Subgroups — C₁₉×#19859 #18025818

Order 4864.

656 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3354	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3334	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3303	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3283	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1723	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1693	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1671	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1669	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1647	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1647	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1646	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1635	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1581	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1580	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#135	—	2	1	no	—
17	C₁₉×#555	C₂²	1	1	yes	characteristic
18	C₁₉×#547	C₂²	1	1	yes	characteristic
19	C₁₉×#547	C₂²	1	1	yes	characteristic
20	C₁₉×#547	C₂²	1	1	yes	characteristic
21	C₁₉×#500	C₂²	1	1	yes	characteristic
22	C₁₉×#500	C₂²	1	1	yes	characteristic
23	C₁₉×#498	C₂²	1	1	yes	characteristic
24	C₁₉×#494	C₂²	1	1	yes	characteristic
25	C₁₉×#487	C₂²	1	1	yes	characteristic
26	C₁₉×#487	C₂²	1	1	yes	characteristic
27	C₁₉×#485	—	2	1	no	—
28	C₁₉×#482	—	2	1	no	—
29	C₁₉×#481	—	2	1	no	—
30	C₁₉×#480	—	2	1	no	—
31	C₁₉×#480	—	2	1	no	—
32	C₁₉×#476	C₂²	1	1	yes	characteristic
33	C₁₉×#476	C₂²	1	1	yes	characteristic
34	C₁₉×#474	C₂²	1	1	yes	characteristic
35	C₁₉×#474	C₂²	1	1	yes	characteristic
36	C₁₉×#474	C₂²	1	1	yes	characteristic
37	C₁₉×#469	—	2	1	no	—
38	C₁₉×#467	—	2	1	no	—
39	C₁₉×#466	—	2	1	no	—
40	C₁₉×#465	—	2	1	no	—
41	C₁₉×#461	C₂²	1	1	yes	characteristic
42	C₁₉×#461	C₂²	1	1	yes	characteristic
43	C₁₉×#461	C₂²	1	1	yes	characteristic
44	C₁₉×#452	—	2	1	no	—
45	C₁₉×#452	—	2	1	no	—
46	C₁₉×#449	—	2	1	no	—
47	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
48	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#436	C₂²	1	1	yes	characteristic
50	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
51	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
53	C₁₉×#428	—	2	1	no	—
54	C₂×C₁₉×#107	—	2	1	no	—
55	C₁₉×#416	—	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×#332	C₂²	1	1	yes	characteristic
60	C₁₉×#332	C₂²	1	1	yes	characteristic
61	C₁₉×#332	C₂²	1	1	yes	characteristic
62	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
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
66	C₁₉×#322	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂×#41×C₁₉	—	2	1	no	—
69	C₂×#41×C₁₉	—	2	1	no	—
70	C₁₉×#135	—	4	4	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×D₈×C₁₉	D₄	1	1	yes	characteristic
77	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
78	C₂×M₁₆×C₁₉	—	2	1	no	—
79	C₂²×C₈×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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₉×#124	—	4	1	no	—
87	C₁₉×#123	—	4	1	no	—
88	C₁₉×#123	—	4	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×#121	—	2	1	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	2	1	no	—
98	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×#117	—	2	1	no	—
103	C₁₉×#117	—	2	1	no	—
104	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	2	1	no	—
109	C₁₉×#107	—	2	1	no	—
110	C₁₉×#107	—	2	1	no	—
111	C₁₉×#107	—	2	1	no	—
112	C₁₉×#107	—	4	1	no	—
113	C₁₉×#107	D₄	1	1	yes	characteristic
114	C₁₉×#107	D₄	1	1	yes	characteristic
115	C₁₉×#106	—	2	1	no	—
116	C₁₉×#106	—	2	1	no	—
117	C₁₉×#106	—	2	1	no	—
118	C₁₉×#106	—	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	—	2	1	no	—
127	C₁₉×#103	—	2	1	no	—
128	C₁₉×#103	—	4	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	D₄	1	1	yes	characteristic
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×C₂²⋊C₈	—	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	—	4	2	no	—
148	#41×C₁₉	—	8	1	no	—
149	#41×C₁₉	—	8	1	no	—
150	#41×C₁₉	—	8	1	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	4	1	no	—
156	C₂×D₄×C₁₉	—	4	1	no	—
157	C₂×D₄×C₁₉	—	4	1	no	—
158	C₂×D₄×C₁₉	—	4	1	no	—
159	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	4	1	no	—
168	C₂²×C₄×C₁₉	—	4	1	no	—
169	C₂²×C₄×C₁₉	—	4	1	no	—
170	Q₁₆×C₁₉	—	4	2	no	—
171	Q₁₆×C₁₉	—	8	1	no	—
172	SD₁₆×C₁₉	—	4	2	no	—
173	SD₁₆×C₁₉	—	4	2	no	—
174	SD₁₆×C₁₉	—	8	1	no	—
175	D₈×C₁₉	—	2	2	no	—
176	D₈×C₁₉	—	2	2	no	—
177	M₁₆×C₁₉	—	4	2	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	—	4	2	no	—
184	C₂×C₈×C₁₉	—	4	2	no	—
185	C₂×C₈×C₁₉	—	8	1	no	—
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	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	4	1	no	—
199	C₄⋊C₄×C₁₉	—	4	1	no	—
200	C₄⋊C₄×C₁₉	—	4	1	no	—
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	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₂²⋊C₄×C₁₉	—	2	1	no	—
206	C₂²⋊C₄×C₁₉	—	2	1	no	—
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	C₄²×C₁₉	—	4	1	no	—
215	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
216	#19859	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	—	2	1	no	—
221	Q₈×C₁₉	—	4	1	no	—
222	Q₈×C₁₉	—	4	1	no	—
223	Q₈×C₁₉	—	4	1	no	—
224	Q₈×C₁₉	—	4	1	no	—
225	Q₈×C₁₉	—	4	1	no	—
226	Q₈×C₁₉	—	4	1	no	—
227	Q₈×C₁₉	—	8	1	no	—
228	D₄×C₁₉	—	2	1	no	—
229	D₄×C₁₉	—	2	1	no	—
230	D₄×C₁₉	—	2	1	no	—
231	D₄×C₁₉	—	2	1	no	—
232	D₄×C₁₉	—	2	1	no	—
233	D₄×C₁₉	—	2	1	no	—
234	D₄×C₁₉	—	2	1	no	—
235	D₄×C₁₉	—	8	2	no	—
236	D₄×C₁₉	—	8	2	no	—
237	D₄×C₁₉	—	8	2	no	—
238	D₄×C₁₉	—	16	1	no	—
239	D₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
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	—	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	—	8	2	no	—
257	C₂×C₄×C₁₉	—	8	2	no	—
258	C₂×C₄×C₁₉	—	8	2	no	—
259	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
262	C₈×C₁₉	—	2	1	no	—
263	C₈×C₁₉	—	2	1	no	—
264	C₈×C₁₉	—	2	1	no	—
265	C₈×C₁₉	—	4	1	no	—
266	C₈×C₁₉	—	4	1	no	—
267	C₈×C₁₉	—	4	1	no	—
268	C₈×C₁₉	—	4	1	no	—
269	C₈×C₁₉	—	4	1	no	—
270	C₈×C₁₉	#135	1	2	yes	complemented
271	#3354	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#3334	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#3303	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#3283	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1723	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1693	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1683	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1671	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1669	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1647	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1647	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1646	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1635	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1581	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1580	C₂×C₁₉	1	1	yes	characteristic, complemented
286	C₂²×C₁₉	—	2	2	no	—
287	C₂²×C₁₉	—	4	1	no	—
288	C₂²×C₁₉	—	4	1	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	—	4	1	no	—
298	C₂²×C₁₉	D₄²	1	1	yes	characteristic
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	4	1	no	—
301	C₄×C₁₉	—	4	1	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	8	1	no	—
305	C₄×C₁₉	—	8	1	no	—
306	C₄×C₁₉	—	8	1	no	—
307	C₄×C₁₉	—	8	1	no	—
308	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
309	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
310	C₄×C₁₉	#576	1	1	yes	characteristic
311	C₄×C₁₉	#578	1	1	yes	characteristic
312	C₂×#135	—	2	1	no	—
313	#555	C₂²×C₁₉	1	1	yes	characteristic
314	#547	C₂²×C₁₉	1	1	yes	characteristic
315	#547	C₂²×C₁₉	1	1	yes	characteristic
316	#547	C₂²×C₁₉	1	1	yes	characteristic
317	#500	C₂²×C₁₉	1	1	yes	characteristic
318	#500	C₂²×C₁₉	1	1	yes	characteristic
319	#498	C₂²×C₁₉	1	1	yes	characteristic
320	#494	C₂²×C₁₉	1	1	yes	characteristic
321	#487	C₂²×C₁₉	1	1	yes	characteristic
322	#487	C₂²×C₁₉	1	1	yes	characteristic
323	#485	—	2	1	no	—
324	#482	—	2	1	no	—
325	#481	—	2	1	no	—
326	#480	—	2	1	no	—
327	#480	—	2	1	no	—
328	#476	C₂²×C₁₉	1	1	yes	characteristic
329	#476	C₂²×C₁₉	1	1	yes	characteristic
330	#474	C₂²×C₁₉	1	1	yes	characteristic
331	#474	C₂²×C₁₉	1	1	yes	characteristic
332	#474	C₂²×C₁₉	1	1	yes	characteristic
333	#469	—	2	1	no	—
334	#467	—	2	1	no	—
335	#466	—	2	1	no	—
336	#465	—	2	1	no	—
337	#461	C₂²×C₁₉	1	1	yes	characteristic
338	#461	C₂²×C₁₉	1	1	yes	characteristic
339	#461	C₂²×C₁₉	1	1	yes	characteristic
340	#452	—	2	1	no	—
341	#452	—	2	1	no	—
342	#449	—	2	1	no	—
343	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
344	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
345	#436	C₂²×C₁₉	1	1	yes	characteristic
346	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
347	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
348	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
349	#428	—	2	1	no	—
350	C₂×#107	—	2	1	no	—
351	#416	—	2	1	no	—
352	#335	C₂²×C₁₉	1	1	yes	characteristic
353	#334	C₂²×C₁₉	1	1	yes	characteristic
354	#333	C₂²×C₁₉	1	1	yes	characteristic
355	#332	C₂²×C₁₉	1	1	yes	characteristic
356	#332	C₂²×C₁₉	1	1	yes	characteristic
357	#332	C₂²×C₁₉	1	1	yes	characteristic
358	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
359	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
360	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
361	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
362	#322	C₂²×C₁₉	1	1	yes	characteristic
363	C₂×C₁₉	—	4	2	no	—
364	C₂×C₁₉	—	8	1	no	—
365	C₂×C₁₉	—	8	1	no	—
366	C₂×C₁₉	—	8	1	no	—
367	C₂×C₁₉	#3264	1	1	yes	characteristic
368	C₂×C₁₉	#3283	1	1	yes	characteristic
369	C₂×C₁₉	#3289	1	1	yes	characteristic
370	C₂×#41	—	2	1	no	—
371	C₂×#41	—	2	1	no	—
372	C₂×#41	—	2	1	no	—
373	#135	—	4	4	no	—
374	C₂×Q₁₆	—	2	1	no	—
375	C₂×Q₁₆	—	2	1	no	—
376	C₂×SD₁₆	—	2	1	no	—
377	C₂×SD₁₆	—	2	1	no	—
378	C₂×SD₁₆	—	2	1	no	—
379	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
380	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
381	C₂×M₁₆	—	2	1	no	—
382	C₂²×C₈	—	2	1	no	—
383	C₂²×C₈	—	2	1	no	—
384	C₂²×C₈	—	2	1	no	—
385	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
386	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
387	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
388	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
389	#124	—	4	1	no	—
390	#123	—	4	1	no	—
391	#123	—	4	1	no	—
392	#123	—	4	1	no	—
393	C₂²⋊Q₈	—	2	1	no	—
394	C₂²⋊Q₈	—	2	1	no	—
395	C₂²⋊Q₈	—	2	1	no	—
396	#121	—	2	1	no	—
397	#121	—	2	1	no	—
398	#121	—	2	1	no	—
399	#121	—	2	1	no	—
400	#121	—	2	1	no	—
401	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
402	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
403	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
404	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
405	#117	—	2	1	no	—
406	#117	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	#107	—	2	1	no	—
411	#107	—	2	1	no	—
412	#107	—	2	1	no	—
413	#107	—	2	1	no	—
414	#107	—	2	1	no	—
415	#107	—	4	1	no	—
416	#107	D₄×C₁₉	1	1	yes	characteristic
417	#107	D₄×C₁₉	1	1	yes	characteristic
418	#106	—	2	1	no	—
419	#106	—	2	1	no	—
420	#106	—	2	1	no	—
421	#106	—	2	1	no	—
422	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
423	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
424	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
425	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
426	#103	—	2	1	no	—
427	#103	—	2	1	no	—
428	#103	—	2	1	no	—
429	#103	—	2	1	no	—
430	#103	—	2	1	no	—
431	#103	—	4	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	D₄×C₁₉	1	1	yes	characteristic
438	#102	D₄×C₁₉	1	1	yes	characteristic
439	#102	D₄×C₁₉	1	1	yes	characteristic
440	#102	D₄×C₁₉	1	1	yes	characteristic
441	C₂²⋊C₈	—	2	1	no	—
442	C₂²⋊C₈	—	2	1	no	—
443	C₂²⋊C₈	—	2	1	no	—
444	C₂²⋊C₈	—	2	1	no	—
445	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
446	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
447	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
448	C₁₉	#19859	1	1	yes	characteristic, direct product factor, Sylow
449	#41	—	4	2	no	—
450	#41	—	4	2	no	—
451	#41	—	4	2	no	—
452	#41	—	8	1	no	—
453	#41	—	8	1	no	—
454	#41	—	8	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×D₄	—	4	1	no	—
460	C₂×D₄	—	4	1	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	4	1	no	—
474	Q₁₆	—	4	2	no	—
475	Q₁₆	—	8	1	no	—
476	SD₁₆	—	4	2	no	—
477	SD₁₆	—	4	2	no	—
478	SD₁₆	—	8	1	no	—
479	D₈	—	2	2	no	—
480	D₈	—	2	2	no	—
481	M₁₆	—	4	2	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	4	2	no	—
488	C₂×C₈	—	4	2	no	—
489	C₂×C₈	—	8	1	no	—
490	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
492	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
503	C₄⋊C₄	—	4	1	no	—
504	C₄⋊C₄	—	4	1	no	—
505	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	C₂²⋊C₄	—	2	1	no	—
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	C₄²	—	4	1	no	—
519	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	—	2	1	no	—
524	Q₈	—	4	1	no	—
525	Q₈	—	4	1	no	—
526	Q₈	—	4	1	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	1	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	8	1	no	—
531	D₄	—	2	1	no	—
532	D₄	—	2	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	2	1	no	—
535	D₄	—	2	1	no	—
536	D₄	—	2	1	no	—
537	D₄	—	2	1	no	—
538	D₄	—	8	2	no	—
539	D₄	—	8	2	no	—
540	D₄	—	8	2	no	—
541	D₄	—	16	1	no	—
542	D₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	8	2	no	—
560	C₂×C₄	—	8	2	no	—
561	C₂×C₄	—	8	2	no	—
562	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
563	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
564	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
565	C₈	—	2	1	no	—
566	C₈	—	2	1	no	—
567	C₈	—	2	1	no	—
568	C₈	—	4	1	no	—
569	C₈	—	4	1	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₈	C₁₉×#135	1	2	yes	complemented
574	C₂²	—	2	2	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	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	D₄²×C₁₉	1	1	yes	characteristic
587	C₄	—	2	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	8	1	no	—
593	C₄	—	8	1	no	—
594	C₄	—	8	1	no	—
595	C₄	—	8	1	no	—
596	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
597	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
598	C₄	C₁₉×#576	1	1	yes	characteristic
599	C₄	C₁₉×#578	1	1	yes	characteristic
600	C₂	—	4	2	no	—
601	C₂	—	8	1	no	—
602	C₂	—	8	1	no	—
603	C₂	—	8	1	no	—
604	C₂	C₁₉×#3264	1	1	yes	characteristic
605	C₂	C₁₉×#3283	1	1	yes	characteristic
606	C₂	C₁₉×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
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×#3354	C₂	semidirect
2. C₁₉×#3334	C₂	semidirect
3. C₁₉×#3303	C₂	semidirect
4. C₁₉×#3283	C₂	semidirect
5. C₁₉×#1723	C₂	semidirect
6. C₁₉×#1693	C₂	semidirect
7. C₁₉×#1683	C₂	semidirect
8. C₁₉×#1671	C₂	semidirect
9. C₁₉×#1669	C₂	semidirect
10. C₁₉×#1647	C₂	semidirect
11. C₁₉×#1647	C₂	semidirect
12. C₁₉×#1646	C₂	semidirect
13. C₁₉×#1635	C₂	semidirect
14. C₁₉×#1581	C₂	semidirect
15. C₁₉×#1580	C₂	semidirect
216. #19859	C₁₉	direct (N × H)
270. C₈×C₁₉	#135	semidirect
271. #3354	C₂×C₁₉	semidirect
272. #3334	C₂×C₁₉	semidirect
273. #3303	C₂×C₁₉	semidirect
274. #3283	C₂×C₁₉	semidirect
275. #1723	C₂×C₁₉	semidirect
276. #1693	C₂×C₁₉	semidirect
277. #1683	C₂×C₁₉	semidirect
278. #1671	C₂×C₁₉	semidirect
279. #1669	C₂×C₁₉	semidirect
280. #1647	C₂×C₁₉	semidirect
281. #1647	C₂×C₁₉	semidirect
282. #1646	C₂×C₁₉	semidirect
283. #1635	C₂×C₁₉	semidirect
284. #1581	C₂×C₁₉	semidirect
285. #1580	C₂×C₁₉	semidirect
448. C₁₉	#19859	direct (N × H)
573. C₈	C₁₉×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3354	2
C₁₉×#3334	2
C₁₉×#3303	2
C₁₉×#3283	2
C₁₉×#1723	2
C₁₉×#1693	2
C₁₉×#1683	2
C₁₉×#1671	2
C₁₉×#1669	2
C₁₉×#1647	2
C₁₉×#1646	2
C₁₉×#1635	2
C₁₉×#1581	2
C₁₉×#1580	2
#19859	19

Subgroups — C19×#19859 #18025818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19859 #18025818