Subgroups — #12121367

Order 1280.

720 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2906	C₂	1	1	yes	maximal, characteristic
2	#10614238	C₂	1	1	yes	maximal, characteristic
3	#10610739	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602810	C₂	1	2	yes	maximal
5	#10602801	C₂	1	2	yes	maximal
6	C₄×#3969	C₂	1	1	yes	maximal, characteristic
7	#10601330	C₂	1	2	yes	maximal, complemented
8	#10601327	C₂	1	2	yes	maximal, complemented
9	#10601313	C₂	1	1	yes	maximal, characteristic, complemented
10	#10601307	C₂	1	1	yes	maximal, characteristic, complemented
11	Dic₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#131	C₂²	1	2	yes	—
13	C₄×C₅×#41	C₂²	1	1	yes	characteristic
14	#65804	C₂²	1	1	yes	characteristic
15	C₅×#424	—	2	2	no	—
16	C₅×#424	C₂²	1	2	yes	—
17	C₅×#423	—	2	1	no	—
18	C₅×#423	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊C₈	—	2	1	no	—
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×#3969	C₂²	1	1	yes	characteristic
22	C₂×#3969	C₂²	1	1	yes	characteristic
23	#65522	C₂²	1	2	yes	—
24	C₂×#3954	C₂²	1	2	yes	—
25	#65391	C₂²	1	2	yes	—
26	#65390	C₂²	1	2	yes	—
27	C₂×C₈×Dic₅	C₂²	1	2	yes	—
28	#65311	C₄	1	2	yes	complemented
29	#65310	C₄	1	1	yes	characteristic, complemented
30	#65309	C₄	1	1	yes	characteristic, complemented
31	#65298	C₄	1	2	yes	complemented
32	#65297	C₄	1	1	yes	characteristic, complemented
33	#65296	C₄	1	1	yes	characteristic, complemented
34	#65287	C₂²	1	2	yes	—
35	C₄²×Dic₅	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
37	C₄×#681	C₂²	1	1	yes	characteristic
38	#65120	—	2	1	no	—
39	#65119	—	2	1	no	—
40	#65117	—	2	2	no	—
41	#64778	C₂²	1	2	yes	—
42	#64775	C₂²	1	2	yes	—
43	#64775	C₂²	1	2	yes	—
44	#64770	C₂²	1	2	yes	—
45	#64752	C₂²	1	1	yes	characteristic
46	#64752	C₂²	1	1	yes	characteristic
47	#22982	—	5	1	no	maximal, Sylow
48	C₂×C₅×#41	C₂³	1	1	yes	characteristic
49	C₅×#131	—	2	4	no	—
50	C₅×#131	—	4	2	no	—
51	C₂×C₅×M₁₆	—	2	2	no	—
52	C₂×C₅×M₁₆	C₂³	1	2	yes	—
53	C₂²×C₅×C₈	—	2	2	no	—
54	C₂²×C₅×C₈	C₂³	1	2	yes	—
55	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
56	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
57	C₄×C₅×D₄	—	2	1	no	—
58	C₄×C₅×D₄	—	2	1	no	—
59	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
60	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
61	C₅×#117	—	2	1	no	—
62	C₅×#117	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₅	—	2	1	no	—
64	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
65	#4072	C₂³	1	2	yes	—
66	#4070	—	2	1	no	—
67	#4070	—	2	1	no	—
68	C₂×C₄×Dic₅	—	2	1	no	—
69	C₂×C₄×Dic₅	—	2	1	no	—
70	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
71	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
72	C₂×#681	C₂³	1	1	yes	characteristic
73	C₂×#681	C₂³	1	1	yes	characteristic
74	C₂²×#168	C₂³	1	2	yes	—
75	#4016	C₂×C₄	1	2	yes	—
76	#4015	C₂×C₄	1	1	yes	characteristic
77	#4015	C₂×C₄	1	1	yes	characteristic
78	C₄×Dic₁₀	—	2	1	no	—
79	C₄×Dic₁₀	—	2	1	no	—
80	C₅×C₄⋊C₈	—	2	2	no	—
81	C₅×C₄⋊C₈	—	2	2	no	—
82	C₅×C₄⋊C₈	—	2	1	no	—
83	C₅×C₄⋊C₈	—	2	1	no	—
84	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
85	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
86	C₅×C₄⋊C₈	D₄	1	2	yes	—
87	#3969	—	2	2	no	—
88	#3969	Q₈	1	4	yes	complemented
89	#3967	C₂×C₄	1	2	yes	—
90	#3967	C₂×C₄	1	2	yes	—
91	#3964	C₂×C₄	1	2	yes	—
92	#3964	C₂×C₄	1	2	yes	—
93	#3954	—	4	2	no	—
94	#3947	—	2	2	no	—
95	#3946	—	2	2	no	—
96	#3946	—	2	2	no	—
97	C₈×Dic₅	—	2	2	no	—
98	C₈×Dic₅	—	4	2	no	—
99	#3940	C₂×C₄	1	2	yes	—
100	#3940	C₂×C₄	1	2	yes	—
101	#3939	C₂×C₄	1	2	yes	—
102	#3939	C₂×C₄	1	2	yes	—
103	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
104	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
105	C₄⋊#168	C₂×C₄	1	2	yes	—
106	#3935	—	2	1	no	—
107	C₄×#168	—	2	1	no	—
108	#3076	—	5	1	no	—
109	#2962	—	5	1	no	—
110	#2906	D₅	1	1	yes	characteristic
111	#1994	—	5	1	no	—
112	#1950	—	5	1	no	—
113	#1945	—	5	2	no	—
114	#1922	—	5	2	no	—
115	#1866	—	5	2	no	—
116	C₄×C₄⋊C₈	—	5	1	no	—
117	#1764	—	5	2	no	—
118	C₄×#104	—	5	1	no	—
119	C₅×#41	—	2	1	no	—
120	C₅×#41	—	2	1	no	—
121	C₅×#41	C₂×Q₈	1	2	yes	—
122	C₅×#41	#41	1	2	yes	—
123	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₅×D₄	—	2	1	no	—
125	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	#41	1	1	yes	characteristic
130	C₂²×C₄×C₅	#41	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₂²×Dic₅	—	2	1	no	—
133	C₂²×Dic₅	—	2	1	no	—
134	C₂×Dic₁₀	—	2	1	no	—
135	C₂×Dic₁₀	—	2	1	no	—
136	C₅×M₁₆	—	2	2	no	—
137	C₅×M₁₆	—	2	2	no	—
138	C₅×M₁₆	—	4	4	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	4	4	no	—
143	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
144	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
148	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
149	C₅×C₂²⋊C₄	—	2	1	no	—
150	C₅×C₂²⋊C₄	—	2	1	no	—
151	C₅×C₂²⋊C₄	—	2	1	no	—
152	C₄²×C₅	—	2	1	no	—
153	C₄²×C₅	—	2	1	no	—
154	C₄²×C₅	—	2	1	no	—
155	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
159	C₂²⋊Dic₅	—	2	2	no	—
160	C₄⋊Dic₅	—	2	1	no	—
161	C₄⋊Dic₅	—	2	1	no	—
162	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
163	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
164	#683	—	2	2	no	—
165	#683	—	2	2	no	—
166	C₄×Dic₅	—	2	4	no	—
167	C₄×Dic₅	—	2	2	no	—
168	C₄×Dic₅	—	2	1	no	—
169	C₄×Dic₅	—	2	1	no	—
170	C₄×Dic₅	—	2	1	no	—
171	C₄×Dic₅	—	4	2	no	—
172	C₄×Dic₅	C₂×Q₈	1	2	yes	—
173	#681	—	2	1	no	—
174	#681	—	2	1	no	—
175	#681	—	2	1	no	—
176	#681	C₂×Q₈	1	2	yes	—
177	C₂×#168	—	2	1	no	—
178	C₂×#168	—	2	2	no	—
179	C₂×#168	—	2	2	no	—
180	C₂×#168	—	2	1	no	—
181	C₂×#168	C₂²×C₄	1	2	yes	—
182	C₂×#168	C₂²×C₄	1	2	yes	—
183	C₂×#131	C₂×D₅	1	2	yes	—
184	#533	—	5	1	no	—
185	C₄×#41	C₂×D₅	1	1	yes	characteristic
186	#479	—	5	2	no	—
187	#478	—	5	2	no	—
188	#477	—	5	1	no	—
189	#476	—	5	1	no	—
190	#475	—	5	1	no	—
191	#474	—	5	1	no	—
192	#446	—	10	2	no	—
193	#446	—	10	1	no	—
194	C₈×Q₈	—	10	1	no	—
195	C₂×#108	—	5	2	no	—
196	#427	—	5	2	no	—
197	#424	—	2	2	no	—
198	#424	—	5	2	no	—
199	#424	C₂×D₅	1	2	yes	—
200	#423	—	2	1	no	—
201	#423	C₂×D₅	1	1	yes	characteristic
202	C₂×C₄⋊C₈	—	2	1	no	—
203	C₂×C₄⋊C₈	—	5	1	no	—
204	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
205	C₂×#104	—	5	1	no	—
206	C₂×#104	—	5	1	no	—
207	#416	—	5	2	no	—
208	#405	—	5	2	no	—
209	C₄×M₁₆	—	5	1	no	—
210	C₂×C₄×C₈	—	5	2	no	—
211	C₄³	—	5	1	no	—
212	#341	—	5	2	no	—
213	#339	—	5	2	no	—
214	#339	—	5	2	no	—
215	#339	—	5	1	no	—
216	#339	—	5	1	no	—
217	#336	—	5	2	no	—
218	C₂³×C₅	—	2	1	no	—
219	C₂³×C₅	C₂×#41	1	1	yes	characteristic
220	C₅×Q₈	—	2	1	no	—
221	C₅×Q₈	C₄×Q₈	1	2	yes	—
222	C₅×D₄	—	2	2	no	—
223	C₅×D₄	—	2	2	no	—
224	C₅×D₄	—	2	1	no	—
225	C₅×D₄	C₄×Q₈	1	2	yes	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	2	no	—
234	C₂×C₄×C₅	—	8	1	no	—
235	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
244	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
245	C₂×Dic₅	—	2	2	no	—
246	C₂×Dic₅	—	2	2	no	—
247	C₂×Dic₅	—	2	2	no	—
248	C₂×Dic₅	—	2	2	no	—
249	C₂×Dic₅	—	2	2	no	—
250	C₂×Dic₅	—	2	2	no	—
251	C₂×Dic₅	—	4	1	no	—
252	C₂×Dic₅	—	4	1	no	—
253	Dic₁₀	—	4	2	no	—
254	Dic₁₀	—	8	1	no	—
255	C₅×C₈	—	2	2	no	—
256	C₅×C₈	—	2	2	no	—
257	C₅×C₈	—	4	2	no	—
258	#168	—	2	2	no	—
259	#168	—	2	2	no	—
260	#168	—	2	2	no	—
261	#168	—	4	1	no	—
262	C₂×#41	C₂²×D₅	1	1	yes	characteristic
263	#131	—	2	4	no	—
264	#131	—	4	2	no	—
265	C₂×M₁₆	—	2	2	no	—
266	C₂×M₁₆	—	5	1	no	—
267	C₂×M₁₆	—	5	1	no	—
268	C₂×M₁₆	C₂²×D₅	1	2	yes	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	5	2	no	—
271	C₂²×C₈	C₂²×D₅	1	2	yes	—
272	C₄⋊Q₈	—	5	1	no	—
273	C₄⋊Q₈	—	5	1	no	—
274	#125	—	5	2	no	—
275	C₂²⋊Q₈	—	10	1	no	—
276	C₂²⋊Q₈	—	10	1	no	—
277	C₄×Q₈	—	10	1	no	—
278	C₄×Q₈	—	10	1	no	—
279	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
280	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	—	2	1	no	—
283	C₄×D₄	C₄×D₅	1	1	yes	characteristic
284	C₄×D₄	C₄×D₅	1	1	yes	characteristic
285	#117	—	2	1	no	—
286	#117	—	5	2	no	—
287	#117	C₂²×D₅	1	1	yes	characteristic
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	5	1	no	—
290	C₂×C₄²	—	5	1	no	—
291	C₂×C₄²	—	10	1	no	—
292	C₂×C₄²	—	10	1	no	—
293	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
294	#108	—	20	2	no	—
295	#107	—	5	2	no	—
296	#107	—	5	2	no	—
297	#106	—	5	2	no	—
298	#106	—	5	2	no	—
299	C₄⋊C₈	—	2	2	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	—	5	1	no	—
304	C₄⋊C₈	—	5	1	no	—
305	C₄⋊C₈	—	5	2	no	—
306	C₄⋊C₈	—	10	2	no	—
307	C₄⋊C₈	—	10	2	no	—
308	C₄⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
309	C₄⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
310	C₄⋊C₈	C₂²⋊D₅	1	2	yes	—
311	#104	—	5	4	no	—
312	#104	—	10	2	no	—
313	#103	—	5	2	no	—
314	#103	—	5	2	no	—
315	#102	—	5	2	no	—
316	#102	—	5	2	no	—
317	#97	—	10	2	no	—
318	#97	—	10	1	no	—
319	C₄×C₈	—	10	2	no	—
320	C₄×C₈	—	10	1	no	—
321	C₄×C₈	—	20	2	no	—
322	C₂²×C₅	—	2	1	no	—
323	C₂²×C₅	—	2	1	no	—
324	C₂²×C₅	—	2	2	no	—
325	C₂²×C₅	—	4	1	no	—
326	C₂²×C₅	—	4	1	no	—
327	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
328	C₂²×C₅	#552	1	1	yes	characteristic
329	C₂²×C₅	#554	1	1	yes	characteristic
330	C₄×C₅	—	2	2	no	—
331	C₄×C₅	—	2	1	no	—
332	C₄×C₅	—	2	1	no	—
333	C₄×C₅	—	2	1	no	—
334	C₄×C₅	—	4	1	no	—
335	C₄×C₅	—	4	1	no	—
336	C₄×C₅	#443	1	2	yes	—
337	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
338	C₄×C₅	#520	1	1	yes	characteristic
339	C₄×C₅	#546	1	1	yes	characteristic
340	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
341	Dic₅	—	2	4	no	—
342	Dic₅	—	4	2	no	—
343	Dic₅	—	4	2	no	—
344	Dic₅	—	4	2	no	—
345	#41	—	2	1	no	—
346	#41	—	2	1	no	—
347	#41	#711	1	2	yes	—
348	#41	Q₈×D₅	1	2	yes	—
349	C₂×Q₈	—	10	1	no	—
350	C₂×Q₈	—	10	1	no	—
351	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	10	1	no	—
358	C₂²×C₄	—	10	1	no	—
359	C₂²×C₄	#709	1	1	yes	characteristic
360	C₂²×C₄	#709	1	1	yes	characteristic
361	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	4	4	no	—
365	M₁₆	—	5	2	no	—
366	M₁₆	—	10	1	no	—
367	M₁₆	—	10	1	no	—
368	M₁₆	—	10	1	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	4	4	no	—
373	C₂×C₈	—	5	2	no	—
374	C₂×C₈	—	5	2	no	—
375	C₂×C₈	—	10	2	no	—
376	C₂×C₈	—	10	2	no	—
377	C₂×C₈	—	10	1	no	—
378	C₂×C₈	—	10	1	no	—
379	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
380	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	5	2	no	—
384	C₄⋊C₄	—	5	2	no	—
385	C₄⋊C₄	—	10	2	no	—
386	C₄⋊C₄	—	10	2	no	—
387	C₄⋊C₄	—	10	1	no	—
388	C₄⋊C₄	—	10	1	no	—
389	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
390	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	2	1	no	—
394	C₂²⋊C₄	—	10	2	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	5	2	no	—
399	C₄²	—	10	4	no	—
400	C₄²	—	10	1	no	—
401	C₄²	—	10	2	no	—
402	C₄²	—	10	1	no	—
403	C₄²	—	10	1	no	—
404	C₄²	—	20	2	no	—
405	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
406	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
407	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
408	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
409	C₂×C₅	—	2	1	no	—
410	C₂×C₅	—	2	1	no	—
411	C₂×C₅	—	4	2	no	—
412	C₂×C₅	#2360	1	1	yes	characteristic
413	C₂×C₅	C₂×#443	1	1	yes	characteristic
414	C₂×C₅	#2956	1	1	yes	characteristic
415	C₂³	—	2	1	no	—
416	C₂³	C₂×#709	1	1	yes	characteristic
417	Q₈	—	2	1	no	—
418	Q₈	—	20	2	no	—
419	Q₈	—	40	1	no	—
420	Q₈	#4033	1	2	yes	—
421	D₄	—	2	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	1	no	—
424	D₄	#4033	1	2	yes	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	8	1	no	—
434	C₂×C₄	—	10	2	no	—
435	C₂×C₄	—	10	2	no	—
436	C₂×C₄	—	10	2	no	—
437	C₂×C₄	—	10	2	no	—
438	C₂×C₄	—	10	2	no	—
439	C₂×C₄	—	10	2	no	—
440	C₂×C₄	—	20	1	no	—
441	C₂×C₄	—	20	1	no	—
442	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
443	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
444	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
445	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
446	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
447	C₂×C₄	C₂×#711	1	1	yes	characteristic
448	C₂×C₄	#4144	1	1	yes	characteristic
449	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
450	C₂×C₄	#4147	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
452	C₈	—	2	2	no	—
453	C₈	—	2	2	no	—
454	C₈	—	4	2	no	—
455	C₈	—	10	2	no	—
456	C₈	—	10	2	no	—
457	C₈	—	10	2	no	—
458	C₈	—	20	1	no	—
459	C₅	#22982	1	1	yes	characteristic, complemented, Sylow
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	#65845	1	1	yes	characteristic
466	C₂²	#65847	1	1	yes	characteristic
467	C₂²	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	1	no	—
474	C₄	—	10	4	no	—
475	C₄	—	20	2	no	—
476	C₄	—	20	2	no	—
477	C₄	—	20	2	no	—
478	C₄	#65433	1	2	yes	—
479	C₄	C₂×#4033	1	1	yes	characteristic
480	C₄	#65838	1	1	yes	characteristic
481	C₄	#66140	1	1	yes	characteristic
482	C₄	Q₈×C₂²⋊D₅	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	4	2	no	—
486	C₂	#10613893	1	1	yes	characteristic
487	C₂	C₂×#65433	1	1	yes	characteristic
488	C₂	#10615542	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₅×#2906	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×C₅×#41	C₂³
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#2906	D₅
hypocenter	C₅	#22982
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #2906

Complements

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

N	H ≅ G/N	type
3. #10610739	C₂	semidirect
7. #10601330	C₂	semidirect
8. #10601327	C₂	semidirect
9. #10601313	C₂	semidirect
10. #10601307	C₂	semidirect
11. Dic₅×C₄⋊C₈	C₂	semidirect
28. #65311	C₄	semidirect
29. #65310	C₄	semidirect
30. #65309	C₄	semidirect
31. #65298	C₄	semidirect
32. #65297	C₄	semidirect
33. #65296	C₄	semidirect
88. #3969	Q₈	semidirect
459. C₅	#22982	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2906	2
#10614238	2
#10610739	2
#10602810	2
#10602801	2
C₄×#3969	2
#10601330	2
#10601327	2
#10601313	2
#10601307	2
Dic₅×C₄⋊C₈	2
#22982	5