Subgroups — C₁₉×#14135 #18020094

Order 4864.

2634 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#123	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#386	C₂	1	2	yes	maximal
4	C₂²×C₁₉×#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1441	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1439	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1437	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1436	C₂	1	2	yes	maximal, complemented
9	C₁₉×C₂²⋊#95	C₂	1	2	yes	maximal, complemented
10	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#123	—	2	4	no	—
14	C₂×C₁₉×#123	—	2	4	no	—
15	C₂×C₁₉×#123	C₄	1	8	yes	complemented
16	C₂×C₁₉×#117	—	2	4	no	—
17	C₂×C₁₉×#117	—	2	8	no	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
22	C₂²×C₂²⋊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	2	yes	—
26	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
27	C₁₉×#386	—	2	8	no	—
28	C₂×C₁₉×#95	—	2	4	no	—
29	C₂×C₁₉×#95	C₂²	1	4	yes	—
30	C₂×C₁₉×#95	C₂²	1	2	yes	—
31	C₂×C₁₉×#95	C₂²	1	4	yes	—
32	C₂×C₁₉×#95	C₂²	1	2	yes	—
33	C₂×C₁₉×#95	C₂²	1	4	yes	—
34	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
35	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₁₉	—	2	4	no	—
37	C₂²×D₄×C₁₉	—	2	2	no	—
38	C₂²×D₄×C₁₉	—	2	2	no	—
39	C₂²×D₄×C₁₉	—	2	4	no	—
40	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
41	C₂³×C₄×C₁₉	—	2	4	no	—
42	C₂³×C₄×C₁₉	—	2	4	no	—
43	C₂³×C₄×C₁₉	—	2	4	no	—
44	C₂³×C₄×C₁₉	—	2	8	no	—
45	C₂³×C₄×C₁₉	—	2	4	no	—
46	C₂³×C₄×C₁₉	—	2	4	no	—
47	C₂³×C₄×C₁₉	—	4	4	no	—
48	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
49	C₂³×C₄×C₁₉	D₄	1	4	yes	—
50	C₂³×C₄×C₁₉	D₄	1	4	yes	—
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
56	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×#123	—	2	32	no	—
59	C₁₉×#117	—	2	32	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
67	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
68	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
79	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
80	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
81	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
82	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
83	C₂×C₄²×C₁₉	—	2	8	no	—
84	C₂×C₄²×C₁₉	—	2	4	no	—
85	C₁₉×#95	—	2	4	no	—
86	C₁₉×#95	—	2	4	no	—
87	C₁₉×#95	—	2	8	no	—
88	C₁₉×#95	—	2	8	no	—
89	C₁₉×#95	—	4	4	no	—
90	C₂⁴×C₁₉	—	2	4	no	—
91	C₂⁴×C₁₉	—	2	2	no	—
92	C₂⁴×C₁₉	—	2	2	no	—
93	C₂⁴×C₁₉	—	2	1	no	—
94	C₂⁴×C₁₉	—	2	1	no	—
95	C₂⁴×C₁₉	—	2	2	no	—
96	C₂⁴×C₁₉	—	2	4	no	—
97	C₂⁴×C₁₉	—	2	2	no	—
98	C₂⁴×C₁₉	—	2	2	no	—
99	C₂⁴×C₁₉	—	2	2	no	—
100	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
101	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
102	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
103	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
104	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
105	C₂⁴×C₁₉	#41	1	4	yes	—
106	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
107	C₂×D₄×C₁₉	—	2	8	no	—
108	C₂×D₄×C₁₉	—	2	16	no	—
109	C₂×D₄×C₁₉	—	4	4	no	—
110	C₂×D₄×C₁₉	—	4	8	no	—
111	C₂×D₄×C₁₉	—	4	4	no	—
112	C₂²×C₄×C₁₉	—	2	16	no	—
113	C₂²×C₄×C₁₉	—	2	8	no	—
114	C₂²×C₄×C₁₉	—	2	16	no	—
115	C₂²×C₄×C₁₉	—	2	8	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	16	no	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	4	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	4	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	4	no	—
133	C₂²×C₄×C₁₉	—	2	4	no	—
134	C₂²×C₄×C₁₉	—	2	4	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	4	no	—
137	C₂²×C₄×C₁₉	—	2	4	no	—
138	C₂²×C₄×C₁₉	—	2	4	no	—
139	C₂²×C₄×C₁₉	—	2	4	no	—
140	C₂²×C₄×C₁₉	—	2	4	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	4	no	—
144	C₂²×C₄×C₁₉	—	4	16	no	—
145	C₂²×C₄×C₁₉	—	4	16	no	—
146	C₂²×C₄×C₁₉	—	4	8	no	—
147	C₂²×C₄×C₁₉	—	4	8	no	—
148	C₂²×C₄×C₁₉	C₂²⋊C₄	1	16	yes	complemented
149	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
153	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
154	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
155	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₉	#41	1	8	yes	—
160	C₄⋊C₄×C₁₉	—	2	16	no	—
161	C₄⋊C₄×C₁₉	—	2	8	no	—
162	C₄⋊C₄×C₁₉	—	2	8	no	—
163	C₂²⋊C₄×C₁₉	—	2	8	no	—
164	C₂²⋊C₄×C₁₉	—	2	16	no	—
165	C₂²⋊C₄×C₁₉	—	2	8	no	—
166	C₂²⋊C₄×C₁₉	—	2	8	no	—
167	C₂²⋊C₄×C₁₉	—	4	16	no	—
168	C₄²×C₁₉	—	2	16	no	—
169	#14135	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂³×C₁₉	—	2	4	no	—
171	C₂³×C₁₉	—	2	4	no	—
172	C₂³×C₁₉	—	2	4	no	—
173	C₂³×C₁₉	—	2	4	no	—
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	2	2	no	—
176	C₂³×C₁₉	—	2	4	no	—
177	C₂³×C₁₉	—	2	8	no	—
178	C₂³×C₁₉	—	2	8	no	—
179	C₂³×C₁₉	—	2	8	no	—
180	C₂³×C₁₉	—	2	8	no	—
181	C₂³×C₁₉	—	2	2	no	—
182	C₂³×C₁₉	—	2	4	no	—
183	C₂³×C₁₉	—	2	4	no	—
184	C₂³×C₁₉	—	2	4	no	—
185	C₂³×C₁₉	—	4	1	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	4	1	no	—
188	C₂³×C₁₉	—	4	2	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	1	no	—
191	C₂³×C₁₉	—	4	1	no	—
192	C₂³×C₁₉	—	4	2	no	—
193	C₂³×C₁₉	—	4	4	no	—
194	C₂³×C₁₉	—	4	4	no	—
195	C₂³×C₁₉	—	4	4	no	—
196	C₂³×C₁₉	—	4	4	no	—
197	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
198	C₂³×C₁₉	C₄×D₄	1	8	yes	—
199	C₂³×C₁₉	#120	1	4	yes	—
200	C₂³×C₁₉	#121	1	8	yes	—
201	C₂³×C₁₉	#123	1	4	yes	—
202	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
203	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
204	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
205	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
206	C₂³×C₁₉	C₂×#41	1	2	yes	—
207	C₂³×C₁₉	C₂×#41	1	4	yes	—
208	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
209	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
210	D₄×C₁₉	—	4	16	no	—
211	C₂×C₄×C₁₉	—	2	4	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	2	4	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	32	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	4	no	—
224	C₂×C₄×C₁₉	—	2	4	no	—
225	C₂×C₄×C₁₉	—	2	4	no	—
226	C₂×C₄×C₁₉	—	2	8	no	—
227	C₂×C₄×C₁₉	—	2	8	no	—
228	C₂×C₄×C₁₉	—	2	8	no	—
229	C₂×C₄×C₁₉	—	2	8	no	—
230	C₂×C₄×C₁₉	—	2	8	no	—
231	C₂×C₄×C₁₉	—	2	8	no	—
232	C₂×C₄×C₁₉	—	4	32	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	4	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	4	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	4	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	4	4	no	—
245	C₂×C₄×C₁₉	—	4	4	no	—
246	C₂×C₄×C₁₉	—	4	4	no	—
247	C₂×C₄×C₁₉	—	4	4	no	—
248	C₂×C₄×C₁₉	—	4	4	no	—
249	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
250	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
251	C₂²×#123	C₂×C₁₉	1	1	yes	characteristic
252	C₂²×#117	C₂×C₁₉	1	1	yes	characteristic, complemented
253	C₂×#386	C₂×C₁₉	1	2	yes	—
254	C₂²×#95	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#1441	C₂×C₁₉	1	2	yes	complemented
256	#1439	C₂×C₁₉	1	2	yes	complemented
257	#1437	C₂×C₁₉	1	2	yes	complemented
258	#1436	C₂×C₁₉	1	2	yes	complemented
259	C₂²⋊#95	C₂×C₁₉	1	2	yes	complemented
260	C₂²×C₁₉	—	2	4	no	—
261	C₂²×C₁₉	—	2	16	no	—
262	C₂²×C₁₉	—	2	8	no	—
263	C₂²×C₁₉	—	2	8	no	—
264	C₂²×C₁₉	—	2	8	no	—
265	C₂²×C₁₉	—	2	8	no	—
266	C₂²×C₁₉	—	2	4	no	—
267	C₂²×C₁₉	—	4	2	no	—
268	C₂²×C₁₉	—	4	8	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	—	4	2	no	—
271	C₂²×C₁₉	—	8	2	no	—
272	C₂²×C₁₉	—	8	2	no	—
273	C₂²×C₁₉	—	8	2	no	—
274	C₂²×C₁₉	—	8	2	no	—
275	C₂²×C₁₉	#386	1	8	yes	—
276	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
277	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
278	C₂²×C₁₉	C₄×#41	1	2	yes	—
279	C₂²×C₁₉	#520	1	2	yes	—
280	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
281	C₂²×C₁₉	C₂×#121	1	2	yes	—
282	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
283	C₂²×C₁₉	#525	1	2	yes	—
284	C₂²×C₁₉	#532	1	2	yes	—
285	C₂²×C₁₉	#535	1	1	yes	characteristic
286	C₂²×C₁₉	#536	1	1	yes	characteristic
287	C₂²×C₁₉	#537	1	2	yes	—
288	C₂²×C₁₉	#546	1	4	yes	—
289	C₂²×C₁₉	#547	1	4	yes	—
290	C₂²×C₁₉	#551	1	4	yes	—
291	C₂²×C₁₉	#552	1	4	yes	—
292	C₄×C₁₉	—	2	4	no	—
293	C₄×C₁₉	—	2	4	no	—
294	C₄×C₁₉	—	4	2	no	—
295	C₄×C₁₉	—	4	8	no	—
296	C₄×C₁₉	—	4	8	no	—
297	C₄×C₁₉	—	4	2	no	—
298	C₄×C₁₉	—	4	2	no	—
299	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
300	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
301	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×#123	—	2	4	no	—
303	C₂×#123	—	2	4	no	—
304	C₂×#123	C₄×C₁₉	1	8	yes	complemented
305	C₂×#117	—	2	4	no	—
306	C₂×#117	—	2	8	no	—
307	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
308	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
309	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
310	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
311	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
312	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
313	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
314	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
315	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
316	#386	—	2	8	no	—
317	C₂×#95	—	2	4	no	—
318	C₂×#95	C₂²×C₁₉	1	4	yes	—
319	C₂×#95	C₂²×C₁₉	1	2	yes	—
320	C₂×#95	C₂²×C₁₉	1	4	yes	—
321	C₂×#95	C₂²×C₁₉	1	2	yes	—
322	C₂×#95	C₂²×C₁₉	1	4	yes	—
323	C₂×C₁₉	—	2	8	no	—
324	C₂×C₁₉	—	8	2	no	—
325	C₂×C₁₉	C₂×#386	1	1	yes	characteristic
326	C₂×C₁₉	#2297	1	1	yes	characteristic
327	C₂×C₁₉	#2311	1	1	yes	characteristic
328	C₂×C₁₉	#2359	1	4	yes	—
329	C₂×C₁₉	#2411	1	2	yes	—
330	C₂×C₁₉	#2413	1	2	yes	—
331	C₂×C₁₉	#2430	1	2	yes	—
332	C₂×C₁₉	#2498	1	2	yes	—
333	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
334	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
335	C₂²×D₄	—	2	2	no	—
336	C₂²×D₄	—	2	2	no	—
337	C₂²×D₄	—	2	4	no	—
338	C₂²×D₄	—	2	4	no	—
339	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
340	C₂³×C₄	—	2	4	no	—
341	C₂³×C₄	—	2	4	no	—
342	C₂³×C₄	—	2	4	no	—
343	C₂³×C₄	—	2	8	no	—
344	C₂³×C₄	—	2	4	no	—
345	C₂³×C₄	—	2	4	no	—
346	C₂³×C₄	—	4	4	no	—
347	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
348	C₂³×C₄	D₄×C₁₉	1	4	yes	—
349	C₂³×C₄	D₄×C₁₉	1	4	yes	—
350	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
352	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
353	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
354	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
355	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
356	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
357	#123	—	2	32	no	—
358	#117	—	2	32	no	—
359	C₂×C₄⋊C₄	—	2	8	no	—
360	C₂×C₄⋊C₄	—	2	4	no	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	2	no	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	—	2	2	no	—
365	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
366	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
367	C₂×C₂²⋊C₄	—	2	4	no	—
368	C₂×C₂²⋊C₄	—	2	4	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	—	2	2	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	2	no	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	2	8	no	—
376	C₂×C₂²⋊C₄	—	2	8	no	—
377	C₂×C₂²⋊C₄	—	4	4	no	—
378	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
379	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
380	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
381	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	—
382	C₂×C₄²	—	2	8	no	—
383	C₂×C₄²	—	2	4	no	—
384	#95	—	2	4	no	—
385	#95	—	2	4	no	—
386	#95	—	2	8	no	—
387	#95	—	2	8	no	—
388	#95	—	4	4	no	—
389	C₁₉	#14135	1	1	yes	characteristic, direct product factor, Sylow
390	C₂⁴	—	2	4	no	—
391	C₂⁴	—	2	2	no	—
392	C₂⁴	—	2	2	no	—
393	C₂⁴	—	2	1	no	—
394	C₂⁴	—	2	1	no	—
395	C₂⁴	—	2	2	no	—
396	C₂⁴	—	2	4	no	—
397	C₂⁴	—	2	2	no	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
401	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
402	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
403	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
404	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
405	C₂⁴	#41×C₁₉	1	4	yes	—
406	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
407	C₂×D₄	—	2	8	no	—
408	C₂×D₄	—	2	16	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	—	4	8	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂²×C₄	—	2	16	no	—
413	C₂²×C₄	—	2	8	no	—
414	C₂²×C₄	—	2	16	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	16	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	4	16	no	—
445	C₂²×C₄	—	4	16	no	—
446	C₂²×C₄	—	4	8	no	—
447	C₂²×C₄	—	4	8	no	—
448	C₂²×C₄	C₂²⋊C₄×C₁₉	1	16	yes	complemented
449	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
450	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
451	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
452	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
453	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
454	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
455	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
456	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
457	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
458	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
459	C₂²×C₄	#41×C₁₉	1	8	yes	—
460	C₄⋊C₄	—	2	16	no	—
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	—	2	16	no	—
465	C₂²⋊C₄	—	2	8	no	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	—	4	16	no	—
468	C₄²	—	2	16	no	—
469	C₂³	—	2	4	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	2	4	no	—
472	C₂³	—	2	4	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	2	8	no	—
477	C₂³	—	2	8	no	—
478	C₂³	—	2	8	no	—
479	C₂³	—	2	8	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	4	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	4	4	no	—
495	C₂³	—	4	4	no	—
496	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
497	C₂³	C₄×D₄×C₁₉	1	8	yes	—
498	C₂³	C₁₉×#120	1	4	yes	—
499	C₂³	C₁₉×#121	1	8	yes	—
500	C₂³	C₁₉×#123	1	4	yes	—
501	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
502	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
503	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
504	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
505	C₂³	C₂×#41×C₁₉	1	2	yes	—
506	C₂³	C₂×#41×C₁₉	1	4	yes	—
507	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
508	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
509	D₄	—	4	16	no	—
510	C₂×C₄	—	2	32	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	8	no	—
526	C₂×C₄	—	2	8	no	—
527	C₂×C₄	—	2	8	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	8	no	—
530	C₂×C₄	—	2	8	no	—
531	C₂×C₄	—	4	32	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	4	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	4	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	4	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	4	4	no	—
547	C₂×C₄	—	4	4	no	—
548	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
549	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
550	C₂²	—	2	8	no	—
551	C₂²	—	2	8	no	—
552	C₂²	—	2	8	no	—
553	C₂²	—	2	8	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	4	no	—
556	C₂²	—	2	16	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	8	no	—
561	C₂²	—	8	2	no	—
562	C₂²	—	8	2	no	—
563	C₂²	—	8	2	no	—
564	C₂²	—	8	2	no	—
565	C₂²	C₁₉×#386	1	8	yes	—
566	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
567	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
568	C₂²	C₄×#41×C₁₉	1	2	yes	—
569	C₂²	C₁₉×#520	1	2	yes	—
570	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
571	C₂²	C₂×C₁₉×#121	1	2	yes	—
572	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
573	C₂²	C₁₉×#525	1	2	yes	—
574	C₂²	C₁₉×#532	1	2	yes	—
575	C₂²	C₁₉×#535	1	1	yes	characteristic
576	C₂²	C₁₉×#536	1	1	yes	characteristic
577	C₂²	C₁₉×#537	1	2	yes	—
578	C₂²	C₁₉×#546	1	4	yes	—
579	C₂²	C₁₉×#547	1	4	yes	—
580	C₂²	C₁₉×#551	1	4	yes	—
581	C₂²	C₁₉×#552	1	4	yes	—
582	C₄	—	2	4	no	—
583	C₄	—	2	4	no	—
584	C₄	—	4	8	no	—
585	C₄	—	4	8	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	2	no	—
589	C₂	—	2	8	no	—
590	C₂	—	8	2	no	—
591	C₂	C₂×C₁₉×#386	1	1	yes	characteristic
592	C₂	C₁₉×#2297	1	1	yes	characteristic
593	C₂	C₁₉×#2311	1	1	yes	characteristic
594	C₂	C₁₉×#2359	1	4	yes	—
595	C₂	C₁₉×#2411	1	2	yes	—
596	C₂	C₁₉×#2413	1	2	yes	—
597	C₂	C₁₉×#2430	1	2	yes	—
598	C₂	C₁₉×#2498	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
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. C₂²×C₁₉×#117	C₂	semidirect
4. C₂²×C₁₉×#95	C₂	semidirect
5. C₁₉×#1441	C₂	semidirect
6. C₁₉×#1439	C₂	semidirect
7. C₁₉×#1437	C₂	semidirect
8. C₁₉×#1436	C₂	semidirect
9. C₁₉×C₂²⋊#95	C₂	semidirect
15. C₂×C₁₉×#123	C₄	semidirect
66. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
67. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
80. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
81. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
148. C₂²×C₄×C₁₉	C₂²⋊C₄	semidirect
169. #14135	C₁₉	direct (N × H)
252. C₂²×#117	C₂×C₁₉	semidirect
254. C₂²×#95	C₂×C₁₉	semidirect
255. #1441	C₂×C₁₉	semidirect
256. #1439	C₂×C₁₉	semidirect
257. #1437	C₂×C₁₉	semidirect
258. #1436	C₂×C₁₉	semidirect
259. C₂²⋊#95	C₂×C₁₉	semidirect
304. C₂×#123	C₄×C₁₉	semidirect
365. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
366. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
379. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
380. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
389. C₁₉	#14135	direct (N × H)
448. C₂²×C₄	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#123	2
C₂²×C₁₉×#117	2
C₂×C₁₉×#386	2
C₂²×C₁₉×#95	2
C₁₉×#1441	2
C₁₉×#1439	2
C₁₉×#1437	2
C₁₉×#1436	2
C₁₉×C₂²⋊#95	2
#14135	19

Subgroups — C19×#14135 #18020094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14135 #18020094