4	4	no	—
609	C₂	—	8	2	no	—
610	C₂	C₄×C₁₉×#120	1	1	yes	characteristic
611	C₂	C₁₉×#3019	1	1	yes	characteristic
612	C₂	C₁₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#453	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×C₁₉×H(5,𝔽₂)	C₂	semidirect
3. C₄×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
4. C₁₉×#2328	C₂	semidirect
5. C₁₉×#1887	C₂	semidirect
6. C₁₉×#1883	C₂	semidirect
7. C₁₉×#1860	C₂	semidirect
8. C₁₉×#1856	C₂	semidirect
9. C₁₉×#1792	C₂	semidirect
10. C₁₉×#1759	C₂	semidirect
11. C₄×C₁₉×#100	C₂	semidirect
25. C₂×C₄×D₄×C₁₉	C₂²	semidirect
26. C₁₉×#453	C₄	semidirect
31. C₁₉×#428	C₂²	semidirect
34. C₁₉×#418	C₂²	semidirect
38. C₄×M₁₆×C₁₉	C₂²	semidirect
40. C₁₉×#390	C₂²	semidirect
43. C₁₉×#382	C₂²	semidirect
44. C₁₉×#376	C₂²	semidirect
45. C₁₉×#343	C₂²	semidirect
46. C₁₉×#339	C₂²	semidirect
47. C₁₉×#339	C₂²	semidirect
50. C₁₉×H(5,𝔽₂)	C₂×C₄	semidirect
62. C₁₉×AGL(1,ℤ/8)	C₂×C₄	semidirect
68. C₁₉×#127	C₂×C₄	semidirect
70. C₄×Q₈×C₁₉	D₄	semidirect
71. C₄×Q₈×C₁₉	D₄	semidirect
86. C₄×D₄×C₁₉	D₄	semidirect
87. C₄×D₄×C₁₉	D₄	semidirect
111. C₁₉×#104	C₂×C₄	semidirect
117. C₁₉×#100	C₂×C₄	semidirect
148. C₂×D₄×C₁₉	C₂²×C₄	semidirect
176. M₁₆×C₁₉	C₂²×C₄	semidirect
202. C₄²×C₁₉	C₂²×C₄	semidirect
205. #21473	C₁₉	direct (N × H)
268. C₄×H(5,𝔽₂)	C₂×C₁₉	semidirect
270. C₄×AGL(1,ℤ/8)	C₂×C₁₉	semidirect
271. #2328	C₂×C₁₉	semidirect
272. #1887	C₂×C₁₉	semidirect
273. #1883	C₂×C₁₉	semidirect
274. #1860	C₂×C₁₉	semidirect
275. #1856	C₂×C₁₉	semidirect
276. #1792	C₂×C₁₉	semidirect
277. #1759	C₂×C₁₉	semidirect
278. C₄×#100	C₂×C₁₉	semidirect
323. C₂×C₄×D₄	C₂²×C₁₉	semidirect
324. #453	C₄×C₁₉	semidirect
329. #428	C₂²×C₁₉	semidirect
332. #418	C₂²×C₁₉	semidirect
336. C₄×M₁₆	C₂²×C₁₉	semidirect
338. #390	C₂²×C₁₉	semidirect
341. #382	C₂²×C₁₉	semidirect
342. #376	C₂²×C₁₉	semidirect
343. #343	C₂²×C₁₉	semidirect
344. #339	C₂²×C₁₉	semidirect
345. #339	C₂²×C₁₉	semidirect
356. H(5,𝔽₂)	C₂×C₄×C₁₉	semidirect
368. AGL(1,ℤ/8)	C₂×C₄×C₁₉	semidirect
374. #127	C₂×C₄×C₁₉	semidirect
376. C₄×Q₈	D₄×C₁₉	semidirect
377. C₄×Q₈	D₄×C₁₉	semidirect
392. C₄×D₄	D₄×C₁₉	semidirect
393. C₄×D₄	D₄×C₁₉	semidirect
417. #104	C₂×C₄×C₁₉	semidirect
423. #100	C₂×C₄×C₁₉	semidirect
429. C₁₉	#21473	direct (N × H)
455. C₂×D₄	C₂²×C₄×C₁₉	semidirect
483. M₁₆	C₂²×C₄×C₁₉	semidirect
509. C₄²	C₂²×C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₉×H(5,𝔽₂)	2
C₂×C₁₉×#453	2
C₄×C₁₉×AGL(1,ℤ/8)	2
C₁₉×#2328	2
C₁₉×#1887	2
C₁₉×#1883	2
C₁₉×#1860	2
C₁₉×#1856	2
C₁₉×#1792	2
C₁₉×#1759	2
C₄×C₁₉×#100	2
#21473	19

Subgroups — C19×#21473 #18027432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21473 #18027432