Subgroups — C₁₉×#19777 #18025736

Order 4864.

648 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3393	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3324	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3302	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3294	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1720	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1699	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1682	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1681	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1669	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1654	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1652	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1639	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1628	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1581	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#556	C₂²	1	1	yes	characteristic
17	C₁₉×#556	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#547	C₂²	1	1	yes	characteristic
19	D₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
21	C₁₉×#495	—	2	1	no	—
22	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#486	C₂²	1	1	yes	characteristic
25	C₁₉×#486	C₂²	1	1	yes	characteristic
26	C₁₉×#486	C₂²	1	1	yes	characteristic
27	C₁₉×#485	—	2	1	no	—
28	C₁₉×#482	—	2	1	no	—
29	C₁₉×#480	—	2	1	no	—
30	C₁₉×#474	C₂²	1	1	yes	characteristic
31	C₁₉×#474	C₂²	1	1	yes	characteristic
32	C₁₉×#474	C₂²	1	1	yes	characteristic
33	C₁₉×#468	—	2	1	no	—
34	C₁₉×#467	—	2	1	no	—
35	C₁₉×#466	—	2	1	no	—
36	C₁₉×#464	—	2	1	no	—
37	C₁₉×#464	—	2	1	no	—
38	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#461	C₂²	1	1	yes	characteristic
40	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#460	C₂²	1	1	yes	characteristic
42	C₁₉×#459	C₂²	1	1	yes	characteristic
43	C₁₉×#452	—	2	1	no	—
44	C₁₉×#450	—	2	1	no	—
45	C₁₉×#447	—	2	1	no	—
46	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
47	C₄×Q₁₆×C₁₉	—	2	1	no	—
48	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
49	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
50	C₁₉×#436	C₂²	1	1	yes	characteristic
51	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#418	—	2	1	no	—
54	C₁₉×#416	—	2	1	no	—
55	C₂×C₁₉×#102	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#331	C₂²	1	1	yes	characteristic
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#322	C₂²	1	1	yes	characteristic, complemented
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂²×D₄×C₁₉	—	2	1	no	—
69	C₂²×D₄×C₁₉	—	2	1	no	—
70	C₂×Q₁₆×C₁₉	—	2	1	no	—
71	C₂×Q₁₆×C₁₉	—	2	1	no	—
72	C₂×Q₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×SD₁₆×C₁₉	—	2	1	no	—
75	C₂×SD₁₆×C₁₉	—	2	1	no	—
76	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
77	C₂×D₈×C₁₉	—	2	1	no	—
78	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
79	C₂×M₁₆×C₁₉	—	2	1	no	—
80	C₂²×C₈×C₁₉	—	2	1	no	—
81	C₂²×C₈×C₁₉	—	2	1	no	—
82	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₉×#127	C₂³	1	1	yes	characteristic
86	C₁₉×#126	—	4	1	no	—
87	C₁₉×#126	—	4	1	no	—
88	C₁₉×#124	—	2	1	no	—
89	C₁₉×#124	—	2	1	no	—
90	C₁₉×#123	—	4	1	no	—
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	—	2	1	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#120	—	4	1	no	—
98	C₄×Q₈×C₁₉	—	2	1	no	—
99	C₄×Q₈×C₁₉	—	2	1	no	—
100	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₁₉×#117	—	2	1	no	—
105	C₁₉×#117	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₁₉×#107	—	2	1	no	—
108	C₁₉×#107	—	2	1	no	—
109	C₁₉×#107	—	2	1	no	—
110	C₁₉×#107	D₄	1	1	yes	characteristic
111	C₁₉×#106	—	4	1	no	—
112	C₁₉×#106	D₄	1	1	yes	characteristic
113	C₁₉×C₄⋊C₈	—	2	1	no	—
114	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₉×#103	—	2	1	no	—
119	C₁₉×#103	—	2	1	no	—
120	C₁₉×#103	—	2	1	no	—
121	C₁₉×#103	—	2	1	no	—
122	C₁₉×#103	—	2	1	no	—
123	C₁₉×#103	D₄	1	1	yes	characteristic
124	C₁₉×#102	—	2	1	no	—
125	C₁₉×#102	—	2	1	no	—
126	C₁₉×#102	—	2	1	no	—
127	C₁₉×#102	—	2	1	no	—
128	C₁₉×#102	—	2	1	no	—
129	C₁₉×#102	—	2	1	no	—
130	C₁₉×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	4	1	no	—
134	C₁₉×#102	D₄	1	1	yes	characteristic
135	C₁₉×#102	D₄	1	1	yes	characteristic
136	C₁₉×#102	D₄	1	1	yes	characteristic
137	C₁₉×C₂²⋊C₈	—	2	1	no	—
138	C₁₉×C₂²⋊C₈	—	2	1	no	—
139	C₁₉×C₂²⋊C₈	—	2	1	no	—
140	C₄×C₈×C₁₉	—	2	1	no	—
141	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₂⁴×C₁₉	—	4	1	no	—
145	#41×C₁₉	—	4	2	no	—
146	#41×C₁₉	—	8	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	4	1	no	—
155	C₂×D₄×C₁₉	—	4	1	no	—
156	C₂×D₄×C₁₉	—	4	2	no	—
157	C₂×D₄×C₁₉	—	4	2	no	—
158	C₂×D₄×C₁₉	—	4	1	no	—
159	C₂×D₄×C₁₉	—	8	1	no	—
160	C₂×D₄×C₁₉	—	8	1	no	—
161	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	4	1	no	—
168	Q₁₆×C₁₉	—	4	2	no	—
169	Q₁₆×C₁₉	—	8	1	no	—
170	Q₁₆×C₁₉	—	8	1	no	—
171	SD₁₆×C₁₉	—	2	2	no	—
172	SD₁₆×C₁₉	—	8	1	no	—
173	SD₁₆×C₁₉	—	8	1	no	—
174	SD₁₆×C₁₉	—	8	1	no	—
175	D₈×C₁₉	—	4	1	no	—
176	D₈×C₁₉	—	8	1	no	—
177	M₁₆×C₁₉	—	8	1	no	—
178	C₂×C₈×C₁₉	—	2	1	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	8	1	no	—
184	C₂×C₈×C₁₉	—	8	1	no	—
185	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	4	1	no	—
197	C₄⋊C₄×C₁₉	—	4	1	no	—
198	C₄⋊C₄×C₁₉	—	4	1	no	—
199	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₂²⋊C₄×C₁₉	—	2	1	no	—
204	C₂²⋊C₄×C₁₉	—	2	1	no	—
205	C₂²⋊C₄×C₁₉	—	2	1	no	—
206	C₂²⋊C₄×C₁₉	—	4	1	no	—
207	C₂²⋊C₄×C₁₉	—	4	1	no	—
208	C₂²⋊C₄×C₁₉	—	4	1	no	—
209	C₂²⋊C₄×C₁₉	—	4	1	no	—
210	C₂²⋊C₄×C₁₉	—	4	1	no	—
211	C₂²⋊C₄×C₁₉	—	4	1	no	—
212	C₄²×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	—	4	1	no	—
214	C₄²×C₁₉	—	4	1	no	—
215	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
216	#19777	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂³×C₁₉	—	2	1	no	—
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	4	1	no	—
221	C₂³×C₁₉	—	8	2	no	—
222	C₂³×C₁₉	—	8	2	no	—
223	C₂³×C₁₉	—	16	1	no	—
224	Q₈×C₁₉	—	2	1	no	—
225	Q₈×C₁₉	—	2	1	no	—
226	Q₈×C₁₉	—	4	1	no	—
227	Q₈×C₁₉	—	4	1	no	—
228	Q₈×C₁₉	—	4	1	no	—
229	Q₈×C₁₉	—	4	1	no	—
230	Q₈×C₁₉	—	4	1	no	—
231	Q₈×C₁₉	—	4	1	no	—
232	D₄×C₁₉	—	2	1	no	—
233	D₄×C₁₉	—	2	1	no	—
234	D₄×C₁₉	—	2	1	no	—
235	D₄×C₁₉	—	2	1	no	—
236	D₄×C₁₉	—	2	1	no	—
237	D₄×C₁₉	—	4	1	no	—
238	D₄×C₁₉	—	4	1	no	—
239	D₄×C₁₉	—	4	1	no	—
240	D₄×C₁₉	—	4	1	no	—
241	D₄×C₁₉	—	8	1	no	—
242	D₄×C₁₉	—	8	2	no	—
243	D₄×C₁₉	—	8	2	no	—
244	D₄×C₁₉	—	8	2	no	—
245	D₄×C₁₉	#135	1	2	yes	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	8	2	no	—
261	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
264	C₈×C₁₉	—	2	1	no	—
265	C₈×C₁₉	—	2	1	no	—
266	C₈×C₁₉	—	2	1	no	—
267	C₈×C₁₉	—	2	1	no	—
268	C₈×C₁₉	—	4	1	no	—
269	C₈×C₁₉	—	4	1	no	—
270	C₈×C₁₉	—	4	1	no	—
271	C₈×C₁₉	—	4	1	no	—
272	C₈×C₁₉	—	4	1	no	—
273	#3393	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#3324	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#3302	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#3294	C₂×C₁₉	1	1	yes	characteristic
277	#1720	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1699	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1682	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1681	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1669	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1654	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1652	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1639	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1628	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1581	C₂×C₁₉	1	1	yes	characteristic, complemented
287	SD₁₆⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
288	C₂²×C₁₉	—	2	2	no	—
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	—	4	1	no	—
293	C₂²×C₁₉	—	4	1	no	—
294	C₂²×C₁₉	—	4	1	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	—	4	1	no	—
297	C₂²×C₁₉	—	8	1	no	—
298	C₂²×C₁₉	—	8	1	no	—
299	C₂²×C₁₉	—	8	1	no	—
300	C₂²×C₁₉	—	16	4	no	—
301	C₂²×C₁₉	D₄²	1	1	yes	characteristic
302	C₄×C₁₉	—	2	1	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	4	1	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	8	1	no	—
309	C₄×C₁₉	—	8	1	no	—
310	C₄×C₁₉	—	8	1	no	—
311	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
312	C₄×C₁₉	#575	1	1	yes	characteristic
313	C₄×C₁₉	#576	1	1	yes	characteristic
314	C₄×C₁₉	#576	1	1	yes	characteristic
315	#556	C₂²×C₁₉	1	1	yes	characteristic
316	#556	C₂²×C₁₉	1	1	yes	characteristic, complemented
317	#547	C₂²×C₁₉	1	1	yes	characteristic
318	D₄²	C₂²×C₁₉	1	1	yes	characteristic
319	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
320	#495	—	2	1	no	—
321	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
322	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
323	#486	C₂²×C₁₉	1	1	yes	characteristic
324	#486	C₂²×C₁₉	1	1	yes	characteristic
325	#486	C₂²×C₁₉	1	1	yes	characteristic
326	#485	—	2	1	no	—
327	#482	—	2	1	no	—
328	#480	—	2	1	no	—
329	#474	C₂²×C₁₉	1	1	yes	characteristic
330	#474	C₂²×C₁₉	1	1	yes	characteristic
331	#474	C₂²×C₁₉	1	1	yes	characteristic
332	#468	—	2	1	no	—
333	#467	—	2	1	no	—
334	#466	—	2	1	no	—
335	#464	—	2	1	no	—
336	#464	—	2	1	no	—
337	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
338	#461	C₂²×C₁₉	1	1	yes	characteristic
339	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
340	#460	C₂²×C₁₉	1	1	yes	characteristic
341	#459	C₂²×C₁₉	1	1	yes	characteristic
342	#452	—	2	1	no	—
343	#450	—	2	1	no	—
344	#447	—	2	1	no	—
345	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
346	C₄×Q₁₆	—	2	1	no	—
347	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
348	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
349	#436	C₂²×C₁₉	1	1	yes	characteristic
350	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
351	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
352	#418	—	2	1	no	—
353	#416	—	2	1	no	—
354	C₂×#102	—	2	1	no	—
355	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
356	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
357	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
358	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
359	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
360	#331	C₂²×C₁₉	1	1	yes	characteristic
361	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
362	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
363	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
364	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
365	#322	C₂²×C₁₉	1	1	yes	characteristic, complemented
366	C₂×C₁₉	—	4	2	no	—
367	C₂×C₁₉	—	8	1	no	—
368	C₂×C₁₉	—	8	1	no	—
369	C₂×C₁₉	—	16	1	no	—
370	C₂×C₁₉	#3268	1	1	yes	characteristic
371	C₂×C₁₉	#3280	1	1	yes	characteristic
372	C₂×C₁₉	#3289	1	1	yes	characteristic
373	C₂×#41	—	2	1	no	—
374	C₂²×D₄	—	2	1	no	—
375	C₂²×D₄	—	2	1	no	—
376	C₂×Q₁₆	—	2	1	no	—
377	C₂×Q₁₆	—	2	1	no	—
378	C₂×Q₁₆	—	2	1	no	—
379	C₂×SD₁₆	—	2	1	no	—
380	C₂×SD₁₆	—	2	1	no	—
381	C₂×SD₁₆	—	2	1	no	—
382	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
383	C₂×D₈	—	2	1	no	—
384	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
385	C₂×M₁₆	—	2	1	no	—
386	C₂²×C₈	—	2	1	no	—
387	C₂²×C₈	—	2	1	no	—
388	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
389	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
390	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
391	#127	C₂³×C₁₉	1	1	yes	characteristic
392	#126	—	4	1	no	—
393	#126	—	4	1	no	—
394	#124	—	2	1	no	—
395	#124	—	2	1	no	—
396	#123	—	4	1	no	—
397	C₂²⋊Q₈	—	2	1	no	—
398	C₂²⋊Q₈	—	2	1	no	—
399	C₂²⋊Q₈	—	2	1	no	—
400	#121	—	2	1	no	—
401	#121	—	2	1	no	—
402	#121	—	2	1	no	—
403	#120	—	4	1	no	—
404	C₄×Q₈	—	2	1	no	—
405	C₄×Q₈	—	2	1	no	—
406	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
407	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
408	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
409	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
410	#117	—	2	1	no	—
411	#117	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	#107	—	2	1	no	—
414	#107	—	2	1	no	—
415	#107	—	2	1	no	—
416	#107	D₄×C₁₉	1	1	yes	characteristic
417	#106	—	4	1	no	—
418	#106	D₄×C₁₉	1	1	yes	characteristic
419	C₄⋊C₈	—	2	1	no	—
420	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
421	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
422	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
423	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
424	#103	—	2	1	no	—
425	#103	—	2	1	no	—
426	#103	—	2	1	no	—
427	#103	—	2	1	no	—
428	#103	—	2	1	no	—
429	#103	D₄×C₁₉	1	1	yes	characteristic
430	#102	—	2	1	no	—
431	#102	—	2	1	no	—
432	#102	—	2	1	no	—
433	#102	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	2	1	no	—
436	#102	—	2	1	no	—
437	#102	—	2	1	no	—
438	#102	—	2	1	no	—
439	#102	—	4	1	no	—
440	#102	D₄×C₁₉	1	1	yes	characteristic
441	#102	D₄×C₁₉	1	1	yes	characteristic
442	#102	D₄×C₁₉	1	1	yes	characteristic
443	C₂²⋊C₈	—	2	1	no	—
444	C₂²⋊C₈	—	2	1	no	—
445	C₂²⋊C₈	—	2	1	no	—
446	C₄×C₈	—	2	1	no	—
447	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
448	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
449	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
450	C₁₉	#19777	1	1	yes	characteristic, direct product factor, Sylow
451	C₂⁴	—	4	1	no	—
452	#41	—	4	2	no	—
453	#41	—	8	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	—	4	2	no	—
464	C₂×D₄	—	4	2	no	—
465	C₂×D₄	—	4	1	no	—
466	C₂×D₄	—	8	1	no	—
467	C₂×D₄	—	8	1	no	—
468	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
470	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	4	1	no	—
475	Q₁₆	—	4	2	no	—
476	Q₁₆	—	8	1	no	—
477	Q₁₆	—	8	1	no	—
478	SD₁₆	—	2	2	no	—
479	SD₁₆	—	8	1	no	—
480	SD₁₆	—	8	1	no	—
481	SD₁₆	—	8	1	no	—
482	D₈	—	4	1	no	—
483	D₈	—	8	1	no	—
484	M₁₆	—	8	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	8	1	no	—
491	C₂×C₈	—	8	1	no	—
492	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	4	1	no	—
504	C₄⋊C₄	—	4	1	no	—
505	C₄⋊C₄	—	4	1	no	—
506	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
507	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
508	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
509	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	4	1	no	—
514	C₂²⋊C₄	—	4	1	no	—
515	C₂²⋊C₄	—	4	1	no	—
516	C₂²⋊C₄	—	4	1	no	—
517	C₂²⋊C₄	—	4	1	no	—
518	C₂²⋊C₄	—	4	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	4	1	no	—
521	C₄²	—	4	1	no	—
522	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
523	C₂³	—	2	1	no	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	8	2	no	—
528	C₂³	—	8	2	no	—
529	C₂³	—	16	1	no	—
530	Q₈	—	2	1	no	—
531	Q₈	—	2	1	no	—
532	Q₈	—	4	1	no	—
533	Q₈	—	4	1	no	—
534	Q₈	—	4	1	no	—
535	Q₈	—	4	1	no	—
536	Q₈	—	4	1	no	—
537	Q₈	—	4	1	no	—
538	D₄	—	2	1	no	—
539	D₄	—	2	1	no	—
540	D₄	—	2	1	no	—
541	D₄	—	2	1	no	—
542	D₄	—	2	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	D₄	—	8	1	no	—
548	D₄	—	8	2	no	—
549	D₄	—	8	2	no	—
550	D₄	—	8	2	no	—
551	D₄	C₁₉×#135	1	2	yes	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	8	2	no	—
567	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
569	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
570	C₈	—	2	1	no	—
571	C₈	—	2	1	no	—
572	C₈	—	2	1	no	—
573	C₈	—	2	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	—	4	1	no	—
577	C₈	—	4	1	no	—
578	C₈	—	4	1	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	8	1	no	—
589	C₂²	—	8	1	no	—
590	C₂²	—	8	1	no	—
591	C₂²	—	16	4	no	—
592	C₂²	D₄²×C₁₉	1	1	yes	characteristic
593	C₄	—	2	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	8	1	no	—
600	C₄	—	8	1	no	—
601	C₄	—	8	1	no	—
602	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
603	C₄	C₁₉×#575	1	1	yes	characteristic
604	C₄	C₁₉×#576	1	1	yes	characteristic
605	C₄	C₁₉×#576	1	1	yes	characteristic
606	C₂	—	4	2	no	—
607	C₂	—	8	1	no	—
608	C₂	—	8	1	no	—
609	C₂	—	16	1	no	—
610	C₂	C₁₉×#3268	1	1	yes	characteristic
611	C₂	C₁₉×#3280	1	1	yes	characteristic
612	C₂	C₁₉×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3294	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3393	C₂	semidirect
2. C₁₉×#3324	C₂	semidirect
3. C₁₉×#3302	C₂	semidirect
5. C₁₉×#1720	C₂	semidirect
6. C₁₉×#1699	C₂	semidirect
7. C₁₉×#1682	C₂	semidirect
8. C₁₉×#1681	C₂	semidirect
9. C₁₉×#1669	C₂	semidirect
10. C₁₉×#1654	C₂	semidirect
11. C₁₉×#1652	C₂	semidirect
12. C₁₉×#1639	C₂	semidirect
13. C₁₉×#1628	C₂	semidirect
14. C₁₉×#1581	C₂	semidirect
15. C₁₉×SD₁₆⋊C₈	C₂	semidirect
17. C₁₉×#556	C₂²	semidirect
20. C₁₉×#498	C₂²	semidirect
22. C₁₉×#494	C₂²	semidirect
23. C₁₉×#487	C₂²	semidirect
38. C₁₉×#462	C₂²	semidirect
40. C₁₉×#461	C₂²	semidirect
46. C₈×Q₈×C₁₉	C₂²	semidirect
52. C₈×D₄×C₁₉	C₂²	semidirect
56. C₁₉×#335	C₂²	semidirect
57. C₁₉×#335	C₂²	semidirect
58. C₁₉×#332	C₂²	semidirect
59. C₁₉×#332	C₂²	semidirect
60. C₁₉×#332	C₂²	semidirect
62. C₁₉×Q₈⋊C₈	C₂²	semidirect
65. C₁₉×D₄⋊C₈	C₂²	semidirect
66. C₁₉×#322	C₂²	semidirect
216. #19777	C₁₉	direct (N × H)
273. #3393	C₂×C₁₉	semidirect
274. #3324	C₂×C₁₉	semidirect
275. #3302	C₂×C₁₉	semidirect
277. #1720	C₂×C₁₉	semidirect
278. #1699	C₂×C₁₉	semidirect
279. #1682	C₂×C₁₉	semidirect
280. #1681	C₂×C₁₉	semidirect
281. #1669	C₂×C₁₉	semidirect
282. #1654	C₂×C₁₉	semidirect
283. #1652	C₂×C₁₉	semidirect
284. #1639	C₂×C₁₉	semidirect
285. #1628	C₂×C₁₉	semidirect
286. #1581	C₂×C₁₉	semidirect
287. SD₁₆⋊C₈	C₂×C₁₉	semidirect
316. #556	C₂²×C₁₉	semidirect
319. #498	C₂²×C₁₉	semidirect
321. #494	C₂²×C₁₉	semidirect
322. #487	C₂²×C₁₉	semidirect
337. #462	C₂²×C₁₉	semidirect
339. #461	C₂²×C₁₉	semidirect
345. C₈×Q₈	C₂²×C₁₉	semidirect
351. C₈×D₄	C₂²×C₁₉	semidirect
355. #335	C₂²×C₁₉	semidirect
356. #335	C₂²×C₁₉	semidirect
357. #332	C₂²×C₁₉	semidirect
358. #332	C₂²×C₁₉	semidirect
359. #332	C₂²×C₁₉	semidirect
361. Q₈⋊C₈	C₂²×C₁₉	semidirect
364. D₄⋊C₈	C₂²×C₁₉	semidirect
365. #322	C₂²×C₁₉	semidirect
450. C₁₉	#19777	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×#3393	2
C₁₉×#3324	2
C₁₉×#3302	2
C₁₉×#3294	2
C₁₉×#1720	2
C₁₉×#1699	2
C₁₉×#1682	2
C₁₉×#1681	2
C₁₉×#1669	2
C₁₉×#1654	2
C₁₉×#1652	2
C₁₉×#1639	2
C₁₉×#1628	2
C₁₉×#1581	2
C₁₉×SD₁₆⋊C₈	2
#19777	19

Subgroups — C19×#19777 #18025736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19777 #18025736