Subgroups — C₁₉×#19872 #18025831

Order 4864.

580 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3398	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3394	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3365	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3342	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1722	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1686	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1681	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1674	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1670	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1650	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, complemented
13	C₁₉×#1628	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×SD₁₆⋊C₈	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×#556	C₂²	1	1	yes	characteristic
19	C₁₉×#556	C₂²	1	1	yes	characteristic
20	C₁₉×#500	C₂²	1	1	yes	characteristic
21	C₁₉×#500	C₂²	1	1	yes	characteristic
22	C₁₉×#497	—	2	1	no	—
23	C₁₉×#495	—	2	1	no	—
24	C₁₉×#494	C₂²	1	1	yes	characteristic
25	C₁₉×#492	C₂²	1	1	yes	characteristic
26	C₁₉×#488	—	2	1	no	—
27	C₁₉×#486	C₂²	1	1	yes	characteristic
28	C₁₉×#486	C₂²	1	1	yes	characteristic
29	C₁₉×#485	—	2	1	no	—
30	C₁₉×#485	—	2	1	no	—
31	C₁₉×#478	—	2	1	no	—
32	C₁₉×#475	C₂²	1	1	yes	characteristic
33	C₁₉×#475	C₂²	1	1	yes	characteristic
34	C₁₉×#475	C₂²	1	1	yes	characteristic
35	C₁₉×#467	—	2	1	no	—
36	C₁₉×#464	—	2	1	no	—
37	C₁₉×#464	—	2	1	no	—
38	C₁₉×#464	—	2	1	no	—
39	C₁₉×#463	—	2	1	no	—
40	C₁₉×#462	—	2	1	no	—
41	C₁₉×#462	C₂²	1	1	yes	characteristic
42	C₁₉×#462	C₂²	1	1	yes	characteristic
43	C₁₉×#461	C₂²	1	1	yes	characteristic
44	C₁₉×#460	C₂²	1	1	yes	characteristic
45	C₁₉×#459	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	C₁₉×#441	—	2	1	no	—
50	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
51	C₄×SD₁₆×C₁₉	—	2	1	no	—
52	C₄×SD₁₆×C₁₉	—	2	1	no	—
53	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
55	C₁₉×#427	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#335	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×D₄⋊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	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
77	C₂×D₈×C₁₉	—	2	1	no	—
78	C₂²×C₈×C₁₉	—	2	1	no	—
79	C₁₉×C₄⋊Q₈	—	2	1	no	—
80	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₉×#127	C₂³	1	1	yes	characteristic
84	C₁₉×#126	—	4	1	no	—
85	C₁₉×#126	—	4	1	no	—
86	C₁₉×#125	—	2	1	no	—
87	C₁₉×#125	—	4	1	no	—
88	C₁₉×#124	—	2	1	no	—
89	C₁₉×#124	—	2	1	no	—
90	C₁₉×#124	—	2	1	no	—
91	C₁₉×#124	—	2	1	no	—
92	C₁₉×#123	—	4	1	no	—
93	C₁₉×C₂²⋊Q₈	—	2	1	no	—
94	C₁₉×C₂²⋊Q₈	—	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	C₂³	1	1	yes	characteristic
100	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
101	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	—	2	1	no	—
104	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₁₉×#117	—	2	1	no	—
106	C₁₉×#117	—	2	1	no	—
107	C₁₉×#107	—	2	1	no	—
108	C₁₉×#107	—	2	1	no	—
109	C₁₉×#107	—	4	1	no	—
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×#106	D₄	1	1	yes	characteristic
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×#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	—	4	1	no	—
136	C₁₉×#102	D₄	1	1	yes	characteristic
137	C₁₉×C₂²⋊C₈	—	2	1	no	—
138	C₁₉×#97	—	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×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	4	1	no	—
156	Q₁₆×C₁₉	—	4	1	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	SD₁₆×C₁₉	—	2	2	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	D₈×C₁₉	—	8	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	—	2	1	no	—
172	C₂×C₈×C₁₉	—	4	2	no	—
173	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	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	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂²⋊C₄×C₁₉	—	2	1	no	—
196	C₂²⋊C₄×C₁₉	—	4	1	no	—
197	C₂²⋊C₄×C₁₉	—	4	1	no	—
198	C₂²⋊C₄×C₁₉	—	4	1	no	—
199	C₂²⋊C₄×C₁₉	—	4	1	no	—
200	C₂²⋊C₄×C₁₉	—	4	1	no	—
201	C₂²⋊C₄×C₁₉	—	4	1	no	—
202	C₂²⋊C₄×C₁₉	—	4	1	no	—
203	C₄²×C₁₉	—	2	1	no	—
204	C₄²×C₁₉	—	2	1	no	—
205	C₄²×C₁₉	—	2	1	no	—
206	C₄²×C₁₉	—	4	1	no	—
207	C₄²×C₁₉	—	4	1	no	—
208	C₄²×C₁₉	—	4	1	no	—
209	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
210	#19872	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂³×C₁₉	—	2	1	no	—
212	C₂³×C₁₉	—	4	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	—	2	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	—	4	1	no	—
225	D₄×C₁₉	—	2	1	no	—
226	D₄×C₁₉	—	2	1	no	—
227	D₄×C₁₉	—	4	1	no	—
228	D₄×C₁₉	—	4	1	no	—
229	D₄×C₁₉	—	4	1	no	—
230	D₄×C₁₉	—	4	1	no	—
231	D₄×C₁₉	—	8	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	—	2	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	16	1	no	—
245	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
248	C₈×C₁₉	—	2	1	no	—
249	C₈×C₁₉	—	2	1	no	—
250	C₈×C₁₉	—	2	1	no	—
251	C₈×C₁₉	—	4	1	no	—
252	C₈×C₁₉	—	4	1	no	—
253	C₈×C₁₉	—	4	1	no	—
254	C₈×C₁₉	—	4	1	no	—
255	C₈×C₁₉	—	4	1	no	—
256	C₈×C₁₉	#135	1	2	yes	—
257	#3398	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#3394	C₂×C₁₉	1	1	yes	characteristic
259	#3365	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#3342	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1722	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1686	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1681	C₂×C₁₉	1	1	yes	characteristic
264	#1674	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1670	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1650	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1648	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#1640	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1628	C₂×C₁₉	1	1	yes	characteristic
270	#1584	C₂×C₁₉	1	1	yes	characteristic, complemented
271	SD₁₆⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
272	C₂²×C₁₉	—	4	1	no	—
273	C₂²×C₁₉	—	4	1	no	—
274	C₂²×C₁₉	—	4	1	no	—
275	C₂²×C₁₉	—	8	1	no	—
276	C₂²×C₁₉	—	8	1	no	—
277	C₂²×C₁₉	—	8	1	no	—
278	C₂²×C₁₉	D₄²	1	1	yes	characteristic
279	C₄×C₁₉	—	2	1	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	4	1	no	—
282	C₄×C₁₉	—	4	1	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	4	1	no	—
285	C₄×C₁₉	—	4	1	no	—
286	C₄×C₁₉	—	4	1	no	—
287	C₄×C₁₉	—	8	1	no	—
288	C₄×C₁₉	—	8	1	no	—
289	C₄×C₁₉	—	8	1	no	—
290	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
291	C₄×C₁₉	#575	1	1	yes	characteristic
292	C₄×C₁₉	#576	1	1	yes	characteristic
293	C₄×C₁₉	#578	1	1	yes	characteristic
294	#559	C₂²×C₁₉	1	1	yes	characteristic
295	#557	C₂²×C₁₉	1	1	yes	characteristic
296	#556	C₂²×C₁₉	1	1	yes	characteristic
297	#556	C₂²×C₁₉	1	1	yes	characteristic
298	#500	C₂²×C₁₉	1	1	yes	characteristic
299	#500	C₂²×C₁₉	1	1	yes	characteristic
300	#497	—	2	1	no	—
301	#495	—	2	1	no	—
302	#494	C₂²×C₁₉	1	1	yes	characteristic
303	#492	C₂²×C₁₉	1	1	yes	characteristic
304	#488	—	2	1	no	—
305	#486	C₂²×C₁₉	1	1	yes	characteristic
306	#486	C₂²×C₁₉	1	1	yes	characteristic
307	#485	—	2	1	no	—
308	#485	—	2	1	no	—
309	#478	—	2	1	no	—
310	#475	C₂²×C₁₉	1	1	yes	characteristic
311	#475	C₂²×C₁₉	1	1	yes	characteristic
312	#475	C₂²×C₁₉	1	1	yes	characteristic
313	#467	—	2	1	no	—
314	#464	—	2	1	no	—
315	#464	—	2	1	no	—
316	#464	—	2	1	no	—
317	#463	—	2	1	no	—
318	#462	—	2	1	no	—
319	#462	C₂²×C₁₉	1	1	yes	characteristic
320	#462	C₂²×C₁₉	1	1	yes	characteristic
321	#461	C₂²×C₁₉	1	1	yes	characteristic
322	#460	C₂²×C₁₉	1	1	yes	characteristic
323	#459	C₂²×C₁₉	1	1	yes	characteristic
324	#446	C₂²×C₁₉	1	1	yes	characteristic
325	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
326	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
327	#441	—	2	1	no	—
328	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
329	C₄×SD₁₆	—	2	1	no	—
330	C₄×SD₁₆	—	2	1	no	—
331	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
332	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
333	#427	—	2	1	no	—
334	#335	C₂²×C₁₉	1	1	yes	characteristic
335	#335	C₂²×C₁₉	1	1	yes	characteristic
336	#332	C₂²×C₁₉	1	1	yes	characteristic
337	#332	C₂²×C₁₉	1	1	yes	characteristic
338	#332	C₂²×C₁₉	1	1	yes	characteristic
339	#331	C₂²×C₁₉	1	1	yes	characteristic
340	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
341	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
342	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
343	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
344	#322	C₂²×C₁₉	1	1	yes	characteristic
345	C₂×C₁₉	—	8	1	no	—
346	C₂×C₁₉	—	16	1	no	—
347	C₂×C₁₉	#3269	1	1	yes	characteristic
348	C₂×C₁₉	#3287	1	1	yes	characteristic
349	C₂×C₁₉	#3289	1	1	yes	characteristic
350	C₂×Q₁₆	—	2	1	no	—
351	C₂×Q₁₆	—	2	1	no	—
352	C₂×Q₁₆	—	2	1	no	—
353	C₂×Q₁₆	—	2	1	no	—
354	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
355	C₂×SD₁₆	—	2	1	no	—
356	C₂×SD₁₆	—	2	1	no	—
357	C₂×SD₁₆	—	2	1	no	—
358	C₂×SD₁₆	—	2	1	no	—
359	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
360	C₂×D₈	—	2	1	no	—
361	C₂²×C₈	—	2	1	no	—
362	C₄⋊Q₈	—	2	1	no	—
363	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
364	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
365	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
366	#127	C₂³×C₁₉	1	1	yes	characteristic
367	#126	—	4	1	no	—
368	#126	—	4	1	no	—
369	#125	—	2	1	no	—
370	#125	—	4	1	no	—
371	#124	—	2	1	no	—
372	#124	—	2	1	no	—
373	#124	—	2	1	no	—
374	#124	—	2	1	no	—
375	#123	—	4	1	no	—
376	C₂²⋊Q₈	—	2	1	no	—
377	C₂²⋊Q₈	—	2	1	no	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	—	2	1	no	—
381	C₄×Q₈	—	2	1	no	—
382	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
383	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
384	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	—	2	1	no	—
387	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
388	#117	—	2	1	no	—
389	#117	—	2	1	no	—
390	#107	—	2	1	no	—
391	#107	—	2	1	no	—
392	#107	—	4	1	no	—
393	#107	D₄×C₁₉	1	1	yes	characteristic
394	#106	—	2	1	no	—
395	#106	—	2	1	no	—
396	#106	—	2	1	no	—
397	#106	D₄×C₁₉	1	1	yes	characteristic
398	C₄⋊C₈	—	2	1	no	—
399	C₄⋊C₈	—	2	1	no	—
400	C₄⋊C₈	—	2	1	no	—
401	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
402	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
403	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
404	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
405	#103	—	2	1	no	—
406	#103	—	2	1	no	—
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	2	1	no	—
410	#103	—	2	1	no	—
411	#103	D₄×C₁₉	1	1	yes	characteristic
412	#103	D₄×C₁₉	1	1	yes	characteristic
413	#103	D₄×C₁₉	1	1	yes	characteristic
414	#102	—	2	1	no	—
415	#102	—	2	1	no	—
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	—	4	1	no	—
419	#102	D₄×C₁₉	1	1	yes	characteristic
420	C₂²⋊C₈	—	2	1	no	—
421	#97	—	2	1	no	—
422	C₄×C₈	—	2	1	no	—
423	C₄×C₈	—	2	1	no	—
424	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
425	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
426	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
427	C₁₉	#19872	1	1	yes	characteristic, direct product factor, Sylow
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
432	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
433	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	4	1	no	—
440	Q₁₆	—	4	1	no	—
441	Q₁₆	—	4	2	no	—
442	Q₁₆	—	8	1	no	—
443	Q₁₆	—	8	1	no	—
444	Q₁₆	—	8	1	no	—
445	SD₁₆	—	2	2	no	—
446	SD₁₆	—	4	2	no	—
447	SD₁₆	—	4	2	no	—
448	SD₁₆	—	8	1	no	—
449	SD₁₆	—	8	1	no	—
450	D₈	—	8	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	4	2	no	—
457	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	—	4	1	no	—
474	C₄⋊C₄	—	4	1	no	—
475	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₂²⋊C₄	—	4	1	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	4	1	no	—
491	C₄²	—	4	1	no	—
492	C₄²	—	4	1	no	—
493	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
494	C₂³	—	2	1	no	—
495	C₂³	—	4	1	no	—
496	Q₈	—	2	1	no	—
497	Q₈	—	2	1	no	—
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	2	1	no	—
501	Q₈	—	2	1	no	—
502	Q₈	—	4	1	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	4	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	2	1	no	—
510	D₄	—	4	1	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	1	no	—
513	D₄	—	4	1	no	—
514	D₄	—	8	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	16	1	no	—
528	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
529	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
530	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₈	C₁₉×#135	1	2	yes	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	D₄²×C₁₉	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
559	C₄	C₁₉×#575	1	1	yes	characteristic
560	C₄	C₁₉×#576	1	1	yes	characteristic
561	C₄	C₁₉×#578	1	1	yes	characteristic
562	C₂	—	8	1	no	—
563	C₂	—	16	1	no	—
564	C₂	C₁₉×#3269	1	1	yes	characteristic
565	C₂	C₁₉×#3287	1	1	yes	characteristic
566	C₂	C₁₉×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#459	C₂²
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×#3398	C₂	semidirect
3. C₁₉×#3365	C₂	semidirect
4. C₁₉×#3342	C₂	semidirect
5. C₁₉×#1722	C₂	semidirect
6. C₁₉×#1686	C₂	semidirect
8. C₁₉×#1674	C₂	semidirect
9. C₁₉×#1670	C₂	semidirect
10. C₁₉×#1650	C₂	semidirect
11. C₁₉×#1648	C₂	semidirect
12. C₁₉×#1640	C₂	semidirect
14. C₁₉×#1584	C₂	semidirect
15. C₁₉×SD₁₆⋊C₈	C₂	semidirect
210. #19872	C₁₉	direct (N × H)
257. #3398	C₂×C₁₉	semidirect
259. #3365	C₂×C₁₉	semidirect
260. #3342	C₂×C₁₉	semidirect
261. #1722	C₂×C₁₉	semidirect
262. #1686	C₂×C₁₉	semidirect
264. #1674	C₂×C₁₉	semidirect
265. #1670	C₂×C₁₉	semidirect
266. #1650	C₂×C₁₉	semidirect
267. #1648	C₂×C₁₉	semidirect
268. #1640	C₂×C₁₉	semidirect
270. #1584	C₂×C₁₉	semidirect
271. SD₁₆⋊C₈	C₂×C₁₉	semidirect
427. C₁₉	#19872	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×#3398	2
C₁₉×#3394	2
C₁₉×#3365	2
C₁₉×#3342	2
C₁₉×#1722	2
C₁₉×#1686	2
C₁₉×#1681	2
C₁₉×#1674	2
C₁₉×#1670	2
C₁₉×#1650	2
C₁₉×#1648	2
C₁₉×#1640	2
C₁₉×#1628	2
C₁₉×#1584	2
C₁₉×SD₁₆⋊C₈	2
#19872	19

Subgroups — C19×#19872 #18025831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19872 #18025831