Subgroups — C₁₉×#19881 #18025840

Order 4864.

562 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3395	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3381	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3364	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3356	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1716	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1689	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1680	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1672	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1672	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1653	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1652	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1644	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1636	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1583	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1579	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#557	C₂²	1	1	yes	characteristic
17	C₁₉×#557	C₂²	1	1	yes	characteristic
18	C₁₉×#556	C₂²	1	1	yes	characteristic
19	C₁₉×#554	C₂²	1	1	yes	characteristic
20	C₁₉×#499	—	2	1	no	—
21	C₁₉×#498	C₂²	1	1	yes	characteristic
22	C₁₉×#498	C₂²	1	1	yes	characteristic
23	C₁₉×#498	C₂²	1	1	yes	characteristic
24	C₁₉×#494	—	2	1	no	—
25	C₁₉×#494	C₂²	1	1	yes	characteristic
26	C₁₉×#488	—	2	1	no	—
27	C₁₉×#487	C₂²	1	1	yes	characteristic
28	C₁₉×#487	C₂²	1	1	yes	characteristic
29	C₁₉×#485	—	2	1	no	—
30	C₁₉×#483	—	2	1	no	—
31	C₁₉×#479	—	2	1	no	—
32	C₁₉×#479	—	2	1	no	—
33	C₁₉×#478	—	2	1	no	—
34	C₁₉×#477	C₂²	1	1	yes	characteristic
35	C₁₉×#477	C₂²	1	1	yes	characteristic
36	C₁₉×#475	C₂²	1	1	yes	characteristic
37	C₁₉×#474	C₂²	1	1	yes	characteristic
38	C₁₉×#474	C₂²	1	1	yes	characteristic
39	C₁₉×#470	—	2	1	no	—
40	C₁₉×#464	—	2	1	no	—
41	C₁₉×#462	—	2	1	no	—
42	C₁₉×#462	—	2	1	no	—
43	C₁₉×#462	C₂²	1	1	yes	characteristic
44	C₁₉×#462	C₂²	1	1	yes	characteristic
45	C₁₉×#462	C₂²	1	1	yes	characteristic
46	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₄×Q₁₆×C₁₉	—	2	1	no	—
50	C₄×Q₁₆×C₁₉	—	2	1	no	—
51	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
52	C₄×SD₁₆×C₁₉	—	2	1	no	—
53	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
54	C₁₉×#436	C₂²	1	1	yes	characteristic
55	C₁₉×#428	—	2	1	no	—
56	C₁₉×#334	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×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	—	2	1	no	—
72	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
73	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
74	C₂×M₁₆×C₁₉	—	2	1	no	—
75	C₁₉×C₄⋊Q₈	—	2	1	no	—
76	C₁₉×C₄⋊Q₈	—	2	1	no	—
77	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₉×#126	—	4	1	no	—
82	C₁₉×#125	—	2	1	no	—
83	C₁₉×#125	—	2	1	no	—
84	C₁₉×#125	—	2	1	no	—
85	C₁₉×#125	—	4	1	no	—
86	C₁₉×#125	—	4	1	no	—
87	C₁₉×#124	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	4	1	no	—
91	C₄×Q₈×C₁₉	—	2	1	no	—
92	C₄×Q₈×C₁₉	—	2	1	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
97	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×#117	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₁₉×#107	—	2	1	no	—
104	C₁₉×#107	—	2	1	no	—
105	C₁₉×#107	—	2	1	no	—
106	C₁₉×#107	—	2	1	no	—
107	C₁₉×#107	D₄	1	1	yes	characteristic
108	C₁₉×#106	—	2	1	no	—
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	—	4	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	—	2	1	no	—
129	C₁₉×#103	—	2	1	no	—
130	C₁₉×#103	—	4	1	no	—
131	C₁₉×#103	D₄	1	1	yes	characteristic
132	C₁₉×#103	D₄	1	1	yes	characteristic
133	C₁₉×#103	D₄	1	1	yes	characteristic
134	C₁₉×#102	—	2	1	no	—
135	C₁₉×#102	—	2	1	no	—
136	C₁₉×#102	D₄	1	1	yes	characteristic
137	C₁₉×C₂²⋊C₈	—	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	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	4	1	no	—
154	Q₁₆×C₁₉	—	2	2	no	—
155	Q₁₆×C₁₉	—	4	2	no	—
156	Q₁₆×C₁₉	—	4	2	no	—
157	Q₁₆×C₁₉	—	8	1	no	—
158	Q₁₆×C₁₉	—	8	1	no	—
159	Q₁₆×C₁₉	—	8	1	no	—
160	SD₁₆×C₁₉	—	2	2	no	—
161	M₁₆×C₁₉	—	4	2	no	—
162	C₂×C₈×C₁₉	—	2	1	no	—
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
183	C₄⋊C₄×C₁₉	—	4	1	no	—
184	C₄⋊C₄×C₁₉	—	4	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	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	C₄²×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	—	2	1	no	—
201	C₄²×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	—	4	1	no	—
203	C₄²×C₁₉	—	4	1	no	—
204	C₄²×C₁₉	—	4	1	no	—
205	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
206	#19881	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₁₉	—	2	1	no	—
208	Q₈×C₁₉	—	2	1	no	—
209	Q₈×C₁₉	—	2	1	no	—
210	Q₈×C₁₉	—	2	1	no	—
211	Q₈×C₁₉	—	2	1	no	—
212	Q₈×C₁₉	—	2	1	no	—
213	Q₈×C₁₉	—	4	1	no	—
214	Q₈×C₁₉	—	4	1	no	—
215	Q₈×C₁₉	—	4	1	no	—
216	Q₈×C₁₉	—	4	1	no	—
217	Q₈×C₁₉	—	4	1	no	—
218	Q₈×C₁₉	—	4	1	no	—
219	Q₈×C₁₉	—	8	1	no	—
220	Q₈×C₁₉	#137	1	2	yes	—
221	D₄×C₁₉	—	2	1	no	—
222	D₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	16	1	no	—
237	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
240	C₈×C₁₉	—	2	1	no	—
241	C₈×C₁₉	—	2	1	no	—
242	C₈×C₁₉	—	2	1	no	—
243	C₈×C₁₉	—	4	1	no	—
244	C₈×C₁₉	—	4	1	no	—
245	C₈×C₁₉	—	4	1	no	—
246	C₈×C₁₉	—	4	1	no	—
247	C₈×C₁₉	—	4	1	no	—
248	C₈×C₁₉	#135	1	2	yes	—
249	#3395	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#3381	C₂×C₁₉	1	1	yes	characteristic
251	#3364	C₂×C₁₉	1	1	yes	characteristic
252	#3356	C₂×C₁₉	1	1	yes	characteristic
253	#1716	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#1689	C₂×C₁₉	1	1	yes	characteristic
255	#1680	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1672	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1672	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1653	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1652	C₂×C₁₉	1	1	yes	characteristic
260	#1644	C₂×C₁₉	1	1	yes	characteristic
261	#1636	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1583	C₂×C₁₉	1	1	yes	characteristic
263	#1579	C₂×C₁₉	1	1	yes	characteristic, complemented
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	—	4	1	no	—
266	C₂²×C₁₉	—	4	1	no	—
267	C₂²×C₁₉	D₄²	1	1	yes	characteristic
268	C₄×C₁₉	—	2	2	no	—
269	C₄×C₁₉	—	2	1	no	—
270	C₄×C₁₉	—	4	1	no	—
271	C₄×C₁₉	—	4	1	no	—
272	C₄×C₁₉	—	4	1	no	—
273	C₄×C₁₉	—	4	1	no	—
274	C₄×C₁₉	—	4	1	no	—
275	C₄×C₁₉	—	4	1	no	—
276	C₄×C₁₉	—	8	1	no	—
277	C₄×C₁₉	—	8	1	no	—
278	C₄×C₁₉	—	8	1	no	—
279	C₄×C₁₉	—	8	1	no	—
280	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
281	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
282	C₄×C₁₉	#577	1	1	yes	characteristic
283	C₄×C₁₉	#578	1	1	yes	characteristic
284	#557	C₂²×C₁₉	1	1	yes	characteristic
285	#557	C₂²×C₁₉	1	1	yes	characteristic
286	#556	C₂²×C₁₉	1	1	yes	characteristic
287	#554	C₂²×C₁₉	1	1	yes	characteristic
288	#499	—	2	1	no	—
289	#498	C₂²×C₁₉	1	1	yes	characteristic
290	#498	C₂²×C₁₉	1	1	yes	characteristic
291	#498	C₂²×C₁₉	1	1	yes	characteristic
292	#494	—	2	1	no	—
293	#494	C₂²×C₁₉	1	1	yes	characteristic
294	#488	—	2	1	no	—
295	#487	C₂²×C₁₉	1	1	yes	characteristic
296	#487	C₂²×C₁₉	1	1	yes	characteristic
297	#485	—	2	1	no	—
298	#483	—	2	1	no	—
299	#479	—	2	1	no	—
300	#479	—	2	1	no	—
301	#478	—	2	1	no	—
302	#477	C₂²×C₁₉	1	1	yes	characteristic
303	#477	C₂²×C₁₉	1	1	yes	characteristic
304	#475	C₂²×C₁₉	1	1	yes	characteristic
305	#474	C₂²×C₁₉	1	1	yes	characteristic
306	#474	C₂²×C₁₉	1	1	yes	characteristic
307	#470	—	2	1	no	—
308	#464	—	2	1	no	—
309	#462	—	2	1	no	—
310	#462	—	2	1	no	—
311	#462	C₂²×C₁₉	1	1	yes	characteristic
312	#462	C₂²×C₁₉	1	1	yes	characteristic
313	#462	C₂²×C₁₉	1	1	yes	characteristic
314	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
315	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
316	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
317	C₄×Q₁₆	—	2	1	no	—
318	C₄×Q₁₆	—	2	1	no	—
319	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
320	C₄×SD₁₆	—	2	1	no	—
321	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
322	#436	C₂²×C₁₉	1	1	yes	characteristic
323	#428	—	2	1	no	—
324	#334	C₂²×C₁₉	1	1	yes	characteristic
325	#334	C₂²×C₁₉	1	1	yes	characteristic
326	#333	C₂²×C₁₉	1	1	yes	characteristic
327	#332	C₂²×C₁₉	1	1	yes	characteristic
328	#332	C₂²×C₁₉	1	1	yes	characteristic
329	#332	C₂²×C₁₉	1	1	yes	characteristic
330	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
331	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
332	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
333	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
334	#322	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×C₁₉	—	8	1	no	—
336	C₂×C₁₉	#3270	1	1	yes	characteristic
337	C₂×C₁₉	#3284	1	1	yes	characteristic
338	C₂×C₁₉	#3289	1	1	yes	characteristic
339	C₂×Q₁₆	—	2	1	no	—
340	C₂×Q₁₆	—	2	1	no	—
341	C₂×Q₁₆	—	2	1	no	—
342	C₂×Q₁₆	—	2	1	no	—
343	C₂×Q₁₆	—	2	1	no	—
344	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
345	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
346	C₂×M₁₆	—	2	1	no	—
347	C₄⋊Q₈	—	2	1	no	—
348	C₄⋊Q₈	—	2	1	no	—
349	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
350	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
351	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
352	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
353	#126	—	4	1	no	—
354	#125	—	2	1	no	—
355	#125	—	2	1	no	—
356	#125	—	2	1	no	—
357	#125	—	4	1	no	—
358	#125	—	4	1	no	—
359	#124	—	2	1	no	—
360	C₂²⋊Q₈	—	2	1	no	—
361	C₂²⋊Q₈	—	2	1	no	—
362	C₂²⋊Q₈	—	4	1	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	—	2	1	no	—
368	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
369	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
370	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
373	#117	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	#107	—	2	1	no	—
376	#107	—	2	1	no	—
377	#107	—	2	1	no	—
378	#107	—	2	1	no	—
379	#107	D₄×C₁₉	1	1	yes	characteristic
380	#106	—	2	1	no	—
381	#106	—	2	1	no	—
382	#106	—	2	1	no	—
383	#106	—	2	1	no	—
384	#106	—	2	1	no	—
385	#106	—	4	1	no	—
386	#106	D₄×C₁₉	1	1	yes	characteristic
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
391	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
392	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
393	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
394	#103	—	2	1	no	—
395	#103	—	2	1	no	—
396	#103	—	2	1	no	—
397	#103	—	2	1	no	—
398	#103	—	2	1	no	—
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	4	1	no	—
403	#103	D₄×C₁₉	1	1	yes	characteristic
404	#103	D₄×C₁₉	1	1	yes	characteristic
405	#103	D₄×C₁₉	1	1	yes	characteristic
406	#102	—	2	1	no	—
407	#102	—	2	1	no	—
408	#102	D₄×C₁₉	1	1	yes	characteristic
409	C₂²⋊C₈	—	2	1	no	—
410	C₄×C₈	—	2	1	no	—
411	C₄×C₈	—	2	1	no	—
412	C₄×C₈	—	2	1	no	—
413	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
414	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
415	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
416	C₁₉	#19881	1	1	yes	characteristic, direct product factor, Sylow
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
422	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
424	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	4	1	no	—
427	Q₁₆	—	2	2	no	—
428	Q₁₆	—	4	2	no	—
429	Q₁₆	—	4	2	no	—
430	Q₁₆	—	8	1	no	—
431	Q₁₆	—	8	1	no	—
432	Q₁₆	—	8	1	no	—
433	SD₁₆	—	2	2	no	—
434	M₁₆	—	4	2	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	4	1	no	—
456	C₄⋊C₄	—	4	1	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
467	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	4	1	no	—
470	C₂²⋊C₄	—	4	1	no	—
471	C₂²⋊C₄	—	4	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	4	1	no	—
476	C₄²	—	4	1	no	—
477	C₄²	—	4	1	no	—
478	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
479	C₂³	—	2	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	2	1	no	—
482	Q₈	—	2	1	no	—
483	Q₈	—	2	1	no	—
484	Q₈	—	2	1	no	—
485	Q₈	—	4	1	no	—
486	Q₈	—	4	1	no	—
487	Q₈	—	4	1	no	—
488	Q₈	—	4	1	no	—
489	Q₈	—	4	1	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	8	1	no	—
492	Q₈	C₁₉×#137	1	2	yes	—
493	D₄	—	2	1	no	—
494	D₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	16	1	no	—
509	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
511	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
512	C₈	—	2	1	no	—
513	C₈	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₈	—	4	1	no	—
516	C₈	—	4	1	no	—
517	C₈	—	4	1	no	—
518	C₈	—	4	1	no	—
519	C₈	—	4	1	no	—
520	C₈	C₁₉×#135	1	2	yes	—
521	C₂²	—	4	1	no	—
522	C₂²	—	4	1	no	—
523	C₂²	—	4	1	no	—
524	C₂²	D₄²×C₁₉	1	1	yes	characteristic
525	C₄	—	2	2	no	—
526	C₄	—	2	1	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	8	1	no	—
534	C₄	—	8	1	no	—
535	C₄	—	8	1	no	—
536	C₄	—	8	1	no	—
537	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
538	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
539	C₄	C₁₉×#577	1	1	yes	characteristic
540	C₄	C₁₉×#578	1	1	yes	characteristic
541	C₂	—	8	1	no	—
542	C₂	C₁₉×#3270	1	1	yes	characteristic
543	C₂	C₁₉×#3284	1	1	yes	characteristic
544	C₂	C₁₉×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×D₄×C₁₉	C₂×D₄
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×#3395	C₂	semidirect
5. C₁₉×#1716	C₂	semidirect
7. C₁₉×#1680	C₂	semidirect
8. C₁₉×#1672	C₂	semidirect
9. C₁₉×#1672	C₂	semidirect
10. C₁₉×#1653	C₂	semidirect
13. C₁₉×#1636	C₂	semidirect
15. C₁₉×#1579	C₂	semidirect
206. #19881	C₁₉	direct (N × H)
249. #3395	C₂×C₁₉	semidirect
253. #1716	C₂×C₁₉	semidirect
255. #1680	C₂×C₁₉	semidirect
256. #1672	C₂×C₁₉	semidirect
257. #1672	C₂×C₁₉	semidirect
258. #1653	C₂×C₁₉	semidirect
261. #1636	C₂×C₁₉	semidirect
263. #1579	C₂×C₁₉	semidirect
416. C₁₉	#19881	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×#3395	2
C₁₉×#3381	2
C₁₉×#3364	2
C₁₉×#3356	2
C₁₉×#1716	2
C₁₉×#1689	2
C₁₉×#1680	2
C₁₉×#1672	2
C₁₉×#1653	2
C₁₉×#1652	2
C₁₉×#1644	2
C₁₉×#1636	2
C₁₉×#1583	2
C₁₉×#1579	2
#19881	19

Subgroups — C19×#19881 #18025840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19881 #18025840