Subgroups — C₁₉×#19812 #18025771

Order 4864.

616 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3386	C₂	1	1	yes	maximal, characteristic
2	Q₈×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3363	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1723	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1692	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1683	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×#1649	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1648	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1645	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1637	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
16	C₂²×Q₁₆×C₁₉	—	2	1	no	—
17	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#557	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#501	—	2	1	no	—
22	C₁₉×#500	C₂²	1	1	yes	characteristic
23	C₁₉×#500	C₂²	1	1	yes	characteristic
24	C₁₉×#498	—	2	1	no	—
25	C₁₉×#498	C₂²	1	1	yes	characteristic
26	C₁₉×#494	C₂²	1	1	yes	characteristic
27	C₁₉×#487	—	2	1	no	—
28	C₁₉×#487	C₂²	1	1	yes	characteristic
29	C₁₉×#487	C₂²	1	1	yes	characteristic
30	C₁₉×#478	—	2	1	no	—
31	C₁₉×#477	—	2	1	no	—
32	C₁₉×#477	—	2	1	no	—
33	C₁₉×#477	C₂²	1	1	yes	characteristic
34	C₁₉×#476	—	2	1	no	—
35	C₁₉×#476	C₂²	1	1	yes	characteristic
36	C₁₉×#475	—	2	1	no	—
37	C₁₉×#475	C₂²	1	1	yes	characteristic
38	C₁₉×#475	C₂²	1	1	yes	characteristic
39	C₁₉×#474	C₂²	1	1	yes	characteristic
40	C₁₉×#467	—	2	1	no	—
41	C₁₉×#462	—	2	1	no	—
42	C₁₉×#462	C₂²	1	1	yes	characteristic
43	C₁₉×#462	C₂²	1	1	yes	characteristic
44	C₁₉×#462	C₂²	1	1	yes	characteristic
45	C₁₉×#451	—	2	1	no	—
46	C₁₉×#451	—	2	1	no	—
47	C₁₉×#446	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	C₂²	1	1	yes	characteristic
53	C₄×SD₁₆×C₁₉	—	2	1	no	—
54	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
55	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#335	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	C₂²×Q₈×C₁₉	—	2	1	no	—
68	C₂²×Q₈×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	—	2	1	no	—
73	C₂×Q₁₆×C₁₉	—	2	1	no	—
74	C₂×Q₁₆×C₁₉	—	4	4	no	—
75	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
76	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
77	C₂²×C₈×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	—	2	1	no	—
82	C₁₉×C₄⋊Q₈	—	2	1	no	—
83	C₁₉×C₄⋊Q₈	—	4	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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₁₉×#125	—	2	1	no	—
89	C₁₉×#125	—	4	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	1	no	—
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	—	4	1	no	—
93	C₁₉×C₂²⋊Q₈	—	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	C₂³	1	1	yes	characteristic
99	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
100	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₁₉×#107	—	2	1	no	—
105	C₁₉×#107	—	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×#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	—	2	1	no	—
115	C₁₉×#106	D₄	1	1	yes	characteristic
116	C₁₉×C₄⋊C₈	—	2	1	no	—
117	C₁₉×C₄⋊C₈	—	2	1	no	—
118	C₁₉×C₄⋊C₈	—	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	—	2	1	no	—
129	C₁₉×#103	—	2	1	no	—
130	C₁₉×#103	—	2	1	no	—
131	C₁₉×#103	—	4	1	no	—
132	C₁₉×#103	D₄	1	1	yes	characteristic
133	C₁₉×#103	D₄	1	1	yes	characteristic
134	C₁₉×#103	D₄	1	1	yes	characteristic
135	C₁₉×#102	—	2	1	no	—
136	C₁₉×#102	—	2	1	no	—
137	C₁₉×#102	D₄	1	1	yes	characteristic
138	C₁₉×C₂²⋊C₈	—	2	1	no	—
139	C₁₉×#97	—	2	1	no	—
140	C₄×C₈×C₁₉	—	2	1	no	—
141	C₄×C₈×C₁₉	—	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	C₂×Q₈×C₁₉	—	2	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	4	1	no	—
150	C₂×Q₈×C₁₉	—	4	1	no	—
151	C₂×Q₈×C₁₉	—	4	1	no	—
152	C₂×Q₈×C₁₉	—	4	2	no	—
153	C₂×Q₈×C₁₉	—	4	2	no	—
154	C₂×Q₈×C₁₉	—	8	1	no	—
155	C₂×Q₈×C₁₉	—	8	1	no	—
156	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	4	1	no	—
162	C₂²×C₄×C₁₉	—	4	1	no	—
163	Q₁₆×C₁₉	—	2	2	no	—
164	Q₁₆×C₁₉	—	4	2	no	—
165	Q₁₆×C₁₉	—	4	2	no	—
166	Q₁₆×C₁₉	—	4	2	no	—
167	Q₁₆×C₁₉	—	4	2	no	—
168	Q₁₆×C₁₉	—	8	1	no	—
169	SD₁₆×C₁₉	Q₁₆	1	4	yes	complemented
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	4	2	no	—
176	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	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	—	4	1	no	—
195	C₄⋊C₄×C₁₉	—	4	1	no	—
196	C₄⋊C₄×C₁₉	—	4	1	no	—
197	C₄⋊C₄×C₁₉	—	4	1	no	—
198	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂²⋊C₄×C₁₉	—	2	1	no	—
203	C₂²⋊C₄×C₁₉	—	4	1	no	—
204	C₂²⋊C₄×C₁₉	—	4	1	no	—
205	C₄²×C₁₉	—	2	1	no	—
206	C₄²×C₁₉	—	2	1	no	—
207	C₄²×C₁₉	—	2	1	no	—
208	C₄²×C₁₉	—	4	1	no	—
209	C₄²×C₁₉	—	4	1	no	—
210	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
211	#19812	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂³×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	—	4	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	—	8	2	no	—
224	Q₈×C₁₉	—	8	1	no	—
225	Q₈×C₁₉	—	8	2	no	—
226	Q₈×C₁₉	—	16	1	no	—
227	Q₈×C₁₉	C₂×Q₁₆	1	2	yes	complemented
228	Q₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
229	D₄×C₁₉	—	2	1	no	—
230	D₄×C₁₉	C₂×Q₁₆	1	2	yes	—
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	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	8	2	no	—
245	C₂×C₄×C₁₉	—	8	2	no	—
246	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
249	C₈×C₁₉	—	2	1	no	—
250	C₈×C₁₉	—	2	1	no	—
251	C₈×C₁₉	—	2	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	—	4	1	no	—
257	C₈×C₁₉	C₂×Q₁₆	1	2	yes	complemented
258	#3386	C₂×C₁₉	1	1	yes	characteristic
259	Q₈×SD₁₆	C₂×C₁₉	1	1	yes	characteristic
260	#3363	C₂×C₁₉	1	1	yes	characteristic, complemented
261	D₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic
262	#1723	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1692	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1683	C₂×C₁₉	1	1	yes	characteristic
265	#1674	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1670	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1649	C₂×C₁₉	1	1	yes	characteristic
268	#1648	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1645	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#1637	C₂×C₁₉	1	1	yes	characteristic
271	#1584	C₂×C₁₉	1	1	yes	characteristic, complemented
272	SD₁₆⋊C₈	C₂×C₁₉	1	1	yes	characteristic
273	C₂²×C₁₉	—	2	2	no	—
274	C₂²×C₁₉	—	4	1	no	—
275	C₂²×C₁₉	—	4	1	no	—
276	C₂²×C₁₉	D₄²	1	1	yes	characteristic
277	C₄×C₁₉	—	2	2	no	—
278	C₄×C₁₉	—	2	2	no	—
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	—	8	1	no	—
286	C₄×C₁₉	—	8	1	no	—
287	C₄×C₁₉	—	8	1	no	—
288	C₄×C₁₉	—	8	1	no	—
289	C₄×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
290	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
291	C₄×C₁₉	#577	1	1	yes	characteristic
292	C₄×C₁₉	#578	1	1	yes	characteristic
293	C₂²×Q₁₆	—	2	1	no	—
294	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
295	#557	C₂²×C₁₉	1	1	yes	characteristic
296	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
297	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
298	#501	—	2	1	no	—
299	#500	C₂²×C₁₉	1	1	yes	characteristic
300	#500	C₂²×C₁₉	1	1	yes	characteristic
301	#498	—	2	1	no	—
302	#498	C₂²×C₁₉	1	1	yes	characteristic
303	#494	C₂²×C₁₉	1	1	yes	characteristic
304	#487	—	2	1	no	—
305	#487	C₂²×C₁₉	1	1	yes	characteristic
306	#487	C₂²×C₁₉	1	1	yes	characteristic
307	#478	—	2	1	no	—
308	#477	—	2	1	no	—
309	#477	—	2	1	no	—
310	#477	C₂²×C₁₉	1	1	yes	characteristic
311	#476	—	2	1	no	—
312	#476	C₂²×C₁₉	1	1	yes	characteristic
313	#475	—	2	1	no	—
314	#475	C₂²×C₁₉	1	1	yes	characteristic
315	#475	C₂²×C₁₉	1	1	yes	characteristic
316	#474	C₂²×C₁₉	1	1	yes	characteristic
317	#467	—	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	#462	C₂²×C₁₉	1	1	yes	characteristic
322	#451	—	2	1	no	—
323	#451	—	2	1	no	—
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	#440	—	2	1	no	—
328	C₄×Q₁₆	—	2	1	no	—
329	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
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	#335	C₂²×C₁₉	1	1	yes	characteristic
334	#335	C₂²×C₁₉	1	1	yes	characteristic
335	#333	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	Q₈⋊C₈	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	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
343	#322	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×C₁₉	—	4	2	no	—
345	C₂×C₁₉	#3265	1	1	yes	characteristic
346	C₂×C₁₉	D₄×Q₁₆	1	1	yes	characteristic
347	C₂×C₁₉	#3289	1	1	yes	characteristic
348	C₂²×Q₈	—	2	1	no	—
349	C₂²×Q₈	—	2	1	no	—
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	—	2	1	no	—
355	C₂×Q₁₆	—	4	4	no	—
356	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
357	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
358	C₂²×C₈	—	2	1	no	—
359	C₄⋊Q₈	—	2	1	no	—
360	C₄⋊Q₈	—	2	1	no	—
361	C₄⋊Q₈	—	2	1	no	—
362	C₄⋊Q₈	—	2	1	no	—
363	C₄⋊Q₈	—	2	1	no	—
364	C₄⋊Q₈	—	4	1	no	—
365	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
366	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
367	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
368	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
369	#125	—	2	1	no	—
370	#125	—	4	1	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	C₂²⋊Q₈	—	4	1	no	—
374	C₂²⋊Q₈	—	4	1	no	—
375	C₄×Q₈	—	2	1	no	—
376	C₄×Q₈	—	2	1	no	—
377	C₄×Q₈	—	2	1	no	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
380	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
381	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
385	#107	—	2	1	no	—
386	#107	—	2	1	no	—
387	#107	—	2	1	no	—
388	#107	—	2	1	no	—
389	#107	—	4	1	no	—
390	#107	D₄×C₁₉	1	1	yes	characteristic
391	#106	—	2	1	no	—
392	#106	—	2	1	no	—
393	#106	—	2	1	no	—
394	#106	—	2	1	no	—
395	#106	—	2	1	no	—
396	#106	D₄×C₁₉	1	1	yes	characteristic
397	C₄⋊C₈	—	2	1	no	—
398	C₄⋊C₈	—	2	1	no	—
399	C₄⋊C₈	—	2	1	no	—
400	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
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	#103	—	2	1	no	—
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	—	2	1	no	—
412	#103	—	4	1	no	—
413	#103	D₄×C₁₉	1	1	yes	characteristic
414	#103	D₄×C₁₉	1	1	yes	characteristic
415	#103	D₄×C₁₉	1	1	yes	characteristic
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	D₄×C₁₉	1	1	yes	characteristic
419	C₂²⋊C₈	—	2	1	no	—
420	#97	—	2	1	no	—
421	C₄×C₈	—	2	1	no	—
422	C₄×C₈	—	2	1	no	—
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	C₁₉	#19812	1	1	yes	characteristic, direct product factor, Sylow
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	4	1	no	—
432	C₂×Q₈	—	4	1	no	—
433	C₂×Q₈	—	4	1	no	—
434	C₂×Q₈	—	4	2	no	—
435	C₂×Q₈	—	4	2	no	—
436	C₂×Q₈	—	8	1	no	—
437	C₂×Q₈	—	8	1	no	—
438	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	Q₁₆	—	2	2	no	—
446	Q₁₆	—	4	2	no	—
447	Q₁₆	—	4	2	no	—
448	Q₁₆	—	4	2	no	—
449	Q₁₆	—	4	2	no	—
450	Q₁₆	—	8	1	no	—
451	SD₁₆	Q₁₆×C₁₉	1	4	yes	complemented
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	—	2	1	no	—
457	C₂×C₈	—	4	2	no	—
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	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	4	1	no	—
474	C₄⋊C₄	—	4	1	no	—
475	C₄⋊C₄	—	4	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂²⋊C₄	—	2	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	C₂⁴×C₁₉	1	1	yes	characteristic
493	C₂³	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	2	1	no	—
496	Q₈	—	2	1	no	—
497	Q₈	—	2	1	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	4	1	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	8	2	no	—
505	Q₈	—	8	1	no	—
506	Q₈	—	8	2	no	—
507	Q₈	—	16	1	no	—
508	Q₈	C₂×Q₁₆×C₁₉	1	2	yes	complemented
509	Q₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
510	D₄	—	2	1	no	—
511	D₄	C₂×Q₁₆×C₁₉	1	2	yes	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	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	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	—	8	2	no	—
527	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
529	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	C₂×Q₁₆×C₁₉	1	2	yes	complemented
539	C₂²	—	2	2	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	D₄²×C₁₉	1	1	yes	characteristic
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	8	1	no	—
552	C₄	—	8	1	no	—
553	C₄	—	8	1	no	—
554	C₄	—	8	1	no	—
555	C₄	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
556	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
557	C₄	C₁₉×#577	1	1	yes	characteristic
558	C₄	C₁₉×#578	1	1	yes	characteristic
559	C₂	—	4	2	no	—
560	C₂	C₁₉×#3265	1	1	yes	characteristic
561	C₂	D₄×Q₁₆×C₁₉	1	1	yes	characteristic
562	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
3. C₁₉×#3363	C₂	semidirect
5. C₁₉×#1723	C₂	semidirect
6. C₁₉×#1692	C₂	semidirect
8. C₁₉×#1674	C₂	semidirect
9. C₁₉×#1670	C₂	semidirect
11. C₁₉×#1648	C₂	semidirect
12. C₁₉×#1645	C₂	semidirect
14. C₁₉×#1584	C₂	semidirect
169. SD₁₆×C₁₉	Q₁₆	semidirect
211. #19812	C₁₉	direct (N × H)
227. Q₈×C₁₉	C₂×Q₁₆	semidirect
257. C₈×C₁₉	C₂×Q₁₆	semidirect
260. #3363	C₂×C₁₉	semidirect
262. #1723	C₂×C₁₉	semidirect
263. #1692	C₂×C₁₉	semidirect
265. #1674	C₂×C₁₉	semidirect
266. #1670	C₂×C₁₉	semidirect
268. #1648	C₂×C₁₉	semidirect
269. #1645	C₂×C₁₉	semidirect
271. #1584	C₂×C₁₉	semidirect
426. C₁₉	#19812	direct (N × H)
451. SD₁₆	Q₁₆×C₁₉	semidirect
508. Q₈	C₂×Q₁₆×C₁₉	semidirect
538. C₈	C₂×Q₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3386	2
Q₈×SD₁₆×C₁₉	2
C₁₉×#3363	2
D₄×Q₁₆×C₁₉	2
C₁₉×#1723	2
C₁₉×#1692	2
C₁₉×#1683	2
C₁₉×#1674	2
C₁₉×#1670	2
C₁₉×#1649	2
C₁₉×#1648	2
C₁₉×#1645	2
C₁₉×#1637	2
C₁₉×#1584	2
C₁₉×SD₁₆⋊C₈	2
#19812	19

Subgroups — C19×#19812 #18025771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19812 #18025771