Subgroups — C₁₉×#12795 #18018754

Order 4864.

600 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2321	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×AΣL(1,𝔽₁₆)	C₂	1	2	yes	maximal
3	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1799	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1390	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#120	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
9	C₁₉×#423	—	2	1	no	—
10	C₂×C₁₉×#100	C₂²	1	2	yes	—
11	C₂×C₁₉×#99	C₂²	1	2	yes	—
12	C₁₉×#390	—	2	1	no	—
13	C₁₉×#388	—	2	1	no	—
14	C₁₉×#388	—	2	1	no	—
15	C₁₉×#386	—	2	1	no	—
16	C₁₉×#386	C₂²	1	1	yes	characteristic
17	C₁₉×#385	C₄	1	1	yes	characteristic, complemented
18	C₁₉×#380	—	2	1	no	—
19	C₁₉×#379	C₄	1	1	yes	characteristic, complemented
20	C₄×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
21	C₁₉×AΣL(1,𝔽₁₆)	—	2	4	no	—
22	C₁₉×#343	—	2	1	no	—
23	C₁₉×#342	—	2	1	no	—
24	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×D₄×C₁₉	—	2	1	no	—
26	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₁₉	—	2	2	no	—
31	C₁₉×#120	—	2	1	no	—
32	C₁₉×#120	—	2	1	no	—
33	C₁₉×#120	D₄	1	2	yes	—
34	C₁₉×#120	Q₈	1	2	yes	—
35	C₄×D₄×C₁₉	—	4	1	no	—
36	C₄×D₄×C₁₉	—	4	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
39	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
49	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₉	—	2	1	no	—
54	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
55	C₁₉×C₄⋊C₈	—	4	1	no	—
56	C₁₉×C₄⋊C₈	—	4	1	no	—
57	C₁₉×#100	—	2	2	no	—
58	C₁₉×#100	—	2	2	no	—
59	C₁₉×#99	—	2	2	no	—
60	C₁₉×#99	—	2	2	no	—
61	C₁₉×#95	—	2	1	no	—
62	C₁₉×#95	—	2	1	no	—
63	C₁₉×#95	—	2	1	no	—
64	C₁₉×#95	—	4	1	no	—
65	C₂⁴×C₁₉	—	2	1	no	—
66	C₂⁴×C₁₉	—	2	1	no	—
67	C₂⁴×C₁₉	—	4	1	no	—
68	C₂⁴×C₁₉	—	4	1	no	—
69	C₂⁴×C₁₉	—	8	1	no	—
70	C₂⁴×C₁₉	—	8	1	no	—
71	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	complemented
72	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
73	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂×D₄×C₁₉	—	2	2	no	—
75	C₂×D₄×C₁₉	—	2	2	no	—
76	C₂×D₄×C₁₉	—	4	1	no	—
77	C₂×D₄×C₁₉	—	4	1	no	—
78	C₂×D₄×C₁₉	—	8	1	no	—
79	C₂×D₄×C₁₉	—	8	1	no	—
80	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂×D₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
82	C₂×D₄×C₁₉	#41	1	1	yes	characteristic
83	C₂×D₄×C₁₉	#41	1	1	yes	characteristic
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	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	—	4	1	no	—
92	C₂²×C₄×C₁₉	—	4	2	no	—
93	C₂²×C₄×C₁₉	—	8	1	no	—
94	C₂²×C₄×C₁₉	—	8	1	no	—
95	C₂²×C₄×C₁₉	—	8	1	no	—
96	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	M₁₆×C₁₉	—	4	2	no	—
102	M₁₆×C₁₉	—	4	2	no	—
103	C₂×C₈×C₁₉	—	4	2	no	—
104	C₄⋊C₄×C₁₉	—	4	1	no	—
105	C₄⋊C₄×C₁₉	—	8	1	no	—
106	C₄⋊C₄×C₁₉	—	8	2	no	—
107	C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂²⋊C₄×C₁₉	—	2	2	no	—
109	C₂²⋊C₄×C₁₉	—	2	2	no	—
110	C₂²⋊C₄×C₁₉	—	4	1	no	—
111	C₂²⋊C₄×C₁₉	—	4	1	no	—
112	C₂²⋊C₄×C₁₉	—	4	2	no	—
113	C₂²⋊C₄×C₁₉	—	4	1	no	—
114	C₂²⋊C₄×C₁₉	—	4	1	no	—
115	C₂²⋊C₄×C₁₉	—	4	1	no	—
116	C₂²⋊C₄×C₁₉	—	4	2	no	—
117	C₂²⋊C₄×C₁₉	—	4	2	no	—
118	C₂²⋊C₄×C₁₉	—	8	1	no	—
119	C₂²⋊C₄×C₁₉	—	8	1	no	—
120	C₂²⋊C₄×C₁₉	—	8	1	no	—
121	C₂²⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	complemented
122	C₄²×C₁₉	—	2	1	no	—
123	C₄²×C₁₉	—	2	1	no	—
124	C₄²×C₁₉	—	8	1	no	—
125	#12795	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₁₉	—	2	1	no	—
127	C₂³×C₁₉	—	2	1	no	—
128	C₂³×C₁₉	—	2	1	no	—
129	C₂³×C₁₉	—	2	1	no	—
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	4	1	no	—
132	C₂³×C₁₉	—	4	1	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	4	1	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	—	4	1	no	—
142	C₂³×C₁₉	—	4	1	no	—
143	C₂³×C₁₉	—	8	2	no	—
144	C₂³×C₁₉	—	8	2	no	—
145	C₂³×C₁₉	—	8	2	no	—
146	C₂³×C₁₉	—	8	2	no	—
147	C₂³×C₁₉	—	8	4	no	—
148	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂³×C₁₉	#117	1	1	yes	characteristic
151	C₂³×C₁₉	#121	1	1	yes	characteristic
152	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
153	D₄×C₁₉	—	4	1	no	—
154	D₄×C₁₉	—	4	1	no	—
155	D₄×C₁₉	—	4	1	no	—
156	D₄×C₁₉	—	4	1	no	—
157	D₄×C₁₉	—	8	2	no	—
158	D₄×C₁₉	—	8	2	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	8	1	no	—
179	C₂×C₄×C₁₉	—	8	1	no	—
180	C₂×C₄×C₁₉	—	8	1	no	—
181	C₂×C₄×C₁₉	—	8	2	no	—
182	C₂×C₄×C₁₉	—	8	2	no	—
183	C₂×C₄×C₁₉	—	8	2	no	—
184	C₂×C₄×C₁₉	—	8	2	no	—
185	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
189	C₈×C₁₉	—	8	2	no	—
190	#2321	C₂×C₁₉	1	1	yes	characteristic
191	C₂×AΣL(1,𝔽₁₆)	C₂×C₁₉	1	2	yes	—
192	#1800	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#1799	C₂×C₁₉	1	1	yes	characteristic, complemented
194	#1390	C₂×C₁₉	1	2	yes	complemented
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	4	1	no	—
202	C₂²×C₁₉	—	4	1	no	—
203	C₂²×C₁₉	—	4	1	no	—
204	C₂²×C₁₉	—	4	1	no	—
205	C₂²×C₁₉	—	4	2	no	—
206	C₂²×C₁₉	—	4	2	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	—	4	1	no	—
209	C₂²×C₁₉	—	4	1	no	—
210	C₂²×C₁₉	—	4	1	no	—
211	C₂²×C₁₉	—	4	1	no	—
212	C₂²×C₁₉	—	4	2	no	—
213	C₂²×C₁₉	—	8	1	no	—
214	C₂²×C₁₉	—	8	1	no	—
215	C₂²×C₁₉	—	8	1	no	—
216	C₂²×C₁₉	—	8	4	no	—
217	C₂²×C₁₉	—	8	4	no	—
218	C₂²×C₁₉	—	8	1	no	—
219	C₂²×C₁₉	—	8	1	no	—
220	C₂²×C₁₉	#380	1	1	yes	characteristic
221	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
222	C₂²×C₁₉	#410	1	1	yes	characteristic
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	2	1	no	—
225	C₄×C₁₉	—	2	1	no	—
226	C₄×C₁₉	—	2	1	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	4	1	no	—
229	C₄×C₁₉	—	4	1	no	—
230	C₄×C₁₉	—	4	1	no	—
231	C₄×C₁₉	—	8	1	no	—
232	C₄×C₁₉	—	8	1	no	—
233	C₄×C₁₉	—	16	2	no	—
234	C₂×#120	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
236	C₂²×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
237	#423	—	2	1	no	—
238	C₂×#100	C₂²×C₁₉	1	2	yes	—
239	C₂×#99	C₂²×C₁₉	1	2	yes	—
240	#390	—	2	1	no	—
241	#388	—	2	1	no	—
242	#388	—	2	1	no	—
243	#386	—	2	1	no	—
244	#386	C₂²×C₁₉	1	1	yes	characteristic
245	#385	C₄×C₁₉	1	1	yes	characteristic, complemented
246	#380	—	2	1	no	—
247	#379	C₄×C₁₉	1	1	yes	characteristic, complemented
248	C₄×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
249	AΣL(1,𝔽₁₆)	—	2	4	no	—
250	#343	—	2	1	no	—
251	#342	—	2	1	no	—
252	C₂×C₁₉	—	2	1	no	—
253	C₂×C₁₉	—	2	1	no	—
254	C₂×C₁₉	—	4	1	no	—
255	C₂×C₁₉	—	4	1	no	—
256	C₂×C₁₉	—	4	1	no	—
257	C₂×C₁₉	—	4	1	no	—
258	C₂×C₁₉	—	8	2	no	—
259	C₂×C₁₉	#1799	1	1	yes	characteristic
260	C₂×C₁₉	#2121	1	1	yes	characteristic
261	C₂×C₁₉	#2122	1	1	yes	characteristic
262	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
265	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
266	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
267	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
268	C₂×M₁₆	—	2	2	no	—
269	#120	—	2	1	no	—
270	#120	—	2	1	no	—
271	#120	D₄×C₁₉	1	2	yes	—
272	#120	Q₈×C₁₉	1	2	yes	—
273	C₄×D₄	—	4	1	no	—
274	C₄×D₄	—	4	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	4	1	no	—
277	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	—	4	1	no	—
286	C₂×C₂²⋊C₄	—	4	1	no	—
287	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
293	C₄⋊C₈	—	4	1	no	—
294	C₄⋊C₈	—	4	1	no	—
295	#100	—	2	2	no	—
296	#100	—	2	2	no	—
297	#99	—	2	2	no	—
298	#99	—	2	2	no	—
299	#95	—	2	1	no	—
300	#95	—	2	1	no	—
301	#95	—	2	1	no	—
302	#95	—	4	1	no	—
303	C₁₉	#12795	1	1	yes	characteristic, direct product factor, Sylow
304	C₂⁴	—	2	1	no	—
305	C₂⁴	—	2	1	no	—
306	C₂⁴	—	4	1	no	—
307	C₂⁴	—	4	1	no	—
308	C₂⁴	—	8	1	no	—
309	C₂⁴	—	8	1	no	—
310	C₂⁴	C₄⋊C₄×C₁₉	1	2	yes	complemented
311	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
312	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	8	1	no	—
318	C₂×D₄	—	8	1	no	—
319	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
320	C₂×D₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
321	C₂×D₄	#41×C₁₉	1	1	yes	characteristic
322	C₂×D₄	#41×C₁₉	1	1	yes	characteristic
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	8	1	no	—
333	C₂²×C₄	—	8	1	no	—
334	C₂²×C₄	—	8	1	no	—
335	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
338	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
340	M₁₆	—	4	2	no	—
341	M₁₆	—	4	2	no	—
342	C₂×C₈	—	4	2	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	8	1	no	—
345	C₄⋊C₄	—	8	2	no	—
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	2	2	no	—
349	C₂²⋊C₄	—	4	1	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₂²⋊C₄	—	4	1	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	8	1	no	—
358	C₂²⋊C₄	—	8	1	no	—
359	C₂²⋊C₄	—	8	1	no	—
360	C₂²⋊C₄	C₄⋊C₄×C₁₉	1	2	yes	complemented
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	8	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	8	2	no	—
382	C₂³	—	8	2	no	—
383	C₂³	—	8	2	no	—
384	C₂³	—	8	2	no	—
385	C₂³	—	8	4	no	—
386	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
387	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
388	C₂³	C₁₉×#117	1	1	yes	characteristic
389	C₂³	C₁₉×#121	1	1	yes	characteristic
390	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
391	D₄	—	4	1	no	—
392	D₄	—	4	1	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	1	no	—
395	D₄	—	8	2	no	—
396	D₄	—	8	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	8	1	no	—
417	C₂×C₄	—	8	1	no	—
418	C₂×C₄	—	8	1	no	—
419	C₂×C₄	—	8	2	no	—
420	C₂×C₄	—	8	2	no	—
421	C₂×C₄	—	8	2	no	—
422	C₂×C₄	—	8	2	no	—
423	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
424	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
425	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
426	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
427	C₈	—	8	2	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	4	no	—
450	C₂²	—	8	4	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	C₁₉×#380	1	1	yes	characteristic
454	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
455	C₂²	C₁₉×#410	1	1	yes	characteristic
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	2	1	no	—
459	C₄	—	2	1	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	1	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	8	1	no	—
465	C₄	—	8	1	no	—
466	C₄	—	16	2	no	—
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	—	4	1	no	—
470	C₂	—	4	1	no	—
471	C₂	—	4	1	no	—
472	C₂	—	4	1	no	—
473	C₂	—	8	2	no	—
474	C₂	C₁₉×#1799	1	1	yes	characteristic
475	C₂	C₁₉×#2121	1	1	yes	characteristic
476	C₂	C₁₉×#2122	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#99
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×D₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#120	C₂²
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1800	C₂	semidirect
4. C₁₉×#1799	C₂	semidirect
5. C₁₉×#1390	C₂	semidirect
8. C₂²×C₂²⋊C₄×C₁₉	C₄	semidirect
17. C₁₉×#385	C₄	semidirect
19. C₁₉×#379	C₄	semidirect
20. C₄×C₂²⋊C₄×C₁₉	C₄	semidirect
71. C₂⁴×C₁₉	C₄⋊C₄	semidirect
121. C₂²⋊C₄×C₁₉	C₄⋊C₄	semidirect
125. #12795	C₁₉	direct (N × H)
192. #1800	C₂×C₁₉	semidirect
193. #1799	C₂×C₁₉	semidirect
194. #1390	C₂×C₁₉	semidirect
236. C₂²×C₂²⋊C₄	C₄×C₁₉	semidirect
245. #385	C₄×C₁₉	semidirect
247. #379	C₄×C₁₉	semidirect
248. C₄×C₂²⋊C₄	C₄×C₁₉	semidirect
303. C₁₉	#12795	direct (N × H)
310. C₂⁴	C₄⋊C₄×C₁₉	semidirect
360. 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×#2321	2
C₂×C₁₉×AΣL(1,𝔽₁₆)	2
C₁₉×#1800	2
C₁₉×#1799	2
C₁₉×#1390	2
#12795	19

Subgroups — C19×#12795 #18018754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12795 #18018754