Subgroups — C₁₉×#26729 #18032688

Order 4864.

860 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2491	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2363	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2054	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2023	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1999	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1934	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1923	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1825	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#124	—	2	1	no	—
19	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#102	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#394	—	2	1	no	—
35	C₁₉×#393	—	2	1	no	—
36	C₁₉×#390	—	2	1	no	—
37	C₁₉×#390	C₂²	1	1	yes	characteristic
38	C₁₉×#390	C₂²	1	1	yes	characteristic
39	C₁₉×#390	C₂²	1	1	yes	characteristic
40	C₁₉×#389	C₂²	1	1	yes	characteristic
41	C₁₉×#388	—	2	1	no	—
42	C₁₉×#388	—	2	1	no	—
43	C₁₉×#386	—	2	1	no	—
44	C₁₉×#380	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
48	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#340	C₂²	1	1	yes	characteristic
50	C₁₉×#340	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	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	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	—	2	1	no	—
62	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	—	2	1	no	—
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×D₈×C₁₉	—	2	2	no	—
67	C₂×D₈×C₁₉	—	4	1	no	—
68	C₂×D₈×C₁₉	—	4	1	no	—
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×C₄⋊Q₈	—	2	2	no	—
74	C₁₉×C₄⋊Q₈	—	4	1	no	—
75	C₁₉×#124	—	4	4	no	—
76	C₁₉×#121	—	2	2	no	—
77	C₁₉×#121	—	2	2	no	—
78	C₁₉×#121	—	2	2	no	—
79	C₁₉×#121	—	4	1	no	—
80	C₄×D₄×C₁₉	—	2	2	no	—
81	C₄×D₄×C₁₉	—	4	1	no	—
82	C₁₉×#117	—	2	2	no	—
83	C₁₉×#117	—	4	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₉	—	2	1	no	—
106	C₂×C₄²×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
110	C₁₉×#106	—	2	2	no	—
111	C₁₉×C₄⋊C₈	—	4	1	no	—
112	C₁₉×#102	—	2	2	no	—
113	C₁₉×#102	—	2	2	no	—
114	C₁₉×#102	—	2	2	no	—
115	C₁₉×#102	—	2	2	no	—
116	C₁₉×#102	—	4	1	no	—
117	C₁₉×#102	—	4	1	no	—
118	C₁₉×C₂²⋊C₈	—	4	1	no	—
119	C₁₉×C₂²⋊C₈	—	4	1	no	—
120	C₄×C₈×C₁₉	—	4	1	no	—
121	C₁₉×#95	—	2	1	no	—
122	C₁₉×#95	—	2	1	no	—
123	C₁₉×#95	—	2	1	no	—
124	C₁₉×#95	—	2	1	no	—
125	C₁₉×#95	D₄	1	1	yes	characteristic
126	C₁₉×#95	D₄	1	1	yes	characteristic
127	C₂⁴×C₁₉	—	2	1	no	—
128	C₂⁴×C₁₉	—	2	1	no	—
129	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂×Q₈×C₁₉	—	4	2	no	—
131	C₂×Q₈×C₁₉	—	4	2	no	—
132	C₂×Q₈×C₁₉	—	8	1	no	—
133	C₂×D₄×C₁₉	—	2	4	no	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	—	2	1	no	—
139	C₂×D₄×C₁₉	—	2	1	no	—
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	—	2	1	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	4	2	no	—
146	C₂×D₄×C₁₉	—	4	2	no	—
147	C₂×D₄×C₁₉	—	8	1	no	—
148	C₂×D₄×C₁₉	—	8	1	no	—
149	C₂×D₄×C₁₉	—	8	1	no	—
150	C₂×D₄×C₁₉	#41	1	2	yes	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	4	2	no	—
164	C₂²×C₄×C₁₉	—	4	2	no	—
165	C₂²×C₄×C₁₉	—	8	1	no	—
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
172	D₈×C₁₉	—	4	4	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
178	C₂×C₈×C₁₉	—	2	1	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	2	1	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	4	2	no	—
195	C₄⋊C₄×C₁₉	—	8	1	no	—
196	C₄⋊C₄×C₁₉	#41	1	2	yes	—
197	C₄⋊C₄×C₁₉	#41	1	2	yes	—
198	C₄⋊C₄×C₁₉	#41	1	2	yes	—
199	C₂²⋊C₄×C₁₉	—	2	4	no	—
200	C₂²⋊C₄×C₁₉	—	2	2	no	—
201	C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₉	—	4	2	no	—
203	C₂²⋊C₄×C₁₉	—	4	2	no	—
204	C₂²⋊C₄×C₁₉	—	4	2	no	—
205	C₂²⋊C₄×C₁₉	—	4	2	no	—
206	C₂²⋊C₄×C₁₉	—	4	2	no	—
207	C₂²⋊C₄×C₁₉	—	4	2	no	—
208	C₂²⋊C₄×C₁₉	—	4	2	no	—
209	C₂²⋊C₄×C₁₉	—	4	2	no	—
210	C₂²⋊C₄×C₁₉	—	8	1	no	—
211	C₂²⋊C₄×C₁₉	—	8	1	no	—
212	C₄²×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	—	2	1	no	—
214	C₄²×C₁₉	—	2	1	no	—
215	C₄²×C₁₉	—	2	1	no	—
216	C₄²×C₁₉	—	4	2	no	—
217	C₄²×C₁₉	—	4	2	no	—
218	C₄²×C₁₉	—	8	1	no	—
219	#26729	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂³×C₁₉	—	2	2	no	—
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	2	1	no	—
223	C₂³×C₁₉	—	2	1	no	—
224	C₂³×C₁₉	—	2	1	no	—
225	C₂³×C₁₉	—	2	1	no	—
226	C₂³×C₁₉	—	2	1	no	—
227	C₂³×C₁₉	—	2	1	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	4	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
242	Q₈×C₁₉	—	8	4	no	—
243	D₄×C₁₉	—	2	2	no	—
244	D₄×C₁₉	—	2	2	no	—
245	D₄×C₁₉	—	4	1	no	—
246	D₄×C₁₉	—	4	1	no	—
247	D₄×C₁₉	—	4	1	no	—
248	D₄×C₁₉	—	4	1	no	—
249	D₄×C₁₉	—	4	1	no	—
250	D₄×C₁₉	—	4	1	no	—
251	D₄×C₁₉	—	8	4	no	—
252	D₄×C₁₉	—	8	4	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	2	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	2	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	2	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	2	1	no	—
268	C₂×C₄×C₁₉	—	2	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	4	1	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	4	1	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	1	no	—
288	C₂×C₄×C₁₉	—	8	4	no	—
289	C₂×C₄×C₁₉	#135	1	2	yes	—
290	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
291	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
295	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
296	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
297	C₈×C₁₉	—	4	1	no	—
298	C₈×C₁₉	—	4	1	no	—
299	C₈×C₁₉	—	4	1	no	—
300	C₈×C₁₉	—	4	1	no	—
301	#2491	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#2363	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#2054	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#2034	C₂×C₁₉	1	1	yes	characteristic, complemented
305	#2023	C₂×C₁₉	1	1	yes	characteristic, complemented
306	#1999	C₂×C₁₉	1	1	yes	characteristic
307	#1987	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#1934	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#1926	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#1923	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#1920	C₂×C₁₉	1	1	yes	characteristic, complemented
312	#1879	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1875	C₂×C₁₉	1	1	yes	characteristic, complemented
314	#1825	C₂×C₁₉	1	1	yes	characteristic, complemented
315	C₄×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
316	C₂²×C₁₉	—	4	1	no	—
317	C₂²×C₁₉	—	4	2	no	—
318	C₂²×C₁₉	—	4	1	no	—
319	C₂²×C₁₉	—	4	2	no	—
320	C₂²×C₁₉	—	4	1	no	—
321	C₂²×C₁₉	—	4	2	no	—
322	C₂²×C₁₉	—	4	1	no	—
323	C₂²×C₁₉	—	4	1	no	—
324	C₂²×C₁₉	—	4	1	no	—
325	C₂²×C₁₉	—	4	1	no	—
326	C₂²×C₁₉	—	8	1	no	—
327	C₂²×C₁₉	—	8	1	no	—
328	C₂²×C₁₉	—	8	1	no	—
329	C₂²×C₁₉	—	8	1	no	—
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	#525	1	1	yes	characteristic
338	C₂²×C₁₉	#546	1	1	yes	characteristic
339	C₂²×C₁₉	#546	1	1	yes	characteristic
340	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
341	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
342	C₂²×C₁₉	#576	1	1	yes	characteristic
343	C₂²×C₁₉	#577	1	1	yes	characteristic
344	C₄×C₁₉	—	2	2	no	—
345	C₄×C₁₉	—	2	2	no	—
346	C₄×C₁₉	—	4	2	no	—
347	C₄×C₁₉	—	4	1	no	—
348	C₄×C₁₉	—	4	1	no	—
349	C₄×C₁₉	—	4	2	no	—
350	C₄×C₁₉	—	4	1	no	—
351	C₄×C₁₉	—	4	2	no	—
352	C₄×C₁₉	—	8	1	no	—
353	C₄×C₁₉	—	8	1	no	—
354	C₄×C₁₉	—	8	1	no	—
355	C₄×C₁₉	#529	1	1	yes	characteristic
356	C₄×C₁₉	#538	1	1	yes	characteristic
357	C₄×C₁₉	#555	1	1	yes	characteristic
358	C₄×C₁₉	#559	1	1	yes	characteristic
359	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
361	C₂×#124	—	2	1	no	—
362	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
363	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
364	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
370	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
371	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
377	#394	—	2	1	no	—
378	#393	—	2	1	no	—
379	#390	—	2	1	no	—
380	#390	C₂²×C₁₉	1	1	yes	characteristic
381	#390	C₂²×C₁₉	1	1	yes	characteristic
382	#390	C₂²×C₁₉	1	1	yes	characteristic
383	#389	C₂²×C₁₉	1	1	yes	characteristic
384	#388	—	2	1	no	—
385	#388	—	2	1	no	—
386	#386	—	2	1	no	—
387	#380	C₂²×C₁₉	1	1	yes	characteristic
388	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
389	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
390	C₄×C₂²⋊C₄	—	2	1	no	—
391	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
392	#340	C₂²×C₁₉	1	1	yes	characteristic
393	#340	C₂²×C₁₉	1	1	yes	characteristic
394	#340	C₂²×C₁₉	1	1	yes	characteristic
395	#340	C₂²×C₁₉	1	1	yes	characteristic
396	#340	C₂²×C₁₉	1	1	yes	characteristic
397	#340	C₂²×C₁₉	1	1	yes	characteristic
398	#340	C₂²×C₁₉	1	1	yes	characteristic
399	#340	C₂²×C₁₉	1	1	yes	characteristic
400	#336	C₂²×C₁₉	1	1	yes	characteristic
401	#336	C₂²×C₁₉	1	1	yes	characteristic
402	C₂×C₁₉	—	8	1	no	—
403	C₂×C₁₉	—	8	2	no	—
404	C₂×C₁₉	—	16	1	no	—
405	C₂×C₁₉	#2459	1	1	yes	characteristic
406	C₂×C₁₉	#3106	1	1	yes	characteristic
407	C₂×C₁₉	#3118	1	1	yes	characteristic
408	C₂×C₁₉	#3301	1	1	yes	characteristic
409	C₂×C₁₉	#3305	1	1	yes	characteristic
410	C₂×C₁₉	#3306	1	1	yes	characteristic
411	C₂×C₁₉	#3325	1	1	yes	characteristic
412	C₂²×Q₈	—	2	1	no	—
413	C₂²×D₄	—	2	1	no	—
414	C₂²×D₄	—	2	1	no	—
415	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
416	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
417	C₂³×C₄	—	2	1	no	—
418	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
419	C₂×D₈	—	2	2	no	—
420	C₂×D₈	—	4	1	no	—
421	C₂×D₈	—	4	1	no	—
422	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
424	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
425	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
426	C₄⋊Q₈	—	2	2	no	—
427	C₄⋊Q₈	—	4	1	no	—
428	#124	—	4	4	no	—
429	#121	—	2	2	no	—
430	#121	—	2	2	no	—
431	#121	—	2	2	no	—
432	#121	—	4	1	no	—
433	C₄×D₄	—	2	2	no	—
434	C₄×D₄	—	4	1	no	—
435	#117	—	2	2	no	—
436	#117	—	4	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
457	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
458	C₂×C₄²	—	2	1	no	—
459	C₂×C₄²	—	2	1	no	—
460	C₂×C₄²	—	2	1	no	—
461	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
463	#106	—	2	2	no	—
464	C₄⋊C₈	—	4	1	no	—
465	#102	—	2	2	no	—
466	#102	—	2	2	no	—
467	#102	—	2	2	no	—
468	#102	—	2	2	no	—
469	#102	—	4	1	no	—
470	#102	—	4	1	no	—
471	C₂²⋊C₈	—	4	1	no	—
472	C₂²⋊C₈	—	4	1	no	—
473	C₄×C₈	—	4	1	no	—
474	#95	—	2	1	no	—
475	#95	—	2	1	no	—
476	#95	—	2	1	no	—
477	#95	—	2	1	no	—
478	#95	D₄×C₁₉	1	1	yes	characteristic
479	#95	D₄×C₁₉	1	1	yes	characteristic
480	C₁₉	#26729	1	1	yes	characteristic, direct product factor, Sylow
481	C₂⁴	—	2	1	no	—
482	C₂⁴	—	2	1	no	—
483	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂×Q₈	—	4	2	no	—
485	C₂×Q₈	—	4	2	no	—
486	C₂×Q₈	—	8	1	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	4	2	no	—
500	C₂×D₄	—	4	2	no	—
501	C₂×D₄	—	8	1	no	—
502	C₂×D₄	—	8	1	no	—
503	C₂×D₄	—	8	1	no	—
504	C₂×D₄	#41×C₁₉	1	2	yes	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	—	8	1	no	—
520	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
521	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
526	D₈	—	4	4	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	8	1	no	—
550	C₄⋊C₄	#41×C₁₉	1	2	yes	—
551	C₄⋊C₄	#41×C₁₉	1	2	yes	—
552	C₄⋊C₄	#41×C₁₉	1	2	yes	—
553	C₂²⋊C₄	—	2	4	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	2	2	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	—	4	2	no	—
559	C₂²⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	—	4	2	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₂²⋊C₄	—	8	1	no	—
565	C₂²⋊C₄	—	8	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	4	2	no	—
571	C₄²	—	4	2	no	—
572	C₄²	—	8	1	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
595	Q₈	—	8	4	no	—
596	D₄	—	2	2	no	—
597	D₄	—	2	2	no	—
598	D₄	—	4	1	no	—
599	D₄	—	4	1	no	—
600	D₄	—	4	1	no	—
601	D₄	—	4	1	no	—
602	D₄	—	4	1	no	—
603	D₄	—	4	1	no	—
604	D₄	—	8	4	no	—
605	D₄	—	8	4	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	8	4	no	—
642	C₂×C₄	C₁₉×#135	1	2	yes	—
643	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
644	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
645	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
646	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
647	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
648	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
649	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
650	C₈	—	4	1	no	—
651	C₈	—	4	1	no	—
652	C₈	—	4	1	no	—
653	C₈	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	2	no	—
664	C₂²	—	8	1	no	—
665	C₂²	—	8	1	no	—
666	C₂²	—	8	1	no	—
667	C₂²	—	8	1	no	—
668	C₂²	—	8	1	no	—
669	C₂²	—	8	1	no	—
670	C₂²	—	8	1	no	—
671	C₂²	—	8	1	no	—
672	C₂²	—	8	1	no	—
673	C₂²	—	8	1	no	—
674	C₂²	—	8	1	no	—
675	C₂²	C₁₉×#525	1	1	yes	characteristic
676	C₂²	C₁₉×#546	1	1	yes	characteristic
677	C₂²	C₁₉×#546	1	1	yes	characteristic
678	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
679	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
680	C₂²	C₁₉×#576	1	1	yes	characteristic
681	C₂²	C₁₉×#577	1	1	yes	characteristic
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	4	1	no	—
685	C₄	—	4	1	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	1	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	2	no	—
690	C₄	—	8	1	no	—
691	C₄	—	8	1	no	—
692	C₄	—	8	1	no	—
693	C₄	C₁₉×#529	1	1	yes	characteristic
694	C₄	C₁₉×#538	1	1	yes	characteristic
695	C₄	C₁₉×#555	1	1	yes	characteristic
696	C₄	C₁₉×#559	1	1	yes	characteristic
697	C₂	—	8	1	no	—
698	C₂	—	8	2	no	—
699	C₂	—	16	1	no	—
700	C₂	C₁₉×#2459	1	1	yes	characteristic
701	C₂	C₁₉×#3106	1	1	yes	characteristic
702	C₂	C₁₉×#3118	1	1	yes	characteristic
703	C₂	C₁₉×#3301	1	1	yes	characteristic
704	C₂	C₁₉×#3305	1	1	yes	characteristic
705	C₂	C₁₉×#3306	1	1	yes	characteristic
706	C₂	C₁₉×#3325	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#1999	C₂
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. C₁₉×#2491	C₂	semidirect
2. C₁₉×#2363	C₂	semidirect
3. C₁₉×#2054	C₂	semidirect
4. C₁₉×#2034	C₂	semidirect
5. C₁₉×#2023	C₂	semidirect
7. C₁₉×#1987	C₂	semidirect
8. C₁₉×#1934	C₂	semidirect
9. C₁₉×#1926	C₂	semidirect
10. C₁₉×#1923	C₂	semidirect
11. C₁₉×#1920	C₂	semidirect
12. C₁₉×#1879	C₂	semidirect
13. C₁₉×#1875	C₂	semidirect
14. C₁₉×#1825	C₂	semidirect
15. C₄×C₁₉×#102	C₂	semidirect
219. #26729	C₁₉	direct (N × H)
301. #2491	C₂×C₁₉	semidirect
302. #2363	C₂×C₁₉	semidirect
303. #2054	C₂×C₁₉	semidirect
304. #2034	C₂×C₁₉	semidirect
305. #2023	C₂×C₁₉	semidirect
307. #1987	C₂×C₁₉	semidirect
308. #1934	C₂×C₁₉	semidirect
309. #1926	C₂×C₁₉	semidirect
310. #1923	C₂×C₁₉	semidirect
311. #1920	C₂×C₁₉	semidirect
312. #1879	C₂×C₁₉	semidirect
313. #1875	C₂×C₁₉	semidirect
314. #1825	C₂×C₁₉	semidirect
315. C₄×#102	C₂×C₁₉	semidirect
480. C₁₉	#26729	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×#2491	2
C₁₉×#2363	2
C₁₉×#2054	2
C₁₉×#2034	2
C₁₉×#2023	2
C₁₉×#1999	2
C₁₉×#1987	2
C₁₉×#1934	2
C₁₉×#1926	2
C₁₉×#1923	2
C₁₉×#1920	2
C₁₉×#1879	2
C₁₉×#1875	2
C₁₉×#1825	2
C₄×C₁₉×#102	2
#26729	19

Subgroups — C19×#26729 #18032688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26729 #18032688