Subgroups — C₁₉×#14486 #18020445

Order 4864.

1918 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#390	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#386	C₂	1	2	yes	maximal
3	C₁₉×#1441	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1439	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1434	C₂	1	2	yes	maximal, complemented
6	C₁₉×C₂²⋊#95	C₂	1	4	yes	maximal, complemented
7	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
12	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#390	C₄	1	8	yes	complemented
16	C₁₉×#386	—	2	8	no	—
17	C₂×C₁₉×#95	C₂²	1	4	yes	—
18	C₂×C₁₉×#95	C₂²	1	4	yes	—
19	C₂×C₁₉×#95	C₂²	1	2	yes	—
20	C₂×C₁₉×#95	C₂²	1	2	yes	—
21	C₂×C₁₉×#95	C₂²	1	4	yes	—
22	C₂×C₁₉×#95	C₂²	1	2	yes	—
23	C₂⁵×C₁₉	C₂³	1	2	yes	—
24	C₂²×D₄×C₁₉	—	4	1	no	—
25	C₂²×D₄×C₁₉	—	4	1	no	—
26	C₂²×D₄×C₁₉	—	4	1	no	—
27	C₂²×D₄×C₁₉	—	4	1	no	—
28	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
29	C₂²×D₄×C₁₉	D₄	1	4	yes	—
30	C₂²×D₄×C₁₉	Q₈	1	4	yes	—
31	C₂³×C₄×C₁₉	—	2	4	no	—
32	C₂³×C₄×C₁₉	—	2	8	no	—
33	C₂³×C₄×C₁₉	—	4	4	no	—
34	C₂³×C₄×C₁₉	—	4	2	no	—
35	C₂³×C₄×C₁₉	—	4	2	no	—
36	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
37	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
42	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
43	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
44	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
45	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
46	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
54	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	16	yes	complemented
55	C₂×C₄²×C₁₉	—	4	1	no	—
56	C₂×C₄²×C₁₉	—	4	1	no	—
57	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	complemented
58	C₁₉×#95	—	2	8	no	—
59	C₁₉×#95	—	2	8	no	—
60	C₁₉×#95	—	4	2	no	—
61	C₁₉×#95	—	4	2	no	—
62	C₁₉×#95	—	4	4	no	—
63	C₁₉×#95	—	4	2	no	—
64	C₂⁴×C₁₉	—	2	4	no	—
65	C₂⁴×C₁₉	—	2	4	no	—
66	C₂⁴×C₁₉	—	2	4	no	—
67	C₂⁴×C₁₉	—	2	4	no	—
68	C₂⁴×C₁₉	—	2	2	no	—
69	C₂⁴×C₁₉	—	2	2	no	—
70	C₂⁴×C₁₉	—	2	2	no	—
71	C₂⁴×C₁₉	—	2	2	no	—
72	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
73	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
74	C₂⁴×C₁₉	C₂×Q₈	1	4	yes	—
75	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
76	C₂×D₄×C₁₉	—	4	4	no	—
77	C₂×D₄×C₁₉	—	4	4	no	—
78	C₂×D₄×C₁₉	—	4	4	no	—
79	C₂×D₄×C₁₉	—	4	4	no	—
80	C₂×D₄×C₁₉	—	4	4	no	—
81	C₂×D₄×C₁₉	—	4	4	no	—
82	C₂×D₄×C₁₉	C₄⋊C₄	1	16	yes	complemented
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	4	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	2	4	no	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	4	no	—
99	C₂²×C₄×C₁₉	—	2	4	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	4	no	—
102	C₂²×C₄×C₁₉	—	2	4	no	—
103	C₂²×C₄×C₁₉	—	2	4	no	—
104	C₂²×C₄×C₁₉	—	2	4	no	—
105	C₂²×C₄×C₁₉	—	2	4	no	—
106	C₂²×C₄×C₁₉	—	2	4	no	—
107	C₂²×C₄×C₁₉	—	2	4	no	—
108	C₂²×C₄×C₁₉	—	4	8	no	—
109	C₂²×C₄×C₁₉	—	4	16	no	—
110	C₂²×C₄×C₁₉	—	4	16	no	—
111	C₂²×C₄×C₁₉	—	4	8	no	—
112	C₂²×C₄×C₁₉	—	4	8	no	—
113	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
114	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
115	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
118	C₂²×C₄×C₁₉	#41	1	8	yes	—
119	C₄⋊C₄×C₁₉	—	4	4	no	—
120	C₄⋊C₄×C₁₉	—	4	8	no	—
121	C₂²⋊C₄×C₁₉	—	4	16	no	—
122	C₂²⋊C₄×C₁₉	—	4	16	no	—
123	C₂²⋊C₄×C₁₉	—	4	8	no	—
124	C₄²×C₁₉	—	4	4	no	—
125	#14486	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₁₉	—	2	8	no	—
127	C₂³×C₁₉	—	2	8	no	—
128	C₂³×C₁₉	—	2	4	no	—
129	C₂³×C₁₉	—	2	4	no	—
130	C₂³×C₁₉	—	2	4	no	—
131	C₂³×C₁₉	—	2	4	no	—
132	C₂³×C₁₉	—	2	4	no	—
133	C₂³×C₁₉	—	2	4	no	—
134	C₂³×C₁₉	—	2	8	no	—
135	C₂³×C₁₉	—	2	8	no	—
136	C₂³×C₁₉	—	2	8	no	—
137	C₂³×C₁₉	—	2	8	no	—
138	C₂³×C₁₉	—	4	4	no	—
139	C₂³×C₁₉	—	4	4	no	—
140	C₂³×C₁₉	—	4	4	no	—
141	C₂³×C₁₉	—	4	4	no	—
142	C₂³×C₁₉	—	4	2	no	—
143	C₂³×C₁₉	—	4	2	no	—
144	C₂³×C₁₉	—	4	4	no	—
145	C₂³×C₁₉	—	4	2	no	—
146	C₂³×C₁₉	—	4	2	no	—
147	C₂³×C₁₉	—	4	4	no	—
148	C₂³×C₁₉	C₂×C₄⋊C₄	1	8	yes	—
149	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
150	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
151	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
152	C₂³×C₁₉	C₂×#41	1	4	yes	—
153	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
155	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
157	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
158	D₄×C₁₉	—	4	16	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	8	no	—
169	C₂×C₄×C₁₉	—	2	4	no	—
170	C₂×C₄×C₁₉	—	2	8	no	—
171	C₂×C₄×C₁₉	—	2	8	no	—
172	C₂×C₄×C₁₉	—	2	8	no	—
173	C₂×C₄×C₁₉	—	4	32	no	—
174	C₂×C₄×C₁₉	—	4	4	no	—
175	C₂×C₄×C₁₉	—	4	4	no	—
176	C₂×C₄×C₁₉	—	4	4	no	—
177	C₂×C₄×C₁₉	—	4	4	no	—
178	C₂×C₄×C₁₉	—	4	4	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	4	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	4	no	—
183	C₂×C₄×C₁₉	—	4	4	no	—
184	C₂×C₄×C₁₉	—	4	4	no	—
185	C₂×C₄×C₁₉	—	4	4	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	—	4	4	no	—
189	C₂×C₄×C₁₉	—	4	4	no	—
190	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
191	C₂×#390	C₂×C₁₉	1	1	yes	characteristic
192	C₂×#386	C₂×C₁₉	1	2	yes	—
193	#1441	C₂×C₁₉	1	2	yes	complemented
194	#1439	C₂×C₁₉	1	4	yes	complemented
195	#1434	C₂×C₁₉	1	2	yes	complemented
196	C₂²⋊#95	C₂×C₁₉	1	4	yes	complemented
197	C₂²×C₁₉	—	2	8	no	—
198	C₂²×C₁₉	—	2	16	no	—
199	C₂²×C₁₉	—	4	8	no	—
200	C₂²×C₁₉	—	4	4	no	—
201	C₂²×C₁₉	—	4	4	no	—
202	C₂²×C₁₉	—	4	4	no	—
203	C₂²×C₁₉	—	4	4	no	—
204	C₂²×C₁₉	—	4	8	no	—
205	C₂²×C₁₉	—	4	4	no	—
206	C₂²×C₁₉	—	4	4	no	—
207	C₂²×C₁₉	—	4	8	no	—
208	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
209	C₂²×C₁₉	C₄×#41	1	2	yes	—
210	C₂²×C₁₉	#518	1	1	yes	characteristic
211	C₂²×C₁₉	#518	1	1	yes	characteristic
212	C₂²×C₁₉	#518	1	2	yes	—
213	C₂²×C₁₉	#534	1	1	yes	characteristic
214	C₂²×C₁₉	#534	1	1	yes	characteristic
215	C₂²×C₁₉	#538	1	4	yes	—
216	C₂²×C₁₉	#540	1	4	yes	—
217	C₂²×C₁₉	#543	1	1	yes	characteristic
218	C₂²×C₁₉	#543	1	1	yes	characteristic
219	C₂²×C₁₉	#546	1	4	yes	—
220	C₂²×C₁₉	#551	1	2	yes	—
221	C₂²×C₁₉	#554	1	4	yes	—
222	C₂²×C₁₉	#555	1	2	yes	—
223	C₂²×C₁₉	#560	1	2	yes	—
224	C₂²×C₁₉	#560	1	2	yes	—
225	C₄×C₁₉	—	2	4	no	—
226	C₄×C₁₉	—	4	4	no	—
227	C₄×C₁₉	—	4	4	no	—
228	C₄×C₁₉	—	4	8	no	—
229	C₄×C₁₉	—	8	4	no	—
230	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
231	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
232	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
233	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
234	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
235	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
236	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
237	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
238	#390	C₄×C₁₉	1	8	yes	complemented
239	#386	—	2	8	no	—
240	C₂×#95	C₂²×C₁₉	1	4	yes	—
241	C₂×#95	C₂²×C₁₉	1	4	yes	—
242	C₂×#95	C₂²×C₁₉	1	2	yes	—
243	C₂×#95	C₂²×C₁₉	1	2	yes	—
244	C₂×#95	C₂²×C₁₉	1	4	yes	—
245	C₂×#95	C₂²×C₁₉	1	2	yes	—
246	C₂×C₁₉	—	4	8	no	—
247	C₂×C₁₉	#2315	1	1	yes	characteristic
248	C₂×C₁₉	#2333	1	2	yes	—
249	C₂×C₁₉	#2349	1	2	yes	—
250	C₂×C₁₉	#2372	1	1	yes	characteristic
251	C₂×C₁₉	#2380	1	1	yes	characteristic
252	C₂×C₁₉	#2697	1	2	yes	—
253	C₂×C₁₉	#2699	1	2	yes	—
254	C₂×C₁₉	#2748	1	2	yes	—
255	C₂×C₁₉	#2784	1	2	yes	—
256	C₂⁵	C₂³×C₁₉	1	2	yes	—
257	C₂²×D₄	—	4	1	no	—
258	C₂²×D₄	—	4	1	no	—
259	C₂²×D₄	—	4	1	no	—
260	C₂²×D₄	—	4	1	no	—
261	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
262	C₂²×D₄	D₄×C₁₉	1	4	yes	—
263	C₂²×D₄	Q₈×C₁₉	1	4	yes	—
264	C₂³×C₄	—	2	4	no	—
265	C₂³×C₄	—	2	8	no	—
266	C₂³×C₄	—	4	2	no	—
267	C₂³×C₄	—	4	2	no	—
268	C₂³×C₄	—	4	4	no	—
269	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
270	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
271	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
272	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
273	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
274	C₂×C₄⋊C₄	—	4	1	no	—
275	C₂×C₄⋊C₄	—	4	1	no	—
276	C₂×C₄⋊C₄	—	4	4	no	—
277	C₂×C₄⋊C₄	—	4	2	no	—
278	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
279	C₂×C₂²⋊C₄	—	2	8	no	—
280	C₂×C₂²⋊C₄	—	2	4	no	—
281	C₂×C₂²⋊C₄	—	2	8	no	—
282	C₂×C₂²⋊C₄	—	4	4	no	—
283	C₂×C₂²⋊C₄	—	4	4	no	—
284	C₂×C₂²⋊C₄	—	4	4	no	—
285	C₂×C₂²⋊C₄	—	4	2	no	—
286	C₂×C₂²⋊C₄	—	4	2	no	—
287	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	16	yes	complemented
288	C₂×C₄²	—	4	1	no	—
289	C₂×C₄²	—	4	1	no	—
290	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	complemented
291	#95	—	2	8	no	—
292	#95	—	2	8	no	—
293	#95	—	4	2	no	—
294	#95	—	4	2	no	—
295	#95	—	4	4	no	—
296	#95	—	4	2	no	—
297	C₁₉	#14486	1	1	yes	characteristic, direct product factor, Sylow
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	2	4	no	—
300	C₂⁴	—	2	4	no	—
301	C₂⁴	—	2	4	no	—
302	C₂⁴	—	2	2	no	—
303	C₂⁴	—	2	2	no	—
304	C₂⁴	—	2	2	no	—
305	C₂⁴	—	2	2	no	—
306	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
307	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
308	C₂⁴	C₂×Q₈×C₁₉	1	4	yes	—
309	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
310	C₂×D₄	—	4	4	no	—
311	C₂×D₄	—	4	4	no	—
312	C₂×D₄	—	4	4	no	—
313	C₂×D₄	—	4	4	no	—
314	C₂×D₄	—	4	4	no	—
315	C₂×D₄	—	4	4	no	—
316	C₂×D₄	C₄⋊C₄×C₁₉	1	16	yes	complemented
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	4	8	no	—
343	C₂²×C₄	—	4	16	no	—
344	C₂²×C₄	—	4	16	no	—
345	C₂²×C₄	—	4	8	no	—
346	C₂²×C₄	—	4	8	no	—
347	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
348	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
349	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
351	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
352	C₂²×C₄	#41×C₁₉	1	8	yes	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	—	4	8	no	—
355	C₂²⋊C₄	—	4	16	no	—
356	C₂²⋊C₄	—	4	16	no	—
357	C₂²⋊C₄	—	4	8	no	—
358	C₄²	—	4	4	no	—
359	C₂³	—	2	8	no	—
360	C₂³	—	2	8	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	2	4	no	—
367	C₂³	—	2	8	no	—
368	C₂³	—	2	8	no	—
369	C₂³	—	2	8	no	—
370	C₂³	—	2	8	no	—
371	C₂³	—	4	4	no	—
372	C₂³	—	4	4	no	—
373	C₂³	—	4	4	no	—
374	C₂³	—	4	4	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	4	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	4	no	—
381	C₂³	C₂×C₄⋊C₄×C₁₉	1	8	yes	—
382	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
383	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
384	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
385	C₂³	C₂×#41×C₁₉	1	4	yes	—
386	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
387	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
388	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
389	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
391	D₄	—	4	16	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	4	32	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
424	C₂²	—	2	8	no	—
425	C₂²	—	2	16	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	8	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	4	8	no	—
432	C₂²	—	4	8	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
436	C₂²	C₄×#41×C₁₉	1	2	yes	—
437	C₂²	C₁₉×#518	1	1	yes	characteristic
438	C₂²	C₁₉×#518	1	1	yes	characteristic
439	C₂²	C₁₉×#518	1	2	yes	—
440	C₂²	C₁₉×#534	1	1	yes	characteristic
441	C₂²	C₁₉×#534	1	1	yes	characteristic
442	C₂²	C₁₉×#538	1	4	yes	—
443	C₂²	C₁₉×#540	1	4	yes	—
444	C₂²	C₁₉×#543	1	1	yes	characteristic
445	C₂²	C₁₉×#543	1	1	yes	characteristic
446	C₂²	C₁₉×#546	1	4	yes	—
447	C₂²	C₁₉×#551	1	2	yes	—
448	C₂²	C₁₉×#554	1	4	yes	—
449	C₂²	C₁₉×#555	1	2	yes	—
450	C₂²	C₁₉×#560	1	2	yes	—
451	C₂²	C₁₉×#560	1	2	yes	—
452	C₄	—	2	4	no	—
453	C₄	—	4	8	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	4	no	—
456	C₄	—	8	4	no	—
457	C₂	—	4	8	no	—
458	C₂	C₁₉×#2315	1	1	yes	characteristic
459	C₂	C₁₉×#2333	1	2	yes	—
460	C₂	C₁₉×#2349	1	2	yes	—
461	C₂	C₁₉×#2372	1	1	yes	characteristic
462	C₂	C₁₉×#2380	1	1	yes	characteristic
463	C₂	C₁₉×#2697	1	2	yes	—
464	C₂	C₁₉×#2699	1	2	yes	—
465	C₂	C₁₉×#2748	1	2	yes	—
466	C₂	C₁₉×#2784	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
3. C₁₉×#1441	C₂	semidirect
4. C₁₉×#1439	C₂	semidirect
5. C₁₉×#1434	C₂	semidirect
6. C₁₉×C₂²⋊#95	C₂	semidirect
15. C₁₉×#390	C₄	semidirect
45. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
54. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
57. C₂×C₄²×C₁₉	C₂×C₄	semidirect
82. C₂×D₄×C₁₉	C₄⋊C₄	semidirect
125. #14486	C₁₉	direct (N × H)
193. #1441	C₂×C₁₉	semidirect
194. #1439	C₂×C₁₉	semidirect
195. #1434	C₂×C₁₉	semidirect
196. C₂²⋊#95	C₂×C₁₉	semidirect
238. #390	C₄×C₁₉	semidirect
278. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
287. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
290. C₂×C₄²	C₂×C₄×C₁₉	semidirect
297. C₁₉	#14486	direct (N × H)
316. C₂×D₄	C₄⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#390	2
C₂×C₁₉×#386	2
C₁₉×#1441	2
C₁₉×#1439	2
C₁₉×#1434	2
C₁₉×C₂²⋊#95	2
#14486	19

Subgroups — C19×#14486 #18020445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14486 #18020445