Subgroups — C₁₉×#14043 #18020002

Order 4864.

2366 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#389	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#385	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#385	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#385	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1444	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1441	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1436	C₂	1	2	yes	maximal, complemented
10	C₁₉×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
11	C₁₉×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	—	2	4	no	—
16	C₂²×C₄⋊C₄×C₁₉	—	2	8	no	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
28	C₁₉×#389	—	2	8	no	—
29	C₁₉×#385	—	2	4	no	—
30	C₁₉×#385	—	2	4	no	—
31	C₁₉×#385	C₄	1	8	yes	complemented
32	C₄×C₂²⋊C₄×C₁₉	—	2	4	no	—
33	C₂×C₁₉×#95	C₂²	1	2	yes	—
34	C₂×C₁₉×#95	C₂²	1	2	yes	—
35	C₂×C₁₉×#95	C₂²	1	2	yes	—
36	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#95	C₂²	1	2	yes	—
38	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#95	C₂²	1	2	yes	—
40	C₂×C₁₉×#95	C₂²	1	2	yes	—
41	C₂×C₁₉×#95	C₂²	1	2	yes	—
42	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₉	—	2	2	no	—
44	C₂³×C₄×C₁₉	—	2	2	no	—
45	C₂³×C₄×C₁₉	—	2	4	no	—
46	C₂³×C₄×C₁₉	—	2	4	no	—
47	C₂³×C₄×C₁₉	—	2	2	no	—
48	C₂³×C₄×C₁₉	—	2	2	no	—
49	C₂³×C₄×C₁₉	—	2	2	no	—
50	C₂³×C₄×C₁₉	—	2	4	no	—
51	C₂³×C₄×C₁₉	—	2	4	no	—
52	C₂³×C₄×C₁₉	—	2	2	no	—
53	C₂³×C₄×C₁₉	—	2	2	no	—
54	C₂³×C₄×C₁₉	—	4	2	no	—
55	C₂³×C₄×C₁₉	—	4	2	no	—
56	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
57	C₂³×C₄×C₁₉	D₄	1	4	yes	—
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₉	—	2	32	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
81	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
82	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
83	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
84	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
93	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
94	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
95	C₂×C₂²⋊C₄×C₁₉	Q₈	1	4	yes	—
96	C₂×C₂²⋊C₄×C₁₉	Q₈	1	4	yes	—
97	C₂×C₄²×C₁₉	—	2	4	no	—
98	C₂×C₄²×C₁₉	—	2	4	no	—
99	C₂×C₄²×C₁₉	—	4	2	no	—
100	C₁₉×#95	—	2	4	no	—
101	C₁₉×#95	—	2	2	no	—
102	C₁₉×#95	—	2	2	no	—
103	C₁₉×#95	—	2	4	no	—
104	C₁₉×#95	—	2	4	no	—
105	C₁₉×#95	—	2	4	no	—
106	C₁₉×#95	—	2	4	no	—
107	C₁₉×#95	—	4	2	no	—
108	C₁₉×#95	C₂×C₄	1	8	yes	complemented
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	C₂²×C₄	1	2	yes	—
114	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
115	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
116	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
117	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
118	C₂⁴×C₁₉	#41	1	2	yes	—
119	C₂⁴×C₁₉	#41	1	2	yes	—
120	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	—	2	8	no	—
122	C₂²×C₄×C₁₉	—	2	16	no	—
123	C₂²×C₄×C₁₉	—	2	8	no	—
124	C₂²×C₄×C₁₉	—	2	8	no	—
125	C₂²×C₄×C₁₉	—	2	1	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	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	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	2	no	—
136	C₂²×C₄×C₁₉	—	2	16	no	—
137	C₂²×C₄×C₁₉	—	2	8	no	—
138	C₂²×C₄×C₁₉	—	2	8	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	1	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	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	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	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	2	2	no	—
163	C₂²×C₄×C₁₉	—	2	8	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	2	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	2	no	—
172	C₂²×C₄×C₁₉	—	2	2	no	—
173	C₂²×C₄×C₁₉	—	2	2	no	—
174	C₂²×C₄×C₁₉	—	4	4	no	—
175	C₂²×C₄×C₁₉	—	4	8	no	—
176	C₂²×C₄×C₁₉	—	4	8	no	—
177	C₂²×C₄×C₁₉	—	4	8	no	—
178	C₂²×C₄×C₁₉	—	4	8	no	—
179	C₂²×C₄×C₁₉	—	4	4	no	—
180	C₂²×C₄×C₁₉	—	4	4	no	—
181	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
182	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
183	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
184	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
185	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
186	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
187	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
188	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
189	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
190	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
192	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
193	C₂²×C₄×C₁₉	#41	1	4	yes	—
194	C₄⋊C₄×C₁₉	—	2	16	no	—
195	C₄⋊C₄×C₁₉	—	2	16	no	—
196	C₄⋊C₄×C₁₉	—	2	16	no	—
197	C₄⋊C₄×C₁₉	—	4	8	no	—
198	C₄⋊C₄×C₁₉	—	4	4	no	—
199	C₄⋊C₄×C₁₉	—	4	4	no	—
200	C₂²⋊C₄×C₁₉	—	2	8	no	—
201	C₂²⋊C₄×C₁₉	—	2	8	no	—
202	C₂²⋊C₄×C₁₉	—	4	4	no	—
203	C₂²⋊C₄×C₁₉	C₄⋊C₄	1	16	yes	complemented
204	C₄²×C₁₉	—	4	8	no	—
205	#14043	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂³×C₁₉	—	2	4	no	—
207	C₂³×C₁₉	—	2	4	no	—
208	C₂³×C₁₉	—	2	2	no	—
209	C₂³×C₁₉	—	2	2	no	—
210	C₂³×C₁₉	—	2	4	no	—
211	C₂³×C₁₉	—	2	2	no	—
212	C₂³×C₁₉	—	2	2	no	—
213	C₂³×C₁₉	—	2	4	no	—
214	C₂³×C₁₉	—	2	4	no	—
215	C₂³×C₁₉	—	2	4	no	—
216	C₂³×C₁₉	—	2	4	no	—
217	C₂³×C₁₉	—	2	4	no	—
218	C₂³×C₁₉	—	2	4	no	—
219	C₂³×C₁₉	—	2	4	no	—
220	C₂³×C₁₉	—	2	4	no	—
221	C₂³×C₁₉	—	2	4	no	—
222	C₂³×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
223	C₂³×C₁₉	C₄×D₄	1	4	yes	—
224	C₂³×C₁₉	C₄×Q₈	1	4	yes	—
225	C₂³×C₁₉	#121	1	4	yes	—
226	C₂³×C₁₉	C₂²⋊Q₈	1	4	yes	—
227	C₂³×C₁₉	#125	1	4	yes	—
228	C₂³×C₁₉	C₄⋊Q₈	1	4	yes	—
229	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
230	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
231	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
232	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
233	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
234	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
235	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
236	C₂³×C₁₉	C₂×#41	1	2	yes	—
237	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
238	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
239	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
240	C₂×C₄×C₁₉	—	2	32	no	—
241	C₂×C₄×C₁₉	—	2	4	no	—
242	C₂×C₄×C₁₉	—	2	4	no	—
243	C₂×C₄×C₁₉	—	2	4	no	—
244	C₂×C₄×C₁₉	—	2	4	no	—
245	C₂×C₄×C₁₉	—	2	4	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	4	no	—
248	C₂×C₄×C₁₉	—	2	4	no	—
249	C₂×C₄×C₁₉	—	2	4	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	4	no	—
252	C₂×C₄×C₁₉	—	2	4	no	—
253	C₂×C₄×C₁₉	—	2	4	no	—
254	C₂×C₄×C₁₉	—	2	4	no	—
255	C₂×C₄×C₁₉	—	2	4	no	—
256	C₂×C₄×C₁₉	—	2	4	no	—
257	C₂×C₄×C₁₉	—	2	2	no	—
258	C₂×C₄×C₁₉	—	2	2	no	—
259	C₂×C₄×C₁₉	—	2	4	no	—
260	C₂×C₄×C₁₉	—	2	4	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	2	4	no	—
263	C₂×C₄×C₁₉	—	2	2	no	—
264	C₂×C₄×C₁₉	—	2	4	no	—
265	C₂×C₄×C₁₉	—	2	2	no	—
266	C₂×C₄×C₁₉	—	2	4	no	—
267	C₂×C₄×C₁₉	—	2	4	no	—
268	C₂×C₄×C₁₉	—	2	4	no	—
269	C₂×C₄×C₁₉	—	2	4	no	—
270	C₂×C₄×C₁₉	—	4	16	no	—
271	C₂×C₄×C₁₉	—	4	16	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	2	no	—
274	C₂×C₄×C₁₉	—	4	2	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	2	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	2	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	2	no	—
281	C₂×C₄×C₁₉	—	4	2	no	—
282	C₂×C₄×C₁₉	—	4	2	no	—
283	C₂×C₄×C₁₉	—	4	2	no	—
284	C₂×C₄×C₁₉	—	4	2	no	—
285	C₂×C₄×C₁₉	—	4	2	no	—
286	C₂×C₄×C₁₉	—	4	2	no	—
287	C₂×C₄×C₁₉	—	4	2	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	2	no	—
295	C₂×C₄×C₁₉	—	4	2	no	—
296	C₂×C₄×C₁₉	—	4	2	no	—
297	C₂×C₄×C₁₉	—	4	2	no	—
298	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	8	yes	complemented
299	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
300	C₂×C₄×C₁₉	#120	1	4	yes	—
301	C₂³×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
302	C₂×#389	C₂×C₁₉	1	2	yes	complemented
303	C₂×#385	C₂×C₁₉	1	1	yes	characteristic
304	C₂×#385	C₂×C₁₉	1	1	yes	characteristic
305	C₂×#385	C₂×C₁₉	1	1	yes	characteristic
306	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
307	#1444	C₂×C₁₉	1	2	yes	complemented
308	#1441	C₂×C₁₉	1	2	yes	complemented
309	#1436	C₂×C₁₉	1	2	yes	complemented
310	C₂²⋊#95	C₂×C₁₉	1	1	yes	characteristic
311	C₂²⋊#95	C₂×C₁₉	1	1	yes	characteristic
312	C₂²×C₁₉	—	2	4	no	—
313	C₂²×C₁₉	—	2	4	no	—
314	C₂²×C₁₉	—	2	8	no	—
315	C₂²×C₁₉	—	2	8	no	—
316	C₂²×C₁₉	—	2	4	no	—
317	C₂²×C₁₉	—	2	4	no	—
318	C₂²×C₁₉	—	2	4	no	—
319	C₂²×C₁₉	—	2	8	no	—
320	C₂²×C₁₉	—	2	8	no	—
321	C₂²×C₁₉	—	2	4	no	—
322	C₂²×C₁₉	#389	1	8	yes	complemented
323	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
324	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
325	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
326	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
327	C₂²×C₁₉	#520	1	2	yes	—
328	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
329	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
330	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
331	C₂²×C₁₉	#525	1	1	yes	characteristic
332	C₂²×C₁₉	#525	1	2	yes	—
333	C₂²×C₁₉	C₂×#125	1	1	yes	characteristic
334	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
335	C₂²×C₁₉	#534	1	1	yes	characteristic
336	C₂²×C₁₉	#536	1	1	yes	characteristic
337	C₂²×C₁₉	#539	1	2	yes	—
338	C₂²×C₁₉	D₄²	1	2	yes	—
339	C₂²×C₁₉	#546	1	2	yes	—
340	C₂²×C₁₉	#547	1	2	yes	—
341	C₂²×C₁₉	D₄×Q₈	1	2	yes	—
342	C₂²×C₁₉	D₄×Q₈	1	2	yes	—
343	C₂²×C₁₉	#552	1	2	yes	—
344	C₂²×C₁₉	#554	1	2	yes	—
345	C₂²×C₁₉	#554	1	2	yes	—
346	C₄×C₁₉	—	2	8	no	—
347	C₄×C₁₉	—	2	4	no	—
348	C₄×C₁₉	—	2	8	no	—
349	C₄×C₁₉	—	4	2	no	—
350	C₄×C₁₉	—	4	2	no	—
351	C₄×C₁₉	—	4	4	no	—
352	C₄×C₁₉	—	4	4	no	—
353	C₄×C₁₉	—	4	2	no	—
354	C₄×C₁₉	—	8	1	no	—
355	C₄×C₁₉	—	8	1	no	—
356	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
357	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
358	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
359	C₂²×C₄⋊C₄	—	2	4	no	—
360	C₂²×C₄⋊C₄	—	2	8	no	—
361	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
362	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
363	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
364	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
365	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
366	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
367	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
368	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
369	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
370	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
371	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
372	#389	—	2	8	no	—
373	#385	—	2	4	no	—
374	#385	—	2	4	no	—
375	#385	C₄×C₁₉	1	8	yes	complemented
376	C₄×C₂²⋊C₄	—	2	4	no	—
377	C₂×#95	C₂²×C₁₉	1	2	yes	—
378	C₂×#95	C₂²×C₁₉	1	2	yes	—
379	C₂×#95	C₂²×C₁₉	1	2	yes	—
380	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×#95	C₂²×C₁₉	1	2	yes	—
382	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
383	C₂×#95	C₂²×C₁₉	1	2	yes	—
384	C₂×#95	C₂²×C₁₉	1	2	yes	—
385	C₂×#95	C₂²×C₁₉	1	2	yes	—
386	C₂×C₁₉	—	2	8	no	—
387	C₂×C₁₉	C₂×#389	1	1	yes	characteristic
388	C₂×C₁₉	C₄×#120	1	1	yes	characteristic
389	C₂×C₁₉	#2322	1	1	yes	characteristic
390	C₂×C₁₉	D₄×C₄⋊C₄	1	2	yes	—
391	C₂×C₁₉	#2360	1	2	yes	—
392	C₂×C₁₉	#2410	1	1	yes	characteristic
393	C₂×C₁₉	#2413	1	1	yes	characteristic
394	C₂×C₁₉	#2434	1	1	yes	characteristic
395	C₂×C₁₉	#2449	1	2	yes	—
396	C₂×C₁₉	#2473	1	2	yes	—
397	C₂×C₁₉	#2583	1	1	yes	characteristic
398	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
399	C₂³×C₄	—	2	2	no	—
400	C₂³×C₄	—	2	2	no	—
401	C₂³×C₄	—	2	4	no	—
402	C₂³×C₄	—	2	4	no	—
403	C₂³×C₄	—	2	2	no	—
404	C₂³×C₄	—	2	2	no	—
405	C₂³×C₄	—	2	2	no	—
406	C₂³×C₄	—	2	4	no	—
407	C₂³×C₄	—	2	4	no	—
408	C₂³×C₄	—	2	2	no	—
409	C₂³×C₄	—	2	2	no	—
410	C₂³×C₄	—	4	2	no	—
411	C₂³×C₄	—	4	2	no	—
412	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
413	C₂³×C₄	D₄×C₁₉	1	4	yes	—
414	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
415	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
418	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
420	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
421	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
422	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
423	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
424	C₂×C₄⋊C₄	—	2	32	no	—
425	C₂×C₄⋊C₄	—	2	4	no	—
426	C₂×C₄⋊C₄	—	2	4	no	—
427	C₂×C₄⋊C₄	—	2	4	no	—
428	C₂×C₄⋊C₄	—	2	4	no	—
429	C₂×C₄⋊C₄	—	2	4	no	—
430	C₂×C₄⋊C₄	—	2	4	no	—
431	C₂×C₄⋊C₄	—	2	4	no	—
432	C₂×C₄⋊C₄	—	2	4	no	—
433	C₂×C₄⋊C₄	—	2	2	no	—
434	C₂×C₄⋊C₄	—	2	2	no	—
435	C₂×C₄⋊C₄	—	2	4	no	—
436	C₂×C₄⋊C₄	—	2	4	no	—
437	C₂×C₄⋊C₄	—	4	2	no	—
438	C₂×C₄⋊C₄	—	4	2	no	—
439	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
440	C₂×C₄⋊C₄	D₄×C₁₉	1	8	yes	—
441	C₂×C₂²⋊C₄	—	2	2	no	—
442	C₂×C₂²⋊C₄	—	2	2	no	—
443	C₂×C₂²⋊C₄	—	2	2	no	—
444	C₂×C₂²⋊C₄	—	2	2	no	—
445	C₂×C₂²⋊C₄	—	2	2	no	—
446	C₂×C₂²⋊C₄	—	2	2	no	—
447	C₂×C₂²⋊C₄	—	2	2	no	—
448	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
449	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
450	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
451	C₂×C₂²⋊C₄	Q₈×C₁₉	1	4	yes	—
452	C₂×C₂²⋊C₄	Q₈×C₁₉	1	4	yes	—
453	C₂×C₄²	—	2	4	no	—
454	C₂×C₄²	—	2	4	no	—
455	C₂×C₄²	—	4	2	no	—
456	#95	—	2	4	no	—
457	#95	—	2	2	no	—
458	#95	—	2	2	no	—
459	#95	—	2	4	no	—
460	#95	—	2	4	no	—
461	#95	—	2	4	no	—
462	#95	—	2	4	no	—
463	#95	—	4	2	no	—
464	#95	C₂×C₄×C₁₉	1	8	yes	complemented
465	C₁₉	#14043	1	1	yes	characteristic, direct product factor, Sylow
466	C₂⁴	—	2	2	no	—
467	C₂⁴	—	2	2	no	—
468	C₂⁴	—	2	2	no	—
469	C₂⁴	—	2	2	no	—
470	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
471	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
472	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
473	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
474	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
475	C₂⁴	#41×C₁₉	1	2	yes	—
476	C₂⁴	#41×C₁₉	1	2	yes	—
477	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
478	C₂²×C₄	—	2	8	no	—
479	C₂²×C₄	—	2	16	no	—
480	C₂²×C₄	—	2	8	no	—
481	C₂²×C₄	—	2	8	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	16	no	—
494	C₂²×C₄	—	2	8	no	—
495	C₂²×C₄	—	2	8	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	8	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	—	4	8	no	—
533	C₂²×C₄	—	4	8	no	—
534	C₂²×C₄	—	4	8	no	—
535	C₂²×C₄	—	4	8	no	—
536	C₂²×C₄	—	4	4	no	—
537	C₂²×C₄	—	4	4	no	—
538	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
539	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
540	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
541	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
542	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
543	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
544	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
545	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
546	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
547	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
548	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
549	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
550	C₂²×C₄	#41×C₁₉	1	4	yes	—
551	C₄⋊C₄	—	2	16	no	—
552	C₄⋊C₄	—	2	16	no	—
553	C₄⋊C₄	—	2	16	no	—
554	C₄⋊C₄	—	4	8	no	—
555	C₄⋊C₄	—	4	4	no	—
556	C₄⋊C₄	—	4	4	no	—
557	C₂²⋊C₄	—	2	8	no	—
558	C₂²⋊C₄	—	2	8	no	—
559	C₂²⋊C₄	—	4	4	no	—
560	C₂²⋊C₄	C₄⋊C₄×C₁₉	1	16	yes	complemented
561	C₄²	—	4	8	no	—
562	C₂³	—	2	4	no	—
563	C₂³	—	2	4	no	—
564	C₂³	—	2	2	no	—
565	C₂³	—	2	2	no	—
566	C₂³	—	2	4	no	—
567	C₂³	—	2	2	no	—
568	C₂³	—	2	2	no	—
569	C₂³	—	2	4	no	—
570	C₂³	—	2	4	no	—
571	C₂³	—	2	4	no	—
572	C₂³	—	2	4	no	—
573	C₂³	—	2	4	no	—
574	C₂³	—	2	4	no	—
575	C₂³	—	2	4	no	—
576	C₂³	—	2	4	no	—
577	C₂³	—	2	4	no	—
578	C₂³	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
579	C₂³	C₄×D₄×C₁₉	1	4	yes	—
580	C₂³	C₄×Q₈×C₁₉	1	4	yes	—
581	C₂³	C₁₉×#121	1	4	yes	—
582	C₂³	C₁₉×C₂²⋊Q₈	1	4	yes	—
583	C₂³	C₁₉×#125	1	4	yes	—
584	C₂³	C₁₉×C₄⋊Q₈	1	4	yes	—
585	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
586	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
587	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
588	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
589	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
590	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
591	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
592	C₂³	C₂×#41×C₁₉	1	2	yes	—
593	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
594	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
595	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
596	C₂×C₄	—	2	32	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	4	16	no	—
627	C₂×C₄	—	4	16	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	2	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	2	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	2	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	—	4	2	no	—
643	C₂×C₄	—	4	2	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	2	no	—
651	C₂×C₄	—	4	2	no	—
652	C₂×C₄	—	4	2	no	—
653	C₂×C₄	—	4	2	no	—
654	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	8	yes	complemented
655	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
656	C₂×C₄	C₁₉×#120	1	4	yes	—
657	C₂²	—	2	4	no	—
658	C₂²	—	2	4	no	—
659	C₂²	—	2	4	no	—
660	C₂²	—	2	8	no	—
661	C₂²	—	2	8	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	2	8	no	—
666	C₂²	—	2	8	no	—
667	C₂²	C₁₉×#389	1	8	yes	complemented
668	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
669	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
670	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
671	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
672	C₂²	C₁₉×#520	1	2	yes	—
673	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
674	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
675	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
676	C₂²	C₁₉×#525	1	1	yes	characteristic
677	C₂²	C₁₉×#525	1	2	yes	—
678	C₂²	C₂×C₁₉×#125	1	1	yes	characteristic
679	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
680	C₂²	C₁₉×#534	1	1	yes	characteristic
681	C₂²	C₁₉×#536	1	1	yes	characteristic
682	C₂²	C₁₉×#539	1	2	yes	—
683	C₂²	D₄²×C₁₉	1	2	yes	—
684	C₂²	C₁₉×#546	1	2	yes	—
685	C₂²	C₁₉×#547	1	2	yes	—
686	C₂²	D₄×Q₈×C₁₉	1	2	yes	—
687	C₂²	D₄×Q₈×C₁₉	1	2	yes	—
688	C₂²	C₁₉×#552	1	2	yes	—
689	C₂²	C₁₉×#554	1	2	yes	—
690	C₂²	C₁₉×#554	1	2	yes	—
691	C₄	—	2	4	no	—
692	C₄	—	2	8	no	—
693	C₄	—	2	8	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	4	no	—
696	C₄	—	4	4	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	2	no	—
699	C₄	—	8	1	no	—
700	C₄	—	8	1	no	—
701	C₂	—	2	8	no	—
702	C₂	C₂×C₁₉×#389	1	1	yes	characteristic
703	C₂	C₄×C₁₉×#120	1	1	yes	characteristic
704	C₂	C₁₉×#2322	1	1	yes	characteristic
705	C₂	D₄×C₄⋊C₄×C₁₉	1	2	yes	—
706	C₂	C₁₉×#2360	1	2	yes	—
707	C₂	C₁₉×#2410	1	1	yes	characteristic
708	C₂	C₁₉×#2413	1	1	yes	characteristic
709	C₂	C₁₉×#2434	1	1	yes	characteristic
710	C₂	C₁₉×#2449	1	2	yes	—
711	C₂	C₁₉×#2473	1	2	yes	—
712	C₂	C₁₉×#2583	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#389	C₂	semidirect
7. C₁₉×#1444	C₂	semidirect
8. C₁₉×#1441	C₂	semidirect
9. C₁₉×#1436	C₂	semidirect
31. C₁₉×#385	C₄	semidirect
83. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
108. C₁₉×#95	C₂×C₄	semidirect
203. C₂²⋊C₄×C₁₉	C₄⋊C₄	semidirect
205. #14043	C₁₉	direct (N × H)
298. C₂×C₄×C₁₉	C₂×C₄⋊C₄	semidirect
302. C₂×#389	C₂×C₁₉	semidirect
307. #1444	C₂×C₁₉	semidirect
308. #1441	C₂×C₁₉	semidirect
309. #1436	C₂×C₁₉	semidirect
322. C₂²×C₁₉	#389	semidirect
375. #385	C₄×C₁₉	semidirect
439. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
464. #95	C₂×C₄×C₁₉	semidirect
465. C₁₉	#14043	direct (N × H)
560. C₂²⋊C₄	C₄⋊C₄×C₁₉	semidirect
654. C₂×C₄	C₂×C₄⋊C₄×C₁₉	semidirect
667. C₂²	C₁₉×#389	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₁₉	2
C₂×C₁₉×#389	2
C₂×C₁₉×#385	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₁₉×#1444	2
C₁₉×#1441	2
C₁₉×#1436	2
C₁₉×C₂²⋊#95	2
#14043	19

Subgroups — C19×#14043 #18020002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14043 #18020002