Subgroups — C₁₉×#23544 #18029503

Order 4864.

1570 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#416	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2309	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2055	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2054	C₂	1	4	yes	maximal, complemented
9	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
13	C₂×C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
14	C₂×C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
15	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
16	C₂²×D₈×C₁₉	C₂²	1	2	yes	—
17	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#424	—	2	4	no	—
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	4	yes	complemented
24	C₁₉×#416	—	2	4	no	—
25	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
26	C₂×C₁₉×#102	—	2	4	no	—
27	C₂×C₁₉×#102	C₂²	1	4	yes	—
28	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
29	C₁₉×#391	C₂²	1	2	yes	complemented
30	C₁₉×#390	—	2	2	no	—
31	C₁₉×#390	C₂²	1	4	yes	—
32	C₁₉×#390	C₂²	1	2	yes	complemented
33	C₁₉×#386	—	2	2	no	—
34	C₁₉×#380	—	2	2	no	—
35	C₁₉×#379	—	2	2	no	—
36	C₁₉×#340	C₂²	1	4	yes	complemented
37	C₂⁵×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	—	2	2	no	—
39	C₂×#41×C₁₉	—	2	2	no	—
40	C₂×#41×C₁₉	—	2	2	no	—
41	C₂×#41×C₁₉	—	2	2	no	—
42	C₂×#41×C₁₉	—	2	2	no	—
43	C₂×#41×C₁₉	D₄	1	4	yes	—
44	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	—	2	2	no	—
47	C₂²×D₄×C₁₉	—	2	2	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	—	2	2	no	—
52	C₂²×D₄×C₁₉	D₄	1	4	yes	—
53	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
54	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	—	2	1	no	—
56	C₂³×C₄×C₁₉	—	2	1	no	—
57	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×AGL(1,ℤ/8)	—	2	32	no	—
59	C₂×SD₁₆×C₁₉	—	2	4	no	—
60	C₂×SD₁₆×C₁₉	—	2	4	no	—
61	C₂×SD₁₆×C₁₉	—	2	4	no	—
62	C₂×D₈×C₁₉	—	2	4	no	—
63	C₂×D₈×C₁₉	—	2	4	no	—
64	C₂×D₈×C₁₉	—	2	4	no	—
65	C₂×M₁₆×C₁₉	—	2	2	no	—
66	C₂×M₁₆×C₁₉	—	2	2	no	—
67	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
68	C₂²×C₈×C₁₉	—	2	2	no	—
69	C₂²×C₈×C₁₉	—	2	2	no	—
70	C₂²×C₈×C₁₉	—	2	2	no	—
71	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
72	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
73	C₁₉×#117	—	2	2	no	—
74	C₁₉×#117	—	2	2	no	—
75	C₁₉×#117	—	2	2	no	—
76	C₁₉×#117	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
90	C₁₉×C₄⋊C₈	—	2	8	no	—
91	C₁₉×#103	—	2	4	no	—
92	C₁₉×#102	—	2	8	no	—
93	C₁₉×#102	—	2	4	no	—
94	C₁₉×#95	—	2	4	no	—
95	C₂⁴×C₁₉	—	2	1	no	—
96	C₂⁴×C₁₉	—	2	2	no	—
97	C₂⁴×C₁₉	—	2	4	no	—
98	C₂⁴×C₁₉	—	4	2	no	—
99	C₂⁴×C₁₉	—	4	2	no	—
100	C₂⁴×C₁₉	—	8	2	no	—
101	C₂⁴×C₁₉	—	8	2	no	—
102	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
103	#41×C₁₉	—	2	8	no	—
104	#41×C₁₉	—	2	8	no	—
105	#41×C₁₉	—	4	4	no	—
106	#41×C₁₉	—	4	4	no	—
107	C₂×Q₈×C₁₉	—	2	1	no	—
108	C₂×Q₈×C₁₉	—	2	1	no	—
109	C₂×Q₈×C₁₉	—	2	1	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
113	C₂×D₄×C₁₉	—	2	4	no	—
114	C₂×D₄×C₁₉	—	2	8	no	—
115	C₂×D₄×C₁₉	—	2	4	no	—
116	C₂×D₄×C₁₉	—	2	8	no	—
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×C₁₉	—	2	1	no	—
119	C₂×D₄×C₁₉	—	2	2	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	1	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	1	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	—	4	4	no	—
132	C₂×D₄×C₁₉	—	4	4	no	—
133	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
134	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	4	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	4	2	no	—
140	C₂²×C₄×C₁₉	—	4	2	no	—
141	C₂²×C₄×C₁₉	—	4	2	no	—
142	C₂²×C₄×C₁₉	—	8	2	no	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	#41	1	2	yes	—
149	C₂²×C₄×C₁₉	#41	1	2	yes	—
150	C₂²×C₄×C₁₉	#41	1	2	yes	—
151	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
152	SD₁₆×C₁₉	—	2	16	no	—
153	D₈×C₁₉	—	2	16	no	—
154	M₁₆×C₁₉	—	2	8	no	—
155	C₂×C₈×C₁₉	—	2	2	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	—	4	4	no	—
161	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
162	C₄⋊C₄×C₁₉	—	2	4	no	—
163	C₄⋊C₄×C₁₉	—	2	2	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	—	4	2	no	—
168	C₂²⋊C₄×C₁₉	—	2	4	no	—
169	C₂²⋊C₄×C₁₉	—	4	2	no	—
170	C₂²⋊C₄×C₁₉	—	8	4	no	—
171	C₂²⋊C₄×C₁₉	—	8	4	no	—
172	C₂²⋊C₄×C₁₉	—	8	4	no	—
173	C₄²×C₁₉	—	2	2	no	—
174	C₄²×C₁₉	—	2	2	no	—
175	C₄²×C₁₉	—	4	2	no	—
176	#23544	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂³×C₁₉	—	2	2	no	—
178	C₂³×C₁₉	—	2	2	no	—
179	C₂³×C₁₉	—	2	2	no	—
180	C₂³×C₁₉	—	2	4	no	—
181	C₂³×C₁₉	—	4	1	no	—
182	C₂³×C₁₉	—	4	1	no	—
183	C₂³×C₁₉	—	4	2	no	—
184	C₂³×C₁₉	—	4	2	no	—
185	C₂³×C₁₉	—	4	2	no	—
186	C₂³×C₁₉	—	4	4	no	—
187	C₂³×C₁₉	—	4	4	no	—
188	C₂³×C₁₉	—	4	2	no	—
189	C₂³×C₁₉	—	4	8	no	—
190	C₂³×C₁₉	—	8	4	no	—
191	C₂³×C₁₉	—	8	4	no	—
192	C₂³×C₁₉	—	8	8	no	—
193	C₂³×C₁₉	—	8	8	no	—
194	C₂³×C₁₉	#121	1	2	yes	—
195	C₂³×C₁₉	#121	1	2	yes	—
196	C₂³×C₁₉	#121	1	2	yes	—
197	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₁₉	—	2	2	no	—
199	Q₈×C₁₉	—	2	2	no	—
200	Q₈×C₁₉	—	4	1	no	—
201	Q₈×C₁₉	—	4	1	no	—
202	D₄×C₁₉	—	2	2	no	—
203	D₄×C₁₉	—	2	4	no	—
204	D₄×C₁₉	—	2	4	no	—
205	D₄×C₁₉	—	2	2	no	—
206	D₄×C₁₉	—	4	8	no	—
207	D₄×C₁₉	—	4	2	no	—
208	D₄×C₁₉	—	4	1	no	—
209	D₄×C₁₉	—	4	2	no	—
210	D₄×C₁₉	—	4	1	no	—
211	D₄×C₁₉	—	4	8	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	4	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	8	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	4	no	—
223	C₂×C₄×C₁₉	—	4	2	no	—
224	C₂×C₄×C₁₉	—	8	4	no	—
225	C₂×C₄×C₁₉	#120	1	4	yes	—
226	C₂×C₄×C₁₉	#121	1	2	yes	—
227	C₂×C₄×C₁₉	#121	1	2	yes	—
228	C₂×C₄×C₁₉	#121	1	2	yes	—
229	C₂×C₄×C₁₉	#123	1	4	yes	—
230	C₂×C₄×C₁₉	#123	1	4	yes	—
231	C₂×C₄×C₁₉	#124	1	4	yes	—
232	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
238	C₈×C₁₉	—	2	4	no	—
239	C₈×C₁₉	—	4	2	no	—
240	C₂²×AGL(1,ℤ/8)	C₂×C₁₉	1	1	yes	characteristic
241	C₂×#424	C₂×C₁₉	1	1	yes	characteristic, complemented
242	C₂×#416	C₂×C₁₉	1	1	yes	characteristic, complemented
243	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
244	#2311	C₂×C₁₉	1	1	yes	characteristic, complemented
245	#2309	C₂×C₁₉	1	1	yes	characteristic, complemented
246	#2055	C₂×C₁₉	1	4	yes	complemented
247	#2054	C₂×C₁₉	1	4	yes	complemented
248	#1736	C₂×C₁₉	1	1	yes	characteristic, complemented
249	C₂²×C₁₉	—	2	2	no	—
250	C₂²×C₁₉	—	2	2	no	—
251	C₂²×C₁₉	—	2	4	no	—
252	C₂²×C₁₉	—	2	4	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	—	4	4	no	—
255	C₂²×C₁₉	—	4	4	no	—
256	C₂²×C₁₉	—	4	4	no	—
257	C₂²×C₁₉	—	4	4	no	—
258	C₂²×C₁₉	—	8	16	no	—
259	C₂²×C₁₉	—	8	1	no	—
260	C₂²×C₁₉	—	8	1	no	—
261	C₂²×C₁₉	—	8	4	no	—
262	C₂²×C₁₉	—	8	2	no	—
263	C₂²×C₁₉	—	8	4	no	—
264	C₂²×C₁₉	#394	1	4	yes	—
265	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
266	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
267	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
268	C₂²×C₁₉	#576	1	2	yes	—
269	C₂²×C₁₉	#577	1	2	yes	—
270	C₄×C₁₉	—	4	2	no	—
271	C₄×C₁₉	—	4	4	no	—
272	C₄×C₁₉	—	8	2	no	—
273	C₄×C₁₉	—	8	2	no	—
274	C₄×C₁₉	#394	1	4	yes	—
275	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
276	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
277	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
278	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
279	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
280	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
281	C₂×AGL(1,ℤ/8)	—	2	4	no	—
282	C₂×AGL(1,ℤ/8)	—	2	4	no	—
283	C₂×AGL(1,ℤ/8)	—	2	4	no	—
284	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
285	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
286	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
287	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
290	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
291	#424	—	2	4	no	—
292	C₂×C₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
293	#416	—	2	4	no	—
294	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
295	C₂×#102	—	2	4	no	—
296	C₂×#102	C₂²×C₁₉	1	4	yes	—
297	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
298	#391	C₂²×C₁₉	1	2	yes	complemented
299	#390	—	2	2	no	—
300	#390	C₂²×C₁₉	1	4	yes	—
301	#390	C₂²×C₁₉	1	2	yes	complemented
302	#386	—	2	2	no	—
303	#380	—	2	2	no	—
304	#379	—	2	2	no	—
305	#340	C₂²×C₁₉	1	4	yes	complemented
306	C₂×C₁₉	—	2	4	no	—
307	C₂×C₁₉	—	8	2	no	—
308	C₂×C₁₉	—	8	4	no	—
309	C₂×C₁₉	C₂×#394	1	1	yes	characteristic
310	C₂×C₁₉	#3041	1	1	yes	characteristic
311	C₂×C₁₉	#3042	1	1	yes	characteristic
312	C₂×C₁₉	#3045	1	2	yes	—
313	C₂×C₁₉	#3062	1	2	yes	—
314	C₂⁵	—	2	1	no	—
315	C₂×#41	—	2	2	no	—
316	C₂×#41	—	2	2	no	—
317	C₂×#41	—	2	2	no	—
318	C₂×#41	—	2	2	no	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	D₄×C₁₉	1	4	yes	—
321	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	—	2	2	no	—
324	C₂²×D₄	—	2	2	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	—	2	2	no	—
327	C₂²×D₄	—	2	2	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	D₄×C₁₉	1	4	yes	—
330	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
331	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	—	2	1	no	—
334	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
335	AGL(1,ℤ/8)	—	2	32	no	—
336	C₂×SD₁₆	—	2	4	no	—
337	C₂×SD₁₆	—	2	4	no	—
338	C₂×SD₁₆	—	2	4	no	—
339	C₂×D₈	—	2	4	no	—
340	C₂×D₈	—	2	4	no	—
341	C₂×D₈	—	2	4	no	—
342	C₂×M₁₆	—	2	2	no	—
343	C₂×M₁₆	—	2	2	no	—
344	C₂×M₁₆	D₄×C₁₉	1	4	yes	—
345	C₂²×C₈	—	2	2	no	—
346	C₂²×C₈	—	2	2	no	—
347	C₂²×C₈	—	2	2	no	—
348	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
349	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
350	#117	—	2	2	no	—
351	#117	—	2	2	no	—
352	#117	—	2	2	no	—
353	#117	—	2	2	no	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	4	no	—
362	C₂×C₂²⋊C₄	—	2	4	no	—
363	C₂×C₂²⋊C₄	—	2	4	no	—
364	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
367	C₄⋊C₈	—	2	8	no	—
368	#103	—	2	4	no	—
369	#102	—	2	8	no	—
370	#102	—	2	4	no	—
371	#95	—	2	4	no	—
372	C₁₉	#23544	1	1	yes	characteristic, direct product factor, Sylow
373	C₂⁴	—	2	1	no	—
374	C₂⁴	—	2	2	no	—
375	C₂⁴	—	2	4	no	—
376	C₂⁴	—	4	2	no	—
377	C₂⁴	—	4	2	no	—
378	C₂⁴	—	8	2	no	—
379	C₂⁴	—	8	2	no	—
380	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
381	#41	—	2	8	no	—
382	#41	—	2	8	no	—
383	#41	—	4	4	no	—
384	#41	—	4	4	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	—	2	8	no	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	8	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	—	4	2	no	—
408	C₂×D₄	—	4	2	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	—	4	4	no	—
411	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
412	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	4	2	no	—
419	C₂²×C₄	—	4	2	no	—
420	C₂²×C₄	—	8	2	no	—
421	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
422	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
423	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
424	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
425	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₂²×C₄	#41×C₁₉	1	2	yes	—
427	C₂²×C₄	#41×C₁₉	1	2	yes	—
428	C₂²×C₄	#41×C₁₉	1	2	yes	—
429	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
430	SD₁₆	—	2	16	no	—
431	D₈	—	2	16	no	—
432	M₁₆	—	2	8	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	4	4	no	—
439	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	4	2	no	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	4	2	no	—
448	C₂²⋊C₄	—	8	4	no	—
449	C₂²⋊C₄	—	8	4	no	—
450	C₂²⋊C₄	—	8	4	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	4	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	4	8	no	—
459	C₂³	—	4	1	no	—
460	C₂³	—	4	1	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	4	no	—
465	C₂³	—	4	4	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	8	4	no	—
468	C₂³	—	8	4	no	—
469	C₂³	—	8	8	no	—
470	C₂³	—	8	8	no	—
471	C₂³	C₁₉×#121	1	2	yes	—
472	C₂³	C₁₉×#121	1	2	yes	—
473	C₂³	C₁₉×#121	1	2	yes	—
474	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
475	Q₈	—	2	2	no	—
476	Q₈	—	2	2	no	—
477	Q₈	—	4	1	no	—
478	Q₈	—	4	1	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	4	no	—
481	D₄	—	2	4	no	—
482	D₄	—	2	2	no	—
483	D₄	—	4	8	no	—
484	D₄	—	4	8	no	—
485	D₄	—	4	2	no	—
486	D₄	—	4	1	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	1	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	8	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	8	4	no	—
502	C₂×C₄	C₁₉×#120	1	4	yes	—
503	C₂×C₄	C₁₉×#121	1	2	yes	—
504	C₂×C₄	C₁₉×#121	1	2	yes	—
505	C₂×C₄	C₁₉×#121	1	2	yes	—
506	C₂×C₄	C₁₉×#123	1	4	yes	—
507	C₂×C₄	C₁₉×#123	1	4	yes	—
508	C₂×C₄	C₁₉×#124	1	4	yes	—
509	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
512	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
513	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
514	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
515	C₈	—	2	4	no	—
516	C₈	—	4	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	4	no	—
526	C₂²	—	8	16	no	—
527	C₂²	—	8	1	no	—
528	C₂²	—	8	1	no	—
529	C₂²	—	8	4	no	—
530	C₂²	—	8	4	no	—
531	C₂²	—	8	2	no	—
532	C₂²	C₁₉×#394	1	4	yes	—
533	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
534	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
535	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
536	C₂²	C₁₉×#576	1	2	yes	—
537	C₂²	C₁₉×#577	1	2	yes	—
538	C₄	—	4	4	no	—
539	C₄	—	4	2	no	—
540	C₄	—	8	2	no	—
541	C₄	—	8	2	no	—
542	C₄	C₁₉×#394	1	4	yes	—
543	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
544	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
545	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
546	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
547	C₂	—	2	4	no	—
548	C₂	—	8	4	no	—
549	C₂	—	8	2	no	—
550	C₂	C₂×C₁₉×#394	1	1	yes	characteristic
551	C₂	C₁₉×#3041	1	1	yes	characteristic
552	C₂	C₁₉×#3042	1	1	yes	characteristic
553	C₂	C₁₉×#3045	1	2	yes	—
554	C₂	C₁₉×#3062	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#424	C₂	semidirect
3. C₂×C₁₉×#416	C₂	semidirect
4. C₂²×C₁₉×#102	C₂	semidirect
5. C₁₉×#2311	C₂	semidirect
6. C₁₉×#2309	C₂	semidirect
7. C₁₉×#2055	C₂	semidirect
8. C₁₉×#2054	C₂	semidirect
9. C₁₉×#1736	C₂	semidirect
23. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
25. C₂×C₁₉×#103	C₂²	semidirect
28. C₂×C₁₉×#102	C₂²	semidirect
29. C₁₉×#391	C₂²	semidirect
32. C₁₉×#390	C₂²	semidirect
36. C₁₉×#340	C₂²	semidirect
176. #23544	C₁₉	direct (N × H)
241. C₂×#424	C₂×C₁₉	semidirect
242. C₂×#416	C₂×C₁₉	semidirect
243. C₂²×#102	C₂×C₁₉	semidirect
244. #2311	C₂×C₁₉	semidirect
245. #2309	C₂×C₁₉	semidirect
246. #2055	C₂×C₁₉	semidirect
247. #2054	C₂×C₁₉	semidirect
248. #1736	C₂×C₁₉	semidirect
292. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
294. C₂×#103	C₂²×C₁₉	semidirect
297. C₂×#102	C₂²×C₁₉	semidirect
298. #391	C₂²×C₁₉	semidirect
301. #390	C₂²×C₁₉	semidirect
305. #340	C₂²×C₁₉	semidirect
372. C₁₉	#23544	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×AGL(1,ℤ/8)	2
C₂×C₁₉×#424	2
C₂×C₁₉×#416	2
C₂²×C₁₉×#102	2
C₁₉×#2311	2
C₁₉×#2309	2
C₁₉×#2055	2
C₁₉×#2054	2
C₁₉×#1736	2
#23544	19

Subgroups — C19×#23544 #18029503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23544 #18029503