Subgroups — C₁₉×#21006 #18026965

Order 4864.

1654 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#137	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#568	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2896	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1908	C₂	1	8	yes	maximal, complemented
7	C₁₉×#1742	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1738	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#137	—	2	4	no	—
12	C₂×C₁₉×#137	—	2	2	no	—
13	C₂×C₁₉×#137	C₄	1	8	yes	complemented
14	C₂×C₁₉×#137	C₂²	1	4	yes	—
15	C₂²×Q₁₆×C₁₉	—	2	1	no	—
16	C₂²×SD₁₆×C₁₉	—	2	1	no	—
17	C₁₉×#568	—	2	4	no	—
18	C₁₉×#568	—	2	4	no	—
19	C₂×C₁₉×#131	—	2	2	no	—
20	C₂×C₁₉×#131	C₂²	1	4	yes	—
21	C₂²×M₁₆×C₁₉	—	2	2	no	—
22	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
27	C₁₉×#419	—	2	1	no	—
28	C₁₉×#419	—	2	2	no	—
29	C₁₉×#419	—	2	2	no	—
30	C₁₉×#418	—	2	1	no	—
31	C₁₉×#417	C₂²	1	4	yes	—
32	C₁₉×#416	—	2	2	no	—
33	C₂×C₁₉×#103	C₂²	1	4	yes	complemented
34	C₂×C₁₉×#101	—	2	4	no	—
35	C₂×C₁₉×#101	C₂²	1	4	yes	complemented
36	C₁₉×#343	C₂²	1	4	yes	complemented
37	C₁₉×#341	C₂²	1	4	yes	complemented
38	C₂×#41×C₁₉	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	2	no	—
40	C₂×#41×C₁₉	—	2	2	no	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
43	C₂×#41×C₁₉	D₄	1	4	yes	—
44	C₂×#41×C₁₉	D₄	1	2	yes	—
45	C₂×#41×C₁₉	C₂³	1	2	yes	—
46	C₂²×Q₈×C₁₉	—	2	2	no	—
47	C₂²×Q₈×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	—	2	1	no	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂²×Q₈×C₁₉	—	2	1	no	—
51	C₂²×Q₈×C₁₉	—	2	1	no	—
52	C₂²×Q₈×C₁₉	—	2	2	no	—
53	C₂²×Q₈×C₁₉	—	2	2	no	—
54	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
55	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
57	C₂²×D₄×C₁₉	—	2	1	no	—
58	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	—	2	1	no	—
60	C₂³×C₄×C₁₉	—	2	1	no	—
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₁₉×#137	—	2	16	no	—
63	C₁₉×#137	—	2	8	no	—
64	C₁₉×#137	C₂×C₄	1	16	yes	—
65	C₂×Q₁₆×C₁₉	—	2	8	no	—
66	C₂×Q₁₆×C₁₉	—	2	4	no	—
67	C₂×SD₁₆×C₁₉	—	2	8	no	—
68	C₂×SD₁₆×C₁₉	—	2	4	no	—
69	C₁₉×#131	—	2	16	no	—
70	C₁₉×#131	—	2	8	no	—
71	C₁₉×#131	—	2	8	no	—
72	C₂×M₁₆×C₁₉	—	2	16	no	—
73	C₂×M₁₆×C₁₉	—	2	1	no	—
74	C₂×M₁₆×C₁₉	—	2	2	no	—
75	C₂×M₁₆×C₁₉	—	2	2	no	—
76	C₂×M₁₆×C₁₉	—	2	2	no	—
77	C₂×M₁₆×C₁₉	—	2	2	no	—
78	C₂×M₁₆×C₁₉	—	2	1	no	—
79	C₂×M₁₆×C₁₉	—	2	1	no	—
80	C₂×M₁₆×C₁₉	—	2	4	no	—
81	C₂×M₁₆×C₁₉	—	2	2	no	—
82	C₂×M₁₆×C₁₉	—	2	2	no	—
83	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
84	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
85	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
86	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
87	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
88	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
89	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
90	C₂²×C₈×C₁₉	—	2	1	no	—
91	C₂²×C₈×C₁₉	—	2	1	no	—
92	C₂²×C₈×C₁₉	—	2	4	no	—
93	C₂²×C₈×C₁₉	—	2	1	no	—
94	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
95	C₁₉×#117	—	2	1	no	—
96	C₁₉×#117	—	2	1	no	—
97	C₁₉×#117	—	2	1	no	—
98	C₁₉×#117	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₄²×C₁₉	—	2	1	no	—
102	C₁₉×#103	—	2	4	no	—
103	C₁₉×#103	—	2	8	no	—
104	C₁₉×#102	—	2	4	no	—
105	C₁₉×#101	—	2	8	no	—
106	C₂⁴×C₁₉	—	2	1	no	—
107	C₂⁴×C₁₉	#41	1	1	yes	characteristic
108	#41×C₁₉	—	2	4	no	—
109	#41×C₁₉	—	2	4	no	—
110	#41×C₁₉	—	2	4	no	—
111	#41×C₁₉	—	2	4	no	—
112	#41×C₁₉	—	2	4	no	—
113	#41×C₁₉	—	2	2	no	—
114	#41×C₁₉	—	2	2	no	—
115	#41×C₁₉	C₂²⋊C₄	1	8	yes	—
116	#41×C₁₉	C₂²×C₄	1	4	yes	—
117	#41×C₁₉	C₂×D₄	1	4	yes	—
118	C₂×Q₈×C₁₉	—	2	4	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	2	2	no	—
121	C₂×Q₈×C₁₉	—	2	2	no	—
122	C₂×Q₈×C₁₉	—	2	4	no	—
123	C₂×Q₈×C₁₉	—	2	4	no	—
124	C₂×Q₈×C₁₉	—	2	4	no	—
125	C₂×Q₈×C₁₉	—	2	4	no	—
126	C₂×Q₈×C₁₉	—	2	2	no	—
127	C₂×Q₈×C₁₉	—	2	2	no	—
128	C₂×Q₈×C₁₉	—	2	2	no	—
129	C₂×Q₈×C₁₉	—	2	2	no	—
130	C₂×Q₈×C₁₉	—	4	2	no	—
131	C₂×Q₈×C₁₉	—	4	2	no	—
132	C₂×Q₈×C₁₉	—	4	1	no	—
133	C₂×Q₈×C₁₉	—	4	1	no	—
134	C₂×Q₈×C₁₉	—	4	2	no	—
135	C₂×Q₈×C₁₉	—	4	2	no	—
136	C₂×Q₈×C₁₉	—	4	2	no	—
137	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
138	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
139	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
140	C₂×D₄×C₁₉	—	2	4	no	—
141	C₂×D₄×C₁₉	—	2	2	no	—
142	C₂×D₄×C₁₉	—	2	4	no	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	1	no	—
146	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
147	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	4	no	—
150	C₂²×C₄×C₁₉	—	2	4	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	4	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	4	1	no	—
157	C₂²×C₄×C₁₉	—	4	1	no	—
158	C₂²×C₄×C₁₉	—	4	2	no	—
159	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	#41	1	2	yes	—
168	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
169	Q₁₆×C₁₉	—	2	16	no	—
170	SD₁₆×C₁₉	—	2	16	no	—
171	M₁₆×C₁₉	—	2	16	no	—
172	M₁₆×C₁₉	—	2	4	no	—
173	M₁₆×C₁₉	—	2	4	no	—
174	M₁₆×C₁₉	—	2	4	no	—
175	M₁₆×C₁₉	—	2	4	no	—
176	M₁₆×C₁₉	—	2	2	no	—
177	M₁₆×C₁₉	—	2	2	no	—
178	M₁₆×C₁₉	—	2	2	no	—
179	M₁₆×C₁₉	—	2	2	no	—
180	M₁₆×C₁₉	—	4	2	no	—
181	M₁₆×C₁₉	C₂²×C₄	1	4	yes	—
182	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
183	C₂×C₈×C₁₉	—	2	16	no	—
184	C₂×C₈×C₁₉	—	2	4	no	—
185	C₂×C₈×C₁₉	—	2	4	no	—
186	C₂×C₈×C₁₉	—	2	2	no	—
187	C₂×C₈×C₁₉	—	2	2	no	—
188	C₂×C₈×C₁₉	—	2	2	no	—
189	C₂×C₈×C₁₉	—	2	2	no	—
190	C₂×C₈×C₁₉	—	2	2	no	—
191	C₂×C₈×C₁₉	—	4	2	no	—
192	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₂²⋊C₄×C₁₉	—	4	1	no	—
196	C₂²⋊C₄×C₁₉	—	4	1	no	—
197	C₄²×C₁₉	—	4	1	no	—
198	C₄²×C₁₉	—	4	1	no	—
199	#21006	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂³×C₁₉	—	2	2	no	—
201	C₂³×C₁₉	—	2	4	no	—
202	C₂³×C₁₉	—	4	2	no	—
203	C₂³×C₁₉	—	8	2	no	—
204	C₂³×C₁₉	C₄×D₄	1	2	yes	—
205	C₂³×C₁₉	#121	1	1	yes	characteristic
206	C₂³×C₁₉	#121	1	1	yes	characteristic
207	C₂³×C₁₉	#123	1	2	yes	—
208	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
209	Q₈×C₁₉	—	2	2	no	—
210	Q₈×C₁₉	—	2	4	no	—
211	Q₈×C₁₉	—	2	4	no	—
212	Q₈×C₁₉	—	2	4	no	—
213	Q₈×C₁₉	—	4	2	no	—
214	Q₈×C₁₉	—	4	2	no	—
215	Q₈×C₁₉	—	4	4	no	—
216	Q₈×C₁₉	—	4	4	no	—
217	Q₈×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
218	D₄×C₁₉	—	2	4	no	—
219	D₄×C₁₉	—	2	4	no	—
220	D₄×C₁₉	—	2	8	no	—
221	D₄×C₁₉	—	2	2	no	—
222	D₄×C₁₉	—	2	4	no	—
223	D₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	4	no	—
226	C₂×C₄×C₁₉	—	2	4	no	—
227	C₂×C₄×C₁₉	—	2	4	no	—
228	C₂×C₄×C₁₉	—	2	8	no	—
229	C₂×C₄×C₁₉	—	2	4	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	4	no	—
233	C₂×C₄×C₁₉	—	4	4	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	8	2	no	—
236	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
237	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
238	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
239	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
240	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
241	C₂×C₄×C₁₉	#120	1	2	yes	—
242	C₂×C₄×C₁₉	#120	1	2	yes	—
243	C₂×C₄×C₁₉	#121	1	2	yes	—
244	C₂×C₄×C₁₉	#121	1	2	yes	—
245	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#123	1	2	yes	—
248	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
254	C₈×C₁₉	—	2	4	no	—
255	C₈×C₁₉	—	2	4	no	—
256	C₈×C₁₉	—	2	4	no	—
257	C₈×C₁₉	—	4	2	no	—
258	C₂²×#137	C₂×C₁₉	1	1	yes	characteristic
259	C₂×#568	C₂×C₁₉	1	1	yes	characteristic
260	#2896	C₂×C₁₉	1	1	yes	characteristic
261	C₂×#419	C₂×C₁₉	1	1	yes	characteristic, complemented
262	C₂²×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1908	C₂×C₁₉	1	8	yes	complemented
264	#1742	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1738	C₂×C₁₉	1	1	yes	characteristic, complemented
266	C₂²×C₁₉	—	2	2	no	—
267	C₂²×C₁₉	—	2	2	no	—
268	C₂²×C₁₉	—	2	2	no	—
269	C₂²×C₁₉	—	2	4	no	—
270	C₂²×C₁₉	—	4	2	no	—
271	C₂²×C₁₉	—	4	2	no	—
272	C₂²×C₁₉	—	4	4	no	—
273	C₂²×C₁₉	—	8	4	no	—
274	C₂²×C₁₉	#386	1	2	yes	—
275	C₂²×C₁₉	#386	1	2	yes	—
276	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
277	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
278	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
279	C₄×C₁₉	—	2	4	no	—
280	C₄×C₁₉	—	4	4	no	—
281	C₄×C₁₉	—	8	2	no	—
282	C₄×C₁₉	#386	1	2	yes	—
283	C₄×C₁₉	#386	1	2	yes	—
284	C₄×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
285	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
286	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
287	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
288	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
289	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
290	C₂×#137	—	2	4	no	—
291	C₂×#137	—	2	2	no	—
292	C₂×#137	C₄×C₁₉	1	8	yes	complemented
293	C₂×#137	C₂²×C₁₉	1	4	yes	—
294	C₂²×Q₁₆	—	2	1	no	—
295	C₂²×SD₁₆	—	2	1	no	—
296	#568	—	2	4	no	—
297	#568	—	2	4	no	—
298	C₂×#131	—	2	2	no	—
299	C₂×#131	C₂²×C₁₉	1	4	yes	—
300	C₂²×M₁₆	—	2	2	no	—
301	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
302	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
303	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
304	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
305	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
306	#419	—	2	1	no	—
307	#419	—	2	2	no	—
308	#419	—	2	2	no	—
309	#418	—	2	1	no	—
310	#417	C₂²×C₁₉	1	4	yes	—
311	#416	—	2	2	no	—
312	C₂×#103	C₂²×C₁₉	1	4	yes	complemented
313	C₂×#101	—	2	4	no	—
314	C₂×#101	C₂²×C₁₉	1	4	yes	complemented
315	#343	C₂²×C₁₉	1	4	yes	complemented
316	#341	C₂²×C₁₉	1	4	yes	complemented
317	C₂×C₁₉	—	2	2	no	—
318	C₂×C₁₉	—	2	1	no	—
319	C₂×C₁₉	—	2	1	no	—
320	C₂×C₁₉	—	2	2	no	—
321	C₂×C₁₉	—	4	4	no	—
322	C₂×C₁₉	C₂×#386	1	1	yes	characteristic
323	C₂×C₁₉	#3069	1	2	yes	—
324	C₂×#41	—	2	1	no	—
325	C₂×#41	—	2	2	no	—
326	C₂×#41	—	2	2	no	—
327	C₂×#41	—	2	1	no	—
328	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
329	C₂×#41	D₄×C₁₉	1	4	yes	—
330	C₂×#41	D₄×C₁₉	1	2	yes	—
331	C₂×#41	C₂³×C₁₉	1	2	yes	—
332	C₂²×Q₈	—	2	2	no	—
333	C₂²×Q₈	—	2	1	no	—
334	C₂²×Q₈	—	2	1	no	—
335	C₂²×Q₈	—	2	1	no	—
336	C₂²×Q₈	—	2	2	no	—
337	C₂²×Q₈	—	2	1	no	—
338	C₂²×Q₈	—	2	1	no	—
339	C₂²×Q₈	—	2	2	no	—
340	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
341	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
342	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
345	C₂³×C₄	—	2	1	no	—
346	C₂³×C₄	—	2	1	no	—
347	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
348	#137	—	2	16	no	—
349	#137	—	2	8	no	—
350	#137	C₂×C₄×C₁₉	1	16	yes	—
351	C₂×Q₁₆	—	2	8	no	—
352	C₂×Q₁₆	—	2	4	no	—
353	C₂×SD₁₆	—	2	8	no	—
354	C₂×SD₁₆	—	2	4	no	—
355	#131	—	2	16	no	—
356	#131	—	2	8	no	—
357	#131	—	2	8	no	—
358	C₂×M₁₆	—	2	16	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	2	no	—
361	C₂×M₁₆	—	2	2	no	—
362	C₂×M₁₆	—	2	2	no	—
363	C₂×M₁₆	—	2	2	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	4	no	—
367	C₂×M₁₆	—	2	2	no	—
368	C₂×M₁₆	—	2	2	no	—
369	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	—
370	C₂×M₁₆	D₄×C₁₉	1	4	yes	—
371	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
372	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
373	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
374	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
375	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	4	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
381	#117	—	2	1	no	—
382	#117	—	2	1	no	—
383	#117	—	2	1	no	—
384	#117	—	2	1	no	—
385	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₄²	—	2	1	no	—
388	#103	—	2	4	no	—
389	#103	—	2	8	no	—
390	#102	—	2	4	no	—
391	#101	—	2	8	no	—
392	C₁₉	#21006	1	1	yes	characteristic, direct product factor, Sylow
393	C₂⁴	—	2	1	no	—
394	C₂⁴	#41×C₁₉	1	1	yes	characteristic
395	#41	—	2	4	no	—
396	#41	—	2	4	no	—
397	#41	—	2	4	no	—
398	#41	—	2	4	no	—
399	#41	—	2	4	no	—
400	#41	—	2	2	no	—
401	#41	—	2	2	no	—
402	#41	C₂²⋊C₄×C₁₉	1	8	yes	—
403	#41	C₂²×C₄×C₁₉	1	4	yes	—
404	#41	C₂×D₄×C₁₉	1	4	yes	—
405	C₂×Q₈	—	2	4	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	4	no	—
410	C₂×Q₈	—	2	4	no	—
411	C₂×Q₈	—	2	4	no	—
412	C₂×Q₈	—	2	4	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	4	2	no	—
418	C₂×Q₈	—	4	2	no	—
419	C₂×Q₈	—	4	2	no	—
420	C₂×Q₈	—	4	2	no	—
421	C₂×Q₈	—	4	1	no	—
422	C₂×Q₈	—	4	1	no	—
423	C₂×Q₈	—	4	2	no	—
424	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
425	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
426	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
434	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
447	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
448	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
453	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
454	C₂²×C₄	#41×C₁₉	1	2	yes	—
455	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
456	Q₁₆	—	2	16	no	—
457	SD₁₆	—	2	16	no	—
458	M₁₆	—	2	16	no	—
459	M₁₆	—	2	4	no	—
460	M₁₆	—	2	4	no	—
461	M₁₆	—	2	4	no	—
462	M₁₆	—	2	4	no	—
463	M₁₆	—	2	2	no	—
464	M₁₆	—	2	2	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	2	2	no	—
467	M₁₆	—	4	2	no	—
468	M₁₆	C₂²×C₄×C₁₉	1	4	yes	—
469	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
470	C₂×C₈	—	2	16	no	—
471	C₂×C₈	—	2	4	no	—
472	C₂×C₈	—	2	4	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	4	2	no	—
479	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₂²⋊C₄	—	4	1	no	—
484	C₄²	—	4	1	no	—
485	C₄²	—	4	1	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	8	2	no	—
490	C₂³	C₄×D₄×C₁₉	1	2	yes	—
491	C₂³	C₁₉×#121	1	1	yes	characteristic
492	C₂³	C₁₉×#121	1	1	yes	characteristic
493	C₂³	C₁₉×#123	1	2	yes	—
494	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
495	Q₈	—	2	4	no	—
496	Q₈	—	2	2	no	—
497	Q₈	—	2	4	no	—
498	Q₈	—	2	4	no	—
499	Q₈	—	4	4	no	—
500	Q₈	—	4	4	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	4	2	no	—
503	Q₈	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
504	D₄	—	2	8	no	—
505	D₄	—	2	4	no	—
506	D₄	—	2	4	no	—
507	D₄	—	2	4	no	—
508	D₄	—	2	2	no	—
509	D₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	8	2	no	—
522	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
523	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
524	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
525	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
526	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
527	C₂×C₄	C₁₉×#120	1	2	yes	—
528	C₂×C₄	C₁₉×#120	1	2	yes	—
529	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
530	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
531	C₂×C₄	C₁₉×#121	1	2	yes	—
532	C₂×C₄	C₁₉×#121	1	2	yes	—
533	C₂×C₄	C₁₉×#123	1	2	yes	—
534	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
536	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
538	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
539	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
540	C₈	—	2	4	no	—
541	C₈	—	2	4	no	—
542	C₈	—	2	4	no	—
543	C₈	—	4	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	8	4	no	—
552	C₂²	C₁₉×#386	1	2	yes	—
553	C₂²	C₁₉×#386	1	2	yes	—
554	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
555	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
556	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
557	C₄	—	2	4	no	—
558	C₄	—	4	4	no	—
559	C₄	—	8	2	no	—
560	C₄	C₁₉×#386	1	2	yes	—
561	C₄	C₁₉×#386	1	2	yes	—
562	C₄	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
563	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
564	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
565	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
566	C₂	—	2	2	no	—
567	C₂	—	2	2	no	—
568	C₂	—	2	1	no	—
569	C₂	—	2	1	no	—
570	C₂	—	4	4	no	—
571	C₂	C₂×C₁₉×#386	1	1	yes	characteristic
572	C₂	C₁₉×#3069	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₂×C₁₉×#419	C₂	semidirect
5. C₂²×C₁₉×#101	C₂	semidirect
6. C₁₉×#1908	C₂	semidirect
7. C₁₉×#1742	C₂	semidirect
8. C₁₉×#1738	C₂	semidirect
13. C₂×C₁₉×#137	C₄	semidirect
33. C₂×C₁₉×#103	C₂²	semidirect
35. C₂×C₁₉×#101	C₂²	semidirect
36. C₁₉×#343	C₂²	semidirect
37. C₁₉×#341	C₂²	semidirect
199. #21006	C₁₉	direct (N × H)
261. C₂×#419	C₂×C₁₉	semidirect
262. C₂²×#101	C₂×C₁₉	semidirect
263. #1908	C₂×C₁₉	semidirect
264. #1742	C₂×C₁₉	semidirect
265. #1738	C₂×C₁₉	semidirect
292. C₂×#137	C₄×C₁₉	semidirect
312. C₂×#103	C₂²×C₁₉	semidirect
314. C₂×#101	C₂²×C₁₉	semidirect
315. #343	C₂²×C₁₉	semidirect
316. #341	C₂²×C₁₉	semidirect
392. C₁₉	#21006	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#137	2
C₂×C₁₉×#568	2
C₁₉×#2896	2
C₂×C₁₉×#419	2
C₂²×C₁₉×#101	2
C₁₉×#1908	2
C₁₉×#1742	2
C₁₉×#1738	2
#21006	19

Subgroups — C19×#21006 #18026965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21006 #18026965