Subgroups — C₁₉×#24573 #18030532

Order 4864.

936 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#481	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3006	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#417	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2880	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2079	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2051	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1907	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1900	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1855	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1821	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1815	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#131	C₂²	1	2	yes	—
16	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#481	—	2	1	no	—
20	C₁₉×#481	—	2	1	no	—
21	C₁₉×#481	—	2	2	no	—
22	C₁₉×#449	—	2	1	no	—
23	C₁₉×#449	—	2	1	no	—
24	C₁₉×#448	—	2	1	no	—
25	C₁₉×#447	—	2	1	no	—
26	C₂×C₁₉×#108	C₂²	1	2	yes	complemented
27	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
28	C₁₉×#417	—	2	1	no	—
29	C₁₉×#417	—	2	1	no	—
30	C₁₉×#417	C₂²	1	2	yes	—
31	C₁₉×#417	C₂²	1	1	yes	characteristic
32	C₁₉×#417	C₂²	1	1	yes	characteristic
33	C₁₉×#417	C₂²	1	2	yes	—
34	C₂×C₁₉×#103	—	2	1	no	—
35	C₂×C₁₉×#102	—	2	1	no	—
36	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
37	C₂×C₁₉×#100	C₂²	1	2	yes	complemented
38	C₁₉×#408	—	2	2	no	—
39	C₁₉×#408	C₂²	1	2	yes	—
40	C₁₉×#407	—	2	1	no	—
41	C₁₉×#407	C₂²	1	1	yes	characteristic
42	C₁₉×#407	C₂²	1	1	yes	characteristic
43	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
44	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₁₉×#343	C₂²	1	2	yes	complemented
46	C₁₉×#343	C₂²	1	2	yes	complemented
47	C₁₉×#343	C₂²	1	2	yes	complemented
48	C₁₉×#341	C₂²	1	2	yes	complemented
49	C₂×#41×C₁₉	—	2	1	no	—
50	C₂×#41×C₁₉	—	2	1	no	—
51	C₂×#41×C₁₉	—	2	4	no	—
52	C₂×#41×C₁₉	—	4	2	no	—
53	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
54	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
55	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
58	C₂²×D₄×C₁₉	—	2	1	no	—
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	—	2	1	no	—
63	C₂³×C₄×C₁₉	—	2	1	no	—
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
66	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
67	C₂×SD₁₆×C₁₉	—	2	1	no	—
68	C₂×SD₁₆×C₁₉	—	2	1	no	—
69	C₂×D₈×C₁₉	—	2	1	no	—
70	C₂×D₈×C₁₉	—	2	1	no	—
71	C₁₉×#131	—	2	4	no	—
72	C₁₉×#131	—	4	2	no	—
73	C₂×M₁₆×C₁₉	—	2	1	no	—
74	C₂×M₁₆×C₁₉	—	2	2	no	—
75	C₂×M₁₆×C₁₉	—	4	2	no	—
76	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
78	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
79	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₉	—	2	1	no	—
81	C₂²×C₈×C₁₉	—	2	2	no	—
82	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
83	C₁₉×#121	—	2	1	no	—
84	C₁₉×#121	—	2	1	no	—
85	C₁₉×#121	—	2	1	no	—
86	C₁₉×#121	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₁₉×#108	—	4	2	no	—
96	C₁₉×#106	—	2	2	no	—
97	C₁₉×#106	—	2	2	no	—
98	C₁₉×#103	—	2	2	no	—
99	C₁₉×#103	—	2	2	no	—
100	C₁₉×#103	—	2	1	no	—
101	C₁₉×#103	—	2	1	no	—
102	C₁₉×#102	—	2	2	no	—
103	C₁₉×#102	—	2	2	no	—
104	C₁₉×#102	—	2	1	no	—
105	C₁₉×#102	—	2	1	no	—
106	C₁₉×#102	—	2	2	no	—
107	C₁₉×#102	—	2	2	no	—
108	C₁₉×#100	—	4	2	no	—
109	C₁₉×C₂²⋊C₈	—	2	1	no	—
110	C₁₉×C₂²⋊C₈	—	2	1	no	—
111	C₁₉×C₂²⋊C₈	—	2	1	no	—
112	C₁₉×C₂²⋊C₈	—	2	1	no	—
113	C₁₉×C₂²⋊C₈	—	2	2	no	—
114	C₁₉×C₂²⋊C₈	—	2	2	no	—
115	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
116	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
117	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
118	C₂⁴×C₁₉	—	2	1	no	—
119	C₂⁴×C₁₉	—	2	1	no	—
120	C₂⁴×C₁₉	#41	1	1	yes	characteristic
121	#41×C₁₉	—	2	2	no	—
122	#41×C₁₉	—	2	2	no	—
123	#41×C₁₉	—	2	2	no	—
124	#41×C₁₉	—	2	2	no	—
125	#41×C₁₉	—	2	2	no	—
126	#41×C₁₉	—	4	4	no	—
127	#41×C₁₉	—	4	1	no	—
128	#41×C₁₉	—	4	1	no	—
129	#41×C₁₉	—	4	4	no	—
130	#41×C₁₉	#41	1	4	yes	—
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	—	2	2	no	—
133	C₂×Q₈×C₁₉	—	4	1	no	—
134	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	2	1	no	—
139	C₂×D₄×C₁₉	—	2	1	no	—
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	—	2	1	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	4	1	no	—
147	C₂×D₄×C₁₉	—	4	4	no	—
148	C₂×D₄×C₁₉	—	4	1	no	—
149	C₂×D₄×C₁₉	—	4	1	no	—
150	C₂×D₄×C₁₉	—	8	2	no	—
151	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	4	4	no	—
163	C₂²×C₄×C₁₉	—	4	1	no	—
164	C₂²×C₄×C₁₉	—	4	1	no	—
165	C₂²×C₄×C₁₉	—	8	2	no	—
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
172	SD₁₆×C₁₉	—	4	2	no	—
173	SD₁₆×C₁₉	—	4	2	no	—
174	D₈×C₁₉	—	4	2	no	—
175	D₈×C₁₉	—	4	2	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	—	2	2	no	—
181	M₁₆×C₁₉	—	2	2	no	—
182	M₁₆×C₁₉	—	4	4	no	—
183	M₁₆×C₁₉	—	4	2	no	—
184	C₂×C₈×C₁₉	—	2	2	no	—
185	C₂×C₈×C₁₉	—	2	2	no	—
186	C₂×C₈×C₁₉	—	2	2	no	—
187	C₂×C₈×C₁₉	—	2	2	no	—
188	C₂×C₈×C₁₉	—	2	1	no	—
189	C₂×C₈×C₁₉	—	2	1	no	—
190	C₂×C₈×C₁₉	—	4	4	no	—
191	C₂×C₈×C₁₉	—	4	2	no	—
192	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
193	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	2	2	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	4	1	no	—
199	C₄⋊C₄×C₁₉	—	4	1	no	—
200	C₂²⋊C₄×C₁₉	—	4	1	no	—
201	C₂²⋊C₄×C₁₉	—	4	1	no	—
202	#24573	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂³×C₁₉	—	2	1	no	—
204	C₂³×C₁₉	—	2	2	no	—
205	C₂³×C₁₉	—	2	2	no	—
206	C₂³×C₁₉	—	2	1	no	—
207	C₂³×C₁₉	—	4	1	no	—
208	C₂³×C₁₉	—	4	2	no	—
209	C₂³×C₁₉	—	4	2	no	—
210	C₂³×C₁₉	—	4	1	no	—
211	C₂³×C₁₉	—	4	2	no	—
212	C₂³×C₁₉	—	8	1	no	—
213	C₂³×C₁₉	—	8	1	no	—
214	C₂³×C₁₉	—	8	1	no	—
215	C₂³×C₁₉	#121	1	1	yes	characteristic
216	C₂³×C₁₉	#121	1	1	yes	characteristic
217	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
218	Q₈×C₁₉	—	2	1	no	—
219	Q₈×C₁₉	—	2	1	no	—
220	Q₈×C₁₉	—	2	1	no	—
221	Q₈×C₁₉	—	4	2	no	—
222	Q₈×C₁₉	#123	1	2	yes	—
223	D₄×C₁₉	—	2	4	no	—
224	D₄×C₁₉	—	2	1	no	—
225	D₄×C₁₉	—	2	1	no	—
226	D₄×C₁₉	—	2	1	no	—
227	D₄×C₁₉	—	4	2	no	—
228	D₄×C₁₉	—	4	2	no	—
229	D₄×C₁₉	—	4	2	no	—
230	D₄×C₁₉	—	4	2	no	—
231	D₄×C₁₉	—	4	1	no	—
232	D₄×C₁₉	—	4	1	no	—
233	D₄×C₁₉	—	4	2	no	—
234	D₄×C₁₉	—	8	2	no	—
235	D₄×C₁₉	—	8	2	no	—
236	D₄×C₁₉	#123	1	2	yes	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	4	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	4	2	no	—
250	C₂×C₄×C₁₉	—	4	2	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	8	2	no	—
254	C₂×C₄×C₁₉	—	8	2	no	—
255	C₂×C₄×C₁₉	—	8	2	no	—
256	C₂×C₄×C₁₉	—	8	1	no	—
257	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
258	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
262	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
263	C₈×C₁₉	—	2	2	no	—
264	C₈×C₁₉	—	2	2	no	—
265	C₈×C₁₉	—	4	1	no	—
266	C₈×C₁₉	—	4	2	no	—
267	C₈×C₁₉	—	4	1	no	—
268	C₈×C₁₉	—	4	2	no	—
269	C₂×#481	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#3006	C₂×C₁₉	1	1	yes	characteristic
271	C₂×#417	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#2880	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#2079	C₂×C₁₉	1	2	yes	complemented
274	#2051	C₂×C₁₉	1	2	yes	complemented
275	#1907	C₂×C₁₉	1	2	yes	complemented
276	#1900	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1855	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1821	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1815	C₂×C₁₉	1	2	yes	complemented
280	C₂²×C₁₉	—	2	1	no	—
281	C₂²×C₁₉	—	2	1	no	—
282	C₂²×C₁₉	—	2	1	no	—
283	C₂²×C₁₉	—	2	1	no	—
284	C₂²×C₁₉	—	2	1	no	—
285	C₂²×C₁₉	—	2	2	no	—
286	C₂²×C₁₉	—	2	1	no	—
287	C₂²×C₁₉	—	2	1	no	—
288	C₂²×C₁₉	—	4	4	no	—
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	—	4	1	no	—
293	C₂²×C₁₉	—	4	1	no	—
294	C₂²×C₁₉	—	8	4	no	—
295	C₂²×C₁₉	—	8	1	no	—
296	C₂²×C₁₉	—	8	1	no	—
297	C₂²×C₁₉	—	8	1	no	—
298	C₂²×C₁₉	—	16	2	no	—
299	C₂²×C₁₉	#471	1	2	yes	—
300	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
301	C₂²×C₁₉	#551	1	2	yes	—
302	C₄×C₁₉	—	2	1	no	—
303	C₄×C₁₉	—	2	1	no	—
304	C₄×C₁₉	—	2	2	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	8	1	no	—
307	C₄×C₁₉	—	8	2	no	—
308	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
309	C₄×C₁₉	#534	1	1	yes	characteristic
310	C₄×C₁₉	#546	1	2	yes	—
311	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
312	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
313	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×#131	C₂²×C₁₉	1	2	yes	—
315	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
317	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
318	#481	—	2	1	no	—
319	#481	—	2	1	no	—
320	#481	—	2	2	no	—
321	#449	—	2	1	no	—
322	#449	—	2	1	no	—
323	#448	—	2	1	no	—
324	#447	—	2	1	no	—
325	C₂×#108	C₂²×C₁₉	1	2	yes	complemented
326	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
327	#417	—	2	1	no	—
328	#417	—	2	1	no	—
329	#417	C₂²×C₁₉	1	2	yes	—
330	#417	C₂²×C₁₉	1	1	yes	characteristic
331	#417	C₂²×C₁₉	1	2	yes	—
332	#417	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×#103	—	2	1	no	—
334	C₂×#102	—	2	1	no	—
335	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
336	C₂×#100	C₂²×C₁₉	1	2	yes	complemented
337	#408	—	2	2	no	—
338	#408	C₂²×C₁₉	1	2	yes	—
339	#407	—	2	1	no	—
340	#407	C₂²×C₁₉	1	1	yes	characteristic
341	#407	C₂²×C₁₉	1	1	yes	characteristic
342	C₂×C₂²⋊C₈	—	2	1	no	—
343	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
344	#343	C₂²×C₁₉	1	2	yes	complemented
345	#343	C₂²×C₁₉	1	2	yes	complemented
346	#343	C₂²×C₁₉	1	2	yes	complemented
347	#341	C₂²×C₁₉	1	2	yes	complemented
348	C₂×C₁₉	—	2	2	no	—
349	C₂×C₁₉	—	2	2	no	—
350	C₂×C₁₉	—	4	1	no	—
351	C₂×C₁₉	—	4	2	no	—
352	C₂×C₁₉	—	8	1	no	—
353	C₂×C₁₉	—	16	1	no	—
354	C₂×C₁₉	#2412	1	1	yes	characteristic
355	C₂×C₁₉	C₂×#471	1	1	yes	characteristic
356	C₂×C₁₉	#3068	1	1	yes	characteristic
357	C₂×#41	—	2	1	no	—
358	C₂×#41	—	2	1	no	—
359	C₂×#41	—	2	4	no	—
360	C₂×#41	—	4	2	no	—
361	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
362	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
363	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
364	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
365	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
366	C₂²×D₄	—	2	1	no	—
367	C₂²×D₄	—	2	1	no	—
368	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
369	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
373	AGL(1,ℤ/8)	—	2	4	no	—
374	AGL(1,ℤ/8)	—	4	2	no	—
375	C₂×SD₁₆	—	2	1	no	—
376	C₂×SD₁₆	—	2	1	no	—
377	C₂×D₈	—	2	1	no	—
378	C₂×D₈	—	2	1	no	—
379	#131	—	2	4	no	—
380	#131	—	4	2	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	2	no	—
383	C₂×M₁₆	—	4	2	no	—
384	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
385	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
386	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
387	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
388	C₂²×C₈	—	2	1	no	—
389	C₂²×C₈	—	2	2	no	—
390	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
391	#121	—	2	1	no	—
392	#121	—	2	1	no	—
393	#121	—	2	1	no	—
394	#121	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	#108	—	4	2	no	—
404	#106	—	2	2	no	—
405	#106	—	2	2	no	—
406	#103	—	2	2	no	—
407	#103	—	2	2	no	—
408	#103	—	2	1	no	—
409	#103	—	2	1	no	—
410	#102	—	2	2	no	—
411	#102	—	2	2	no	—
412	#102	—	2	1	no	—
413	#102	—	2	1	no	—
414	#102	—	2	2	no	—
415	#102	—	2	2	no	—
416	#100	—	4	2	no	—
417	C₂²⋊C₈	—	2	1	no	—
418	C₂²⋊C₈	—	2	1	no	—
419	C₂²⋊C₈	—	2	1	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	2	no	—
422	C₂²⋊C₈	—	2	2	no	—
423	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
424	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
425	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
426	C₁₉	#24573	1	1	yes	characteristic, direct product factor, Sylow
427	C₂⁴	—	2	1	no	—
428	C₂⁴	—	2	1	no	—
429	C₂⁴	#41×C₁₉	1	1	yes	characteristic
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	2	2	no	—
435	#41	—	4	4	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	4	4	no	—
439	#41	#41×C₁₉	1	4	yes	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	4	1	no	—
443	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	—	4	1	no	—
459	C₂×D₄	—	8	2	no	—
460	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	4	4	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	4	1	no	—
474	C₂²×C₄	—	8	2	no	—
475	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
481	SD₁₆	—	4	2	no	—
482	SD₁₆	—	4	2	no	—
483	D₈	—	4	2	no	—
484	D₈	—	4	2	no	—
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	2	2	no	—
489	M₁₆	—	2	2	no	—
490	M₁₆	—	2	2	no	—
491	M₁₆	—	4	4	no	—
492	M₁₆	—	4	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	4	4	no	—
500	C₂×C₈	—	4	2	no	—
501	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
502	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	4	1	no	—
508	C₄⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	1	no	—
519	C₂³	—	4	2	no	—
520	C₂³	—	8	1	no	—
521	C₂³	—	8	1	no	—
522	C₂³	—	8	1	no	—
523	C₂³	C₁₉×#121	1	1	yes	characteristic
524	C₂³	C₁₉×#121	1	1	yes	characteristic
525	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
526	Q₈	—	2	1	no	—
527	Q₈	—	2	1	no	—
528	Q₈	—	2	1	no	—
529	Q₈	—	4	2	no	—
530	Q₈	C₁₉×#123	1	2	yes	—
531	D₄	—	2	4	no	—
532	D₄	—	2	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	2	1	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	2	no	—
542	D₄	—	8	2	no	—
543	D₄	—	8	2	no	—
544	D₄	C₁₉×#123	1	2	yes	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	8	2	no	—
562	C₂×C₄	—	8	2	no	—
563	C₂×C₄	—	8	2	no	—
564	C₂×C₄	—	8	1	no	—
565	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
566	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
569	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
570	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
571	C₈	—	2	2	no	—
572	C₈	—	2	2	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	2	no	—
575	C₈	—	4	1	no	—
576	C₈	—	4	2	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	8	4	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	16	2	no	—
596	C₂²	C₁₉×#471	1	2	yes	—
597	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
598	C₂²	C₁₉×#551	1	2	yes	—
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	2	no	—
602	C₄	—	4	1	no	—
603	C₄	—	8	1	no	—
604	C₄	—	8	2	no	—
605	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
606	C₄	C₁₉×#534	1	1	yes	characteristic
607	C₄	C₁₉×#546	1	2	yes	—
608	C₂	—	2	2	no	—
609	C₂	—	2	2	no	—
610	C₂	—	4	1	no	—
611	C₂	—	4	2	no	—
612	C₂	—	8	1	no	—
613	C₂	—	16	1	no	—
614	C₂	C₁₉×#2412	1	1	yes	characteristic
615	C₂	C₂×C₁₉×#471	1	1	yes	characteristic
616	C₂	C₁₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3006	C₂
LCS	G ▷ C₂²×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
1. C₂×C₁₉×#481	C₂	semidirect
3. C₂×C₁₉×#417	C₂	semidirect
4. C₁₉×#2880	C₂	semidirect
5. C₁₉×#2079	C₂	semidirect
6. C₁₉×#2051	C₂	semidirect
7. C₁₉×#1907	C₂	semidirect
8. C₁₉×#1900	C₂	semidirect
9. C₁₉×#1855	C₂	semidirect
10. C₁₉×#1821	C₂	semidirect
11. C₁₉×#1815	C₂	semidirect
26. C₂×C₁₉×#108	C₂²	semidirect
27. C₂×C₁₉×#106	C₂²	semidirect
36. C₂×C₁₉×#102	C₂²	semidirect
37. C₂×C₁₉×#100	C₂²	semidirect
45. C₁₉×#343	C₂²	semidirect
46. C₁₉×#343	C₂²	semidirect
47. C₁₉×#343	C₂²	semidirect
48. C₁₉×#341	C₂²	semidirect
202. #24573	C₁₉	direct (N × H)
269. C₂×#481	C₂×C₁₉	semidirect
271. C₂×#417	C₂×C₁₉	semidirect
272. #2880	C₂×C₁₉	semidirect
273. #2079	C₂×C₁₉	semidirect
274. #2051	C₂×C₁₉	semidirect
275. #1907	C₂×C₁₉	semidirect
276. #1900	C₂×C₁₉	semidirect
277. #1855	C₂×C₁₉	semidirect
278. #1821	C₂×C₁₉	semidirect
279. #1815	C₂×C₁₉	semidirect
325. C₂×#108	C₂²×C₁₉	semidirect
326. C₂×#106	C₂²×C₁₉	semidirect
335. C₂×#102	C₂²×C₁₉	semidirect
336. C₂×#100	C₂²×C₁₉	semidirect
344. #343	C₂²×C₁₉	semidirect
345. #343	C₂²×C₁₉	semidirect
346. #343	C₂²×C₁₉	semidirect
347. #341	C₂²×C₁₉	semidirect
426. C₁₉	#24573	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×#481	2
C₁₉×#3006	2
C₂×C₁₉×#417	2
C₁₉×#2880	2
C₁₉×#2079	2
C₁₉×#2051	2
C₁₉×#1907	2
C₁₉×#1900	2
C₁₉×#1855	2
C₁₉×#1821	2
C₁₉×#1815	2
#24573	19

Subgroups — C19×#24573 #18030532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24573 #18030532