Subgroups — C₁₉×#19768 #18025727

Order 4864.

642 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3385	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3362	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3335	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3284	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1714	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1686	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1675	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1672	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1645	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1635	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1631	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1622	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1582	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#135	—	2	1	no	—
17	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#554	C₂²	1	1	yes	characteristic
19	C₁₉×#550	C₂²	1	1	yes	characteristic
20	C₁₉×#547	C₂²	1	1	yes	characteristic
21	C₁₉×#501	—	2	1	no	—
22	C₁₉×#500	C₂²	1	1	yes	characteristic
23	C₁₉×#498	C₂²	1	1	yes	characteristic
24	C₁₉×#492	C₂²	1	1	yes	characteristic
25	C₁₉×#492	C₂²	1	1	yes	characteristic
26	C₁₉×#487	C₂²	1	1	yes	characteristic
27	C₁₉×#486	—	2	1	no	—
28	C₁₉×#486	C₂²	1	1	yes	characteristic
29	C₁₉×#483	—	2	1	no	—
30	C₁₉×#481	—	2	1	no	—
31	C₁₉×#479	—	2	1	no	—
32	C₁₉×#477	C₂²	1	1	yes	characteristic
33	C₁₉×#476	—	2	1	no	—
34	C₁₉×#476	C₂²	1	1	yes	characteristic
35	C₁₉×#476	C₂²	1	1	yes	characteristic
36	C₁₉×#476	C₂²	1	1	yes	characteristic
37	C₁₉×#475	C₂²	1	1	yes	characteristic
38	C₁₉×#474	—	2	1	no	—
39	C₁₉×#465	—	2	1	no	—
40	C₁₉×#465	—	2	1	no	—
41	C₁₉×#462	C₂²	1	1	yes	characteristic
42	C₁₉×#460	—	2	1	no	—
43	C₁₉×#460	C₂²	1	1	yes	characteristic
44	C₁₉×#459	C₂²	1	1	yes	characteristic
45	C₁₉×#452	—	2	1	no	—
46	C₁₉×#449	—	2	1	no	—
47	C₁₉×#446	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#440	—	2	1	no	—
50	C₄×SD₁₆×C₁₉	—	2	1	no	—
51	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
52	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#106	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#333	C₂²	1	1	yes	characteristic
59	C₁₉×#333	C₂²	1	1	yes	characteristic
60	C₁₉×#332	C₂²	1	1	yes	characteristic
61	C₁₉×#331	C₂²	1	1	yes	characteristic
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₉×#322	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂×#41×C₁₉	—	2	1	no	—
69	C₁₉×#135	—	4	4	no	—
70	C₂×Q₁₆×C₁₉	—	2	1	no	—
71	C₂×SD₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×SD₁₆×C₁₉	—	4	1	no	—
75	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
76	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
77	C₂×D₈×C₁₉	—	2	1	no	—
78	C₂²×C₈×C₁₉	—	2	1	no	—
79	C₂²×C₈×C₁₉	—	2	1	no	—
80	C₁₉×C₄⋊Q₈	—	2	1	no	—
81	C₁₉×C₄⋊Q₈	—	2	1	no	—
82	C₁₉×C₄⋊Q₈	—	4	1	no	—
83	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₉×#127	—	2	1	no	—
87	C₁₉×#127	C₂³	1	1	yes	characteristic
88	C₁₉×#125	—	2	1	no	—
89	C₁₉×#123	—	4	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	1	no	—
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	—	4	1	no	—
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	4	1	no	—
96	C₄×Q₈×C₁₉	—	2	1	no	—
97	C₄×Q₈×C₁₉	—	2	1	no	—
98	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
99	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₁₉×#107	—	2	1	no	—
107	C₁₉×#107	—	2	1	no	—
108	C₁₉×#107	—	2	1	no	—
109	C₁₉×#106	—	2	1	no	—
110	C₁₉×#106	—	2	1	no	—
111	C₁₉×#106	—	2	1	no	—
112	C₁₉×#106	—	2	1	no	—
113	C₁₉×#106	—	2	1	no	—
114	C₁₉×#106	—	2	1	no	—
115	C₁₉×#106	D₄	1	1	yes	characteristic
116	C₁₉×#106	D₄	1	1	yes	characteristic
117	C₁₉×C₄⋊C₈	—	2	1	no	—
118	C₁₉×C₄⋊C₈	—	2	1	no	—
119	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₁₉×#103	—	2	1	no	—
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	—	2	1	no	—
126	C₁₉×#103	—	4	1	no	—
127	C₁₉×#103	D₄	1	1	yes	characteristic
128	C₁₉×#103	D₄	1	1	yes	characteristic
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	—	2	1	no	—
134	C₁₉×#102	—	2	1	no	—
135	C₁₉×#102	—	2	1	no	—
136	C₁₉×#102	D₄	1	1	yes	characteristic
137	C₁₉×#102	D₄	1	1	yes	characteristic
138	C₁₉×C₂²⋊C₈	—	2	1	no	—
139	C₁₉×C₂²⋊C₈	—	2	1	no	—
140	C₁₉×#97	—	2	1	no	—
141	C₄×C₈×C₁₉	—	2	1	no	—
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
145	#41×C₁₉	—	4	2	no	—
146	#41×C₁₉	—	4	2	no	—
147	#41×C₁₉	—	8	1	no	—
148	#41×C₁₉	—	8	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	4	1	no	—
153	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	4	1	no	—
159	C₂×D₄×C₁₉	—	4	1	no	—
160	C₂×D₄×C₁₉	—	4	1	no	—
161	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	4	1	no	—
166	C₂²×C₄×C₁₉	—	4	1	no	—
167	C₂²×C₄×C₁₉	—	4	1	no	—
168	Q₁₆×C₁₉	—	4	2	no	—
169	SD₁₆×C₁₉	—	4	1	no	—
170	SD₁₆×C₁₉	—	4	2	no	—
171	SD₁₆×C₁₉	—	4	2	no	—
172	SD₁₆×C₁₉	—	8	1	no	—
173	SD₁₆×C₁₉	—	8	2	no	—
174	SD₁₆×C₁₉	SD₁₆	1	4	yes	complemented
175	D₈×C₁₉	—	4	2	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	2	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	—	4	2	no	—
182	C₂×C₈×C₁₉	—	4	2	no	—
183	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	4	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	—	4	1	no	—
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	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₁₉	—	2	1	no	—
210	C₄²×C₁₉	—	2	1	no	—
211	C₄²×C₁₉	—	4	1	no	—
212	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
213	#19768	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂³×C₁₉	—	2	1	no	—
215	C₂³×C₁₉	—	2	1	no	—
216	C₂³×C₁₉	—	4	1	no	—
217	Q₈×C₁₉	—	2	1	no	—
218	Q₈×C₁₉	—	2	1	no	—
219	Q₈×C₁₉	—	2	1	no	—
220	Q₈×C₁₉	—	4	1	no	—
221	Q₈×C₁₉	—	4	1	no	—
222	Q₈×C₁₉	—	8	1	no	—
223	Q₈×C₁₉	—	8	1	no	—
224	Q₈×C₁₉	—	16	1	no	—
225	Q₈×C₁₉	C₂×SD₁₆	1	2	yes	—
226	D₄×C₁₉	—	2	1	no	—
227	D₄×C₁₉	—	2	1	no	—
228	D₄×C₁₉	—	2	1	no	—
229	D₄×C₁₉	—	4	1	no	—
230	D₄×C₁₉	—	4	1	no	—
231	D₄×C₁₉	—	4	1	no	—
232	D₄×C₁₉	—	4	1	no	—
233	D₄×C₁₉	—	8	2	no	—
234	D₄×C₁₉	—	8	1	no	—
235	D₄×C₁₉	—	8	2	no	—
236	D₄×C₁₉	—	16	1	no	—
237	D₄×C₁₉	C₂×SD₁₆	1	2	yes	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	8	2	no	—
252	C₂×C₄×C₁₉	—	8	2	no	—
253	C₂×C₄×C₁₉	—	16	1	no	—
254	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
257	C₈×C₁₉	—	2	1	no	—
258	C₈×C₁₉	—	2	1	no	—
259	C₈×C₁₉	—	2	1	no	—
260	C₈×C₁₉	—	4	1	no	—
261	C₈×C₁₉	—	4	1	no	—
262	C₈×C₁₉	—	4	1	no	—
263	C₈×C₁₉	—	4	1	no	—
264	C₈×C₁₉	—	4	1	no	—
265	C₈×C₁₉	C₂×SD₁₆	1	2	yes	—
266	#3385	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#3362	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#3335	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#3284	C₂×C₁₉	1	1	yes	characteristic
270	#1714	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#1686	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1677	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1675	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1672	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1645	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1635	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1631	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1622	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1582	C₂×C₁₉	1	1	yes	characteristic, complemented
280	SD₁₆⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
281	C₂²×C₁₉	—	2	2	no	—
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	1	no	—
284	C₂²×C₁₉	—	4	1	no	—
285	C₂²×C₁₉	—	4	1	no	—
286	C₂²×C₁₉	—	4	1	no	—
287	C₂²×C₁₉	—	8	1	no	—
288	C₂²×C₁₉	—	8	1	no	—
289	C₂²×C₁₉	—	8	1	no	—
290	C₂²×C₁₉	D₄²	1	1	yes	characteristic
291	C₄×C₁₉	—	2	2	no	—
292	C₄×C₁₉	—	2	1	no	—
293	C₄×C₁₉	—	4	1	no	—
294	C₄×C₁₉	—	4	1	no	—
295	C₄×C₁₉	—	4	1	no	—
296	C₄×C₁₉	—	4	1	no	—
297	C₄×C₁₉	—	4	1	no	—
298	C₄×C₁₉	—	8	1	no	—
299	C₄×C₁₉	—	8	1	no	—
300	C₄×C₁₉	—	8	1	no	—
301	C₄×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
302	C₄×C₁₉	#575	1	1	yes	characteristic
303	C₄×C₁₉	#577	1	1	yes	characteristic
304	C₄×C₁₉	#578	1	1	yes	characteristic
305	C₂×#135	—	2	1	no	—
306	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
307	#554	C₂²×C₁₉	1	1	yes	characteristic
308	#550	C₂²×C₁₉	1	1	yes	characteristic
309	#547	C₂²×C₁₉	1	1	yes	characteristic
310	#501	—	2	1	no	—
311	#500	C₂²×C₁₉	1	1	yes	characteristic
312	#498	C₂²×C₁₉	1	1	yes	characteristic
313	#492	C₂²×C₁₉	1	1	yes	characteristic
314	#492	C₂²×C₁₉	1	1	yes	characteristic
315	#487	C₂²×C₁₉	1	1	yes	characteristic
316	#486	—	2	1	no	—
317	#486	C₂²×C₁₉	1	1	yes	characteristic
318	#483	—	2	1	no	—
319	#481	—	2	1	no	—
320	#479	—	2	1	no	—
321	#477	C₂²×C₁₉	1	1	yes	characteristic
322	#476	—	2	1	no	—
323	#476	C₂²×C₁₉	1	1	yes	characteristic
324	#476	C₂²×C₁₉	1	1	yes	characteristic
325	#476	C₂²×C₁₉	1	1	yes	characteristic
326	#475	C₂²×C₁₉	1	1	yes	characteristic
327	#474	—	2	1	no	—
328	#465	—	2	1	no	—
329	#465	—	2	1	no	—
330	#462	C₂²×C₁₉	1	1	yes	characteristic
331	#460	—	2	1	no	—
332	#460	C₂²×C₁₉	1	1	yes	characteristic
333	#459	C₂²×C₁₉	1	1	yes	characteristic
334	#452	—	2	1	no	—
335	#449	—	2	1	no	—
336	#446	C₂²×C₁₉	1	1	yes	characteristic
337	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
338	#440	—	2	1	no	—
339	C₄×SD₁₆	—	2	1	no	—
340	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
341	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
342	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
343	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×#106	—	2	1	no	—
345	#335	C₂²×C₁₉	1	1	yes	characteristic
346	#334	C₂²×C₁₉	1	1	yes	characteristic
347	#333	C₂²×C₁₉	1	1	yes	characteristic
348	#333	C₂²×C₁₉	1	1	yes	characteristic
349	#332	C₂²×C₁₉	1	1	yes	characteristic
350	#331	C₂²×C₁₉	1	1	yes	characteristic
351	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
352	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
353	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
354	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
355	#322	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×C₁₉	—	4	2	no	—
357	C₂×C₁₉	—	8	1	no	—
358	C₂×C₁₉	—	16	1	no	—
359	C₂×C₁₉	#3269	1	1	yes	characteristic
360	C₂×C₁₉	D₄×SD₁₆	1	1	yes	characteristic
361	C₂×C₁₉	#3288	1	1	yes	characteristic
362	C₂×#41	—	2	1	no	—
363	C₂×#41	—	2	1	no	—
364	#135	—	4	4	no	—
365	C₂×Q₁₆	—	2	1	no	—
366	C₂×SD₁₆	—	2	1	no	—
367	C₂×SD₁₆	—	2	1	no	—
368	C₂×SD₁₆	—	2	1	no	—
369	C₂×SD₁₆	—	4	1	no	—
370	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
371	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
372	C₂×D₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₄⋊Q₈	—	2	1	no	—
376	C₄⋊Q₈	—	2	1	no	—
377	C₄⋊Q₈	—	4	1	no	—
378	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
379	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
380	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
381	#127	—	2	1	no	—
382	#127	C₂³×C₁₉	1	1	yes	characteristic
383	#125	—	2	1	no	—
384	#123	—	4	1	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	—	2	1	no	—
387	C₂²⋊Q₈	—	4	1	no	—
388	#121	—	2	1	no	—
389	#121	—	2	1	no	—
390	#121	—	4	1	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	—	2	1	no	—
393	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
394	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
398	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	#107	—	2	1	no	—
402	#107	—	2	1	no	—
403	#107	—	2	1	no	—
404	#106	—	2	1	no	—
405	#106	—	2	1	no	—
406	#106	—	2	1	no	—
407	#106	—	2	1	no	—
408	#106	—	2	1	no	—
409	#106	—	2	1	no	—
410	#106	D₄×C₁₉	1	1	yes	characteristic
411	#106	D₄×C₁₉	1	1	yes	characteristic
412	C₄⋊C₈	—	2	1	no	—
413	C₄⋊C₈	—	2	1	no	—
414	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
415	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
416	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
418	#103	—	2	1	no	—
419	#103	—	2	1	no	—
420	#103	—	2	1	no	—
421	#103	—	4	1	no	—
422	#103	D₄×C₁₉	1	1	yes	characteristic
423	#103	D₄×C₁₉	1	1	yes	characteristic
424	#102	—	2	1	no	—
425	#102	—	2	1	no	—
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	—	2	1	no	—
429	#102	—	2	1	no	—
430	#102	—	2	1	no	—
431	#102	D₄×C₁₉	1	1	yes	characteristic
432	#102	D₄×C₁₉	1	1	yes	characteristic
433	C₂²⋊C₈	—	2	1	no	—
434	C₂²⋊C₈	—	2	1	no	—
435	#97	—	2	1	no	—
436	C₄×C₈	—	2	1	no	—
437	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
438	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
439	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
440	C₁₉	#19768	1	1	yes	characteristic, direct product factor, Sylow
441	#41	—	4	2	no	—
442	#41	—	4	2	no	—
443	#41	—	8	1	no	—
444	#41	—	8	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	4	1	no	—
449	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	4	1	no	—
462	C₂²×C₄	—	4	1	no	—
463	C₂²×C₄	—	4	1	no	—
464	Q₁₆	—	4	2	no	—
465	SD₁₆	—	4	1	no	—
466	SD₁₆	—	4	2	no	—
467	SD₁₆	—	4	2	no	—
468	SD₁₆	—	8	1	no	—
469	SD₁₆	—	8	2	no	—
470	SD₁₆	SD₁₆×C₁₉	1	4	yes	complemented
471	D₈	—	4	2	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	4	2	no	—
478	C₂×C₈	—	4	2	no	—
479	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	—	4	1	no	—
494	C₄⋊C₄	—	4	1	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
499	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	4	1	no	—
503	C₂²⋊C₄	—	4	1	no	—
504	C₂²⋊C₄	—	4	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	4	1	no	—
508	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
509	C₂³	—	2	1	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	4	1	no	—
512	Q₈	—	2	1	no	—
513	Q₈	—	2	1	no	—
514	Q₈	—	2	1	no	—
515	Q₈	—	4	1	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	8	1	no	—
518	Q₈	—	8	1	no	—
519	Q₈	—	16	1	no	—
520	Q₈	C₂×SD₁₆×C₁₉	1	2	yes	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	1	no	—
528	D₄	—	8	2	no	—
529	D₄	—	8	1	no	—
530	D₄	—	8	2	no	—
531	D₄	—	16	1	no	—
532	D₄	C₂×SD₁₆×C₁₉	1	2	yes	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	8	2	no	—
547	C₂×C₄	—	8	2	no	—
548	C₂×C₄	—	16	1	no	—
549	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
551	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
552	C₈	—	2	1	no	—
553	C₈	—	2	1	no	—
554	C₈	—	2	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	4	1	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	C₂×SD₁₆×C₁₉	1	2	yes	—
561	C₂²	—	2	2	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	8	1	no	—
569	C₂²	—	8	1	no	—
570	C₂²	D₄²×C₁₉	1	1	yes	characteristic
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	8	1	no	—
579	C₄	—	8	1	no	—
580	C₄	—	8	1	no	—
581	C₄	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
582	C₄	C₁₉×#575	1	1	yes	characteristic
583	C₄	C₁₉×#577	1	1	yes	characteristic
584	C₄	C₁₉×#578	1	1	yes	characteristic
585	C₂	—	4	2	no	—
586	C₂	—	8	1	no	—
587	C₂	—	16	1	no	—
588	C₂	C₁₉×#3269	1	1	yes	characteristic
589	C₂	D₄×SD₁₆×C₁₉	1	1	yes	characteristic
590	C₂	C₁₉×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3284	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×#3385	C₂	semidirect
2. C₁₉×#3362	C₂	semidirect
3. C₁₉×#3335	C₂	semidirect
5. C₁₉×#1714	C₂	semidirect
6. C₁₉×#1686	C₂	semidirect
7. C₁₉×#1677	C₂	semidirect
8. C₁₉×#1675	C₂	semidirect
9. C₁₉×#1672	C₂	semidirect
10. C₁₉×#1645	C₂	semidirect
11. C₁₉×#1635	C₂	semidirect
12. C₁₉×#1631	C₂	semidirect
13. C₁₉×#1622	C₂	semidirect
14. C₁₉×#1582	C₂	semidirect
15. C₁₉×SD₁₆⋊C₈	C₂	semidirect
174. SD₁₆×C₁₉	SD₁₆	semidirect
213. #19768	C₁₉	direct (N × H)
266. #3385	C₂×C₁₉	semidirect
267. #3362	C₂×C₁₉	semidirect
268. #3335	C₂×C₁₉	semidirect
270. #1714	C₂×C₁₉	semidirect
271. #1686	C₂×C₁₉	semidirect
272. #1677	C₂×C₁₉	semidirect
273. #1675	C₂×C₁₉	semidirect
274. #1672	C₂×C₁₉	semidirect
275. #1645	C₂×C₁₉	semidirect
276. #1635	C₂×C₁₉	semidirect
277. #1631	C₂×C₁₉	semidirect
278. #1622	C₂×C₁₉	semidirect
279. #1582	C₂×C₁₉	semidirect
280. SD₁₆⋊C₈	C₂×C₁₉	semidirect
440. C₁₉	#19768	direct (N × H)
470. SD₁₆	SD₁₆×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3385	2
C₁₉×#3362	2
C₁₉×#3335	2
C₁₉×#3284	2
C₁₉×#1714	2
C₁₉×#1686	2
C₁₉×#1677	2
C₁₉×#1675	2
C₁₉×#1672	2
C₁₉×#1645	2
C₁₉×#1635	2
C₁₉×#1631	2
C₁₉×#1622	2
C₁₉×#1582	2
C₁₉×SD₁₆⋊C₈	2
#19768	19

Subgroups — C19×#19768 #18025727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19768 #18025727