Subgroups — C₁₉×#10402 #18016361

Order 4864.

760 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2656	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1874	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#327	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1444	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1280	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#121	—	2	1	no	—
7	C₂×C₁₉×#121	—	2	1	no	—
8	C₂×C₁₉×#121	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#102	—	2	2	no	—
12	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
13	C₁₉×#399	—	2	2	no	—
14	C₁₉×#392	—	2	2	no	—
15	C₂×C₁₉×#95	—	2	1	no	—
16	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
18	C₁₉×#340	—	2	2	no	—
19	C₁₉×#327	—	2	4	no	—
20	C₂²×D₄×C₁₉	—	2	2	no	—
21	C₂²×D₄×C₁₉	—	2	1	no	—
22	C₂²×D₄×C₁₉	—	2	1	no	—
23	C₂²×D₄×C₁₉	D₄	1	2	yes	—
24	C₂³×C₄×C₁₉	—	2	1	no	—
25	C₂³×C₄×C₁₉	—	2	1	no	—
26	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₁₉	—	2	2	no	—
30	C₁₉×#121	—	2	2	no	—
31	C₁₉×#121	—	2	2	no	—
32	C₁₉×#121	—	2	2	no	—
33	C₁₉×#121	—	2	2	no	—
34	C₁₉×#121	—	4	2	no	—
35	C₁₉×#121	—	4	2	no	—
36	C₁₉×#121	—	4	2	no	—
37	C₁₉×#121	—	4	2	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
42	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
43	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
44	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
45	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
49	C₁₉×#102	—	4	4	no	—
50	C₁₉×C₂²⋊C₈	—	2	2	no	—
51	C₁₉×C₂²⋊C₈	—	2	2	no	—
52	C₁₉×#95	—	2	2	no	—
53	C₁₉×#95	—	2	1	no	—
54	C₁₉×#95	—	4	2	no	—
55	C₁₉×#95	D₄	1	2	yes	complemented
56	C₂⁴×C₁₉	—	2	2	no	—
57	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂×D₄×C₁₉	—	2	2	no	—
59	C₂×D₄×C₁₉	—	2	2	no	—
60	C₂×D₄×C₁₉	—	4	2	no	—
61	C₂×D₄×C₁₉	—	4	2	no	—
62	C₂×D₄×C₁₉	—	4	2	no	—
63	C₂×D₄×C₁₉	—	4	2	no	—
64	C₂×D₄×C₁₉	—	4	2	no	—
65	C₂×D₄×C₁₉	—	4	2	no	—
66	C₂×D₄×C₁₉	—	4	2	no	—
67	C₂×D₄×C₁₉	—	4	2	no	—
68	C₂×D₄×C₁₉	—	4	2	no	—
69	C₂×D₄×C₁₉	—	4	2	no	—
70	C₂×D₄×C₁₉	—	8	1	no	—
71	C₂×D₄×C₁₉	—	8	1	no	—
72	C₂×D₄×C₁₉	—	8	1	no	—
73	C₂×D₄×C₁₉	—	8	1	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	—	4	1	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	4	1	no	—
92	C₂²×C₄×C₁₉	—	4	1	no	—
93	C₂²×C₄×C₁₉	—	4	1	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	D₈	1	2	yes	—
100	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	#41	1	2	yes	—
104	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
105	C₂×C₈×C₁₉	—	4	2	no	—
106	C₂×C₈×C₁₉	—	4	2	no	—
107	C₂×C₈×C₁₉	—	4	2	no	—
108	C₄⋊C₄×C₁₉	—	2	4	no	—
109	C₄⋊C₄×C₁₉	—	2	2	no	—
110	C₄⋊C₄×C₁₉	—	2	2	no	—
111	C₄⋊C₄×C₁₉	—	4	2	no	—
112	C₄⋊C₄×C₁₉	—	4	2	no	—
113	C₄⋊C₄×C₁₉	—	4	2	no	—
114	C₄⋊C₄×C₁₉	—	4	8	no	—
115	C₂²⋊C₄×C₁₉	—	4	4	no	—
116	C₂²⋊C₄×C₁₉	—	4	4	no	—
117	C₂²⋊C₄×C₁₉	—	4	2	no	—
118	C₂²⋊C₄×C₁₉	—	4	2	no	—
119	#10402	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₁₉	—	2	1	no	—
121	C₂³×C₁₉	—	2	1	no	—
122	C₂³×C₁₉	—	2	1	no	—
123	C₂³×C₁₉	—	2	1	no	—
124	C₂³×C₁₉	—	4	2	no	—
125	C₂³×C₁₉	—	4	2	no	—
126	C₂³×C₁₉	—	4	2	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	—	4	2	no	—
130	C₂³×C₁₉	—	4	2	no	—
131	C₂³×C₁₉	#120	1	1	yes	characteristic
132	C₂³×C₁₉	#121	1	1	yes	characteristic
133	C₂³×C₁₉	#124	1	1	yes	characteristic
134	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
135	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
136	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
137	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
138	D₄×C₁₉	—	4	4	no	—
139	D₄×C₁₉	—	8	2	no	—
140	D₄×C₁₉	—	8	4	no	—
141	D₄×C₁₉	—	8	4	no	—
142	D₄×C₁₉	—	8	2	no	—
143	D₄×C₁₉	—	8	2	no	—
144	D₄×C₁₉	—	8	2	no	—
145	D₄×C₁₉	—	8	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	4	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	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	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	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	—	8	1	no	—
173	C₂×C₄×C₁₉	—	8	1	no	—
174	C₂×C₄×C₁₉	—	8	1	no	—
175	C₂×C₄×C₁₉	—	8	1	no	—
176	C₂×C₄×C₁₉	—	8	1	no	—
177	C₂×C₄×C₁₉	—	8	1	no	—
178	C₂×C₄×C₁₉	#121	1	2	yes	—
179	C₂×C₄×C₁₉	#123	1	2	yes	—
180	C₈×C₁₉	—	8	2	no	—
181	#2656	C₂×C₁₉	1	1	yes	characteristic
182	#1874	C₂×C₁₉	1	2	yes	complemented
183	C₂×#327	C₂×C₁₉	1	2	yes	complemented
184	#1444	C₂×C₁₉	1	1	yes	characteristic, complemented
185	#1280	C₂×C₁₉	1	1	yes	characteristic, complemented
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	2	1	no	—
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	8	2	no	—
199	C₂²×C₁₉	—	8	2	no	—
200	C₂²×C₁₉	—	8	2	no	—
201	C₂²×C₁₉	—	8	2	no	—
202	C₂²×C₁₉	—	8	2	no	—
203	C₂²×C₁₉	—	8	2	no	—
204	C₂²×C₁₉	—	8	2	no	—
205	C₂²×C₁₉	#394	1	1	yes	characteristic
206	C₂²×C₁₉	#447	1	1	yes	characteristic
207	C₂²×C₁₉	#450	1	1	yes	characteristic
208	C₂²×C₁₉	#453	1	1	yes	characteristic
209	C₂²×C₁₉	#456	1	1	yes	characteristic
210	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
211	C₂²×C₁₉	#458	1	1	yes	characteristic
212	C₂²×C₁₉	#459	1	1	yes	characteristic
213	C₂²×C₁₉	#460	1	1	yes	characteristic
214	C₂²×C₁₉	#486	1	1	yes	characteristic
215	C₂²×C₁₉	#490	1	1	yes	characteristic
216	C₄×C₁₉	—	2	2	no	—
217	C₄×C₁₉	—	2	2	no	—
218	C₄×C₁₉	—	4	4	no	—
219	C₄×C₁₉	—	4	2	no	—
220	C₄×C₁₉	—	4	2	no	—
221	C₄×C₁₉	—	8	2	no	—
222	C₄×C₁₉	—	8	2	no	—
223	C₂×#121	—	2	1	no	—
224	C₂×#121	—	2	1	no	—
225	C₂×#121	C₂²×C₁₉	1	2	yes	—
226	C₂²×C₄⋊C₄	—	2	1	no	—
227	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×#102	—	2	2	no	—
229	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
230	#399	—	2	2	no	—
231	#392	—	2	2	no	—
232	C₂×#95	—	2	1	no	—
233	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
235	#340	—	2	2	no	—
236	#327	—	2	4	no	—
237	C₂×C₁₉	—	2	1	no	—
238	C₂×C₁₉	—	2	1	no	—
239	C₂×C₁₉	—	2	1	no	—
240	C₂×C₁₉	—	2	1	no	—
241	C₂×C₁₉	—	16	2	no	—
242	C₂×C₁₉	#1595	1	1	yes	characteristic
243	C₂×C₁₉	#1604	1	1	yes	characteristic
244	C₂×C₁₉	#1610	1	1	yes	characteristic
245	C₂×C₁₉	#1613	1	1	yes	characteristic
246	C₂×C₁₉	#2039	1	1	yes	characteristic
247	C₂×C₁₉	#2041	1	1	yes	characteristic
248	C₂×C₁₉	#2044	1	1	yes	characteristic
249	C₂²×D₄	—	2	2	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	D₄×C₁₉	1	2	yes	—
253	C₂³×C₄	—	2	1	no	—
254	C₂³×C₄	—	2	1	no	—
255	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
256	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
258	C₂²×C₈	—	2	2	no	—
259	#121	—	2	2	no	—
260	#121	—	2	2	no	—
261	#121	—	2	2	no	—
262	#121	—	2	2	no	—
263	#121	—	4	2	no	—
264	#121	—	4	2	no	—
265	#121	—	4	2	no	—
266	#121	—	4	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	4	2	no	—
271	C₂×C₄⋊C₄	—	4	2	no	—
272	C₂×C₄⋊C₄	—	4	2	no	—
273	C₂×C₄⋊C₄	—	4	2	no	—
274	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	#102	—	4	4	no	—
279	C₂²⋊C₈	—	2	2	no	—
280	C₂²⋊C₈	—	2	2	no	—
281	#95	—	2	2	no	—
282	#95	—	2	1	no	—
283	#95	—	4	2	no	—
284	#95	D₄×C₁₉	1	2	yes	complemented
285	C₁₉	#10402	1	1	yes	characteristic, direct product factor, Sylow
286	C₂⁴	—	2	2	no	—
287	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	8	1	no	—
301	C₂×D₄	—	8	1	no	—
302	C₂×D₄	—	8	1	no	—
303	C₂×D₄	—	8	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	D₈×C₁₉	1	2	yes	—
330	C₂²×C₄	SD₁₆×C₁₉	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
333	C₂²×C₄	#41×C₁₉	1	2	yes	—
334	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
335	C₂×C₈	—	4	2	no	—
336	C₂×C₈	—	4	2	no	—
337	C₂×C₈	—	4	2	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	8	no	—
345	C₂²⋊C₄	—	4	4	no	—
346	C₂²⋊C₄	—	4	4	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	C₁₉×#120	1	1	yes	characteristic
361	C₂³	C₁₉×#121	1	1	yes	characteristic
362	C₂³	C₁₉×#124	1	1	yes	characteristic
363	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
364	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
365	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
366	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
367	D₄	—	4	4	no	—
368	D₄	—	8	2	no	—
369	D₄	—	8	4	no	—
370	D₄	—	8	4	no	—
371	D₄	—	8	2	no	—
372	D₄	—	8	2	no	—
373	D₄	—	8	2	no	—
374	D₄	—	8	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	8	1	no	—
402	C₂×C₄	—	8	1	no	—
403	C₂×C₄	—	8	1	no	—
404	C₂×C₄	—	8	1	no	—
405	C₂×C₄	—	8	1	no	—
406	C₂×C₄	—	8	1	no	—
407	C₂×C₄	C₁₉×#121	1	2	yes	—
408	C₂×C₄	C₁₉×#123	1	2	yes	—
409	C₈	—	8	2	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	C₁₉×#394	1	1	yes	characteristic
430	C₂²	C₁₉×#447	1	1	yes	characteristic
431	C₂²	C₁₉×#450	1	1	yes	characteristic
432	C₂²	C₁₉×#453	1	1	yes	characteristic
433	C₂²	C₁₉×#456	1	1	yes	characteristic
434	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
435	C₂²	C₁₉×#458	1	1	yes	characteristic
436	C₂²	C₁₉×#459	1	1	yes	characteristic
437	C₂²	C₁₉×#460	1	1	yes	characteristic
438	C₂²	C₁₉×#486	1	1	yes	characteristic
439	C₂²	C₁₉×#490	1	1	yes	characteristic
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	4	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	8	2	no	—
446	C₄	—	8	2	no	—
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	2	1	no	—
451	C₂	—	16	2	no	—
452	C₂	C₁₉×#1595	1	1	yes	characteristic
453	C₂	C₁₉×#1604	1	1	yes	characteristic
454	C₂	C₁₉×#1610	1	1	yes	characteristic
455	C₂	C₁₉×#1613	1	1	yes	characteristic
456	C₂	C₁₉×#2039	1	1	yes	characteristic
457	C₂	C₁₉×#2041	1	1	yes	characteristic
458	C₂	C₁₉×#2044	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₁₉×#2656	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1874	C₂	semidirect
3. C₂×C₁₉×#327	C₂	semidirect
4. C₁₉×#1444	C₂	semidirect
5. C₁₉×#1280	C₂	semidirect
55. C₁₉×#95	D₄	semidirect
119. #10402	C₁₉	direct (N × H)
182. #1874	C₂×C₁₉	semidirect
183. C₂×#327	C₂×C₁₉	semidirect
184. #1444	C₂×C₁₉	semidirect
185. #1280	C₂×C₁₉	semidirect
284. #95	D₄×C₁₉	semidirect
285. C₁₉	#10402	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×#2656	2
C₁₉×#1874	2
C₂×C₁₉×#327	2
C₁₉×#1444	2
C₁₉×#1280	2
#10402	19

Subgroups — C19×#10402 #18016361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10402 #18016361