Subgroups — C₁₉×#62276 #18068235

Order 4864.

1812 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3539	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3339	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3336	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3317	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3307	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3287	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3283	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3260	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3204	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3197	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3177	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3176	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3061	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3050	C₂	1	2	yes	maximal, complemented
15	C₁₉×#2929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#135	C₂²	1	2	yes	—
17	C₂×C₁₉×#135	C₂²	1	2	yes	complemented
18	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#560	—	2	4	no	—
21	C₁₉×#553	—	2	4	no	—
22	C₁₉×#553	C₂²	1	4	yes	—
23	C₁₉×#552	C₂²	1	4	yes	—
24	C₁₉×#550	C₂²	1	4	yes	—
25	C₁₉×#547	C₂²	1	4	yes	—
26	C₁₉×#541	C₂²	1	2	yes	—
27	C₁₉×#540	—	2	4	no	—
28	C₁₉×#540	C₂²	1	2	yes	—
29	C₁₉×#539	—	2	4	no	—
30	C₁₉×#537	C₂²	1	4	yes	—
31	C₁₉×#525	C₂²	1	4	yes	—
32	C₁₉×#525	C₂²	1	1	yes	characteristic
33	C₁₉×#499	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#499	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#493	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#491	C₂²	1	2	yes	complemented
38	C₁₉×#490	C₂²	1	2	yes	complemented
39	C₁₉×#485	C₂²	1	4	yes	—
40	C₁₉×#483	C₂²	1	4	yes	complemented
41	C₁₉×#482	C₂²	1	4	yes	—
42	C₁₉×#481	C₂²	1	4	yes	complemented
43	C₁₉×#479	C₂²	1	4	yes	complemented
44	C₁₉×#478	C₂²	1	4	yes	complemented
45	C₁₉×#470	C₂²	1	2	yes	—
46	C₁₉×#469	C₂²	1	2	yes	—
47	C₁₉×#468	C₂²	1	4	yes	—
48	C₁₉×#468	C₂²	1	4	yes	complemented
49	C₁₉×#467	C₂²	1	2	yes	—
50	C₁₉×#467	C₂²	1	2	yes	—
51	C₁₉×#467	C₂²	1	2	yes	complemented
52	C₁₉×#466	C₂²	1	2	yes	—
53	C₁₉×#466	C₂²	1	2	yes	—
54	C₁₉×#466	C₂²	1	2	yes	complemented
55	C₁₉×#465	C₂²	1	4	yes	—
56	C₁₉×#465	C₂²	1	4	yes	—
57	C₁₉×#461	C₂²	1	4	yes	complemented
58	C₁₉×#460	C₂²	1	4	yes	complemented
59	C₁₉×#452	C₂²	1	4	yes	—
60	C₁₉×#452	C₂²	1	4	yes	complemented
61	C₁₉×#449	C₂²	1	4	yes	—
62	C₁₉×#449	C₂²	1	4	yes	complemented
63	C₁₉×#442	C₂²	1	2	yes	complemented
64	C₁₉×#441	C₂²	1	2	yes	complemented
65	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
66	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
67	C₁₉×#435	C₂²	1	2	yes	—
68	C₁₉×#435	C₂²	1	2	yes	—
69	C₈×D₄×C₁₉	C₂²	1	2	yes	—
70	C₈×D₄×C₁₉	C₂²	1	2	yes	—
71	C₁₉×#427	C₂²	1	2	yes	—
72	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
73	C₁₉×#424	C₂²	1	1	yes	characteristic
74	C₁₉×#417	C₂²	1	4	yes	complemented
75	C₁₉×#416	C₂²	1	4	yes	—
76	C₁₉×#408	C₂²	1	1	yes	characteristic
77	C₁₉×#407	C₂²	1	1	yes	characteristic
78	C₁₉×#405	C₂²	1	1	yes	characteristic
79	C₂×#41×C₁₉	C₂³	1	4	yes	—
80	C₂×#41×C₁₉	C₂³	1	4	yes	—
81	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₁₉×#135	—	4	4	no	—
84	C₁₉×#135	—	4	4	no	—
85	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
86	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
87	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
88	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
89	C₂×D₈×C₁₉	C₂³	1	2	yes	—
90	C₂×D₈×C₁₉	C₂³	1	2	yes	—
91	C₁₉×#131	—	4	2	no	—
92	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
95	C₂²×C₈×C₁₉	—	4	2	no	—
96	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
98	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
99	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
101	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
102	C₁₉×#127	—	2	4	no	—
103	C₁₉×#127	C₂³	1	2	yes	—
104	C₁₉×#126	—	2	4	no	—
105	C₁₉×#126	—	2	4	no	—
106	C₁₉×#126	—	2	4	no	—
107	C₁₉×#125	—	2	4	no	—
108	C₁₉×#125	—	2	4	no	—
109	C₁₉×#125	C₂³	1	2	yes	—
110	C₁₉×#125	C₂³	1	2	yes	—
111	C₁₉×#123	—	2	4	no	—
112	C₁₉×#123	—	2	4	no	—
113	C₁₉×#123	—	2	4	no	—
114	C₁₉×#123	—	2	4	no	—
115	C₁₉×#123	—	2	4	no	—
116	C₁₉×#123	—	2	4	no	—
117	C₁₉×#123	D₄	1	2	yes	—
118	C₁₉×C₂²⋊Q₈	—	2	4	no	—
119	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
120	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
121	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
122	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
123	C₁₉×#121	—	2	4	no	—
124	C₁₉×#121	—	2	4	no	—
125	C₁₉×#121	—	2	4	no	—
126	C₁₉×#121	—	2	4	no	—
127	C₁₉×#121	—	2	4	no	—
128	C₁₉×#121	—	2	4	no	—
129	C₁₉×#121	—	2	4	no	—
130	C₁₉×#121	—	2	4	no	—
131	C₁₉×#121	D₄	1	2	yes	—
132	C₁₉×#121	C₂³	1	4	yes	—
133	C₁₉×#121	C₂³	1	4	yes	—
134	C₁₉×#121	C₂³	1	4	yes	—
135	C₁₉×#120	—	2	4	no	—
136	C₁₉×#120	D₄	1	2	yes	—
137	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
138	C₄×D₄×C₁₉	—	2	4	no	—
139	C₄×D₄×C₁₉	—	2	4	no	—
140	C₄×D₄×C₁₉	—	2	4	no	—
141	C₄×D₄×C₁₉	—	2	4	no	—
142	C₄×D₄×C₁₉	C₂³	1	4	yes	—
143	C₄×D₄×C₁₉	C₂³	1	2	yes	—
144	C₄×D₄×C₁₉	C₂³	1	2	yes	—
145	C₁₉×#117	—	2	4	no	—
146	C₁₉×#117	C₂³	1	4	yes	—
147	C₁₉×#117	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
149	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
150	C₁₉×#107	C₂³	1	2	yes	—
151	C₁₉×#107	C₂³	1	2	yes	—
152	C₁₉×#107	C₂³	1	4	yes	—
153	C₁₉×#106	C₂³	1	4	yes	—
154	C₁₉×#106	C₂³	1	2	yes	—
155	C₁₉×#106	C₂³	1	2	yes	—
156	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
157	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
158	C₁₉×#103	C₂³	1	4	yes	—
159	C₁₉×#103	C₂³	1	4	yes	—
160	C₁₉×#103	C₂³	1	4	yes	—
161	C₁₉×#103	C₂³	1	4	yes	—
162	C₁₉×#102	C₂³	1	4	yes	—
163	C₁₉×#102	C₂³	1	4	yes	—
164	C₁₉×#102	C₂³	1	4	yes	—
165	C₁₉×#102	C₂³	1	4	yes	—
166	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
167	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
168	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
169	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
170	C₁₉×#97	C₂³	1	1	yes	characteristic
171	C₁₉×#97	C₂³	1	1	yes	characteristic
172	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
173	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
174	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
175	#41×C₁₉	—	4	1	no	—
176	#41×C₁₉	—	4	1	no	—
177	#41×C₁₉	—	4	4	no	—
178	#41×C₁₉	—	4	4	no	—
179	#41×C₁₉	—	4	4	no	—
180	#41×C₁₉	—	4	4	no	—
181	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
183	C₂×D₄×C₁₉	—	2	4	no	—
184	C₂×D₄×C₁₉	—	2	4	no	—
185	C₂×D₄×C₁₉	—	2	4	no	—
186	C₂×D₄×C₁₉	—	2	4	no	—
187	C₂×D₄×C₁₉	—	2	4	no	—
188	C₂×D₄×C₁₉	—	2	4	no	—
189	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
190	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
191	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
192	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₁₉	—	2	4	no	—
195	C₂²×C₄×C₁₉	—	2	4	no	—
196	C₂²×C₄×C₁₉	—	2	4	no	—
197	C₂²×C₄×C₁₉	—	2	4	no	—
198	C₂²×C₄×C₁₉	—	4	1	no	—
199	C₂²×C₄×C₁₉	—	4	1	no	—
200	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
205	Q₁₆×C₁₉	—	2	4	no	—
206	Q₁₆×C₁₉	—	4	2	no	—
207	SD₁₆×C₁₉	—	4	4	no	—
208	SD₁₆×C₁₉	—	4	4	no	—
209	D₈×C₁₉	—	2	4	no	—
210	D₈×C₁₉	—	4	2	no	—
211	M₁₆×C₁₉	—	4	1	no	—
212	M₁₆×C₁₉	—	4	2	no	—
213	M₁₆×C₁₉	—	4	1	no	—
214	C₂×C₈×C₁₉	—	2	2	no	—
215	C₂×C₈×C₁₉	—	2	4	no	—
216	C₂×C₈×C₁₉	—	2	4	no	—
217	C₂×C₈×C₁₉	—	4	2	no	—
218	C₂×C₈×C₁₉	—	4	1	no	—
219	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
220	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
221	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
222	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
223	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
224	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
225	C₄⋊C₄×C₁₉	—	2	4	no	—
226	C₄⋊C₄×C₁₉	—	2	4	no	—
227	C₄⋊C₄×C₁₉	—	2	4	no	—
228	C₄⋊C₄×C₁₉	—	2	4	no	—
229	C₄⋊C₄×C₁₉	—	2	4	no	—
230	C₄⋊C₄×C₁₉	—	2	4	no	—
231	C₄⋊C₄×C₁₉	—	2	4	no	—
232	C₄⋊C₄×C₁₉	—	2	4	no	—
233	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
234	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
235	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
236	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
237	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
238	C₂²⋊C₄×C₁₉	—	2	4	no	—
239	C₂²⋊C₄×C₁₉	—	2	4	no	—
240	C₂²⋊C₄×C₁₉	—	2	4	no	—
241	C₂²⋊C₄×C₁₉	—	2	4	no	—
242	C₂²⋊C₄×C₁₉	—	2	4	no	—
243	C₂²⋊C₄×C₁₉	—	2	4	no	—
244	C₂²⋊C₄×C₁₉	—	2	4	no	—
245	C₂²⋊C₄×C₁₉	—	2	4	no	—
246	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
247	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
248	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
249	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
250	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
251	C₄²×C₁₉	—	2	4	no	—
252	C₄²×C₁₉	—	2	4	no	—
253	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
254	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
255	#62276	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂³×C₁₉	—	2	4	no	—
257	C₂³×C₁₉	—	4	1	no	—
258	C₂³×C₁₉	—	4	2	no	—
259	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
260	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
261	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
262	Q₈×C₁₉	—	2	4	no	—
263	Q₈×C₁₉	—	2	4	no	—
264	Q₈×C₁₉	—	4	1	no	—
265	D₄×C₁₉	—	2	4	no	—
266	D₄×C₁₉	—	2	4	no	—
267	D₄×C₁₉	—	4	2	no	—
268	D₄×C₁₉	—	4	2	no	—
269	D₄×C₁₉	—	4	1	no	—
270	D₄×C₁₉	—	4	2	no	—
271	D₄×C₁₉	—	8	4	no	—
272	D₄×C₁₉	—	8	4	no	—
273	D₄×C₁₉	—	8	4	no	—
274	D₄×C₁₉	—	8	4	no	—
275	D₄×C₁₉	—	8	4	no	—
276	D₄×C₁₉	—	8	4	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	2	no	—
279	C₂×C₄×C₁₉	—	2	2	no	—
280	C₂×C₄×C₁₉	—	2	1	no	—
281	C₂×C₄×C₁₉	—	2	2	no	—
282	C₂×C₄×C₁₉	—	2	2	no	—
283	C₂×C₄×C₁₉	—	2	4	no	—
284	C₂×C₄×C₁₉	—	2	4	no	—
285	C₂×C₄×C₁₉	—	2	4	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	2	no	—
288	C₂×C₄×C₁₉	—	8	4	no	—
289	C₂×C₄×C₁₉	—	8	4	no	—
290	C₂×C₄×C₁₉	—	8	4	no	—
291	C₂×C₄×C₁₉	—	8	4	no	—
292	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
293	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
294	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
297	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
298	C₈×C₁₉	—	2	1	no	—
299	C₈×C₁₉	—	2	2	no	—
300	C₈×C₁₉	—	2	2	no	—
301	C₈×C₁₉	—	2	1	no	—
302	C₈×C₁₉	—	2	1	no	—
303	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
304	#3539	C₂×C₁₉	1	2	yes	complemented
305	#3339	C₂×C₁₉	1	2	yes	complemented
306	#3336	C₂×C₁₉	1	2	yes	complemented
307	#3317	C₂×C₁₉	1	4	yes	complemented
308	#3307	C₂×C₁₉	1	4	yes	complemented
309	#3287	C₂×C₁₉	1	2	yes	complemented
310	#3283	C₂×C₁₉	1	2	yes	complemented
311	#3260	C₂×C₁₉	1	2	yes	complemented
312	#3204	C₂×C₁₉	1	2	yes	complemented
313	#3197	C₂×C₁₉	1	2	yes	complemented
314	#3177	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#3176	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#3061	C₂×C₁₉	1	2	yes	complemented
317	#3050	C₂×C₁₉	1	2	yes	complemented
318	#2929	C₂×C₁₉	1	1	yes	characteristic, complemented
319	C₂²×C₁₉	—	2	2	no	—
320	C₂²×C₁₉	—	2	2	no	—
321	C₂²×C₁₉	—	2	2	no	—
322	C₂²×C₁₉	—	2	2	no	—
323	C₂²×C₁₉	—	2	2	no	—
324	C₂²×C₁₉	—	2	1	no	—
325	C₂²×C₁₉	—	2	2	no	—
326	C₂²×C₁₉	—	2	2	no	—
327	C₂²×C₁₉	—	4	4	no	—
328	C₂²×C₁₉	—	4	4	no	—
329	C₂²×C₁₉	—	4	4	no	—
330	C₂²×C₁₉	—	4	4	no	—
331	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
332	C₄×C₁₉	—	2	2	no	—
333	C₄×C₁₉	—	2	2	no	—
334	C₄×C₁₉	—	2	2	no	—
335	C₄×C₁₉	—	2	1	no	—
336	C₄×C₁₉	—	2	2	no	—
337	C₄×C₁₉	—	4	4	no	—
338	C₄×C₁₉	—	4	4	no	—
339	C₄×C₁₉	—	4	4	no	—
340	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
341	C₄×C₁₉	#585	1	1	yes	characteristic
342	C₂×#135	C₂²×C₁₉	1	2	yes	—
343	C₂×#135	C₂²×C₁₉	1	2	yes	complemented
344	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
345	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
346	#560	—	2	4	no	—
347	#553	—	2	4	no	—
348	#553	C₂²×C₁₉	1	4	yes	—
349	#552	C₂²×C₁₉	1	4	yes	—
350	#550	C₂²×C₁₉	1	4	yes	—
351	#547	C₂²×C₁₉	1	4	yes	—
352	#541	C₂²×C₁₉	1	2	yes	—
353	#540	—	2	4	no	—
354	#540	C₂²×C₁₉	1	2	yes	—
355	#539	—	2	4	no	—
356	#537	C₂²×C₁₉	1	4	yes	—
357	#525	C₂²×C₁₉	1	4	yes	—
358	#525	C₂²×C₁₉	1	1	yes	characteristic
359	#499	C₂²×C₁₉	1	1	yes	characteristic, complemented
360	#499	C₂²×C₁₉	1	1	yes	characteristic, complemented
361	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
362	#493	C₂²×C₁₉	1	1	yes	characteristic, complemented
363	#491	C₂²×C₁₉	1	2	yes	complemented
364	#490	C₂²×C₁₉	1	2	yes	complemented
365	#485	C₂²×C₁₉	1	4	yes	—
366	#483	C₂²×C₁₉	1	4	yes	complemented
367	#482	C₂²×C₁₉	1	4	yes	—
368	#481	C₂²×C₁₉	1	4	yes	complemented
369	#479	C₂²×C₁₉	1	4	yes	complemented
370	#478	C₂²×C₁₉	1	4	yes	complemented
371	#470	C₂²×C₁₉	1	2	yes	—
372	#469	C₂²×C₁₉	1	2	yes	—
373	#468	C₂²×C₁₉	1	4	yes	—
374	#468	C₂²×C₁₉	1	4	yes	complemented
375	#467	C₂²×C₁₉	1	2	yes	—
376	#467	C₂²×C₁₉	1	2	yes	—
377	#467	C₂²×C₁₉	1	2	yes	complemented
378	#466	C₂²×C₁₉	1	2	yes	—
379	#466	C₂²×C₁₉	1	2	yes	—
380	#466	C₂²×C₁₉	1	2	yes	complemented
381	#465	C₂²×C₁₉	1	4	yes	—
382	#465	C₂²×C₁₉	1	4	yes	—
383	#461	C₂²×C₁₉	1	4	yes	complemented
384	#460	C₂²×C₁₉	1	4	yes	complemented
385	#452	C₂²×C₁₉	1	4	yes	—
386	#452	C₂²×C₁₉	1	4	yes	complemented
387	#449	C₂²×C₁₉	1	4	yes	—
388	#449	C₂²×C₁₉	1	4	yes	complemented
389	#442	C₂²×C₁₉	1	2	yes	complemented
390	#441	C₂²×C₁₉	1	2	yes	complemented
391	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
392	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
393	#435	C₂²×C₁₉	1	2	yes	—
394	#435	C₂²×C₁₉	1	2	yes	—
395	C₈×D₄	C₂²×C₁₉	1	2	yes	—
396	C₈×D₄	C₂²×C₁₉	1	2	yes	—
397	#427	C₂²×C₁₉	1	2	yes	—
398	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
399	#424	C₂²×C₁₉	1	1	yes	characteristic
400	#417	C₂²×C₁₉	1	4	yes	complemented
401	#416	C₂²×C₁₉	1	4	yes	—
402	#408	C₂²×C₁₉	1	1	yes	characteristic
403	#407	C₂²×C₁₉	1	1	yes	characteristic
404	#405	C₂²×C₁₉	1	1	yes	characteristic
405	C₂×C₁₉	—	4	2	no	—
406	C₂×C₁₉	—	4	2	no	—
407	C₂×C₁₉	—	4	1	no	—
408	C₂×C₁₉	—	8	4	no	—
409	C₂×C₁₉	#3496	1	1	yes	characteristic
410	C₂×C₁₉	#3584	1	2	yes	—
411	C₂×#41	C₂³×C₁₉	1	4	yes	—
412	C₂×#41	C₂³×C₁₉	1	4	yes	—
413	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
414	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
415	#135	—	4	4	no	—
416	#135	—	4	4	no	—
417	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
418	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
419	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
420	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
421	C₂×D₈	C₂³×C₁₉	1	2	yes	—
422	C₂×D₈	C₂³×C₁₉	1	2	yes	—
423	#131	—	4	2	no	—
424	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
425	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
426	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
427	C₂²×C₈	—	4	2	no	—
428	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
429	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
430	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
431	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
432	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
433	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
434	#127	—	2	4	no	—
435	#127	C₂³×C₁₉	1	2	yes	—
436	#126	—	2	4	no	—
437	#126	—	2	4	no	—
438	#126	—	2	4	no	—
439	#125	—	2	4	no	—
440	#125	—	2	4	no	—
441	#125	C₂³×C₁₉	1	2	yes	—
442	#125	C₂³×C₁₉	1	2	yes	—
443	#123	—	2	4	no	—
444	#123	—	2	4	no	—
445	#123	—	2	4	no	—
446	#123	—	2	4	no	—
447	#123	—	2	4	no	—
448	#123	—	2	4	no	—
449	#123	D₄×C₁₉	1	2	yes	—
450	C₂²⋊Q₈	—	2	4	no	—
451	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
452	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
453	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
454	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
455	#121	—	2	4	no	—
456	#121	—	2	4	no	—
457	#121	—	2	4	no	—
458	#121	—	2	4	no	—
459	#121	—	2	4	no	—
460	#121	—	2	4	no	—
461	#121	—	2	4	no	—
462	#121	—	2	4	no	—
463	#121	D₄×C₁₉	1	2	yes	—
464	#121	C₂³×C₁₉	1	4	yes	—
465	#121	C₂³×C₁₉	1	4	yes	—
466	#121	C₂³×C₁₉	1	4	yes	—
467	#120	—	2	4	no	—
468	#120	D₄×C₁₉	1	2	yes	—
469	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
470	C₄×D₄	—	2	4	no	—
471	C₄×D₄	—	2	4	no	—
472	C₄×D₄	—	2	4	no	—
473	C₄×D₄	—	2	4	no	—
474	C₄×D₄	C₂³×C₁₉	1	4	yes	—
475	C₄×D₄	C₂³×C₁₉	1	2	yes	—
476	C₄×D₄	C₂³×C₁₉	1	2	yes	—
477	#117	—	2	4	no	—
478	#117	C₂³×C₁₉	1	4	yes	—
479	#117	C₂³×C₁₉	1	1	yes	characteristic
480	C₂×C₄⋊C₄	—	2	4	no	—
481	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
482	#107	C₂³×C₁₉	1	2	yes	—
483	#107	C₂³×C₁₉	1	2	yes	—
484	#107	C₂³×C₁₉	1	4	yes	—
485	#106	C₂³×C₁₉	1	4	yes	—
486	#106	C₂³×C₁₉	1	2	yes	—
487	#106	C₂³×C₁₉	1	2	yes	—
488	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
489	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
490	#103	C₂³×C₁₉	1	4	yes	—
491	#103	C₂³×C₁₉	1	4	yes	—
492	#103	C₂³×C₁₉	1	4	yes	—
493	#103	C₂³×C₁₉	1	4	yes	—
494	#102	C₂³×C₁₉	1	4	yes	—
495	#102	C₂³×C₁₉	1	4	yes	—
496	#102	C₂³×C₁₉	1	4	yes	—
497	#102	C₂³×C₁₉	1	4	yes	—
498	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
499	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
500	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
501	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
502	#97	C₂³×C₁₉	1	1	yes	characteristic
503	#97	C₂³×C₁₉	1	1	yes	characteristic
504	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
505	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
506	C₁₉	#62276	1	1	yes	characteristic, direct product factor, Sylow
507	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
508	#41	—	4	1	no	—
509	#41	—	4	1	no	—
510	#41	—	4	4	no	—
511	#41	—	4	4	no	—
512	#41	—	4	4	no	—
513	#41	—	4	4	no	—
514	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
515	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	—	2	4	no	—
519	C₂×D₄	—	2	4	no	—
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	2	4	no	—
522	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
523	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
524	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
525	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
526	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
527	C₂²×C₄	—	2	4	no	—
528	C₂²×C₄	—	2	4	no	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	4	1	no	—
532	C₂²×C₄	—	4	1	no	—
533	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
534	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
537	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
538	Q₁₆	—	2	4	no	—
539	Q₁₆	—	4	2	no	—
540	SD₁₆	—	4	4	no	—
541	SD₁₆	—	4	4	no	—
542	D₈	—	2	4	no	—
543	D₈	—	4	2	no	—
544	M₁₆	—	4	1	no	—
545	M₁₆	—	4	2	no	—
546	M₁₆	—	4	1	no	—
547	C₂×C₈	—	2	2	no	—
548	C₂×C₈	—	2	4	no	—
549	C₂×C₈	—	2	4	no	—
550	C₂×C₈	—	4	2	no	—
551	C₂×C₈	—	4	1	no	—
552	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
553	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
554	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
555	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
556	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
557	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
567	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
568	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
569	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
570	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
580	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
581	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
582	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
583	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
584	C₄²	—	2	4	no	—
585	C₄²	—	2	4	no	—
586	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
587	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
588	C₂³	—	2	4	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	2	no	—
591	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
592	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
593	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
594	Q₈	—	2	4	no	—
595	Q₈	—	2	4	no	—
596	Q₈	—	4	1	no	—
597	D₄	—	2	4	no	—
598	D₄	—	2	4	no	—
599	D₄	—	4	1	no	—
600	D₄	—	4	2	no	—
601	D₄	—	4	2	no	—
602	D₄	—	4	2	no	—
603	D₄	—	8	4	no	—
604	D₄	—	8	4	no	—
605	D₄	—	8	4	no	—
606	D₄	—	8	4	no	—
607	D₄	—	8	4	no	—
608	D₄	—	8	4	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	8	4	no	—
621	C₂×C₄	—	8	4	no	—
622	C₂×C₄	—	8	4	no	—
623	C₂×C₄	—	8	4	no	—
624	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
625	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
626	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
627	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
628	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
629	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
630	C₈	—	2	1	no	—
631	C₈	—	2	2	no	—
632	C₈	—	2	2	no	—
633	C₈	—	2	1	no	—
634	C₈	—	2	1	no	—
635	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	4	4	no	—
645	C₂²	—	4	4	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	4	no	—
648	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
649	C₄	—	2	2	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	4	4	no	—
655	C₄	—	4	4	no	—
656	C₄	—	4	4	no	—
657	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
658	C₄	C₁₉×#585	1	1	yes	characteristic
659	C₂	—	4	1	no	—
660	C₂	—	4	2	no	—
661	C₂	—	4	2	no	—
662	C₂	—	8	4	no	—
663	C₂	C₁₉×#3496	1	1	yes	characteristic
664	C₂	C₁₉×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3539	C₂	semidirect
2. C₁₉×#3339	C₂	semidirect
3. C₁₉×#3336	C₂	semidirect
4. C₁₉×#3317	C₂	semidirect
5. C₁₉×#3307	C₂	semidirect
6. C₁₉×#3287	C₂	semidirect
7. C₁₉×#3283	C₂	semidirect
8. C₁₉×#3260	C₂	semidirect
9. C₁₉×#3204	C₂	semidirect
10. C₁₉×#3197	C₂	semidirect
11. C₁₉×#3177	C₂	semidirect
12. C₁₉×#3176	C₂	semidirect
13. C₁₉×#3061	C₂	semidirect
14. C₁₉×#3050	C₂	semidirect
15. C₁₉×#2929	C₂	semidirect
17. C₂×C₁₉×#135	C₂²	semidirect
33. C₁₉×#499	C₂²	semidirect
34. C₁₉×#499	C₂²	semidirect
35. C₁₉×#494	C₂²	semidirect
36. C₁₉×#493	C₂²	semidirect
37. C₁₉×#491	C₂²	semidirect
38. C₁₉×#490	C₂²	semidirect
40. C₁₉×#483	C₂²	semidirect
42. C₁₉×#481	C₂²	semidirect
43. C₁₉×#479	C₂²	semidirect
44. C₁₉×#478	C₂²	semidirect
48. C₁₉×#468	C₂²	semidirect
51. C₁₉×#467	C₂²	semidirect
54. C₁₉×#466	C₂²	semidirect
57. C₁₉×#461	C₂²	semidirect
58. C₁₉×#460	C₂²	semidirect
60. C₁₉×#452	C₂²	semidirect
62. C₁₉×#449	C₂²	semidirect
63. C₁₉×#442	C₂²	semidirect
64. C₁₉×#441	C₂²	semidirect
65. C₄×Q₁₆×C₁₉	C₂²	semidirect
66. C₄×D₈×C₁₉	C₂²	semidirect
72. C₂×C₁₉×#107	C₂²	semidirect
74. C₁₉×#417	C₂²	semidirect
255. #62276	C₁₉	direct (N × H)
304. #3539	C₂×C₁₉	semidirect
305. #3339	C₂×C₁₉	semidirect
306. #3336	C₂×C₁₉	semidirect
307. #3317	C₂×C₁₉	semidirect
308. #3307	C₂×C₁₉	semidirect
309. #3287	C₂×C₁₉	semidirect
310. #3283	C₂×C₁₉	semidirect
311. #3260	C₂×C₁₉	semidirect
312. #3204	C₂×C₁₉	semidirect
313. #3197	C₂×C₁₉	semidirect
314. #3177	C₂×C₁₉	semidirect
315. #3176	C₂×C₁₉	semidirect
316. #3061	C₂×C₁₉	semidirect
317. #3050	C₂×C₁₉	semidirect
318. #2929	C₂×C₁₉	semidirect
343. C₂×#135	C₂²×C₁₉	semidirect
359. #499	C₂²×C₁₉	semidirect
360. #499	C₂²×C₁₉	semidirect
361. #494	C₂²×C₁₉	semidirect
362. #493	C₂²×C₁₉	semidirect
363. #491	C₂²×C₁₉	semidirect
364. #490	C₂²×C₁₉	semidirect
366. #483	C₂²×C₁₉	semidirect
368. #481	C₂²×C₁₉	semidirect
369. #479	C₂²×C₁₉	semidirect
370. #478	C₂²×C₁₉	semidirect
374. #468	C₂²×C₁₉	semidirect
377. #467	C₂²×C₁₉	semidirect
380. #466	C₂²×C₁₉	semidirect
383. #461	C₂²×C₁₉	semidirect
384. #460	C₂²×C₁₉	semidirect
386. #452	C₂²×C₁₉	semidirect
388. #449	C₂²×C₁₉	semidirect
389. #442	C₂²×C₁₉	semidirect
390. #441	C₂²×C₁₉	semidirect
391. C₄×Q₁₆	C₂²×C₁₉	semidirect
392. C₄×D₈	C₂²×C₁₉	semidirect
398. C₂×#107	C₂²×C₁₉	semidirect
400. #417	C₂²×C₁₉	semidirect
506. C₁₉	#62276	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×#3539	2
C₁₉×#3339	2
C₁₉×#3336	2
C₁₉×#3317	2
C₁₉×#3307	2
C₁₉×#3287	2
C₁₉×#3283	2
C₁₉×#3260	2
C₁₉×#3204	2
C₁₉×#3197	2
C₁₉×#3177	2
C₁₉×#3176	2
C₁₉×#3061	2
C₁₉×#3050	2
C₁₉×#2929	2
#62276	19

Subgroups — C19×#62276 #18068235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62276 #18068235