Subgroups — C₁₉×#22097 #18028056

Order 4864.

712 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×#3091	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2930	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2905	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1945	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1938	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1937	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1922	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1922	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1871	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1866	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1866	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1855	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1826	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1753	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	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#525	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×#436	—	2	1	no	—
31	C₁₉×#435	—	2	1	no	—
32	C₁₉×#435	—	2	1	no	—
33	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
35	C₁₉×#427	C₂²	1	1	yes	characteristic
36	C₁₉×#427	C₂²	1	1	yes	characteristic
37	C₁₉×#424	—	2	1	no	—
38	C₁₉×#424	—	2	1	no	—
39	C₁₉×#424	C₂²	1	1	yes	characteristic
40	C₁₉×#424	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	C₁₉×#423	—	2	1	no	—
45	C₁₉×#423	—	2	1	no	—
46	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
48	C₁₉×#416	C₂²	1	1	yes	characteristic
49	C₁₉×#416	C₂²	1	1	yes	characteristic
50	C₁₉×#408	C₂²	1	1	yes	characteristic
51	C₁₉×#407	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
53	C₁₉×#405	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×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	—	4	1	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	—	4	1	no	—
74	C₂×M₁₆×C₁₉	—	4	1	no	—
75	C₂×M₁₆×C₁₉	—	4	1	no	—
76	C₂×M₁₆×C₁₉	—	4	1	no	—
77	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
78	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
79	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
80	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
81	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₉	—	2	1	no	—
86	C₂²×C₈×C₁₉	—	2	1	no	—
87	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₁₉×#123	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
93	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
94	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
95	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
96	C₁₉×#120	—	2	1	no	—
97	C₄×D₄×C₁₉	—	2	1	no	—
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₁₉×#117	—	2	1	no	—
100	C₁₉×#117	—	2	1	no	—
101	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
102	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
103	C₁₉×#117	C₂³	1	1	yes	characteristic
104	C₁₉×#117	C₂³	1	1	yes	characteristic
105	C₁₉×#117	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
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	C₁₉×#108	—	4	1	no	—
114	C₁₉×#108	—	4	1	no	—
115	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
116	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
117	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
118	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
119	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
120	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
121	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
122	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
123	C₁₉×C₄⋊C₈	—	2	1	no	—
124	C₁₉×C₄⋊C₈	—	2	1	no	—
125	C₁₉×C₄⋊C₈	—	2	1	no	—
126	C₁₉×C₄⋊C₈	—	2	1	no	—
127	C₁₉×C₄⋊C₈	—	2	1	no	—
128	C₁₉×C₄⋊C₈	—	2	1	no	—
129	C₁₉×C₄⋊C₈	—	2	1	no	—
130	C₁₉×C₄⋊C₈	—	2	1	no	—
131	C₁₉×C₄⋊C₈	—	2	1	no	—
132	C₁₉×C₄⋊C₈	—	2	1	no	—
133	C₁₉×#104	—	4	1	no	—
134	C₁₉×#104	—	4	1	no	—
135	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
136	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
137	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
138	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
139	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
140	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
141	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
142	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
143	C₁₉×C₂²⋊C₈	—	2	1	no	—
144	C₁₉×C₂²⋊C₈	—	2	1	no	—
145	C₁₉×C₂²⋊C₈	—	2	1	no	—
146	C₁₉×C₂²⋊C₈	—	2	1	no	—
147	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
148	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
149	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
150	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
151	C₁₉×#97	—	2	1	no	—
152	C₁₉×#97	—	4	1	no	—
153	C₄×C₈×C₁₉	—	2	1	no	—
154	C₄×C₈×C₁₉	—	4	1	no	—
155	C₁₉×#95	—	2	1	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	—	2	1	no	—
189	M₁₆×C₁₉	—	4	1	no	—
190	M₁₆×C₁₉	—	4	1	no	—
191	M₁₆×C₁₉	—	4	1	no	—
192	M₁₆×C₁₉	—	4	1	no	—
193	M₁₆×C₁₉	—	4	2	no	—
194	M₁₆×C₁₉	—	4	2	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	—	2	1	no	—
204	C₂×C₈×C₁₉	—	2	1	no	—
205	C₂×C₈×C₁₉	—	2	1	no	—
206	C₂×C₈×C₁₉	—	2	1	no	—
207	C₂×C₈×C₁₉	—	4	2	no	—
208	C₂×C₈×C₁₉	—	4	2	no	—
209	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
210	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
213	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₄⋊C₄×C₁₉	—	2	1	no	—
218	C₄⋊C₄×C₁₉	—	2	1	no	—
219	C₄⋊C₄×C₁₉	—	2	1	no	—
220	C₄⋊C₄×C₁₉	—	2	1	no	—
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	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
225	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
226	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
234	C₂²⋊C₄×C₁₉	—	2	1	no	—
235	C₂²⋊C₄×C₁₉	—	2	1	no	—
236	C₂²⋊C₄×C₁₉	—	4	2	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	—	2	1	no	—
243	C₄²×C₁₉	—	2	1	no	—
244	C₄²×C₁₉	—	2	1	no	—
245	C₄²×C₁₉	—	2	1	no	—
246	#22097	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂³×C₁₉	—	2	1	no	—
248	C₂³×C₁₉	—	2	1	no	—
249	C₂³×C₁₉	—	2	1	no	—
250	C₂³×C₁₉	—	4	1	no	—
251	C₂³×C₁₉	—	4	1	no	—
252	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
253	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
254	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
255	Q₈×C₁₉	—	2	1	no	—
256	Q₈×C₁₉	—	2	1	no	—
257	D₄×C₁₉	—	2	1	no	—
258	D₄×C₁₉	—	2	1	no	—
259	D₄×C₁₉	—	4	1	no	—
260	D₄×C₁₉	—	4	1	no	—
261	D₄×C₁₉	—	8	1	no	—
262	D₄×C₁₉	—	8	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	2	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	—	2	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	—	8	1	no	—
289	C₂×C₄×C₁₉	—	8	1	no	—
290	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
291	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
292	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
293	C₂×C₄×C₁₉	C₂²×D₄	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	2₋¹⁺⁴	1	1	yes	characteristic
297	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
298	C₈×C₁₉	—	2	1	no	—
299	C₈×C₁₉	—	2	1	no	—
300	C₈×C₁₉	—	2	1	no	—
301	C₈×C₁₉	—	2	1	no	—
302	C₈×C₁₉	—	2	1	no	—
303	C₈×C₁₉	—	2	1	no	—
304	C₈×C₁₉	—	2	1	no	—
305	C₈×C₁₉	—	2	1	no	—
306	C₈×C₁₉	—	4	1	no	—
307	C₈×C₁₉	—	4	1	no	—
308	C₈×C₁₉	—	4	1	no	—
309	C₈×C₁₉	—	4	1	no	—
310	#3091	C₂×C₁₉	1	1	yes	characteristic
311	#2930	C₂×C₁₉	1	1	yes	characteristic
312	#2905	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1946	C₂×C₁₉	1	1	yes	characteristic, complemented
314	#1945	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#1938	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#1937	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#1922	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#1922	C₂×C₁₉	1	1	yes	characteristic, complemented
319	#1871	C₂×C₁₉	1	1	yes	characteristic
320	#1866	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#1866	C₂×C₁₉	1	1	yes	characteristic, complemented
322	#1855	C₂×C₁₉	1	1	yes	characteristic, complemented
323	#1826	C₂×C₁₉	1	1	yes	characteristic, complemented
324	#1753	C₂×C₁₉	1	1	yes	characteristic, complemented
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	—	2	1	no	—
331	C₂²×C₁₉	—	2	1	no	—
332	C₂²×C₁₉	—	2	1	no	—
333	C₂²×C₁₉	—	4	1	no	—
334	C₂²×C₁₉	—	4	1	no	—
335	C₂²×C₁₉	—	4	1	no	—
336	C₂²×C₁₉	—	8	1	no	—
337	C₂²×C₁₉	—	8	1	no	—
338	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
339	C₂²×C₁₉	#539	1	1	yes	characteristic
340	C₂²×C₁₉	#539	1	1	yes	characteristic
341	C₄×C₁₉	—	2	1	no	—
342	C₄×C₁₉	—	2	1	no	—
343	C₄×C₁₉	—	4	2	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	—	4	1	no	—
349	C₄×C₁₉	—	4	1	no	—
350	C₄×C₁₉	—	4	1	no	—
351	C₄×C₁₉	—	8	1	no	—
352	C₄×C₁₉	#520	1	1	yes	characteristic
353	C₄×C₁₉	#520	1	1	yes	characteristic
354	C₄×C₁₉	#534	1	1	yes	characteristic
355	C₄×C₁₉	#536	1	1	yes	characteristic
356	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
357	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
358	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
359	#525	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
361	#485	C₄×C₁₉	1	1	yes	characteristic, complemented
362	#485	C₄×C₁₉	1	1	yes	characteristic, complemented
363	#484	C₄×C₁₉	1	1	yes	characteristic, complemented
364	#483	C₄×C₁₉	1	1	yes	characteristic, complemented
365	#482	C₄×C₁₉	1	1	yes	characteristic, complemented
366	#482	C₄×C₁₉	1	1	yes	characteristic, complemented
367	#481	C₄×C₁₉	1	1	yes	characteristic, complemented
368	#480	C₄×C₁₉	1	1	yes	characteristic, complemented
369	#436	—	2	1	no	—
370	#436	—	2	1	no	—
371	#435	—	2	1	no	—
372	#435	—	2	1	no	—
373	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
375	#427	C₂²×C₁₉	1	1	yes	characteristic
376	#427	C₂²×C₁₉	1	1	yes	characteristic
377	#424	—	2	1	no	—
378	#424	—	2	1	no	—
379	#424	C₂²×C₁₉	1	1	yes	characteristic
380	#424	C₂²×C₁₉	1	1	yes	characteristic
381	#424	C₂²×C₁₉	1	1	yes	characteristic
382	#424	C₂²×C₁₉	1	1	yes	characteristic
383	#424	C₂²×C₁₉	1	1	yes	characteristic
384	#423	—	2	1	no	—
385	#423	—	2	1	no	—
386	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
388	#416	C₂²×C₁₉	1	1	yes	characteristic
389	#416	C₂²×C₁₉	1	1	yes	characteristic
390	#408	C₂²×C₁₉	1	1	yes	characteristic
391	#407	C₂²×C₁₉	1	1	yes	characteristic
392	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
393	#405	C₂²×C₁₉	1	1	yes	characteristic
394	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
395	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
396	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
397	#341	C₂²×C₁₉	1	1	yes	characteristic
398	#341	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	#339	C₂²×C₁₉	1	1	yes	characteristic
403	#339	C₂²×C₁₉	1	1	yes	characteristic
404	#339	C₂²×C₁₉	1	1	yes	characteristic
405	#336	C₂²×C₁₉	1	1	yes	characteristic
406	#336	C₂²×C₁₉	1	1	yes	characteristic
407	C₂×C₁₉	—	2	1	no	—
408	C₂×C₁₉	—	2	1	no	—
409	C₂×C₁₉	—	4	1	no	—
410	C₂×C₁₉	—	4	1	no	—
411	C₂×C₁₉	—	8	1	no	—
412	C₂×C₁₉	#2322	1	1	yes	characteristic
413	C₂×C₁₉	#2956	1	1	yes	characteristic
414	C₂×C₁₉	#2957	1	1	yes	characteristic
415	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
417	#131	—	4	1	no	—
418	#131	—	4	1	no	—
419	C₂×M₁₆	—	2	1	no	—
420	C₂×M₁₆	—	2	1	no	—
421	C₂×M₁₆	—	4	1	no	—
422	C₂×M₁₆	—	4	1	no	—
423	C₂×M₁₆	—	4	1	no	—
424	C₂×M₁₆	—	4	1	no	—
425	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
426	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
427	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
428	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
429	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
430	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
431	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
432	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
433	C₂²×C₈	—	2	1	no	—
434	C₂²×C₈	—	2	1	no	—
435	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
436	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
437	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
438	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
439	#123	—	2	1	no	—
440	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
441	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
442	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
443	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
444	#120	—	2	1	no	—
445	C₄×D₄	—	2	1	no	—
446	C₄×D₄	—	2	1	no	—
447	#117	—	2	1	no	—
448	#117	—	2	1	no	—
449	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
450	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
451	#117	C₂³×C₁₉	1	1	yes	characteristic
452	#117	C₂³×C₁₉	1	1	yes	characteristic
453	#117	C₂³×C₁₉	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₄²	—	2	1	no	—
459	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
460	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
461	#108	—	4	1	no	—
462	#108	—	4	1	no	—
463	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
464	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
465	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
466	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
467	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
468	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
469	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
470	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
471	C₄⋊C₈	—	2	1	no	—
472	C₄⋊C₈	—	2	1	no	—
473	C₄⋊C₈	—	2	1	no	—
474	C₄⋊C₈	—	2	1	no	—
475	C₄⋊C₈	—	2	1	no	—
476	C₄⋊C₈	—	2	1	no	—
477	C₄⋊C₈	—	2	1	no	—
478	C₄⋊C₈	—	2	1	no	—
479	C₄⋊C₈	—	2	1	no	—
480	C₄⋊C₈	—	2	1	no	—
481	#104	—	4	1	no	—
482	#104	—	4	1	no	—
483	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
484	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
485	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
486	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
487	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
488	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
489	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
490	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
491	C₂²⋊C₈	—	2	1	no	—
492	C₂²⋊C₈	—	2	1	no	—
493	C₂²⋊C₈	—	2	1	no	—
494	C₂²⋊C₈	—	2	1	no	—
495	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
496	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
497	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
498	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
499	#97	—	2	1	no	—
500	#97	—	4	1	no	—
501	C₄×C₈	—	2	1	no	—
502	C₄×C₈	—	4	1	no	—
503	#95	—	2	1	no	—
504	C₁₉	#22097	1	1	yes	characteristic, direct product factor, Sylow
505	C₂⁴	#41×C₁₉	1	1	yes	characteristic
506	#41	—	2	1	no	—
507	#41	—	2	1	no	—
508	#41	—	2	1	no	—
509	#41	—	2	1	no	—
510	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
525	C₂²×C₄	C₂²×C₄×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	#41×C₁₉	1	1	yes	characteristic
529	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
530	M₁₆	—	2	1	no	—
531	M₁₆	—	2	1	no	—
532	M₁₆	—	2	1	no	—
533	M₁₆	—	2	1	no	—
534	M₁₆	—	2	1	no	—
535	M₁₆	—	2	1	no	—
536	M₁₆	—	2	1	no	—
537	M₁₆	—	2	1	no	—
538	M₁₆	—	4	1	no	—
539	M₁₆	—	4	1	no	—
540	M₁₆	—	4	1	no	—
541	M₁₆	—	4	1	no	—
542	M₁₆	—	4	2	no	—
543	M₁₆	—	4	2	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	—	2	1	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	—	4	2	no	—
557	C₂×C₈	—	4	2	no	—
558	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
559	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
560	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
561	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
562	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
563	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
564	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
565	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	C₂²×C₄×C₁₉	1	1	yes	characteristic
571	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
572	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
573	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
574	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
575	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
576	C₂²⋊C₄	—	2	1	no	—
577	C₂²⋊C₄	—	2	1	no	—
578	C₂²⋊C₄	—	2	1	no	—
579	C₂²⋊C₄	—	2	1	no	—
580	C₂²⋊C₄	—	2	1	no	—
581	C₂²⋊C₄	—	2	1	no	—
582	C₂²⋊C₄	—	2	1	no	—
583	C₂²⋊C₄	—	2	1	no	—
584	C₂²⋊C₄	—	2	1	no	—
585	C₂²⋊C₄	—	4	2	no	—
586	C₄²	—	2	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	2	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	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	C₄×D₄×C₁₉	1	1	yes	characteristic
601	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
602	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
603	Q₈	—	2	1	no	—
604	Q₈	—	2	1	no	—
605	D₄	—	2	1	no	—
606	D₄	—	2	1	no	—
607	D₄	—	4	1	no	—
608	D₄	—	4	1	no	—
609	D₄	—	8	1	no	—
610	D₄	—	8	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	2	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	—	2	1	no	—
628	C₂×C₄	—	2	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	—	8	1	no	—
637	C₂×C₄	—	8	1	no	—
638	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
639	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
640	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
641	C₂×C₄	C₂²×D₄×C₁₉	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	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
645	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
646	C₈	—	2	1	no	—
647	C₈	—	2	1	no	—
648	C₈	—	2	1	no	—
649	C₈	—	2	1	no	—
650	C₈	—	2	1	no	—
651	C₈	—	2	1	no	—
652	C₈	—	2	1	no	—
653	C₈	—	2	1	no	—
654	C₈	—	4	1	no	—
655	C₈	—	4	1	no	—
656	C₈	—	4	1	no	—
657	C₈	—	4	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	8	1	no	—
670	C₂²	—	8	1	no	—
671	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
672	C₂²	C₁₉×#539	1	1	yes	characteristic
673	C₂²	C₁₉×#539	1	1	yes	characteristic
674	C₄	—	2	1	no	—
675	C₄	—	2	1	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	1	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	1	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	1	no	—
684	C₄	—	8	1	no	—
685	C₄	C₁₉×#520	1	1	yes	characteristic
686	C₄	C₁₉×#520	1	1	yes	characteristic
687	C₄	C₁₉×#534	1	1	yes	characteristic
688	C₄	C₁₉×#536	1	1	yes	characteristic
689	C₂	—	2	1	no	—
690	C₂	—	2	1	no	—
691	C₂	—	4	1	no	—
692	C₂	—	4	1	no	—
693	C₂	—	8	1	no	—
694	C₂	C₁₉×#2322	1	1	yes	characteristic
695	C₂	C₁₉×#2956	1	1	yes	characteristic
696	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 ◁ C₂²×M₁₆×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#2905	C₂	semidirect
4. C₁₉×#1946	C₂	semidirect
5. C₁₉×#1945	C₂	semidirect
6. C₁₉×#1938	C₂	semidirect
7. C₁₉×#1937	C₂	semidirect
8. C₁₉×#1922	C₂	semidirect
9. C₁₉×#1922	C₂	semidirect
11. C₁₉×#1866	C₂	semidirect
12. C₁₉×#1866	C₂	semidirect
13. C₁₉×#1855	C₂	semidirect
14. C₁₉×#1826	C₂	semidirect
15. C₁₉×#1753	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
246. #22097	C₁₉	direct (N × H)
312. #2905	C₂×C₁₉	semidirect
313. #1946	C₂×C₁₉	semidirect
314. #1945	C₂×C₁₉	semidirect
315. #1938	C₂×C₁₉	semidirect
316. #1937	C₂×C₁₉	semidirect
317. #1922	C₂×C₁₉	semidirect
318. #1922	C₂×C₁₉	semidirect
320. #1866	C₂×C₁₉	semidirect
321. #1866	C₂×C₁₉	semidirect
322. #1855	C₂×C₁₉	semidirect
323. #1826	C₂×C₁₉	semidirect
324. #1753	C₂×C₁₉	semidirect
361. #485	C₄×C₁₉	semidirect
362. #485	C₄×C₁₉	semidirect
363. #484	C₄×C₁₉	semidirect
364. #483	C₄×C₁₉	semidirect
365. #482	C₄×C₁₉	semidirect
366. #482	C₄×C₁₉	semidirect
367. #481	C₄×C₁₉	semidirect
368. #480	C₄×C₁₉	semidirect
504. C₁₉	#22097	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×#2930	2
C₁₉×#2905	2
C₁₉×#1946	2
C₁₉×#1945	2
C₁₉×#1938	2
C₁₉×#1937	2
C₁₉×#1922	2
C₁₉×#1871	2
C₁₉×#1866	2
C₁₉×#1855	2
C₁₉×#1826	2
C₁₉×#1753	2
#22097	19

Subgroups — C19×#22097 #18028056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22097 #18028056