Subgroups — #18077323

Order 4864.

692 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14566584	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564563	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#459	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597372	—	2	1	no	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×#10597289	—	2	2	no	—
11	C₂×#10597289	—	2	1	no	—
12	C₂×#10597289	—	2	1	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926447	—	2	1	no	—
15	#11926437	—	2	2	no	—
16	#11926414	C₂²	1	1	yes	characteristic
17	#11926404	—	2	1	no	—
18	C₄⋊C₄×Dic₁₉	—	2	1	no	—
19	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
20	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
21	C₂²×D₈×C₁₉	—	2	1	no	—
22	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#459	—	2	2	no	—
25	C₁₉×#459	C₄	1	4	yes	complemented
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#102	—	2	1	no	—
28	C₂²×D₄×C₁₉	—	2	1	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	C₂³×C₄×C₁₉	—	2	1	no	—
33	C₂×D₈×C₁₉	—	2	4	no	—
34	C₂×D₈×C₁₉	—	4	2	no	—
35	C₂×D₈×C₁₉	—	4	2	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	C₂×C₄	1	2	yes	—
41	C₄×D₄×C₁₉	—	2	1	no	—
42	C₄×D₄×C₁₉	—	2	1	no	—
43	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
44	C₄×D₄×C₁₉	D₄	1	2	yes	—
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×C₂²⋊Dic₁₉	—	2	2	no	—
49	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
50	#10597372	—	4	2	no	—
51	#10597372	—	4	2	no	—
52	C₂×C₄⋊Dic₁₉	—	2	1	no	—
53	C₂×C₄⋊Dic₁₉	—	2	1	no	—
54	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
55	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
56	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
57	C₂×C₄×Dic₁₉	—	2	2	no	—
58	C₂×C₄×Dic₁₉	—	2	1	no	—
59	C₂²×C₁₉⋊C₈	—	2	1	no	—
60	C₂²×C₁₉⋊C₈	—	2	1	no	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
63	C₁₉×#102	—	2	4	no	—
64	#10597289	—	4	4	no	—
65	#10597289	—	4	2	no	—
66	#10597289	—	4	2	no	—
67	C₁₉⋊#95	—	2	2	no	—
68	C₁₉⋊#95	—	2	1	no	—
69	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₄×C₁₉⋊C₈	—	2	1	no	—
72	C₄×C₁₉⋊C₈	—	2	1	no	—
73	C₂⁴×C₁₉	—	2	1	no	—
74	C₂⁴×C₁₉	—	4	1	no	—
75	C₂×D₄×C₁₉	—	2	2	no	—
76	C₂×D₄×C₁₉	—	2	2	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	—	2	1	no	—
82	C₂×D₄×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	—	4	2	no	—
84	C₂×D₄×C₁₉	—	4	2	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	1	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	C₂²⋊C₄	1	2	yes	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×Dic₁₉	—	2	1	no	—
108	C₂²×Dic₁₉	—	2	1	no	—
109	C₂²×Dic₁₉	—	2	2	no	—
110	D₈×C₁₉	—	4	8	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
116	C₂²⋊C₄×C₁₉	—	2	2	no	—
117	C₂²⋊C₄×C₁₉	—	2	2	no	—
118	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₁₉	#41	1	1	yes	characteristic
121	C₄²×C₁₉	#41	1	1	yes	characteristic
122	C₂²⋊Dic₁₉	—	4	4	no	—
123	C₂²⋊Dic₁₉	—	8	2	no	—
124	C₄⋊Dic₁₉	—	2	1	no	—
125	C₄⋊Dic₁₉	—	2	1	no	—
126	C₄⋊Dic₁₉	—	2	1	no	—
127	C₄⋊Dic₁₉	—	4	1	no	—
128	C₄⋊Dic₁₉	—	4	1	no	—
129	C₄⋊Dic₁₉	—	4	1	no	—
130	C₄⋊Dic₁₉	—	4	1	no	—
131	C₄⋊Dic₁₉	—	4	2	no	—
132	C₄⋊Dic₁₉	D₈	1	2	yes	complemented
133	C₄×Dic₁₉	—	4	4	no	—
134	C₄×Dic₁₉	—	4	1	no	—
135	C₄×Dic₁₉	—	4	1	no	—
136	C₂×C₁₉⋊C₈	—	2	2	no	—
137	C₂×C₁₉⋊C₈	—	4	1	no	—
138	C₂×C₁₉⋊C₈	—	4	1	no	—
139	C₂×C₁₉⋊C₈	—	4	1	no	—
140	C₂×C₁₉⋊C₈	—	4	1	no	—
141	C₂×C₁₉⋊C₈	—	4	1	no	—
142	#8980	—	19	1	no	maximal, Sylow
143	C₂³×C₁₉	—	2	2	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	—	4	1	no	—
147	C₂³×C₁₉	—	4	1	no	—
148	C₂³×C₁₉	—	4	1	no	—
149	C₂³×C₁₉	—	4	1	no	—
150	C₂³×C₁₉	—	4	2	no	—
151	C₂³×C₁₉	—	8	1	no	—
152	C₂³×C₁₉	—	8	1	no	—
153	C₂³×C₁₉	—	8	1	no	—
154	C₂³×C₁₉	—	8	1	no	—
155	C₂³×C₁₉	—	8	1	no	—
156	C₂³×C₁₉	—	8	1	no	—
157	C₂³×C₁₉	#120	1	1	yes	characteristic
158	D₄×C₁₉	—	2	2	no	—
159	D₄×C₁₉	—	2	2	no	—
160	D₄×C₁₉	—	4	4	no	—
161	D₄×C₁₉	—	4	2	no	—
162	D₄×C₁₉	—	4	2	no	—
163	D₄×C₁₉	—	4	2	no	—
164	D₄×C₁₉	—	4	2	no	—
165	D₄×C₁₉	—	4	1	no	—
166	D₄×C₁₉	—	4	1	no	—
167	D₄×C₁₉	—	8	2	no	—
168	D₄×C₁₉	—	8	1	no	—
169	D₄×C₁₉	—	8	1	no	—
170	D₄×C₁₉	—	8	1	no	—
171	D₄×C₁₉	—	8	1	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
191	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
192	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂×Dic₁₉	—	2	2	no	—
196	C₂×Dic₁₉	—	4	1	no	—
197	C₂×Dic₁₉	—	4	1	no	—
198	C₂×Dic₁₉	—	4	2	no	—
199	C₂×Dic₁₉	—	4	1	no	—
200	C₂×Dic₁₉	—	4	1	no	—
201	C₂×Dic₁₉	—	4	2	no	—
202	C₂×Dic₁₉	—	4	2	no	—
203	C₂×Dic₁₉	—	4	1	no	—
204	C₈×C₁₉	—	4	2	no	—
205	C₁₉⋊C₈	—	4	2	no	—
206	C₁₉⋊C₈	—	8	1	no	—
207	C₂×#459	D₁₉	1	1	yes	characteristic
208	#2354	—	19	1	no	—
209	#1982	—	19	1	no	—
210	#1957	—	19	1	no	—
211	C₂×D₄⋊C₈	—	19	1	no	—
212	#1296	—	19	1	no	—
213	#1279	—	19	1	no	—
214	C₂²×C₁₉	—	4	2	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	4	2	no	—
217	C₂²×C₁₉	—	8	1	no	—
218	C₂²×C₁₉	—	8	1	no	—
219	C₂²×C₁₉	—	8	1	no	—
220	C₂²×C₁₉	—	8	1	no	—
221	C₂²×C₁₉	—	8	2	no	—
222	C₂²×C₁₉	—	8	2	no	—
223	C₂²×C₁₉	—	8	2	no	—
224	C₂²×C₁₉	—	16	1	no	—
225	C₂²×C₁₉	—	16	1	no	—
226	C₂²×C₁₉	—	16	1	no	—
227	C₂²×C₁₉	—	16	1	no	—
228	C₂²×C₁₉	#386	1	1	yes	characteristic
229	C₂²×C₁₉	#447	1	1	yes	characteristic
230	C₂²×C₁₉	#449	1	1	yes	characteristic
231	C₂²×C₁₉	#449	1	1	yes	characteristic
232	C₂²×C₁₉	#449	1	1	yes	characteristic
233	C₂²×C₁₉	#453	1	1	yes	characteristic
234	C₂²×C₁₉	#454	1	1	yes	characteristic
235	C₄×C₁₉	—	2	1	no	—
236	C₄×C₁₉	—	2	1	no	—
237	C₄×C₁₉	—	4	2	no	—
238	C₄×C₁₉	#416	1	1	yes	characteristic
239	C₄×C₁₉	#418	1	1	yes	characteristic
240	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
241	C₄×C₁₉	#442	1	1	yes	characteristic
242	C₄×C₁₉	#459	1	1	yes	characteristic
243	C₄×C₁₉	#463	1	1	yes	characteristic
244	C₄×C₁₉	#482	1	1	yes	characteristic
245	C₄×C₁₉	#482	1	1	yes	characteristic
246	Dic₁₉	—	4	2	no	—
247	Dic₁₉	—	8	2	no	—
248	Dic₁₉	—	8	1	no	—
249	C₂²×D₈	—	2	1	no	—
250	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
251	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
252	C₂×#117	—	38	1	no	—
253	#459	—	2	2	no	—
254	#459	Dic₁₉	1	4	yes	complemented
255	C₂×C₄⋊C₈	—	19	1	no	—
256	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
257	C₂×#102	—	2	1	no	—
258	C₂×#102	—	38	2	no	—
259	C₂×#102	—	38	1	no	—
260	C₂×#102	—	38	1	no	—
261	C₂×C₄×C₈	—	19	1	no	—
262	#390	—	38	1	no	—
263	#388	—	38	2	no	—
264	#384	—	19	1	no	—
265	#380	—	38	1	no	—
266	C₄×C₄⋊C₄	—	19	1	no	—
267	C₄×C₄⋊C₄	—	38	1	no	—
268	D₄⋊C₈	—	38	2	no	—
269	C₂×C₁₉	—	8	2	no	—
270	C₂×C₁₉	—	16	2	no	—
271	C₂×C₁₉	#1621	1	1	yes	characteristic
272	C₂×C₁₉	#1624	1	1	yes	characteristic
273	C₂×C₁₉	#1625	1	1	yes	characteristic
274	C₂×C₁₉	#1628	1	1	yes	characteristic
275	C₂×C₁₉	#1875	1	1	yes	characteristic
276	C₂×C₁₉	#1879	1	1	yes	characteristic
277	C₂×C₁₉	#1883	1	1	yes	characteristic
278	C₂²×D₄	—	2	1	no	—
279	C₂²×D₄	—	2	1	no	—
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
282	C₂³×C₄	—	2	1	no	—
283	C₂×D₈	—	2	4	no	—
284	C₂×D₈	—	4	2	no	—
285	C₂×D₈	—	4	2	no	—
286	C₂²×C₈	—	2	1	no	—
287	C₂²×C₈	—	38	1	no	—
288	C₂²×C₈	—	38	1	no	—
289	#127	—	2	1	no	—
290	#127	—	2	1	no	—
291	#127	—	2	1	no	—
292	#127	C₂×Dic₁₉	1	2	yes	—
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	C₂×Dic₁₉	1	2	yes	—
296	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
297	#117	—	76	2	no	—
298	#117	—	76	2	no	—
299	C₂×C₄⋊C₄	—	19	1	no	—
300	C₂×C₄⋊C₄	—	19	1	no	—
301	C₂×C₄⋊C₄	—	19	2	no	—
302	C₂×C₄⋊C₄	—	38	1	no	—
303	C₂×C₄⋊C₄	—	38	1	no	—
304	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	38	2	no	—
307	C₂×C₂²⋊C₄	—	38	2	no	—
308	C₂×C₄²	—	38	2	no	—
309	C₂×C₄²	—	38	1	no	—
310	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	38	1	no	—
313	C₄⋊C₈	—	38	1	no	—
314	C₄⋊C₈	C₂×Dic₁₉	1	2	yes	—
315	#102	—	2	4	no	—
316	#102	—	76	2	no	—
317	#102	—	76	2	no	—
318	#102	—	76	4	no	—
319	C₄×C₈	—	38	1	no	—
320	C₄×C₈	—	38	1	no	—
321	#95	—	38	2	no	—
322	#95	—	38	1	no	—
323	C₁₉	#8980	1	1	yes	characteristic, complemented, Sylow
324	C₂⁴	—	2	1	no	—
325	C₂⁴	—	4	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂×D₄	—	4	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	—	4	1	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂×D₄	—	4	1	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	C₂²⋊Dic₁₉	1	2	yes	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	—	38	1	no	—
356	C₂²×C₄	—	38	1	no	—
357	C₂²×C₄	—	38	2	no	—
358	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
359	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
361	D₈	—	4	8	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	38	2	no	—
366	C₂×C₈	—	76	1	no	—
367	C₂×C₈	—	76	1	no	—
368	C₂×C₈	—	76	1	no	—
369	C₂×C₈	—	76	1	no	—
370	C₂×C₈	—	76	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	19	2	no	—
373	C₄⋊C₄	—	38	1	no	—
374	C₄⋊C₄	—	38	1	no	—
375	C₄⋊C₄	—	38	1	no	—
376	C₄⋊C₄	—	76	2	no	—
377	C₄⋊C₄	—	76	1	no	—
378	C₄⋊C₄	—	76	1	no	—
379	C₄⋊C₄	—	76	1	no	—
380	C₄⋊C₄	—	76	1	no	—
381	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	76	4	no	—
385	C₂²⋊C₄	—	152	2	no	—
386	C₄²	—	76	4	no	—
387	C₄²	—	76	1	no	—
388	C₄²	—	76	1	no	—
389	C₄²	#64543	1	1	yes	characteristic
390	C₄²	#64543	1	1	yes	characteristic
391	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
392	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
393	C₂³	—	2	2	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	8	1	no	—
402	C₂³	—	8	1	no	—
403	C₂³	—	8	1	no	—
404	C₂³	—	8	1	no	—
405	C₂³	—	8	1	no	—
406	C₂³	—	8	1	no	—
407	C₂³	#10597383	1	1	yes	characteristic
408	D₄	—	2	2	no	—
409	D₄	—	2	2	no	—
410	D₄	—	4	4	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	1	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	8	2	no	—
418	D₄	—	8	1	no	—
419	D₄	—	8	1	no	—
420	D₄	—	8	1	no	—
421	D₄	—	8	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	38	2	no	—
432	C₂×C₄	—	76	1	no	—
433	C₂×C₄	—	76	1	no	—
434	C₂×C₄	—	76	2	no	—
435	C₂×C₄	—	76	1	no	—
436	C₂×C₄	—	76	1	no	—
437	C₂×C₄	—	76	2	no	—
438	C₂×C₄	—	76	1	no	—
439	C₂×C₄	—	76	2	no	—
440	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
441	C₂×C₄	#10597357	1	1	yes	characteristic
442	C₂×C₄	#10597357	1	1	yes	characteristic
443	C₂×C₄	#10597358	1	1	yes	characteristic
444	C₂×C₄	#10597378	1	1	yes	characteristic
445	C₂×C₄	#10597378	1	1	yes	characteristic
446	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
447	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
448	C₂×C₄	#10597381	1	1	yes	characteristic
449	C₂×C₄	#10597385	1	1	yes	characteristic
450	C₂×C₄	#10597385	1	1	yes	characteristic
451	C₂×C₄	#10597396	1	1	yes	characteristic
452	C₂×C₄	#10597396	1	1	yes	characteristic
453	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
454	C₈	—	4	2	no	—
455	C₈	—	76	2	no	—
456	C₈	—	152	1	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	8	1	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	8	1	no	—
463	C₂²	—	8	1	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	16	1	no	—
468	C₂²	—	16	1	no	—
469	C₂²	—	16	1	no	—
470	C₂²	—	16	1	no	—
471	C₂²	#11926424	1	1	yes	characteristic
472	C₂²	#11926676	1	1	yes	characteristic
473	C₂²	#11926686	1	1	yes	characteristic
474	C₂²	#11926687	1	1	yes	characteristic
475	C₂²	#11926687	1	1	yes	characteristic
476	C₂²	#11926710	1	1	yes	characteristic
477	C₂²	#11926715	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	4	2	no	—
481	C₄	—	76	2	no	—
482	C₄	—	152	2	no	—
483	C₄	—	152	1	no	—
484	C₄	#11926540	1	1	yes	characteristic
485	C₄	#11926549	1	1	yes	characteristic
486	C₄	D₈×Dic₁₉	1	1	yes	characteristic
487	C₄	#11926656	1	1	yes	characteristic
488	C₄	#11926737	1	1	yes	characteristic
489	C₄	#11926757	1	1	yes	characteristic
490	C₄	#11926865	1	1	yes	characteristic
491	C₄	#11926865	1	1	yes	characteristic
492	C₂	—	8	2	no	—
493	C₂	—	16	2	no	—
494	C₂	#14562699	1	1	yes	characteristic
495	C₂	#14562717	1	1	yes	characteristic
496	C₂	#14562723	1	1	yes	characteristic
497	C₂	#14562743	1	1	yes	characteristic
498	C₂	#14563958	1	1	yes	characteristic
499	C₂	#14563985	1	1	yes	characteristic
500	C₂	#14564013	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×#459	C₂
socle	C₂³×C₁₉	#120
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#459	D₁₉
hypocenter	C₁₉	#8980
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#459

Complements

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

N	H ≅ G/N	type
1. #14566584	C₂	semidirect
2. #14564563	C₂	semidirect
3. #14564442	C₂	semidirect
4. C₂×D₄⋊(C₁₉⋊C₈)	C₂	semidirect
5. #14561519	C₂	semidirect
6. #14561474	C₂	semidirect
25. C₁₉×#459	C₄	semidirect
132. C₄⋊Dic₁₉	D₈	semidirect
254. #459	Dic₁₉	semidirect
323. C₁₉	#8980	semidirect

Maximal subgroups

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

subgroup	index
#14566584	2
#14564563	2
#14564442	2
C₂×D₄⋊(C₁₉⋊C₈)	2
#14561519	2
#14561474	2
C₂×C₁₉×#459	2
#8980	19