Subgroups — C₁₉×#26199 #18032158

Order 4864.

844 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2414	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2352	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2077	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2073	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1918	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1869	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1824	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1735	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#106	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₁₉×#394	—	2	1	no	—
33	C₁₉×#392	—	2	1	no	—
34	C₁₉×#390	—	2	1	no	—
35	C₁₉×#390	C₂²	1	1	yes	characteristic
36	C₁₉×#389	C₂²	1	1	yes	characteristic
37	C₁₉×#388	—	2	1	no	—
38	C₁₉×#388	—	2	1	no	—
39	C₁₉×#387	—	2	1	no	—
40	C₁₉×#386	—	2	1	no	—
41	C₁₉×#382	C₂²	1	1	yes	characteristic
42	C₁₉×#380	C₂²	1	1	yes	characteristic
43	C₁₉×#380	C₂²	1	1	yes	characteristic
44	C₁₉×#380	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₁₉×#340	C₂²	1	1	yes	characteristic
48	C₁₉×#340	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×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	—	2	1	no	—
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₉	—	2	2	no	—
67	C₂²×C₈×C₁₉	—	4	1	no	—
68	C₂²×C₈×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×#121	—	2	2	no	—
74	C₁₉×#121	—	2	2	no	—
75	C₁₉×#121	—	2	2	no	—
76	C₁₉×#121	—	4	1	no	—
77	C₄×D₄×C₁₉	—	2	2	no	—
78	C₄×D₄×C₁₉	—	2	2	no	—
79	C₁₉×#117	—	2	2	no	—
80	C₁₉×#117	—	2	2	no	—
81	C₁₉×#117	—	4	1	no	—
82	C₁₉×#117	—	4	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
87	C₂×C₄⋊C₄×C₁₉	D₄	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×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×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	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	—	2	1	no	—
109	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
110	C₁₉×#107	—	2	2	no	—
111	C₁₉×#106	—	4	1	no	—
112	C₁₉×#102	—	2	2	no	—
113	C₁₉×#102	—	4	1	no	—
114	C₁₉×#102	—	4	1	no	—
115	C₁₉×#102	—	4	1	no	—
116	C₁₉×C₂²⋊C₈	—	2	2	no	—
117	C₁₉×C₂²⋊C₈	—	4	1	no	—
118	C₁₉×C₂²⋊C₈	—	4	1	no	—
119	C₁₉×#95	—	2	1	no	—
120	C₁₉×#95	—	2	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	—	2	1	no	—
126	C₂⁴×C₁₉	—	2	1	no	—
127	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	2	1	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	—	4	1	no	—
138	C₂×D₄×C₁₉	—	4	2	no	—
139	C₂×D₄×C₁₉	—	4	2	no	—
140	C₂×D₄×C₁₉	—	4	2	no	—
141	C₂×D₄×C₁₉	—	8	1	no	—
142	C₂×D₄×C₁₉	—	8	1	no	—
143	C₂×D₄×C₁₉	—	8	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
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	—	4	2	no	—
162	C₂²×C₄×C₁₉	—	4	2	no	—
163	C₂²×C₄×C₁₉	—	8	1	no	—
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	#41	1	2	yes	—
169	C₂²×C₄×C₁₉	#41	1	2	yes	—
170	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	2	1	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	—	4	4	no	—
184	C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	4	2	no	—
198	C₄⋊C₄×C₁₉	—	8	1	no	—
199	C₄⋊C₄×C₁₉	#41	1	2	yes	—
200	C₄⋊C₄×C₁₉	#41	1	2	yes	—
201	C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₉	—	2	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	—	8	1	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	—	4	2	no	—
215	C₄²×C₁₉	—	4	2	no	—
216	C₄²×C₁₉	—	8	1	no	—
217	#26199	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	2	1	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	—	2	1	no	—
229	C₂³×C₁₉	—	2	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	#123	1	2	yes	—
238	C₂³×C₁₉	#135	1	2	yes	—
239	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
240	D₄×C₁₉	—	4	4	no	—
241	D₄×C₁₉	—	4	1	no	—
242	D₄×C₁₉	—	4	1	no	—
243	D₄×C₁₉	—	4	1	no	—
244	D₄×C₁₉	—	4	1	no	—
245	D₄×C₁₉	—	8	4	no	—
246	D₄×C₁₉	—	8	4	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	2	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	2	no	—
257	C₂×C₄×C₁₉	—	2	2	no	—
258	C₂×C₄×C₁₉	—	2	1	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	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	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	—	8	4	no	—
288	C₂×C₄×C₁₉	#123	1	2	yes	—
289	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
294	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
295	C₈×C₁₉	—	4	1	no	—
296	C₈×C₁₉	—	4	1	no	—
297	C₈×C₁₉	—	4	1	no	—
298	C₈×C₁₉	—	4	1	no	—
299	#2414	C₂×C₁₉	1	1	yes	characteristic
300	#2352	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#2101	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#2077	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#2073	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#2033	C₂×C₁₉	1	1	yes	characteristic, complemented
305	#1926	C₂×C₁₉	1	1	yes	characteristic, complemented
306	#1918	C₂×C₁₉	1	1	yes	characteristic, complemented
307	#1893	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#1875	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#1869	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#1854	C₂×C₁₉	1	1	yes	characteristic, complemented
312	#1824	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1735	C₂×C₁₉	1	1	yes	characteristic, complemented
314	C₂²×C₁₉	—	2	2	no	—
315	C₂²×C₁₉	—	2	2	no	—
316	C₂²×C₁₉	—	2	2	no	—
317	C₂²×C₁₉	—	2	2	no	—
318	C₂²×C₁₉	—	2	2	no	—
319	C₂²×C₁₉	—	2	2	no	—
320	C₂²×C₁₉	—	4	1	no	—
321	C₂²×C₁₉	—	4	1	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	—	4	1	no	—
327	C₂²×C₁₉	—	4	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	C₂×#123	1	1	yes	characteristic
336	C₂²×C₁₉	#546	1	1	yes	characteristic
337	C₂²×C₁₉	#546	1	1	yes	characteristic
338	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
339	C₂²×C₁₉	#575	1	1	yes	characteristic
340	C₂²×C₁₉	#576	1	1	yes	characteristic
341	C₂²×C₁₉	#577	1	1	yes	characteristic
342	C₄×C₁₉	—	2	2	no	—
343	C₄×C₁₉	—	4	1	no	—
344	C₄×C₁₉	—	4	1	no	—
345	C₄×C₁₉	—	4	1	no	—
346	C₄×C₁₉	—	4	2	no	—
347	C₄×C₁₉	—	4	2	no	—
348	C₄×C₁₉	—	8	1	no	—
349	C₄×C₁₉	—	8	1	no	—
350	C₄×C₁₉	—	8	1	no	—
351	C₄×C₁₉	—	8	1	no	—
352	C₄×C₁₉	—	8	1	no	—
353	C₄×C₁₉	#529	1	1	yes	characteristic
354	C₄×C₁₉	#538	1	1	yes	characteristic
355	C₄×C₁₉	#553	1	1	yes	characteristic
356	C₄×C₁₉	#553	1	1	yes	characteristic
357	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
361	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
362	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
363	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
364	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×#102	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×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
371	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
373	#394	—	2	1	no	—
374	#392	—	2	1	no	—
375	#390	—	2	1	no	—
376	#390	C₂²×C₁₉	1	1	yes	characteristic
377	#389	C₂²×C₁₉	1	1	yes	characteristic
378	#388	—	2	1	no	—
379	#388	—	2	1	no	—
380	#387	—	2	1	no	—
381	#386	—	2	1	no	—
382	#382	C₂²×C₁₉	1	1	yes	characteristic
383	#380	C₂²×C₁₉	1	1	yes	characteristic
384	#380	C₂²×C₁₉	1	1	yes	characteristic
385	#380	C₂²×C₁₉	1	1	yes	characteristic
386	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
387	C₄×C₂²⋊C₄	—	2	1	no	—
388	#340	C₂²×C₁₉	1	1	yes	characteristic
389	#340	C₂²×C₁₉	1	1	yes	characteristic
390	#340	C₂²×C₁₉	1	1	yes	characteristic
391	#340	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	#336	C₂²×C₁₉	1	1	yes	characteristic
399	#336	C₂²×C₁₉	1	1	yes	characteristic
400	C₂×C₁₉	—	4	2	no	—
401	C₂×C₁₉	—	4	2	no	—
402	C₂×C₁₉	—	16	1	no	—
403	C₂×C₁₉	#2444	1	1	yes	characteristic
404	C₂×C₁₉	#3091	1	1	yes	characteristic
405	C₂×C₁₉	#3096	1	1	yes	characteristic
406	C₂×C₁₉	#3297	1	1	yes	characteristic
407	C₂×C₁₉	#3301	1	1	yes	characteristic
408	C₂×C₁₉	#3317	1	1	yes	characteristic
409	C₂×C₁₉	#3319	1	1	yes	characteristic
410	C₂²×D₄	—	2	1	no	—
411	C₂²×D₄	—	2	1	no	—
412	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
413	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
414	C₂³×C₄	—	2	1	no	—
415	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
417	C₂²×C₈	—	2	2	no	—
418	C₂²×C₈	—	4	1	no	—
419	C₂²×C₈	—	4	1	no	—
420	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
422	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
424	#121	—	2	2	no	—
425	#121	—	2	2	no	—
426	#121	—	2	2	no	—
427	#121	—	4	1	no	—
428	C₄×D₄	—	2	2	no	—
429	C₄×D₄	—	2	2	no	—
430	#117	—	2	2	no	—
431	#117	—	2	2	no	—
432	#117	—	4	1	no	—
433	#117	—	4	1	no	—
434	C₂×C₄⋊C₄	—	2	2	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	4	1	no	—
438	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
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	D₄×C₁₉	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
457	C₂×C₄²	—	2	1	no	—
458	C₂×C₄²	—	2	1	no	—
459	C₂×C₄²	—	2	1	no	—
460	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
461	#107	—	2	2	no	—
462	#106	—	4	1	no	—
463	#102	—	2	2	no	—
464	#102	—	4	1	no	—
465	#102	—	4	1	no	—
466	#102	—	4	1	no	—
467	C₂²⋊C₈	—	2	2	no	—
468	C₂²⋊C₈	—	4	1	no	—
469	C₂²⋊C₈	—	4	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	—	2	1	no	—
475	#95	—	2	1	no	—
476	#95	—	2	1	no	—
477	C₁₉	#26199	1	1	yes	characteristic, direct product factor, Sylow
478	C₂⁴	—	2	1	no	—
479	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	4	1	no	—
490	C₂×D₄	—	4	2	no	—
491	C₂×D₄	—	4	2	no	—
492	C₂×D₄	—	4	2	no	—
493	C₂×D₄	—	8	1	no	—
494	C₂×D₄	—	8	1	no	—
495	C₂×D₄	—	8	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
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	—	4	2	no	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	—	8	1	no	—
516	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
519	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
520	C₂²×C₄	#41×C₁₉	1	2	yes	—
521	C₂²×C₄	#41×C₁₉	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	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	—	4	4	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	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	—	2	1	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	—	8	1	no	—
551	C₄⋊C₄	#41×C₁₉	1	2	yes	—
552	C₄⋊C₄	#41×C₁₉	1	2	yes	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	4	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	—	8	1	no	—
562	C₂²⋊C₄	—	8	1	no	—
563	C₂²⋊C₄	—	8	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	4	2	no	—
567	C₄²	—	4	2	no	—
568	C₄²	—	8	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	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	C₁₉×#123	1	2	yes	—
589	C₂³	C₁₉×#135	1	2	yes	—
590	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
591	D₄	—	4	4	no	—
592	D₄	—	4	1	no	—
593	D₄	—	4	1	no	—
594	D₄	—	4	1	no	—
595	D₄	—	4	1	no	—
596	D₄	—	8	4	no	—
597	D₄	—	8	4	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	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	—	8	4	no	—
639	C₂×C₄	C₁₉×#123	1	2	yes	—
640	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
641	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
642	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
643	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
644	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
645	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
646	C₈	—	4	1	no	—
647	C₈	—	4	1	no	—
648	C₈	—	4	1	no	—
649	C₈	—	4	1	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	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	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	1	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	C₂×C₁₉×#123	1	1	yes	characteristic
672	C₂²	C₁₉×#546	1	1	yes	characteristic
673	C₂²	C₁₉×#546	1	1	yes	characteristic
674	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
675	C₂²	C₁₉×#575	1	1	yes	characteristic
676	C₂²	C₁₉×#576	1	1	yes	characteristic
677	C₂²	C₁₉×#577	1	1	yes	characteristic
678	C₄	—	2	2	no	—
679	C₄	—	4	1	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	1	no	—
684	C₄	—	8	1	no	—
685	C₄	—	8	1	no	—
686	C₄	—	8	1	no	—
687	C₄	—	8	1	no	—
688	C₄	—	8	1	no	—
689	C₄	C₁₉×#529	1	1	yes	characteristic
690	C₄	C₁₉×#538	1	1	yes	characteristic
691	C₄	C₁₉×#553	1	1	yes	characteristic
692	C₄	C₁₉×#553	1	1	yes	characteristic
693	C₂	—	4	2	no	—
694	C₂	—	4	2	no	—
695	C₂	—	16	1	no	—
696	C₂	C₁₉×#2444	1	1	yes	characteristic
697	C₂	C₁₉×#3091	1	1	yes	characteristic
698	C₂	C₁₉×#3096	1	1	yes	characteristic
699	C₂	C₁₉×#3297	1	1	yes	characteristic
700	C₂	C₁₉×#3301	1	1	yes	characteristic
701	C₂	C₁₉×#3317	1	1	yes	characteristic
702	C₂	C₁₉×#3319	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2414	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2352	C₂	semidirect
3. C₁₉×#2101	C₂	semidirect
4. C₁₉×#2077	C₂	semidirect
5. C₁₉×#2073	C₂	semidirect
6. C₁₉×#2033	C₂	semidirect
7. C₁₉×#1926	C₂	semidirect
8. C₁₉×#1918	C₂	semidirect
9. C₁₉×#1893	C₂	semidirect
10. C₁₉×#1875	C₂	semidirect
11. C₁₉×#1874	C₂	semidirect
12. C₁₉×#1869	C₂	semidirect
13. C₁₉×#1854	C₂	semidirect
14. C₁₉×#1824	C₂	semidirect
15. C₁₉×#1735	C₂	semidirect
217. #26199	C₁₉	direct (N × H)
300. #2352	C₂×C₁₉	semidirect
301. #2101	C₂×C₁₉	semidirect
302. #2077	C₂×C₁₉	semidirect
303. #2073	C₂×C₁₉	semidirect
304. #2033	C₂×C₁₉	semidirect
305. #1926	C₂×C₁₉	semidirect
306. #1918	C₂×C₁₉	semidirect
307. #1893	C₂×C₁₉	semidirect
308. #1875	C₂×C₁₉	semidirect
309. #1874	C₂×C₁₉	semidirect
310. #1869	C₂×C₁₉	semidirect
311. #1854	C₂×C₁₉	semidirect
312. #1824	C₂×C₁₉	semidirect
313. #1735	C₂×C₁₉	semidirect
477. C₁₉	#26199	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×#2414	2
C₁₉×#2352	2
C₁₉×#2101	2
C₁₉×#2077	2
C₁₉×#2073	2
C₁₉×#2033	2
C₁₉×#1926	2
C₁₉×#1918	2
C₁₉×#1893	2
C₁₉×#1875	2
C₁₉×#1874	2
C₁₉×#1869	2
C₁₉×#1854	2
C₁₉×#1824	2
C₁₉×#1735	2
#26199	19

Subgroups — C19×#26199 #18032158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26199 #18032158