Subgroups — #12069268

Order 1280.

720 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2966	C₂	1	1	yes	maximal, characteristic, complemented
2	#10614872	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602544	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601747	C₂	1	2	yes	maximal, complemented
6	C₈×#688	C₂	1	2	yes	maximal, complemented
7	#10601656	C₂	1	2	yes	maximal, complemented
8	C₈×#686	C₂	1	2	yes	maximal, complemented
9	#10601592	C₂	1	1	yes	maximal, characteristic, complemented
10	#10601590	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#681	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#529	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₅	—	2	1	no	—
14	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic
15	C₅×#446	C₂²	1	1	yes	characteristic, complemented
16	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₅×#436	C₂²	1	1	yes	characteristic, complemented
18	C₅×#435	—	2	1	no	—
19	C₅×C₈×D₄	—	2	1	no	—
20	C₅×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₅×#433	—	2	1	no	—
22	C₅×#432	C₂²	1	1	yes	characteristic
23	C₅×#405	—	2	1	no	—
24	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₂×#3952	—	2	1	no	—
26	#65355	C₄	1	2	yes	—
27	#65346	C₄	1	2	yes	—
28	#65335	C₄	1	1	yes	characteristic
29	#65333	C₄	1	1	yes	characteristic
30	#65325	C₄	1	1	yes	characteristic
31	#65323	C₄	1	1	yes	characteristic
32	C₄×#688	C₂²	1	2	yes	—
33	C₄×#686	C₂²	1	2	yes	—
34	#65214	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
36	C₄×#681	C₂²	1	1	yes	characteristic
37	C₈×D₂₀	—	2	1	no	—
38	C₈×D₂₀	—	2	1	no	—
39	C₈×D₂₀	C₂²	1	2	yes	—
40	C₈×D₂₀	C₂²	1	2	yes	—
41	Q₈⋊#168	C₂²	1	2	yes	complemented
42	D₄⋊#168	C₂²	1	2	yes	complemented
43	#64703	C₂²	1	2	yes	—
44	#64703	C₂²	1	2	yes	—
45	#64700	C₂²	1	2	yes	complemented
46	#64699	C₂²	1	2	yes	complemented
47	#64674	C₂²	1	2	yes	complemented
48	C₈×#168	C₂²	1	2	yes	complemented
49	#17910	—	5	1	no	maximal, Sylow
50	C₂²×D₂₀	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄×D₅	—	2	1	no	—
52	C₂×C₅×M₁₆	—	2	1	no	—
53	C₂²×C₅×C₈	—	2	1	no	—
54	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
55	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
56	C₅×#126	—	2	1	no	—
57	C₅×#125	C₂×C₄	1	1	yes	characteristic
58	C₅×#124	C₂×C₄	1	1	yes	characteristic
59	C₅×#123	—	2	1	no	—
60	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
61	C₅×#121	C₂×C₄	1	1	yes	characteristic
62	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₄×C₅×D₄	—	2	1	no	—
64	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₅×#117	—	2	1	no	—
66	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₂×#688	C₂×C₄	1	2	yes	—
68	C₂×#686	C₂×C₄	1	2	yes	—
69	C₂×#685	—	2	1	no	—
70	C₂×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
71	C₂×#681	—	2	1	no	—
72	C₂²×#168	—	2	1	no	—
73	C₂×C₈×D₅	—	2	2	no	—
74	C₂×C₈×D₅	—	2	2	no	—
75	C₂×C₈×D₅	—	4	4	no	—
76	C₄×D₂₀	—	2	1	no	—
77	C₄×D₂₀	—	2	1	no	—
78	C₄×D₂₀	C₂×C₄	1	2	yes	—
79	C₄×D₂₀	C₂³	1	2	yes	—
80	C₅×C₄⋊C₈	—	2	1	no	—
81	C₅×C₄⋊C₈	—	2	1	no	—
82	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₅×C₂²⋊C₈	—	2	1	no	—
85	C₅×C₂²⋊C₈	—	2	1	no	—
86	C₅×C₂²⋊C₈	—	2	1	no	—
87	C₅×#97	—	2	1	no	—
88	C₅×#97	—	2	1	no	—
89	C₄×C₅×C₈	—	2	1	no	—
90	C₄×C₅×C₈	D₄	1	1	yes	characteristic
91	C₄×C₅×C₈	D₄	1	1	yes	characteristic
92	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
94	#3967	C₂×C₄	1	2	yes	—
95	#3964	C₂×C₄	1	2	yes	—
96	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
97	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
98	#3952	—	2	2	no	—
99	#3952	—	2	2	no	—
100	#3941	C₂×C₄	1	2	yes	—
101	#3941	C₂×C₄	1	2	yes	—
102	#3940	C₂×C₄	1	2	yes	—
103	#3939	C₂×C₄	1	2	yes	—
104	C₄⋊#168	—	2	1	no	—
105	C₄⋊#168	C₂×C₄	1	2	yes	—
106	C₄⋊#168	C₂³	1	2	yes	—
107	#3935	—	2	1	no	—
108	C₄×#168	C₂³	1	2	yes	—
109	C₄×#168	C₂³	1	2	yes	—
110	#3105	—	5	1	no	—
111	#2966	D₅	1	1	yes	characteristic, complemented
112	C₂×C₈×D₄	—	5	1	no	—
113	#1586	—	5	2	no	—
114	#1585	—	5	2	no	—
115	C₈×SD₁₆	—	5	2	no	—
116	C₈×D₈	—	5	2	no	—
117	#1573	—	5	1	no	—
118	#1490	—	5	1	no	—
119	#1483	—	5	1	no	—
120	C₈×M₁₆	—	5	1	no	—
121	C₂³×D₅	—	2	1	no	—
122	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₅×D₄	—	2	1	no	—
124	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	#41	1	1	yes	characteristic
129	C₂²×Dic₅	—	2	1	no	—
130	C₂×D₂₀	—	2	1	no	—
131	C₂×D₂₀	—	2	4	no	—
132	C₂×D₂₀	C₂²×C₄	1	2	yes	—
133	C₂×C₄×D₅	—	2	2	no	—
134	C₂×C₄×D₅	—	2	2	no	—
135	C₂×C₄×D₅	—	4	2	no	—
136	C₂×C₄×D₅	—	4	2	no	—
137	C₅×M₁₆	—	4	2	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	4	1	no	—
142	C₂×C₅×C₈	—	4	2	no	—
143	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
145	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
146	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	1	no	—
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
152	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
153	C₅×C₂²⋊C₄	—	2	1	no	—
154	C₅×C₂²⋊C₄	—	2	1	no	—
155	C₅×C₂²⋊C₄	—	2	1	no	—
156	C₅×C₂²⋊C₄	—	2	1	no	—
157	C₅×C₂²⋊C₄	—	2	1	no	—
158	C₄²×C₅	—	2	1	no	—
159	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₅	#41	1	1	yes	characteristic
162	C₄²×C₅	C₂⁴	1	1	yes	characteristic
163	#688	—	2	4	no	—
164	#686	—	2	4	no	—
165	#685	—	2	2	no	—
166	#685	—	2	2	no	—
167	C₄⋊Dic₅	—	2	1	no	—
168	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
169	#681	—	2	4	no	—
170	C₂×#168	—	2	2	no	—
171	C₂×#168	—	2	2	no	—
172	C₂×#168	—	4	2	no	—
173	C₂×#168	C₂²×C₄	1	2	yes	—
174	C₂×#168	C₂²×C₄	1	2	yes	—
175	C₈×D₅	—	4	4	no	—
176	C₈×D₅	—	4	4	no	—
177	C₂³×C₈	—	10	1	no	—
178	#529	C₂×D₅	1	1	yes	characteristic
179	C₂×C₄×D₄	—	5	1	no	—
180	#484	—	5	1	no	—
181	#481	—	5	1	no	—
182	#478	—	5	2	no	—
183	#463	—	5	2	no	—
184	#450	—	5	1	no	—
185	#447	—	5	1	no	—
186	#446	C₂×D₅	1	1	yes	characteristic, complemented
187	C₈×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
188	C₄×SD₁₆	—	5	2	no	—
189	C₄×D₈	—	5	2	no	—
190	#436	C₂×D₅	1	1	yes	characteristic, complemented
191	#435	—	2	1	no	—
192	C₈×D₄	—	2	1	no	—
193	C₈×D₄	—	5	2	no	—
194	C₈×D₄	—	5	2	no	—
195	C₈×D₄	—	10	1	no	—
196	C₈×D₄	—	10	1	no	—
197	C₈×D₄	C₂×D₅	1	1	yes	characteristic, complemented
198	#433	—	2	1	no	—
199	#432	C₂×D₅	1	1	yes	characteristic
200	#431	—	5	1	no	—
201	C₂×C₄⋊C₈	—	5	1	no	—
202	C₂×C₂²⋊C₈	—	10	1	no	—
203	#405	—	2	1	no	—
204	C₄×M₁₆	—	5	1	no	—
205	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
206	#335	—	5	2	no	—
207	#334	—	5	2	no	—
208	Q₈⋊C₈	—	5	2	no	—
209	D₄⋊C₈	—	5	2	no	—
210	D₄⋊C₈	—	5	2	no	—
211	D₄⋊C₈	—	5	2	no	—
212	#322	—	5	2	no	—
213	C₈²	—	5	2	no	—
214	C₂³×C₅	—	2	1	no	—
215	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
216	C₂²×D₅	—	2	4	no	—
217	C₂²×D₅	—	2	2	no	—
218	C₂²×D₅	—	4	2	no	—
219	C₂²×D₅	—	4	2	no	—
220	C₅×Q₈	—	2	2	no	—
221	C₅×D₄	—	2	2	no	—
222	C₅×D₄	—	4	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
238	C₂×Dic₅	—	2	2	no	—
239	C₂×Dic₅	—	4	2	no	—
240	D₂₀	—	2	4	no	—
241	D₂₀	—	2	2	no	—
242	D₂₀	#131	1	4	yes	—
243	C₄×D₅	—	4	4	no	—
244	C₄×D₅	—	4	2	no	—
245	C₄×D₅	—	4	2	no	—
246	C₅×C₈	—	2	1	no	—
247	C₅×C₈	—	2	1	no	—
248	C₅×C₈	—	2	1	no	—
249	C₅×C₈	—	4	1	no	—
250	C₅×C₈	—	4	1	no	—
251	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
252	#168	—	2	4	no	—
253	#168	—	2	2	no	—
254	#168	—	2	2	no	—
255	#168	—	4	2	no	—
256	C₂²×D₄	—	5	1	no	—
257	C₂³×C₄	—	10	1	no	—
258	C₂×SD₁₆	—	5	2	no	—
259	C₂×D₈	—	5	2	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	10	1	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	10	1	no	—
264	C₂²×C₈	—	10	2	no	—
265	C₂²×C₈	—	10	2	no	—
266	C₂²×C₈	—	20	4	no	—
267	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
268	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
269	#126	—	2	1	no	—
270	#125	C₄×D₅	1	1	yes	characteristic
271	#124	C₄×D₅	1	1	yes	characteristic
272	#123	—	2	1	no	—
273	C₂²⋊Q₈	C₄×D₅	1	1	yes	characteristic
274	#121	C₄×D₅	1	1	yes	characteristic
275	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	5	2	no	—
278	C₄×D₄	—	5	2	no	—
279	C₄×D₄	—	10	1	no	—
280	C₄×D₄	—	10	1	no	—
281	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
282	#117	—	2	1	no	—
283	C₂×C₄⋊C₄	—	5	1	no	—
284	C₂×C₂²⋊C₄	—	10	1	no	—
285	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
286	#107	—	5	2	no	—
287	#106	—	5	2	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	5	2	no	—
291	C₄⋊C₈	—	5	2	no	—
292	C₄⋊C₈	—	10	1	no	—
293	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
294	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
295	#103	—	5	2	no	—
296	#102	—	5	2	no	—
297	#102	—	5	2	no	—
298	#102	—	5	2	no	—
299	C₂²⋊C₈	—	2	1	no	—
300	C₂²⋊C₈	—	2	1	no	—
301	C₂²⋊C₈	—	2	1	no	—
302	C₂²⋊C₈	—	5	1	no	—
303	C₂²⋊C₈	—	5	1	no	—
304	C₂²⋊C₈	—	10	2	no	—
305	C₂²⋊C₈	—	10	2	no	—
306	#97	—	2	1	no	—
307	#97	—	2	1	no	—
308	#97	—	10	1	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	—	5	2	no	—
311	C₄×C₈	—	5	2	no	—
312	C₄×C₈	C₂²⋊D₅	1	1	yes	characteristic
313	C₄×C₈	C₂²⋊D₅	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
316	C₂²×C₅	—	2	1	no	—
317	C₂²×C₅	—	2	1	no	—
318	C₂²×C₅	—	4	1	no	—
319	C₂²×C₅	—	4	1	no	—
320	C₂²×C₅	—	4	1	no	—
321	C₂²×C₅	#443	1	2	yes	—
322	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
323	C₂×D₅	—	2	4	no	—
324	C₂×D₅	—	4	8	no	—
325	C₂×D₅	—	4	2	no	—
326	C₂×D₅	—	4	2	no	—
327	C₄×C₅	—	2	1	no	—
328	C₄×C₅	—	2	1	no	—
329	C₄×C₅	—	2	1	no	—
330	C₄×C₅	—	2	1	no	—
331	C₄×C₅	—	4	1	no	—
332	C₄×C₅	—	4	1	no	—
333	C₄×C₅	—	4	1	no	—
334	C₄×C₅	C₂×#131	1	2	yes	—
335	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
336	C₄×C₅	#575	1	1	yes	characteristic
337	Dic₅	—	4	2	no	—
338	C₂⁴	—	10	1	no	—
339	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	5	2	no	—
342	C₂×D₄	—	10	4	no	—
343	C₂×D₄	—	10	1	no	—
344	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	10	1	no	—
347	C₂²×C₄	—	10	2	no	—
348	C₂²×C₄	—	10	2	no	—
349	C₂²×C₄	—	20	2	no	—
350	C₂²×C₄	—	20	2	no	—
351	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
352	C₂²×C₄	#709	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
354	SD₁₆	—	10	4	no	—
355	D₈	—	10	4	no	—
356	M₁₆	—	4	2	no	—
357	M₁₆	—	10	4	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	—	4	2	no	—
363	C₂×C₈	—	5	2	no	—
364	C₂×C₈	—	5	2	no	—
365	C₂×C₈	—	10	2	no	—
366	C₂×C₈	—	10	2	no	—
367	C₂×C₈	—	20	4	no	—
368	C₂×C₈	—	20	2	no	—
369	C₂×C₈	—	20	4	no	—
370	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
371	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
372	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
373	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	5	2	no	—
379	C₄⋊C₄	—	10	1	no	—
380	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
381	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₂²⋊C₄	—	10	2	no	—
388	C₂²⋊C₄	—	10	2	no	—
389	C₄²	—	2	1	no	—
390	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
391	C₄²	#709	1	1	yes	characteristic
392	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
393	C₄²	C₂³×D₅	1	1	yes	characteristic
394	C₂×C₅	—	2	2	no	—
395	C₂×C₅	—	8	1	no	—
396	C₂×C₅	#2929	1	1	yes	characteristic
397	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
398	C₂×C₅	C₂×#443	1	1	yes	characteristic
399	D₅	—	4	4	no	—
400	C₂³	—	2	1	no	—
401	C₂³	—	10	4	no	—
402	C₂³	—	10	2	no	—
403	C₂³	—	20	2	no	—
404	C₂³	—	20	2	no	—
405	C₂³	C₄×C₂²⋊D₅	1	1	yes	characteristic
406	Q₈	—	2	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	5	4	no	—
410	D₄	—	10	4	no	—
411	D₄	—	10	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	10	2	no	—
422	C₂×C₄	—	20	4	no	—
423	C₂×C₄	—	20	2	no	—
424	C₂×C₄	—	20	2	no	—
425	C₂×C₄	—	20	2	no	—
426	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
427	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
428	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
429	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
430	C₂×C₄	C₂×#709	1	1	yes	characteristic
431	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
432	C₈	—	2	1	no	—
433	C₈	—	2	1	no	—
434	C₈	—	2	1	no	—
435	C₈	—	4	1	no	—
436	C₈	—	4	1	no	—
437	C₈	—	10	4	no	—
438	C₈	—	10	2	no	—
439	C₈	—	10	2	no	—
440	C₈	—	20	2	no	—
441	C₈	#4095	1	2	yes	—
442	C₅	#17910	1	1	yes	characteristic, complemented, Sylow
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	10	4	no	—
449	C₂²	—	20	8	no	—
450	C₂²	—	20	2	no	—
451	C₂²	—	20	2	no	—
452	C₂²	#65433	1	2	yes	—
453	C₂²	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	1	no	—
461	C₄	—	20	2	no	—
462	C₄	D₅×#131	1	2	yes	—
463	C₄	C₂×#4095	1	1	yes	characteristic
464	C₄	#66156	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	8	1	no	—
467	C₂	—	20	4	no	—
468	C₂	C₄×#4095	1	1	yes	characteristic
469	C₂	C₂×#65433	1	1	yes	characteristic
470	C₂	#10615525	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#2966	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	#65325	C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#2966	D₅
hypocenter	C₅	#17910
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2966

Complements

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

N	H ≅ G/N	type
1. C₅×#2966	C₂	semidirect
3. C₂×C₈×D₂₀	C₂	semidirect
4. #10602544	C₂	semidirect
5. #10601747	C₂	semidirect
6. C₈×#688	C₂	semidirect
7. #10601656	C₂	semidirect
8. C₈×#686	C₂	semidirect
9. #10601592	C₂	semidirect
10. #10601590	C₂	semidirect
11. C₈×#681	C₂	semidirect
15. C₅×#446	C₂²	semidirect
16. C₅×C₈×Q₈	C₂²	semidirect
17. C₅×#436	C₂²	semidirect
20. C₅×C₈×D₄	C₂²	semidirect
41. Q₈⋊#168	C₂²	semidirect
42. D₄⋊#168	C₂²	semidirect
45. #64700	C₂²	semidirect
46. #64699	C₂²	semidirect
47. #64674	C₂²	semidirect
48. C₈×#168	C₂²	semidirect
111. #2966	D₅	semidirect
186. #446	C₂×D₅	semidirect
187. C₈×Q₈	C₂×D₅	semidirect
190. #436	C₂×D₅	semidirect
197. C₈×D₄	C₂×D₅	semidirect
442. C₅	#17910	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2966	2
#10614872	2
C₂×C₈×D₂₀	2
#10602544	2
#10601747	2
C₈×#688	2
#10601656	2
C₈×#686	2
#10601592	2
#10601590	2
C₈×#681	2
#17910	5