Subgroups — C₁₉×#24546 #18030505

Order 4864.

996 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#452	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#417	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2502	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2341	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2071	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2055	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1894	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1878	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1851	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1823	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1803	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#452	—	2	4	no	—
20	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
21	C₁₉×#417	—	2	4	no	—
22	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#103	C₂²	1	2	yes	—
24	C₂×C₁₉×#103	C₂²	1	2	yes	—
25	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₉×#398	—	2	1	no	—
29	C₁₉×#398	—	2	1	no	—
30	C₁₉×#391	C₂²	1	2	yes	—
31	C₁₉×#390	—	2	2	no	—
32	C₁₉×#390	C₂²	1	2	yes	—
33	C₁₉×#385	—	2	2	no	—
34	C₁₉×#384	C₂²	1	2	yes	—
35	C₁₉×#380	—	2	1	no	—
36	C₁₉×#380	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#336	C₂²	1	2	yes	—
43	C₂×#41×C₁₉	—	2	2	no	—
44	C₂×#41×C₁₉	—	2	4	no	—
45	C₂×#41×C₁₉	—	4	2	no	—
46	C₂×#41×C₁₉	D₄	1	4	yes	—
47	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	—	2	1	no	—
53	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂×Q₁₆×C₁₉	—	2	2	no	—
55	C₂×Q₁₆×C₁₉	—	2	4	no	—
56	C₂×SD₁₆×C₁₉	—	2	2	no	—
57	C₂×SD₁₆×C₁₉	—	4	2	no	—
58	C₂×M₁₆×C₁₉	—	2	2	no	—
59	C₂×M₁₆×C₁₉	—	4	2	no	—
60	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
63	C₁₉×C₂²⋊Q₈	—	2	2	no	—
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₄×Q₈×C₁₉	—	2	4	no	—
66	C₄×Q₈×C₁₉	—	4	2	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
82	C₂×C₄²×C₁₉	—	2	2	no	—
83	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
84	C₁₉×C₄⋊C₈	—	4	2	no	—
85	C₁₉×#103	—	2	4	no	—
86	C₁₉×#103	—	2	2	no	—
87	C₁₉×#103	—	4	2	no	—
88	C₁₉×#102	—	2	4	no	—
89	C₁₉×#102	—	2	2	no	—
90	C₁₉×C₂²⋊C₈	—	2	2	no	—
91	C₁₉×#95	—	2	1	no	—
92	C₁₉×#95	—	2	2	no	—
93	C₁₉×#95	—	2	2	no	—
94	C₁₉×#95	D₄	1	1	yes	characteristic
95	C₁₉×#95	D₄	1	1	yes	characteristic
96	C₂⁴×C₁₉	—	2	1	no	—
97	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
98	#41×C₁₉	—	2	8	no	—
99	#41×C₁₉	—	4	4	no	—
100	#41×C₁₉	—	4	8	no	—
101	C₂×Q₈×C₁₉	—	2	1	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	2	1	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
108	C₂×Q₈×C₁₉	#41	1	4	yes	—
109	C₂×D₄×C₁₉	—	2	4	no	—
110	C₂×D₄×C₁₉	—	2	2	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	4	4	no	—
114	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	4	4	no	—
124	C₂²×C₄×C₁₉	—	4	2	no	—
125	C₂²×C₄×C₁₉	—	8	1	no	—
126	C₂²×C₄×C₁₉	—	8	1	no	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₉	#41	1	2	yes	—
132	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
133	Q₁₆×C₁₉	—	4	4	no	—
134	SD₁₆×C₁₉	—	4	4	no	—
135	M₁₆×C₁₉	—	4	4	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	1	no	—
138	C₂×C₈×C₁₉	—	2	1	no	—
139	C₂×C₈×C₁₉	—	2	2	no	—
140	C₂×C₈×C₁₉	—	2	2	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	4	4	no	—
150	C₄⋊C₄×C₁₉	—	4	2	no	—
151	C₄⋊C₄×C₁₉	—	4	2	no	—
152	C₄⋊C₄×C₁₉	—	8	2	no	—
153	C₄⋊C₄×C₁₉	—	8	2	no	—
154	C₂²⋊C₄×C₁₉	—	2	4	no	—
155	C₂²⋊C₄×C₁₉	—	4	2	no	—
156	C₂²⋊C₄×C₁₉	—	4	4	no	—
157	C₂²⋊C₄×C₁₉	—	8	2	no	—
158	C₂²⋊C₄×C₁₉	—	8	1	no	—
159	C₄²×C₁₉	—	2	2	no	—
160	C₄²×C₁₉	—	2	2	no	—
161	C₄²×C₁₉	—	4	4	no	—
162	#24546	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂³×C₁₉	—	2	2	no	—
164	C₂³×C₁₉	—	2	2	no	—
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	—	2	1	no	—
167	C₂³×C₁₉	—	2	2	no	—
168	C₂³×C₁₉	—	4	2	no	—
169	C₂³×C₁₉	—	4	2	no	—
170	C₂³×C₁₉	—	4	1	no	—
171	C₂³×C₁₉	—	4	1	no	—
172	C₂³×C₁₉	#121	1	2	yes	—
173	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₁₉	—	2	2	no	—
175	Q₈×C₁₉	—	2	4	no	—
176	Q₈×C₁₉	—	4	1	no	—
177	Q₈×C₁₉	—	4	1	no	—
178	Q₈×C₁₉	—	4	2	no	—
179	Q₈×C₁₉	#123	1	4	yes	—
180	D₄×C₁₉	—	2	2	no	—
181	D₄×C₁₉	—	2	2	no	—
182	D₄×C₁₉	—	4	8	no	—
183	D₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	4	8	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	8	4	no	—
208	C₂×C₄×C₁₉	#121	1	2	yes	—
209	C₂×C₄×C₁₉	#137	1	4	yes	—
210	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
212	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
214	C₈×C₁₉	—	4	1	no	—
215	C₈×C₁₉	—	4	2	no	—
216	C₈×C₁₉	—	4	1	no	—
217	C₂×#452	C₂×C₁₉	1	1	yes	characteristic
218	C₂×#417	C₂×C₁₉	1	1	yes	characteristic
219	#2502	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#2341	C₂×C₁₉	1	1	yes	characteristic
221	#2071	C₂×C₁₉	1	2	yes	complemented
222	#2055	C₂×C₁₉	1	2	yes	complemented
223	#1894	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#1878	C₂×C₁₉	1	2	yes	complemented
225	#1851	C₂×C₁₉	1	1	yes	characteristic, complemented
226	#1823	C₂×C₁₉	1	1	yes	characteristic, complemented
227	#1803	C₂×C₁₉	1	2	yes	complemented
228	C₂²×C₁₉	—	2	2	no	—
229	C₂²×C₁₉	—	2	2	no	—
230	C₂²×C₁₉	—	2	2	no	—
231	C₂²×C₁₉	—	4	2	no	—
232	C₂²×C₁₉	—	4	2	no	—
233	C₂²×C₁₉	—	4	2	no	—
234	C₂²×C₁₉	—	4	2	no	—
235	C₂²×C₁₉	—	4	2	no	—
236	C₂²×C₁₉	—	8	2	no	—
237	C₂²×C₁₉	—	8	2	no	—
238	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
239	C₂²×C₁₉	#546	1	2	yes	—
240	C₂²×C₁₉	C₂×#137	1	2	yes	—
241	C₂²×C₁₉	#576	1	1	yes	characteristic
242	C₂²×C₁₉	#577	1	1	yes	characteristic
243	C₄×C₁₉	—	2	2	no	—
244	C₄×C₁₉	—	2	4	no	—
245	C₄×C₁₉	—	2	4	no	—
246	C₄×C₁₉	—	4	2	no	—
247	C₄×C₁₉	—	8	2	no	—
248	C₄×C₁₉	—	8	1	no	—
249	C₄×C₁₉	—	8	1	no	—
250	C₄×C₁₉	—	8	2	no	—
251	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
252	C₄×C₁₉	#534	1	1	yes	characteristic
253	C₄×C₁₉	#551	1	2	yes	—
254	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
255	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
256	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
257	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
258	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
259	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
260	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
261	#452	—	2	4	no	—
262	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
263	#417	—	2	4	no	—
264	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×#103	C₂²×C₁₉	1	2	yes	—
266	C₂×#103	C₂²×C₁₉	1	2	yes	—
267	C₂×#102	C₂²×C₁₉	1	2	yes	—
268	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
269	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
270	#398	—	2	1	no	—
271	#398	—	2	1	no	—
272	#391	C₂²×C₁₉	1	2	yes	—
273	#390	—	2	2	no	—
274	#390	C₂²×C₁₉	1	2	yes	—
275	#385	—	2	2	no	—
276	#384	C₂²×C₁₉	1	2	yes	—
277	#380	—	2	1	no	—
278	#380	C₂²×C₁₉	1	1	yes	characteristic
279	C₄×C₂²⋊C₄	—	2	1	no	—
280	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
281	#340	C₂²×C₁₉	1	2	yes	—
282	#340	C₂²×C₁₉	1	2	yes	—
283	#340	C₂²×C₁₉	1	2	yes	—
284	#336	C₂²×C₁₉	1	2	yes	—
285	C₂×C₁₉	—	4	2	no	—
286	C₂×C₁₉	—	8	2	no	—
287	C₂×C₁₉	#2412	1	1	yes	characteristic
288	C₂×C₁₉	#3039	1	1	yes	characteristic
289	C₂×C₁₉	#3045	1	1	yes	characteristic
290	C₂×C₁₉	#3316	1	2	yes	—
291	C₂×C₁₉	#3333	1	2	yes	—
292	C₂×#41	—	2	2	no	—
293	C₂×#41	—	2	4	no	—
294	C₂×#41	—	4	2	no	—
295	C₂×#41	D₄×C₁₉	1	4	yes	—
296	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
297	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
298	C₂²×D₄	—	2	1	no	—
299	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
300	C₂³×C₄	—	2	1	no	—
301	C₂³×C₄	—	2	1	no	—
302	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
303	C₂×Q₁₆	—	2	2	no	—
304	C₂×Q₁₆	—	2	4	no	—
305	C₂×SD₁₆	—	2	2	no	—
306	C₂×SD₁₆	—	4	2	no	—
307	C₂×M₁₆	—	2	2	no	—
308	C₂×M₁₆	—	4	2	no	—
309	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
310	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
312	C₂²⋊Q₈	—	2	2	no	—
313	C₂²⋊Q₈	—	2	2	no	—
314	C₄×Q₈	—	2	4	no	—
315	C₄×Q₈	—	4	2	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
331	C₂×C₄²	—	2	2	no	—
332	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
333	C₄⋊C₈	—	4	2	no	—
334	#103	—	2	4	no	—
335	#103	—	2	2	no	—
336	#103	—	4	2	no	—
337	#102	—	2	4	no	—
338	#102	—	2	2	no	—
339	C₂²⋊C₈	—	2	2	no	—
340	#95	—	2	1	no	—
341	#95	—	2	2	no	—
342	#95	—	2	2	no	—
343	#95	D₄×C₁₉	1	1	yes	characteristic
344	#95	D₄×C₁₉	1	1	yes	characteristic
345	C₁₉	#24546	1	1	yes	characteristic, direct product factor, Sylow
346	C₂⁴	—	2	1	no	—
347	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
348	#41	—	2	8	no	—
349	#41	—	4	4	no	—
350	#41	—	4	8	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
358	C₂×Q₈	#41×C₁₉	1	4	yes	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	4	4	no	—
364	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	8	1	no	—
376	C₂²×C₄	—	8	1	no	—
377	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
381	C₂²×C₄	#41×C₁₉	1	2	yes	—
382	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
383	Q₁₆	—	4	4	no	—
384	SD₁₆	—	4	4	no	—
385	M₁₆	—	4	4	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	4	4	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₄⋊C₄	—	8	2	no	—
403	C₄⋊C₄	—	8	2	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	4	2	no	—
406	C₂²⋊C₄	—	4	4	no	—
407	C₂²⋊C₄	—	8	2	no	—
408	C₂²⋊C₄	—	8	1	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	4	4	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	1	no	—
421	C₂³	C₁₉×#121	1	2	yes	—
422	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
423	Q₈	—	2	2	no	—
424	Q₈	—	2	4	no	—
425	Q₈	—	4	1	no	—
426	Q₈	—	4	1	no	—
427	Q₈	—	4	2	no	—
428	Q₈	C₁₉×#123	1	4	yes	—
429	D₄	—	2	2	no	—
430	D₄	—	2	2	no	—
431	D₄	—	4	8	no	—
432	D₄	—	4	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	8	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	8	4	no	—
457	C₂×C₄	C₁₉×#121	1	2	yes	—
458	C₂×C₄	C₁₉×#137	1	4	yes	—
459	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
460	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
461	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
462	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
463	C₈	—	4	1	no	—
464	C₈	—	4	2	no	—
465	C₈	—	4	1	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
477	C₂²	C₁₉×#546	1	2	yes	—
478	C₂²	C₂×C₁₉×#137	1	2	yes	—
479	C₂²	C₁₉×#576	1	1	yes	characteristic
480	C₂²	C₁₉×#577	1	1	yes	characteristic
481	C₄	—	2	2	no	—
482	C₄	—	2	4	no	—
483	C₄	—	2	4	no	—
484	C₄	—	4	2	no	—
485	C₄	—	8	1	no	—
486	C₄	—	8	2	no	—
487	C₄	—	8	1	no	—
488	C₄	—	8	2	no	—
489	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
490	C₄	C₁₉×#534	1	1	yes	characteristic
491	C₄	C₁₉×#551	1	2	yes	—
492	C₂	—	4	2	no	—
493	C₂	—	8	2	no	—
494	C₂	C₁₉×#2412	1	1	yes	characteristic
495	C₂	C₁₉×#3039	1	1	yes	characteristic
496	C₂	C₁₉×#3045	1	1	yes	characteristic
497	C₂	C₁₉×#3316	1	2	yes	—
498	C₂	C₁₉×#3333	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₂²⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#2502	C₂	semidirect
5. C₁₉×#2071	C₂	semidirect
6. C₁₉×#2055	C₂	semidirect
7. C₁₉×#1894	C₂	semidirect
8. C₁₉×#1878	C₂	semidirect
9. C₁₉×#1851	C₂	semidirect
10. C₁₉×#1823	C₂	semidirect
11. C₁₉×#1803	C₂	semidirect
162. #24546	C₁₉	direct (N × H)
219. #2502	C₂×C₁₉	semidirect
221. #2071	C₂×C₁₉	semidirect
222. #2055	C₂×C₁₉	semidirect
223. #1894	C₂×C₁₉	semidirect
224. #1878	C₂×C₁₉	semidirect
225. #1851	C₂×C₁₉	semidirect
226. #1823	C₂×C₁₉	semidirect
227. #1803	C₂×C₁₉	semidirect
345. C₁₉	#24546	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#452	2
C₂×C₁₉×#417	2
C₁₉×#2502	2
C₁₉×#2341	2
C₁₉×#2071	2
C₁₉×#2055	2
C₁₉×#1894	2
C₁₉×#1878	2
C₁₉×#1851	2
C₁₉×#1823	2
C₁₉×#1803	2
#24546	19

Subgroups — C19×#24546 #18030505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24546 #18030505