Subgroups — C₁₉×#16177 #18022136

Order 4864.

990 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#1445	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1445	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1443	C₂	1	2	yes	maximal
4	C₁₉×#1442	C₂	1	2	yes	maximal
5	C₁₉×#1442	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1442	C₂	1	2	yes	maximal
7	C₁₉×#1436	C₂	1	2	yes	maximal
8	C₁₉×#1434	C₂	1	2	yes	maximal
9	C₁₉×#1434	C₂	1	2	yes	maximal
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
14	C₂×C₁₉×#95	C₂²	1	2	yes	—
15	C₂×C₁₉×#95	C₂²	1	2	yes	—
16	C₂×C₁₉×#95	C₂²	1	2	yes	—
17	C₂×C₁₉×#95	C₂²	1	2	yes	—
18	C₂×C₁₉×#95	C₂²	1	2	yes	—
19	C₂×C₁₉×#95	C₂²	1	2	yes	—
20	C₂×C₁₉×#95	C₂²	1	2	yes	—
21	C₂×C₁₉×#95	C₂²	1	2	yes	—
22	C₂×C₁₉×#95	C₂²	1	2	yes	—
23	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#95	C₂²	1	2	yes	—
27	C₂×C₁₉×#95	C₂²	1	2	yes	—
28	C₂×C₁₉×#95	C₂²	1	2	yes	—
29	C₂×C₁₉×#95	C₂²	1	2	yes	—
30	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
32	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
40	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
44	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
45	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
48	C₂×C₄²×C₁₉	—	2	4	no	—
49	C₂×C₄²×C₁₉	—	2	4	no	—
50	C₂×C₄²×C₁₉	—	4	2	no	—
51	C₁₉×#95	—	2	4	no	—
52	C₁₉×#95	—	2	4	no	—
53	C₁₉×#95	—	2	4	no	—
54	C₁₉×#95	—	2	4	no	—
55	C₁₉×#95	—	2	4	no	—
56	C₁₉×#95	—	2	4	no	—
57	C₁₉×#95	—	2	4	no	—
58	C₁₉×#95	—	2	4	no	—
59	C₁₉×#95	—	2	4	no	—
60	C₁₉×#95	—	2	2	no	—
61	C₁₉×#95	—	4	1	no	—
62	C₁₉×#95	—	4	2	no	—
63	C₁₉×#95	—	4	1	no	—
64	C₁₉×#95	—	4	1	no	—
65	C₁₉×#95	—	4	2	no	—
66	C₁₉×#95	—	4	2	no	—
67	C₁₉×#95	—	4	2	no	—
68	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	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	#41	1	4	yes	—
121	C₂²×C₄×C₁₉	#41	1	4	yes	—
122	C₂²×C₄×C₁₉	#41	1	2	yes	—
123	C₂²×C₄×C₁₉	#41	1	2	yes	—
124	C₂²×C₄×C₁₉	#41	1	2	yes	—
125	C₂²×C₄×C₁₉	#41	1	4	yes	—
126	C₄⋊C₄×C₁₉	—	4	4	no	—
127	C₄⋊C₄×C₁₉	—	4	4	no	—
128	C₄⋊C₄×C₁₉	—	4	4	no	—
129	C₄²×C₁₉	—	4	8	no	—
130	#16177	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
132	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
133	C₂³×C₁₉	C₂×#41	1	2	yes	—
134	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
135	C₂³×C₁₉	C₂×#41	1	2	yes	—
136	C₂³×C₁₉	C₂×#41	1	2	yes	—
137	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
138	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
139	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
140	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
141	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
142	C₂×C₄×C₁₉	—	2	4	no	—
143	C₂×C₄×C₁₉	—	2	4	no	—
144	C₂×C₄×C₁₉	—	2	4	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	4	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	4	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	#1445	C₂×C₁₉	1	1	yes	characteristic
200	#1445	C₂×C₁₉	1	1	yes	characteristic
201	#1443	C₂×C₁₉	1	2	yes	—
202	#1442	C₂×C₁₉	1	1	yes	characteristic
203	#1442	C₂×C₁₉	1	2	yes	—
204	#1442	C₂×C₁₉	1	2	yes	—
205	#1436	C₂×C₁₉	1	2	yes	—
206	#1434	C₂×C₁₉	1	2	yes	—
207	#1434	C₂×C₁₉	1	2	yes	—
208	C₂²×C₁₉	#529	1	2	yes	—
209	C₂²×C₁₉	#529	1	2	yes	—
210	C₂²×C₁₉	#529	1	2	yes	—
211	C₂²×C₁₉	#538	1	1	yes	characteristic
212	C₂²×C₁₉	#538	1	1	yes	characteristic
213	C₂²×C₁₉	#539	1	2	yes	—
214	C₂²×C₁₉	#539	1	1	yes	characteristic
215	C₂²×C₁₉	#541	1	2	yes	—
216	C₂²×C₁₉	#542	1	2	yes	—
217	C₂²×C₁₉	#551	1	2	yes	—
218	C₂²×C₁₉	#551	1	1	yes	characteristic
219	C₂²×C₁₉	#552	1	2	yes	—
220	C₂²×C₁₉	#552	1	2	yes	—
221	C₂²×C₁₉	#552	1	2	yes	—
222	C₂²×C₁₉	#552	1	2	yes	—
223	C₂²×C₁₉	#553	1	2	yes	—
224	C₂²×C₁₉	#555	1	1	yes	characteristic
225	C₂²×C₁₉	#555	1	1	yes	characteristic
226	C₂²×C₁₉	#556	1	1	yes	characteristic
227	C₂²×C₁₉	#559	1	1	yes	characteristic
228	C₂²×C₁₉	#559	1	1	yes	characteristic
229	C₂²×C₁₉	#562	1	1	yes	characteristic
230	C₂²×C₁₉	#563	1	1	yes	characteristic
231	C₄×C₁₉	—	4	4	no	—
232	C₄×C₁₉	—	4	4	no	—
233	C₄×C₁₉	—	4	4	no	—
234	C₄×C₁₉	—	4	2	no	—
235	C₄×C₁₉	—	4	2	no	—
236	C₄×C₁₉	—	4	2	no	—
237	C₄×C₁₉	—	8	2	no	—
238	C₄×C₁₉	—	8	2	no	—
239	C₄×C₁₉	—	8	2	no	—
240	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
243	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
244	C₂×#95	C₂²×C₁₉	1	2	yes	—
245	C₂×#95	C₂²×C₁₉	1	2	yes	—
246	C₂×#95	C₂²×C₁₉	1	2	yes	—
247	C₂×#95	C₂²×C₁₉	1	2	yes	—
248	C₂×#95	C₂²×C₁₉	1	2	yes	—
249	C₂×#95	C₂²×C₁₉	1	2	yes	—
250	C₂×#95	C₂²×C₁₉	1	2	yes	—
251	C₂×#95	C₂²×C₁₉	1	2	yes	—
252	C₂×#95	C₂²×C₁₉	1	2	yes	—
253	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
254	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
256	C₂×#95	C₂²×C₁₉	1	2	yes	—
257	C₂×#95	C₂²×C₁₉	1	2	yes	—
258	C₂×#95	C₂²×C₁₉	1	2	yes	—
259	C₂×#95	C₂²×C₁₉	1	2	yes	—
260	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
261	C₂×C₁₉	#2517	1	1	yes	characteristic
262	C₂×C₁₉	#2528	1	2	yes	—
263	C₂×C₁₉	#2529	1	2	yes	—
264	C₂×C₁₉	#2572	1	1	yes	characteristic
265	C₂×C₁₉	#2575	1	2	yes	—
266	C₂×C₁₉	#2593	1	1	yes	characteristic
267	C₂×C₁₉	#2747	1	2	yes	—
268	C₂×C₁₉	#2764	1	1	yes	characteristic
269	C₂×C₁₉	#2769	1	1	yes	characteristic
270	C₂×C₁₉	#2771	1	1	yes	characteristic
271	C₂×C₁₉	#2808	1	1	yes	characteristic
272	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
273	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
274	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
275	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
277	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
279	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
280	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
281	C₂×C₄⋊C₄	—	2	4	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	4	1	no	—
285	C₂×C₄⋊C₄	—	4	1	no	—
286	C₂×C₄⋊C₄	—	4	1	no	—
287	C₂×C₄⋊C₄	—	4	1	no	—
288	C₂×C₄⋊C₄	—	4	1	no	—
289	C₂×C₄²	—	2	4	no	—
290	C₂×C₄²	—	2	4	no	—
291	C₂×C₄²	—	4	2	no	—
292	#95	—	2	4	no	—
293	#95	—	2	4	no	—
294	#95	—	2	4	no	—
295	#95	—	2	4	no	—
296	#95	—	2	4	no	—
297	#95	—	2	4	no	—
298	#95	—	2	4	no	—
299	#95	—	2	4	no	—
300	#95	—	2	2	no	—
301	#95	—	2	4	no	—
302	#95	—	4	1	no	—
303	#95	—	4	2	no	—
304	#95	—	4	1	no	—
305	#95	—	4	2	no	—
306	#95	—	4	1	no	—
307	#95	—	4	2	no	—
308	#95	—	4	2	no	—
309	C₁₉	#16177	1	1	yes	characteristic, direct product factor, Sylow
310	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	#41×C₁₉	1	2	yes	—
363	C₂²×C₄	#41×C₁₉	1	4	yes	—
364	C₂²×C₄	#41×C₁₉	1	4	yes	—
365	C₂²×C₄	#41×C₁₉	1	2	yes	—
366	C₂²×C₄	#41×C₁₉	1	2	yes	—
367	C₂²×C₄	#41×C₁₉	1	4	yes	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄²	—	4	8	no	—
372	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
373	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
374	C₂³	C₂×#41×C₁₉	1	2	yes	—
375	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
376	C₂³	C₂×#41×C₁₉	1	2	yes	—
377	C₂³	C₂×#41×C₁₉	1	2	yes	—
378	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
379	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
381	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
382	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂²	C₁₉×#529	1	2	yes	—
441	C₂²	C₁₉×#529	1	2	yes	—
442	C₂²	C₁₉×#529	1	2	yes	—
443	C₂²	C₁₉×#538	1	1	yes	characteristic
444	C₂²	C₁₉×#538	1	1	yes	characteristic
445	C₂²	C₁₉×#539	1	2	yes	—
446	C₂²	C₁₉×#539	1	1	yes	characteristic
447	C₂²	C₁₉×#541	1	2	yes	—
448	C₂²	C₁₉×#542	1	2	yes	—
449	C₂²	C₁₉×#551	1	2	yes	—
450	C₂²	C₁₉×#551	1	1	yes	characteristic
451	C₂²	C₁₉×#552	1	2	yes	—
452	C₂²	C₁₉×#552	1	2	yes	—
453	C₂²	C₁₉×#552	1	2	yes	—
454	C₂²	C₁₉×#552	1	2	yes	—
455	C₂²	C₁₉×#553	1	2	yes	—
456	C₂²	C₁₉×#555	1	1	yes	characteristic
457	C₂²	C₁₉×#555	1	1	yes	characteristic
458	C₂²	C₁₉×#556	1	1	yes	characteristic
459	C₂²	C₁₉×#559	1	1	yes	characteristic
460	C₂²	C₁₉×#559	1	1	yes	characteristic
461	C₂²	C₁₉×#562	1	1	yes	characteristic
462	C₂²	C₁₉×#563	1	1	yes	characteristic
463	C₄	—	4	4	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	4	no	—
468	C₄	—	4	4	no	—
469	C₄	—	8	2	no	—
470	C₄	—	8	2	no	—
471	C₄	—	8	2	no	—
472	C₂	C₁₉×#2517	1	1	yes	characteristic
473	C₂	C₁₉×#2528	1	2	yes	—
474	C₂	C₁₉×#2529	1	2	yes	—
475	C₂	C₁₉×#2572	1	1	yes	characteristic
476	C₂	C₁₉×#2575	1	2	yes	—
477	C₂	C₁₉×#2593	1	1	yes	characteristic
478	C₂	C₁₉×#2747	1	2	yes	—
479	C₂	C₁₉×#2764	1	1	yes	characteristic
480	C₂	C₁₉×#2769	1	1	yes	characteristic
481	C₂	C₁₉×#2771	1	1	yes	characteristic
482	C₂	C₁₉×#2808	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
130. #16177	C₁₉	direct (N × H)
309. C₁₉	#16177	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×#1445	2
C₁₉×#1443	2
C₁₉×#1442	2
C₁₉×#1436	2
C₁₉×#1434	2
#16177	19

Subgroups — C19×#16177 #18022136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#16177 #18022136