Subgroups — C₁₉×#24492 #18030451

Order 4864.

1198 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#418	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2433	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2347	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2067	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2041	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1982	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1926	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1786	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#127	C₂²	1	2	yes	—
15	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#120	—	2	2	no	—
17	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₁₉×#482	—	2	4	no	—
19	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
22	C₁₉×#418	—	2	4	no	—
23	C₂×C₁₉×#102	C₂²	1	2	yes	—
24	C₂×C₁₉×#102	C₂²	1	2	yes	—
25	C₂×C₁₉×#102	C₂²	1	2	yes	—
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
30	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₁₉×#392	—	2	1	no	—
32	C₁₉×#392	—	2	1	no	—
33	C₁₉×#390	C₂²	1	2	yes	—
34	C₁₉×#389	C₂²	1	2	yes	complemented
35	C₁₉×#388	—	2	2	no	—
36	C₁₉×#383	—	2	1	no	—
37	C₁₉×#380	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
40	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#340	C₂²	1	2	yes	complemented
42	C₁₉×#336	C₂²	1	2	yes	complemented
43	C₂⁵×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	—	2	4	no	—
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	—	2	2	no	—
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	—	2	2	no	—
49	C₂²×D₄×C₁₉	—	2	2	no	—
50	C₂²×D₄×C₁₉	—	2	2	no	—
51	C₂²×D₄×C₁₉	—	4	2	no	—
52	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₁₉	—	2	2	no	—
56	C₂×M₁₆×C₁₉	—	4	2	no	—
57	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₁₉×#127	—	2	4	no	—
61	C₁₉×#127	—	4	2	no	—
62	C₁₉×#121	—	2	2	no	—
63	C₁₉×#121	—	2	2	no	—
64	C₁₉×#120	—	4	8	no	—
65	C₁₉×#117	—	2	2	no	—
66	C₁₉×#117	D₄	1	4	yes	complemented
67	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
78	C₂×C₄²×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	—	2	2	no	—
80	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
81	C₁₉×#107	—	2	2	no	—
82	C₁₉×#106	—	2	2	no	—
83	C₁₉×C₄⋊C₈	—	4	2	no	—
84	C₁₉×#102	—	2	4	no	—
85	C₁₉×#102	—	2	4	no	—
86	C₁₉×#102	—	2	4	no	—
87	C₁₉×#102	—	2	2	no	—
88	C₁₉×#102	—	2	2	no	—
89	C₁₉×#102	—	4	2	no	—
90	C₁₉×#102	—	4	2	no	—
91	C₁₉×C₂²⋊C₈	—	2	2	no	—
92	C₁₉×#95	—	2	1	no	—
93	C₁₉×#95	—	2	2	no	—
94	C₁₉×#95	—	2	2	no	—
95	C₁₉×#95	D₄	1	1	yes	characteristic
96	C₁₉×#95	D₄	1	1	yes	characteristic
97	C₂⁴×C₁₉	—	2	2	no	—
98	C₂⁴×C₁₉	—	2	1	no	—
99	C₂⁴×C₁₉	—	4	4	no	—
100	C₂⁴×C₁₉	—	4	4	no	—
101	C₂⁴×C₁₉	—	4	2	no	—
102	C₂⁴×C₁₉	—	8	1	no	—
103	C₂⁴×C₁₉	—	8	1	no	—
104	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₁₉	—	2	8	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	2	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	4	8	no	—
116	C₂×D₄×C₁₉	—	4	4	no	—
117	C₂×D₄×C₁₉	—	4	4	no	—
118	C₂×D₄×C₁₉	—	4	4	no	—
119	C₂×D₄×C₁₉	—	4	4	no	—
120	C₂×D₄×C₁₉	—	4	4	no	—
121	C₂×D₄×C₁₉	—	4	4	no	—
122	C₂×D₄×C₁₉	—	4	2	no	—
123	C₂×D₄×C₁₉	—	4	2	no	—
124	C₂×D₄×C₁₉	—	4	4	no	—
125	C₂×D₄×C₁₉	—	8	2	no	—
126	C₂×D₄×C₁₉	—	8	2	no	—
127	C₂×D₄×C₁₉	#41	1	4	yes	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₉	#41	1	2	yes	—
139	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
140	M₁₆×C₁₉	—	4	4	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	2	1	no	—
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	—	2	2	no	—
145	C₂×C₈×C₁₉	—	2	2	no	—
146	C₂×C₈×C₁₉	—	2	2	no	—
147	C₂×C₈×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	4	4	no	—
155	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
156	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
157	C₂²⋊C₄×C₁₉	—	2	4	no	—
158	C₂²⋊C₄×C₁₉	—	2	4	no	—
159	C₂²⋊C₄×C₁₉	—	4	4	no	—
160	C₂²⋊C₄×C₁₉	—	4	2	no	—
161	C₂²⋊C₄×C₁₉	—	4	4	no	—
162	C₂²⋊C₄×C₁₉	—	8	1	no	—
163	C₄²×C₁₉	—	2	4	no	—
164	C₄²×C₁₉	—	2	2	no	—
165	C₄²×C₁₉	—	2	2	no	—
166	C₄²×C₁₉	—	8	2	no	—
167	#24492	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	2	2	no	—
170	C₂³×C₁₉	—	2	1	no	—
171	C₂³×C₁₉	—	2	1	no	—
172	C₂³×C₁₉	—	2	4	no	—
173	C₂³×C₁₉	—	4	8	no	—
174	C₂³×C₁₉	—	4	2	no	—
175	C₂³×C₁₉	—	4	2	no	—
176	C₂³×C₁₉	—	4	2	no	—
177	C₂³×C₁₉	—	4	2	no	—
178	C₂³×C₁₉	—	4	2	no	—
179	C₂³×C₁₉	—	4	2	no	—
180	C₂³×C₁₉	—	4	1	no	—
181	C₂³×C₁₉	—	4	2	no	—
182	C₂³×C₁₉	—	4	2	no	—
183	C₂³×C₁₉	—	4	1	no	—
184	C₂³×C₁₉	—	4	1	no	—
185	C₂³×C₁₉	—	8	4	no	—
186	C₂³×C₁₉	—	8	4	no	—
187	C₂³×C₁₉	—	8	8	no	—
188	C₂³×C₁₉	—	8	8	no	—
189	C₂³×C₁₉	#121	1	2	yes	—
190	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
191	D₄×C₁₉	—	2	4	no	—
192	D₄×C₁₉	—	2	4	no	—
193	D₄×C₁₉	—	4	8	no	—
194	D₄×C₁₉	—	4	1	no	—
195	D₄×C₁₉	—	4	2	no	—
196	D₄×C₁₉	—	4	1	no	—
197	D₄×C₁₉	—	4	2	no	—
198	D₄×C₁₉	—	4	2	no	—
199	D₄×C₁₉	—	8	8	no	—
200	D₄×C₁₉	—	8	8	no	—
201	D₄×C₁₉	—	8	4	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	#121	1	2	yes	—
222	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
223	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
225	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
227	C₈×C₁₉	—	4	1	no	—
228	C₈×C₁₉	—	4	1	no	—
229	C₈×C₁₉	—	4	2	no	—
230	C₂×#482	C₂×C₁₉	1	1	yes	characteristic, complemented
231	C₂×#418	C₂×C₁₉	1	1	yes	characteristic, complemented
232	#2433	C₂×C₁₉	1	1	yes	characteristic
233	#2347	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#2067	C₂×C₁₉	1	2	yes	complemented
235	#2041	C₂×C₁₉	1	2	yes	complemented
236	#1982	C₂×C₁₉	1	2	yes	complemented
237	#1926	C₂×C₁₉	1	2	yes	complemented
238	#1895	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#1851	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#1786	C₂×C₁₉	1	1	yes	characteristic, complemented
241	C₂²×C₁₉	—	2	2	no	—
242	C₂²×C₁₉	—	2	2	no	—
243	C₂²×C₁₉	—	2	2	no	—
244	C₂²×C₁₉	—	4	2	no	—
245	C₂²×C₁₉	—	4	2	no	—
246	C₂²×C₁₉	—	4	4	no	—
247	C₂²×C₁₉	—	4	4	no	—
248	C₂²×C₁₉	—	4	4	no	—
249	C₂²×C₁₉	—	8	16	no	—
250	C₂²×C₁₉	—	8	2	no	—
251	C₂²×C₁₉	—	8	2	no	—
252	C₂²×C₁₉	—	8	2	no	—
253	C₂²×C₁₉	—	8	2	no	—
254	C₂²×C₁₉	—	8	1	no	—
255	C₂²×C₁₉	—	8	1	no	—
256	C₂²×C₁₉	—	8	1	no	—
257	C₂²×C₁₉	—	8	2	no	—
258	C₂²×C₁₉	—	8	2	no	—
259	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
260	C₂²×C₁₉	#546	1	2	yes	—
261	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
262	C₂²×C₁₉	#576	1	1	yes	characteristic
263	C₂²×C₁₉	#577	1	1	yes	characteristic
264	C₄×C₁₉	—	2	2	no	—
265	C₄×C₁₉	—	2	4	no	—
266	C₄×C₁₉	—	4	2	no	—
267	C₄×C₁₉	—	4	2	no	—
268	C₄×C₁₉	—	4	2	no	—
269	C₄×C₁₉	—	8	1	no	—
270	C₄×C₁₉	—	8	2	no	—
271	C₄×C₁₉	#525	1	1	yes	characteristic
272	C₄×C₁₉	#535	1	1	yes	characteristic
273	C₄×C₁₉	#551	1	2	yes	—
274	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
275	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×#127	C₂²×C₁₉	1	2	yes	—
277	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
278	C₂×#120	—	2	2	no	—
279	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
280	#482	—	2	4	no	—
281	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
282	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic, complemented
283	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
284	#418	—	2	4	no	—
285	C₂×#102	C₂²×C₁₉	1	2	yes	—
286	C₂×#102	C₂²×C₁₉	1	2	yes	—
287	C₂×#102	C₂²×C₁₉	1	2	yes	—
288	C₂×#102	C₂²×C₁₉	1	2	yes	—
289	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
290	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
291	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
292	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
293	#392	—	2	1	no	—
294	#392	—	2	1	no	—
295	#390	C₂²×C₁₉	1	2	yes	—
296	#389	C₂²×C₁₉	1	2	yes	complemented
297	#388	—	2	2	no	—
298	#383	—	2	1	no	—
299	#380	C₂²×C₁₉	1	1	yes	characteristic
300	C₄×C₄⋊C₄	—	2	1	no	—
301	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
302	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
303	#340	C₂²×C₁₉	1	2	yes	complemented
304	#336	C₂²×C₁₉	1	2	yes	complemented
305	C₂×C₁₉	—	4	2	no	—
306	C₂×C₁₉	—	8	4	no	—
307	C₂×C₁₉	—	16	1	no	—
308	C₂×C₁₉	#2411	1	1	yes	characteristic
309	C₂×C₁₉	#3038	1	1	yes	characteristic
310	C₂×C₁₉	#3045	1	1	yes	characteristic
311	C₂×C₁₉	#3318	1	2	yes	—
312	C₂×C₁₉	#3324	1	2	yes	—
313	C₂⁵	—	2	1	no	—
314	C₂²×D₄	—	2	4	no	—
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	—	2	2	no	—
319	C₂²×D₄	—	2	2	no	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	—	4	2	no	—
322	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
323	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
324	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
325	C₂×M₁₆	—	2	2	no	—
326	C₂×M₁₆	—	4	2	no	—
327	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
328	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
330	#127	—	2	4	no	—
331	#127	—	4	2	no	—
332	#121	—	2	2	no	—
333	#121	—	2	2	no	—
334	#120	—	4	8	no	—
335	#117	—	2	2	no	—
336	#117	D₄×C₁₉	1	4	yes	complemented
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	—	2	2	no	—
350	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
351	#107	—	2	2	no	—
352	#106	—	2	2	no	—
353	C₄⋊C₈	—	4	2	no	—
354	#102	—	2	4	no	—
355	#102	—	2	4	no	—
356	#102	—	2	4	no	—
357	#102	—	2	2	no	—
358	#102	—	2	2	no	—
359	#102	—	4	2	no	—
360	#102	—	4	2	no	—
361	C₂²⋊C₈	—	2	2	no	—
362	#95	—	2	1	no	—
363	#95	—	2	2	no	—
364	#95	—	2	2	no	—
365	#95	D₄×C₁₉	1	1	yes	characteristic
366	#95	D₄×C₁₉	1	1	yes	characteristic
367	C₁₉	#24492	1	1	yes	characteristic, direct product factor, Sylow
368	C₂⁴	—	2	2	no	—
369	C₂⁴	—	2	1	no	—
370	C₂⁴	—	4	4	no	—
371	C₂⁴	—	4	4	no	—
372	C₂⁴	—	4	2	no	—
373	C₂⁴	—	8	1	no	—
374	C₂⁴	—	8	1	no	—
375	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
376	C₂×D₄	—	2	8	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	4	8	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂×D₄	—	4	4	no	—
389	C₂×D₄	—	4	4	no	—
390	C₂×D₄	—	4	4	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	—	4	4	no	—
393	C₂×D₄	—	4	2	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	—	4	4	no	—
396	C₂×D₄	—	8	2	no	—
397	C₂×D₄	—	8	2	no	—
398	C₂×D₄	#41×C₁₉	1	4	yes	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
408	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
409	C₂²×C₄	#41×C₁₉	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
411	M₁₆	—	4	4	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	4	4	no	—
426	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
427	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
428	C₂²⋊C₄	—	2	4	no	—
429	C₂²⋊C₄	—	2	4	no	—
430	C₂²⋊C₄	—	4	4	no	—
431	C₂²⋊C₄	—	4	2	no	—
432	C₂²⋊C₄	—	4	4	no	—
433	C₂²⋊C₄	—	8	1	no	—
434	C₄²	—	2	4	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	8	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	4	8	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	1	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	1	no	—
455	C₂³	—	8	4	no	—
456	C₂³	—	8	4	no	—
457	C₂³	—	8	8	no	—
458	C₂³	—	8	8	no	—
459	C₂³	C₁₉×#121	1	2	yes	—
460	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
461	D₄	—	2	4	no	—
462	D₄	—	2	4	no	—
463	D₄	—	4	8	no	—
464	D₄	—	4	1	no	—
465	D₄	—	4	2	no	—
466	D₄	—	4	1	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	8	8	no	—
470	D₄	—	8	8	no	—
471	D₄	—	8	4	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	C₁₉×#121	1	2	yes	—
492	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
493	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
494	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
495	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
496	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
497	C₈	—	4	1	no	—
498	C₈	—	4	2	no	—
499	C₈	—	4	1	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	8	16	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	2	no	—
513	C₂²	—	8	1	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	1	no	—
516	C₂²	—	8	2	no	—
517	C₂²	—	8	2	no	—
518	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
519	C₂²	C₁₉×#546	1	2	yes	—
520	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
521	C₂²	C₁₉×#576	1	1	yes	characteristic
522	C₂²	C₁₉×#577	1	1	yes	characteristic
523	C₄	—	2	2	no	—
524	C₄	—	2	4	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	8	1	no	—
529	C₄	—	8	2	no	—
530	C₄	C₁₉×#525	1	1	yes	characteristic
531	C₄	C₁₉×#535	1	1	yes	characteristic
532	C₄	C₁₉×#551	1	2	yes	—
533	C₂	—	4	2	no	—
534	C₂	—	8	4	no	—
535	C₂	—	16	1	no	—
536	C₂	C₁₉×#2411	1	1	yes	characteristic
537	C₂	C₁₉×#3038	1	1	yes	characteristic
538	C₂	C₁₉×#3045	1	1	yes	characteristic
539	C₂	C₁₉×#3318	1	2	yes	—
540	C₂	C₁₉×#3324	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2433	C₂
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
1. C₂×C₁₉×#482	C₂	semidirect
2. C₂×C₁₉×#418	C₂	semidirect
4. C₁₉×#2347	C₂	semidirect
5. C₁₉×#2067	C₂	semidirect
6. C₁₉×#2041	C₂	semidirect
7. C₁₉×#1982	C₂	semidirect
8. C₁₉×#1926	C₂	semidirect
9. C₁₉×#1895	C₂	semidirect
10. C₁₉×#1851	C₂	semidirect
11. C₁₉×#1786	C₂	semidirect
19. C₂×C₁₉×#107	C₂²	semidirect
20. C₂×C₁₉×#106	C₂²	semidirect
21. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
27. C₂×C₁₉×#102	C₂²	semidirect
28. C₂×C₁₉×#102	C₂²	semidirect
29. C₂×C₁₉×#102	C₂²	semidirect
34. C₁₉×#389	C₂²	semidirect
39. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
41. C₁₉×#340	C₂²	semidirect
42. C₁₉×#336	C₂²	semidirect
66. C₁₉×#117	D₄	semidirect
167. #24492	C₁₉	direct (N × H)
230. C₂×#482	C₂×C₁₉	semidirect
231. C₂×#418	C₂×C₁₉	semidirect
233. #2347	C₂×C₁₉	semidirect
234. #2067	C₂×C₁₉	semidirect
235. #2041	C₂×C₁₉	semidirect
236. #1982	C₂×C₁₉	semidirect
237. #1926	C₂×C₁₉	semidirect
238. #1895	C₂×C₁₉	semidirect
239. #1851	C₂×C₁₉	semidirect
240. #1786	C₂×C₁₉	semidirect
281. C₂×#107	C₂²×C₁₉	semidirect
282. C₂×#106	C₂²×C₁₉	semidirect
283. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
289. C₂×#102	C₂²×C₁₉	semidirect
290. C₂×#102	C₂²×C₁₉	semidirect
291. C₂×#102	C₂²×C₁₉	semidirect
296. #389	C₂²×C₁₉	semidirect
301. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
303. #340	C₂²×C₁₉	semidirect
304. #336	C₂²×C₁₉	semidirect
336. #117	D₄×C₁₉	semidirect
367. C₁₉	#24492	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×#482	2
C₂×C₁₉×#418	2
C₁₉×#2433	2
C₁₉×#2347	2
C₁₉×#2067	2
C₁₉×#2041	2
C₁₉×#1982	2
C₁₉×#1926	2
C₁₉×#1895	2
C₁₉×#1851	2
C₁₉×#1786	2
#24492	19

Subgroups — C19×#24492 #18030451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24492 #18030451