Subgroups — C₁₉×#32729 #18038688

Order 4864.

776 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2855	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2850	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2097	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2067	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2066	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2034	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#2015	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2001	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2000	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1797	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	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#103	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×#102	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₁₉×#391	C₂²	1	1	yes	characteristic
38	C₁₉×#391	C₂²	1	1	yes	characteristic
39	C₁₉×#391	C₂²	1	1	yes	characteristic
40	C₁₉×#390	C₂²	1	1	yes	characteristic
41	C₁₉×#389	C₂²	1	1	yes	characteristic
42	C₁₉×#389	C₂²	1	1	yes	characteristic
43	C₁₉×#388	—	2	1	no	—
44	C₁₉×#388	—	2	1	no	—
45	C₁₉×#387	—	2	1	no	—
46	C₁₉×#387	—	2	1	no	—
47	C₁₉×#386	—	2	1	no	—
48	C₁₉×#386	—	2	1	no	—
49	C₁₉×#385	—	2	1	no	—
50	C₁₉×#382	C₂²	1	1	yes	characteristic
51	C₁₉×#381	—	2	1	no	—
52	C₁₉×#380	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	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×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₁₉	—	2	1	no	—
62	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×Q₁₆×C₁₉	—	4	1	no	—
67	C₂×Q₁₆×C₁₉	—	4	1	no	—
68	C₂×Q₁₆×C₁₉	—	4	1	no	—
69	C₂×SD₁₆×C₁₉	—	4	1	no	—
70	C₂×SD₁₆×C₁₉	—	4	1	no	—
71	C₂×SD₁₆×C₁₉	—	4	1	no	—
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₁₉×#124	—	4	1	no	—
77	C₁₉×#124	—	4	1	no	—
78	C₁₉×C₂²⋊Q₈	—	4	1	no	—
79	C₁₉×C₂²⋊Q₈	—	4	1	no	—
80	C₁₉×C₂²⋊Q₈	—	4	1	no	—
81	C₁₉×C₂²⋊Q₈	—	4	1	no	—
82	C₁₉×#121	—	4	1	no	—
83	C₁₉×#121	—	4	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₄²×C₁₉	—	4	1	no	—
102	C₂×C₄²×C₁₉	—	4	1	no	—
103	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
107	C₁₉×#107	—	4	1	no	—
108	C₁₉×#106	—	4	1	no	—
109	C₁₉×C₄⋊C₈	—	4	1	no	—
110	C₁₉×C₄⋊C₈	—	4	1	no	—
111	C₁₉×#103	—	4	1	no	—
112	C₁₉×#103	—	4	1	no	—
113	C₁₉×#103	—	4	1	no	—
114	C₁₉×#103	—	4	1	no	—
115	C₁₉×#103	—	4	1	no	—
116	C₁₉×#102	—	4	1	no	—
117	C₁₉×#102	—	4	1	no	—
118	C₁₉×#102	—	4	1	no	—
119	C₁₉×C₂²⋊C₈	—	4	1	no	—
120	C₁₉×C₂²⋊C₈	—	4	1	no	—
121	C₁₉×#95	—	2	1	no	—
122	C₁₉×#95	—	2	1	no	—
123	C₁₉×#95	—	2	1	no	—
124	C₁₉×#95	—	2	1	no	—
125	C₁₉×#95	—	2	1	no	—
126	C₁₉×#95	—	2	1	no	—
127	C₁₉×#95	—	2	1	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	C₂⁴×C₁₉	—	2	1	no	—
133	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂×Q₈×C₁₉	—	2	1	no	—
135	C₂×Q₈×C₁₉	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×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×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	—	2	1	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	4	2	no	—
153	C₂×D₄×C₁₉	—	4	2	no	—
154	C₂×D₄×C₁₉	—	4	2	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
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	1	no	—
171	C₂²×C₄×C₁₉	—	4	1	no	—
172	C₂²×C₄×C₁₉	—	4	1	no	—
173	C₂²×C₄×C₁₉	—	4	1	no	—
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	—	4	4	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	2	1	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	—	2	1	no	—
193	C₂×C₈×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	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	—	4	2	no	—
205	C₄⋊C₄×C₁₉	—	4	2	no	—
206	C₄⋊C₄×C₁₉	—	4	2	no	—
207	C₄⋊C₄×C₁₉	—	4	2	no	—
208	C₂²⋊C₄×C₁₉	—	4	2	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	C₄²×C₁₉	—	2	1	no	—
217	C₄²×C₁₉	—	2	1	no	—
218	C₄²×C₁₉	—	2	1	no	—
219	C₄²×C₁₉	—	2	1	no	—
220	C₄²×C₁₉	—	4	1	no	—
221	C₄²×C₁₉	—	4	1	no	—
222	#32729	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂³×C₁₉	—	2	1	no	—
224	C₂³×C₁₉	—	2	1	no	—
225	C₂³×C₁₉	—	2	1	no	—
226	C₂³×C₁₉	—	2	1	no	—
227	C₂³×C₁₉	—	2	1	no	—
228	C₂³×C₁₉	—	2	1	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	#137	1	2	yes	—
237	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
238	Q₈×C₁₉	—	4	1	no	—
239	Q₈×C₁₉	—	4	1	no	—
240	Q₈×C₁₉	—	4	1	no	—
241	Q₈×C₁₉	—	4	1	no	—
242	Q₈×C₁₉	—	4	1	no	—
243	Q₈×C₁₉	—	4	1	no	—
244	Q₈×C₁₉	—	4	1	no	—
245	Q₈×C₁₉	—	4	1	no	—
246	D₄×C₁₉	—	4	1	no	—
247	D₄×C₁₉	—	4	1	no	—
248	D₄×C₁₉	—	4	1	no	—
249	D₄×C₁₉	—	4	1	no	—
250	D₄×C₁₉	—	8	4	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	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	—	4	4	no	—
266	C₂×C₄×C₁₉	—	4	4	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	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	#135	1	2	yes	—
293	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
294	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
295	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
296	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
297	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
298	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
299	C₈×C₁₉	—	4	1	no	—
300	C₈×C₁₉	—	4	1	no	—
301	C₈×C₁₉	—	4	1	no	—
302	C₈×C₁₉	—	4	1	no	—
303	#2855	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#2850	C₂×C₁₉	1	1	yes	characteristic
305	#2101	C₂×C₁₉	1	1	yes	characteristic, complemented
306	#2097	C₂×C₁₉	1	1	yes	characteristic, complemented
307	#2067	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#2066	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#2056	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#2055	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#2042	C₂×C₁₉	1	1	yes	characteristic, complemented
312	#2036	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#2034	C₂×C₁₉	1	1	yes	characteristic
314	#2015	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#2001	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#2000	C₂×C₁₉	1	1	yes	characteristic
317	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
318	C₂²×C₁₉	—	2	2	no	—
319	C₂²×C₁₉	—	2	2	no	—
320	C₂²×C₁₉	—	2	2	no	—
321	C₂²×C₁₉	—	4	1	no	—
322	C₂²×C₁₉	—	4	1	no	—
323	C₂²×C₁₉	—	4	1	no	—
324	C₂²×C₁₉	—	4	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	#534	1	1	yes	characteristic
333	C₂²×C₁₉	#535	1	1	yes	characteristic
334	C₂²×C₁₉	#537	1	1	yes	characteristic
335	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
336	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
337	C₂²×C₁₉	#575	1	1	yes	characteristic
338	C₂²×C₁₉	#575	1	1	yes	characteristic
339	C₄×C₁₉	—	2	2	no	—
340	C₄×C₁₉	—	4	1	no	—
341	C₄×C₁₉	—	4	1	no	—
342	C₄×C₁₉	—	4	1	no	—
343	C₄×C₁₉	—	4	1	no	—
344	C₄×C₁₉	—	8	1	no	—
345	C₄×C₁₉	—	8	1	no	—
346	C₄×C₁₉	—	8	1	no	—
347	C₄×C₁₉	—	8	1	no	—
348	C₄×C₁₉	—	8	1	no	—
349	C₄×C₁₉	—	8	1	no	—
350	C₄×C₁₉	—	8	1	no	—
351	C₄×C₁₉	#560	1	1	yes	characteristic
352	C₄×C₁₉	#560	1	1	yes	characteristic
353	C₄×C₁₉	#562	1	1	yes	characteristic
354	C₄×C₁₉	#562	1	1	yes	characteristic
355	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
356	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
361	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
362	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
363	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
364	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
370	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
371	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
376	#391	C₂²×C₁₉	1	1	yes	characteristic
377	#391	C₂²×C₁₉	1	1	yes	characteristic
378	#391	C₂²×C₁₉	1	1	yes	characteristic
379	#390	C₂²×C₁₉	1	1	yes	characteristic
380	#389	C₂²×C₁₉	1	1	yes	characteristic
381	#389	C₂²×C₁₉	1	1	yes	characteristic
382	#388	—	2	1	no	—
383	#388	—	2	1	no	—
384	#387	—	2	1	no	—
385	#387	—	2	1	no	—
386	#386	—	2	1	no	—
387	#386	—	2	1	no	—
388	#385	—	2	1	no	—
389	#382	C₂²×C₁₉	1	1	yes	characteristic
390	#381	—	2	1	no	—
391	#380	C₂²×C₁₉	1	1	yes	characteristic
392	#340	C₂²×C₁₉	1	1	yes	characteristic
393	#340	C₂²×C₁₉	1	1	yes	characteristic
394	#340	C₂²×C₁₉	1	1	yes	characteristic
395	#340	C₂²×C₁₉	1	1	yes	characteristic
396	#336	C₂²×C₁₉	1	1	yes	characteristic
397	#336	C₂²×C₁₉	1	1	yes	characteristic
398	C₂×C₁₉	—	4	2	no	—
399	C₂×C₁₉	—	16	1	no	—
400	C₂×C₁₉	#2813	1	1	yes	characteristic
401	C₂×C₁₉	#3191	1	1	yes	characteristic
402	C₂×C₁₉	#3196	1	1	yes	characteristic
403	C₂×C₁₉	#3212	1	1	yes	characteristic
404	C₂×C₁₉	#3215	1	1	yes	characteristic
405	C₂×C₁₉	#3248	1	1	yes	characteristic
406	C₂×C₁₉	#3256	1	1	yes	characteristic
407	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
408	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
409	C₂²×D₄	—	2	1	no	—
410	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
411	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
412	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
413	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
414	C₂×Q₁₆	—	4	1	no	—
415	C₂×Q₁₆	—	4	1	no	—
416	C₂×Q₁₆	—	4	1	no	—
417	C₂×SD₁₆	—	4	1	no	—
418	C₂×SD₁₆	—	4	1	no	—
419	C₂×SD₁₆	—	4	1	no	—
420	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
422	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
424	#124	—	4	1	no	—
425	#124	—	4	1	no	—
426	C₂²⋊Q₈	—	4	1	no	—
427	C₂²⋊Q₈	—	4	1	no	—
428	C₂²⋊Q₈	—	4	1	no	—
429	C₂²⋊Q₈	—	4	1	no	—
430	#121	—	4	1	no	—
431	#121	—	4	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₄²	—	4	1	no	—
450	C₂×C₄²	—	4	1	no	—
451	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
452	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
453	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
454	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
455	#107	—	4	1	no	—
456	#106	—	4	1	no	—
457	C₄⋊C₈	—	4	1	no	—
458	C₄⋊C₈	—	4	1	no	—
459	#103	—	4	1	no	—
460	#103	—	4	1	no	—
461	#103	—	4	1	no	—
462	#103	—	4	1	no	—
463	#103	—	4	1	no	—
464	#102	—	4	1	no	—
465	#102	—	4	1	no	—
466	#102	—	4	1	no	—
467	C₂²⋊C₈	—	4	1	no	—
468	C₂²⋊C₈	—	4	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	—	2	1	no	—
475	#95	—	2	1	no	—
476	#95	—	2	1	no	—
477	#95	—	2	1	no	—
478	#95	—	2	1	no	—
479	#95	—	2	1	no	—
480	C₁₉	#32729	1	1	yes	characteristic, direct product factor, Sylow
481	C₂⁴	—	2	1	no	—
482	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	4	2	no	—
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	—	4	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	4	1	no	—
520	C₂²×C₄	—	4	1	no	—
521	C₂²×C₄	—	4	1	no	—
522	C₂²×C₄	—	4	1	no	—
523	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	C₂⁴×C₁₉	1	1	yes	characteristic
529	Q₁₆	—	4	4	no	—
530	SD₁₆	—	4	4	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	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	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	4	2	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	—	4	2	no	—
556	C₄⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	—	4	2	no	—
559	C₂²⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	4	2	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	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	4	1	no	—
570	C₄²	—	4	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	4	1	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	C₁₉×#137	1	2	yes	—
585	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
586	Q₈	—	4	1	no	—
587	Q₈	—	4	1	no	—
588	Q₈	—	4	1	no	—
589	Q₈	—	4	1	no	—
590	Q₈	—	4	1	no	—
591	Q₈	—	4	1	no	—
592	Q₈	—	4	1	no	—
593	Q₈	—	4	1	no	—
594	D₄	—	4	1	no	—
595	D₄	—	4	1	no	—
596	D₄	—	4	1	no	—
597	D₄	—	4	1	no	—
598	D₄	—	8	4	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	4	4	no	—
614	C₂×C₄	—	4	4	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	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	C₁₉×#135	1	2	yes	—
641	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
642	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
643	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
644	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
645	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
646	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
647	C₈	—	4	1	no	—
648	C₈	—	4	1	no	—
649	C₈	—	4	1	no	—
650	C₈	—	4	1	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	8	1	no	—
659	C₂²	—	8	1	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	C₁₉×#534	1	1	yes	characteristic
666	C₂²	C₁₉×#535	1	1	yes	characteristic
667	C₂²	C₁₉×#537	1	1	yes	characteristic
668	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
669	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
670	C₂²	C₁₉×#575	1	1	yes	characteristic
671	C₂²	C₁₉×#575	1	1	yes	characteristic
672	C₄	—	2	2	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	1	no	—
676	C₄	—	4	1	no	—
677	C₄	—	8	1	no	—
678	C₄	—	8	1	no	—
679	C₄	—	8	1	no	—
680	C₄	—	8	1	no	—
681	C₄	—	8	1	no	—
682	C₄	—	8	1	no	—
683	C₄	—	8	1	no	—
684	C₄	C₁₉×#560	1	1	yes	characteristic
685	C₄	C₁₉×#560	1	1	yes	characteristic
686	C₄	C₁₉×#562	1	1	yes	characteristic
687	C₄	C₁₉×#562	1	1	yes	characteristic
688	C₂	—	4	2	no	—
689	C₂	—	16	1	no	—
690	C₂	C₁₉×#2813	1	1	yes	characteristic
691	C₂	C₁₉×#3191	1	1	yes	characteristic
692	C₂	C₁₉×#3196	1	1	yes	characteristic
693	C₂	C₁₉×#3212	1	1	yes	characteristic
694	C₂	C₁₉×#3215	1	1	yes	characteristic
695	C₂	C₁₉×#3248	1	1	yes	characteristic
696	C₂	C₁₉×#3256	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2855	C₂	semidirect
3. C₁₉×#2101	C₂	semidirect
4. C₁₉×#2097	C₂	semidirect
5. C₁₉×#2067	C₂	semidirect
6. C₁₉×#2066	C₂	semidirect
7. C₁₉×#2056	C₂	semidirect
8. C₁₉×#2055	C₂	semidirect
9. C₁₉×#2042	C₂	semidirect
10. C₁₉×#2036	C₂	semidirect
12. C₁₉×#2015	C₂	semidirect
13. C₁₉×#2001	C₂	semidirect
15. C₁₉×#1797	C₂	semidirect
222. #32729	C₁₉	direct (N × H)
303. #2855	C₂×C₁₉	semidirect
305. #2101	C₂×C₁₉	semidirect
306. #2097	C₂×C₁₉	semidirect
307. #2067	C₂×C₁₉	semidirect
308. #2066	C₂×C₁₉	semidirect
309. #2056	C₂×C₁₉	semidirect
310. #2055	C₂×C₁₉	semidirect
311. #2042	C₂×C₁₉	semidirect
312. #2036	C₂×C₁₉	semidirect
314. #2015	C₂×C₁₉	semidirect
315. #2001	C₂×C₁₉	semidirect
317. #1797	C₂×C₁₉	semidirect
480. C₁₉	#32729	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×#2855	2
C₁₉×#2850	2
C₁₉×#2101	2
C₁₉×#2097	2
C₁₉×#2067	2
C₁₉×#2066	2
C₁₉×#2056	2
C₁₉×#2055	2
C₁₉×#2042	2
C₁₉×#2036	2
C₁₉×#2034	2
C₁₉×#2015	2
C₁₉×#2001	2
C₁₉×#2000	2
C₁₉×#1797	2
#32729	19

Subgroups — C19×#32729 #18038688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32729 #18038688