Subgroups — C₁₉×#26251 #18032210

Order 4864.

880 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2448	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2447	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2056	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2054	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1941	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1879	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#495	—	2	4	no	—
25	C₄×SD₁₆×C₁₉	—	2	4	no	—
26	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
40	C₁₉×#399	—	2	1	no	—
41	C₁₉×#397	—	2	1	no	—
42	C₁₉×#397	—	2	1	no	—
43	C₁₉×#397	—	2	1	no	—
44	C₁₉×#391	C₂²	1	1	yes	characteristic
45	C₁₉×#391	C₂²	1	1	yes	characteristic
46	C₁₉×#391	C₂²	1	1	yes	characteristic
47	C₁₉×#390	C₂²	1	1	yes	characteristic
48	C₁₉×#390	C₂²	1	1	yes	characteristic
49	C₁₉×#390	C₂²	1	1	yes	characteristic
50	C₁₉×#389	C₂²	1	1	yes	characteristic
51	C₁₉×#389	C₂²	1	1	yes	characteristic
52	C₁₉×#388	—	2	1	no	—
53	C₁₉×#388	—	2	1	no	—
54	C₁₉×#385	—	2	1	no	—
55	C₁₉×#381	—	2	1	no	—
56	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
57	C₁₉×#340	C₂²	1	1	yes	characteristic
58	C₁₉×#340	C₂²	1	1	yes	characteristic
59	C₁₉×#336	C₂²	1	1	yes	characteristic
60	C₁₉×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₉	—	2	1	no	—
66	C₂×Q₁₆×C₁₉	—	2	2	no	—
67	C₂×Q₁₆×C₁₉	—	2	2	no	—
68	C₂×Q₁₆×C₁₉	—	4	1	no	—
69	C₂×SD₁₆×C₁₉	—	2	2	no	—
70	C₂×SD₁₆×C₁₉	—	2	2	no	—
71	C₂×SD₁₆×C₁₉	—	2	2	no	—
72	C₂×SD₁₆×C₁₉	—	2	2	no	—
73	C₂×SD₁₆×C₁₉	—	2	2	no	—
74	C₂×SD₁₆×C₁₉	D₄	1	4	yes	—
75	C₂×D₈×C₁₉	—	2	2	no	—
76	C₂×D₈×C₁₉	—	2	2	no	—
77	C₂×D₈×C₁₉	—	4	1	no	—
78	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
82	C₁₉×#124	—	2	2	no	—
83	C₁₉×#124	—	2	2	no	—
84	C₁₉×#124	—	4	1	no	—
85	C₁₉×#124	—	4	1	no	—
86	C₄×Q₈×C₁₉	—	2	2	no	—
87	C₄×Q₈×C₁₉	—	4	1	no	—
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₄×D₄×C₁₉	—	4	1	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₉	C₂³	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×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₄²×C₁₉	—	2	1	no	—
111	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₁₉×#106	—	2	2	no	—
115	C₁₉×#106	—	2	2	no	—
116	C₁₉×C₄⋊C₈	—	2	2	no	—
117	C₁₉×#103	—	2	2	no	—
118	C₁₉×#103	—	4	1	no	—
119	C₁₉×#103	—	4	1	no	—
120	C₁₉×#103	—	4	1	no	—
121	C₁₉×#102	—	2	2	no	—
122	C₁₉×#102	—	4	1	no	—
123	C₁₉×#102	—	4	1	no	—
124	C₁₉×#102	—	4	1	no	—
125	C₄×C₈×C₁₉	—	2	2	no	—
126	C₄×C₈×C₁₉	—	2	2	no	—
127	C₄×C₈×C₁₉	—	2	2	no	—
128	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	—	2	1	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	—	2	1	no	—
133	C₁₉×#95	—	2	1	no	—
134	C₁₉×#95	—	2	1	no	—
135	C₁₉×#95	—	2	1	no	—
136	C₁₉×#95	D₄	1	1	yes	characteristic
137	C₁₉×#95	D₄	1	1	yes	characteristic
138	C₂⁴×C₁₉	—	2	1	no	—
139	C₂⁴×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	2	1	no	—
143	C₂×Q₈×C₁₉	—	2	1	no	—
144	C₂×Q₈×C₁₉	—	2	1	no	—
145	C₂×Q₈×C₁₉	—	2	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	4	2	no	—
171	C₂²×C₄×C₁₉	—	4	2	no	—
172	C₂²×C₄×C₁₉	—	8	1	no	—
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
180	Q₁₆×C₁₉	—	4	4	no	—
181	SD₁₆×C₁₉	—	2	8	no	—
182	SD₁₆×C₁₉	—	4	4	no	—
183	D₈×C₁₉	—	4	4	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	—	2	1	no	—
186	C₂×C₈×C₁₉	—	2	1	no	—
187	C₂×C₈×C₁₉	—	2	1	no	—
188	C₂×C₈×C₁₉	—	2	1	no	—
189	C₂×C₈×C₁₉	—	2	1	no	—
190	C₂×C₈×C₁₉	—	2	1	no	—
191	C₂×C₈×C₁₉	—	2	1	no	—
192	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
193	C₂×C₈×C₁₉	#41	1	2	yes	—
194	C₂×C₈×C₁₉	#41	1	2	yes	—
195	C₂×C₈×C₁₉	#41	1	2	yes	—
196	C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₄⋊C₄×C₁₉	—	2	2	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	4	2	no	—
207	C₄⋊C₄×C₁₉	—	8	1	no	—
208	C₄⋊C₄×C₁₉	—	8	1	no	—
209	C₂²⋊C₄×C₁₉	—	4	2	no	—
210	C₂²⋊C₄×C₁₉	—	4	2	no	—
211	C₂²⋊C₄×C₁₉	—	4	2	no	—
212	C₂²⋊C₄×C₁₉	—	4	2	no	—
213	C₂²⋊C₄×C₁₉	—	4	2	no	—
214	C₂²⋊C₄×C₁₉	—	4	2	no	—
215	C₂²⋊C₄×C₁₉	—	4	2	no	—
216	C₂²⋊C₄×C₁₉	—	4	2	no	—
217	C₂²⋊C₄×C₁₉	—	8	1	no	—
218	C₂²⋊C₄×C₁₉	—	8	1	no	—
219	C₂²⋊C₄×C₁₉	—	8	1	no	—
220	C₄²×C₁₉	—	2	1	no	—
221	C₄²×C₁₉	—	2	1	no	—
222	C₄²×C₁₉	—	2	1	no	—
223	C₄²×C₁₉	—	2	1	no	—
224	C₄²×C₁₉	—	2	1	no	—
225	C₄²×C₁₉	—	2	1	no	—
226	C₄²×C₁₉	—	4	2	no	—
227	#26251	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂³×C₁₉	—	2	2	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	—	4	1	no	—
232	C₂³×C₁₉	—	4	1	no	—
233	C₂³×C₁₉	—	4	1	no	—
234	C₂³×C₁₉	—	4	1	no	—
235	C₂³×C₁₉	—	4	1	no	—
236	C₂³×C₁₉	—	4	1	no	—
237	C₂³×C₁₉	—	4	1	no	—
238	C₂³×C₁₉	—	4	1	no	—
239	C₂³×C₁₉	—	4	1	no	—
240	C₂³×C₁₉	—	4	1	no	—
241	C₂³×C₁₉	—	4	1	no	—
242	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
243	Q₈×C₁₉	—	2	2	no	—
244	Q₈×C₁₉	—	2	2	no	—
245	Q₈×C₁₉	—	4	1	no	—
246	Q₈×C₁₉	—	4	1	no	—
247	Q₈×C₁₉	—	4	1	no	—
248	Q₈×C₁₉	—	4	1	no	—
249	Q₈×C₁₉	—	4	1	no	—
250	Q₈×C₁₉	—	4	1	no	—
251	D₄×C₁₉	—	2	2	no	—
252	D₄×C₁₉	—	2	2	no	—
253	D₄×C₁₉	—	4	1	no	—
254	D₄×C₁₉	—	4	1	no	—
255	D₄×C₁₉	—	4	1	no	—
256	D₄×C₁₉	—	4	1	no	—
257	D₄×C₁₉	—	4	1	no	—
258	D₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	2	2	no	—
268	C₂×C₄×C₁₉	—	2	1	no	—
269	C₂×C₄×C₁₉	—	2	1	no	—
270	C₂×C₄×C₁₉	—	2	1	no	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	2	1	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	4	1	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	4	1	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	1	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	8	4	no	—
294	C₂×C₄×C₁₉	#135	1	2	yes	—
295	C₂×C₄×C₁₉	#135	1	2	yes	—
296	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
300	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
301	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
302	C₈×C₁₉	—	2	2	no	—
303	C₈×C₁₉	—	4	1	no	—
304	C₈×C₁₉	—	4	1	no	—
305	C₈×C₁₉	#123	1	4	yes	—
306	C₂×#495	C₂×C₁₉	1	1	yes	characteristic
307	C₂×C₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#2448	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#2447	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#2056	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#2054	C₂×C₁₉	1	1	yes	characteristic
312	#2042	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#2042	C₂×C₁₉	1	1	yes	characteristic, complemented
314	#1968	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#1968	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#1968	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#1941	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#1879	C₂×C₁₉	1	1	yes	characteristic
319	#1878	C₂×C₁₉	1	1	yes	characteristic, complemented
320	C₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
321	C₂²×C₁₉	—	4	2	no	—
322	C₂²×C₁₉	—	4	2	no	—
323	C₂²×C₁₉	—	4	2	no	—
324	C₂²×C₁₉	—	8	1	no	—
325	C₂²×C₁₉	—	8	1	no	—
326	C₂²×C₁₉	—	8	1	no	—
327	C₂²×C₁₉	—	8	1	no	—
328	C₂²×C₁₉	—	8	1	no	—
329	C₂²×C₁₉	—	8	1	no	—
330	C₂²×C₁₉	—	8	1	no	—
331	C₂²×C₁₉	—	8	1	no	—
332	C₂²×C₁₉	—	8	1	no	—
333	C₂²×C₁₉	—	8	1	no	—
334	C₂²×C₁₉	—	8	1	no	—
335	C₂²×C₁₉	#532	1	1	yes	characteristic
336	C₂²×C₁₉	D₄²	1	1	yes	characteristic
337	C₂²×C₁₉	#550	1	1	yes	characteristic
338	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
339	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
340	C₂²×C₁₉	#577	1	1	yes	characteristic
341	C₂²×C₁₉	#577	1	1	yes	characteristic
342	C₄×C₁₉	—	2	2	no	—
343	C₄×C₁₉	—	2	2	no	—
344	C₄×C₁₉	—	4	1	no	—
345	C₄×C₁₉	—	4	2	no	—
346	C₄×C₁₉	—	4	1	no	—
347	C₄×C₁₉	—	4	1	no	—
348	C₄×C₁₉	—	4	1	no	—
349	C₄×C₁₉	—	8	1	no	—
350	C₄×C₁₉	—	8	1	no	—
351	C₄×C₁₉	—	8	1	no	—
352	C₄×C₁₉	—	8	1	no	—
353	C₄×C₁₉	—	8	1	no	—
354	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
355	C₄×C₁₉	#540	1	1	yes	characteristic
356	C₄×C₁₉	#546	1	1	yes	characteristic
357	C₄×C₁₉	#559	1	1	yes	characteristic
358	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
359	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
360	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
361	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
362	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
363	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
364	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
366	#495	—	2	4	no	—
367	C₄×SD₁₆	—	2	4	no	—
368	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
370	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
371	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
377	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
380	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
382	#399	—	2	1	no	—
383	#397	—	2	1	no	—
384	#397	—	2	1	no	—
385	#397	—	2	1	no	—
386	#391	C₂²×C₁₉	1	1	yes	characteristic
387	#391	C₂²×C₁₉	1	1	yes	characteristic
388	#391	C₂²×C₁₉	1	1	yes	characteristic
389	#390	C₂²×C₁₉	1	1	yes	characteristic
390	#390	C₂²×C₁₉	1	1	yes	characteristic
391	#390	C₂²×C₁₉	1	1	yes	characteristic
392	#389	C₂²×C₁₉	1	1	yes	characteristic
393	#389	C₂²×C₁₉	1	1	yes	characteristic
394	#388	—	2	1	no	—
395	#388	—	2	1	no	—
396	#385	—	2	1	no	—
397	#381	—	2	1	no	—
398	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
399	#340	C₂²×C₁₉	1	1	yes	characteristic
400	#340	C₂²×C₁₉	1	1	yes	characteristic
401	#336	C₂²×C₁₉	1	1	yes	characteristic
402	#336	C₂²×C₁₉	1	1	yes	characteristic
403	C₂×C₁₉	—	8	2	no	—
404	C₂×C₁₉	—	16	1	no	—
405	C₂×C₁₉	#2445	1	1	yes	characteristic
406	C₂×C₁₉	#3168	1	1	yes	characteristic
407	C₂×C₁₉	#3173	1	1	yes	characteristic
408	C₂×C₁₉	#3282	1	1	yes	characteristic
409	C₂×C₁₉	#3284	1	1	yes	characteristic
410	C₂×C₁₉	#3394	1	1	yes	characteristic
411	C₂×C₁₉	#3394	1	1	yes	characteristic
412	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
413	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
414	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
415	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
416	C₂³×C₄	—	2	1	no	—
417	C₂×Q₁₆	—	2	2	no	—
418	C₂×Q₁₆	—	2	2	no	—
419	C₂×Q₁₆	—	4	1	no	—
420	C₂×SD₁₆	—	2	2	no	—
421	C₂×SD₁₆	—	2	2	no	—
422	C₂×SD₁₆	—	2	2	no	—
423	C₂×SD₁₆	—	2	2	no	—
424	C₂×SD₁₆	—	2	2	no	—
425	C₂×SD₁₆	D₄×C₁₉	1	4	yes	—
426	C₂×D₈	—	2	2	no	—
427	C₂×D₈	—	2	2	no	—
428	C₂×D₈	—	4	1	no	—
429	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
430	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
431	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
432	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
433	#124	—	2	2	no	—
434	#124	—	2	2	no	—
435	#124	—	4	1	no	—
436	#124	—	4	1	no	—
437	C₄×Q₈	—	2	2	no	—
438	C₄×Q₈	—	4	1	no	—
439	C₄×D₄	—	2	2	no	—
440	C₄×D₄	—	4	1	no	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
445	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₄²	—	2	1	no	—
462	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
463	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
465	#106	—	2	2	no	—
466	#106	—	2	2	no	—
467	C₄⋊C₈	—	2	2	no	—
468	#103	—	2	2	no	—
469	#103	—	4	1	no	—
470	#103	—	4	1	no	—
471	#103	—	4	1	no	—
472	#102	—	2	2	no	—
473	#102	—	4	1	no	—
474	#102	—	4	1	no	—
475	#102	—	4	1	no	—
476	C₄×C₈	—	2	2	no	—
477	C₄×C₈	—	2	2	no	—
478	C₄×C₈	—	2	2	no	—
479	#95	—	2	1	no	—
480	#95	—	2	1	no	—
481	#95	—	2	1	no	—
482	#95	—	2	1	no	—
483	#95	—	2	1	no	—
484	#95	—	2	1	no	—
485	#95	—	2	1	no	—
486	#95	—	2	1	no	—
487	#95	D₄×C₁₉	1	1	yes	characteristic
488	#95	D₄×C₁₉	1	1	yes	characteristic
489	C₁₉	#26251	1	1	yes	characteristic, direct product factor, Sylow
490	C₂⁴	—	2	1	no	—
491	C₂⁴	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	8	1	no	—
525	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
530	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
532	Q₁₆	—	4	4	no	—
533	SD₁₆	—	2	8	no	—
534	SD₁₆	—	4	4	no	—
535	D₈	—	4	4	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
545	C₂×C₈	#41×C₁₉	1	2	yes	—
546	C₂×C₈	#41×C₁₉	1	2	yes	—
547	C₂×C₈	#41×C₁₉	1	2	yes	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	2	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	4	2	no	—
559	C₄⋊C₄	—	8	1	no	—
560	C₄⋊C₄	—	8	1	no	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	—	4	2	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₂²⋊C₄	—	4	2	no	—
565	C₂²⋊C₄	—	4	2	no	—
566	C₂²⋊C₄	—	4	2	no	—
567	C₂²⋊C₄	—	4	2	no	—
568	C₂²⋊C₄	—	4	2	no	—
569	C₂²⋊C₄	—	8	1	no	—
570	C₂²⋊C₄	—	8	1	no	—
571	C₂²⋊C₄	—	8	1	no	—
572	C₄²	—	2	1	no	—
573	C₄²	—	2	1	no	—
574	C₄²	—	2	1	no	—
575	C₄²	—	2	1	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	4	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
594	Q₈	—	2	2	no	—
595	Q₈	—	2	2	no	—
596	Q₈	—	4	1	no	—
597	Q₈	—	4	1	no	—
598	Q₈	—	4	1	no	—
599	Q₈	—	4	1	no	—
600	Q₈	—	4	1	no	—
601	Q₈	—	4	1	no	—
602	D₄	—	2	2	no	—
603	D₄	—	2	2	no	—
604	D₄	—	4	1	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	1	no	—
607	D₄	—	4	1	no	—
608	D₄	—	4	1	no	—
609	D₄	—	4	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	8	4	no	—
645	C₂×C₄	C₁₉×#135	1	2	yes	—
646	C₂×C₄	C₁₉×#135	1	2	yes	—
647	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
648	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
649	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
650	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
651	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
652	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
653	C₈	—	2	2	no	—
654	C₈	—	4	1	no	—
655	C₈	—	4	1	no	—
656	C₈	C₁₉×#123	1	4	yes	—
657	C₂²	—	4	2	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	2	no	—
660	C₂²	—	8	1	no	—
661	C₂²	—	8	1	no	—
662	C₂²	—	8	1	no	—
663	C₂²	—	8	1	no	—
664	C₂²	—	8	1	no	—
665	C₂²	—	8	1	no	—
666	C₂²	—	8	1	no	—
667	C₂²	—	8	1	no	—
668	C₂²	—	8	1	no	—
669	C₂²	—	8	1	no	—
670	C₂²	—	8	1	no	—
671	C₂²	C₁₉×#532	1	1	yes	characteristic
672	C₂²	D₄²×C₁₉	1	1	yes	characteristic
673	C₂²	C₁₉×#550	1	1	yes	characteristic
674	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
675	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
676	C₂²	C₁₉×#577	1	1	yes	characteristic
677	C₂²	C₁₉×#577	1	1	yes	characteristic
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	1	no	—
684	C₄	—	4	1	no	—
685	C₄	—	8	1	no	—
686	C₄	—	8	1	no	—
687	C₄	—	8	1	no	—
688	C₄	—	8	1	no	—
689	C₄	—	8	1	no	—
690	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
691	C₄	C₁₉×#540	1	1	yes	characteristic
692	C₄	C₁₉×#546	1	1	yes	characteristic
693	C₄	C₁₉×#559	1	1	yes	characteristic
694	C₂	—	8	2	no	—
695	C₂	—	16	1	no	—
696	C₂	C₁₉×#2445	1	1	yes	characteristic
697	C₂	C₁₉×#3168	1	1	yes	characteristic
698	C₂	C₁₉×#3173	1	1	yes	characteristic
699	C₂	C₁₉×#3282	1	1	yes	characteristic
700	C₂	C₁₉×#3284	1	1	yes	characteristic
701	C₂	C₁₉×#3394	1	1	yes	characteristic
702	C₂	C₁₉×#3394	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₈×C₁₉	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. C₂×C₄×SD₁₆×C₁₉	C₂	semidirect
3. C₁₉×#2448	C₂	semidirect
4. C₁₉×#2447	C₂	semidirect
5. C₁₉×#2056	C₂	semidirect
7. C₁₉×#2042	C₂	semidirect
8. C₁₉×#2042	C₂	semidirect
9. C₁₉×#1968	C₂	semidirect
10. C₁₉×#1968	C₂	semidirect
11. C₁₉×#1968	C₂	semidirect
12. C₁₉×#1941	C₂	semidirect
14. C₁₉×#1878	C₂	semidirect
15. C₈×C₄⋊C₄×C₁₉	C₂	semidirect
227. #26251	C₁₉	direct (N × H)
307. C₂×C₄×SD₁₆	C₂×C₁₉	semidirect
308. #2448	C₂×C₁₉	semidirect
309. #2447	C₂×C₁₉	semidirect
310. #2056	C₂×C₁₉	semidirect
312. #2042	C₂×C₁₉	semidirect
313. #2042	C₂×C₁₉	semidirect
314. #1968	C₂×C₁₉	semidirect
315. #1968	C₂×C₁₉	semidirect
316. #1968	C₂×C₁₉	semidirect
317. #1941	C₂×C₁₉	semidirect
319. #1878	C₂×C₁₉	semidirect
320. C₈×C₄⋊C₄	C₂×C₁₉	semidirect
489. C₁₉	#26251	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×#495	2
C₂×C₄×SD₁₆×C₁₉	2
C₁₉×#2448	2
C₁₉×#2447	2
C₁₉×#2056	2
C₁₉×#2054	2
C₁₉×#2042	2
C₁₉×#1968	2
C₁₉×#1941	2
C₁₉×#1879	2
C₁₉×#1878	2
C₈×C₄⋊C₄×C₁₉	2
#26251	19

Subgroups — C19×#26251 #18032210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26251 #18032210