Subgroups — C₁₉×#32731 #18038690

Order 4864.

782 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2625	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2619	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×#2065	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2014	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1798	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	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×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#102	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×#400	—	2	1	no	—
38	C₁₉×#398	—	2	1	no	—
39	C₁₉×#397	—	2	1	no	—
40	C₁₉×#397	—	2	1	no	—
41	C₁₉×#394	—	2	1	no	—
42	C₁₉×#394	—	2	1	no	—
43	C₁₉×#392	—	2	1	no	—
44	C₁₉×#392	—	2	1	no	—
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×#389	C₂²	1	1	yes	characteristic
50	C₁₉×#389	C₂²	1	1	yes	characteristic
51	C₁₉×#382	C₂²	1	1	yes	characteristic
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×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	—	2	1	no	—
62	C₂²×D₄×C₁₉	—	2	1	no	—
63	C₂²×D₄×C₁₉	—	2	1	no	—
64	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×SD₁₆×C₁₉	—	4	1	no	—
68	C₂×SD₁₆×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	C₂×SD₁₆×C₁₉	—	4	1	no	—
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	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
77	C₁₉×#127	—	4	1	no	—
78	C₁₉×#127	—	4	1	no	—
79	C₁₉×C₂²⋊Q₈	—	4	1	no	—
80	C₁₉×C₂²⋊Q₈	—	4	1	no	—
81	C₁₉×#121	—	4	1	no	—
82	C₁₉×#121	—	4	1	no	—
83	C₁₉×#121	—	4	1	no	—
84	C₁₉×#121	—	4	1	no	—
85	C₁₉×#117	—	4	1	no	—
86	C₁₉×#117	—	4	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₉	C₂³	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×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×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	D₄	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
109	C₁₉×#107	—	4	1	no	—
110	C₁₉×#106	—	4	1	no	—
111	C₁₉×C₄⋊C₈	—	4	1	no	—
112	C₁₉×C₄⋊C₈	—	4	1	no	—
113	C₁₉×#103	—	4	1	no	—
114	C₁₉×#103	—	4	1	no	—
115	C₁₉×#102	—	4	1	no	—
116	C₁₉×#102	—	4	1	no	—
117	C₁₉×#102	—	4	1	no	—
118	C₁₉×#102	—	4	1	no	—
119	C₁₉×#102	—	4	1	no	—
120	C₁₉×#102	—	4	1	no	—
121	C₁₉×C₂²⋊C₈	—	4	1	no	—
122	C₁₉×C₂²⋊C₈	—	4	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	—	2	1	no	—
134	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
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×D₄×C₁₉	—	2	1	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×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	—	2	1	no	—
153	C₂×D₄×C₁₉	—	4	2	no	—
154	C₂×D₄×C₁₉	—	4	2	no	—
155	C₂×D₄×C₁₉	—	4	2	no	—
156	C₂×D₄×C₁₉	—	4	2	no	—
157	C₂×D₄×C₁₉	—	8	1	no	—
158	C₂×D₄×C₁₉	—	8	1	no	—
159	C₂×D₄×C₁₉	—	8	1	no	—
160	C₂×D₄×C₁₉	—	8	1	no	—
161	C₂×D₄×C₁₉	—	8	1	no	—
162	C₂×D₄×C₁₉	—	8	1	no	—
163	C₂×D₄×C₁₉	—	8	1	no	—
164	C₂×D₄×C₁₉	—	8	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	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
183	SD₁₆×C₁₉	—	4	4	no	—
184	SD₁₆×C₁₉	—	4	4	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	C₂×C₈×C₁₉	—	2	1	no	—
195	C₂×C₈×C₁₉	—	2	1	no	—
196	C₂×C₈×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	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	4	1	no	—
208	C₄⋊C₄×C₁₉	—	4	1	no	—
209	C₄⋊C₄×C₁₉	—	4	2	no	—
210	C₄⋊C₄×C₁₉	—	8	1	no	—
211	C₄⋊C₄×C₁₉	—	8	1	no	—
212	C₂²⋊C₄×C₁₉	—	4	1	no	—
213	C₂²⋊C₄×C₁₉	—	4	1	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	C₂²⋊C₄×C₁₉	—	8	1	no	—
221	C₂²⋊C₄×C₁₉	—	8	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	#32731	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂³×C₁₉	—	2	1	no	—
228	C₂³×C₁₉	—	2	1	no	—
229	C₂³×C₁₉	—	2	1	no	—
230	C₂³×C₁₉	—	2	1	no	—
231	C₂³×C₁₉	—	2	1	no	—
232	C₂³×C₁₉	—	2	1	no	—
233	C₂³×C₁₉	—	2	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	—	4	1	no	—
243	C₂³×C₁₉	—	4	1	no	—
244	C₂³×C₁₉	—	4	1	no	—
245	C₂³×C₁₉	—	4	1	no	—
246	C₂³×C₁₉	—	4	1	no	—
247	C₂³×C₁₉	—	4	1	no	—
248	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
249	Q₈×C₁₉	—	4	1	no	—
250	Q₈×C₁₉	—	4	1	no	—
251	Q₈×C₁₉	—	4	1	no	—
252	Q₈×C₁₉	—	4	1	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	D₄×C₁₉	—	4	1	no	—
260	D₄×C₁₉	—	4	1	no	—
261	D₄×C₁₉	—	8	4	no	—
262	D₄×C₁₉	—	8	4	no	—
263	D₄×C₁₉	—	8	4	no	—
264	D₄×C₁₉	—	8	4	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	2	1	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	—	2	1	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	1	no	—
279	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
294	C₂×C₄×C₁₉	—	4	1	no	—
295	C₂×C₄×C₁₉	—	4	1	no	—
296	C₂×C₄×C₁₉	—	4	1	no	—
297	C₂×C₄×C₁₉	—	4	1	no	—
298	C₂×C₄×C₁₉	—	4	1	no	—
299	C₂×C₄×C₁₉	—	4	1	no	—
300	C₂×C₄×C₁₉	—	4	1	no	—
301	C₂×C₄×C₁₉	—	4	1	no	—
302	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
303	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
304	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
305	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
306	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
307	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
308	C₈×C₁₉	—	4	1	no	—
309	C₈×C₁₉	—	4	1	no	—
310	C₈×C₁₉	—	4	1	no	—
311	C₈×C₁₉	—	4	1	no	—
312	#2625	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#2619	C₂×C₁₉	1	1	yes	characteristic
314	#2101	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#2097	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#2067	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#2065	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#2055	C₂×C₁₉	1	1	yes	characteristic, complemented
319	#2055	C₂×C₁₉	1	1	yes	characteristic, complemented
320	#2041	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#2034	C₂×C₁₉	1	1	yes	characteristic, complemented
322	#2033	C₂×C₁₉	1	1	yes	characteristic, complemented
323	#2014	C₂×C₁₉	1	1	yes	characteristic, complemented
324	#2000	C₂×C₁₉	1	1	yes	characteristic, complemented
325	#2000	C₂×C₁₉	1	1	yes	characteristic, complemented
326	#1798	C₂×C₁₉	1	1	yes	characteristic, complemented
327	C₂²×C₁₉	—	4	1	no	—
328	C₂²×C₁₉	—	4	1	no	—
329	C₂²×C₁₉	—	4	1	no	—
330	C₂²×C₁₉	—	4	1	no	—
331	C₂²×C₁₉	—	4	1	no	—
332	C₂²×C₁₉	—	4	1	no	—
333	C₂²×C₁₉	—	4	1	no	—
334	C₂²×C₁₉	—	8	1	no	—
335	C₂²×C₁₉	—	8	1	no	—
336	C₂²×C₁₉	—	8	1	no	—
337	C₂²×C₁₉	—	8	1	no	—
338	C₂²×C₁₉	—	8	1	no	—
339	C₂²×C₁₉	—	8	1	no	—
340	C₂²×C₁₉	—	8	1	no	—
341	C₂²×C₁₉	—	8	1	no	—
342	C₂²×C₁₉	—	8	1	no	—
343	C₂²×C₁₉	—	8	1	no	—
344	C₂²×C₁₉	—	8	1	no	—
345	C₂²×C₁₉	—	8	1	no	—
346	C₂²×C₁₉	—	8	1	no	—
347	C₂²×C₁₉	—	8	1	no	—
348	C₂²×C₁₉	#534	1	1	yes	characteristic
349	C₂²×C₁₉	#535	1	1	yes	characteristic
350	C₂²×C₁₉	#537	1	1	yes	characteristic
351	C₂²×C₁₉	#576	1	1	yes	characteristic
352	C₂²×C₁₉	#577	1	1	yes	characteristic
353	C₂²×C₁₉	#577	1	1	yes	characteristic
354	C₂²×C₁₉	#577	1	1	yes	characteristic
355	C₄×C₁₉	—	4	1	no	—
356	C₄×C₁₉	—	4	1	no	—
357	C₄×C₁₉	—	4	1	no	—
358	C₄×C₁₉	—	4	1	no	—
359	C₄×C₁₉	—	4	1	no	—
360	C₄×C₁₉	—	8	1	no	—
361	C₄×C₁₉	—	8	1	no	—
362	C₄×C₁₉	—	8	1	no	—
363	C₄×C₁₉	—	8	1	no	—
364	C₄×C₁₉	—	8	1	no	—
365	C₄×C₁₉	—	8	1	no	—
366	C₄×C₁₉	#560	1	1	yes	characteristic
367	C₄×C₁₉	#560	1	1	yes	characteristic
368	C₄×C₁₉	#562	1	1	yes	characteristic
369	C₄×C₁₉	#562	1	1	yes	characteristic
370	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
371	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
377	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×#106	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×#103	C₂²×C₁₉	1	1	yes	characteristic
382	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
383	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
384	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
385	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
386	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
389	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
390	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
391	#400	—	2	1	no	—
392	#398	—	2	1	no	—
393	#397	—	2	1	no	—
394	#397	—	2	1	no	—
395	#394	—	2	1	no	—
396	#394	—	2	1	no	—
397	#392	—	2	1	no	—
398	#392	—	2	1	no	—
399	#391	C₂²×C₁₉	1	1	yes	characteristic
400	#391	C₂²×C₁₉	1	1	yes	characteristic
401	#390	C₂²×C₁₉	1	1	yes	characteristic
402	#390	C₂²×C₁₉	1	1	yes	characteristic
403	#389	C₂²×C₁₉	1	1	yes	characteristic
404	#389	C₂²×C₁₉	1	1	yes	characteristic
405	#382	C₂²×C₁₉	1	1	yes	characteristic
406	#380	C₂²×C₁₉	1	1	yes	characteristic
407	#340	C₂²×C₁₉	1	1	yes	characteristic
408	#340	C₂²×C₁₉	1	1	yes	characteristic
409	#340	C₂²×C₁₉	1	1	yes	characteristic
410	#340	C₂²×C₁₉	1	1	yes	characteristic
411	#336	C₂²×C₁₉	1	1	yes	characteristic
412	#336	C₂²×C₁₉	1	1	yes	characteristic
413	C₂×C₁₉	—	8	1	no	—
414	C₂×C₁₉	—	16	1	no	—
415	C₂×C₁₉	—	16	1	no	—
416	C₂×C₁₉	#2813	1	1	yes	characteristic
417	C₂×C₁₉	#3198	1	1	yes	characteristic
418	C₂×C₁₉	#3200	1	1	yes	characteristic
419	C₂×C₁₉	#3222	1	1	yes	characteristic
420	C₂×C₁₉	#3224	1	1	yes	characteristic
421	C₂×C₁₉	#3257	1	1	yes	characteristic
422	C₂×C₁₉	#3260	1	1	yes	characteristic
423	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
424	C₂²×D₄	—	2	1	no	—
425	C₂²×D₄	—	2	1	no	—
426	C₂²×D₄	—	2	1	no	—
427	C₂²×D₄	—	2	1	no	—
428	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
429	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
430	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
431	C₂×SD₁₆	—	4	1	no	—
432	C₂×SD₁₆	—	4	1	no	—
433	C₂×SD₁₆	—	4	1	no	—
434	C₂×SD₁₆	—	4	1	no	—
435	C₂×SD₁₆	—	4	1	no	—
436	C₂×SD₁₆	—	4	1	no	—
437	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
438	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
439	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
440	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
441	#127	—	4	1	no	—
442	#127	—	4	1	no	—
443	C₂²⋊Q₈	—	4	1	no	—
444	C₂²⋊Q₈	—	4	1	no	—
445	#121	—	4	1	no	—
446	#121	—	4	1	no	—
447	#121	—	4	1	no	—
448	#121	—	4	1	no	—
449	#117	—	4	1	no	—
450	#117	—	4	1	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
455	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
471	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
473	#107	—	4	1	no	—
474	#106	—	4	1	no	—
475	C₄⋊C₈	—	4	1	no	—
476	C₄⋊C₈	—	4	1	no	—
477	#103	—	4	1	no	—
478	#103	—	4	1	no	—
479	#102	—	4	1	no	—
480	#102	—	4	1	no	—
481	#102	—	4	1	no	—
482	#102	—	4	1	no	—
483	#102	—	4	1	no	—
484	#102	—	4	1	no	—
485	C₂²⋊C₈	—	4	1	no	—
486	C₂²⋊C₈	—	4	1	no	—
487	#95	—	2	1	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	#95	—	2	1	no	—
491	#95	—	2	1	no	—
492	#95	—	2	1	no	—
493	#95	—	2	1	no	—
494	#95	—	2	1	no	—
495	#95	—	2	1	no	—
496	C₁₉	#32731	1	1	yes	characteristic, direct product factor, Sylow
497	C₂⁴	—	2	1	no	—
498	C₂⁴	—	2	1	no	—
499	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	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	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	4	2	no	—
519	C₂×D₄	—	4	2	no	—
520	C₂×D₄	—	4	2	no	—
521	C₂×D₄	—	4	2	no	—
522	C₂×D₄	—	8	1	no	—
523	C₂×D₄	—	8	1	no	—
524	C₂×D₄	—	8	1	no	—
525	C₂×D₄	—	8	1	no	—
526	C₂×D₄	—	8	1	no	—
527	C₂×D₄	—	8	1	no	—
528	C₂×D₄	—	8	1	no	—
529	C₂×D₄	—	8	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
543	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
544	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
545	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
546	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
548	SD₁₆	—	4	4	no	—
549	SD₁₆	—	4	4	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	4	1	no	—
573	C₄⋊C₄	—	4	1	no	—
574	C₄⋊C₄	—	4	2	no	—
575	C₄⋊C₄	—	8	1	no	—
576	C₄⋊C₄	—	8	1	no	—
577	C₂²⋊C₄	—	4	1	no	—
578	C₂²⋊C₄	—	4	1	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	4	2	no	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	8	1	no	—
583	C₂²⋊C₄	—	8	1	no	—
584	C₂²⋊C₄	—	8	1	no	—
585	C₂²⋊C₄	—	8	1	no	—
586	C₂²⋊C₄	—	8	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
613	Q₈	—	4	1	no	—
614	Q₈	—	4	1	no	—
615	Q₈	—	4	1	no	—
616	Q₈	—	4	1	no	—
617	D₄	—	4	1	no	—
618	D₄	—	4	1	no	—
619	D₄	—	4	1	no	—
620	D₄	—	4	1	no	—
621	D₄	—	4	1	no	—
622	D₄	—	4	1	no	—
623	D₄	—	4	1	no	—
624	D₄	—	4	1	no	—
625	D₄	—	8	4	no	—
626	D₄	—	8	4	no	—
627	D₄	—	8	4	no	—
628	D₄	—	8	4	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
667	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
668	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
669	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
670	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
671	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
672	C₈	—	4	1	no	—
673	C₈	—	4	1	no	—
674	C₈	—	4	1	no	—
675	C₈	—	4	1	no	—
676	C₂²	—	4	1	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	4	1	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	8	1	no	—
684	C₂²	—	8	1	no	—
685	C₂²	—	8	1	no	—
686	C₂²	—	8	1	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	—	8	1	no	—
692	C₂²	—	8	1	no	—
693	C₂²	—	8	1	no	—
694	C₂²	—	8	1	no	—
695	C₂²	—	8	1	no	—
696	C₂²	—	8	1	no	—
697	C₂²	C₁₉×#534	1	1	yes	characteristic
698	C₂²	C₁₉×#535	1	1	yes	characteristic
699	C₂²	C₁₉×#537	1	1	yes	characteristic
700	C₂²	C₁₉×#576	1	1	yes	characteristic
701	C₂²	C₁₉×#577	1	1	yes	characteristic
702	C₂²	C₁₉×#577	1	1	yes	characteristic
703	C₂²	C₁₉×#577	1	1	yes	characteristic
704	C₄	—	4	1	no	—
705	C₄	—	4	1	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	8	1	no	—
710	C₄	—	8	1	no	—
711	C₄	—	8	1	no	—
712	C₄	—	8	1	no	—
713	C₄	—	8	1	no	—
714	C₄	—	8	1	no	—
715	C₄	C₁₉×#560	1	1	yes	characteristic
716	C₄	C₁₉×#560	1	1	yes	characteristic
717	C₄	C₁₉×#562	1	1	yes	characteristic
718	C₄	C₁₉×#562	1	1	yes	characteristic
719	C₂	—	8	1	no	—
720	C₂	—	16	1	no	—
721	C₂	—	16	1	no	—
722	C₂	C₁₉×#2813	1	1	yes	characteristic
723	C₂	C₁₉×#3198	1	1	yes	characteristic
724	C₂	C₁₉×#3200	1	1	yes	characteristic
725	C₂	C₁₉×#3222	1	1	yes	characteristic
726	C₂	C₁₉×#3224	1	1	yes	characteristic
727	C₂	C₁₉×#3257	1	1	yes	characteristic
728	C₂	C₁₉×#3260	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2619	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2625	C₂	semidirect
3. C₁₉×#2101	C₂	semidirect
4. C₁₉×#2097	C₂	semidirect
5. C₁₉×#2067	C₂	semidirect
6. C₁₉×#2065	C₂	semidirect
7. C₁₉×#2055	C₂	semidirect
8. C₁₉×#2055	C₂	semidirect
9. C₁₉×#2041	C₂	semidirect
10. C₁₉×#2034	C₂	semidirect
11. C₁₉×#2033	C₂	semidirect
12. C₁₉×#2014	C₂	semidirect
13. C₁₉×#2000	C₂	semidirect
14. C₁₉×#2000	C₂	semidirect
15. C₁₉×#1798	C₂	semidirect
226. #32731	C₁₉	direct (N × H)
312. #2625	C₂×C₁₉	semidirect
314. #2101	C₂×C₁₉	semidirect
315. #2097	C₂×C₁₉	semidirect
316. #2067	C₂×C₁₉	semidirect
317. #2065	C₂×C₁₉	semidirect
318. #2055	C₂×C₁₉	semidirect
319. #2055	C₂×C₁₉	semidirect
320. #2041	C₂×C₁₉	semidirect
321. #2034	C₂×C₁₉	semidirect
322. #2033	C₂×C₁₉	semidirect
323. #2014	C₂×C₁₉	semidirect
324. #2000	C₂×C₁₉	semidirect
325. #2000	C₂×C₁₉	semidirect
326. #1798	C₂×C₁₉	semidirect
496. C₁₉	#32731	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×#2625	2
C₁₉×#2619	2
C₁₉×#2101	2
C₁₉×#2097	2
C₁₉×#2067	2
C₁₉×#2065	2
C₁₉×#2055	2
C₁₉×#2041	2
C₁₉×#2034	2
C₁₉×#2033	2
C₁₉×#2014	2
C₁₉×#2000	2
C₁₉×#1798	2
#32731	19

Subgroups — C19×#32731 #18038690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32731 #18038690