Subgroups — C₁₉×#19891 #18025850

Order 4864.

686 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3384	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3298	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3272	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1708	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1691	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1686	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1679	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1643	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1639	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1635	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1627	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
17	C₁₉×#554	C₂²	1	1	yes	characteristic
18	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
19	C₁₉×#547	C₂²	1	1	yes	characteristic
20	D₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#501	—	2	1	no	—
22	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#492	C₂²	1	1	yes	characteristic
24	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#486	C₂²	1	1	yes	characteristic
27	C₁₉×#486	C₂²	1	1	yes	characteristic
28	C₁₉×#483	—	2	1	no	—
29	C₁₉×#481	—	2	1	no	—
30	C₁₉×#478	—	2	1	no	—
31	C₁₉×#476	—	2	1	no	—
32	C₁₉×#476	C₂²	1	1	yes	characteristic
33	C₁₉×#476	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#474	C₂²	1	1	yes	characteristic
36	C₁₉×#468	—	2	1	no	—
37	C₁₉×#465	—	2	1	no	—
38	C₁₉×#465	—	2	1	no	—
39	C₁₉×#461	C₂²	1	1	yes	characteristic
40	C₁₉×#461	C₂²	1	1	yes	characteristic
41	C₁₉×#460	C₂²	1	1	yes	characteristic
42	C₁₉×#459	C₂²	1	1	yes	characteristic
43	C₁₉×#450	—	2	1	no	—
44	C₁₉×#450	—	2	1	no	—
45	C₁₉×#449	—	2	1	no	—
46	C₁₉×#448	—	2	1	no	—
47	C₁₉×#446	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#442	—	2	1	no	—
49	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
50	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
51	C₁₉×#436	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₁₉×#103	—	2	1	no	—
55	C₂×C₁₉×#102	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#333	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	C₈²×C₁₉	C₂²	1	1	yes	characteristic, complemented
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂²×Q₈×C₁₉	—	2	1	no	—
69	C₂²×D₄×C₁₉	—	2	1	no	—
70	C₂²×D₄×C₁₉	—	2	1	no	—
71	C₁₉×AGL(1,ℤ/8)	—	4	4	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	D₄	1	1	yes	characteristic
78	C₂×D₈×C₁₉	—	2	1	no	—
79	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
80	C₂×M₁₆×C₁₉	—	2	1	no	—
81	C₂²×C₈×C₁₉	—	2	1	no	—
82	C₂²×C₈×C₁₉	—	2	1	no	—
83	C₁₉×C₄⋊Q₈	—	2	1	no	—
84	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	—	4	1	no	—
94	C₁₉×C₂²⋊Q₈	—	4	1	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	2	1	no	—
98	C₁₉×#120	—	4	1	no	—
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	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₁₉×#107	—	2	1	no	—
108	C₁₉×#107	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
115	C₁₉×C₄⋊C₈	—	2	1	no	—
116	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₉×#103	—	2	1	no	—
121	C₁₉×#103	—	2	1	no	—
122	C₁₉×#103	—	2	1	no	—
123	C₁₉×#103	—	2	1	no	—
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	—	4	1	no	—
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	—	4	1	no	—
135	C₁₉×#102	D₄	1	1	yes	characteristic
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×C₂²⋊C₈	—	2	1	no	—
141	C₁₉×#97	—	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	#41×C₁₉	—	4	2	no	—
147	#41×C₁₉	—	8	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	4	1	no	—
152	C₂×Q₈×C₁₉	—	4	2	no	—
153	C₂×Q₈×C₁₉	—	8	1	no	—
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	2	no	—
161	C₂×D₄×C₁₉	—	4	2	no	—
162	C₂×D₄×C₁₉	—	4	1	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	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
172	C₂²×C₄×C₁₉	—	4	1	no	—
173	C₂²×C₄×C₁₉	—	4	1	no	—
174	SD₁₆×C₁₉	—	4	1	no	—
175	SD₁₆×C₁₉	—	4	2	no	—
176	SD₁₆×C₁₉	—	4	2	no	—
177	SD₁₆×C₁₉	—	8	1	no	—
178	SD₁₆×C₁₉	—	8	1	no	—
179	SD₁₆×C₁₉	—	8	1	no	—
180	D₈×C₁₉	—	4	2	no	—
181	D₈×C₁₉	SD₁₆	1	4	yes	complemented
182	M₁₆×C₁₉	—	4	2	no	—
183	C₂×C₈×C₁₉	—	2	1	no	—
184	C₂×C₈×C₁₉	—	2	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	—	8	1	no	—
189	C₂×C₈×C₁₉	—	8	1	no	—
190	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
204	C₄⋊C₄×C₁₉	—	4	1	no	—
205	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₂²⋊C₄×C₁₉	—	2	1	no	—
210	C₂²⋊C₄×C₁₉	—	2	1	no	—
211	C₂²⋊C₄×C₁₉	—	2	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	C₂⁴	1	1	yes	characteristic
218	#19891	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	2	1	no	—
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	4	1	no	—
223	C₂³×C₁₉	—	8	2	no	—
224	C₂³×C₁₉	—	8	2	no	—
225	C₂³×C₁₉	—	16	1	no	—
226	Q₈×C₁₉	—	2	1	no	—
227	Q₈×C₁₉	—	2	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	Q₈×C₁₉	—	8	1	no	—
233	Q₈×C₁₉	—	8	2	no	—
234	D₄×C₁₉	—	2	1	no	—
235	D₄×C₁₉	—	2	1	no	—
236	D₄×C₁₉	—	2	1	no	—
237	D₄×C₁₉	—	2	1	no	—
238	D₄×C₁₉	—	4	1	no	—
239	D₄×C₁₉	—	4	1	no	—
240	D₄×C₁₉	—	4	1	no	—
241	D₄×C₁₉	—	4	1	no	—
242	D₄×C₁₉	—	8	1	no	—
243	D₄×C₁₉	—	8	2	no	—
244	D₄×C₁₉	—	8	2	no	—
245	D₄×C₁₉	—	8	2	no	—
246	D₄×C₁₉	C₂×SD₁₆	1	2	yes	—
247	D₄×C₁₉	C₂×SD₁₆	1	2	yes	—
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	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	8	2	no	—
263	C₂×C₄×C₁₉	—	8	2	no	—
264	C₂×C₄×C₁₉	—	16	1	no	—
265	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
268	C₈×C₁₉	—	2	1	no	—
269	C₈×C₁₉	—	2	1	no	—
270	C₈×C₁₉	—	2	1	no	—
271	C₈×C₁₉	—	4	1	no	—
272	C₈×C₁₉	—	4	1	no	—
273	C₈×C₁₉	—	4	1	no	—
274	C₈×C₁₉	—	4	1	no	—
275	C₈×C₁₉	—	4	1	no	—
276	C₈×C₁₉	C₂×SD₁₆	1	2	yes	—
277	#3384	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#3298	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#3295	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#3272	C₂×C₁₉	1	1	yes	characteristic
281	#1708	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1691	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1686	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1679	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1677	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1643	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1639	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1635	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1627	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1590	C₂×C₁₉	1	1	yes	characteristic, complemented
291	C₈×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
292	C₂²×C₁₉	—	2	2	no	—
293	C₂²×C₁₉	—	2	2	no	—
294	C₂²×C₁₉	—	4	1	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	—	4	1	no	—
301	C₂²×C₁₉	—	8	1	no	—
302	C₂²×C₁₉	—	8	1	no	—
303	C₂²×C₁₉	—	8	1	no	—
304	C₂²×C₁₉	—	16	4	no	—
305	C₂²×C₁₉	D₄²	1	1	yes	characteristic
306	C₄×C₁₉	—	2	1	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	4	1	no	—
309	C₄×C₁₉	—	4	1	no	—
310	C₄×C₁₉	—	4	1	no	—
311	C₄×C₁₉	—	4	1	no	—
312	C₄×C₁₉	—	8	1	no	—
313	C₄×C₁₉	—	8	1	no	—
314	C₄×C₁₉	—	8	1	no	—
315	C₄×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
316	C₄×C₁₉	#575	1	1	yes	characteristic
317	C₄×C₁₉	#576	1	1	yes	characteristic
318	C₄×C₁₉	#577	1	1	yes	characteristic
319	C₂×AGL(1,ℤ/8)	—	2	1	no	—
320	#554	C₂²×C₁₉	1	1	yes	characteristic
321	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
322	#547	C₂²×C₁₉	1	1	yes	characteristic
323	D₄²	C₂²×C₁₉	1	1	yes	characteristic
324	#501	—	2	1	no	—
325	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
326	#492	C₂²×C₁₉	1	1	yes	characteristic
327	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
328	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
329	#486	C₂²×C₁₉	1	1	yes	characteristic
330	#486	C₂²×C₁₉	1	1	yes	characteristic
331	#483	—	2	1	no	—
332	#481	—	2	1	no	—
333	#478	—	2	1	no	—
334	#476	—	2	1	no	—
335	#476	C₂²×C₁₉	1	1	yes	characteristic
336	#476	C₂²×C₁₉	1	1	yes	characteristic, complemented
337	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
338	#474	C₂²×C₁₉	1	1	yes	characteristic
339	#468	—	2	1	no	—
340	#465	—	2	1	no	—
341	#465	—	2	1	no	—
342	#461	C₂²×C₁₉	1	1	yes	characteristic
343	#461	C₂²×C₁₉	1	1	yes	characteristic
344	#460	C₂²×C₁₉	1	1	yes	characteristic
345	#459	C₂²×C₁₉	1	1	yes	characteristic
346	#450	—	2	1	no	—
347	#450	—	2	1	no	—
348	#449	—	2	1	no	—
349	#448	—	2	1	no	—
350	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
351	#442	—	2	1	no	—
352	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
353	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
354	#436	C₂²×C₁₉	1	1	yes	characteristic
355	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
356	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
357	C₂×#103	—	2	1	no	—
358	C₂×#102	—	2	1	no	—
359	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
360	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
361	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
362	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
363	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
364	#331	C₂²×C₁₉	1	1	yes	characteristic
365	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
366	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
367	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
368	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
369	C₈²	C₂²×C₁₉	1	1	yes	characteristic, complemented
370	C₂×C₁₉	—	4	2	no	—
371	C₂×C₁₉	—	4	2	no	—
372	C₂×C₁₉	—	8	1	no	—
373	C₂×C₁₉	—	16	1	no	—
374	C₂×C₁₉	#3273	1	1	yes	characteristic
375	C₂×C₁₉	D₄×SD₁₆	1	1	yes	characteristic
376	C₂×C₁₉	#3290	1	1	yes	characteristic
377	C₂×#41	—	2	1	no	—
378	C₂²×Q₈	—	2	1	no	—
379	C₂²×D₄	—	2	1	no	—
380	C₂²×D₄	—	2	1	no	—
381	AGL(1,ℤ/8)	—	4	4	no	—
382	C₂×SD₁₆	—	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	D₄×C₁₉	1	1	yes	characteristic
388	C₂×D₈	—	2	1	no	—
389	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
390	C₂×M₁₆	—	2	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	—	2	1	no	—
393	C₄⋊Q₈	—	2	1	no	—
394	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
395	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
396	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
397	#127	C₂³×C₁₉	1	1	yes	characteristic
398	#125	—	2	1	no	—
399	#123	—	4	1	no	—
400	C₂²⋊Q₈	—	2	1	no	—
401	C₂²⋊Q₈	—	2	1	no	—
402	C₂²⋊Q₈	—	2	1	no	—
403	C₂²⋊Q₈	—	4	1	no	—
404	C₂²⋊Q₈	—	4	1	no	—
405	#121	—	2	1	no	—
406	#121	—	2	1	no	—
407	#121	—	2	1	no	—
408	#120	—	4	1	no	—
409	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
413	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
414	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	#107	—	2	1	no	—
418	#107	D₄×C₁₉	1	1	yes	characteristic
419	#106	—	2	1	no	—
420	#106	—	2	1	no	—
421	#106	—	2	1	no	—
422	#106	—	2	1	no	—
423	#106	—	2	1	no	—
424	#106	D₄×C₁₉	1	1	yes	characteristic
425	C₄⋊C₈	—	2	1	no	—
426	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
427	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
428	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
429	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
430	#103	—	2	1	no	—
431	#103	—	2	1	no	—
432	#103	—	2	1	no	—
433	#103	—	2	1	no	—
434	#103	—	2	1	no	—
435	#103	—	4	1	no	—
436	#103	D₄×C₁₉	1	1	yes	characteristic
437	#102	—	2	1	no	—
438	#102	—	2	1	no	—
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	—	4	1	no	—
445	#102	D₄×C₁₉	1	1	yes	characteristic
446	#102	D₄×C₁₉	1	1	yes	characteristic
447	#102	D₄×C₁₉	1	1	yes	characteristic
448	C₂²⋊C₈	—	2	1	no	—
449	C₂²⋊C₈	—	2	1	no	—
450	C₂²⋊C₈	—	2	1	no	—
451	#97	—	2	1	no	—
452	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
453	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
454	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
455	C₁₉	#19891	1	1	yes	characteristic, direct product factor, Sylow
456	C₂⁴	—	4	1	no	—
457	#41	—	4	2	no	—
458	#41	—	8	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	4	1	no	—
463	C₂×Q₈	—	4	2	no	—
464	C₂×Q₈	—	8	1	no	—
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	—	4	1	no	—
470	C₂×D₄	—	4	1	no	—
471	C₂×D₄	—	4	2	no	—
472	C₂×D₄	—	4	2	no	—
473	C₂×D₄	—	4	1	no	—
474	C₂×D₄	—	8	1	no	—
475	C₂×D₄	—	8	1	no	—
476	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₂²×C₄	—	2	1	no	—
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	C₂²×C₄	—	4	1	no	—
485	SD₁₆	—	4	1	no	—
486	SD₁₆	—	4	2	no	—
487	SD₁₆	—	4	2	no	—
488	SD₁₆	—	8	1	no	—
489	SD₁₆	—	8	1	no	—
490	SD₁₆	—	8	1	no	—
491	D₈	—	4	2	no	—
492	D₈	SD₁₆×C₁₉	1	4	yes	complemented
493	M₁₆	—	4	2	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	8	1	no	—
500	C₂×C₈	—	8	1	no	—
501	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
502	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
503	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
513	C₄⋊C₄	—	4	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	—	2	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	C₄²	—	2	1	no	—
528	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	4	1	no	—
533	C₂³	—	8	2	no	—
534	C₂³	—	8	2	no	—
535	C₂³	—	16	1	no	—
536	Q₈	—	2	1	no	—
537	Q₈	—	2	1	no	—
538	Q₈	—	4	1	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	1	no	—
541	Q₈	—	4	1	no	—
542	Q₈	—	8	1	no	—
543	Q₈	—	8	2	no	—
544	D₄	—	2	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	2	1	no	—
547	D₄	—	2	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	1	no	—
552	D₄	—	8	1	no	—
553	D₄	—	8	2	no	—
554	D₄	—	8	2	no	—
555	D₄	—	8	2	no	—
556	D₄	C₂×SD₁₆×C₁₉	1	2	yes	—
557	D₄	C₂×SD₁₆×C₁₉	1	2	yes	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	8	2	no	—
573	C₂×C₄	—	8	2	no	—
574	C₂×C₄	—	16	1	no	—
575	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
577	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
578	C₈	—	2	1	no	—
579	C₈	—	2	1	no	—
580	C₈	—	2	1	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₈	—	4	1	no	—
584	C₈	—	4	1	no	—
585	C₈	—	4	1	no	—
586	C₈	C₂×SD₁₆×C₁₉	1	2	yes	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	8	1	no	—
597	C₂²	—	8	1	no	—
598	C₂²	—	8	1	no	—
599	C₂²	—	16	4	no	—
600	C₂²	D₄²×C₁₉	1	1	yes	characteristic
601	C₄	—	2	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	8	1	no	—
608	C₄	—	8	1	no	—
609	C₄	—	8	1	no	—
610	C₄	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
611	C₄	C₁₉×#575	1	1	yes	characteristic
612	C₄	C₁₉×#576	1	1	yes	characteristic
613	C₄	C₁₉×#577	1	1	yes	characteristic
614	C₂	—	4	2	no	—
615	C₂	—	4	2	no	—
616	C₂	—	8	1	no	—
617	C₂	—	16	1	no	—
618	C₂	C₁₉×#3273	1	1	yes	characteristic
619	C₂	D₄×SD₁₆×C₁₉	1	1	yes	characteristic
620	C₂	C₁₉×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3272	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×#3384	C₂	semidirect
2. C₁₉×#3298	C₂	semidirect
3. C₁₉×#3295	C₂	semidirect
5. C₁₉×#1708	C₂	semidirect
6. C₁₉×#1691	C₂	semidirect
7. C₁₉×#1686	C₂	semidirect
8. C₁₉×#1679	C₂	semidirect
9. C₁₉×#1677	C₂	semidirect
10. C₁₉×#1643	C₂	semidirect
11. C₁₉×#1639	C₂	semidirect
12. C₁₉×#1635	C₂	semidirect
13. C₁₉×#1627	C₂	semidirect
14. C₁₉×#1590	C₂	semidirect
15. C₈×D₈×C₁₉	C₂	semidirect
18. D₄×Q₈×C₁₉	C₂²	semidirect
22. C₁₉×#498	C₂²	semidirect
24. C₁₉×#487	C₂²	semidirect
25. C₁₉×#487	C₂²	semidirect
33. C₁₉×#476	C₂²	semidirect
34. C₁₉×#475	C₂²	semidirect
47. C₁₉×#446	C₂²	semidirect
53. C₈×D₄×C₁₉	C₂²	semidirect
56. C₁₉×#335	C₂²	semidirect
57. C₁₉×#334	C₂²	semidirect
58. C₁₉×#333	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. C₈²×C₁₉	C₂²	semidirect
181. D₈×C₁₉	SD₁₆	semidirect
218. #19891	C₁₉	direct (N × H)
277. #3384	C₂×C₁₉	semidirect
278. #3298	C₂×C₁₉	semidirect
279. #3295	C₂×C₁₉	semidirect
281. #1708	C₂×C₁₉	semidirect
282. #1691	C₂×C₁₉	semidirect
283. #1686	C₂×C₁₉	semidirect
284. #1679	C₂×C₁₉	semidirect
285. #1677	C₂×C₁₉	semidirect
286. #1643	C₂×C₁₉	semidirect
287. #1639	C₂×C₁₉	semidirect
288. #1635	C₂×C₁₉	semidirect
289. #1627	C₂×C₁₉	semidirect
290. #1590	C₂×C₁₉	semidirect
291. C₈×D₈	C₂×C₁₉	semidirect
321. D₄×Q₈	C₂²×C₁₉	semidirect
325. #498	C₂²×C₁₉	semidirect
327. #487	C₂²×C₁₉	semidirect
328. #487	C₂²×C₁₉	semidirect
336. #476	C₂²×C₁₉	semidirect
337. #475	C₂²×C₁₉	semidirect
350. #446	C₂²×C₁₉	semidirect
356. C₈×D₄	C₂²×C₁₉	semidirect
359. #335	C₂²×C₁₉	semidirect
360. #334	C₂²×C₁₉	semidirect
361. #333	C₂²×C₁₉	semidirect
362. #332	C₂²×C₁₉	semidirect
363. #332	C₂²×C₁₉	semidirect
365. Q₈⋊C₈	C₂²×C₁₉	semidirect
368. D₄⋊C₈	C₂²×C₁₉	semidirect
369. C₈²	C₂²×C₁₉	semidirect
455. C₁₉	#19891	direct (N × H)
492. D₈	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×#3384	2
C₁₉×#3298	2
C₁₉×#3295	2
C₁₉×#3272	2
C₁₉×#1708	2
C₁₉×#1691	2
C₁₉×#1686	2
C₁₉×#1679	2
C₁₉×#1677	2
C₁₉×#1643	2
C₁₉×#1639	2
C₁₉×#1635	2
C₁₉×#1627	2
C₁₉×#1590	2
C₈×D₈×C₁₉	2
#19891	19

Subgroups — C19×#19891 #18025850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19891 #18025850