Subgroups — C₁₉×#29537 #18035496

Order 4864.

764 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2295	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2293	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2087	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2068	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2065	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2055	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1925	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1919	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1918	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1880	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1877	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1862	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#117	—	2	1	no	—
20	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	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	C₁₉×#391	C₂²	1	1	yes	characteristic
32	C₁₉×#391	C₂²	1	1	yes	characteristic
33	C₁₉×#390	C₂²	1	1	yes	characteristic
34	C₁₉×#390	C₂²	1	1	yes	characteristic
35	C₁₉×#389	C₂²	1	1	yes	characteristic
36	C₁₉×#389	C₂²	1	1	yes	characteristic
37	C₁₉×#389	C₂²	1	1	yes	characteristic
38	C₁₉×#389	C₂²	1	1	yes	characteristic
39	C₁₉×#388	—	2	1	no	—
40	C₁₉×#388	—	2	1	no	—
41	C₁₉×#387	—	2	1	no	—
42	C₁₉×#387	—	2	1	no	—
43	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₁₉×#376	—	2	1	no	—
48	C₄³×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×Q₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	—	2	1	no	—
62	C₂×SD₁₆×C₁₉	—	2	2	no	—
63	C₂×SD₁₆×C₁₉	—	2	2	no	—
64	C₂×SD₁₆×C₁₉	—	4	1	no	—
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	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₄×Q₈×C₁₉	—	2	2	no	—
71	C₄×D₄×C₁₉	—	2	2	no	—
72	C₄×D₄×C₁₉	—	2	2	no	—
73	C₁₉×#117	—	4	4	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	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	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	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×C₂²⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄²×C₁₉	—	2	1	no	—
91	C₂×C₄²×C₁₉	—	2	1	no	—
92	C₂×C₄²×C₁₉	—	2	1	no	—
93	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
100	C₁₉×#107	—	2	2	no	—
101	C₁₉×#107	—	4	1	no	—
102	C₁₉×#106	—	2	2	no	—
103	C₁₉×C₄⋊C₈	—	4	1	no	—
104	C₁₉×C₄⋊C₈	—	4	1	no	—
105	C₁₉×#103	—	2	2	no	—
106	C₁₉×#103	—	2	2	no	—
107	C₁₉×#103	—	4	1	no	—
108	C₁₉×#102	—	2	2	no	—
109	C₁₉×#102	—	2	2	no	—
110	C₁₉×#102	—	4	1	no	—
111	C₁₉×#95	—	2	1	no	—
112	C₁₉×#95	—	2	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	—	2	1	no	—
120	C₁₉×#95	—	2	1	no	—
121	C₂⁴×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	#41	1	2	yes	—
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	#41	1	2	yes	—
134	C₂²×C₄×C₁₉	—	2	4	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	1	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	4	2	no	—
143	C₂²×C₄×C₁₉	—	4	2	no	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
151	SD₁₆×C₁₉	—	4	4	no	—
152	C₂×C₈×C₁₉	—	2	1	no	—
153	C₂×C₈×C₁₉	—	2	1	no	—
154	C₂×C₈×C₁₉	—	2	1	no	—
155	C₂×C₈×C₁₉	—	2	1	no	—
156	C₂×C₈×C₁₉	—	2	1	no	—
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	C₄⋊C₄×C₁₉	—	2	4	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	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	—	4	2	no	—
176	C₄⋊C₄×C₁₉	—	4	2	no	—
177	C₄⋊C₄×C₁₉	—	4	2	no	—
178	C₄⋊C₄×C₁₉	—	4	2	no	—
179	C₄⋊C₄×C₁₉	#41	1	2	yes	—
180	C₄⋊C₄×C₁₉	#41	1	2	yes	—
181	C₂²⋊C₄×C₁₉	—	2	4	no	—
182	C₂²⋊C₄×C₁₉	—	4	2	no	—
183	C₂²⋊C₄×C₁₉	—	4	2	no	—
184	C₂²⋊C₄×C₁₉	—	4	2	no	—
185	C₂²⋊C₄×C₁₉	—	4	2	no	—
186	C₄²×C₁₉	—	2	4	no	—
187	C₄²×C₁₉	—	2	2	no	—
188	C₄²×C₁₉	—	2	2	no	—
189	C₄²×C₁₉	—	2	2	no	—
190	C₄²×C₁₉	—	2	1	no	—
191	C₄²×C₁₉	—	2	1	no	—
192	C₄²×C₁₉	—	2	1	no	—
193	C₄²×C₁₉	—	2	1	no	—
194	C₄²×C₁₉	—	2	1	no	—
195	C₄²×C₁₉	—	2	1	no	—
196	C₄²×C₁₉	—	4	1	no	—
197	C₄²×C₁₉	—	4	2	no	—
198	C₄²×C₁₉	—	4	2	no	—
199	#29537	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂³×C₁₉	—	2	2	no	—
201	C₂³×C₁₉	—	4	1	no	—
202	C₂³×C₁₉	—	4	1	no	—
203	C₂³×C₁₉	—	4	1	no	—
204	C₂³×C₁₉	—	4	1	no	—
205	C₂³×C₁₉	—	4	1	no	—
206	C₂³×C₁₉	—	4	1	no	—
207	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
208	Q₈×C₁₉	—	2	2	no	—
209	Q₈×C₁₉	—	2	2	no	—
210	Q₈×C₁₉	—	4	1	no	—
211	Q₈×C₁₉	—	4	1	no	—
212	D₄×C₁₉	—	2	2	no	—
213	D₄×C₁₉	—	2	2	no	—
214	D₄×C₁₉	—	4	1	no	—
215	D₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	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	—	4	8	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	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	#135	1	2	yes	—
254	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
255	C₂×C₄×C₁₉	#137	1	2	yes	—
256	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
260	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
261	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
262	C₈×C₁₉	—	4	1	no	—
263	C₈×C₁₉	—	4	1	no	—
264	C₈×C₁₉	—	4	1	no	—
265	C₈×C₁₉	—	4	1	no	—
266	#2295	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#2293	C₂×C₁₉	1	1	yes	characteristic
268	#2087	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#2068	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#2065	C₂×C₁₉	1	1	yes	characteristic
271	#2055	C₂×C₁₉	1	1	yes	characteristic
272	#1928	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1925	C₂×C₁₉	1	1	yes	characteristic
274	#1919	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1918	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1880	C₂×C₁₉	1	1	yes	characteristic
277	#1877	C₂×C₁₉	1	1	yes	characteristic
278	#1865	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1862	C₂×C₁₉	1	1	yes	characteristic
280	#1831	C₂×C₁₉	1	1	yes	characteristic, complemented
281	C₂²×C₁₉	—	4	2	no	—
282	C₂²×C₁₉	—	4	2	no	—
283	C₂²×C₁₉	—	4	2	no	—
284	C₂²×C₁₉	—	8	1	no	—
285	C₂²×C₁₉	—	8	1	no	—
286	C₂²×C₁₉	—	8	1	no	—
287	C₂²×C₁₉	—	8	1	no	—
288	C₂²×C₁₉	#525	1	1	yes	characteristic
289	C₂²×C₁₉	#525	1	1	yes	characteristic
290	C₂²×C₁₉	#537	1	1	yes	characteristic
291	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
292	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
293	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
294	C₂²×C₁₉	#575	1	1	yes	characteristic
295	C₄×C₁₉	—	2	2	no	—
296	C₄×C₁₉	—	2	2	no	—
297	C₄×C₁₉	—	2	2	no	—
298	C₄×C₁₉	—	4	1	no	—
299	C₄×C₁₉	—	4	2	no	—
300	C₄×C₁₉	—	4	2	no	—
301	C₄×C₁₉	—	4	1	no	—
302	C₄×C₁₉	—	4	2	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	8	1	no	—
305	C₄×C₁₉	—	8	1	no	—
306	C₄×C₁₉	—	8	1	no	—
307	C₄×C₁₉	—	8	1	no	—
308	C₄×C₁₉	#551	1	1	yes	characteristic
309	C₄×C₁₉	#552	1	1	yes	characteristic
310	C₄×C₁₉	#552	1	1	yes	characteristic
311	C₄×C₁₉	#555	1	1	yes	characteristic
312	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
313	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×#117	—	2	1	no	—
316	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
317	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
321	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
324	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
327	#391	C₂²×C₁₉	1	1	yes	characteristic
328	#391	C₂²×C₁₉	1	1	yes	characteristic
329	#390	C₂²×C₁₉	1	1	yes	characteristic
330	#390	C₂²×C₁₉	1	1	yes	characteristic
331	#389	C₂²×C₁₉	1	1	yes	characteristic
332	#389	C₂²×C₁₉	1	1	yes	characteristic
333	#389	C₂²×C₁₉	1	1	yes	characteristic
334	#389	C₂²×C₁₉	1	1	yes	characteristic
335	#388	—	2	1	no	—
336	#388	—	2	1	no	—
337	#387	—	2	1	no	—
338	#387	—	2	1	no	—
339	C₄×C₄⋊C₄	—	2	1	no	—
340	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
341	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
342	C₄×C₂²⋊C₄	—	2	1	no	—
343	#376	—	2	1	no	—
344	C₄³	C₂²×C₁₉	1	1	yes	characteristic
345	#340	C₂²×C₁₉	1	1	yes	characteristic
346	#340	C₂²×C₁₉	1	1	yes	characteristic
347	#340	C₂²×C₁₉	1	1	yes	characteristic
348	#340	C₂²×C₁₉	1	1	yes	characteristic
349	#340	C₂²×C₁₉	1	1	yes	characteristic
350	#340	C₂²×C₁₉	1	1	yes	characteristic
351	#336	C₂²×C₁₉	1	1	yes	characteristic
352	#336	C₂²×C₁₉	1	1	yes	characteristic
353	#336	C₂²×C₁₉	1	1	yes	characteristic
354	#336	C₂²×C₁₉	1	1	yes	characteristic
355	C₂×C₁₉	—	8	2	no	—
356	C₂×C₁₉	#2609	1	1	yes	characteristic
357	C₂×C₁₉	#3102	1	1	yes	characteristic
358	C₂×C₁₉	#3105	1	1	yes	characteristic
359	C₂×C₁₉	#3112	1	1	yes	characteristic
360	C₂×C₁₉	#3116	1	1	yes	characteristic
361	C₂×C₁₉	#3248	1	1	yes	characteristic
362	C₂×C₁₉	#3251	1	1	yes	characteristic
363	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
364	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
365	C₂³×C₄	—	2	1	no	—
366	C₂×SD₁₆	—	2	2	no	—
367	C₂×SD₁₆	—	2	2	no	—
368	C₂×SD₁₆	—	4	1	no	—
369	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
373	C₄×Q₈	—	2	2	no	—
374	C₄×Q₈	—	2	2	no	—
375	C₄×D₄	—	2	2	no	—
376	C₄×D₄	—	2	2	no	—
377	#117	—	4	4	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
398	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
399	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
400	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
404	#107	—	2	2	no	—
405	#107	—	4	1	no	—
406	#106	—	2	2	no	—
407	C₄⋊C₈	—	4	1	no	—
408	C₄⋊C₈	—	4	1	no	—
409	#103	—	2	2	no	—
410	#103	—	2	2	no	—
411	#103	—	4	1	no	—
412	#102	—	2	2	no	—
413	#102	—	2	2	no	—
414	#102	—	4	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	C₁₉	#29537	1	1	yes	characteristic, direct product factor, Sylow
426	C₂⁴	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	#41×C₁₉	1	2	yes	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	#41×C₁₉	1	2	yes	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	—	4	2	no	—
449	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
456	SD₁₆	—	4	4	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	4	2	no	—
481	C₄⋊C₄	—	4	2	no	—
482	C₄⋊C₄	—	4	2	no	—
483	C₄⋊C₄	—	4	2	no	—
484	C₄⋊C₄	#41×C₁₉	1	2	yes	—
485	C₄⋊C₄	#41×C₁₉	1	2	yes	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	—	4	2	no	—
488	C₂²⋊C₄	—	4	2	no	—
489	C₂²⋊C₄	—	4	2	no	—
490	C₂²⋊C₄	—	4	2	no	—
491	C₄²	—	2	4	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	2	2	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	4	1	no	—
502	C₄²	—	4	2	no	—
503	C₄²	—	4	2	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	4	1	no	—
506	C₂³	—	4	1	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	4	1	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	1	no	—
511	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
512	Q₈	—	2	2	no	—
513	Q₈	—	2	2	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	4	1	no	—
516	D₄	—	2	2	no	—
517	D₄	—	2	2	no	—
518	D₄	—	4	1	no	—
519	D₄	—	4	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	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	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	4	8	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	C₁₉×#135	1	2	yes	—
558	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
559	C₂×C₄	C₁₉×#137	1	2	yes	—
560	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
561	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
562	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
563	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
564	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
565	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₈	—	4	1	no	—
569	C₈	—	4	1	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	8	1	no	—
574	C₂²	—	8	1	no	—
575	C₂²	—	8	1	no	—
576	C₂²	—	8	1	no	—
577	C₂²	C₁₉×#525	1	1	yes	characteristic
578	C₂²	C₁₉×#525	1	1	yes	characteristic
579	C₂²	C₁₉×#537	1	1	yes	characteristic
580	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
581	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
582	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
583	C₂²	C₁₉×#575	1	1	yes	characteristic
584	C₄	—	2	2	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	2	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	2	no	—
593	C₄	—	8	1	no	—
594	C₄	—	8	1	no	—
595	C₄	—	8	1	no	—
596	C₄	—	8	1	no	—
597	C₄	C₁₉×#551	1	1	yes	characteristic
598	C₄	C₁₉×#552	1	1	yes	characteristic
599	C₄	C₁₉×#552	1	1	yes	characteristic
600	C₄	C₁₉×#555	1	1	yes	characteristic
601	C₂	—	8	2	no	—
602	C₂	C₁₉×#2609	1	1	yes	characteristic
603	C₂	C₁₉×#3102	1	1	yes	characteristic
604	C₂	C₁₉×#3105	1	1	yes	characteristic
605	C₂	C₁₉×#3112	1	1	yes	characteristic
606	C₂	C₁₉×#3116	1	1	yes	characteristic
607	C₂	C₁₉×#3248	1	1	yes	characteristic
608	C₂	C₁₉×#3251	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2295	C₂	semidirect
3. C₁₉×#2087	C₂	semidirect
4. C₁₉×#2068	C₂	semidirect
7. C₁₉×#1928	C₂	semidirect
9. C₁₉×#1919	C₂	semidirect
10. C₁₉×#1918	C₂	semidirect
13. C₁₉×#1865	C₂	semidirect
15. C₁₉×#1831	C₂	semidirect
199. #29537	C₁₉	direct (N × H)
266. #2295	C₂×C₁₉	semidirect
268. #2087	C₂×C₁₉	semidirect
269. #2068	C₂×C₁₉	semidirect
272. #1928	C₂×C₁₉	semidirect
274. #1919	C₂×C₁₉	semidirect
275. #1918	C₂×C₁₉	semidirect
278. #1865	C₂×C₁₉	semidirect
280. #1831	C₂×C₁₉	semidirect
425. C₁₉	#29537	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×#2295	2
C₁₉×#2293	2
C₁₉×#2087	2
C₁₉×#2068	2
C₁₉×#2065	2
C₁₉×#2055	2
C₁₉×#1928	2
C₁₉×#1925	2
C₁₉×#1919	2
C₁₉×#1918	2
C₁₉×#1880	2
C₁₉×#1877	2
C₁₉×#1865	2
C₁₉×#1862	2
C₁₉×#1831	2
#29537	19

Subgroups — C19×#29537 #18035496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#29537 #18035496