Subgroups — C₁₉×#32674 #18038633

Order 4864.

842 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2592	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2548	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2054	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2014	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2011	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1984	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1970	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1925	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#124	—	2	1	no	—
22	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#397	—	2	1	no	—
37	C₁₉×#394	—	2	1	no	—
38	C₁₉×#394	—	2	1	no	—
39	C₁₉×#393	—	2	1	no	—
40	C₁₉×#391	C₂²	1	1	yes	characteristic
41	C₁₉×#391	C₂²	1	1	yes	characteristic
42	C₁₉×#390	—	2	1	no	—
43	C₁₉×#390	C₂²	1	1	yes	characteristic
44	C₁₉×#390	C₂²	1	1	yes	characteristic
45	C₁₉×#390	C₂²	1	1	yes	characteristic
46	C₁₉×#390	C₂²	1	1	yes	characteristic
47	C₁₉×#390	C₂²	1	1	yes	characteristic
48	C₁₉×#390	C₂²	1	1	yes	characteristic
49	C₁₉×#388	—	2	1	no	—
50	C₁₉×#388	—	2	1	no	—
51	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#336	C₂²	1	1	yes	characteristic
56	C₁₉×#336	C₂²	1	1	yes	characteristic
57	C₁₉×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
60	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₁₉	—	2	1	no	—
62	C₂²×D₄×C₁₉	—	2	1	no	—
63	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×SD₁₆×C₁₉	—	2	2	no	—
67	C₂×SD₁₆×C₁₉	—	4	1	no	—
68	C₂×SD₁₆×C₁₉	—	4	1	no	—
69	C₂×SD₁₆×C₁₉	—	4	1	no	—
70	C₂×SD₁₆×C₁₉	—	4	1	no	—
71	C₂×SD₁₆×C₁₉	—	4	1	no	—
72	C₂×D₈×C₁₉	—	2	2	no	—
73	C₂×D₈×C₁₉	—	4	1	no	—
74	C₂×D₈×C₁₉	—	4	1	no	—
75	C₂×D₈×C₁₉	—	4	1	no	—
76	C₂×D₈×C₁₉	—	4	1	no	—
77	C₂×D₈×C₁₉	—	4	1	no	—
78	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
82	C₁₉×#127	—	4	1	no	—
83	C₁₉×#127	—	4	1	no	—
84	C₁₉×#124	—	4	1	no	—
85	C₁₉×#124	—	4	1	no	—
86	C₁₉×#124	—	4	4	no	—
87	C₄×Q₈×C₁₉	—	4	1	no	—
88	C₄×Q₈×C₁₉	—	4	1	no	—
89	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₄²×C₁₉	—	2	1	no	—
111	C₂×C₄²×C₁₉	—	2	1	no	—
112	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
115	C₁₉×#107	—	4	1	no	—
116	C₁₉×#106	—	4	1	no	—
117	C₁₉×C₄⋊C₈	—	4	1	no	—
118	C₁₉×#103	—	2	2	no	—
119	C₁₉×#103	—	4	1	no	—
120	C₁₉×#102	—	2	2	no	—
121	C₁₉×#102	—	2	2	no	—
122	C₁₉×#102	—	2	2	no	—
123	C₁₉×#102	—	4	1	no	—
124	C₁₉×#102	—	4	1	no	—
125	C₁₉×#102	—	4	1	no	—
126	C₄×C₈×C₁₉	—	4	1	no	—
127	C₁₉×#95	—	2	1	no	—
128	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	—	2	1	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	—	2	1	no	—
133	C₂⁴×C₁₉	—	2	1	no	—
134	C₂⁴×C₁₉	—	2	1	no	—
135	C₂⁴×C₁₉	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	2	2	no	—
137	C₂×Q₈×C₁₉	—	2	2	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	2	1	no	—
143	C₂×Q₈×C₁₉	—	2	1	no	—
144	C₂×Q₈×C₁₉	—	4	1	no	—
145	C₂×D₄×C₁₉	—	2	1	no	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	—	2	1	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	4	2	no	—
164	C₂×D₄×C₁₉	—	4	2	no	—
165	C₂×D₄×C₁₉	—	4	2	no	—
166	C₂×D₄×C₁₉	—	4	2	no	—
167	C₂×D₄×C₁₉	—	8	1	no	—
168	C₂×D₄×C₁₉	—	8	1	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
181	SD₁₆×C₁₉	—	4	4	no	—
182	SD₁₆×C₁₉	—	4	4	no	—
183	D₈×C₁₉	—	4	4	no	—
184	D₈×C₁₉	—	4	4	no	—
185	C₂×C₈×C₁₉	—	2	1	no	—
186	C₂×C₈×C₁₉	—	2	1	no	—
187	C₂×C₈×C₁₉	—	2	1	no	—
188	C₂×C₈×C₁₉	—	2	1	no	—
189	C₂×C₈×C₁₉	—	2	1	no	—
190	C₂×C₈×C₁₉	—	2	1	no	—
191	C₂×C₈×C₁₉	—	2	1	no	—
192	C₂×C₈×C₁₉	—	2	1	no	—
193	C₂×C₈×C₁₉	—	2	1	no	—
194	C₂×C₈×C₁₉	—	2	1	no	—
195	C₂×C₈×C₁₉	#41	1	2	yes	—
196	C₂×C₈×C₁₉	#41	1	2	yes	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	4	1	no	—
206	C₄⋊C₄×C₁₉	—	4	1	no	—
207	C₄⋊C₄×C₁₉	—	4	1	no	—
208	C₂²⋊C₄×C₁₉	—	4	2	no	—
209	C₂²⋊C₄×C₁₉	—	4	2	no	—
210	C₂²⋊C₄×C₁₉	—	4	2	no	—
211	C₂²⋊C₄×C₁₉	—	4	2	no	—
212	C₂²⋊C₄×C₁₉	—	4	2	no	—
213	C₂²⋊C₄×C₁₉	—	4	2	no	—
214	C₂²⋊C₄×C₁₉	—	4	2	no	—
215	C₂²⋊C₄×C₁₉	—	4	2	no	—
216	C₂²⋊C₄×C₁₉	—	8	1	no	—
217	C₂²⋊C₄×C₁₉	—	8	1	no	—
218	C₂²⋊C₄×C₁₉	—	8	1	no	—
219	C₂²⋊C₄×C₁₉	—	8	1	no	—
220	C₂²⋊C₄×C₁₉	—	8	1	no	—
221	C₂²⋊C₄×C₁₉	—	8	1	no	—
222	C₄²×C₁₉	—	2	1	no	—
223	C₄²×C₁₉	—	2	1	no	—
224	C₄²×C₁₉	—	2	1	no	—
225	C₄²×C₁₉	—	2	1	no	—
226	C₄²×C₁₉	—	2	1	no	—
227	C₄²×C₁₉	—	2	1	no	—
228	C₄²×C₁₉	—	4	2	no	—
229	C₄²×C₁₉	—	8	1	no	—
230	#32674	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂³×C₁₉	—	4	1	no	—
232	C₂³×C₁₉	—	4	1	no	—
233	C₂³×C₁₉	—	4	1	no	—
234	C₂³×C₁₉	—	4	1	no	—
235	C₂³×C₁₉	—	4	1	no	—
236	C₂³×C₁₉	—	4	1	no	—
237	C₂³×C₁₉	—	4	1	no	—
238	C₂³×C₁₉	—	4	1	no	—
239	C₂³×C₁₉	—	4	1	no	—
240	C₂³×C₁₉	—	4	1	no	—
241	C₂³×C₁₉	—	4	1	no	—
242	C₂³×C₁₉	—	4	1	no	—
243	C₂³×C₁₉	—	4	1	no	—
244	C₂³×C₁₉	—	4	1	no	—
245	C₂³×C₁₉	—	4	1	no	—
246	C₂³×C₁₉	—	4	1	no	—
247	C₂³×C₁₉	—	4	1	no	—
248	C₂³×C₁₉	—	4	1	no	—
249	C₂³×C₁₉	—	4	1	no	—
250	C₂³×C₁₉	—	4	1	no	—
251	C₂³×C₁₉	—	4	1	no	—
252	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
253	Q₈×C₁₉	—	4	4	no	—
254	Q₈×C₁₉	—	4	1	no	—
255	Q₈×C₁₉	—	4	1	no	—
256	Q₈×C₁₉	—	4	1	no	—
257	Q₈×C₁₉	—	4	1	no	—
258	D₄×C₁₉	—	4	1	no	—
259	D₄×C₁₉	—	4	1	no	—
260	D₄×C₁₉	—	4	1	no	—
261	D₄×C₁₉	—	4	1	no	—
262	D₄×C₁₉	—	4	1	no	—
263	D₄×C₁₉	—	4	1	no	—
264	D₄×C₁₉	—	4	1	no	—
265	D₄×C₁₉	—	4	1	no	—
266	D₄×C₁₉	—	4	1	no	—
267	D₄×C₁₉	—	4	1	no	—
268	D₄×C₁₉	—	4	1	no	—
269	D₄×C₁₉	—	4	1	no	—
270	D₄×C₁₉	—	8	4	no	—
271	D₄×C₁₉	—	8	4	no	—
272	C₂×C₄×C₁₉	—	2	1	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	1	no	—
276	C₂×C₄×C₁₉	—	2	1	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	1	no	—
279	C₂×C₄×C₁₉	—	2	1	no	—
280	C₂×C₄×C₁₉	—	2	1	no	—
281	C₂×C₄×C₁₉	—	2	1	no	—
282	C₂×C₄×C₁₉	—	2	1	no	—
283	C₂×C₄×C₁₉	—	2	1	no	—
284	C₂×C₄×C₁₉	—	2	1	no	—
285	C₂×C₄×C₁₉	—	2	1	no	—
286	C₂×C₄×C₁₉	—	2	1	no	—
287	C₂×C₄×C₁₉	—	2	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	1	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	4	1	no	—
294	C₂×C₄×C₁₉	—	4	1	no	—
295	C₂×C₄×C₁₉	—	4	1	no	—
296	C₂×C₄×C₁₉	—	4	1	no	—
297	C₂×C₄×C₁₉	—	4	1	no	—
298	C₂×C₄×C₁₉	—	4	1	no	—
299	C₂×C₄×C₁₉	—	4	1	no	—
300	C₂×C₄×C₁₉	—	4	1	no	—
301	C₂×C₄×C₁₉	—	4	1	no	—
302	C₂×C₄×C₁₉	—	4	1	no	—
303	C₂×C₄×C₁₉	#135	1	2	yes	—
304	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
305	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
308	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
311	C₈×C₁₉	—	2	2	no	—
312	C₈×C₁₉	—	2	2	no	—
313	C₈×C₁₉	—	4	1	no	—
314	C₈×C₁₉	—	4	1	no	—
315	#2592	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#2548	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#2055	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#2054	C₂×C₁₉	1	1	yes	characteristic, complemented
319	#2014	C₂×C₁₉	1	1	yes	characteristic, complemented
320	#2012	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#2012	C₂×C₁₉	1	1	yes	characteristic, complemented
322	#2011	C₂×C₁₉	1	1	yes	characteristic
323	#1984	C₂×C₁₉	1	1	yes	characteristic, complemented
324	#1970	C₂×C₁₉	1	1	yes	characteristic, complemented
325	#1968	C₂×C₁₉	1	1	yes	characteristic, complemented
326	#1928	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#1926	C₂×C₁₉	1	1	yes	characteristic, complemented
328	#1926	C₂×C₁₉	1	1	yes	characteristic, complemented
329	#1925	C₂×C₁₉	1	1	yes	characteristic, complemented
330	C₂²×C₁₉	—	8	1	no	—
331	C₂²×C₁₉	—	8	1	no	—
332	C₂²×C₁₉	—	8	1	no	—
333	C₂²×C₁₉	—	8	1	no	—
334	C₂²×C₁₉	—	8	1	no	—
335	C₂²×C₁₉	—	8	1	no	—
336	C₂²×C₁₉	—	8	1	no	—
337	C₂²×C₁₉	—	8	1	no	—
338	C₂²×C₁₉	—	8	1	no	—
339	C₂²×C₁₉	—	8	1	no	—
340	C₂²×C₁₉	—	8	1	no	—
341	C₂²×C₁₉	—	8	1	no	—
342	C₂²×C₁₉	—	8	1	no	—
343	C₂²×C₁₉	—	8	1	no	—
344	C₂²×C₁₉	—	8	1	no	—
345	C₂²×C₁₉	—	8	1	no	—
346	C₂²×C₁₉	—	8	1	no	—
347	C₂²×C₁₉	—	8	1	no	—
348	C₂²×C₁₉	—	8	1	no	—
349	C₂²×C₁₉	—	8	1	no	—
350	C₂²×C₁₉	—	8	1	no	—
351	C₂²×C₁₉	#534	1	1	yes	characteristic
352	C₂²×C₁₉	#550	1	1	yes	characteristic
353	C₂²×C₁₉	#550	1	1	yes	characteristic
354	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
355	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
356	C₂²×C₁₉	#576	1	1	yes	characteristic
357	C₂²×C₁₉	#577	1	1	yes	characteristic
358	C₄×C₁₉	—	2	2	no	—
359	C₄×C₁₉	—	2	2	no	—
360	C₄×C₁₉	—	4	1	no	—
361	C₄×C₁₉	—	4	1	no	—
362	C₄×C₁₉	—	4	1	no	—
363	C₄×C₁₉	—	4	1	no	—
364	C₄×C₁₉	—	8	1	no	—
365	C₄×C₁₉	—	8	1	no	—
366	C₄×C₁₉	—	8	1	no	—
367	C₄×C₁₉	—	8	1	no	—
368	C₄×C₁₉	—	8	1	no	—
369	C₄×C₁₉	#538	1	1	yes	characteristic
370	C₄×C₁₉	#538	1	1	yes	characteristic
371	C₄×C₁₉	#555	1	1	yes	characteristic
372	C₄×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
373	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
374	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
375	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
376	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
377	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×#124	—	2	1	no	—
379	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
380	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
382	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
383	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
384	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
385	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
386	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
389	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
390	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
391	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
392	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
393	#397	—	2	1	no	—
394	#394	—	2	1	no	—
395	#394	—	2	1	no	—
396	#393	—	2	1	no	—
397	#391	C₂²×C₁₉	1	1	yes	characteristic
398	#391	C₂²×C₁₉	1	1	yes	characteristic
399	#390	—	2	1	no	—
400	#390	C₂²×C₁₉	1	1	yes	characteristic
401	#390	C₂²×C₁₉	1	1	yes	characteristic
402	#390	C₂²×C₁₉	1	1	yes	characteristic
403	#390	C₂²×C₁₉	1	1	yes	characteristic
404	#390	C₂²×C₁₉	1	1	yes	characteristic
405	#390	C₂²×C₁₉	1	1	yes	characteristic
406	#388	—	2	1	no	—
407	#388	—	2	1	no	—
408	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
409	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
410	#340	C₂²×C₁₉	1	1	yes	characteristic
411	#340	C₂²×C₁₉	1	1	yes	characteristic
412	#336	C₂²×C₁₉	1	1	yes	characteristic
413	#336	C₂²×C₁₉	1	1	yes	characteristic
414	#336	C₂²×C₁₉	1	1	yes	characteristic
415	#336	C₂²×C₁₉	1	1	yes	characteristic
416	C₂×C₁₉	—	16	1	no	—
417	C₂×C₁₉	—	16	1	no	—
418	C₂×C₁₉	—	16	1	no	—
419	C₂×C₁₉	#2733	1	1	yes	characteristic
420	C₂×C₁₉	#3188	1	1	yes	characteristic
421	C₂×C₁₉	#3198	1	1	yes	characteristic
422	C₂×C₁₉	#3394	1	1	yes	characteristic
423	C₂×C₁₉	#3396	1	1	yes	characteristic
424	C₂×C₁₉	#3397	1	1	yes	characteristic
425	C₂×C₁₉	#3399	1	1	yes	characteristic
426	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
427	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
428	C₂²×D₄	—	2	1	no	—
429	C₂²×D₄	—	2	1	no	—
430	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
431	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
432	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
433	C₂×SD₁₆	—	2	2	no	—
434	C₂×SD₁₆	—	4	1	no	—
435	C₂×SD₁₆	—	4	1	no	—
436	C₂×SD₁₆	—	4	1	no	—
437	C₂×SD₁₆	—	4	1	no	—
438	C₂×SD₁₆	—	4	1	no	—
439	C₂×D₈	—	2	2	no	—
440	C₂×D₈	—	4	1	no	—
441	C₂×D₈	—	4	1	no	—
442	C₂×D₈	—	4	1	no	—
443	C₂×D₈	—	4	1	no	—
444	C₂×D₈	—	4	1	no	—
445	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
449	#127	—	4	1	no	—
450	#127	—	4	1	no	—
451	#124	—	4	1	no	—
452	#124	—	4	1	no	—
453	#124	—	4	4	no	—
454	C₄×Q₈	—	4	1	no	—
455	C₄×Q₈	—	4	1	no	—
456	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
457	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
458	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	—	2	1	no	—
472	C₂×C₂²⋊C₄	—	2	1	no	—
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	2	1	no	—
477	C₂×C₄²	—	2	1	no	—
478	C₂×C₄²	—	2	1	no	—
479	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
482	#107	—	4	1	no	—
483	#106	—	4	1	no	—
484	C₄⋊C₈	—	4	1	no	—
485	#103	—	2	2	no	—
486	#103	—	4	1	no	—
487	#102	—	2	2	no	—
488	#102	—	2	2	no	—
489	#102	—	2	2	no	—
490	#102	—	4	1	no	—
491	#102	—	4	1	no	—
492	#102	—	4	1	no	—
493	C₄×C₈	—	4	1	no	—
494	#95	—	2	1	no	—
495	#95	—	2	1	no	—
496	#95	—	2	1	no	—
497	#95	—	2	1	no	—
498	#95	—	2	1	no	—
499	#95	—	2	1	no	—
500	C₁₉	#32674	1	1	yes	characteristic, direct product factor, Sylow
501	C₂⁴	—	2	1	no	—
502	C₂⁴	—	2	1	no	—
503	C₂⁴	—	2	1	no	—
504	C₂×Q₈	—	2	2	no	—
505	C₂×Q₈	—	2	2	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	4	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	4	2	no	—
532	C₂×D₄	—	4	2	no	—
533	C₂×D₄	—	4	2	no	—
534	C₂×D₄	—	4	2	no	—
535	C₂×D₄	—	8	1	no	—
536	C₂×D₄	—	8	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
543	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
544	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
545	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
546	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
549	SD₁₆	—	4	4	no	—
550	SD₁₆	—	4	4	no	—
551	D₈	—	4	4	no	—
552	D₈	—	4	4	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	#41×C₁₉	1	2	yes	—
564	C₂×C₈	#41×C₁₉	1	2	yes	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	4	1	no	—
574	C₄⋊C₄	—	4	1	no	—
575	C₄⋊C₄	—	4	1	no	—
576	C₂²⋊C₄	—	4	2	no	—
577	C₂²⋊C₄	—	4	2	no	—
578	C₂²⋊C₄	—	4	2	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	4	2	no	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	4	2	no	—
583	C₂²⋊C₄	—	4	2	no	—
584	C₂²⋊C₄	—	8	1	no	—
585	C₂²⋊C₄	—	8	1	no	—
586	C₂²⋊C₄	—	8	1	no	—
587	C₂²⋊C₄	—	8	1	no	—
588	C₂²⋊C₄	—	8	1	no	—
589	C₂²⋊C₄	—	8	1	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	2	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	2	1	no	—
595	C₄²	—	2	1	no	—
596	C₄²	—	4	2	no	—
597	C₄²	—	8	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	1	no	—
619	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
620	Q₈	—	4	4	no	—
621	Q₈	—	4	1	no	—
622	Q₈	—	4	1	no	—
623	Q₈	—	4	1	no	—
624	Q₈	—	4	1	no	—
625	D₄	—	4	1	no	—
626	D₄	—	4	1	no	—
627	D₄	—	4	1	no	—
628	D₄	—	4	1	no	—
629	D₄	—	4	1	no	—
630	D₄	—	4	1	no	—
631	D₄	—	4	1	no	—
632	D₄	—	4	1	no	—
633	D₄	—	4	1	no	—
634	D₄	—	4	1	no	—
635	D₄	—	4	1	no	—
636	D₄	—	4	1	no	—
637	D₄	—	8	4	no	—
638	D₄	—	8	4	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	C₁₉×#135	1	2	yes	—
671	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
672	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
673	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
674	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
675	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
676	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
677	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
678	C₈	—	2	2	no	—
679	C₈	—	2	2	no	—
680	C₈	—	4	1	no	—
681	C₈	—	4	1	no	—
682	C₂²	—	8	1	no	—
683	C₂²	—	8	1	no	—
684	C₂²	—	8	1	no	—
685	C₂²	—	8	1	no	—
686	C₂²	—	8	1	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	—	8	1	no	—
692	C₂²	—	8	1	no	—
693	C₂²	—	8	1	no	—
694	C₂²	—	8	1	no	—
695	C₂²	—	8	1	no	—
696	C₂²	—	8	1	no	—
697	C₂²	—	8	1	no	—
698	C₂²	—	8	1	no	—
699	C₂²	—	8	1	no	—
700	C₂²	—	8	1	no	—
701	C₂²	—	8	1	no	—
702	C₂²	—	8	1	no	—
703	C₂²	C₁₉×#534	1	1	yes	characteristic
704	C₂²	C₁₉×#550	1	1	yes	characteristic
705	C₂²	C₁₉×#550	1	1	yes	characteristic
706	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
707	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
708	C₂²	C₁₉×#576	1	1	yes	characteristic
709	C₂²	C₁₉×#577	1	1	yes	characteristic
710	C₄	—	2	2	no	—
711	C₄	—	2	2	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	1	no	—
714	C₄	—	4	1	no	—
715	C₄	—	4	1	no	—
716	C₄	—	8	1	no	—
717	C₄	—	8	1	no	—
718	C₄	—	8	1	no	—
719	C₄	—	8	1	no	—
720	C₄	—	8	1	no	—
721	C₄	C₁₉×#538	1	1	yes	characteristic
722	C₄	C₁₉×#538	1	1	yes	characteristic
723	C₄	C₁₉×#555	1	1	yes	characteristic
724	C₄	C₁₉×H(3,𝔽₄)	1	1	yes	characteristic
725	C₂	—	16	1	no	—
726	C₂	—	16	1	no	—
727	C₂	—	16	1	no	—
728	C₂	C₁₉×#2733	1	1	yes	characteristic
729	C₂	C₁₉×#3188	1	1	yes	characteristic
730	C₂	C₁₉×#3198	1	1	yes	characteristic
731	C₂	C₁₉×#3394	1	1	yes	characteristic
732	C₂	C₁₉×#3396	1	1	yes	characteristic
733	C₂	C₁₉×#3397	1	1	yes	characteristic
734	C₂	C₁₉×#3399	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2011	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2592	C₂	semidirect
2. C₁₉×#2548	C₂	semidirect
3. C₁₉×#2055	C₂	semidirect
4. C₁₉×#2054	C₂	semidirect
5. C₁₉×#2014	C₂	semidirect
6. C₁₉×#2012	C₂	semidirect
7. C₁₉×#2012	C₂	semidirect
9. C₁₉×#1984	C₂	semidirect
10. C₁₉×#1970	C₂	semidirect
11. C₁₉×#1968	C₂	semidirect
12. C₁₉×#1928	C₂	semidirect
13. C₁₉×#1926	C₂	semidirect
14. C₁₉×#1926	C₂	semidirect
15. C₁₉×#1925	C₂	semidirect
230. #32674	C₁₉	direct (N × H)
315. #2592	C₂×C₁₉	semidirect
316. #2548	C₂×C₁₉	semidirect
317. #2055	C₂×C₁₉	semidirect
318. #2054	C₂×C₁₉	semidirect
319. #2014	C₂×C₁₉	semidirect
320. #2012	C₂×C₁₉	semidirect
321. #2012	C₂×C₁₉	semidirect
323. #1984	C₂×C₁₉	semidirect
324. #1970	C₂×C₁₉	semidirect
325. #1968	C₂×C₁₉	semidirect
326. #1928	C₂×C₁₉	semidirect
327. #1926	C₂×C₁₉	semidirect
328. #1926	C₂×C₁₉	semidirect
329. #1925	C₂×C₁₉	semidirect
500. C₁₉	#32674	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2592	2
C₁₉×#2548	2
C₁₉×#2055	2
C₁₉×#2054	2
C₁₉×#2014	2
C₁₉×#2012	2
C₁₉×#2011	2
C₁₉×#1984	2
C₁₉×#1970	2
C₁₉×#1968	2
C₁₉×#1928	2
C₁₉×#1926	2
C₁₉×#1925	2
#32674	19

Subgroups — C19×#32674 #18038633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32674 #18038633