Subgroups — C₁₉×#19873 #18025832

Order 4864.

572 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3400	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3395	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3365	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1722	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1690	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1682	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1674	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1666	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1648	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1648	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1640	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1626	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1579	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#559	C₂²	1	1	yes	characteristic
17	C₁₉×#557	C₂²	1	1	yes	characteristic
18	C₁₉×#557	C₂²	1	1	yes	characteristic
19	C₁₉×#557	C₂²	1	1	yes	characteristic
20	C₁₉×#500	C₂²	1	1	yes	characteristic
21	C₁₉×#500	C₂²	1	1	yes	characteristic
22	C₁₉×#499	—	2	1	no	—
23	C₁₉×#497	—	2	1	no	—
24	C₁₉×#494	—	2	1	no	—
25	C₁₉×#494	C₂²	1	1	yes	characteristic
26	C₁₉×#492	C₂²	1	1	yes	characteristic
27	C₁₉×#488	—	2	1	no	—
28	C₁₉×#486	C₂²	1	1	yes	characteristic
29	C₁₉×#486	C₂²	1	1	yes	characteristic
30	C₁₉×#479	—	2	1	no	—
31	C₁₉×#479	—	2	1	no	—
32	C₁₉×#478	—	2	1	no	—
33	C₁₉×#475	C₂²	1	1	yes	characteristic
34	C₁₉×#475	C₂²	1	1	yes	characteristic
35	C₁₉×#475	C₂²	1	1	yes	characteristic
36	C₁₉×#464	—	2	1	no	—
37	C₁₉×#464	—	2	1	no	—
38	C₁₉×#462	—	2	1	no	—
39	C₁₉×#462	—	2	1	no	—
40	C₁₉×#462	C₂²	1	1	yes	characteristic
41	C₁₉×#462	C₂²	1	1	yes	characteristic
42	C₁₉×#462	C₂²	1	1	yes	characteristic
43	C₁₉×#461	—	2	1	no	—
44	C₁₉×#460	C₂²	1	1	yes	characteristic
45	C₁₉×#460	C₂²	1	1	yes	characteristic
46	C₁₉×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
50	C₁₉×#440	—	2	1	no	—
51	C₄×Q₁₆×C₁₉	—	2	1	no	—
52	C₄×Q₁₆×C₁₉	—	2	1	no	—
53	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
54	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
55	C₄×SD₁₆×C₁₉	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#332	C₂²	1	1	yes	characteristic
59	C₁₉×#332	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×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₉×#322	C₂²	1	1	yes	characteristic
67	C₂×Q₁₆×C₁₉	—	2	1	no	—
68	C₂×Q₁₆×C₁₉	—	2	1	no	—
69	C₂×Q₁₆×C₁₉	—	2	1	no	—
70	C₂×Q₁₆×C₁₉	—	2	1	no	—
71	C₂×Q₁₆×C₁₉	—	2	1	no	—
72	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
73	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
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	C₁₉×C₄⋊Q₈	—	2	1	no	—
79	C₁₉×C₄⋊Q₈	—	2	1	no	—
80	C₁₉×C₄⋊Q₈	—	2	1	no	—
81	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₉×#127	C₂³	1	1	yes	characteristic
85	C₁₉×#125	—	2	1	no	—
86	C₁₉×#125	—	2	1	no	—
87	C₁₉×#125	—	2	1	no	—
88	C₁₉×#125	—	4	1	no	—
89	C₁₉×#125	—	4	1	no	—
90	C₁₉×#125	—	4	1	no	—
91	C₁₉×#124	—	2	1	no	—
92	C₁₉×#124	—	2	1	no	—
93	C₁₉×#123	—	4	1	no	—
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	—	2	1	no	—
97	C₄×Q₈×C₁₉	—	2	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×Q₈×C₁₉	C₂³	1	1	yes	characteristic
102	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
103	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
104	C₄×D₄×C₁₉	—	2	1	no	—
105	C₄×D₄×C₁₉	—	2	1	no	—
106	C₁₉×#107	—	2	1	no	—
107	C₁₉×#107	—	2	1	no	—
108	C₁₉×#107	—	4	1	no	—
109	C₁₉×#107	D₄	1	1	yes	characteristic
110	C₁₉×#107	D₄	1	1	yes	characteristic
111	C₁₉×#106	—	2	1	no	—
112	C₁₉×#106	—	2	1	no	—
113	C₁₉×#106	—	2	1	no	—
114	C₁₉×C₄⋊C₈	—	2	1	no	—
115	C₁₉×C₄⋊C₈	—	2	1	no	—
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	—	2	1	no	—
126	C₁₉×#103	—	2	1	no	—
127	C₁₉×#103	—	2	1	no	—
128	C₁₉×#103	D₄	1	1	yes	characteristic
129	C₁₉×#103	D₄	1	1	yes	characteristic
130	C₁₉×#103	D₄	1	1	yes	characteristic
131	C₁₉×#103	D₄	1	1	yes	characteristic
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	—	4	1	no	—
137	C₁₉×#97	—	2	1	no	—
138	C₄×C₈×C₁₉	—	2	1	no	—
139	C₄×C₈×C₁₉	—	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	C₂×Q₈×C₁₉	—	2	1	no	—
145	C₂×Q₈×C₁₉	—	2	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄×C₁₉	—	4	1	no	—
155	Q₁₆×C₁₉	—	2	2	no	—
156	Q₁₆×C₁₉	—	2	2	no	—
157	Q₁₆×C₁₉	—	4	2	no	—
158	Q₁₆×C₁₉	—	8	1	no	—
159	Q₁₆×C₁₉	—	8	1	no	—
160	Q₁₆×C₁₉	—	8	1	no	—
161	Q₁₆×C₁₉	—	8	1	no	—
162	SD₁₆×C₁₉	—	4	2	no	—
163	SD₁₆×C₁₉	—	4	2	no	—
164	SD₁₆×C₁₉	—	8	1	no	—
165	SD₁₆×C₁₉	—	8	1	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	4	1	no	—
186	C₄⋊C₄×C₁₉	—	4	1	no	—
187	C₄⋊C₄×C₁₉	—	4	1	no	—
188	C₄⋊C₄×C₁₉	—	4	1	no	—
189	C₄⋊C₄×C₁₉	—	4	1	no	—
190	C₄⋊C₄×C₁₉	—	4	1	no	—
191	C₄⋊C₄×C₁₉	—	4	1	no	—
192	C₄⋊C₄×C₁₉	—	4	1	no	—
193	C₄⋊C₄×C₁₉	—	4	1	no	—
194	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₂²⋊C₄×C₁₉	—	4	1	no	—
199	C₂²⋊C₄×C₁₉	—	4	1	no	—
200	C₂²⋊C₄×C₁₉	—	4	1	no	—
201	C₄²×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	—	2	1	no	—
203	C₄²×C₁₉	—	2	1	no	—
204	C₄²×C₁₉	—	2	1	no	—
205	C₄²×C₁₉	—	4	1	no	—
206	C₄²×C₁₉	—	4	1	no	—
207	C₄²×C₁₉	—	4	1	no	—
208	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
209	#19873	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂³×C₁₉	—	4	1	no	—
211	Q₈×C₁₉	—	2	1	no	—
212	Q₈×C₁₉	—	2	1	no	—
213	Q₈×C₁₉	—	2	1	no	—
214	Q₈×C₁₉	—	2	1	no	—
215	Q₈×C₁₉	—	2	1	no	—
216	Q₈×C₁₉	—	2	1	no	—
217	Q₈×C₁₉	—	2	1	no	—
218	Q₈×C₁₉	—	4	1	no	—
219	Q₈×C₁₉	—	4	1	no	—
220	Q₈×C₁₉	—	4	1	no	—
221	Q₈×C₁₉	—	4	1	no	—
222	Q₈×C₁₉	—	4	1	no	—
223	Q₈×C₁₉	—	4	1	no	—
224	Q₈×C₁₉	#137	1	2	yes	—
225	D₄×C₁₉	—	4	1	no	—
226	D₄×C₁₉	—	4	1	no	—
227	D₄×C₁₉	—	4	1	no	—
228	D₄×C₁₉	—	4	1	no	—
229	D₄×C₁₉	—	8	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	16	1	no	—
242	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
245	C₈×C₁₉	—	2	1	no	—
246	C₈×C₁₉	—	2	1	no	—
247	C₈×C₁₉	—	2	1	no	—
248	C₈×C₁₉	—	4	1	no	—
249	C₈×C₁₉	—	4	1	no	—
250	C₈×C₁₉	—	4	1	no	—
251	C₈×C₁₉	—	4	1	no	—
252	C₈×C₁₉	—	4	1	no	—
253	C₈×C₁₉	#135	1	2	yes	—
254	#3400	C₂×C₁₉	1	1	yes	characteristic
255	#3395	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#3383	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#3365	C₂×C₁₉	1	1	yes	characteristic
258	#1722	C₂×C₁₉	1	1	yes	characteristic
259	#1690	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1682	C₂×C₁₉	1	1	yes	characteristic
261	#1674	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1666	C₂×C₁₉	1	1	yes	characteristic
263	#1648	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1648	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1640	C₂×C₁₉	1	1	yes	characteristic
266	#1626	C₂×C₁₉	1	1	yes	characteristic
267	#1584	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#1579	C₂×C₁₉	1	1	yes	characteristic, complemented
269	C₂²×C₁₉	—	8	1	no	—
270	C₂²×C₁₉	—	8	1	no	—
271	C₂²×C₁₉	—	8	1	no	—
272	C₂²×C₁₉	D₄²	1	1	yes	characteristic
273	C₄×C₁₉	—	2	2	no	—
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	4	1	no	—
276	C₄×C₁₉	—	4	1	no	—
277	C₄×C₁₉	—	4	1	no	—
278	C₄×C₁₉	—	4	1	no	—
279	C₄×C₁₉	—	4	1	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	4	1	no	—
282	C₄×C₁₉	—	8	1	no	—
283	C₄×C₁₉	—	8	1	no	—
284	C₄×C₁₉	—	8	1	no	—
285	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
286	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
287	C₄×C₁₉	#576	1	1	yes	characteristic
288	C₄×C₁₉	#578	1	1	yes	characteristic
289	#559	C₂²×C₁₉	1	1	yes	characteristic
290	#557	C₂²×C₁₉	1	1	yes	characteristic
291	#557	C₂²×C₁₉	1	1	yes	characteristic
292	#557	C₂²×C₁₉	1	1	yes	characteristic
293	#500	C₂²×C₁₉	1	1	yes	characteristic
294	#500	C₂²×C₁₉	1	1	yes	characteristic
295	#499	—	2	1	no	—
296	#497	—	2	1	no	—
297	#494	—	2	1	no	—
298	#494	C₂²×C₁₉	1	1	yes	characteristic
299	#492	C₂²×C₁₉	1	1	yes	characteristic
300	#488	—	2	1	no	—
301	#486	C₂²×C₁₉	1	1	yes	characteristic
302	#486	C₂²×C₁₉	1	1	yes	characteristic
303	#479	—	2	1	no	—
304	#479	—	2	1	no	—
305	#478	—	2	1	no	—
306	#475	C₂²×C₁₉	1	1	yes	characteristic
307	#475	C₂²×C₁₉	1	1	yes	characteristic
308	#475	C₂²×C₁₉	1	1	yes	characteristic
309	#464	—	2	1	no	—
310	#464	—	2	1	no	—
311	#462	—	2	1	no	—
312	#462	—	2	1	no	—
313	#462	C₂²×C₁₉	1	1	yes	characteristic
314	#462	C₂²×C₁₉	1	1	yes	characteristic
315	#462	C₂²×C₁₉	1	1	yes	characteristic
316	#461	—	2	1	no	—
317	#460	C₂²×C₁₉	1	1	yes	characteristic
318	#460	C₂²×C₁₉	1	1	yes	characteristic
319	#446	C₂²×C₁₉	1	1	yes	characteristic
320	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
321	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
322	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
323	#440	—	2	1	no	—
324	C₄×Q₁₆	—	2	1	no	—
325	C₄×Q₁₆	—	2	1	no	—
326	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
327	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
328	C₄×SD₁₆	—	2	1	no	—
329	#335	C₂²×C₁₉	1	1	yes	characteristic
330	#334	C₂²×C₁₉	1	1	yes	characteristic
331	#332	C₂²×C₁₉	1	1	yes	characteristic
332	#332	C₂²×C₁₉	1	1	yes	characteristic
333	#332	C₂²×C₁₉	1	1	yes	characteristic
334	#331	C₂²×C₁₉	1	1	yes	characteristic
335	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
336	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
337	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
338	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
339	#322	C₂²×C₁₉	1	1	yes	characteristic
340	C₂×C₁₉	—	16	1	no	—
341	C₂×C₁₉	#3270	1	1	yes	characteristic
342	C₂×C₁₉	#3287	1	1	yes	characteristic
343	C₂×C₁₉	#3289	1	1	yes	characteristic
344	C₂×Q₁₆	—	2	1	no	—
345	C₂×Q₁₆	—	2	1	no	—
346	C₂×Q₁₆	—	2	1	no	—
347	C₂×Q₁₆	—	2	1	no	—
348	C₂×Q₁₆	—	2	1	no	—
349	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
350	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
351	C₂×SD₁₆	—	2	1	no	—
352	C₂×SD₁₆	—	2	1	no	—
353	C₂×SD₁₆	—	2	1	no	—
354	C₂×SD₁₆	—	2	1	no	—
355	C₄⋊Q₈	—	2	1	no	—
356	C₄⋊Q₈	—	2	1	no	—
357	C₄⋊Q₈	—	2	1	no	—
358	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
359	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
360	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
361	#127	C₂³×C₁₉	1	1	yes	characteristic
362	#125	—	2	1	no	—
363	#125	—	2	1	no	—
364	#125	—	2	1	no	—
365	#125	—	4	1	no	—
366	#125	—	4	1	no	—
367	#125	—	4	1	no	—
368	#124	—	2	1	no	—
369	#124	—	2	1	no	—
370	#123	—	4	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	—	2	1	no	—
375	C₄×Q₈	—	2	1	no	—
376	C₄×Q₈	—	2	1	no	—
377	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
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	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	#107	—	2	1	no	—
384	#107	—	2	1	no	—
385	#107	—	4	1	no	—
386	#107	D₄×C₁₉	1	1	yes	characteristic
387	#107	D₄×C₁₉	1	1	yes	characteristic
388	#106	—	2	1	no	—
389	#106	—	2	1	no	—
390	#106	—	2	1	no	—
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
396	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
397	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
398	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#103	—	2	1	no	—
405	#103	D₄×C₁₉	1	1	yes	characteristic
406	#103	D₄×C₁₉	1	1	yes	characteristic
407	#103	D₄×C₁₉	1	1	yes	characteristic
408	#103	D₄×C₁₉	1	1	yes	characteristic
409	#102	—	2	1	no	—
410	#102	—	2	1	no	—
411	#102	—	2	1	no	—
412	#102	—	2	1	no	—
413	#102	—	4	1	no	—
414	#97	—	2	1	no	—
415	C₄×C₈	—	2	1	no	—
416	C₄×C₈	—	2	1	no	—
417	C₄×C₈	—	2	1	no	—
418	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
419	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
420	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
421	C₁₉	#19873	1	1	yes	characteristic, direct product factor, Sylow
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂²×C₄	—	4	1	no	—
433	Q₁₆	—	2	2	no	—
434	Q₁₆	—	2	2	no	—
435	Q₁₆	—	4	2	no	—
436	Q₁₆	—	8	1	no	—
437	Q₁₆	—	8	1	no	—
438	Q₁₆	—	8	1	no	—
439	Q₁₆	—	8	1	no	—
440	SD₁₆	—	4	2	no	—
441	SD₁₆	—	4	2	no	—
442	SD₁₆	—	8	1	no	—
443	SD₁₆	—	8	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
452	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
473	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂²⋊C₄	—	4	1	no	—
477	C₂²⋊C₄	—	4	1	no	—
478	C₂²⋊C₄	—	4	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	4	1	no	—
484	C₄²	—	4	1	no	—
485	C₄²	—	4	1	no	—
486	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
487	C₂³	—	4	1	no	—
488	Q₈	—	2	1	no	—
489	Q₈	—	2	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	4	1	no	—
496	Q₈	—	4	1	no	—
497	Q₈	—	4	1	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	C₁₉×#137	1	2	yes	—
502	D₄	—	4	1	no	—
503	D₄	—	4	1	no	—
504	D₄	—	4	1	no	—
505	D₄	—	4	1	no	—
506	D₄	—	8	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	16	1	no	—
519	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
521	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	4	1	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	C₁₉×#135	1	2	yes	—
531	C₂²	—	8	1	no	—
532	C₂²	—	8	1	no	—
533	C₂²	—	8	1	no	—
534	C₂²	D₄²×C₁₉	1	1	yes	characteristic
535	C₄	—	2	2	no	—
536	C₄	—	2	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	1	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	8	1	no	—
545	C₄	—	8	1	no	—
546	C₄	—	8	1	no	—
547	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
548	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
549	C₄	C₁₉×#576	1	1	yes	characteristic
550	C₄	C₁₉×#578	1	1	yes	characteristic
551	C₂	—	16	1	no	—
552	C₂	C₁₉×#3270	1	1	yes	characteristic
553	C₂	C₁₉×#3287	1	1	yes	characteristic
554	C₂	C₁₉×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#127	C₂³
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
2. C₁₉×#3395	C₂	semidirect
3. C₁₉×#3383	C₂	semidirect
6. C₁₉×#1690	C₂	semidirect
8. C₁₉×#1674	C₂	semidirect
10. C₁₉×#1648	C₂	semidirect
11. C₁₉×#1648	C₂	semidirect
14. C₁₉×#1584	C₂	semidirect
15. C₁₉×#1579	C₂	semidirect
209. #19873	C₁₉	direct (N × H)
255. #3395	C₂×C₁₉	semidirect
256. #3383	C₂×C₁₉	semidirect
259. #1690	C₂×C₁₉	semidirect
261. #1674	C₂×C₁₉	semidirect
263. #1648	C₂×C₁₉	semidirect
264. #1648	C₂×C₁₉	semidirect
267. #1584	C₂×C₁₉	semidirect
268. #1579	C₂×C₁₉	semidirect
421. C₁₉	#19873	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×#3400	2
C₁₉×#3395	2
C₁₉×#3383	2
C₁₉×#3365	2
C₁₉×#1722	2
C₁₉×#1690	2
C₁₉×#1682	2
C₁₉×#1674	2
C₁₉×#1666	2
C₁₉×#1648	2
C₁₉×#1640	2
C₁₉×#1626	2
C₁₉×#1584	2
C₁₉×#1579	2
#19873	19

Subgroups — C19×#19873 #18025832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19873 #18025832