Subgroups — C₁₉×#10408 #18016367

Order 4864.

708 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2541	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1957	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1947	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1802	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#127	—	2	1	no	—
9	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#121	—	2	1	no	—
11	C₂×C₁₉×#121	—	2	1	no	—
12	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#107	—	2	1	no	—
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#102	—	2	2	no	—
17	C₂×C₁₉×#102	—	2	1	no	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#392	—	2	2	no	—
20	C₁₉×#390	—	2	1	no	—
21	C₁₉×#384	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#340	—	2	1	no	—
24	C₁₉×#340	—	2	1	no	—
25	C₁₉×#331	—	2	2	no	—
26	C₁₉×D₄⋊C₈	—	2	2	no	—
27	C₂²×D₄×C₁₉	—	2	2	no	—
28	C₂²×D₄×C₁₉	—	2	2	no	—
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₉	D₄	1	2	yes	—
33	C₂³×C₄×C₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₁₉×#127	—	2	1	no	—
38	C₁₉×#127	—	2	1	no	—
39	C₁₉×#127	—	2	1	no	—
40	C₁₉×#127	—	2	1	no	—
41	C₁₉×#127	—	4	2	no	—
42	C₁₉×#127	—	4	2	no	—
43	C₁₉×#121	—	4	2	no	—
44	C₁₉×#121	—	4	2	no	—
45	C₁₉×#121	—	4	2	no	—
46	C₁₉×#121	—	4	2	no	—
47	C₄×D₄×C₁₉	—	2	1	no	—
48	C₄×D₄×C₁₉	—	2	1	no	—
49	C₄×D₄×C₁₉	—	2	1	no	—
50	C₄×D₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄²×C₁₉	—	2	1	no	—
61	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
62	C₁₉×#107	—	4	2	no	—
63	C₁₉×C₄⋊C₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₁₉×C₄⋊C₈	—	2	1	no	—
66	C₁₉×C₄⋊C₈	D₄	1	2	yes	complemented
67	C₁₉×#102	—	4	4	no	—
68	C₁₉×#102	—	4	2	no	—
69	C₄×C₈×C₁₉	—	2	1	no	—
70	C₄×C₈×C₁₉	—	2	1	no	—
71	C₁₉×#95	—	2	1	no	—
72	C₂⁴×C₁₉	—	2	1	no	—
73	C₂⁴×C₁₉	—	2	2	no	—
74	C₂×D₄×C₁₉	—	2	1	no	—
75	C₂×D₄×C₁₉	—	2	2	no	—
76	C₂×D₄×C₁₉	—	2	1	no	—
77	C₂×D₄×C₁₉	—	2	2	no	—
78	C₂×D₄×C₁₉	—	2	1	no	—
79	C₂×D₄×C₁₉	—	2	1	no	—
80	C₂×D₄×C₁₉	—	2	1	no	—
81	C₂×D₄×C₁₉	—	4	2	no	—
82	C₂×D₄×C₁₉	—	4	2	no	—
83	C₂×D₄×C₁₉	—	4	4	no	—
84	C₂×D₄×C₁₉	—	4	4	no	—
85	C₂×D₄×C₁₉	—	4	4	no	—
86	C₂×D₄×C₁₉	—	4	4	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	4	1	no	—
92	C₂×D₄×C₁₉	—	4	1	no	—
93	C₂×D₄×C₁₉	—	4	1	no	—
94	C₂×D₄×C₁₉	—	4	1	no	—
95	C₂×D₄×C₁₉	—	4	1	no	—
96	C₂×D₄×C₁₉	—	4	1	no	—
97	C₂×D₄×C₁₉	—	4	1	no	—
98	C₂×D₄×C₁₉	—	4	1	no	—
99	C₂×D₄×C₁₉	—	8	2	no	—
100	C₂×D₄×C₁₉	—	8	2	no	—
101	C₂×D₄×C₁₉	D₈	1	2	yes	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	4	1	no	—
106	C₂²×C₄×C₁₉	—	4	1	no	—
107	C₂²×C₄×C₁₉	—	4	1	no	—
108	C₂²×C₄×C₁₉	—	4	1	no	—
109	C₂²×C₄×C₁₉	—	4	1	no	—
110	C₂²×C₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	—	4	1	no	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	4	1	no	—
118	C₂×C₈×C₁₉	—	4	1	no	—
119	C₂×C₈×C₁₉	—	4	1	no	—
120	C₂×C₈×C₁₉	—	4	1	no	—
121	C₂×C₈×C₁₉	—	4	1	no	—
122	C₂×C₈×C₁₉	—	4	1	no	—
123	C₂×C₈×C₁₉	—	4	1	no	—
124	C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	4	2	no	—
129	C₄⋊C₄×C₁₉	—	4	1	no	—
130	C₄⋊C₄×C₁₉	—	4	1	no	—
131	C₄⋊C₄×C₁₉	—	4	1	no	—
132	C₄⋊C₄×C₁₉	—	4	1	no	—
133	C₄⋊C₄×C₁₉	D₈	1	2	yes	—
134	C₄⋊C₄×C₁₉	SD₁₆	1	2	yes	—
135	C₂²⋊C₄×C₁₉	—	4	4	no	—
136	C₂²⋊C₄×C₁₉	—	4	4	no	—
137	C₂²⋊C₄×C₁₉	—	4	1	no	—
138	C₂²⋊C₄×C₁₉	—	4	1	no	—
139	C₄²×C₁₉	—	4	1	no	—
140	C₄²×C₁₉	—	4	1	no	—
141	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₉	#41	1	1	yes	characteristic
143	C₄²×C₁₉	#41	1	1	yes	characteristic
144	C₄²×C₁₉	#41	1	1	yes	characteristic
145	#10408	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂³×C₁₉	—	2	2	no	—
147	C₂³×C₁₉	—	4	1	no	—
148	C₂³×C₁₉	—	4	1	no	—
149	C₂³×C₁₉	—	4	1	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	—	4	2	no	—
154	C₂³×C₁₉	—	4	2	no	—
155	C₂³×C₁₉	—	4	2	no	—
156	C₂³×C₁₉	—	4	2	no	—
157	C₂³×C₁₉	—	4	2	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	#120	1	1	yes	characteristic
161	D₄×C₁₉	—	2	2	no	—
162	D₄×C₁₉	—	2	2	no	—
163	D₄×C₁₉	—	4	4	no	—
164	D₄×C₁₉	—	4	1	no	—
165	D₄×C₁₉	—	4	1	no	—
166	D₄×C₁₉	—	8	2	no	—
167	D₄×C₁₉	—	8	8	no	—
168	D₄×C₁₉	—	8	8	no	—
169	D₄×C₁₉	—	8	1	no	—
170	D₄×C₁₉	—	8	1	no	—
171	D₄×C₁₉	—	8	1	no	—
172	D₄×C₁₉	—	8	1	no	—
173	D₄×C₁₉	—	8	1	no	—
174	D₄×C₁₉	—	8	1	no	—
175	D₄×C₁₉	—	8	1	no	—
176	D₄×C₁₉	—	8	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	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	—	8	1	no	—
189	C₂×C₄×C₁₉	—	8	1	no	—
190	C₂×C₄×C₁₉	—	8	1	no	—
191	C₂×C₄×C₁₉	—	8	1	no	—
192	C₂×C₄×C₁₉	—	8	1	no	—
193	C₂×C₄×C₁₉	—	8	1	no	—
194	C₂×C₄×C₁₉	—	8	1	no	—
195	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
200	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
205	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
206	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
207	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
209	C₈×C₁₉	—	4	2	no	—
210	C₈×C₁₉	—	4	2	no	—
211	C₈×C₁₉	—	8	1	no	—
212	#2541	C₂×C₁₉	1	1	yes	characteristic
213	#1957	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#1947	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#1802	C₂×C₁₉	1	1	yes	characteristic, complemented
216	C₂×#331	C₂×C₁₉	1	1	yes	characteristic, complemented
217	C₂×D₄⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#1279	C₂×C₁₉	1	1	yes	characteristic, complemented
219	C₂²×C₁₉	—	4	2	no	—
220	C₂²×C₁₉	—	4	2	no	—
221	C₂²×C₁₉	—	4	2	no	—
222	C₂²×C₁₉	—	8	1	no	—
223	C₂²×C₁₉	—	8	1	no	—
224	C₂²×C₁₉	—	8	1	no	—
225	C₂²×C₁₉	—	8	1	no	—
226	C₂²×C₁₉	—	8	2	no	—
227	C₂²×C₁₉	—	8	2	no	—
228	C₂²×C₁₉	—	8	2	no	—
229	C₂²×C₁₉	—	8	2	no	—
230	C₂²×C₁₉	—	8	2	no	—
231	C₂²×C₁₉	—	8	2	no	—
232	C₂²×C₁₉	—	8	2	no	—
233	C₂²×C₁₉	#394	1	1	yes	characteristic
234	C₂²×C₁₉	#447	1	1	yes	characteristic
235	C₂²×C₁₉	#447	1	1	yes	characteristic
236	C₂²×C₁₉	#450	1	1	yes	characteristic
237	C₂²×C₁₉	#452	1	1	yes	characteristic
238	C₂²×C₁₉	#453	1	1	yes	characteristic
239	C₂²×C₁₉	#455	1	1	yes	characteristic
240	C₄×C₁₉	—	2	1	no	—
241	C₄×C₁₉	—	2	1	no	—
242	C₄×C₁₉	—	4	2	no	—
243	C₄×C₁₉	—	4	2	no	—
244	C₄×C₁₉	—	8	1	no	—
245	C₄×C₁₉	—	16	1	no	—
246	C₄×C₁₉	#459	1	1	yes	characteristic
247	C₄×C₁₉	#460	1	1	yes	characteristic
248	C₄×C₁₉	#466	1	1	yes	characteristic
249	C₄×C₁₉	#468	1	1	yes	characteristic
250	C₄×C₁₉	#480	1	1	yes	characteristic
251	C₄×C₁₉	#482	1	1	yes	characteristic
252	C₄×C₁₉	#486	1	1	yes	characteristic
253	C₄×C₁₉	#490	1	1	yes	characteristic
254	C₂×#127	—	2	1	no	—
255	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
256	C₂×#121	—	2	1	no	—
257	C₂×#121	—	2	1	no	—
258	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
259	C₂×#107	—	2	1	no	—
260	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
262	C₂×#102	—	2	1	no	—
263	C₂×#102	—	2	2	no	—
264	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
265	#392	—	2	2	no	—
266	#390	—	2	1	no	—
267	#384	C₂²×C₁₉	1	1	yes	characteristic
268	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
269	#340	—	2	1	no	—
270	#340	—	2	1	no	—
271	#331	—	2	2	no	—
272	D₄⋊C₈	—	2	2	no	—
273	C₂×C₁₉	—	8	2	no	—
274	C₂×C₁₉	—	16	2	no	—
275	C₂×C₁₉	#1619	1	1	yes	characteristic
276	C₂×C₁₉	#1631	1	1	yes	characteristic
277	C₂×C₁₉	#1639	1	1	yes	characteristic
278	C₂×C₁₉	#1641	1	1	yes	characteristic
279	C₂×C₁₉	#2033	1	1	yes	characteristic
280	C₂×C₁₉	#2037	1	1	yes	characteristic
281	C₂×C₁₉	#2041	1	1	yes	characteristic
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	—	2	2	no	—
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
287	C₂²×D₄	D₄×C₁₉	1	2	yes	—
288	C₂³×C₄	—	2	1	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	—	2	1	no	—
292	#127	—	2	1	no	—
293	#127	—	2	1	no	—
294	#127	—	2	1	no	—
295	#127	—	2	1	no	—
296	#127	—	4	2	no	—
297	#127	—	4	2	no	—
298	#121	—	4	2	no	—
299	#121	—	4	2	no	—
300	#121	—	4	2	no	—
301	#121	—	4	2	no	—
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
310	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
311	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
317	#107	—	4	2	no	—
318	C₄⋊C₈	—	2	1	no	—
319	C₄⋊C₈	—	2	1	no	—
320	C₄⋊C₈	—	2	1	no	—
321	C₄⋊C₈	D₄×C₁₉	1	2	yes	complemented
322	#102	—	4	4	no	—
323	#102	—	4	2	no	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	2	1	no	—
326	#95	—	2	1	no	—
327	C₁₉	#10408	1	1	yes	characteristic, direct product factor, Sylow
328	C₂⁴	—	2	1	no	—
329	C₂⁴	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	—	4	4	no	—
341	C₂×D₄	—	4	4	no	—
342	C₂×D₄	—	4	4	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	4	1	no	—
350	C₂×D₄	—	4	1	no	—
351	C₂×D₄	—	4	1	no	—
352	C₂×D₄	—	4	1	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂×D₄	—	4	1	no	—
355	C₂×D₄	—	8	2	no	—
356	C₂×D₄	—	8	2	no	—
357	C₂×D₄	D₈×C₁₉	1	2	yes	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	4	1	no	—
362	C₂²×C₄	—	4	1	no	—
363	C₂²×C₄	—	4	1	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	—	4	1	no	—
366	C₂²×C₄	—	4	1	no	—
367	C₂²×C₄	—	4	1	no	—
368	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	4	1	no	—
374	C₂×C₈	—	4	1	no	—
375	C₂×C₈	—	4	1	no	—
376	C₂×C₈	—	4	1	no	—
377	C₂×C₈	—	4	1	no	—
378	C₂×C₈	—	4	1	no	—
379	C₂×C₈	—	4	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	1	no	—
386	C₄⋊C₄	—	4	1	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₄⋊C₄	D₈×C₁₉	1	2	yes	—
390	C₄⋊C₄	SD₁₆×C₁₉	1	2	yes	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₄²	—	4	1	no	—
396	C₄²	—	4	1	no	—
397	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₄²	#41×C₁₉	1	1	yes	characteristic
399	C₄²	#41×C₁₉	1	1	yes	characteristic
400	C₄²	#41×C₁₉	1	1	yes	characteristic
401	C₂³	—	2	2	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	C₁₉×#120	1	1	yes	characteristic
416	D₄	—	2	2	no	—
417	D₄	—	2	2	no	—
418	D₄	—	4	4	no	—
419	D₄	—	4	1	no	—
420	D₄	—	4	1	no	—
421	D₄	—	8	2	no	—
422	D₄	—	8	8	no	—
423	D₄	—	8	8	no	—
424	D₄	—	8	1	no	—
425	D₄	—	8	1	no	—
426	D₄	—	8	1	no	—
427	D₄	—	8	1	no	—
428	D₄	—	8	1	no	—
429	D₄	—	8	1	no	—
430	D₄	—	8	1	no	—
431	D₄	—	8	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	8	1	no	—
444	C₂×C₄	—	8	1	no	—
445	C₂×C₄	—	8	1	no	—
446	C₂×C₄	—	8	1	no	—
447	C₂×C₄	—	8	1	no	—
448	C₂×C₄	—	8	1	no	—
449	C₂×C₄	—	8	1	no	—
450	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
451	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
452	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
453	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
454	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
455	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
456	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
457	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
458	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
459	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
460	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
461	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
462	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
463	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
464	C₈	—	4	2	no	—
465	C₈	—	4	2	no	—
466	C₈	—	8	1	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	2	no	—
481	C₂²	C₁₉×#394	1	1	yes	characteristic
482	C₂²	C₁₉×#447	1	1	yes	characteristic
483	C₂²	C₁₉×#447	1	1	yes	characteristic
484	C₂²	C₁₉×#450	1	1	yes	characteristic
485	C₂²	C₁₉×#452	1	1	yes	characteristic
486	C₂²	C₁₉×#453	1	1	yes	characteristic
487	C₂²	C₁₉×#455	1	1	yes	characteristic
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	2	no	—
492	C₄	—	8	1	no	—
493	C₄	—	16	1	no	—
494	C₄	C₁₉×#459	1	1	yes	characteristic
495	C₄	C₁₉×#460	1	1	yes	characteristic
496	C₄	C₁₉×#466	1	1	yes	characteristic
497	C₄	C₁₉×#468	1	1	yes	characteristic
498	C₄	C₁₉×#480	1	1	yes	characteristic
499	C₄	C₁₉×#482	1	1	yes	characteristic
500	C₄	C₁₉×#486	1	1	yes	characteristic
501	C₄	C₁₉×#490	1	1	yes	characteristic
502	C₂	—	8	2	no	—
503	C₂	—	16	2	no	—
504	C₂	C₁₉×#1619	1	1	yes	characteristic
505	C₂	C₁₉×#1631	1	1	yes	characteristic
506	C₂	C₁₉×#1639	1	1	yes	characteristic
507	C₂	C₁₉×#1641	1	1	yes	characteristic
508	C₂	C₁₉×#2033	1	1	yes	characteristic
509	C₂	C₁₉×#2037	1	1	yes	characteristic
510	C₂	C₁₉×#2041	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#2541	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1957	C₂	semidirect
3. C₁₉×#1947	C₂	semidirect
4. C₁₉×#1802	C₂	semidirect
5. C₂×C₁₉×#331	C₂	semidirect
6. C₂×C₁₉×D₄⋊C₈	C₂	semidirect
7. C₁₉×#1279	C₂	semidirect
66. C₁₉×C₄⋊C₈	D₄	semidirect
145. #10408	C₁₉	direct (N × H)
213. #1957	C₂×C₁₉	semidirect
214. #1947	C₂×C₁₉	semidirect
215. #1802	C₂×C₁₉	semidirect
216. C₂×#331	C₂×C₁₉	semidirect
217. C₂×D₄⋊C₈	C₂×C₁₉	semidirect
218. #1279	C₂×C₁₉	semidirect
321. C₄⋊C₈	D₄×C₁₉	semidirect
327. C₁₉	#10408	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×#2541	2
C₁₉×#1957	2
C₁₉×#1947	2
C₁₉×#1802	2
C₂×C₁₉×#331	2
C₂×C₁₉×D₄⋊C₈	2
C₁₉×#1279	2
#10408	19

Subgroups — C19×#10408 #18016367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10408 #18016367