Subgroups — C₁₉×#24500 #18030459

Order 4864.

1270 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#447	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2854	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2067	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2054	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1970	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1934	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1852	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×D₈×C₁₉	C₂²	1	2	yes	—
14	C₂×C₁₉×#123	—	2	1	no	—
15	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
18	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#447	—	2	4	no	—
21	C₁₉×#431	—	2	4	no	—
22	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
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	2	yes	complemented
28	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	complemented
31	C₁₉×#390	—	2	1	no	—
32	C₁₉×#390	—	2	1	no	—
33	C₁₉×#390	C₂²	1	2	yes	—
34	C₁₉×#390	C₂²	1	2	yes	—
35	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#389	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#389	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#388	—	2	1	no	—
40	C₁₉×#388	—	2	1	no	—
41	C₁₉×#386	—	2	1	no	—
42	C₁₉×#380	C₂²	1	1	yes	characteristic
43	C₁₉×#340	C₂²	1	2	yes	complemented
44	C₁₉×#340	C₂²	1	2	yes	complemented
45	C₂⁵×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	—	2	4	no	—
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	—	2	1	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	—	2	1	no	—
55	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×D₈×C₁₉	—	2	4	no	—
59	C₂×D₈×C₁₉	—	2	4	no	—
60	C₂×D₈×C₁₉	—	4	2	no	—
61	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
63	C₁₉×#123	—	4	4	no	—
64	C₁₉×#121	—	2	2	no	—
65	C₁₉×#121	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
86	C₂×C₄²×C₁₉	—	2	2	no	—
87	C₂×C₄²×C₁₉	—	2	2	no	—
88	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
92	C₁₉×#107	—	4	2	no	—
93	C₁₉×C₄⋊C₈	—	2	4	no	—
94	C₁₉×#102	—	2	4	no	—
95	C₁₉×#102	—	2	4	no	—
96	C₁₉×#102	—	4	2	no	—
97	C₁₉×#102	—	4	2	no	—
98	C₁₉×C₂²⋊C₈	—	2	2	no	—
99	C₁₉×C₂²⋊C₈	D₄	1	4	yes	—
100	C₄×C₈×C₁₉	—	2	4	no	—
101	C₁₉×#95	—	2	1	no	—
102	C₁₉×#95	—	2	1	no	—
103	C₁₉×#95	—	2	1	no	—
104	C₂⁴×C₁₉	—	2	4	no	—
105	C₂⁴×C₁₉	—	2	2	no	—
106	C₂⁴×C₁₉	—	2	1	no	—
107	C₂⁴×C₁₉	—	4	2	no	—
108	C₂⁴×C₁₉	—	4	2	no	—
109	C₂⁴×C₁₉	—	4	2	no	—
110	C₂⁴×C₁₉	—	4	2	no	—
111	C₂⁴×C₁₉	—	4	2	no	—
112	C₂⁴×C₁₉	—	4	2	no	—
113	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂×D₄×C₁₉	—	2	4	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	1	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	1	no	—
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	4	8	no	—
125	C₂×D₄×C₁₉	—	4	8	no	—
126	C₂×D₄×C₁₉	—	4	2	no	—
127	C₂×D₄×C₁₉	—	4	2	no	—
128	C₂×D₄×C₁₉	—	4	2	no	—
129	C₂×D₄×C₁₉	—	4	2	no	—
130	C₂×D₄×C₁₉	—	4	2	no	—
131	C₂×D₄×C₁₉	#41	1	4	yes	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	4	1	no	—
143	C₂²×C₄×C₁₉	—	4	2	no	—
144	C₂²×C₄×C₁₉	—	4	2	no	—
145	C₂²×C₄×C₁₉	—	4	2	no	—
146	C₂²×C₄×C₁₉	D₈	1	4	yes	complemented
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	#41	1	2	yes	—
154	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
155	D₈×C₁₉	—	4	8	no	—
156	C₂×C₈×C₁₉	—	2	2	no	—
157	C₂×C₈×C₁₉	—	2	2	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	4	2	no	—
169	C₄⋊C₄×C₁₉	—	4	2	no	—
170	C₄⋊C₄×C₁₉	—	4	2	no	—
171	C₂²⋊C₄×C₁₉	—	4	2	no	—
172	C₂²⋊C₄×C₁₉	—	4	4	no	—
173	C₂²⋊C₄×C₁₉	—	4	2	no	—
174	C₂²⋊C₄×C₁₉	—	4	2	no	—
175	C₂²⋊C₄×C₁₉	—	4	4	no	—
176	C₂²⋊C₄×C₁₉	—	4	4	no	—
177	C₂²⋊C₄×C₁₉	—	4	2	no	—
178	C₂²⋊C₄×C₁₉	—	4	2	no	—
179	C₂²⋊C₄×C₁₉	—	4	2	no	—
180	C₂²⋊C₄×C₁₉	—	4	4	no	—
181	C₄²×C₁₉	—	2	2	no	—
182	C₄²×C₁₉	—	2	2	no	—
183	C₄²×C₁₉	—	2	1	no	—
184	C₄²×C₁₉	—	2	1	no	—
185	C₄²×C₁₉	—	2	1	no	—
186	C₄²×C₁₉	—	2	1	no	—
187	#24500	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂³×C₁₉	—	2	1	no	—
189	C₂³×C₁₉	—	2	1	no	—
190	C₂³×C₁₉	—	2	1	no	—
191	C₂³×C₁₉	—	2	1	no	—
192	C₂³×C₁₉	—	2	4	no	—
193	C₂³×C₁₉	—	4	8	no	—
194	C₂³×C₁₉	—	4	8	no	—
195	C₂³×C₁₉	—	4	8	no	—
196	C₂³×C₁₉	—	4	2	no	—
197	C₂³×C₁₉	—	4	2	no	—
198	C₂³×C₁₉	—	4	2	no	—
199	C₂³×C₁₉	—	4	2	no	—
200	C₂³×C₁₉	—	4	2	no	—
201	C₂³×C₁₉	—	4	2	no	—
202	C₂³×C₁₉	—	4	1	no	—
203	C₂³×C₁₉	—	4	1	no	—
204	C₂³×C₁₉	—	4	1	no	—
205	C₂³×C₁₉	—	4	1	no	—
206	C₂³×C₁₉	—	4	1	no	—
207	C₂³×C₁₉	—	4	1	no	—
208	C₂³×C₁₉	—	4	1	no	—
209	C₂³×C₁₉	—	8	4	no	—
210	C₂³×C₁₉	—	8	4	no	—
211	C₂³×C₁₉	—	8	4	no	—
212	C₂³×C₁₉	—	8	4	no	—
213	C₂³×C₁₉	#121	1	2	yes	—
214	C₂³×C₁₉	C₂×D₈	1	2	yes	—
215	C₂³×C₁₉	#135	1	2	yes	—
216	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
217	D₄×C₁₉	—	2	4	no	—
218	D₄×C₁₉	—	2	4	no	—
219	D₄×C₁₉	—	4	8	no	—
220	D₄×C₁₉	—	4	2	no	—
221	D₄×C₁₉	—	4	2	no	—
222	D₄×C₁₉	—	4	2	no	—
223	D₄×C₁₉	—	4	2	no	—
224	D₄×C₁₉	—	8	4	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	8	no	—
234	C₂×C₄×C₁₉	—	2	4	no	—
235	C₂×C₄×C₁₉	—	2	4	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	4	4	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	2	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	8	4	no	—
253	C₂×C₄×C₁₉	#121	1	2	yes	—
254	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
255	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
256	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
257	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
259	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
260	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
261	C₈×C₁₉	—	2	4	no	—
262	C₈×C₁₉	—	4	2	no	—
263	C₂×#447	C₂×C₁₉	1	1	yes	characteristic
264	C₂×#431	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#2854	C₂×C₁₉	1	1	yes	characteristic, complemented
266	C₂×#390	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#2067	C₂×C₁₉	1	2	yes	complemented
268	#2054	C₂×C₁₉	1	2	yes	complemented
269	#1970	C₂×C₁₉	1	2	yes	complemented
270	#1934	C₂×C₁₉	1	2	yes	complemented
271	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1852	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1786	C₂×C₁₉	1	1	yes	characteristic, complemented
274	C₂²×C₁₉	—	2	2	no	—
275	C₂²×C₁₉	—	2	2	no	—
276	C₂²×C₁₉	—	2	2	no	—
277	C₂²×C₁₉	—	2	2	no	—
278	C₂²×C₁₉	—	2	2	no	—
279	C₂²×C₁₉	—	2	2	no	—
280	C₂²×C₁₉	—	4	4	no	—
281	C₂²×C₁₉	—	4	4	no	—
282	C₂²×C₁₉	—	4	4	no	—
283	C₂²×C₁₉	—	8	16	no	—
284	C₂²×C₁₉	—	8	2	no	—
285	C₂²×C₁₉	—	8	2	no	—
286	C₂²×C₁₉	—	8	2	no	—
287	C₂²×C₁₉	—	8	2	no	—
288	C₂²×C₁₉	—	8	1	no	—
289	C₂²×C₁₉	—	8	1	no	—
290	C₂²×C₁₉	—	8	1	no	—
291	C₂²×C₁₉	—	8	1	no	—
292	C₂²×C₁₉	—	8	1	no	—
293	C₂²×C₁₉	—	8	1	no	—
294	C₂²×C₁₉	—	8	1	no	—
295	C₂²×C₁₉	#466	1	4	yes	—
296	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
297	C₂²×C₁₉	#525	1	1	yes	characteristic
298	C₂²×C₁₉	#535	1	1	yes	characteristic
299	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
300	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
301	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
302	C₂²×C₁₉	#575	1	1	yes	characteristic
303	C₄×C₁₉	—	2	2	no	—
304	C₄×C₁₉	—	2	2	no	—
305	C₄×C₁₉	—	2	2	no	—
306	C₄×C₁₉	—	2	2	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	8	1	no	—
309	C₄×C₁₉	—	8	1	no	—
310	C₄×C₁₉	—	8	2	no	—
311	C₄×C₁₉	—	8	1	no	—
312	C₄×C₁₉	#546	1	2	yes	—
313	C₄×C₁₉	#551	1	2	yes	—
314	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
315	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
316	C₂×#123	—	2	1	no	—
317	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
318	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
319	C₂²×C₂²⋊C₄	—	2	1	no	—
320	C₂²×C₂²⋊C₄	—	2	1	no	—
321	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
322	#447	—	2	4	no	—
323	#431	—	2	4	no	—
324	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
325	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
326	C₂×#102	C₂²×C₁₉	1	2	yes	—
327	C₂×#102	C₂²×C₁₉	1	2	yes	—
328	C₂×#102	C₂²×C₁₉	1	2	yes	—
329	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
330	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
331	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	complemented
333	#390	—	2	1	no	—
334	#390	—	2	1	no	—
335	#390	C₂²×C₁₉	1	2	yes	—
336	#390	C₂²×C₁₉	1	2	yes	—
337	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
338	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	#389	C₂²×C₁₉	1	1	yes	characteristic, complemented
340	#389	C₂²×C₁₉	1	1	yes	characteristic, complemented
341	#388	—	2	1	no	—
342	#388	—	2	1	no	—
343	#386	—	2	1	no	—
344	#380	C₂²×C₁₉	1	1	yes	characteristic
345	#340	C₂²×C₁₉	1	2	yes	complemented
346	#340	C₂²×C₁₉	1	2	yes	complemented
347	C₂×C₁₉	—	2	4	no	—
348	C₂×C₁₉	—	8	4	no	—
349	C₂×C₁₉	—	16	1	no	—
350	C₂×C₁₉	#2411	1	1	yes	characteristic
351	C₂×C₁₉	C₂×#466	1	1	yes	characteristic
352	C₂×C₁₉	#3055	1	1	yes	characteristic
353	C₂×C₁₉	#3100	1	1	yes	characteristic
354	C₂×C₁₉	#3105	1	1	yes	characteristic
355	C₂×C₁₉	#3205	1	1	yes	characteristic
356	C₂×C₁₉	#3211	1	1	yes	characteristic
357	C₂⁵	—	2	1	no	—
358	C₂²×D₄	—	2	4	no	—
359	C₂²×D₄	—	2	1	no	—
360	C₂²×D₄	—	2	1	no	—
361	C₂²×D₄	—	2	2	no	—
362	C₂²×D₄	—	2	2	no	—
363	C₂²×D₄	—	4	2	no	—
364	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
365	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
366	C₂³×C₄	—	2	1	no	—
367	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
368	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
370	C₂×D₈	—	2	4	no	—
371	C₂×D₈	—	2	4	no	—
372	C₂×D₈	—	4	2	no	—
373	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
374	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
375	#123	—	4	4	no	—
376	#121	—	2	2	no	—
377	#121	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	4	2	no	—
382	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	—	2	2	no	—
390	C₂×C₂²⋊C₄	—	2	2	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	4	4	no	—
397	C₂×C₂²⋊C₄	—	4	4	no	—
398	C₂×C₄²	—	2	2	no	—
399	C₂×C₄²	—	2	2	no	—
400	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
401	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
404	#107	—	4	2	no	—
405	C₄⋊C₈	—	2	4	no	—
406	#102	—	2	4	no	—
407	#102	—	2	4	no	—
408	#102	—	4	2	no	—
409	#102	—	4	2	no	—
410	C₂²⋊C₈	—	2	2	no	—
411	C₂²⋊C₈	D₄×C₁₉	1	4	yes	—
412	C₄×C₈	—	2	4	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	C₁₉	#24500	1	1	yes	characteristic, direct product factor, Sylow
417	C₂⁴	—	2	4	no	—
418	C₂⁴	—	2	2	no	—
419	C₂⁴	—	2	1	no	—
420	C₂⁴	—	4	2	no	—
421	C₂⁴	—	4	2	no	—
422	C₂⁴	—	4	2	no	—
423	C₂⁴	—	4	2	no	—
424	C₂⁴	—	4	2	no	—
425	C₂⁴	—	4	2	no	—
426	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	4	8	no	—
438	C₂×D₄	—	4	8	no	—
439	C₂×D₄	—	4	2	no	—
440	C₂×D₄	—	4	2	no	—
441	C₂×D₄	—	4	2	no	—
442	C₂×D₄	—	4	2	no	—
443	C₂×D₄	—	4	2	no	—
444	C₂×D₄	#41×C₁₉	1	4	yes	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	—	4	2	no	—
457	C₂²×C₄	—	4	2	no	—
458	C₂²×C₄	—	4	2	no	—
459	C₂²×C₄	D₈×C₁₉	1	4	yes	complemented
460	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
463	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₂²×C₄	#41×C₁₉	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
468	D₈	—	4	8	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	4	2	no	—
482	C₄⋊C₄	—	4	2	no	—
483	C₄⋊C₄	—	4	2	no	—
484	C₂²⋊C₄	—	4	2	no	—
485	C₂²⋊C₄	—	4	4	no	—
486	C₂²⋊C₄	—	4	2	no	—
487	C₂²⋊C₄	—	4	2	no	—
488	C₂²⋊C₄	—	4	4	no	—
489	C₂²⋊C₄	—	4	4	no	—
490	C₂²⋊C₄	—	4	2	no	—
491	C₂²⋊C₄	—	4	2	no	—
492	C₂²⋊C₄	—	4	2	no	—
493	C₂²⋊C₄	—	4	4	no	—
494	C₄²	—	2	2	no	—
495	C₄²	—	2	2	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	1	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	4	8	no	—
506	C₂³	—	4	8	no	—
507	C₂³	—	4	8	no	—
508	C₂³	—	4	2	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	1	no	—
517	C₂³	—	4	1	no	—
518	C₂³	—	4	1	no	—
519	C₂³	—	4	1	no	—
520	C₂³	—	4	1	no	—
521	C₂³	—	8	4	no	—
522	C₂³	—	8	4	no	—
523	C₂³	—	8	4	no	—
524	C₂³	—	8	4	no	—
525	C₂³	C₁₉×#121	1	2	yes	—
526	C₂³	C₂×D₈×C₁₉	1	2	yes	—
527	C₂³	C₁₉×#135	1	2	yes	—
528	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
529	D₄	—	2	4	no	—
530	D₄	—	2	4	no	—
531	D₄	—	4	8	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	8	4	no	—
537	C₂×C₄	—	2	8	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	8	4	no	—
565	C₂×C₄	C₁₉×#121	1	2	yes	—
566	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
567	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
568	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
569	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
570	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
571	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
572	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
573	C₈	—	2	4	no	—
574	C₈	—	4	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	8	16	no	—
585	C₂²	—	8	2	no	—
586	C₂²	—	8	2	no	—
587	C₂²	—	8	2	no	—
588	C₂²	—	8	2	no	—
589	C₂²	—	8	1	no	—
590	C₂²	—	8	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	8	1	no	—
596	C₂²	C₁₉×#466	1	4	yes	—
597	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
598	C₂²	C₁₉×#525	1	1	yes	characteristic
599	C₂²	C₁₉×#535	1	1	yes	characteristic
600	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
601	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
602	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
603	C₂²	C₁₉×#575	1	1	yes	characteristic
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	4	1	no	—
609	C₄	—	8	2	no	—
610	C₄	—	8	1	no	—
611	C₄	—	8	1	no	—
612	C₄	—	8	1	no	—
613	C₄	C₁₉×#546	1	2	yes	—
614	C₄	C₁₉×#551	1	2	yes	—
615	C₂	—	2	4	no	—
616	C₂	—	8	4	no	—
617	C₂	—	16	1	no	—
618	C₂	C₁₉×#2411	1	1	yes	characteristic
619	C₂	C₂×C₁₉×#466	1	1	yes	characteristic
620	C₂	C₁₉×#3055	1	1	yes	characteristic
621	C₂	C₁₉×#3100	1	1	yes	characteristic
622	C₂	C₁₉×#3105	1	1	yes	characteristic
623	C₂	C₁₉×#3205	1	1	yes	characteristic
624	C₂	C₁₉×#3211	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#447	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#431	C₂	semidirect
3. C₁₉×#2854	C₂	semidirect
4. C₂×C₁₉×#390	C₂	semidirect
5. C₁₉×#2067	C₂	semidirect
6. C₁₉×#2054	C₂	semidirect
7. C₁₉×#1970	C₂	semidirect
8. C₁₉×#1934	C₂	semidirect
9. C₁₉×#1874	C₂	semidirect
10. C₁₉×#1852	C₂	semidirect
11. C₁₉×#1786	C₂	semidirect
22. C₂×C₁₉×#107	C₂²	semidirect
23. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
27. C₂×C₁₉×#102	C₂²	semidirect
30. C₂×C₄×C₈×C₁₉	C₂²	semidirect
35. C₁₉×#390	C₂²	semidirect
36. C₁₉×#390	C₂²	semidirect
37. C₁₉×#389	C₂²	semidirect
38. C₁₉×#389	C₂²	semidirect
43. C₁₉×#340	C₂²	semidirect
44. C₁₉×#340	C₂²	semidirect
146. C₂²×C₄×C₁₉	D₈	semidirect
187. #24500	C₁₉	direct (N × H)
264. C₂×#431	C₂×C₁₉	semidirect
265. #2854	C₂×C₁₉	semidirect
266. C₂×#390	C₂×C₁₉	semidirect
267. #2067	C₂×C₁₉	semidirect
268. #2054	C₂×C₁₉	semidirect
269. #1970	C₂×C₁₉	semidirect
270. #1934	C₂×C₁₉	semidirect
271. #1874	C₂×C₁₉	semidirect
272. #1852	C₂×C₁₉	semidirect
273. #1786	C₂×C₁₉	semidirect
324. C₂×#107	C₂²×C₁₉	semidirect
325. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
329. C₂×#102	C₂²×C₁₉	semidirect
332. C₂×C₄×C₈	C₂²×C₁₉	semidirect
337. #390	C₂²×C₁₉	semidirect
338. #390	C₂²×C₁₉	semidirect
339. #389	C₂²×C₁₉	semidirect
340. #389	C₂²×C₁₉	semidirect
345. #340	C₂²×C₁₉	semidirect
346. #340	C₂²×C₁₉	semidirect
416. C₁₉	#24500	direct (N × H)
459. C₂²×C₄	D₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#447	2
C₂×C₁₉×#431	2
C₁₉×#2854	2
C₂×C₁₉×#390	2
C₁₉×#2067	2
C₁₉×#2054	2
C₁₉×#1970	2
C₁₉×#1934	2
C₁₉×#1874	2
C₁₉×#1852	2
C₁₉×#1786	2
#24500	19

Subgroups — C19×#24500 #18030459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24500 #18030459