Subgroups — C₁₉×#24010 #18029969

Order 4864.

1428 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#485	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2280	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2036	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2035	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1873	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1852	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1787	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1787	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1779	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
16	C₂×C₁₉×C₂²⋊Q₈	—	2	8	no	—
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
24	C₁₉×#485	—	2	8	no	—
25	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
26	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
27	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
28	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
29	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
30	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
31	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₁₉×#381	—	2	1	no	—
36	C₁₉×#380	C₂²	1	1	yes	characteristic
37	C₁₉×#380	C₂²	1	1	yes	characteristic
38	C₁₉×#380	C₂²	1	1	yes	characteristic
39	C₁₉×#380	C₂²	1	1	yes	characteristic
40	C₁₉×#379	—	2	1	no	—
41	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₁₉×#340	C₂²	1	2	yes	complemented
44	C₁₉×#340	C₂²	1	2	yes	complemented
45	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₉	—	2	4	no	—
47	C₂²×Q₈×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	—	2	2	no	—
49	C₂²×Q₈×C₁₉	—	2	2	no	—
50	C₂²×Q₈×C₁₉	—	4	2	no	—
51	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₉	—	2	1	no	—
53	C₂³×C₄×C₁₉	—	2	1	no	—
54	C₂³×C₄×C₁₉	—	2	4	no	—
55	C₂³×C₄×C₁₉	—	2	2	no	—
56	C₂³×C₄×C₁₉	—	2	2	no	—
57	C₂³×C₄×C₁₉	—	4	2	no	—
58	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
65	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
66	C₁₉×C₂²⋊Q₈	—	2	8	no	—
67	C₁₉×C₂²⋊Q₈	—	2	8	no	—
68	C₁₉×C₂²⋊Q₈	—	2	4	no	—
69	C₁₉×C₂²⋊Q₈	—	2	4	no	—
70	C₁₉×C₂²⋊Q₈	—	2	4	no	—
71	C₁₉×C₂²⋊Q₈	D₄	1	8	yes	—
72	C₁₉×#117	—	2	4	no	—
73	C₁₉×#117	—	4	2	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄²×C₁₉	—	2	1	no	—
94	C₂×C₄²×C₁₉	—	2	1	no	—
95	C₁₉×#107	—	2	4	no	—
96	C₁₉×#106	—	2	4	no	—
97	C₁₉×#103	—	2	4	no	—
98	C₁₉×#103	—	2	4	no	—
99	C₁₉×#103	—	4	2	no	—
100	C₁₉×#103	—	4	2	no	—
101	C₁₉×C₂²⋊C₈	—	2	4	no	—
102	C₁₉×C₂²⋊C₈	—	2	2	no	—
103	C₁₉×C₂²⋊C₈	—	2	2	no	—
104	C₁₉×C₂²⋊C₈	—	4	2	no	—
105	C₁₉×#95	—	2	1	no	—
106	C₁₉×#95	—	2	1	no	—
107	C₁₉×#95	—	2	1	no	—
108	C₁₉×#95	—	2	1	no	—
109	C₂⁴×C₁₉	—	2	2	no	—
110	C₂⁴×C₁₉	—	2	2	no	—
111	C₂⁴×C₁₉	—	2	2	no	—
112	C₂⁴×C₁₉	—	2	2	no	—
113	C₂⁴×C₁₉	—	2	2	no	—
114	C₂⁴×C₁₉	—	4	1	no	—
115	C₂⁴×C₁₉	—	4	1	no	—
116	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂×Q₈×C₁₉	—	2	4	no	—
120	C₂×Q₈×C₁₉	—	2	2	no	—
121	C₂×Q₈×C₁₉	—	2	2	no	—
122	C₂×Q₈×C₁₉	—	2	2	no	—
123	C₂×Q₈×C₁₉	—	2	2	no	—
124	C₂×Q₈×C₁₉	—	2	2	no	—
125	C₂×Q₈×C₁₉	—	4	8	no	—
126	C₂×Q₈×C₁₉	—	4	8	no	—
127	C₂×Q₈×C₁₉	—	4	2	no	—
128	C₂×Q₈×C₁₉	—	4	2	no	—
129	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	4	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	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	2	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	—	4	1	no	—
154	C₂²×C₄×C₁₉	—	4	1	no	—
155	C₂²×C₄×C₁₉	—	4	1	no	—
156	C₂²×C₄×C₁₉	—	4	8	no	—
157	C₂²×C₄×C₁₉	—	4	8	no	—
158	C₂²×C₄×C₁₉	—	4	2	no	—
159	C₂²×C₄×C₁₉	—	4	2	no	—
160	C₂²×C₄×C₁₉	—	4	2	no	—
161	C₂²×C₄×C₁₉	—	4	2	no	—
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	#41	1	2	yes	—
167	C₂²×C₄×C₁₉	#41	1	2	yes	—
168	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
169	C₂×C₈×C₁₉	—	2	2	no	—
170	C₂×C₈×C₁₉	—	2	2	no	—
171	C₂×C₈×C₁₉	—	2	2	no	—
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	4	no	—
176	C₄⋊C₄×C₁₉	—	2	8	no	—
177	C₄⋊C₄×C₁₉	—	2	8	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
184	C₂²⋊C₄×C₁₉	—	2	8	no	—
185	C₂²⋊C₄×C₁₉	—	2	8	no	—
186	C₂²⋊C₄×C₁₉	—	4	2	no	—
187	C₂²⋊C₄×C₁₉	—	4	2	no	—
188	C₂²⋊C₄×C₁₉	—	4	2	no	—
189	C₂²⋊C₄×C₁₉	—	4	2	no	—
190	C₂²⋊C₄×C₁₉	—	4	2	no	—
191	C₂²⋊C₄×C₁₉	—	4	2	no	—
192	C₄²×C₁₉	—	4	2	no	—
193	C₄²×C₁₉	—	4	2	no	—
194	#24010	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂³×C₁₉	—	2	1	no	—
196	C₂³×C₁₉	—	2	1	no	—
197	C₂³×C₁₉	—	2	1	no	—
198	C₂³×C₁₉	—	2	1	no	—
199	C₂³×C₁₉	—	2	8	no	—
200	C₂³×C₁₉	—	2	1	no	—
201	C₂³×C₁₉	—	2	1	no	—
202	C₂³×C₁₉	—	2	1	no	—
203	C₂³×C₁₉	—	2	1	no	—
204	C₂³×C₁₉	—	2	1	no	—
205	C₂³×C₁₉	—	2	1	no	—
206	C₂³×C₁₉	—	2	1	no	—
207	C₂³×C₁₉	—	2	1	no	—
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×C₁₉	—	2	1	no	—
210	C₂³×C₁₉	—	2	1	no	—
211	C₂³×C₁₉	—	2	1	no	—
212	C₂³×C₁₉	—	4	4	no	—
213	C₂³×C₁₉	—	4	4	no	—
214	C₂³×C₁₉	—	4	4	no	—
215	C₂³×C₁₉	—	4	4	no	—
216	C₂³×C₁₉	—	4	4	no	—
217	C₂³×C₁₉	—	4	4	no	—
218	C₂³×C₁₉	#120	1	2	yes	—
219	C₂³×C₁₉	#123	1	2	yes	—
220	C₂³×C₁₉	#135	1	2	yes	—
221	C₂³×C₁₉	#137	1	2	yes	—
222	C₂³×C₁₉	#137	1	2	yes	—
223	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₁₉	—	2	4	no	—
225	Q₈×C₁₉	—	2	4	no	—
226	Q₈×C₁₉	—	4	8	no	—
227	Q₈×C₁₉	—	4	2	no	—
228	Q₈×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	4	no	—
235	C₂×C₄×C₁₉	—	2	4	no	—
236	C₂×C₄×C₁₉	—	2	4	no	—
237	C₂×C₄×C₁₉	—	2	4	no	—
238	C₂×C₄×C₁₉	—	2	4	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	4	4	no	—
243	C₂×C₄×C₁₉	—	4	4	no	—
244	C₂×C₄×C₁₉	—	4	4	no	—
245	C₂×C₄×C₁₉	—	4	8	no	—
246	C₂×C₄×C₁₉	—	4	8	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	4	2	no	—
250	C₂×C₄×C₁₉	—	4	2	no	—
251	C₂×C₄×C₁₉	—	4	2	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	#120	1	2	yes	—
266	C₂×C₄×C₁₉	#123	1	2	yes	—
267	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
271	C₈×C₁₉	—	4	2	no	—
272	C₈×C₁₉	—	4	2	no	—
273	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
274	C₂×#485	C₂×C₁₉	1	2	yes	complemented
275	#2280	C₂×C₁₉	1	1	yes	characteristic
276	#2036	C₂×C₁₉	1	2	yes	complemented
277	#2035	C₂×C₁₉	1	2	yes	complemented
278	#1873	C₂×C₁₉	1	2	yes	complemented
279	#1853	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1852	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1787	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1787	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1779	C₂×C₁₉	1	1	yes	characteristic
284	C₂²×C₁₉	—	2	2	no	—
285	C₂²×C₁₉	—	2	2	no	—
286	C₂²×C₁₉	—	2	2	no	—
287	C₂²×C₁₉	—	2	2	no	—
288	C₂²×C₁₉	—	2	2	no	—
289	C₂²×C₁₉	—	2	2	no	—
290	C₂²×C₁₉	—	2	2	no	—
291	C₂²×C₁₉	—	2	2	no	—
292	C₂²×C₁₉	—	2	2	no	—
293	C₂²×C₁₉	—	2	2	no	—
294	C₂²×C₁₉	—	2	2	no	—
295	C₂²×C₁₉	—	2	2	no	—
296	C₂²×C₁₉	—	4	16	no	—
297	C₂²×C₁₉	—	4	1	no	—
298	C₂²×C₁₉	—	4	1	no	—
299	C₂²×C₁₉	—	4	1	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	1	no	—
303	C₂²×C₁₉	—	4	1	no	—
304	C₂²×C₁₉	—	4	1	no	—
305	C₂²×C₁₉	#485	1	4	yes	complemented
306	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
307	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
308	C₂²×C₁₉	#534	1	1	yes	characteristic
309	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
310	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
311	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
312	C₂²×C₁₉	#575	1	1	yes	characteristic
313	C₄×C₁₉	—	2	2	no	—
314	C₄×C₁₉	—	2	2	no	—
315	C₄×C₁₉	—	4	1	no	—
316	C₄×C₁₉	—	4	4	no	—
317	C₄×C₁₉	—	4	4	no	—
318	C₄×C₁₉	—	8	1	no	—
319	C₄×C₁₉	—	8	1	no	—
320	C₄×C₁₉	—	8	1	no	—
321	C₄×C₁₉	—	8	1	no	—
322	C₄×C₁₉	#546	1	2	yes	—
323	C₄×C₁₉	#546	1	2	yes	—
324	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
325	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×C₂²⋊Q₈	—	2	1	no	—
327	C₂×C₂²⋊Q₈	—	2	1	no	—
328	C₂×C₂²⋊Q₈	—	2	8	no	—
329	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
330	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
331	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
333	C₂²×C₄⋊C₄	—	2	1	no	—
334	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
335	C₂²×C₂²⋊C₄	—	2	1	no	—
336	#485	—	2	8	no	—
337	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
338	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
339	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
340	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
341	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
342	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
343	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
344	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
345	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
346	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
347	#381	—	2	1	no	—
348	#380	C₂²×C₁₉	1	1	yes	characteristic
349	#380	C₂²×C₁₉	1	1	yes	characteristic
350	#380	C₂²×C₁₉	1	1	yes	characteristic
351	#380	C₂²×C₁₉	1	1	yes	characteristic
352	#379	—	2	1	no	—
353	C₄×C₂²⋊C₄	—	2	1	no	—
354	C₄×C₂²⋊C₄	—	2	1	no	—
355	#340	C₂²×C₁₉	1	2	yes	complemented
356	#340	C₂²×C₁₉	1	2	yes	complemented
357	C₂×C₁₉	—	2	4	no	—
358	C₂×C₁₉	—	4	2	no	—
359	C₂×C₁₉	—	4	2	no	—
360	C₂×C₁₉	#2405	1	1	yes	characteristic
361	C₂×C₁₉	#3002	1	1	yes	characteristic
362	C₂×C₁₉	#3004	1	1	yes	characteristic
363	C₂×C₁₉	C₂×#485	1	1	yes	characteristic
364	C₂×C₁₉	#3095	1	1	yes	characteristic
365	C₂×C₁₉	#3190	1	1	yes	characteristic
366	C₂×C₁₉	#3196	1	1	yes	characteristic
367	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
368	C₂²×Q₈	—	2	4	no	—
369	C₂²×Q₈	—	2	1	no	—
370	C₂²×Q₈	—	2	2	no	—
371	C₂²×Q₈	—	2	2	no	—
372	C₂²×Q₈	—	4	2	no	—
373	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
374	C₂³×C₄	—	2	1	no	—
375	C₂³×C₄	—	2	1	no	—
376	C₂³×C₄	—	2	4	no	—
377	C₂³×C₄	—	2	2	no	—
378	C₂³×C₄	—	2	2	no	—
379	C₂³×C₄	—	4	2	no	—
380	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
381	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
382	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
383	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
384	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
385	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
386	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
387	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
388	C₂²⋊Q₈	—	2	8	no	—
389	C₂²⋊Q₈	—	2	8	no	—
390	C₂²⋊Q₈	—	2	4	no	—
391	C₂²⋊Q₈	—	2	4	no	—
392	C₂²⋊Q₈	—	2	4	no	—
393	C₂²⋊Q₈	D₄×C₁₉	1	8	yes	—
394	#117	—	2	4	no	—
395	#117	—	4	2	no	—
396	C₂×C₄⋊C₄	—	2	8	no	—
397	C₂×C₄⋊C₄	—	2	2	no	—
398	C₂×C₄⋊C₄	—	2	2	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	4	no	—
401	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
406	C₂×C₂²⋊C₄	—	2	8	no	—
407	C₂×C₂²⋊C₄	—	2	2	no	—
408	C₂×C₂²⋊C₄	—	2	2	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	—	2	1	no	—
417	#107	—	2	4	no	—
418	#106	—	2	4	no	—
419	#103	—	2	4	no	—
420	#103	—	2	4	no	—
421	#103	—	4	2	no	—
422	#103	—	4	2	no	—
423	C₂²⋊C₈	—	2	4	no	—
424	C₂²⋊C₈	—	2	2	no	—
425	C₂²⋊C₈	—	2	2	no	—
426	C₂²⋊C₈	—	4	2	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	C₁₉	#24010	1	1	yes	characteristic, direct product factor, Sylow
432	C₂⁴	—	2	2	no	—
433	C₂⁴	—	2	2	no	—
434	C₂⁴	—	2	2	no	—
435	C₂⁴	—	2	2	no	—
436	C₂⁴	—	2	2	no	—
437	C₂⁴	—	4	1	no	—
438	C₂⁴	—	4	1	no	—
439	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂×Q₈	—	2	4	no	—
443	C₂×Q₈	—	2	2	no	—
444	C₂×Q₈	—	2	2	no	—
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	4	8	no	—
449	C₂×Q₈	—	4	8	no	—
450	C₂×Q₈	—	4	2	no	—
451	C₂×Q₈	—	4	2	no	—
452	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	4	1	no	—
477	C₂²×C₄	—	4	1	no	—
478	C₂²×C₄	—	4	1	no	—
479	C₂²×C₄	—	4	8	no	—
480	C₂²×C₄	—	4	8	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
488	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂²×C₄	#41×C₁₉	1	2	yes	—
490	C₂²×C₄	#41×C₁₉	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	—	2	2	no	—
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	—	2	8	no	—
500	C₄⋊C₄	—	2	8	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
507	C₂²⋊C₄	—	2	8	no	—
508	C₂²⋊C₄	—	2	8	no	—
509	C₂²⋊C₄	—	4	2	no	—
510	C₂²⋊C₄	—	4	2	no	—
511	C₂²⋊C₄	—	4	2	no	—
512	C₂²⋊C₄	—	4	2	no	—
513	C₂²⋊C₄	—	4	2	no	—
514	C₂²⋊C₄	—	4	2	no	—
515	C₄²	—	4	2	no	—
516	C₄²	—	4	2	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	2	8	no	—
522	C₂³	—	2	1	no	—
523	C₂³	—	2	1	no	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	4	4	no	—
535	C₂³	—	4	4	no	—
536	C₂³	—	4	4	no	—
537	C₂³	—	4	4	no	—
538	C₂³	—	4	4	no	—
539	C₂³	—	4	4	no	—
540	C₂³	C₁₉×#120	1	2	yes	—
541	C₂³	C₁₉×#123	1	2	yes	—
542	C₂³	C₁₉×#135	1	2	yes	—
543	C₂³	C₁₉×#137	1	2	yes	—
544	C₂³	C₁₉×#137	1	2	yes	—
545	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
546	Q₈	—	2	4	no	—
547	Q₈	—	2	4	no	—
548	Q₈	—	4	8	no	—
549	Q₈	—	4	2	no	—
550	Q₈	—	4	2	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	—	4	4	no	—
566	C₂×C₄	—	4	4	no	—
567	C₂×C₄	—	4	8	no	—
568	C₂×C₄	—	4	8	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	C₁₉×#120	1	2	yes	—
588	C₂×C₄	C₁₉×#123	1	2	yes	—
589	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
590	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
591	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
592	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
593	C₈	—	4	2	no	—
594	C₈	—	4	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	4	16	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	C₁₉×#485	1	4	yes	complemented
617	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
618	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
619	C₂²	C₁₉×#534	1	1	yes	characteristic
620	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
621	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
622	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
623	C₂²	C₁₉×#575	1	1	yes	characteristic
624	C₄	—	2	2	no	—
625	C₄	—	2	2	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	4	no	—
628	C₄	—	4	4	no	—
629	C₄	—	8	1	no	—
630	C₄	—	8	1	no	—
631	C₄	—	8	1	no	—
632	C₄	—	8	1	no	—
633	C₄	C₁₉×#546	1	2	yes	—
634	C₄	C₁₉×#546	1	2	yes	—
635	C₂	—	2	4	no	—
636	C₂	—	4	2	no	—
637	C₂	—	4	2	no	—
638	C₂	C₁₉×#2405	1	1	yes	characteristic
639	C₂	C₁₉×#3002	1	1	yes	characteristic
640	C₂	C₁₉×#3004	1	1	yes	characteristic
641	C₂	C₂×C₁₉×#485	1	1	yes	characteristic
642	C₂	C₁₉×#3095	1	1	yes	characteristic
643	C₂	C₁₉×#3190	1	1	yes	characteristic
644	C₂	C₁₉×#3196	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#485	C₂	semidirect
4. C₁₉×#2036	C₂	semidirect
5. C₁₉×#2035	C₂	semidirect
6. C₁₉×#1873	C₂	semidirect
7. C₁₉×#1853	C₂	semidirect
8. C₁₉×#1852	C₂	semidirect
9. C₁₉×#1787	C₂	semidirect
10. C₁₉×#1787	C₂	semidirect
25. C₂×C₁₉×#107	C₂²	semidirect
26. C₂×C₁₉×#106	C₂²	semidirect
27. C₂×C₁₉×#103	C₂²	semidirect
28. C₂×C₁₉×#103	C₂²	semidirect
29. C₂×C₁₉×#103	C₂²	semidirect
30. C₂×C₁₉×#103	C₂²	semidirect
43. C₁₉×#340	C₂²	semidirect
44. C₁₉×#340	C₂²	semidirect
194. #24010	C₁₉	direct (N × H)
274. C₂×#485	C₂×C₁₉	semidirect
276. #2036	C₂×C₁₉	semidirect
277. #2035	C₂×C₁₉	semidirect
278. #1873	C₂×C₁₉	semidirect
279. #1853	C₂×C₁₉	semidirect
280. #1852	C₂×C₁₉	semidirect
281. #1787	C₂×C₁₉	semidirect
282. #1787	C₂×C₁₉	semidirect
305. C₂²×C₁₉	#485	semidirect
337. C₂×#107	C₂²×C₁₉	semidirect
338. C₂×#106	C₂²×C₁₉	semidirect
339. C₂×#103	C₂²×C₁₉	semidirect
340. C₂×#103	C₂²×C₁₉	semidirect
341. C₂×#103	C₂²×C₁₉	semidirect
342. C₂×#103	C₂²×C₁₉	semidirect
355. #340	C₂²×C₁₉	semidirect
356. #340	C₂²×C₁₉	semidirect
431. C₁₉	#24010	direct (N × H)
616. C₂²	C₁₉×#485	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×C₂²⋊Q₈	2
C₂×C₁₉×#485	2
C₁₉×#2280	2
C₁₉×#2036	2
C₁₉×#2035	2
C₁₉×#1873	2
C₁₉×#1853	2
C₁₉×#1852	2
C₁₉×#1787	2
C₁₉×#1779	2
#24010	19

Subgroups — C19×#24010 #18029969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24010 #18029969