Subgroups — C₁₉×#19912 #18025871

Order 4864.

684 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3394	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3373	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3324	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1706	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1702	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1701	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1666	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1650	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1649	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1620	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1619	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₁₉	—	2	1	no	—
17	C₁₉×#559	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#556	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	D₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×#495	—	2	1	no	—
23	C₁₉×#493	C₂²	1	1	yes	characteristic
24	C₁₉×#492	C₂²	1	1	yes	characteristic
25	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#489	—	2	1	no	—
27	C₁₉×#486	C₂²	1	1	yes	characteristic
28	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#482	—	2	1	no	—
30	C₁₉×#476	—	2	1	no	—
31	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#474	C₂²	1	1	yes	characteristic
33	C₁₉×#468	—	2	1	no	—
34	C₁₉×#465	—	2	1	no	—
35	C₁₉×#464	—	2	1	no	—
36	C₁₉×#463	—	2	1	no	—
37	C₁₉×#463	—	2	1	no	—
38	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#461	C₂²	1	1	yes	characteristic
40	C₁₉×#460	C₂²	1	1	yes	characteristic
41	C₁₉×#460	C₂²	1	1	yes	characteristic
42	C₁₉×#459	C₂²	1	1	yes	characteristic
43	C₁₉×#459	C₂²	1	1	yes	characteristic
44	C₁₉×#450	—	2	1	no	—
45	C₁₉×#450	—	2	1	no	—
46	C₁₉×#448	—	2	1	no	—
47	C₁₉×#446	C₂²	1	1	yes	characteristic, complemented
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#442	—	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	C₁₉×#436	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
55	C₁₉×#418	—	2	1	no	—
56	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#334	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×#331	C₂²	1	1	yes	characteristic
61	C₁₉×#331	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₈²×C₁₉	C₂²	1	1	yes	characteristic, complemented
67	C₂²×Q₈×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×SD₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×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	—	2	1	no	—
77	C₂×SD₁₆×C₁₉	—	2	1	no	—
78	C₂×SD₁₆×C₁₉	—	4	4	no	—
79	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
80	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
81	C₂×D₈×C₁₉	—	2	1	no	—
82	C₂×D₈×C₁₉	—	2	1	no	—
83	C₂×D₈×C₁₉	—	4	1	no	—
84	C₂×M₁₆×C₁₉	—	2	1	no	—
85	C₂²×C₈×C₁₉	—	2	1	no	—
86	C₁₉×C₄⋊Q₈	—	2	1	no	—
87	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₁₉×#127	C₂³	1	1	yes	characteristic
90	C₁₉×#127	C₂³	1	1	yes	characteristic
91	C₁₉×#126	—	4	1	no	—
92	C₁₉×#124	—	2	1	no	—
93	C₁₉×#124	—	2	1	no	—
94	C₁₉×#124	—	2	1	no	—
95	C₁₉×#123	—	4	1	no	—
96	C₁₉×C₂²⋊Q₈	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	—	2	1	no	—
98	C₁₉×C₂²⋊Q₈	—	4	1	no	—
99	C₁₉×#121	—	2	1	no	—
100	C₁₉×#121	—	2	1	no	—
101	C₁₉×#120	—	4	1	no	—
102	C₄×Q₈×C₁₉	—	2	1	no	—
103	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
104	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₁₉	—	2	1	no	—
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	—	2	1	no	—
108	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₁₉×#117	—	2	1	no	—
111	C₁₉×#107	—	2	1	no	—
112	C₁₉×#107	—	4	1	no	—
113	C₁₉×#106	—	2	1	no	—
114	C₁₉×#106	D₄	1	1	yes	characteristic
115	C₁₉×#106	D₄	1	1	yes	characteristic
116	C₁₉×C₄⋊C₈	—	2	1	no	—
117	C₁₉×C₄⋊C₈	—	2	1	no	—
118	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#103	—	2	1	no	—
123	C₁₉×#103	—	2	1	no	—
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	D₄	1	1	yes	characteristic
126	C₁₉×#103	D₄	1	1	yes	characteristic
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	—	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	C₂⁴×C₁₉	—	4	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	4	1	no	—
149	C₂×Q₈×C₁₉	—	4	2	no	—
150	C₂×Q₈×C₁₉	—	8	1	no	—
151	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
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	—	2	1	no	—
159	C₂×D₄×C₁₉	—	4	1	no	—
160	C₂×D₄×C₁₉	—	4	1	no	—
161	C₂×D₄×C₁₉	—	4	2	no	—
162	C₂×D₄×C₁₉	—	4	2	no	—
163	C₂×D₄×C₁₉	—	8	1	no	—
164	C₂×D₄×C₁₉	—	8	1	no	—
165	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	4	1	no	—
170	C₂²×C₄×C₁₉	—	4	1	no	—
171	Q₁₆×C₁₉	—	8	1	no	—
172	SD₁₆×C₁₉	—	2	2	no	—
173	SD₁₆×C₁₉	—	2	2	no	—
174	SD₁₆×C₁₉	—	4	2	no	—
175	SD₁₆×C₁₉	—	4	2	no	—
176	SD₁₆×C₁₉	—	4	2	no	—
177	SD₁₆×C₁₉	—	4	2	no	—
178	SD₁₆×C₁₉	—	8	1	no	—
179	SD₁₆×C₁₉	—	8	1	no	—
180	SD₁₆×C₁₉	—	8	1	no	—
181	D₈×C₁₉	—	4	2	no	—
182	D₈×C₁₉	—	8	2	no	—
183	D₈×C₁₉	—	8	1	no	—
184	M₁₆×C₁₉	—	8	1	no	—
185	C₂×C₈×C₁₉	—	2	1	no	—
186	C₂×C₈×C₁₉	—	2	1	no	—
187	C₂×C₈×C₁₉	—	2	1	no	—
188	C₂×C₈×C₁₉	—	2	1	no	—
189	C₂×C₈×C₁₉	—	2	1	no	—
190	C₂×C₈×C₁₉	—	4	2	no	—
191	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	4	1	no	—
202	C₄⋊C₄×C₁₉	—	4	1	no	—
203	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₂²⋊C₄×C₁₉	—	2	1	no	—
208	C₂²⋊C₄×C₁₉	—	2	1	no	—
209	C₂²⋊C₄×C₁₉	—	4	1	no	—
210	C₂²⋊C₄×C₁₉	—	4	1	no	—
211	C₂²⋊C₄×C₁₉	—	4	1	no	—
212	C₂²⋊C₄×C₁₉	—	4	1	no	—
213	C₂²⋊C₄×C₁₉	—	4	1	no	—
214	C₂²⋊C₄×C₁₉	—	4	1	no	—
215	C₂²⋊C₄×C₁₉	—	4	1	no	—
216	C₄²×C₁₉	—	2	1	no	—
217	C₄²×C₁₉	—	2	1	no	—
218	C₄²×C₁₉	—	4	1	no	—
219	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
220	#19912	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	2	1	no	—
223	C₂³×C₁₉	—	4	1	no	—
224	C₂³×C₁₉	—	4	1	no	—
225	C₂³×C₁₉	—	8	2	no	—
226	C₂³×C₁₉	—	8	2	no	—
227	C₂³×C₁₉	—	16	1	no	—
228	Q₈×C₁₉	—	2	1	no	—
229	Q₈×C₁₉	—	2	1	no	—
230	Q₈×C₁₉	—	2	1	no	—
231	Q₈×C₁₉	—	2	1	no	—
232	Q₈×C₁₉	—	4	1	no	—
233	Q₈×C₁₉	—	4	1	no	—
234	Q₈×C₁₉	—	4	1	no	—
235	Q₈×C₁₉	—	4	1	no	—
236	Q₈×C₁₉	—	8	2	no	—
237	D₄×C₁₉	—	2	1	no	—
238	D₄×C₁₉	—	2	1	no	—
239	D₄×C₁₉	—	2	1	no	—
240	D₄×C₁₉	—	4	1	no	—
241	D₄×C₁₉	—	4	1	no	—
242	D₄×C₁₉	—	4	1	no	—
243	D₄×C₁₉	—	4	1	no	—
244	D₄×C₁₉	—	4	1	no	—
245	D₄×C₁₉	—	4	1	no	—
246	D₄×C₁₉	—	4	1	no	—
247	D₄×C₁₉	—	4	1	no	—
248	D₄×C₁₉	—	8	1	no	—
249	D₄×C₁₉	—	8	1	no	—
250	D₄×C₁₉	—	8	2	no	—
251	D₄×C₁₉	—	8	2	no	—
252	D₄×C₁₉	#135	1	2	yes	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	8	2	no	—
266	C₂×C₄×C₁₉	—	16	1	no	—
267	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
270	C₈×C₁₉	—	2	2	no	—
271	C₈×C₁₉	—	2	1	no	—
272	C₈×C₁₉	—	2	1	no	—
273	C₈×C₁₉	—	2	1	no	—
274	C₈×C₁₉	—	4	1	no	—
275	C₈×C₁₉	—	4	1	no	—
276	C₈×C₁₉	—	4	1	no	—
277	C₈×C₁₉	—	4	1	no	—
278	C₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
279	#3394	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#3373	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#3324	C₂×C₁₉	1	1	yes	characteristic, complemented
282	D₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1706	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1702	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1701	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1666	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1665	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1650	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1649	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1620	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1619	C₂×C₁₉	1	1	yes	characteristic
292	#1590	C₂×C₁₉	1	1	yes	characteristic, complemented
293	C₈×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
294	C₂²×C₁₉	—	2	2	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	—	4	1	no	—
297	C₂²×C₁₉	—	4	1	no	—
298	C₂²×C₁₉	—	4	1	no	—
299	C₂²×C₁₉	—	4	1	no	—
300	C₂²×C₁₉	—	8	1	no	—
301	C₂²×C₁₉	—	8	1	no	—
302	C₂²×C₁₉	—	8	1	no	—
303	C₂²×C₁₉	—	8	1	no	—
304	C₂²×C₁₉	—	8	1	no	—
305	C₂²×C₁₉	—	8	1	no	—
306	C₂²×C₁₉	—	16	4	no	—
307	C₂²×C₁₉	D₄²	1	1	yes	characteristic
308	C₄×C₁₉	—	2	1	no	—
309	C₄×C₁₉	—	4	1	no	—
310	C₄×C₁₉	—	4	1	no	—
311	C₄×C₁₉	—	4	1	no	—
312	C₄×C₁₉	—	4	1	no	—
313	C₄×C₁₉	—	4	1	no	—
314	C₄×C₁₉	—	4	1	no	—
315	C₄×C₁₉	—	8	1	no	—
316	C₄×C₁₉	—	8	1	no	—
317	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
318	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₄×C₁₉	#576	1	1	yes	characteristic
320	C₄×C₁₉	#577	1	1	yes	characteristic
321	C₂²×SD₁₆	—	2	1	no	—
322	#559	C₂²×C₁₉	1	1	yes	characteristic, complemented
323	#556	C₂²×C₁₉	1	1	yes	characteristic
324	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
325	D₄²	C₂²×C₁₉	1	1	yes	characteristic
326	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
327	#495	—	2	1	no	—
328	#493	C₂²×C₁₉	1	1	yes	characteristic
329	#492	C₂²×C₁₉	1	1	yes	characteristic
330	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
331	#489	—	2	1	no	—
332	#486	C₂²×C₁₉	1	1	yes	characteristic
333	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
334	#482	—	2	1	no	—
335	#476	—	2	1	no	—
336	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
337	#474	C₂²×C₁₉	1	1	yes	characteristic
338	#468	—	2	1	no	—
339	#465	—	2	1	no	—
340	#464	—	2	1	no	—
341	#463	—	2	1	no	—
342	#463	—	2	1	no	—
343	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
344	#461	C₂²×C₁₉	1	1	yes	characteristic
345	#460	C₂²×C₁₉	1	1	yes	characteristic
346	#460	C₂²×C₁₉	1	1	yes	characteristic
347	#459	C₂²×C₁₉	1	1	yes	characteristic
348	#459	C₂²×C₁₉	1	1	yes	characteristic
349	#450	—	2	1	no	—
350	#450	—	2	1	no	—
351	#448	—	2	1	no	—
352	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
353	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
354	#442	—	2	1	no	—
355	C₄×SD₁₆	—	2	1	no	—
356	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
357	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
358	#436	C₂²×C₁₉	1	1	yes	characteristic
359	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
360	#418	—	2	1	no	—
361	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
362	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
363	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
364	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
365	#331	C₂²×C₁₉	1	1	yes	characteristic
366	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
367	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
368	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
369	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
370	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
371	C₈²	C₂²×C₁₉	1	1	yes	characteristic, complemented
372	C₂×C₁₉	—	4	2	no	—
373	C₂×C₁₉	—	8	1	no	—
374	C₂×C₁₉	—	16	1	no	—
375	C₂×C₁₉	—	16	1	no	—
376	C₂×C₁₉	#3274	1	1	yes	characteristic
377	C₂×C₁₉	#3282	1	1	yes	characteristic
378	C₂×C₁₉	#3291	1	1	yes	characteristic
379	C₂²×Q₈	—	2	1	no	—
380	C₂²×D₄	—	2	1	no	—
381	C₂²×D₄	—	2	1	no	—
382	C₂×Q₁₆	—	2	1	no	—
383	C₂×SD₁₆	—	2	1	no	—
384	C₂×SD₁₆	—	2	1	no	—
385	C₂×SD₁₆	—	2	1	no	—
386	C₂×SD₁₆	—	2	1	no	—
387	C₂×SD₁₆	—	2	1	no	—
388	C₂×SD₁₆	—	2	1	no	—
389	C₂×SD₁₆	—	2	1	no	—
390	C₂×SD₁₆	—	4	4	no	—
391	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
392	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
393	C₂×D₈	—	2	1	no	—
394	C₂×D₈	—	2	1	no	—
395	C₂×D₈	—	4	1	no	—
396	C₂×M₁₆	—	2	1	no	—
397	C₂²×C₈	—	2	1	no	—
398	C₄⋊Q₈	—	2	1	no	—
399	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
400	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
401	#127	C₂³×C₁₉	1	1	yes	characteristic
402	#127	C₂³×C₁₉	1	1	yes	characteristic
403	#126	—	4	1	no	—
404	#124	—	2	1	no	—
405	#124	—	2	1	no	—
406	#124	—	2	1	no	—
407	#123	—	4	1	no	—
408	C₂²⋊Q₈	—	2	1	no	—
409	C₂²⋊Q₈	—	2	1	no	—
410	C₂²⋊Q₈	—	4	1	no	—
411	#121	—	2	1	no	—
412	#121	—	2	1	no	—
413	#120	—	4	1	no	—
414	C₄×Q₈	—	2	1	no	—
415	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
416	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
421	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
422	#117	—	2	1	no	—
423	#107	—	2	1	no	—
424	#107	—	4	1	no	—
425	#106	—	2	1	no	—
426	#106	D₄×C₁₉	1	1	yes	characteristic
427	#106	D₄×C₁₉	1	1	yes	characteristic
428	C₄⋊C₈	—	2	1	no	—
429	C₄⋊C₈	—	2	1	no	—
430	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
431	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
432	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
433	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
434	#103	—	2	1	no	—
435	#103	—	2	1	no	—
436	#103	—	2	1	no	—
437	#103	D₄×C₁₉	1	1	yes	characteristic
438	#103	D₄×C₁₉	1	1	yes	characteristic
439	#102	—	2	1	no	—
440	#102	—	2	1	no	—
441	#102	—	2	1	no	—
442	#102	—	2	1	no	—
443	#102	—	2	1	no	—
444	#102	—	2	1	no	—
445	#102	—	2	1	no	—
446	#102	—	2	1	no	—
447	#102	—	2	1	no	—
448	#102	D₄×C₁₉	1	1	yes	characteristic
449	#102	D₄×C₁₉	1	1	yes	characteristic
450	C₂²⋊C₈	—	2	1	no	—
451	C₂²⋊C₈	—	2	1	no	—
452	#97	—	2	1	no	—
453	C₄×C₈	—	2	1	no	—
454	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
455	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
456	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
457	C₁₉	#19912	1	1	yes	characteristic, direct product factor, Sylow
458	C₂⁴	—	4	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	4	1	no	—
462	C₂×Q₈	—	4	2	no	—
463	C₂×Q₈	—	8	1	no	—
464	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	4	1	no	—
473	C₂×D₄	—	4	1	no	—
474	C₂×D₄	—	4	2	no	—
475	C₂×D₄	—	4	2	no	—
476	C₂×D₄	—	8	1	no	—
477	C₂×D₄	—	8	1	no	—
478	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	4	1	no	—
483	C₂²×C₄	—	4	1	no	—
484	Q₁₆	—	8	1	no	—
485	SD₁₆	—	2	2	no	—
486	SD₁₆	—	2	2	no	—
487	SD₁₆	—	4	2	no	—
488	SD₁₆	—	4	2	no	—
489	SD₁₆	—	4	2	no	—
490	SD₁₆	—	4	2	no	—
491	SD₁₆	—	8	1	no	—
492	SD₁₆	—	8	1	no	—
493	SD₁₆	—	8	1	no	—
494	D₈	—	4	2	no	—
495	D₈	—	8	2	no	—
496	D₈	—	8	1	no	—
497	M₁₆	—	8	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	4	2	no	—
504	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
505	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
506	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
507	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	4	1	no	—
515	C₄⋊C₄	—	4	1	no	—
516	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
519	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	4	1	no	—
523	C₂²⋊C₄	—	4	1	no	—
524	C₂²⋊C₄	—	4	1	no	—
525	C₂²⋊C₄	—	4	1	no	—
526	C₂²⋊C₄	—	4	1	no	—
527	C₂²⋊C₄	—	4	1	no	—
528	C₂²⋊C₄	—	4	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	4	1	no	—
532	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	8	2	no	—
538	C₂³	—	8	2	no	—
539	C₂³	—	16	1	no	—
540	Q₈	—	2	1	no	—
541	Q₈	—	2	1	no	—
542	Q₈	—	2	1	no	—
543	Q₈	—	2	1	no	—
544	Q₈	—	4	1	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	4	1	no	—
547	Q₈	—	4	1	no	—
548	Q₈	—	8	2	no	—
549	D₄	—	2	1	no	—
550	D₄	—	2	1	no	—
551	D₄	—	2	1	no	—
552	D₄	—	4	1	no	—
553	D₄	—	4	1	no	—
554	D₄	—	4	1	no	—
555	D₄	—	4	1	no	—
556	D₄	—	4	1	no	—
557	D₄	—	4	1	no	—
558	D₄	—	4	1	no	—
559	D₄	—	4	1	no	—
560	D₄	—	8	1	no	—
561	D₄	—	8	1	no	—
562	D₄	—	8	2	no	—
563	D₄	—	8	2	no	—
564	D₄	C₁₉×#135	1	2	yes	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	8	2	no	—
578	C₂×C₄	—	16	1	no	—
579	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
580	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
581	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
582	C₈	—	2	2	no	—
583	C₈	—	2	1	no	—
584	C₈	—	2	1	no	—
585	C₈	—	2	1	no	—
586	C₈	—	4	1	no	—
587	C₈	—	4	1	no	—
588	C₈	—	4	1	no	—
589	C₈	—	4	1	no	—
590	C₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
591	C₂²	—	2	2	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	8	1	no	—
598	C₂²	—	8	1	no	—
599	C₂²	—	8	1	no	—
600	C₂²	—	8	1	no	—
601	C₂²	—	8	1	no	—
602	C₂²	—	8	1	no	—
603	C₂²	—	16	4	no	—
604	C₂²	D₄²×C₁₉	1	1	yes	characteristic
605	C₄	—	2	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	8	1	no	—
613	C₄	—	8	1	no	—
614	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
615	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
616	C₄	C₁₉×#576	1	1	yes	characteristic
617	C₄	C₁₉×#577	1	1	yes	characteristic
618	C₂	—	4	2	no	—
619	C₂	—	8	1	no	—
620	C₂	—	16	1	no	—
621	C₂	—	16	1	no	—
622	C₂	C₁₉×#3274	1	1	yes	characteristic
623	C₂	C₁₉×#3282	1	1	yes	characteristic
624	C₂	C₁₉×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#1619	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×#3394	C₂	semidirect
2. C₁₉×#3373	C₂	semidirect
3. C₁₉×#3324	C₂	semidirect
4. D₄×SD₁₆×C₁₉	C₂	semidirect
5. C₁₉×#1706	C₂	semidirect
6. C₁₉×#1702	C₂	semidirect
7. C₁₉×#1701	C₂	semidirect
8. C₁₉×#1666	C₂	semidirect
9. C₁₉×#1665	C₂	semidirect
10. C₁₉×#1650	C₂	semidirect
11. C₁₉×#1649	C₂	semidirect
12. C₁₉×#1620	C₂	semidirect
14. C₁₉×#1590	C₂	semidirect
15. C₈×SD₁₆×C₁₉	C₂	semidirect
17. C₁₉×#559	C₂²	semidirect
21. C₁₉×#500	C₂²	semidirect
25. C₁₉×#492	C₂²	semidirect
28. C₁₉×#486	C₂²	semidirect
31. C₁₉×#475	C₂²	semidirect
38. C₁₉×#462	C₂²	semidirect
47. C₁₉×#446	C₂²	semidirect
48. C₈×Q₈×C₁₉	C₂²	semidirect
56. C₁₉×#334	C₂²	semidirect
57. C₁₉×#334	C₂²	semidirect
58. C₁₉×#332	C₂²	semidirect
59. C₁₉×#332	C₂²	semidirect
61. C₁₉×#331	C₂²	semidirect
62. C₁₉×Q₈⋊C₈	C₂²	semidirect
63. C₁₉×Q₈⋊C₈	C₂²	semidirect
66. C₈²×C₁₉	C₂²	semidirect
220. #19912	C₁₉	direct (N × H)
279. #3394	C₂×C₁₉	semidirect
280. #3373	C₂×C₁₉	semidirect
281. #3324	C₂×C₁₉	semidirect
282. D₄×SD₁₆	C₂×C₁₉	semidirect
283. #1706	C₂×C₁₉	semidirect
284. #1702	C₂×C₁₉	semidirect
285. #1701	C₂×C₁₉	semidirect
286. #1666	C₂×C₁₉	semidirect
287. #1665	C₂×C₁₉	semidirect
288. #1650	C₂×C₁₉	semidirect
289. #1649	C₂×C₁₉	semidirect
290. #1620	C₂×C₁₉	semidirect
292. #1590	C₂×C₁₉	semidirect
293. C₈×SD₁₆	C₂×C₁₉	semidirect
322. #559	C₂²×C₁₉	semidirect
326. #500	C₂²×C₁₉	semidirect
330. #492	C₂²×C₁₉	semidirect
333. #486	C₂²×C₁₉	semidirect
336. #475	C₂²×C₁₉	semidirect
343. #462	C₂²×C₁₉	semidirect
352. #446	C₂²×C₁₉	semidirect
353. C₈×Q₈	C₂²×C₁₉	semidirect
361. #334	C₂²×C₁₉	semidirect
362. #334	C₂²×C₁₉	semidirect
363. #332	C₂²×C₁₉	semidirect
364. #332	C₂²×C₁₉	semidirect
366. #331	C₂²×C₁₉	semidirect
367. Q₈⋊C₈	C₂²×C₁₉	semidirect
368. Q₈⋊C₈	C₂²×C₁₉	semidirect
371. C₈²	C₂²×C₁₉	semidirect
457. C₁₉	#19912	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×#3394	2
C₁₉×#3373	2
C₁₉×#3324	2
D₄×SD₁₆×C₁₉	2
C₁₉×#1706	2
C₁₉×#1702	2
C₁₉×#1701	2
C₁₉×#1666	2
C₁₉×#1665	2
C₁₉×#1650	2
C₁₉×#1649	2
C₁₉×#1620	2
C₁₉×#1619	2
C₁₉×#1590	2
C₈×SD₁₆×C₁₉	2
#19912	19

Subgroups — C19×#19912 #18025871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19912 #18025871