Subgroups — C₁₉×#26716 #18032675

Order 4864.

772 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2445	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2370	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2088	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2041	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2025	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2025	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1982	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1936	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1925	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1925	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1918	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1917	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#123	—	2	1	no	—
19	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
32	C₁₉×#394	—	2	1	no	—
33	C₁₉×#394	—	2	1	no	—
34	C₁₉×#390	C₂²	1	1	yes	characteristic
35	C₁₉×#390	C₂²	1	1	yes	characteristic
36	C₁₉×#390	C₂²	1	1	yes	characteristic
37	C₁₉×#389	—	2	1	no	—
38	C₁₉×#389	C₂²	1	1	yes	characteristic
39	C₁₉×#389	C₂²	1	1	yes	characteristic
40	C₁₉×#389	C₂²	1	1	yes	characteristic
41	C₁₉×#387	—	2	1	no	—
42	C₁₉×#387	—	2	1	no	—
43	C₁₉×#386	—	2	1	no	—
44	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#340	C₂²	1	1	yes	characteristic
50	C₁₉×#340	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#336	C₂²	1	1	yes	characteristic
56	C₁₉×#336	C₂²	1	1	yes	characteristic
57	C₁₉×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	—	2	1	no	—
64	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₁₉×#127	—	2	2	no	—
69	C₁₉×#127	—	4	1	no	—
70	C₁₉×#125	—	2	2	no	—
71	C₁₉×#125	—	2	2	no	—
72	C₁₉×#123	—	4	4	no	—
73	C₄×D₄×C₁₉	—	2	2	no	—
74	C₄×D₄×C₁₉	—	4	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄²×C₁₉	—	2	1	no	—
96	C₂×C₄²×C₁₉	—	2	1	no	—
97	C₂×C₄²×C₁₉	—	2	1	no	—
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×#107	—	2	2	no	—
102	C₁₉×#106	—	4	1	no	—
103	C₁₉×C₄⋊C₈	—	4	1	no	—
104	C₁₉×#102	—	2	2	no	—
105	C₁₉×#102	—	2	2	no	—
106	C₁₉×#102	—	2	2	no	—
107	C₁₉×#102	—	2	2	no	—
108	C₁₉×#102	—	2	2	no	—
109	C₁₉×#102	—	2	2	no	—
110	C₁₉×#102	—	2	2	no	—
111	C₁₉×#102	—	4	1	no	—
112	C₁₉×#97	—	4	1	no	—
113	C₁₉×#95	—	2	1	no	—
114	C₁₉×#95	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₁₉×#95	—	2	1	no	—
118	C₁₉×#95	—	2	1	no	—
119	C₁₉×#95	D₄	1	1	yes	characteristic
120	C₁₉×#95	D₄	1	1	yes	characteristic
121	C₂⁴×C₁₉	—	2	1	no	—
122	C₂⁴×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	—	2	1	no	—
126	C₂×D₄×C₁₉	—	2	1	no	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	2	1	no	—
129	C₂×D₄×C₁₉	—	2	1	no	—
130	C₂×D₄×C₁₉	—	2	1	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	—	4	2	no	—
135	C₂×D₄×C₁₉	—	4	2	no	—
136	C₂×D₄×C₁₉	—	4	2	no	—
137	C₂×D₄×C₁₉	—	4	2	no	—
138	C₂×D₄×C₁₉	—	8	1	no	—
139	C₂×D₄×C₁₉	—	8	1	no	—
140	C₂×D₄×C₁₉	#41	1	2	yes	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	4	2	no	—
148	C₂²×C₄×C₁₉	—	4	2	no	—
149	C₂²×C₄×C₁₉	—	8	1	no	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
157	C₂×C₈×C₁₉	—	2	1	no	—
158	C₂×C₈×C₁₉	—	2	1	no	—
159	C₂×C₈×C₁₉	—	2	1	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	—	2	1	no	—
162	C₂×C₈×C₁₉	—	2	1	no	—
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	4	no	—
170	C₄⋊C₄×C₁₉	—	2	4	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	4	1	no	—
182	C₄⋊C₄×C₁₉	—	4	2	no	—
183	C₄⋊C₄×C₁₉	—	4	2	no	—
184	C₄⋊C₄×C₁₉	—	8	1	no	—
185	C₄⋊C₄×C₁₉	#41	1	2	yes	—
186	C₄⋊C₄×C₁₉	#41	1	2	yes	—
187	C₄⋊C₄×C₁₉	#41	1	2	yes	—
188	C₂²⋊C₄×C₁₉	—	4	2	no	—
189	C₂²⋊C₄×C₁₉	—	4	2	no	—
190	C₂²⋊C₄×C₁₉	—	4	2	no	—
191	C₂²⋊C₄×C₁₉	—	4	2	no	—
192	C₂²⋊C₄×C₁₉	—	8	1	no	—
193	C₂²⋊C₄×C₁₉	—	8	1	no	—
194	C₂²⋊C₄×C₁₉	—	8	1	no	—
195	C₄²×C₁₉	—	2	1	no	—
196	C₄²×C₁₉	—	2	1	no	—
197	C₄²×C₁₉	—	2	1	no	—
198	C₄²×C₁₉	—	2	1	no	—
199	C₄²×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	—	2	1	no	—
201	C₄²×C₁₉	—	4	2	no	—
202	C₄²×C₁₉	—	8	1	no	—
203	C₄²×C₁₉	—	8	1	no	—
204	#26716	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	1	no	—
210	C₂³×C₁₉	—	4	1	no	—
211	C₂³×C₁₉	—	4	1	no	—
212	C₂³×C₁₉	—	4	1	no	—
213	C₂³×C₁₉	—	4	1	no	—
214	C₂³×C₁₉	—	4	1	no	—
215	C₂³×C₁₉	—	4	1	no	—
216	C₂³×C₁₉	—	4	1	no	—
217	C₂³×C₁₉	—	4	1	no	—
218	C₂³×C₁₉	—	4	1	no	—
219	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
220	D₄×C₁₉	—	2	2	no	—
221	D₄×C₁₉	—	2	2	no	—
222	D₄×C₁₉	—	4	1	no	—
223	D₄×C₁₉	—	4	1	no	—
224	D₄×C₁₉	—	4	1	no	—
225	D₄×C₁₉	—	4	1	no	—
226	D₄×C₁₉	—	4	1	no	—
227	D₄×C₁₉	—	4	1	no	—
228	D₄×C₁₉	—	8	4	no	—
229	D₄×C₁₉	—	8	4	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	8	4	no	—
266	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
267	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
268	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
272	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
273	C₈×C₁₉	—	4	1	no	—
274	C₈×C₁₉	—	4	1	no	—
275	C₈×C₁₉	—	4	1	no	—
276	C₈×C₁₉	—	4	1	no	—
277	#2445	C₂×C₁₉	1	1	yes	characteristic
278	#2370	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#2088	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#2041	C₂×C₁₉	1	1	yes	characteristic
281	#2025	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#2025	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1982	C₂×C₁₉	1	1	yes	characteristic
284	#1936	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1926	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1925	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1925	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1918	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1917	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1864	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1762	C₂×C₁₉	1	1	yes	characteristic, complemented
292	C₂²×C₁₉	—	4	2	no	—
293	C₂²×C₁₉	—	4	2	no	—
294	C₂²×C₁₉	—	4	2	no	—
295	C₂²×C₁₉	—	8	1	no	—
296	C₂²×C₁₉	—	8	1	no	—
297	C₂²×C₁₉	—	8	1	no	—
298	C₂²×C₁₉	—	8	1	no	—
299	C₂²×C₁₉	—	8	1	no	—
300	C₂²×C₁₉	—	8	1	no	—
301	C₂²×C₁₉	—	8	1	no	—
302	C₂²×C₁₉	—	8	1	no	—
303	C₂²×C₁₉	—	8	1	no	—
304	C₂²×C₁₉	—	8	1	no	—
305	C₂²×C₁₉	—	8	1	no	—
306	C₂²×C₁₉	#525	1	1	yes	characteristic
307	C₂²×C₁₉	#546	1	1	yes	characteristic
308	C₂²×C₁₉	#548	1	1	yes	characteristic
309	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
310	C₂²×C₁₉	#575	1	1	yes	characteristic
311	C₂²×C₁₉	#576	1	1	yes	characteristic
312	C₂²×C₁₉	#577	1	1	yes	characteristic
313	C₄×C₁₉	—	2	2	no	—
314	C₄×C₁₉	—	4	2	no	—
315	C₄×C₁₉	—	4	1	no	—
316	C₄×C₁₉	—	4	2	no	—
317	C₄×C₁₉	—	4	1	no	—
318	C₄×C₁₉	—	4	2	no	—
319	C₄×C₁₉	—	4	1	no	—
320	C₄×C₁₉	—	4	1	no	—
321	C₄×C₁₉	—	4	1	no	—
322	C₄×C₁₉	—	8	1	no	—
323	C₄×C₁₉	—	8	1	no	—
324	C₄×C₁₉	—	8	1	no	—
325	C₄×C₁₉	#529	1	1	yes	characteristic
326	C₄×C₁₉	#542	1	1	yes	characteristic
327	C₄×C₁₉	#552	1	1	yes	characteristic
328	C₄×C₁₉	#559	1	1	yes	characteristic
329	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
330	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
331	C₂×#123	—	2	1	no	—
332	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
339	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
340	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
341	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
342	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
343	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
345	#394	—	2	1	no	—
346	#394	—	2	1	no	—
347	#390	C₂²×C₁₉	1	1	yes	characteristic
348	#390	C₂²×C₁₉	1	1	yes	characteristic
349	#390	C₂²×C₁₉	1	1	yes	characteristic
350	#389	—	2	1	no	—
351	#389	C₂²×C₁₉	1	1	yes	characteristic
352	#389	C₂²×C₁₉	1	1	yes	characteristic
353	#389	C₂²×C₁₉	1	1	yes	characteristic
354	#387	—	2	1	no	—
355	#387	—	2	1	no	—
356	#386	—	2	1	no	—
357	C₄×C₄⋊C₄	—	2	1	no	—
358	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
359	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
360	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
361	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
362	#340	C₂²×C₁₉	1	1	yes	characteristic
363	#340	C₂²×C₁₉	1	1	yes	characteristic
364	#340	C₂²×C₁₉	1	1	yes	characteristic
365	#340	C₂²×C₁₉	1	1	yes	characteristic
366	#340	C₂²×C₁₉	1	1	yes	characteristic
367	#340	C₂²×C₁₉	1	1	yes	characteristic
368	#336	C₂²×C₁₉	1	1	yes	characteristic
369	#336	C₂²×C₁₉	1	1	yes	characteristic
370	#336	C₂²×C₁₉	1	1	yes	characteristic
371	#336	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×C₁₉	—	8	2	no	—
373	C₂×C₁₉	—	16	1	no	—
374	C₂×C₁₉	#2458	1	1	yes	characteristic
375	C₂×C₁₉	#3115	1	1	yes	characteristic
376	C₂×C₁₉	#3119	1	1	yes	characteristic
377	C₂×C₁₉	#3310	1	1	yes	characteristic
378	C₂×C₁₉	#3322	1	1	yes	characteristic
379	C₂×C₁₉	#3366	1	1	yes	characteristic
380	C₂×C₁₉	#3371	1	1	yes	characteristic
381	C₂²×D₄	—	2	1	no	—
382	C₂²×D₄	—	2	1	no	—
383	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
384	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
385	C₂³×C₄	—	2	1	no	—
386	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
387	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
390	#127	—	2	2	no	—
391	#127	—	4	1	no	—
392	#125	—	2	2	no	—
393	#125	—	2	2	no	—
394	#123	—	4	4	no	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	4	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
403	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₄²	—	2	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
423	#107	—	2	2	no	—
424	#106	—	4	1	no	—
425	C₄⋊C₈	—	4	1	no	—
426	#102	—	2	2	no	—
427	#102	—	2	2	no	—
428	#102	—	2	2	no	—
429	#102	—	2	2	no	—
430	#102	—	2	2	no	—
431	#102	—	2	2	no	—
432	#102	—	2	2	no	—
433	#102	—	4	1	no	—
434	#97	—	4	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	D₄×C₁₉	1	1	yes	characteristic
442	#95	D₄×C₁₉	1	1	yes	characteristic
443	C₁₉	#26716	1	1	yes	characteristic, direct product factor, Sylow
444	C₂⁴	—	2	1	no	—
445	C₂⁴	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	4	2	no	—
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	—	4	2	no	—
460	C₂×D₄	—	4	2	no	—
461	C₂×D₄	—	8	1	no	—
462	C₂×D₄	—	8	1	no	—
463	C₂×D₄	#41×C₁₉	1	2	yes	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	8	1	no	—
473	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	4	1	no	—
505	C₄⋊C₄	—	4	2	no	—
506	C₄⋊C₄	—	4	2	no	—
507	C₄⋊C₄	—	8	1	no	—
508	C₄⋊C₄	#41×C₁₉	1	2	yes	—
509	C₄⋊C₄	#41×C₁₉	1	2	yes	—
510	C₄⋊C₄	#41×C₁₉	1	2	yes	—
511	C₂²⋊C₄	—	4	2	no	—
512	C₂²⋊C₄	—	4	2	no	—
513	C₂²⋊C₄	—	4	2	no	—
514	C₂²⋊C₄	—	4	2	no	—
515	C₂²⋊C₄	—	8	1	no	—
516	C₂²⋊C₄	—	8	1	no	—
517	C₂²⋊C₄	—	8	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	4	2	no	—
525	C₄²	—	8	1	no	—
526	C₄²	—	8	1	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	4	1	no	—
532	C₂³	—	4	1	no	—
533	C₂³	—	4	1	no	—
534	C₂³	—	4	1	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	1	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
542	D₄	—	2	2	no	—
543	D₄	—	2	2	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	8	4	no	—
551	D₄	—	8	4	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	8	4	no	—
588	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
589	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
590	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
591	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
592	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
593	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
594	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
595	C₈	—	4	1	no	—
596	C₈	—	4	1	no	—
597	C₈	—	4	1	no	—
598	C₈	—	4	1	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	8	1	no	—
603	C₂²	—	8	1	no	—
604	C₂²	—	8	1	no	—
605	C₂²	—	8	1	no	—
606	C₂²	—	8	1	no	—
607	C₂²	—	8	1	no	—
608	C₂²	—	8	1	no	—
609	C₂²	—	8	1	no	—
610	C₂²	—	8	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	C₁₉×#525	1	1	yes	characteristic
614	C₂²	C₁₉×#546	1	1	yes	characteristic
615	C₂²	C₁₉×#548	1	1	yes	characteristic
616	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
617	C₂²	C₁₉×#575	1	1	yes	characteristic
618	C₂²	C₁₉×#576	1	1	yes	characteristic
619	C₂²	C₁₉×#577	1	1	yes	characteristic
620	C₄	—	2	2	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	2	no	—
629	C₄	—	8	1	no	—
630	C₄	—	8	1	no	—
631	C₄	—	8	1	no	—
632	C₄	C₁₉×#529	1	1	yes	characteristic
633	C₄	C₁₉×#542	1	1	yes	characteristic
634	C₄	C₁₉×#552	1	1	yes	characteristic
635	C₄	C₁₉×#559	1	1	yes	characteristic
636	C₂	—	8	2	no	—
637	C₂	—	16	1	no	—
638	C₂	C₁₉×#2458	1	1	yes	characteristic
639	C₂	C₁₉×#3115	1	1	yes	characteristic
640	C₂	C₁₉×#3119	1	1	yes	characteristic
641	C₂	C₁₉×#3310	1	1	yes	characteristic
642	C₂	C₁₉×#3322	1	1	yes	characteristic
643	C₂	C₁₉×#3366	1	1	yes	characteristic
644	C₂	C₁₉×#3371	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₄⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2370	C₂	semidirect
3. C₁₉×#2088	C₂	semidirect
5. C₁₉×#2025	C₂	semidirect
6. C₁₉×#2025	C₂	semidirect
8. C₁₉×#1936	C₂	semidirect
9. C₁₉×#1926	C₂	semidirect
10. C₁₉×#1925	C₂	semidirect
11. C₁₉×#1925	C₂	semidirect
12. C₁₉×#1918	C₂	semidirect
13. C₁₉×#1917	C₂	semidirect
14. C₁₉×#1864	C₂	semidirect
15. C₁₉×#1762	C₂	semidirect
204. #26716	C₁₉	direct (N × H)
278. #2370	C₂×C₁₉	semidirect
279. #2088	C₂×C₁₉	semidirect
281. #2025	C₂×C₁₉	semidirect
282. #2025	C₂×C₁₉	semidirect
284. #1936	C₂×C₁₉	semidirect
285. #1926	C₂×C₁₉	semidirect
286. #1925	C₂×C₁₉	semidirect
287. #1925	C₂×C₁₉	semidirect
288. #1918	C₂×C₁₉	semidirect
289. #1917	C₂×C₁₉	semidirect
290. #1864	C₂×C₁₉	semidirect
291. #1762	C₂×C₁₉	semidirect
443. C₁₉	#26716	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2445	2
C₁₉×#2370	2
C₁₉×#2088	2
C₁₉×#2041	2
C₁₉×#2025	2
C₁₉×#1982	2
C₁₉×#1936	2
C₁₉×#1926	2
C₁₉×#1925	2
C₁₉×#1918	2
C₁₉×#1917	2
C₁₉×#1864	2
C₁₉×#1762	2
#26716	19

Subgroups — C19×#26716 #18032675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26716 #18032675