Subgroups — C₁₉×#24477 #18030436

Order 4864.

1130 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2435	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2344	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2065	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2042	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1983	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1926	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1786	C₂	1	1	yes	maximal, characteristic
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#124	C₂²	1	2	yes	—
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#483	—	2	4	no	—
19	C₂×C₁₉×#106	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	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
25	C₂×C₁₉×#102	—	2	4	no	—
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₂×C₁₉×#102	C₂²	1	2	yes	—
28	C₂×C₁₉×#102	C₂²	1	2	yes	—
29	C₂×C₁₉×#102	C₂²	1	2	yes	—
30	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₁₉×#394	—	2	2	no	—
32	C₁₉×#390	C₂²	1	2	yes	—
33	C₁₉×#389	C₂²	1	2	yes	complemented
34	C₁₉×#387	—	2	2	no	—
35	C₁₉×#381	—	2	1	no	—
36	C₁₉×#380	C₂²	1	1	yes	characteristic
37	C₁₉×#379	—	2	1	no	—
38	C₁₉×#379	—	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×Q₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₉	—	2	4	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	—	4	2	no	—
50	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₉	—	2	2	no	—
54	C₂²×C₈×C₁₉	—	4	2	no	—
55	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×#124	—	2	4	no	—
59	C₁₉×#124	—	4	2	no	—
60	C₁₉×C₂²⋊Q₈	—	2	2	no	—
61	C₁₉×C₂²⋊Q₈	—	2	2	no	—
62	C₁₉×#117	—	4	4	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
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	1	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₁₉	—	2	2	no	—
81	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
82	C₁₉×#106	—	2	2	no	—
83	C₁₉×#106	—	2	2	no	—
84	C₁₉×C₄⋊C₈	—	4	2	no	—
85	C₁₉×#103	—	2	2	no	—
86	C₁₉×#103	—	2	2	no	—
87	C₁₉×#103	—	4	2	no	—
88	C₁₉×#102	—	2	4	no	—
89	C₁₉×#102	—	2	4	no	—
90	C₁₉×#102	—	2	4	no	—
91	C₁₉×#102	—	4	2	no	—
92	C₁₉×C₂²⋊C₈	—	2	2	no	—
93	C₁₉×#95	—	2	2	no	—
94	C₁₉×#95	—	2	1	no	—
95	C₁₉×#95	—	2	2	no	—
96	C₁₉×#95	D₄	1	2	yes	—
97	C₂⁴×C₁₉	—	2	2	no	—
98	C₂⁴×C₁₉	—	4	4	no	—
99	C₂⁴×C₁₉	—	4	2	no	—
100	C₂⁴×C₁₉	—	4	2	no	—
101	C₂⁴×C₁₉	—	4	2	no	—
102	C₂⁴×C₁₉	—	8	2	no	—
103	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂×Q₈×C₁₉	—	2	1	no	—
105	C₂×Q₈×C₁₉	—	2	1	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	8	no	—
109	C₂×D₄×C₁₉	—	2	2	no	—
110	C₂×D₄×C₁₉	—	2	2	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	—	4	8	no	—
115	C₂×D₄×C₁₉	—	4	4	no	—
116	C₂×D₄×C₁₉	—	4	4	no	—
117	C₂×D₄×C₁₉	—	4	2	no	—
118	C₂×D₄×C₁₉	#41	1	4	yes	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	4	2	no	—
128	C₂²×C₄×C₁₉	—	4	2	no	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₉	#41	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	1	no	—
137	C₂×C₈×C₁₉	—	2	1	no	—
138	C₂×C₈×C₁₉	—	2	2	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	—	4	4	no	—
143	C₄⋊C₄×C₁₉	—	2	4	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	4	4	no	—
151	C₄⋊C₄×C₁₉	—	4	2	no	—
152	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
154	C₂²⋊C₄×C₁₉	—	2	2	no	—
155	C₂²⋊C₄×C₁₉	—	2	2	no	—
156	C₂²⋊C₄×C₁₉	—	4	4	no	—
157	C₂²⋊C₄×C₁₉	—	4	4	no	—
158	C₂²⋊C₄×C₁₉	—	4	2	no	—
159	C₂²⋊C₄×C₁₉	—	4	2	no	—
160	C₂²⋊C₄×C₁₉	—	8	2	no	—
161	C₂²⋊C₄×C₁₉	—	8	2	no	—
162	C₄²×C₁₉	—	2	2	no	—
163	C₄²×C₁₉	—	2	2	no	—
164	C₄²×C₁₉	—	4	4	no	—
165	#24477	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₁₉	—	2	2	no	—
167	C₂³×C₁₉	—	2	2	no	—
168	C₂³×C₁₉	—	2	4	no	—
169	C₂³×C₁₉	—	4	8	no	—
170	C₂³×C₁₉	—	4	2	no	—
171	C₂³×C₁₉	—	4	2	no	—
172	C₂³×C₁₉	—	4	2	no	—
173	C₂³×C₁₉	—	4	2	no	—
174	C₂³×C₁₉	—	4	2	no	—
175	C₂³×C₁₉	—	4	2	no	—
176	C₂³×C₁₉	—	8	8	no	—
177	C₂³×C₁₉	—	8	8	no	—
178	C₂³×C₁₉	—	8	4	no	—
179	C₂³×C₁₉	—	8	4	no	—
180	C₂³×C₁₉	#121	1	2	yes	—
181	C₂³×C₁₉	#135	1	2	yes	—
182	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
183	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₁₉	—	4	1	no	—
185	Q₈×C₁₉	—	4	1	no	—
186	Q₈×C₁₉	—	4	2	no	—
187	D₄×C₁₉	—	2	4	no	—
188	D₄×C₁₉	—	2	4	no	—
189	D₄×C₁₉	—	4	8	no	—
190	D₄×C₁₉	—	4	2	no	—
191	D₄×C₁₉	—	4	2	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	—	2	4	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	8	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	#121	1	2	yes	—
217	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
219	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
221	C₈×C₁₉	—	4	1	no	—
222	C₈×C₁₉	—	4	1	no	—
223	C₈×C₁₉	—	4	2	no	—
224	C₂×#483	C₂×C₁₉	1	1	yes	characteristic, complemented
225	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic
226	#2435	C₂×C₁₉	1	1	yes	characteristic
227	#2344	C₂×C₁₉	1	1	yes	characteristic, complemented
228	#2065	C₂×C₁₉	1	2	yes	complemented
229	#2042	C₂×C₁₉	1	2	yes	complemented
230	#1983	C₂×C₁₉	1	2	yes	complemented
231	#1926	C₂×C₁₉	1	2	yes	complemented
232	#1892	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#1850	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#1786	C₂×C₁₉	1	1	yes	characteristic
235	C₂²×C₁₉	—	2	2	no	—
236	C₂²×C₁₉	—	2	4	no	—
237	C₂²×C₁₉	—	2	2	no	—
238	C₂²×C₁₉	—	2	4	no	—
239	C₂²×C₁₉	—	4	4	no	—
240	C₂²×C₁₉	—	4	4	no	—
241	C₂²×C₁₉	—	4	4	no	—
242	C₂²×C₁₉	—	8	16	no	—
243	C₂²×C₁₉	—	8	2	no	—
244	C₂²×C₁₉	—	8	2	no	—
245	C₂²×C₁₉	—	8	2	no	—
246	C₂²×C₁₉	—	8	2	no	—
247	C₂²×C₁₉	#463	1	4	yes	—
248	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
249	C₂²×C₁₉	#546	1	2	yes	—
250	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
251	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
252	C₂²×C₁₉	#577	1	2	yes	—
253	C₄×C₁₉	—	2	2	no	—
254	C₄×C₁₉	—	4	2	no	—
255	C₄×C₁₉	—	4	2	no	—
256	C₄×C₁₉	—	4	2	no	—
257	C₄×C₁₉	—	4	2	no	—
258	C₄×C₁₉	—	8	1	no	—
259	C₄×C₁₉	—	8	1	no	—
260	C₄×C₁₉	—	8	2	no	—
261	C₄×C₁₉	#525	1	1	yes	characteristic
262	C₄×C₁₉	#535	1	1	yes	characteristic
263	C₄×C₁₉	#551	1	2	yes	—
264	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
265	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×#124	C₂²×C₁₉	1	2	yes	—
267	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
268	C₂×#117	—	2	1	no	—
269	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
270	#483	—	2	4	no	—
271	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic, complemented
272	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic, complemented
273	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
274	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
275	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
276	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
277	C₂×#102	—	2	4	no	—
278	C₂×#102	C₂²×C₁₉	1	2	yes	—
279	C₂×#102	C₂²×C₁₉	1	2	yes	—
280	C₂×#102	C₂²×C₁₉	1	2	yes	—
281	C₂×#102	C₂²×C₁₉	1	2	yes	—
282	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
283	#394	—	2	2	no	—
284	#390	C₂²×C₁₉	1	2	yes	—
285	#389	C₂²×C₁₉	1	2	yes	complemented
286	#387	—	2	2	no	—
287	#381	—	2	1	no	—
288	#380	C₂²×C₁₉	1	1	yes	characteristic
289	#379	—	2	1	no	—
290	#379	—	2	1	no	—
291	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
292	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
293	#340	C₂²×C₁₉	1	2	yes	complemented
294	#336	C₂²×C₁₉	1	2	yes	complemented
295	C₂×C₁₉	—	2	4	no	—
296	C₂×C₁₉	—	8	4	no	—
297	C₂×C₁₉	#2411	1	1	yes	characteristic
298	C₂×C₁₉	C₂×#463	1	1	yes	characteristic
299	C₂×C₁₉	#3043	1	1	yes	characteristic
300	C₂×C₁₉	#3296	1	2	yes	—
301	C₂×C₁₉	#3306	1	2	yes	—
302	C₂⁵	—	2	1	no	—
303	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
304	C₂²×D₄	—	2	4	no	—
305	C₂²×D₄	—	2	2	no	—
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	—	2	2	no	—
308	C₂²×D₄	—	4	2	no	—
309	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
310	C₂³×C₄	—	2	1	no	—
311	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	—	4	2	no	—
314	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
315	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
317	#124	—	2	4	no	—
318	#124	—	4	2	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	#117	—	4	4	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
339	C₂×C₄²	—	2	2	no	—
340	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
341	#106	—	2	2	no	—
342	#106	—	2	2	no	—
343	C₄⋊C₈	—	4	2	no	—
344	#103	—	2	2	no	—
345	#103	—	2	2	no	—
346	#103	—	4	2	no	—
347	#102	—	2	4	no	—
348	#102	—	2	4	no	—
349	#102	—	2	4	no	—
350	#102	—	4	2	no	—
351	C₂²⋊C₈	—	2	2	no	—
352	#95	—	2	2	no	—
353	#95	—	2	1	no	—
354	#95	—	2	2	no	—
355	#95	D₄×C₁₉	1	2	yes	—
356	C₁₉	#24477	1	1	yes	characteristic, direct product factor, Sylow
357	C₂⁴	—	2	2	no	—
358	C₂⁴	—	4	4	no	—
359	C₂⁴	—	4	2	no	—
360	C₂⁴	—	4	2	no	—
361	C₂⁴	—	4	2	no	—
362	C₂⁴	—	8	2	no	—
363	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×D₄	—	2	8	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	4	8	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	—	4	4	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	#41×C₁₉	1	4	yes	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
391	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
393	C₂²×C₄	#41×C₁₉	1	2	yes	—
394	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	4	4	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	4	4	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
413	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	4	4	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₂²⋊C₄	—	8	2	no	—
421	C₂²⋊C₄	—	8	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	4	4	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	4	8	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	8	8	no	—
436	C₂³	—	8	8	no	—
437	C₂³	—	8	4	no	—
438	C₂³	—	8	4	no	—
439	C₂³	C₁₉×#121	1	2	yes	—
440	C₂³	C₁₉×#135	1	2	yes	—
441	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
442	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
443	Q₈	—	4	1	no	—
444	Q₈	—	4	1	no	—
445	Q₈	—	4	2	no	—
446	D₄	—	2	4	no	—
447	D₄	—	2	4	no	—
448	D₄	—	4	8	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	C₁₉×#121	1	2	yes	—
476	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
477	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
478	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
479	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
480	C₈	—	4	1	no	—
481	C₈	—	4	2	no	—
482	C₈	—	4	1	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	8	16	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	2	no	—
494	C₂²	—	8	2	no	—
495	C₂²	C₁₉×#463	1	4	yes	—
496	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
497	C₂²	C₁₉×#546	1	2	yes	—
498	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
499	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
500	C₂²	C₁₉×#577	1	2	yes	—
501	C₄	—	2	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	8	1	no	—
507	C₄	—	8	1	no	—
508	C₄	—	8	2	no	—
509	C₄	C₁₉×#525	1	1	yes	characteristic
510	C₄	C₁₉×#535	1	1	yes	characteristic
511	C₄	C₁₉×#551	1	2	yes	—
512	C₂	—	2	4	no	—
513	C₂	—	8	4	no	—
514	C₂	C₁₉×#2411	1	1	yes	characteristic
515	C₂	C₂×C₁₉×#463	1	1	yes	characteristic
516	C₂	C₁₉×#3043	1	1	yes	characteristic
517	C₂	C₁₉×#3296	1	2	yes	—
518	C₂	C₁₉×#3306	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂³×D₄×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
1. C₂×C₁₉×#483	C₂	semidirect
4. C₁₉×#2344	C₂	semidirect
5. C₁₉×#2065	C₂	semidirect
6. C₁₉×#2042	C₂	semidirect
7. C₁₉×#1983	C₂	semidirect
8. C₁₉×#1926	C₂	semidirect
9. C₁₉×#1892	C₂	semidirect
10. C₁₉×#1850	C₂	semidirect
19. C₂×C₁₉×#106	C₂²	semidirect
20. C₂×C₁₉×#106	C₂²	semidirect
21. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
22. C₂×C₁₉×#103	C₂²	semidirect
23. C₂×C₁₉×#103	C₂²	semidirect
24. C₂×C₁₉×#103	C₂²	semidirect
33. C₁₉×#389	C₂²	semidirect
39. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
41. C₁₉×#340	C₂²	semidirect
42. C₁₉×#336	C₂²	semidirect
165. #24477	C₁₉	direct (N × H)
224. C₂×#483	C₂×C₁₉	semidirect
227. #2344	C₂×C₁₉	semidirect
228. #2065	C₂×C₁₉	semidirect
229. #2042	C₂×C₁₉	semidirect
230. #1983	C₂×C₁₉	semidirect
231. #1926	C₂×C₁₉	semidirect
232. #1892	C₂×C₁₉	semidirect
233. #1850	C₂×C₁₉	semidirect
271. C₂×#106	C₂²×C₁₉	semidirect
272. C₂×#106	C₂²×C₁₉	semidirect
273. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
274. C₂×#103	C₂²×C₁₉	semidirect
275. C₂×#103	C₂²×C₁₉	semidirect
276. C₂×#103	C₂²×C₁₉	semidirect
285. #389	C₂²×C₁₉	semidirect
291. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
293. #340	C₂²×C₁₉	semidirect
294. #336	C₂²×C₁₉	semidirect
356. C₁₉	#24477	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×#483	2
C₂²×C₁₉×#102	2
C₁₉×#2435	2
C₁₉×#2344	2
C₁₉×#2065	2
C₁₉×#2042	2
C₁₉×#1983	2
C₁₉×#1926	2
C₁₉×#1892	2
C₁₉×#1850	2
C₁₉×#1786	2
#24477	19

Subgroups — C19×#24477 #18030436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24477 #18030436