Subgroups — #12121374

Order 1280.

708 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×#2962	C₂	1	1	yes	maximal, characteristic, complemented
2	#10615080	C₂	1	1	yes	maximal, characteristic
3	#10610743	C₂	1	1	yes	maximal, characteristic
4	#10602632	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601338	C₂	1	2	yes	maximal
6	#10601331	C₂	1	2	yes	maximal, complemented
7	#10601234	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600692	C₂	1	2	yes	maximal, complemented
9	#10600681	C₂	1	2	yes	maximal
10	#10600668	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#3957	C₂	1	1	yes	maximal, characteristic
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₂×#4047	C₂²	1	2	yes	—
14	C₄×#709	C₂²	1	1	yes	characteristic
15	C₅×#446	—	2	1	no	—
16	C₅×#446	—	2	2	no	—
17	C₅×C₈×Q₈	—	2	1	no	—
18	C₅×#424	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₅×#405	C₂²	1	2	yes	—
21	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
22	C₂×#3957	C₂²	1	1	yes	characteristic
23	C₂×#3957	C₂²	1	1	yes	characteristic
24	C₂×#3954	C₂²	1	2	yes	—
25	#65391	C₂²	1	2	yes	—
26	C₂×#3947	C₂²	1	2	yes	—
27	#65383	C₄	1	1	yes	characteristic, complemented
28	#65380	C₄	1	1	yes	characteristic, complemented
29	#65376	C₄	1	1	yes	characteristic, complemented
30	#65373	C₄	1	1	yes	characteristic, complemented
31	#65355	C₄	1	2	yes	complemented
32	#65352	C₄	1	2	yes	complemented
33	#65291	C₂²	1	2	yes	—
34	#65287	C₂²	1	2	yes	—
35	C₄²×Dic₅	C₂²	1	1	yes	characteristic
36	#65213	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
38	#65128	—	2	2	no	—
39	#65126	—	2	1	no	—
40	D₅×C₄⋊C₈	—	2	1	no	—
41	#64778	C₂²	1	2	yes	—
42	#64775	C₂²	1	1	yes	characteristic
43	#64775	C₂²	1	1	yes	characteristic
44	#64770	C₂²	1	2	yes	—
45	#64752	C₂²	1	2	yes	—
46	#64752	C₂²	1	2	yes	—
47	#22983	—	5	1	no	maximal, Sylow
48	C₂×#709	C₂³	1	1	yes	characteristic
49	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
50	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
51	C₂²×C₅×C₈	C₂³	1	2	yes	—
52	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₅×#125	C₂×C₄	1	2	yes	—
55	C₅×C₂²⋊Q₈	—	2	1	no	—
56	C₅×C₂²⋊Q₈	—	2	1	no	—
57	C₄×C₅×Q₈	—	2	1	no	—
58	C₄×C₅×Q₈	—	2	1	no	—
59	C₅×#117	C₂³	1	2	yes	—
60	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₄×C₂²⋊D₅	—	2	1	no	—
62	C₄×C₂²⋊D₅	—	2	1	no	—
63	#4072	C₂³	1	1	yes	characteristic
64	C₂×C₄×Dic₅	—	2	1	no	—
65	C₂×C₄×Dic₅	—	2	1	no	—
66	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
68	C₂×#681	C₂³	1	2	yes	—
69	C₂²×#168	C₂³	1	2	yes	—
70	#4047	—	2	4	no	—
71	#4047	—	4	2	no	—
72	C₂×#676	—	2	2	no	—
73	C₂×C₈×D₅	—	2	2	no	—
74	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
75	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
76	#4018	—	2	1	no	—
77	C₄²×D₅	—	2	1	no	—
78	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
80	C₅×C₄⋊C₈	—	2	2	no	—
81	C₅×C₄⋊C₈	—	2	2	no	—
82	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
84	C₅×C₄⋊C₈	D₄	1	2	yes	—
85	C₅×#97	—	2	2	no	—
86	C₅×#97	—	2	1	no	—
87	C₄×C₅×C₈	—	2	2	no	—
88	C₄×C₅×C₈	—	2	1	no	—
89	#3957	—	2	2	no	—
90	#3957	Q₈	1	4	yes	complemented
91	#3954	—	4	2	no	—
92	#3947	—	4	2	no	—
93	#3946	—	2	2	no	—
94	#3946	—	2	2	no	—
95	#3942	C₂×C₄	1	2	yes	—
96	#3942	C₂×C₄	1	2	yes	—
97	#3941	C₂×C₄	1	2	yes	—
98	#3941	C₂×C₄	1	2	yes	—
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	—	2	1	no	—
104	C₄⋊#168	—	2	1	no	—
105	C₄⋊#168	C₂×C₄	1	2	yes	—
106	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
107	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
108	#3076	—	5	1	no	—
109	#2962	D₅	1	1	yes	characteristic, complemented
110	#2906	—	5	1	no	—
111	#1994	—	5	1	no	—
112	#1950	—	5	1	no	—
113	#1946	—	5	2	no	—
114	#1922	—	5	2	no	—
115	#1866	—	5	2	no	—
116	#1767	—	5	1	no	—
117	#1765	—	5	2	no	—
118	C₄×#104	—	5	1	no	—
119	C₂×C₅×Q₈	—	2	1	no	—
120	C₂×C₅×Q₈	—	2	1	no	—
121	C₂²×C₄×C₅	#41	1	1	yes	characteristic
122	C₂²×C₄×C₅	#41	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	C₂×C₂²⋊D₅	—	2	1	no	—
125	C₂²×Dic₅	—	2	1	no	—
126	C₂²×Dic₅	—	2	1	no	—
127	#709	—	2	1	no	—
128	#709	—	2	1	no	—
129	#709	C₂×Q₈	1	2	yes	—
130	#709	#41	1	2	yes	—
131	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×D₅	—	2	1	no	—
133	C₂×C₄×D₅	—	2	1	no	—
134	C₂×C₄×D₅	—	2	1	no	—
135	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
136	C₅×M₁₆	—	2	1	no	—
137	C₅×M₁₆	—	2	1	no	—
138	C₅×M₁₆	—	2	1	no	—
139	C₅×M₁₆	C₂×Q₈	1	2	yes	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
145	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	1	no	—
150	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
151	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
152	C₅×C₂²⋊C₄	—	2	2	no	—
153	C₄²×C₅	—	2	2	no	—
154	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
155	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂²⋊Dic₅	—	2	1	no	—
159	#685	—	2	1	no	—
160	#685	—	2	1	no	—
161	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
162	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
163	#683	—	2	1	no	—
164	#683	—	2	1	no	—
165	C₄×Dic₅	—	2	1	no	—
166	C₄×Dic₅	—	2	1	no	—
167	C₄×Dic₅	—	2	1	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	—	4	2	no	—
173	C₄×Dic₅	C₂×Q₈	1	2	yes	—
174	#681	—	2	2	no	—
175	#681	—	2	2	no	—
176	C₂×#168	—	2	2	no	—
177	C₂×#168	—	2	2	no	—
178	C₂×#168	—	2	2	no	—
179	C₂×#168	C₂²×C₄	1	2	yes	—
180	C₂×#168	C₂²×C₄	1	2	yes	—
181	#676	—	4	4	no	—
182	C₈×D₅	—	4	4	no	—
183	C₂×#131	—	5	2	no	—
184	#533	C₂×D₅	1	1	yes	characteristic
185	C₄×#41	—	5	1	no	—
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	—	2	2	no	—
193	#446	—	2	1	no	—
194	C₈×Q₈	—	2	1	no	—
195	C₂×#108	—	5	2	no	—
196	#427	—	5	2	no	—
197	#424	—	5	2	no	—
198	#424	—	10	2	no	—
199	#424	C₂×D₅	1	2	yes	—
200	#423	—	5	1	no	—
201	#423	—	10	1	no	—
202	C₂×C₄⋊C₈	—	5	1	no	—
203	C₂×C₄⋊C₈	—	10	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	C₂×D₅	1	2	yes	—
209	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
210	C₂×#97	—	5	2	no	—
211	C₄³	—	5	1	no	—
212	#341	—	5	2	no	—
213	#339	—	5	1	no	—
214	#339	—	5	1	no	—
215	#339	—	5	2	no	—
216	#339	—	5	2	no	—
217	#336	—	5	2	no	—
218	C₂³×C₅	C₂×#41	1	1	yes	characteristic
219	C₂²×D₅	—	2	1	no	—
220	C₅×Q₈	—	4	2	no	—
221	C₅×Q₈	—	8	1	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
236	C₂²⋊D₅	—	2	2	no	—
237	C₂²⋊D₅	—	2	2	no	—
238	C₂×Dic₅	—	2	1	no	—
239	C₂×Dic₅	—	2	2	no	—
240	C₂×Dic₅	—	2	1	no	—
241	C₂×Dic₅	—	2	1	no	—
242	C₂×Dic₅	—	2	2	no	—
243	C₂×Dic₅	—	4	1	no	—
244	C₂×Dic₅	—	4	1	no	—
245	C₂×Dic₅	—	4	1	no	—
246	C₂×Dic₅	—	4	1	no	—
247	D₂₀	—	2	1	no	—
248	D₂₀	C₄×Q₈	1	2	yes	—
249	C₄×D₅	—	2	2	no	—
250	C₄×D₅	—	2	2	no	—
251	C₄×D₅	—	4	2	no	—
252	C₄×D₅	—	8	1	no	—
253	Dic₁₀	—	2	1	no	—
254	Dic₁₀	C₄×Q₈	1	2	yes	—
255	C₅×C₈	—	2	2	no	—
256	C₅×C₈	—	2	2	no	—
257	C₅×C₈	—	2	2	no	—
258	C₅×C₈	—	4	1	no	—
259	#168	—	2	2	no	—
260	#168	—	2	2	no	—
261	#168	—	4	2	no	—
262	C₂×#41	—	5	1	no	—
263	#131	—	10	4	no	—
264	#131	—	20	2	no	—
265	C₂×M₁₆	—	5	2	no	—
266	C₂×M₁₆	—	10	2	no	—
267	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
268	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
269	C₂²×C₈	—	5	2	no	—
270	C₂²×C₈	—	10	2	no	—
271	C₂²×C₈	C₂²×D₅	1	2	yes	—
272	C₄⋊Q₈	C₄×D₅	1	1	yes	characteristic
273	C₄⋊Q₈	C₄×D₅	1	1	yes	characteristic
274	#125	C₄×D₅	1	2	yes	—
275	C₂²⋊Q₈	—	2	1	no	—
276	C₂²⋊Q₈	—	2	1	no	—
277	C₄×Q₈	—	2	1	no	—
278	C₄×Q₈	—	2	1	no	—
279	C₄×Q₈	—	5	1	no	—
280	C₄×Q₈	—	5	1	no	—
281	C₄×D₄	—	5	1	no	—
282	C₄×D₄	—	5	1	no	—
283	C₄×D₄	—	10	1	no	—
284	C₄×D₄	—	10	1	no	—
285	#117	—	5	1	no	—
286	#117	—	10	1	no	—
287	#117	C₂²×D₅	1	2	yes	—
288	C₂×C₄²	—	5	1	no	—
289	C₂×C₄²	—	5	1	no	—
290	C₂×C₄²	—	10	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	—	5	1	no	—
302	C₄⋊C₈	—	5	1	no	—
303	C₄⋊C₈	—	5	2	no	—
304	C₄⋊C₈	—	10	2	no	—
305	C₄⋊C₈	—	10	2	no	—
306	C₄⋊C₈	—	10	1	no	—
307	C₄⋊C₈	—	10	1	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	—	2	2	no	—
318	#97	—	2	1	no	—
319	#97	—	20	2	no	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	—	2	1	no	—
322	C₂²×C₅	—	2	1	no	—
323	C₂²×C₅	—	2	1	no	—
324	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
325	C₂²×C₅	#552	1	1	yes	characteristic
326	C₂²×C₅	#554	1	1	yes	characteristic
327	C₂×D₅	—	2	2	no	—
328	C₂×D₅	—	4	1	no	—
329	C₂×D₅	—	4	1	no	—
330	C₄×C₅	—	2	1	no	—
331	C₄×C₅	—	2	1	no	—
332	C₄×C₅	—	2	1	no	—
333	C₄×C₅	—	4	2	no	—
334	C₄×C₅	—	4	2	no	—
335	C₄×C₅	#444	1	2	yes	—
336	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
337	C₄×C₅	#520	1	1	yes	characteristic
338	C₄×C₅	#546	1	1	yes	characteristic
339	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
340	Dic₅	—	2	2	no	—
341	Dic₅	—	4	2	no	—
342	Dic₅	—	4	2	no	—
343	Dic₅	—	4	1	no	—
344	Dic₅	—	4	1	no	—
345	#41	—	5	2	no	—
346	#41	—	5	2	no	—
347	#41	—	10	1	no	—
348	#41	—	10	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	5	1	no	—
352	C₂×D₄	—	5	1	no	—
353	C₂×D₄	—	10	1	no	—
354	C₂²×C₄	—	10	1	no	—
355	C₂²×C₄	—	10	1	no	—
356	C₂²×C₄	—	10	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	1	no	—
363	M₁₆	—	2	1	no	—
364	M₁₆	—	2	1	no	—
365	M₁₆	—	10	2	no	—
366	M₁₆	—	10	2	no	—
367	M₁₆	—	20	4	no	—
368	M₁₆	Q₈×D₅	1	2	yes	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	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	2	no	—
378	C₂×C₈	—	20	4	no	—
379	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
380	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	5	1	no	—
386	C₄⋊C₄	—	5	1	no	—
387	C₄⋊C₄	—	10	1	no	—
388	C₄⋊C₄	—	10	1	no	—
389	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
390	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	10	1	no	—
393	C₂²⋊C₄	—	10	1	no	—
394	C₂²⋊C₄	—	10	1	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	5	2	no	—
397	C₄²	—	10	1	no	—
398	C₄²	—	10	1	no	—
399	C₄²	—	10	1	no	—
400	C₄²	—	10	1	no	—
401	C₄²	—	10	1	no	—
402	C₄²	—	10	1	no	—
403	C₄²	—	20	2	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	#2360	1	1	yes	characteristic
412	C₂×C₅	C₂×#444	1	1	yes	characteristic
413	C₂×C₅	#2956	1	1	yes	characteristic
414	D₅	—	4	2	no	—
415	C₂³	—	10	1	no	—
416	C₂³	C₂×#709	1	1	yes	characteristic
417	Q₈	—	4	2	no	—
418	Q₈	—	5	2	no	—
419	Q₈	—	8	1	no	—
420	Q₈	—	10	1	no	—
421	D₄	—	5	2	no	—
422	D₄	—	10	2	no	—
423	D₄	—	10	2	no	—
424	D₄	—	10	1	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	10	1	no	—
430	C₂×C₄	—	10	2	no	—
431	C₂×C₄	—	10	2	no	—
432	C₂×C₄	—	10	2	no	—
433	C₂×C₄	—	10	1	no	—
434	C₂×C₄	—	10	1	no	—
435	C₂×C₄	—	10	2	no	—
436	C₂×C₄	—	20	1	no	—
437	C₂×C₄	—	20	1	no	—
438	C₂×C₄	—	20	1	no	—
439	C₂×C₄	—	20	1	no	—
440	C₂×C₄	—	20	2	no	—
441	C₂×C₄	—	40	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×Q₈×D₅	1	1	yes	characteristic
448	C₂×C₄	#4147	1	1	yes	characteristic
449	C₂×C₄	D₅×#41	1	1	yes	characteristic
450	C₂×C₄	#4149	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	—	2	2	no	—
455	C₈	—	4	1	no	—
456	C₈	—	10	2	no	—
457	C₈	—	10	2	no	—
458	C₈	—	20	2	no	—
459	C₅	#22983	1	1	yes	characteristic, complemented, Sylow
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	10	2	no	—
463	C₂²	—	20	1	no	—
464	C₂²	—	20	1	no	—
465	C₂²	#65913	1	1	yes	characteristic
466	C₂²	#65915	1	1	yes	characteristic
467	C₂²	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	10	2	no	—
474	C₄	—	20	2	no	—
475	C₄	—	20	2	no	—
476	C₄	—	20	1	no	—
477	C₄	—	20	1	no	—
478	C₄	#65434	1	2	yes	—
479	C₄	C₄×Q₈×D₅	1	1	yes	characteristic
480	C₄	#65908	1	1	yes	characteristic
481	C₄	Q₈×C₂²⋊D₅	1	1	yes	characteristic
482	C₄	#66163	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	20	2	no	—
486	C₂	#10614221	1	1	yes	characteristic
487	C₂	C₂×#65434	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×#2962	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×#709	C₂³
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#2962	D₅
hypocenter	C₅	#22983
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #2962

Complements

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

N	H ≅ G/N	type
1. C₅×#2962	C₂	semidirect
4. #10602632	C₂	semidirect
6. #10601331	C₂	semidirect
7. #10601234	C₂	semidirect
8. #10600692	C₂	semidirect
10. #10600668	C₂	semidirect
27. #65383	C₄	semidirect
28. #65380	C₄	semidirect
29. #65376	C₄	semidirect
30. #65373	C₄	semidirect
31. #65355	C₄	semidirect
32. #65352	C₄	semidirect
90. #3957	Q₈	semidirect
109. #2962	D₅	semidirect
459. C₅	#22983	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2962	2
#10615080	2
#10610743	2
#10602632	2
#10601338	2
#10601331	2
#10601234	2
#10600692	2
#10600681	2
#10600668	2
C₄×#3957	2
#22983	5