Subgroups — C₁₉×#22951 #18028910

Order 4864.

730 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3091	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2933	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1937	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1929	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1922	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1922	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1897	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1866	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1855	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1772	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1765	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1750	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1733	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#525	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₁₉×#485	C₄	1	1	yes	characteristic, complemented
22	C₁₉×#485	C₄	1	1	yes	characteristic, complemented
23	C₁₉×#484	C₄	1	1	yes	characteristic, complemented
24	C₁₉×#483	C₄	1	1	yes	characteristic, complemented
25	C₁₉×#482	C₄	1	1	yes	characteristic, complemented
26	C₁₉×#482	C₄	1	1	yes	characteristic, complemented
27	C₁₉×#481	C₄	1	1	yes	characteristic, complemented
28	C₁₉×#480	C₄	1	1	yes	characteristic, complemented
29	C₁₉×#436	—	2	1	no	—
30	C₁₉×#435	—	2	1	no	—
31	C₁₉×#435	—	2	1	no	—
32	C₈×D₄×C₁₉	—	2	1	no	—
33	C₁₉×#433	—	2	1	no	—
34	C₁₉×#433	—	2	1	no	—
35	C₁₉×#432	—	2	1	no	—
36	C₁₉×#431	—	2	1	no	—
37	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
39	C₁₉×#427	C₂²	1	1	yes	characteristic
40	C₁₉×#427	C₂²	1	1	yes	characteristic
41	C₁₉×#424	C₂²	1	1	yes	characteristic
42	C₁₉×#424	C₂²	1	1	yes	characteristic
43	C₁₉×#424	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
46	C₁₉×#416	C₂²	1	1	yes	characteristic
47	C₁₉×#416	C₂²	1	1	yes	characteristic
48	C₁₉×#408	C₂²	1	1	yes	characteristic
49	C₁₉×#407	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	C₁₉×#405	C₂²	1	1	yes	characteristic
53	C₁₉×#405	C₂²	1	1	yes	characteristic
54	C₁₉×#405	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
57	C₁₉×#341	C₂²	1	1	yes	characteristic
58	C₁₉×#341	C₂²	1	1	yes	characteristic
59	C₁₉×#339	C₂²	1	1	yes	characteristic
60	C₁₉×#339	C₂²	1	1	yes	characteristic
61	C₁₉×#339	C₂²	1	1	yes	characteristic
62	C₁₉×#339	C₂²	1	1	yes	characteristic
63	C₁₉×#339	C₂²	1	1	yes	characteristic
64	C₁₉×#339	C₂²	1	1	yes	characteristic
65	C₁₉×#336	C₂²	1	1	yes	characteristic
66	C₁₉×#336	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×#131	—	2	2	no	—
70	C₁₉×#131	—	4	1	no	—
71	C₂×M₁₆×C₁₉	—	2	1	no	—
72	C₂×M₁₆×C₁₉	—	2	1	no	—
73	C₂×M₁₆×C₁₉	—	2	2	no	—
74	C₂×M₁₆×C₁₉	—	4	1	no	—
75	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₉	—	2	1	no	—
80	C₂²×C₈×C₁₉	—	2	1	no	—
81	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
85	C₁₉×#123	—	2	1	no	—
86	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
87	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
88	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
89	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
90	C₁₉×#120	—	2	1	no	—
91	C₄×D₄×C₁₉	—	2	1	no	—
92	C₄×D₄×C₁₉	—	2	1	no	—
93	C₁₉×#117	—	2	1	no	—
94	C₁₉×#117	—	2	1	no	—
95	C₁₉×#117	—	2	2	no	—
96	C₁₉×#117	—	4	1	no	—
97	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
98	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
99	C₁₉×#117	C₂³	1	1	yes	characteristic
100	C₁₉×#117	C₂³	1	1	yes	characteristic
101	C₁₉×#117	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
110	C₁₉×#108	—	2	2	no	—
111	C₁₉×#108	—	4	1	no	—
112	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
113	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
114	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
115	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
116	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
117	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
118	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
119	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
120	C₁₉×C₄⋊C₈	—	2	1	no	—
121	C₁₉×C₄⋊C₈	—	2	1	no	—
122	C₁₉×C₄⋊C₈	—	2	1	no	—
123	C₁₉×C₄⋊C₈	—	2	1	no	—
124	C₁₉×C₄⋊C₈	—	2	1	no	—
125	C₁₉×C₄⋊C₈	—	2	1	no	—
126	C₁₉×#104	—	2	2	no	—
127	C₁₉×#104	—	4	1	no	—
128	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
129	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
130	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
131	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
132	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
133	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
134	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
135	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
136	C₁₉×C₂²⋊C₈	—	2	1	no	—
137	C₁₉×C₂²⋊C₈	—	2	1	no	—
138	C₁₉×C₂²⋊C₈	—	2	1	no	—
139	C₁₉×C₂²⋊C₈	—	2	1	no	—
140	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
141	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
142	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
143	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
144	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
145	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
146	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
147	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
148	C₁₉×#97	—	2	1	no	—
149	C₁₉×#97	—	2	1	no	—
150	C₁₉×#97	—	2	1	no	—
151	C₁₉×#97	—	4	1	no	—
152	C₄×C₈×C₁₉	—	2	1	no	—
153	C₄×C₈×C₁₉	—	2	1	no	—
154	C₄×C₈×C₁₉	—	2	1	no	—
155	C₄×C₈×C₁₉	—	2	2	no	—
156	C₂⁴×C₁₉	#41	1	1	yes	characteristic
157	#41×C₁₉	—	2	1	no	—
158	#41×C₁₉	—	2	1	no	—
159	#41×C₁₉	—	2	1	no	—
160	#41×C₁₉	—	2	1	no	—
161	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	2	1	no	—
165	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂²×C₄	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	#41	1	1	yes	characteristic
180	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
181	M₁₆×C₁₉	—	2	1	no	—
182	M₁₆×C₁₉	—	2	1	no	—
183	M₁₆×C₁₉	—	2	1	no	—
184	M₁₆×C₁₉	—	2	1	no	—
185	M₁₆×C₁₉	—	2	1	no	—
186	M₁₆×C₁₉	—	2	1	no	—
187	M₁₆×C₁₉	—	2	1	no	—
188	M₁₆×C₁₉	—	4	2	no	—
189	M₁₆×C₁₉	—	4	2	no	—
190	M₁₆×C₁₉	#41	1	2	yes	—
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	C₂×C₈×C₁₉	—	2	1	no	—
198	C₂×C₈×C₁₉	—	2	1	no	—
199	C₂×C₈×C₁₉	—	2	1	no	—
200	C₂×C₈×C₁₉	—	2	1	no	—
201	C₂×C₈×C₁₉	—	2	1	no	—
202	C₂×C₈×C₁₉	—	2	1	no	—
203	C₂×C₈×C₁₉	—	4	2	no	—
204	C₂×C₈×C₁₉	—	4	2	no	—
205	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
208	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
209	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	—	2	1	no	—
215	C₄⋊C₄×C₁₉	—	2	1	no	—
216	C₄⋊C₄×C₁₉	—	2	1	no	—
217	C₄⋊C₄×C₁₉	—	4	2	no	—
218	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
219	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
220	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
221	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
222	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
223	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
224	C₂²⋊C₄×C₁₉	—	2	1	no	—
225	C₂²⋊C₄×C₁₉	—	2	1	no	—
226	C₂²⋊C₄×C₁₉	—	2	1	no	—
227	C₂²⋊C₄×C₁₉	—	2	1	no	—
228	C₂²⋊C₄×C₁₉	—	2	1	no	—
229	C₂²⋊C₄×C₁₉	—	2	1	no	—
230	C₂²⋊C₄×C₁₉	—	2	1	no	—
231	C₂²⋊C₄×C₁₉	—	2	1	no	—
232	C₂²⋊C₄×C₁₉	—	2	1	no	—
233	C₂²⋊C₄×C₁₉	—	4	2	no	—
234	C₄²×C₁₉	—	2	1	no	—
235	C₄²×C₁₉	—	2	1	no	—
236	C₄²×C₁₉	—	2	1	no	—
237	C₄²×C₁₉	—	2	1	no	—
238	C₄²×C₁₉	—	2	1	no	—
239	C₄²×C₁₉	—	2	1	no	—
240	C₄²×C₁₉	—	2	1	no	—
241	C₄²×C₁₉	—	2	1	no	—
242	C₄²×C₁₉	#41	1	2	yes	—
243	#22951	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂³×C₁₉	—	2	1	no	—
245	C₂³×C₁₉	—	2	1	no	—
246	C₂³×C₁₉	—	2	1	no	—
247	C₂³×C₁₉	—	4	1	no	—
248	C₂³×C₁₉	—	4	1	no	—
249	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
250	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
251	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
252	Q₈×C₁₉	—	2	1	no	—
253	Q₈×C₁₉	—	2	1	no	—
254	D₄×C₁₉	—	2	1	no	—
255	D₄×C₁₉	—	2	1	no	—
256	D₄×C₁₉	—	4	2	no	—
257	D₄×C₁₉	—	4	1	no	—
258	D₄×C₁₉	—	4	1	no	—
259	D₄×C₁₉	—	8	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	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	2	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	2	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	—	8	1	no	—
287	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
288	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
289	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
290	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
294	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
295	C₈×C₁₉	—	2	1	no	—
296	C₈×C₁₉	—	2	1	no	—
297	C₈×C₁₉	—	2	1	no	—
298	C₈×C₁₉	—	2	1	no	—
299	C₈×C₁₉	—	2	1	no	—
300	C₈×C₁₉	—	2	1	no	—
301	C₈×C₁₉	—	2	2	no	—
302	C₈×C₁₉	—	2	1	no	—
303	C₈×C₁₉	—	2	1	no	—
304	C₈×C₁₉	—	4	1	no	—
305	C₈×C₁₉	—	4	1	no	—
306	C₈×C₁₉	—	4	1	no	—
307	#3091	C₂×C₁₉	1	1	yes	characteristic
308	#2933	C₂×C₁₉	1	1	yes	characteristic
309	#2924	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#1946	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#1937	C₂×C₁₉	1	1	yes	characteristic, complemented
312	#1929	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1922	C₂×C₁₉	1	1	yes	characteristic, complemented
314	#1922	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#1897	C₂×C₁₉	1	1	yes	characteristic
316	#1866	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#1855	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#1772	C₂×C₁₉	1	1	yes	characteristic, complemented
319	#1765	C₂×C₁₉	1	1	yes	characteristic, complemented
320	#1750	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#1733	C₂×C₁₉	1	1	yes	characteristic, complemented
322	C₂²×C₁₉	—	2	1	no	—
323	C₂²×C₁₉	—	2	1	no	—
324	C₂²×C₁₉	—	2	1	no	—
325	C₂²×C₁₉	—	2	1	no	—
326	C₂²×C₁₉	—	2	1	no	—
327	C₂²×C₁₉	—	2	1	no	—
328	C₂²×C₁₉	—	2	1	no	—
329	C₂²×C₁₉	—	2	1	no	—
330	C₂²×C₁₉	—	4	1	no	—
331	C₂²×C₁₉	—	4	1	no	—
332	C₂²×C₁₉	—	4	1	no	—
333	C₂²×C₁₉	—	8	1	no	—
334	C₂²×C₁₉	—	8	1	no	—
335	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
336	C₂²×C₁₉	#551	1	1	yes	characteristic
337	C₂²×C₁₉	#552	1	1	yes	characteristic
338	C₄×C₁₉	—	2	1	no	—
339	C₄×C₁₉	—	2	1	no	—
340	C₄×C₁₉	—	4	2	no	—
341	C₄×C₁₉	—	4	1	no	—
342	C₄×C₁₉	—	4	1	no	—
343	C₄×C₁₉	—	4	1	no	—
344	C₄×C₁₉	—	4	1	no	—
345	C₄×C₁₉	—	4	1	no	—
346	C₄×C₁₉	—	4	1	no	—
347	C₄×C₁₉	—	4	1	no	—
348	C₄×C₁₉	—	8	1	no	—
349	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
350	C₄×C₁₉	#520	1	1	yes	characteristic
351	C₄×C₁₉	#546	1	1	yes	characteristic
352	C₄×C₁₉	#547	1	1	yes	characteristic
353	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
354	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
355	#525	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
358	#485	C₄×C₁₉	1	1	yes	characteristic, complemented
359	#485	C₄×C₁₉	1	1	yes	characteristic, complemented
360	#484	C₄×C₁₉	1	1	yes	characteristic, complemented
361	#483	C₄×C₁₉	1	1	yes	characteristic, complemented
362	#482	C₄×C₁₉	1	1	yes	characteristic, complemented
363	#482	C₄×C₁₉	1	1	yes	characteristic, complemented
364	#481	C₄×C₁₉	1	1	yes	characteristic, complemented
365	#480	C₄×C₁₉	1	1	yes	characteristic, complemented
366	#436	—	2	1	no	—
367	#435	—	2	1	no	—
368	#435	—	2	1	no	—
369	C₈×D₄	—	2	1	no	—
370	#433	—	2	1	no	—
371	#433	—	2	1	no	—
372	#432	—	2	1	no	—
373	#431	—	2	1	no	—
374	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
376	#427	C₂²×C₁₉	1	1	yes	characteristic
377	#427	C₂²×C₁₉	1	1	yes	characteristic
378	#424	C₂²×C₁₉	1	1	yes	characteristic
379	#424	C₂²×C₁₉	1	1	yes	characteristic
380	#424	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
382	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
383	#416	C₂²×C₁₉	1	1	yes	characteristic
384	#416	C₂²×C₁₉	1	1	yes	characteristic
385	#408	C₂²×C₁₉	1	1	yes	characteristic
386	#407	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
389	#405	C₂²×C₁₉	1	1	yes	characteristic
390	#405	C₂²×C₁₉	1	1	yes	characteristic
391	#405	C₂²×C₁₉	1	1	yes	characteristic
392	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
393	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
394	#341	C₂²×C₁₉	1	1	yes	characteristic
395	#341	C₂²×C₁₉	1	1	yes	characteristic
396	#339	C₂²×C₁₉	1	1	yes	characteristic
397	#339	C₂²×C₁₉	1	1	yes	characteristic
398	#339	C₂²×C₁₉	1	1	yes	characteristic
399	#339	C₂²×C₁₉	1	1	yes	characteristic
400	#339	C₂²×C₁₉	1	1	yes	characteristic
401	#339	C₂²×C₁₉	1	1	yes	characteristic
402	#336	C₂²×C₁₉	1	1	yes	characteristic
403	#336	C₂²×C₁₉	1	1	yes	characteristic
404	C₂×C₁₉	—	2	1	no	—
405	C₂×C₁₉	—	2	1	no	—
406	C₂×C₁₉	—	4	1	no	—
407	C₂×C₁₉	—	4	1	no	—
408	C₂×C₁₉	—	8	1	no	—
409	C₂×C₁₉	#2359	1	1	yes	characteristic
410	C₂×C₁₉	#2955	1	1	yes	characteristic
411	C₂×C₁₉	#2957	1	1	yes	characteristic
412	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
413	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
414	#131	—	2	2	no	—
415	#131	—	4	1	no	—
416	C₂×M₁₆	—	2	1	no	—
417	C₂×M₁₆	—	2	1	no	—
418	C₂×M₁₆	—	2	2	no	—
419	C₂×M₁₆	—	4	1	no	—
420	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
421	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
422	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
423	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
424	C₂²×C₈	—	2	1	no	—
425	C₂²×C₈	—	2	1	no	—
426	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
427	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
428	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
429	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
430	#123	—	2	1	no	—
431	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
432	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
433	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
434	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
435	#120	—	2	1	no	—
436	C₄×D₄	—	2	1	no	—
437	C₄×D₄	—	2	1	no	—
438	#117	—	2	1	no	—
439	#117	—	2	1	no	—
440	#117	—	2	2	no	—
441	#117	—	4	1	no	—
442	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
443	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
444	#117	C₂³×C₁₉	1	1	yes	characteristic
445	#117	C₂³×C₁₉	1	1	yes	characteristic
446	#117	C₂³×C₁₉	1	1	yes	characteristic
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₄²	—	2	1	no	—
453	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
454	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
455	#108	—	2	2	no	—
456	#108	—	4	1	no	—
457	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
458	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
459	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
460	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
461	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
462	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
463	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
464	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
465	C₄⋊C₈	—	2	1	no	—
466	C₄⋊C₈	—	2	1	no	—
467	C₄⋊C₈	—	2	1	no	—
468	C₄⋊C₈	—	2	1	no	—
469	C₄⋊C₈	—	2	1	no	—
470	C₄⋊C₈	—	2	1	no	—
471	#104	—	2	2	no	—
472	#104	—	4	1	no	—
473	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
474	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
475	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
476	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
477	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
478	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
479	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
480	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
481	C₂²⋊C₈	—	2	1	no	—
482	C₂²⋊C₈	—	2	1	no	—
483	C₂²⋊C₈	—	2	1	no	—
484	C₂²⋊C₈	—	2	1	no	—
485	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
486	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
487	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
488	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
489	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
490	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
491	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
492	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
493	#97	—	2	1	no	—
494	#97	—	2	1	no	—
495	#97	—	2	1	no	—
496	#97	—	4	1	no	—
497	C₄×C₈	—	2	1	no	—
498	C₄×C₈	—	2	1	no	—
499	C₄×C₈	—	2	1	no	—
500	C₄×C₈	—	2	2	no	—
501	C₁₉	#22951	1	1	yes	characteristic, direct product factor, Sylow
502	C₂⁴	#41×C₁₉	1	1	yes	characteristic
503	#41	—	2	1	no	—
504	#41	—	2	1	no	—
505	#41	—	2	1	no	—
506	#41	—	2	1	no	—
507	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
522	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
527	M₁₆	—	2	1	no	—
528	M₁₆	—	2	1	no	—
529	M₁₆	—	2	1	no	—
530	M₁₆	—	2	1	no	—
531	M₁₆	—	2	1	no	—
532	M₁₆	—	2	1	no	—
533	M₁₆	—	2	1	no	—
534	M₁₆	—	4	2	no	—
535	M₁₆	—	4	2	no	—
536	M₁₆	#41×C₁₉	1	2	yes	—
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	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	4	2	no	—
550	C₂×C₈	—	4	2	no	—
551	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
552	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
553	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
554	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
555	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
556	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
557	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
558	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	4	2	no	—
564	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
565	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
566	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
567	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
568	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
569	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
570	C₂²⋊C₄	—	2	1	no	—
571	C₂²⋊C₄	—	2	1	no	—
572	C₂²⋊C₄	—	2	1	no	—
573	C₂²⋊C₄	—	2	1	no	—
574	C₂²⋊C₄	—	2	1	no	—
575	C₂²⋊C₄	—	2	1	no	—
576	C₂²⋊C₄	—	2	1	no	—
577	C₂²⋊C₄	—	2	1	no	—
578	C₂²⋊C₄	—	2	1	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	2	1	no	—
582	C₄²	—	2	1	no	—
583	C₄²	—	2	1	no	—
584	C₄²	—	2	1	no	—
585	C₄²	—	2	1	no	—
586	C₄²	—	2	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	#41×C₁₉	1	2	yes	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
595	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
596	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
597	Q₈	—	2	1	no	—
598	Q₈	—	2	1	no	—
599	D₄	—	2	1	no	—
600	D₄	—	2	1	no	—
601	D₄	—	4	2	no	—
602	D₄	—	4	1	no	—
603	D₄	—	4	1	no	—
604	D₄	—	8	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	—	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	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	2	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	—	8	1	no	—
632	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
633	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
634	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
635	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
636	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
637	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
638	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
639	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
640	C₈	—	2	1	no	—
641	C₈	—	2	1	no	—
642	C₈	—	2	1	no	—
643	C₈	—	2	1	no	—
644	C₈	—	2	1	no	—
645	C₈	—	2	1	no	—
646	C₈	—	2	2	no	—
647	C₈	—	2	1	no	—
648	C₈	—	2	1	no	—
649	C₈	—	4	1	no	—
650	C₈	—	4	1	no	—
651	C₈	—	4	1	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	8	1	no	—
664	C₂²	—	8	1	no	—
665	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
666	C₂²	C₁₉×#551	1	1	yes	characteristic
667	C₂²	C₁₉×#552	1	1	yes	characteristic
668	C₄	—	2	1	no	—
669	C₄	—	2	1	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	1	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	1	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	1	no	—
678	C₄	—	8	1	no	—
679	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
680	C₄	C₁₉×#520	1	1	yes	characteristic
681	C₄	C₁₉×#546	1	1	yes	characteristic
682	C₄	C₁₉×#547	1	1	yes	characteristic
683	C₂	—	2	1	no	—
684	C₂	—	2	1	no	—
685	C₂	—	4	1	no	—
686	C₂	—	4	1	no	—
687	C₂	—	8	1	no	—
688	C₂	C₁₉×#2359	1	1	yes	characteristic
689	C₂	C₁₉×#2955	1	1	yes	characteristic
690	C₂	C₁₉×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×C₄×D₄
prime radical	C₁₉×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₁₉×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#2924	C₂	semidirect
4. C₁₉×#1946	C₂	semidirect
5. C₁₉×#1937	C₂	semidirect
6. C₁₉×#1929	C₂	semidirect
7. C₁₉×#1922	C₂	semidirect
8. C₁₉×#1922	C₂	semidirect
10. C₁₉×#1866	C₂	semidirect
11. C₁₉×#1855	C₂	semidirect
12. C₁₉×#1772	C₂	semidirect
13. C₁₉×#1765	C₂	semidirect
14. C₁₉×#1750	C₂	semidirect
15. C₁₉×#1733	C₂	semidirect
21. C₁₉×#485	C₄	semidirect
22. C₁₉×#485	C₄	semidirect
23. C₁₉×#484	C₄	semidirect
24. C₁₉×#483	C₄	semidirect
25. C₁₉×#482	C₄	semidirect
26. C₁₉×#482	C₄	semidirect
27. C₁₉×#481	C₄	semidirect
28. C₁₉×#480	C₄	semidirect
243. #22951	C₁₉	direct (N × H)
309. #2924	C₂×C₁₉	semidirect
310. #1946	C₂×C₁₉	semidirect
311. #1937	C₂×C₁₉	semidirect
312. #1929	C₂×C₁₉	semidirect
313. #1922	C₂×C₁₉	semidirect
314. #1922	C₂×C₁₉	semidirect
316. #1866	C₂×C₁₉	semidirect
317. #1855	C₂×C₁₉	semidirect
318. #1772	C₂×C₁₉	semidirect
319. #1765	C₂×C₁₉	semidirect
320. #1750	C₂×C₁₉	semidirect
321. #1733	C₂×C₁₉	semidirect
358. #485	C₄×C₁₉	semidirect
359. #485	C₄×C₁₉	semidirect
360. #484	C₄×C₁₉	semidirect
361. #483	C₄×C₁₉	semidirect
362. #482	C₄×C₁₉	semidirect
363. #482	C₄×C₁₉	semidirect
364. #481	C₄×C₁₉	semidirect
365. #480	C₄×C₁₉	semidirect
501. C₁₉	#22951	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×#3091	2
C₁₉×#2933	2
C₁₉×#2924	2
C₁₉×#1946	2
C₁₉×#1937	2
C₁₉×#1929	2
C₁₉×#1922	2
C₁₉×#1897	2
C₁₉×#1866	2
C₁₉×#1855	2
C₁₉×#1772	2
C₁₉×#1765	2
C₁₉×#1750	2
C₁₉×#1733	2
#22951	19

Subgroups — C19×#22951 #18028910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22951 #18028910