Subgroups — C₁₉×#12958 #18018917

Order 4864.

728 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2358	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×AΣL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1889	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1867	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1856	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1393	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1390	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#120	C₂²	1	1	yes	characteristic
9	C₁₉×#518	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₉	—	2	1	no	—
11	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
12	C₁₉×#428	—	2	1	no	—
13	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#99	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#99	C₂²	1	1	yes	characteristic
16	C₁₉×#390	C₂²	1	1	yes	characteristic
17	C₁₉×#388	—	2	1	no	—
18	C₁₉×#386	—	2	1	no	—
19	C₁₉×#386	C₂²	1	1	yes	characteristic
20	C₁₉×#385	—	2	1	no	—
21	C₁₉×#385	—	2	1	no	—
22	C₁₉×#379	—	2	1	no	—
23	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
24	C₁₉×AΣL(1,𝔽₁₆)	C₄	1	4	yes	complemented
25	C₁₉×#342	—	2	1	no	—
26	C₁₉×#342	—	2	1	no	—
27	C₁₉×#339	—	2	1	no	—
28	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂³×C₄×C₁₉	—	2	1	no	—
33	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₁₉×#120	—	2	1	no	—
36	C₁₉×#120	—	2	1	no	—
37	C₁₉×#120	C₂×C₄	1	2	yes	—
38	C₁₉×#120	Q₈	1	2	yes	—
39	C₄×D₄×C₁₉	—	4	4	no	—
40	C₄×D₄×C₁₉	—	4	1	no	—
41	C₄×D₄×C₁₉	—	4	1	no	—
42	C₁₉×#117	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
45	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
59	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₉	—	2	1	no	—
62	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
63	C₁₉×#107	—	4	1	no	—
64	C₁₉×#106	—	4	1	no	—
65	C₁₉×#100	—	2	1	no	—
66	C₁₉×#100	C₂×C₄	1	2	yes	complemented
67	C₁₉×#99	—	2	1	no	—
68	C₁₉×#99	—	2	1	no	—
69	C₁₉×#99	—	2	1	no	—
70	C₁₉×#99	C₂×C₄	1	2	yes	complemented
71	C₁₉×#95	—	2	1	no	—
72	C₁₉×#95	—	2	1	no	—
73	C₁₉×#95	—	2	1	no	—
74	C₁₉×#95	—	4	1	no	—
75	C₂⁴×C₁₉	—	2	1	no	—
76	C₂⁴×C₁₉	—	2	1	no	—
77	C₂⁴×C₁₉	—	4	2	no	—
78	C₂⁴×C₁₉	—	4	1	no	—
79	C₂⁴×C₁₉	—	4	2	no	—
80	C₂⁴×C₁₉	—	4	1	no	—
81	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	complemented
82	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂×D₄×C₁₉	—	2	2	no	—
85	C₂×D₄×C₁₉	—	2	2	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	2	no	—
89	C₂×D₄×C₁₉	—	4	2	no	—
90	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
91	C₂×D₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
92	C₂×D₄×C₁₉	#41	1	1	yes	characteristic
93	C₂×D₄×C₁₉	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	4	2	no	—
104	C₂²×C₄×C₁₉	—	4	2	no	—
105	C₂²×C₄×C₁₉	—	4	2	no	—
106	C₂²×C₄×C₁₉	—	4	1	no	—
107	C₂²×C₄×C₁₉	—	4	1	no	—
108	C₂²×C₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	—	4	2	no	—
110	C₂²×C₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	—	8	1	no	—
112	C₂²×C₄×C₁₉	—	8	1	no	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	M₁₆×C₁₉	—	2	2	no	—
115	M₁₆×C₁₉	—	4	1	no	—
116	C₂×C₈×C₁₉	—	4	1	no	—
117	C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₄⋊C₄×C₁₉	—	4	1	no	—
120	C₄⋊C₄×C₁₉	—	4	2	no	—
121	C₄⋊C₄×C₁₉	—	8	2	no	—
122	C₂²⋊C₄×C₁₉	—	2	4	no	—
123	C₂²⋊C₄×C₁₉	—	2	1	no	—
124	C₂²⋊C₄×C₁₉	—	2	2	no	—
125	C₂²⋊C₄×C₁₉	—	2	2	no	—
126	C₂²⋊C₄×C₁₉	—	2	2	no	—
127	C₂²⋊C₄×C₁₉	—	4	2	no	—
128	C₂²⋊C₄×C₁₉	—	4	2	no	—
129	C₂²⋊C₄×C₁₉	—	4	2	no	—
130	C₂²⋊C₄×C₁₉	—	4	1	no	—
131	C₂²⋊C₄×C₁₉	—	4	2	no	—
132	C₂²⋊C₄×C₁₉	—	4	1	no	—
133	C₂²⋊C₄×C₁₉	—	4	1	no	—
134	C₂²⋊C₄×C₁₉	—	4	1	no	—
135	C₂²⋊C₄×C₁₉	—	4	1	no	—
136	C₂²⋊C₄×C₁₉	—	4	1	no	—
137	C₂²⋊C₄×C₁₉	—	4	1	no	—
138	C₂²⋊C₄×C₁₉	—	8	2	no	—
139	C₂²⋊C₄×C₁₉	—	8	2	no	—
140	C₂²⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	complemented
141	C₄²×C₁₉	—	4	1	no	—
142	C₄²×C₁₉	—	4	2	no	—
143	C₄²×C₁₉	—	4	1	no	—
144	#12958	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	2	2	no	—
147	C₂³×C₁₉	—	2	2	no	—
148	C₂³×C₁₉	—	2	1	no	—
149	C₂³×C₁₉	—	2	1	no	—
150	C₂³×C₁₉	—	2	1	no	—
151	C₂³×C₁₉	—	2	1	no	—
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	—	4	1	no	—
154	C₂³×C₁₉	—	4	1	no	—
155	C₂³×C₁₉	—	4	1	no	—
156	C₂³×C₁₉	—	4	1	no	—
157	C₂³×C₁₉	—	4	4	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	4	1	no	—
160	C₂³×C₁₉	—	4	4	no	—
161	C₂³×C₁₉	—	4	1	no	—
162	C₂³×C₁₉	—	4	1	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	—	4	2	no	—
165	C₂³×C₁₉	—	8	1	no	—
166	C₂³×C₁₉	—	8	4	no	—
167	C₂³×C₁₉	—	8	1	no	—
168	C₂³×C₁₉	—	8	1	no	—
169	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
171	C₂³×C₁₉	#120	1	1	yes	characteristic
172	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
173	C₂³×C₁₉	#123	1	1	yes	characteristic
174	D₄×C₁₉	—	4	1	no	—
175	D₄×C₁₉	—	4	1	no	—
176	D₄×C₁₉	—	4	1	no	—
177	D₄×C₁₉	—	4	1	no	—
178	D₄×C₁₉	—	4	4	no	—
179	D₄×C₁₉	—	4	4	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	8	1	no	—
202	C₂×C₄×C₁₉	—	8	4	no	—
203	C₂×C₄×C₁₉	—	8	4	no	—
204	C₂×C₄×C₁₉	—	8	1	no	—
205	C₂×C₄×C₁₉	—	8	1	no	—
206	C₂×C₄×C₁₉	—	8	1	no	—
207	C₂×C₄×C₁₉	—	8	1	no	—
208	C₂×C₄×C₁₉	—	8	1	no	—
209	C₂×C₄×C₁₉	—	8	1	no	—
210	C₂×C₄×C₁₉	—	8	1	no	—
211	C₂×C₄×C₁₉	—	8	1	no	—
212	C₂×C₄×C₁₉	—	8	1	no	—
213	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
215	C₈×C₁₉	—	4	2	no	—
216	#2358	C₂×C₁₉	1	1	yes	characteristic
217	C₂×AΣL(1,𝔽₁₆)	C₂×C₁₉	1	1	yes	characteristic
218	#1889	C₂×C₁₉	1	1	yes	characteristic
219	#1867	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#1856	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#1393	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#1390	C₂×C₁₉	1	1	yes	characteristic, complemented
223	C₂²×C₁₉	—	2	1	no	—
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	2	4	no	—
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	—	2	1	no	—
228	C₂²×C₁₉	—	2	1	no	—
229	C₂²×C₁₉	—	2	1	no	—
230	C₂²×C₁₉	—	4	1	no	—
231	C₂²×C₁₉	—	4	1	no	—
232	C₂²×C₁₉	—	4	1	no	—
233	C₂²×C₁₉	—	4	1	no	—
234	C₂²×C₁₉	—	4	2	no	—
235	C₂²×C₁₉	—	4	2	no	—
236	C₂²×C₁₉	—	4	2	no	—
237	C₂²×C₁₉	—	4	4	no	—
238	C₂²×C₁₉	—	4	2	no	—
239	C₂²×C₁₉	—	4	1	no	—
240	C₂²×C₁₉	—	4	1	no	—
241	C₂²×C₁₉	—	4	2	no	—
242	C₂²×C₁₉	—	4	1	no	—
243	C₂²×C₁₉	—	4	1	no	—
244	C₂²×C₁₉	—	4	2	no	—
245	C₂²×C₁₉	—	8	1	no	—
246	C₂²×C₁₉	—	8	1	no	—
247	C₂²×C₁₉	—	8	2	no	—
248	C₂²×C₁₉	—	8	2	no	—
249	C₂²×C₁₉	—	8	2	no	—
250	C₂²×C₁₉	#385	1	1	yes	characteristic
251	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
252	C₂²×C₁₉	#458	1	1	yes	characteristic
253	C₄×C₁₉	—	2	1	no	—
254	C₄×C₁₉	—	2	1	no	—
255	C₄×C₁₉	—	4	2	no	—
256	C₄×C₁₉	—	4	2	no	—
257	C₄×C₁₉	—	4	2	no	—
258	C₄×C₁₉	—	8	1	no	—
259	C₄×C₁₉	—	8	2	no	—
260	C₄×C₁₉	—	8	1	no	—
261	C₄×C₁₉	—	8	1	no	—
262	C₄×C₁₉	—	8	1	no	—
263	C₄×C₁₉	—	16	1	no	—
264	C₂×#120	C₂²×C₁₉	1	1	yes	characteristic
265	#518	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×C₄×D₄	—	2	1	no	—
267	C₂²×C₂²⋊C₄	—	2	1	no	—
268	#428	—	2	1	no	—
269	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
270	C₂×#99	C₂²×C₁₉	1	1	yes	characteristic
271	C₂×#99	C₂²×C₁₉	1	1	yes	characteristic
272	#390	C₂²×C₁₉	1	1	yes	characteristic
273	#388	—	2	1	no	—
274	#386	—	2	1	no	—
275	#386	C₂²×C₁₉	1	1	yes	characteristic
276	#385	—	2	1	no	—
277	#385	—	2	1	no	—
278	#379	—	2	1	no	—
279	C₄×C₂²⋊C₄	—	2	1	no	—
280	AΣL(1,𝔽₁₆)	C₄×C₁₉	1	4	yes	complemented
281	#342	—	2	1	no	—
282	#342	—	2	1	no	—
283	#339	—	2	1	no	—
284	C₂×C₁₉	—	2	1	no	—
285	C₂×C₁₉	—	2	1	no	—
286	C₂×C₁₉	—	4	1	no	—
287	C₂×C₁₉	—	4	1	no	—
288	C₂×C₁₉	—	4	4	no	—
289	C₂×C₁₉	—	4	1	no	—
290	C₂×C₁₉	—	4	1	no	—
291	C₂×C₁₉	#1867	1	1	yes	characteristic
292	C₂×C₁₉	#2196	1	1	yes	characteristic
293	C₂×C₁₉	#2197	1	1	yes	characteristic
294	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
297	C₂³×C₄	—	2	1	no	—
298	C₂³×C₄	—	2	1	no	—
299	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
300	C₂×M₁₆	—	2	1	no	—
301	#120	—	2	1	no	—
302	#120	—	2	1	no	—
303	#120	C₂×C₄×C₁₉	1	2	yes	—
304	#120	Q₈×C₁₉	1	2	yes	—
305	C₄×D₄	—	4	4	no	—
306	C₄×D₄	—	4	1	no	—
307	C₄×D₄	—	4	1	no	—
308	#117	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	4	1	no	—
311	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	4	4	no	—
323	C₂×C₂²⋊C₄	—	4	1	no	—
324	C₂×C₂²⋊C₄	—	4	1	no	—
325	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
329	#107	—	4	1	no	—
330	#106	—	4	1	no	—
331	#100	—	2	1	no	—
332	#100	C₂×C₄×C₁₉	1	2	yes	complemented
333	#99	—	2	1	no	—
334	#99	—	2	1	no	—
335	#99	—	2	1	no	—
336	#99	C₂×C₄×C₁₉	1	2	yes	complemented
337	#95	—	2	1	no	—
338	#95	—	2	1	no	—
339	#95	—	2	1	no	—
340	#95	—	4	1	no	—
341	C₁₉	#12958	1	1	yes	characteristic, direct product factor, Sylow
342	C₂⁴	—	2	1	no	—
343	C₂⁴	—	2	1	no	—
344	C₂⁴	—	4	2	no	—
345	C₂⁴	—	4	1	no	—
346	C₂⁴	—	4	2	no	—
347	C₂⁴	—	4	1	no	—
348	C₂⁴	C₄⋊C₄×C₁₉	1	2	yes	complemented
349	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
350	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂×D₄	—	4	1	no	—
355	C₂×D₄	—	4	2	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
358	C₂×D₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
359	C₂×D₄	#41×C₁₉	1	1	yes	characteristic
360	C₂×D₄	#41×C₁₉	1	1	yes	characteristic
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	1	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	—	8	1	no	—
379	C₂²×C₄	—	8	1	no	—
380	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
381	M₁₆	—	2	2	no	—
382	M₁₆	—	4	1	no	—
383	C₂×C₈	—	4	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	4	1	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	—	8	2	no	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	—	4	1	no	—
398	C₂²⋊C₄	—	4	2	no	—
399	C₂²⋊C₄	—	4	1	no	—
400	C₂²⋊C₄	—	4	1	no	—
401	C₂²⋊C₄	—	4	1	no	—
402	C₂²⋊C₄	—	4	1	no	—
403	C₂²⋊C₄	—	4	1	no	—
404	C₂²⋊C₄	—	4	1	no	—
405	C₂²⋊C₄	—	8	2	no	—
406	C₂²⋊C₄	—	8	2	no	—
407	C₂²⋊C₄	C₄⋊C₄×C₁₉	1	2	yes	complemented
408	C₄²	—	4	1	no	—
409	C₄²	—	4	2	no	—
410	C₄²	—	4	1	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	4	4	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	8	1	no	—
432	C₂³	—	8	4	no	—
433	C₂³	—	8	1	no	—
434	C₂³	—	8	1	no	—
435	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
436	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
437	C₂³	C₁₉×#120	1	1	yes	characteristic
438	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
439	C₂³	C₁₉×#123	1	1	yes	characteristic
440	D₄	—	4	1	no	—
441	D₄	—	4	1	no	—
442	D₄	—	4	1	no	—
443	D₄	—	4	1	no	—
444	D₄	—	4	4	no	—
445	D₄	—	4	4	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	8	1	no	—
468	C₂×C₄	—	8	4	no	—
469	C₂×C₄	—	8	4	no	—
470	C₂×C₄	—	8	1	no	—
471	C₂×C₄	—	8	1	no	—
472	C₂×C₄	—	8	1	no	—
473	C₂×C₄	—	8	1	no	—
474	C₂×C₄	—	8	1	no	—
475	C₂×C₄	—	8	1	no	—
476	C₂×C₄	—	8	1	no	—
477	C₂×C₄	—	8	1	no	—
478	C₂×C₄	—	8	1	no	—
479	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
480	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
481	C₈	—	4	2	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	4	1	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	1	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	8	1	no	—
505	C₂²	—	8	1	no	—
506	C₂²	—	8	2	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	C₁₉×#385	1	1	yes	characteristic
510	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
511	C₂²	C₁₉×#458	1	1	yes	characteristic
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	4	2	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	2	no	—
517	C₄	—	8	1	no	—
518	C₄	—	8	2	no	—
519	C₄	—	8	1	no	—
520	C₄	—	8	1	no	—
521	C₄	—	8	1	no	—
522	C₄	—	16	1	no	—
523	C₂	—	2	1	no	—
524	C₂	—	2	1	no	—
525	C₂	—	4	1	no	—
526	C₂	—	4	1	no	—
527	C₂	—	4	4	no	—
528	C₂	—	4	1	no	—
529	C₂	—	4	1	no	—
530	C₂	C₁₉×#1867	1	1	yes	characteristic
531	C₂	C₁₉×#2196	1	1	yes	characteristic
532	C₂	C₁₉×#2197	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	B(4,𝔽₂)
commutator	C₂×D₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×D₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#120	C₂²
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1867	C₂	semidirect
5. C₁₉×#1856	C₂	semidirect
6. C₁₉×#1393	C₂	semidirect
7. C₁₉×#1390	C₂	semidirect
24. C₁₉×AΣL(1,𝔽₁₆)	C₄	semidirect
66. C₁₉×#100	C₂×C₄	semidirect
70. C₁₉×#99	C₂×C₄	semidirect
81. C₂⁴×C₁₉	C₄⋊C₄	semidirect
140. C₂²⋊C₄×C₁₉	C₄⋊C₄	semidirect
144. #12958	C₁₉	direct (N × H)
219. #1867	C₂×C₁₉	semidirect
220. #1856	C₂×C₁₉	semidirect
221. #1393	C₂×C₁₉	semidirect
222. #1390	C₂×C₁₉	semidirect
280. AΣL(1,𝔽₁₆)	C₄×C₁₉	semidirect
332. #100	C₂×C₄×C₁₉	semidirect
336. #99	C₂×C₄×C₁₉	semidirect
341. C₁₉	#12958	direct (N × H)
348. C₂⁴	C₄⋊C₄×C₁₉	semidirect
407. C₂²⋊C₄	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
C₁₉×#2358	2
C₂×C₁₉×AΣL(1,𝔽₁₆)	2
C₁₉×#1889	2
C₁₉×#1867	2
C₁₉×#1856	2
C₁₉×#1393	2
C₁₉×#1390	2
#12958	19

Subgroups — C19×#12958 #18018917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12958 #18018917