Subgroups — C₁₉×#32903 #18038862

Order 4864.

1576 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#460	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#448	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2856	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1880	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1874	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1803	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×SD₁₆×C₁₉	C₂²	1	4	yes	—
11	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#121	—	2	1	no	—
13	C₂×C₁₉×#121	—	2	1	no	—
14	C₂×C₁₉×#121	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₉	—	2	8	no	—
16	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
17	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
18	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₉	—	2	1	no	—
23	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#460	—	2	8	no	—
25	C₁₉×#448	—	2	8	no	—
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
27	C₂×C₁₉×#103	C₂²	1	4	yes	—
28	C₂×C₁₉×#102	C₂²	1	4	yes	—
29	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₁₉×#390	—	2	1	no	—
31	C₁₉×#390	—	2	1	no	—
32	C₁₉×#390	C₂²	1	2	yes	—
33	C₁₉×#384	C₂²	1	1	yes	characteristic
34	C₁₉×#340	C₂²	1	4	yes	—
35	C₁₉×#336	C₂²	1	2	yes	—
36	C₂²×Q₈×C₁₉	—	2	4	no	—
37	C₂²×Q₈×C₁₉	—	2	4	no	—
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₂²×Q₈×C₁₉	—	2	2	no	—
40	C₂²×Q₈×C₁₉	D₄	1	4	yes	complemented
41	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
42	C₂²×D₄×C₁₉	—	2	2	no	—
43	C₂²×D₄×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	—	2	1	no	—
45	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂×SD₁₆×C₁₉	—	2	8	no	—
52	C₂×SD₁₆×C₁₉	—	2	8	no	—
53	C₂×SD₁₆×C₁₉	—	2	8	no	—
54	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
55	C₁₉×#127	—	2	4	no	—
56	C₁₉×#121	—	2	4	no	—
57	C₁₉×#121	—	2	4	no	—
58	C₁₉×#121	—	4	4	no	—
59	C₁₉×#121	—	4	4	no	—
60	C₄×Q₈×C₁₉	—	2	8	no	—
61	C₄×Q₈×C₁₉	—	2	8	no	—
62	C₄×Q₈×C₁₉	—	2	4	no	—
63	C₄×Q₈×C₁₉	—	2	4	no	—
64	C₄×Q₈×C₁₉	—	2	4	no	—
65	C₄×Q₈×C₁₉	D₄	1	8	yes	complemented
66	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
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×C₄²×C₁₉	—	2	8	no	—
79	C₂×C₄²×C₁₉	—	2	2	no	—
80	C₂×C₄²×C₁₉	—	2	2	no	—
81	C₂×C₄²×C₁₉	—	2	4	no	—
82	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₁₉×C₄⋊C₈	—	2	4	no	—
87	C₁₉×#103	—	2	8	no	—
88	C₁₉×#102	—	2	8	no	—
89	C₁₉×C₂²⋊C₈	—	2	4	no	—
90	C₂⁴×C₁₉	—	2	2	no	—
91	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂×Q₈×C₁₉	—	2	4	no	—
93	C₂×Q₈×C₁₉	—	2	16	no	—
94	C₂×Q₈×C₁₉	—	2	4	no	—
95	C₂×Q₈×C₁₉	—	2	16	no	—
96	C₂×Q₈×C₁₉	—	2	4	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
101	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
102	C₂×Q₈×C₁₉	#41	1	4	yes	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	2	4	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	4	no	—
107	C₂×D₄×C₁₉	—	4	2	no	—
108	C₂×D₄×C₁₉	—	4	2	no	—
109	C₂×D₄×C₁₉	—	4	4	no	—
110	C₂×D₄×C₁₉	—	4	4	no	—
111	C₂×D₄×C₁₉	—	4	4	no	—
112	C₂×D₄×C₁₉	—	4	2	no	—
113	C₂×D₄×C₁₉	—	4	2	no	—
114	C₂×D₄×C₁₉	—	4	2	no	—
115	C₂×D₄×C₁₉	—	4	2	no	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	2	4	no	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	4	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	4	1	no	—
130	C₂²×C₄×C₁₉	—	4	2	no	—
131	C₂²×C₄×C₁₉	—	4	2	no	—
132	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	complemented
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	#41	1	2	yes	—
140	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
141	SD₁₆×C₁₉	—	4	16	no	—
142	C₂×C₈×C₁₉	—	2	4	no	—
143	C₂×C₈×C₁₉	—	2	4	no	—
144	C₂×C₈×C₁₉	—	2	4	no	—
145	C₄⋊C₄×C₁₉	—	2	8	no	—
146	C₄⋊C₄×C₁₉	—	2	4	no	—
147	C₄⋊C₄×C₁₉	—	2	8	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	4	2	no	—
152	C₄⋊C₄×C₁₉	—	4	2	no	—
153	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
154	C₂²⋊C₄×C₁₉	—	4	4	no	—
155	C₂²⋊C₄×C₁₉	—	4	4	no	—
156	C₂²⋊C₄×C₁₉	—	4	4	no	—
157	C₄²×C₁₉	—	2	8	no	—
158	C₄²×C₁₉	—	2	8	no	—
159	C₄²×C₁₉	—	2	2	no	—
160	C₄²×C₁₉	—	2	2	no	—
161	C₄²×C₁₉	—	2	2	no	—
162	C₄²×C₁₉	C₂×D₄	1	4	yes	—
163	#32903	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₁₉	—	2	1	no	—
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	—	2	1	no	—
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	—	4	2	no	—
169	C₂³×C₁₉	—	4	2	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	#121	1	2	yes	—
176	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
177	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
178	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₁₉	—	2	16	no	—
180	Q₈×C₁₉	—	2	4	no	—
181	Q₈×C₁₉	—	2	4	no	—
182	Q₈×C₁₉	—	2	4	no	—
183	Q₈×C₁₉	#121	1	8	yes	complemented
184	D₄×C₁₉	—	4	4	no	—
185	D₄×C₁₉	—	4	4	no	—
186	D₄×C₁₉	—	8	4	no	—
187	D₄×C₁₉	—	8	8	no	—
188	D₄×C₁₉	—	8	4	no	—
189	C₂×C₄×C₁₉	—	2	16	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	2	4	no	—
194	C₂×C₄×C₁₉	—	2	4	no	—
195	C₂×C₄×C₁₉	—	2	1	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	8	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	4	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	4	4	no	—
207	C₂×C₄×C₁₉	—	4	8	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	#120	1	2	yes	—
214	C₂×C₄×C₁₉	#120	1	2	yes	—
215	C₂×C₄×C₁₉	#121	1	2	yes	—
216	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
217	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
218	C₂×C₄×C₁₉	#137	1	2	yes	—
219	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
222	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
223	C₈×C₁₉	—	4	4	no	—
224	C₂²×C₄×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
225	C₂×#460	C₂×C₁₉	1	2	yes	complemented
226	C₂×#448	C₂×C₁₉	1	2	yes	complemented
227	#2856	C₂×C₁₉	1	1	yes	characteristic
228	#1880	C₂×C₁₉	1	4	yes	complemented
229	#1874	C₂×C₁₉	1	2	yes	complemented
230	#1803	C₂×C₁₉	1	2	yes	complemented
231	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
232	C₂²×C₁₉	—	2	2	no	—
233	C₂²×C₁₉	—	2	2	no	—
234	C₂²×C₁₉	—	2	2	no	—
235	C₂²×C₁₉	—	2	2	no	—
236	C₂²×C₁₉	—	2	2	no	—
237	C₂²×C₁₉	—	2	2	no	—
238	C₂²×C₁₉	—	8	2	no	—
239	C₂²×C₁₉	—	8	2	no	—
240	C₂²×C₁₉	—	8	2	no	—
241	C₂²×C₁₉	—	8	2	no	—
242	C₂²×C₁₉	—	8	2	no	—
243	C₂²×C₁₉	—	8	2	no	—
244	C₂²×C₁₉	—	8	2	no	—
245	C₂²×C₁₉	#460	1	4	yes	complemented
246	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
247	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
248	C₂²×C₁₉	#525	1	1	yes	characteristic
249	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
250	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
251	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
252	C₂²×C₁₉	#575	1	1	yes	characteristic
253	C₄×C₁₉	—	2	8	no	—
254	C₄×C₁₉	—	2	2	no	—
255	C₄×C₁₉	—	2	2	no	—
256	C₄×C₁₉	—	2	2	no	—
257	C₄×C₁₉	—	4	1	no	—
258	C₄×C₁₉	—	4	4	no	—
259	C₄×C₁₉	—	8	2	no	—
260	C₄×C₁₉	#448	1	4	yes	complemented
261	C₄×C₁₉	C₂×#121	1	2	yes	—
262	C₄×C₁₉	#525	1	2	yes	—
263	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
264	C₂²×SD₁₆	C₂²×C₁₉	1	4	yes	—
265	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×#121	—	2	1	no	—
267	C₂×#121	—	2	1	no	—
268	C₂×#121	C₂²×C₁₉	1	2	yes	—
269	C₂×C₄×Q₈	—	2	8	no	—
270	C₂×C₄×Q₈	—	2	1	no	—
271	C₂×C₄×Q₈	—	2	1	no	—
272	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
273	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
274	C₂²×C₄⋊C₄	—	2	1	no	—
275	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
276	C₂²×C₄²	—	2	1	no	—
277	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
278	#460	—	2	8	no	—
279	#448	—	2	8	no	—
280	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
281	C₂×#103	C₂²×C₁₉	1	4	yes	—
282	C₂×#102	C₂²×C₁₉	1	4	yes	—
283	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
284	#390	—	2	1	no	—
285	#390	—	2	1	no	—
286	#390	C₂²×C₁₉	1	2	yes	—
287	#384	C₂²×C₁₉	1	1	yes	characteristic
288	#340	C₂²×C₁₉	1	4	yes	—
289	#336	C₂²×C₁₉	1	2	yes	—
290	C₂×C₁₉	—	2	4	no	—
291	C₂×C₁₉	—	16	2	no	—
292	C₂×C₁₉	#2847	1	1	yes	characteristic
293	C₂×C₁₉	C₂×#448	1	1	yes	characteristic
294	C₂×C₁₉	#3006	1	1	yes	characteristic
295	C₂×C₁₉	C₂×#460	1	1	yes	characteristic
296	C₂×C₁₉	#3037	1	1	yes	characteristic
297	C₂×C₁₉	#3103	1	1	yes	characteristic
298	C₂×C₁₉	#3112	1	1	yes	characteristic
299	C₂²×Q₈	—	2	4	no	—
300	C₂²×Q₈	—	2	4	no	—
301	C₂²×Q₈	—	2	1	no	—
302	C₂²×Q₈	—	2	2	no	—
303	C₂²×Q₈	D₄×C₁₉	1	4	yes	complemented
304	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
305	C₂²×D₄	—	2	2	no	—
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
309	C₂³×C₄	—	2	1	no	—
310	C₂³×C₄	—	2	1	no	—
311	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
312	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
313	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
314	C₂×SD₁₆	—	2	8	no	—
315	C₂×SD₁₆	—	2	8	no	—
316	C₂×SD₁₆	—	2	8	no	—
317	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
318	#127	—	2	4	no	—
319	#121	—	2	4	no	—
320	#121	—	2	4	no	—
321	#121	—	4	4	no	—
322	#121	—	4	4	no	—
323	C₄×Q₈	—	2	8	no	—
324	C₄×Q₈	—	2	8	no	—
325	C₄×Q₈	—	2	4	no	—
326	C₄×Q₈	—	2	4	no	—
327	C₄×Q₈	—	2	4	no	—
328	C₄×Q₈	D₄×C₁₉	1	8	yes	complemented
329	C₂×C₄⋊C₄	—	2	8	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	4	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₄²	—	2	8	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	—	2	4	no	—
345	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
346	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
347	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
349	C₄⋊C₈	—	2	4	no	—
350	#103	—	2	8	no	—
351	#102	—	2	8	no	—
352	C₂²⋊C₈	—	2	4	no	—
353	C₁₉	#32903	1	1	yes	characteristic, direct product factor, Sylow
354	C₂⁴	—	2	2	no	—
355	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
356	C₂×Q₈	—	2	4	no	—
357	C₂×Q₈	—	2	16	no	—
358	C₂×Q₈	—	2	4	no	—
359	C₂×Q₈	—	2	16	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
365	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
366	C₂×Q₈	#41×C₁₉	1	4	yes	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	4	no	—
374	C₂×D₄	—	4	4	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	SD₁₆×C₁₉	1	4	yes	complemented
397	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
401	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
403	C₂²×C₄	#41×C₁₉	1	2	yes	—
404	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
405	SD₁₆	—	4	16	no	—
406	C₂×C₈	—	2	4	no	—
407	C₂×C₈	—	2	4	no	—
408	C₂×C₈	—	2	4	no	—
409	C₄⋊C₄	—	2	8	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	8	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₄⋊C₄	—	4	2	no	—
417	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
418	C₂²⋊C₄	—	4	4	no	—
419	C₂²⋊C₄	—	4	4	no	—
420	C₂²⋊C₄	—	4	4	no	—
421	C₄²	—	2	8	no	—
422	C₄²	—	2	8	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	C₂×D₄×C₁₉	1	4	yes	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	1	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	C₁₉×#121	1	2	yes	—
439	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
440	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
441	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
442	Q₈	—	2	16	no	—
443	Q₈	—	2	4	no	—
444	Q₈	—	2	4	no	—
445	Q₈	—	2	4	no	—
446	Q₈	C₁₉×#121	1	8	yes	complemented
447	D₄	—	4	4	no	—
448	D₄	—	4	4	no	—
449	D₄	—	8	4	no	—
450	D₄	—	8	8	no	—
451	D₄	—	8	4	no	—
452	C₂×C₄	—	2	16	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	8	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	—	4	2	no	—
476	C₂×C₄	C₁₉×#120	1	2	yes	—
477	C₂×C₄	C₁₉×#120	1	2	yes	—
478	C₂×C₄	C₁₉×#121	1	2	yes	—
479	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
480	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
481	C₂×C₄	C₁₉×#137	1	2	yes	—
482	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
484	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
485	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
486	C₈	—	4	4	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	8	2	no	—
494	C₂²	—	8	2	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	—	8	2	no	—
499	C₂²	—	8	2	no	—
500	C₂²	C₁₉×#460	1	4	yes	complemented
501	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
502	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
503	C₂²	C₁₉×#525	1	1	yes	characteristic
504	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
505	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
506	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
507	C₂²	C₁₉×#575	1	1	yes	characteristic
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	8	no	—
511	C₄	—	2	2	no	—
512	C₄	—	4	1	no	—
513	C₄	—	4	4	no	—
514	C₄	—	8	2	no	—
515	C₄	C₁₉×#448	1	4	yes	complemented
516	C₄	C₂×C₁₉×#121	1	2	yes	—
517	C₄	C₁₉×#525	1	2	yes	—
518	C₂	—	2	4	no	—
519	C₂	—	16	2	no	—
520	C₂	C₁₉×#2847	1	1	yes	characteristic
521	C₂	C₂×C₁₉×#448	1	1	yes	characteristic
522	C₂	C₁₉×#3006	1	1	yes	characteristic
523	C₂	C₂×C₁₉×#460	1	1	yes	characteristic
524	C₂	C₁₉×#3037	1	1	yes	characteristic
525	C₂	C₁₉×#3103	1	1	yes	characteristic
526	C₂	C₁₉×#3112	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2856	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
1. C₂²×C₄×Q₈×C₁₉	C₂	semidirect
2. C₂×C₁₉×#460	C₂	semidirect
3. C₂×C₁₉×#448	C₂	semidirect
5. C₁₉×#1880	C₂	semidirect
6. C₁₉×#1874	C₂	semidirect
7. C₁₉×#1803	C₂	semidirect
8. C₁₉×#1797	C₂	semidirect
40. C₂²×Q₈×C₁₉	D₄	semidirect
65. C₄×Q₈×C₁₉	D₄	semidirect
132. C₂²×C₄×C₁₉	SD₁₆	semidirect
163. #32903	C₁₉	direct (N × H)
183. Q₈×C₁₉	#121	semidirect
224. C₂²×C₄×Q₈	C₂×C₁₉	semidirect
225. C₂×#460	C₂×C₁₉	semidirect
226. C₂×#448	C₂×C₁₉	semidirect
228. #1880	C₂×C₁₉	semidirect
229. #1874	C₂×C₁₉	semidirect
230. #1803	C₂×C₁₉	semidirect
231. #1797	C₂×C₁₉	semidirect
245. C₂²×C₁₉	#460	semidirect
260. C₄×C₁₉	#448	semidirect
303. C₂²×Q₈	D₄×C₁₉	semidirect
328. C₄×Q₈	D₄×C₁₉	semidirect
353. C₁₉	#32903	direct (N × H)
396. C₂²×C₄	SD₁₆×C₁₉	semidirect
446. Q₈	C₁₉×#121	semidirect
500. C₂²	C₁₉×#460	semidirect
515. C₄	C₁₉×#448	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₁₉	2
C₂×C₁₉×#460	2
C₂×C₁₉×#448	2
C₁₉×#2856	2
C₁₉×#1880	2
C₁₉×#1874	2
C₁₉×#1803	2
C₁₉×#1797	2
#32903	19

Subgroups — C19×#32903 #18038862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32903 #18038862