Subgroups — #18078694

Order 4864.

610 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#14564597	C₂	1	1	yes	maximal, characteristic, complemented
3	#14563635	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926290	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#461	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₁₉⋊C₈	—	2	1	no	—
9	D₄×C₁₉⋊C₈	—	2	2	no	—
10	D₄×C₁₉⋊C₈	—	2	2	no	—
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×#10597289	—	2	1	no	—
14	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
15	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	#11926414	C₂²	1	1	yes	characteristic
17	#11926306	—	2	1	no	—
18	#11926306	—	2	1	no	—
19	#11926306	—	2	1	no	—
20	#11926290	—	2	2	no	—
21	C₂²×SD₁₆×C₁₉	—	2	1	no	—
22	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#461	—	2	2	no	—
25	C₁₉×#461	C₄	1	4	yes	complemented
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	—	2	1	no	—
28	C₂²×Q₈×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂×SD₁₆×C₁₉	—	2	4	no	—
32	C₂×SD₁₆×C₁₉	—	4	2	no	—
33	C₂×SD₁₆×C₁₉	—	4	2	no	—
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
39	C₄×D₄×C₁₉	—	2	1	no	—
40	C₄×D₄×C₁₉	—	2	1	no	—
41	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
42	C₄×D₄×C₁₉	D₄	1	2	yes	—
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×C₄⋊Dic₁₉	—	2	1	no	—
49	C₂×C₄⋊Dic₁₉	—	2	1	no	—
50	C₂×C₄⋊Dic₁₉	—	2	1	no	—
51	C₂²×C₁₉⋊C₈	—	2	4	no	—
52	C₂²×C₁₉⋊C₈	—	2	1	no	—
53	C₂²×C₁₉⋊C₈	—	2	1	no	—
54	C₂²×C₁₉⋊C₈	—	4	2	no	—
55	C₂²×C₁₉⋊C₈	—	4	2	no	—
56	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
57	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
58	C₁₉×C₄⋊C₈	—	2	1	no	—
59	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
60	C₁₉×#103	—	2	4	no	—
61	#10597289	—	4	2	no	—
62	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
63	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
67	C₄×C₁₉⋊C₈	—	2	1	no	—
68	C₄×C₁₉⋊C₈	—	2	1	no	—
69	C₂⁴×C₁₉	—	2	1	no	—
70	C₂×Q₈×C₁₉	—	2	2	no	—
71	C₂×Q₈×C₁₉	—	4	1	no	—
72	C₂×Q₈×C₁₉	—	4	1	no	—
73	C₂×Q₈×C₁₉	—	4	1	no	—
74	C₂×Q₈×C₁₉	—	4	1	no	—
75	C₂×Q₈×C₁₉	—	4	1	no	—
76	C₂×D₄×C₁₉	—	2	1	no	—
77	C₂×D₄×C₁₉	—	2	1	no	—
78	C₂×D₄×C₁₉	—	2	1	no	—
79	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
80	C₂×D₄×C₁₉	D₈	1	2	yes	—
81	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	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	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
93	C₂²×Dic₁₉	—	4	1	no	—
94	SD₁₆×C₁₉	—	4	8	no	—
95	C₂×C₈×C₁₉	—	2	2	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₄⋊C₄×C₁₉	—	2	2	no	—
101	C₄⋊C₄×C₁₉	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	4	1	no	—
103	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
104	C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂²⋊C₄×C₁₉	—	2	2	no	—
106	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₉	#41	1	1	yes	characteristic
110	C₄⋊Dic₁₉	—	4	1	no	—
111	C₄⋊Dic₁₉	—	4	1	no	—
112	C₄⋊Dic₁₉	—	4	1	no	—
113	C₄⋊Dic₁₉	—	4	1	no	—
114	C₄⋊Dic₁₉	—	8	1	no	—
115	C₂×C₁₉⋊C₈	—	2	1	no	—
116	C₂×C₁₉⋊C₈	—	2	1	no	—
117	C₂×C₁₉⋊C₈	—	2	1	no	—
118	C₂×C₁₉⋊C₈	—	2	2	no	—
119	C₂×C₁₉⋊C₈	—	2	1	no	—
120	C₂×C₁₉⋊C₈	—	2	1	no	—
121	C₂×C₁₉⋊C₈	—	4	8	no	—
122	C₂×C₁₉⋊C₈	—	4	1	no	—
123	C₂×C₁₉⋊C₈	—	4	1	no	—
124	C₂×C₁₉⋊C₈	—	4	1	no	—
125	C₂×C₁₉⋊C₈	—	4	1	no	—
126	C₂×C₁₉⋊C₈	—	4	1	no	—
127	C₂×C₁₉⋊C₈	SD₁₆	1	2	yes	complemented
128	#9217	—	19	1	no	maximal, Sylow
129	C₂³×C₁₉	—	2	2	no	—
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	2	2	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	#121	1	1	yes	characteristic
137	Q₈×C₁₉	—	4	2	no	—
138	Q₈×C₁₉	—	4	2	no	—
139	Q₈×C₁₉	—	8	1	no	—
140	Q₈×C₁₉	—	8	1	no	—
141	D₄×C₁₉	—	2	2	no	—
142	D₄×C₁₉	—	2	2	no	—
143	D₄×C₁₉	—	2	2	no	—
144	D₄×C₁₉	#102	1	4	yes	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	2	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	8	1	no	—
156	C₂×C₄×C₁₉	—	8	1	no	—
157	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
169	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
171	C₂×Dic₁₉	—	8	1	no	—
172	C₂×Dic₁₉	—	8	1	no	—
173	C₂×Dic₁₉	—	8	1	no	—
174	C₈×C₁₉	—	4	2	no	—
175	C₁₉⋊C₈	—	2	2	no	—
176	C₁₉⋊C₈	—	4	2	no	—
177	C₁₉⋊C₈	—	4	1	no	—
178	C₁₉⋊C₈	—	8	1	no	—
179	C₂×#461	D₁₉	1	1	yes	characteristic
180	C₂×C₈×D₄	—	19	1	no	—
181	#1990	—	19	1	no	—
182	#1802	—	19	1	no	—
183	C₂×#332	—	19	1	no	—
184	#1296	—	19	1	no	—
185	#1277	—	19	1	no	—
186	C₂²×C₁₉	—	2	4	no	—
187	C₂²×C₁₉	—	4	2	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	—	4	2	no	—
190	C₂²×C₁₉	—	4	2	no	—
191	C₂²×C₁₉	—	4	2	no	—
192	C₂²×C₁₉	—	4	2	no	—
193	C₂²×C₁₉	#386	1	1	yes	characteristic
194	C₂²×C₁₉	#461	1	1	yes	characteristic
195	C₂²×C₁₉	#463	1	1	yes	characteristic
196	C₂²×C₁₉	#465	1	1	yes	characteristic
197	C₂²×C₁₉	#466	1	1	yes	characteristic
198	C₂²×C₁₉	#471	1	1	yes	characteristic
199	C₂²×C₁₉	#473	1	1	yes	characteristic
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	4	2	no	—
203	C₄×C₁₉	—	8	2	no	—
204	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
205	C₄×C₁₉	#416	1	1	yes	characteristic
206	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
207	C₄×C₁₉	#440	1	1	yes	characteristic
208	C₄×C₁₉	#450	1	1	yes	characteristic
209	C₄×C₁₉	#452	1	1	yes	characteristic
210	C₄×C₁₉	#465	1	1	yes	characteristic
211	C₄×C₁₉	#466	1	1	yes	characteristic
212	Dic₁₉	—	16	1	no	—
213	C₂²×SD₁₆	—	2	1	no	—
214	C₂³×C₈	—	38	1	no	—
215	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
217	#461	—	2	2	no	—
218	#461	Dic₁₉	1	4	yes	complemented
219	C₈×D₄	—	38	2	no	—
220	C₈×D₄	—	38	2	no	—
221	C₂×C₄⋊C₈	—	19	1	no	—
222	C₂×C₄⋊C₈	—	19	1	no	—
223	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
224	C₂×#103	—	2	1	no	—
225	C₂×#102	—	38	1	no	—
226	C₂×C₂²⋊C₈	—	38	1	no	—
227	C₂×C₄×C₈	—	19	1	no	—
228	#384	—	19	1	no	—
229	#340	—	38	1	no	—
230	#340	—	38	1	no	—
231	#340	—	38	1	no	—
232	#332	—	38	2	no	—
233	C₂×C₁₉	—	4	4	no	—
234	C₂×C₁₉	#1671	1	1	yes	characteristic
235	C₂×C₁₉	#1673	1	1	yes	characteristic
236	C₂×C₁₉	#1679	1	1	yes	characteristic
237	C₂×C₁₉	#1681	1	1	yes	characteristic
238	C₂×C₁₉	#1877	1	1	yes	characteristic
239	C₂×C₁₉	#1893	1	1	yes	characteristic
240	C₂×C₁₉	#1908	1	1	yes	characteristic
241	C₂²×Q₈	—	2	1	no	—
242	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
243	C₂³×C₄	—	2	1	no	—
244	C₂×SD₁₆	—	2	4	no	—
245	C₂×SD₁₆	—	4	2	no	—
246	C₂×SD₁₆	—	4	2	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	19	1	no	—
249	C₂²×C₈	—	19	1	no	—
250	C₂²×C₈	—	38	4	no	—
251	C₂²×C₈	—	38	1	no	—
252	C₂²×C₈	—	38	1	no	—
253	C₂²×C₈	—	76	2	no	—
254	C₂²×C₈	—	76	2	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	C₂×Dic₁₉	1	2	yes	—
262	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	38	1	no	—
266	C₂×C₄⋊C₄	—	38	1	no	—
267	C₂×C₄⋊C₄	—	38	1	no	—
268	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	19	2	no	—
273	C₄⋊C₈	—	38	1	no	—
274	C₄⋊C₈	—	38	1	no	—
275	C₄⋊C₈	—	38	1	no	—
276	C₄⋊C₈	C₂×Dic₁₉	1	2	yes	—
277	#103	—	2	4	no	—
278	#102	—	76	2	no	—
279	C₂²⋊C₈	—	38	4	no	—
280	C₄×C₈	—	38	1	no	—
281	C₄×C₈	—	38	1	no	—
282	C₁₉	#9217	1	1	yes	characteristic, complemented, Sylow
283	C₂⁴	—	2	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	4	1	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	#64525	1	2	yes	—
294	C₂×D₄	#64526	1	2	yes	—
295	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	76	1	no	—
305	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
306	C₂²×C₄	#64543	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
308	SD₁₆	—	4	8	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	19	2	no	—
313	C₂×C₈	—	38	1	no	—
314	C₂×C₈	—	38	1	no	—
315	C₂×C₈	—	38	1	no	—
316	C₂×C₈	—	38	2	no	—
317	C₂×C₈	—	38	1	no	—
318	C₂×C₈	—	38	1	no	—
319	C₂×C₈	—	76	8	no	—
320	C₂×C₈	—	76	1	no	—
321	C₂×C₈	—	76	1	no	—
322	C₂×C₈	—	76	1	no	—
323	C₂×C₈	—	76	1	no	—
324	C₂×C₈	—	76	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	76	1	no	—
331	C₄⋊C₄	—	76	1	no	—
332	C₄⋊C₄	—	76	1	no	—
333	C₄⋊C₄	—	76	1	no	—
334	C₄⋊C₄	—	152	1	no	—
335	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₄²	D₄×D₁₉	1	1	yes	characteristic
339	C₄²	#64543	1	1	yes	characteristic
340	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
341	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	4	1	no	—
349	C₂³	#10597385	1	1	yes	characteristic
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	8	1	no	—
353	Q₈	—	8	1	no	—
354	D₄	—	2	2	no	—
355	D₄	—	2	2	no	—
356	D₄	—	2	2	no	—
357	D₄	#10597289	1	4	yes	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	1	no	—
369	C₂×C₄	—	8	1	no	—
370	C₂×C₄	—	152	1	no	—
371	C₂×C₄	—	152	1	no	—
372	C₂×C₄	—	152	1	no	—
373	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
374	C₂×C₄	#10597360	1	1	yes	characteristic
375	C₂×C₄	#10597361	1	1	yes	characteristic
376	C₂×C₄	#10597362	1	1	yes	characteristic
377	C₂×C₄	C₂×#64525	1	1	yes	characteristic
378	C₂×C₄	C₂×#64526	1	1	yes	characteristic
379	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
380	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
381	C₂×C₄	#10597381	1	1	yes	characteristic
382	C₂×C₄	#10597383	1	1	yes	characteristic
383	C₂×C₄	#10597385	1	1	yes	characteristic
384	C₂×C₄	#10597396	1	1	yes	characteristic
385	C₂×C₄	#10597396	1	1	yes	characteristic
386	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
387	C₈	—	4	2	no	—
388	C₈	—	38	2	no	—
389	C₈	—	76	2	no	—
390	C₈	—	76	1	no	—
391	C₈	—	152	1	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	#11926424	1	1	yes	characteristic
400	C₂²	#11926747	1	1	yes	characteristic
401	C₂²	#11926761	1	1	yes	characteristic
402	C₂²	#11926771	1	1	yes	characteristic
403	C₂²	#11926778	1	1	yes	characteristic
404	C₂²	#11926809	1	1	yes	characteristic
405	C₂²	#11926817	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	4	2	no	—
409	C₄	—	8	2	no	—
410	C₄	—	304	1	no	—
411	C₄	C₂×#10597289	1	1	yes	characteristic
412	C₄	#11926540	1	1	yes	characteristic
413	C₄	SD₁₆×Dic₁₉	1	1	yes	characteristic
414	C₄	#11926645	1	1	yes	characteristic
415	C₄	#11926693	1	1	yes	characteristic
416	C₄	#11926703	1	1	yes	characteristic
417	C₄	#11926771	1	1	yes	characteristic
418	C₄	#11926778	1	1	yes	characteristic
419	C₂	—	4	4	no	—
420	C₂	#14563008	1	1	yes	characteristic
421	C₂	#14563022	1	1	yes	characteristic
422	C₂	#14563060	1	1	yes	characteristic
423	C₂	#14563074	1	1	yes	characteristic
424	C₂	#14563971	1	1	yes	characteristic
425	C₂	#14564064	1	1	yes	characteristic
426	C₂	#14564152	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597385
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#461	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#461	D₁₉
hypocenter	C₁₉	#9217
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#461

Complements

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

N	H ≅ G/N	type
2. #14564597	C₂	semidirect
4. C₂×#11926290	C₂	semidirect
5. #14561519	C₂	semidirect
6. #14561469	C₂	semidirect
25. C₁₉×#461	C₄	semidirect
127. C₂×C₁₉⋊C₈	SD₁₆	semidirect
218. #461	Dic₁₉	semidirect
282. C₁₉	#9217	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₄×C₁₉⋊C₈	2
#14564597	2
#14563635	2
C₂×#11926290	2
#14561519	2
#14561469	2
C₂×C₁₉×#461	2
#9217	19