Subgroups — #18078946

Order 4864.

612 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#64520	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564476	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562303	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562060	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561510	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#459	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	—	2	1	no	—
9	#11926622	—	2	1	no	—
10	#11926616	—	2	2	no	—
11	D₄×C₁₉⋊C₈	—	2	1	no	—
12	#11926597	C₂²	1	1	yes	characteristic
13	#11926568	C₂²	1	1	yes	characteristic
14	#11926568	C₂²	1	1	yes	characteristic
15	C₂×#10597290	—	2	1	no	—
16	C₂×#10597290	—	2	1	no	—
17	#11926508	—	2	1	no	—
18	C₄×#64520	C₂²	1	1	yes	characteristic
19	#11926288	—	2	2	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
22	C₂²×D₈×C₁₉	C₄	1	2	yes	—
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#459	—	2	1	no	—
26	C₁₉×#459	—	2	1	no	—
27	C₁₉×#459	—	2	1	no	—
28	C₁₉×#459	—	2	1	no	—
29	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#102	C₄	1	2	yes	—
31	C₂²×D₄×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₉	—	2	1	no	—
36	C₂×D₈×C₁₉	—	2	2	no	—
37	C₂×D₈×C₁₉	—	2	2	no	—
38	C₂×D₈×C₁₉	—	4	4	no	—
39	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
40	C₁₉×#127	—	2	1	no	—
41	C₁₉×#127	—	2	1	no	—
42	C₁₉×#127	—	2	1	no	—
43	C₁₉×#127	—	2	1	no	—
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	—	2	1	no	—
46	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
47	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
48	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
49	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
53	C₂×#64520	—	2	2	no	—
54	C₂×#64520	—	2	1	no	—
55	C₂×#64520	—	2	1	no	—
56	C₂×#64520	—	4	2	no	—
57	C₂×#64520	—	4	2	no	—
58	C₂×#64520	D₄	1	1	yes	characteristic
59	C₂×#64520	D₄	1	1	yes	characteristic
60	C₂²×C₁₉⋊C₈	—	2	2	no	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	—	2	1	no	—
63	C₁₉×#102	—	2	2	no	—
64	C₁₉×#102	—	2	2	no	—
65	#10597290	—	4	2	no	—
66	#10597290	—	4	2	no	—
67	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
68	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
69	C₂²⋊(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	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
74	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
75	#10597260	—	2	1	no	—
76	C₄×C₁₉⋊C₈	—	2	1	no	—
77	C₄×C₁₉⋊C₈	—	2	1	no	—
78	C₂⁴×C₁₉	—	2	1	no	—
79	C₂⁴×C₁₉	—	2	2	no	—
80	C₂×D₄×C₁₉	—	2	2	no	—
81	C₂×D₄×C₁₉	—	2	2	no	—
82	C₂×D₄×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	4	2	no	—
86	C₂×D₄×C₁₉	—	4	2	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	—	8	2	no	—
96	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	—	4	1	no	—
106	C₂²×C₄×C₁₉	—	4	1	no	—
107	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
110	D₈×C₁₉	—	4	4	no	—
111	D₈×C₁₉	—	4	4	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	4	2	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₁₉	—	2	1	no	—
118	C₂²⋊C₄×C₁₉	—	2	1	no	—
119	C₂²⋊C₄×C₁₉	—	2	1	no	—
120	C₂²⋊C₄×C₁₉	—	2	1	no	—
121	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₁₉	#41	1	1	yes	characteristic
125	#64520	—	2	1	no	—
126	#64520	—	2	1	no	—
127	#64520	—	2	1	no	—
128	#64520	—	4	4	no	—
129	#64520	—	4	1	no	—
130	#64520	—	4	1	no	—
131	#64520	—	4	1	no	—
132	#64520	—	4	1	no	—
133	#64520	D₈	1	2	yes	complemented
134	C₂×C₁₉⋊C₈	—	2	1	no	—
135	C₂×C₁₉⋊C₈	—	2	1	no	—
136	C₂×C₁₉⋊C₈	—	2	2	no	—
137	C₂×C₁₉⋊C₈	—	4	4	no	—
138	C₂×C₁₉⋊C₈	—	4	1	no	—
139	C₂×C₁₉⋊C₈	—	4	1	no	—
140	#9253	—	19	1	no	maximal, Sylow
141	C₂³×C₁₉	—	2	1	no	—
142	C₂³×C₁₉	—	2	1	no	—
143	C₂³×C₁₉	—	4	2	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	—	4	2	no	—
147	C₂³×C₁₉	—	4	2	no	—
148	C₂³×C₁₉	—	4	2	no	—
149	C₂³×C₁₉	—	8	1	no	—
150	C₂³×C₁₉	—	8	2	no	—
151	C₂³×C₁₉	—	8	2	no	—
152	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
153	D₄×C₁₉	—	2	1	no	—
154	D₄×C₁₉	—	2	1	no	—
155	D₄×C₁₉	—	2	1	no	—
156	D₄×C₁₉	—	4	2	no	—
157	D₄×C₁₉	—	4	2	no	—
158	D₄×C₁₉	—	4	2	no	—
159	D₄×C₁₉	—	8	2	no	—
160	D₄×C₁₉	—	8	2	no	—
161	D₄×C₁₉	—	8	2	no	—
162	D₄×C₁₉	—	8	1	no	—
163	D₄×C₁₉	—	8	1	no	—
164	D₄×C₁₉	—	8	1	no	—
165	D₄×C₁₉	—	8	1	no	—
166	D₄×C₁₉	#100	1	2	yes	complemented
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
190	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
192	C₈×C₁₉	—	4	2	no	—
193	C₁₉⋊C₈	—	2	2	no	—
194	C₁₉⋊C₈	—	4	2	no	—
195	C₁₉⋊C₈	—	4	1	no	—
196	C₁₉⋊C₈	—	8	1	no	—
197	C₁₉⋊C₈	—	8	1	no	—
198	C₂×#459	D₁₉	1	1	yes	characteristic
199	D₄×M₁₆	—	19	1	no	—
200	#1965	—	19	1	no	—
201	#1545	—	19	1	no	—
202	#1486	—	19	1	no	—
203	#1292	—	19	1	no	—
204	#1283	—	19	1	no	—
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	2	1	no	—
207	C₂²×C₁₉	—	2	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	1	no	—
213	C₂²×C₁₉	—	8	2	no	—
214	C₂²×C₁₉	—	8	2	no	—
215	C₂²×C₁₉	—	8	2	no	—
216	C₂²×C₁₉	—	8	2	no	—
217	C₂²×C₁₉	—	8	2	no	—
218	C₂²×C₁₉	—	16	2	no	—
219	C₂²×C₁₉	—	16	2	no	—
220	C₂²×C₁₉	#386	1	1	yes	characteristic
221	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
222	C₂²×C₁₉	#442	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	—	4	1	no	—
227	C₄×C₁₉	—	4	1	no	—
228	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
229	C₄×C₁₉	#413	1	1	yes	characteristic
230	C₄×C₁₉	#447	1	1	yes	characteristic
231	C₄×C₁₉	#449	1	1	yes	characteristic
232	C₄×C₁₉	#459	1	1	yes	characteristic
233	C₄×C₁₉	#463	1	1	yes	characteristic
234	C₂²×D₈	Dic₁₉	1	2	yes	—
235	C₂²×M₁₆	—	38	1	no	—
236	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
237	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
238	#459	—	2	1	no	—
239	#459	—	2	1	no	—
240	#459	—	2	1	no	—
241	#459	—	2	1	no	—
242	#436	—	38	1	no	—
243	#435	—	38	2	no	—
244	C₈×D₄	—	38	1	no	—
245	#431	—	19	1	no	—
246	#423	—	19	1	no	—
247	#423	—	19	1	no	—
248	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
249	C₂×#102	Dic₁₉	1	2	yes	—
250	C₂×#100	—	38	1	no	—
251	C₂×#100	—	38	1	no	—
252	#407	—	38	1	no	—
253	C₄×M₁₆	—	19	1	no	—
254	#331	—	38	2	no	—
255	D₄⋊C₈	—	38	1	no	—
256	D₄⋊C₈	—	38	1	no	—
257	C₂×C₁₉	—	2	1	no	—
258	C₂×C₁₉	—	2	1	no	—
259	C₂×C₁₉	—	4	2	no	—
260	C₂×C₁₉	—	8	1	no	—
261	C₂×C₁₉	—	16	2	no	—
262	C₂×C₁₉	#1879	1	1	yes	characteristic
263	C₂×C₁₉	#1900	1	1	yes	characteristic
264	C₂×C₁₉	#1903	1	1	yes	characteristic
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
268	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
269	C₂³×C₄	—	2	1	no	—
270	C₂×D₈	—	2	2	no	—
271	C₂×D₈	—	2	2	no	—
272	C₂×D₈	—	4	4	no	—
273	C₂×M₁₆	—	19	1	no	—
274	C₂×M₁₆	—	19	1	no	—
275	C₂×M₁₆	—	38	2	no	—
276	C₂×M₁₆	—	38	1	no	—
277	C₂×M₁₆	—	38	1	no	—
278	C₂×M₁₆	—	76	2	no	—
279	C₂×M₁₆	—	76	2	no	—
280	C₂²×C₈	—	38	2	no	—
281	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
282	#127	—	2	1	no	—
283	#127	—	2	1	no	—
284	#127	—	2	1	no	—
285	#127	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
289	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
290	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
291	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	19	2	no	—
298	C₄⋊C₈	—	38	1	no	—
299	C₄⋊C₈	—	38	1	no	—
300	C₄⋊C₈	—	38	1	no	—
301	C₄⋊C₈	—	38	1	no	—
302	#102	—	2	2	no	—
303	#102	—	2	2	no	—
304	#100	—	76	2	no	—
305	#100	—	76	2	no	—
306	C₂²⋊C₈	—	38	2	no	—
307	C₂²⋊C₈	—	38	2	no	—
308	C₂²⋊C₈	—	38	1	no	—
309	#97	—	38	1	no	—
310	C₄×C₈	—	38	1	no	—
311	C₄×C₈	—	38	1	no	—
312	C₁₉	#9253	1	1	yes	characteristic, complemented, Sylow
313	C₂⁴	—	2	1	no	—
314	C₂⁴	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	8	2	no	—
331	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
332	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
343	C₂²×C₄	#64543	1	1	yes	characteristic
344	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
345	D₈	—	4	4	no	—
346	D₈	—	4	4	no	—
347	M₁₆	—	19	2	no	—
348	M₁₆	—	38	1	no	—
349	M₁₆	—	38	1	no	—
350	M₁₆	—	38	1	no	—
351	M₁₆	—	76	4	no	—
352	M₁₆	—	76	1	no	—
353	M₁₆	—	76	1	no	—
354	M₁₆	—	76	1	no	—
355	M₁₆	—	76	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	38	1	no	—
359	C₂×C₈	—	38	1	no	—
360	C₂×C₈	—	38	2	no	—
361	C₂×C₈	—	76	4	no	—
362	C₂×C₈	—	76	1	no	—
363	C₂×C₈	—	76	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
366	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₄²	D₄×D₁₉	1	1	yes	characteristic
372	C₄²	#64543	1	1	yes	characteristic
373	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
374	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	8	1	no	—
384	C₂³	—	8	2	no	—
385	C₂³	—	8	2	no	—
386	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
387	D₄	—	2	1	no	—
388	D₄	—	2	1	no	—
389	D₄	—	2	1	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	2	no	—
395	D₄	—	8	2	no	—
396	D₄	—	8	1	no	—
397	D₄	—	8	1	no	—
398	D₄	—	8	1	no	—
399	D₄	—	8	1	no	—
400	D₄	#10597290	1	2	yes	complemented
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	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	D₈×D₁₉	1	1	yes	characteristic
417	C₂×C₄	#10597357	1	1	yes	characteristic
418	C₂×C₄	#10597357	1	1	yes	characteristic
419	C₂×C₄	#10597358	1	1	yes	characteristic
420	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
421	C₂×C₄	#10597381	1	1	yes	characteristic
422	C₂×C₄	#10597383	1	1	yes	characteristic
423	C₂×C₄	#10597385	1	1	yes	characteristic
424	C₂×C₄	#10597385	1	1	yes	characteristic
425	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
426	C₈	—	4	2	no	—
427	C₈	—	38	2	no	—
428	C₈	—	76	2	no	—
429	C₈	—	76	1	no	—
430	C₈	—	152	1	no	—
431	C₈	—	152	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	8	2	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	16	2	no	—
446	C₂²	—	16	2	no	—
447	C₂²	#11926424	1	1	yes	characteristic
448	C₂²	D₈×Dic₁₉	1	1	yes	characteristic
449	C₂²	#11926656	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	1	no	—
455	C₄	C₂×#10597290	1	1	yes	characteristic
456	C₄	#11926528	1	1	yes	characteristic
457	C₄	#11926676	1	1	yes	characteristic
458	C₄	#11926686	1	1	yes	characteristic
459	C₄	#11926737	1	1	yes	characteristic
460	C₄	#11926757	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	4	2	no	—
464	C₂	—	8	1	no	—
465	C₂	—	16	2	no	—
466	C₂	#14563985	1	1	yes	characteristic
467	C₂	#14564099	1	1	yes	characteristic
468	C₂	#14564117	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×#459	C₂
socle	C₂²×C₁₉	#386
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#459	D₁₉
hypocenter	C₁₉	#9253
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#459

Complements

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

N	H ≅ G/N	type
1. D₄×#64520	C₂	semidirect
2. #14564476	C₂	semidirect
3. #14562303	C₂	semidirect
4. #14562060	C₂	semidirect
5. #14561510	C₂	semidirect
6. #14561485	C₂	semidirect
133. #64520	D₈	semidirect
166. D₄×C₁₉	#100	semidirect
312. C₁₉	#9253	semidirect
400. D₄	#10597290	semidirect

Maximal subgroups

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

subgroup	index
D₄×#64520	2
#14564476	2
#14562303	2
#14562060	2
#14561510	2
#14561485	2
C₂×C₁₉×#459	2
#9253	19