Subgroups — #12107134

Order 1280.

738 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#4094	C₂	1	1	yes	maximal, characteristic
2	#10614238	C₂	1	1	yes	maximal, characteristic
3	#10610775	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1806	C₂	1	1	yes	maximal, characteristic
5	#10601313	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601169	C₂	1	2	yes	maximal
7	#10601163	C₂	1	2	yes	maximal
8	#10600286	C₂	1	1	yes	maximal, characteristic, complemented
9	#10600270	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599536	C₂	1	2	yes	maximal, complemented
11	#10599535	C₂	1	2	yes	maximal, complemented
12	C₄×C₅×#41	C₂²	1	1	yes	characteristic
13	C₂×#4094	C₂²	1	1	yes	characteristic
14	C₂×#4094	C₂²	1	1	yes	characteristic
15	#65804	C₂²	1	1	yes	characteristic
16	C₅×#423	C₂²	1	1	yes	characteristic
17	C₂×C₅×#104	C₂²	1	2	yes	—
18	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	#65522	C₂²	1	2	yes	—
20	C₂×#3954	C₂²	1	2	yes	—
21	#65411	C₂²	1	2	yes	—
22	#65408	C₂²	1	2	yes	—
23	#65311	C₄	1	2	yes	complemented
24	#65310	C₄	1	1	yes	characteristic, complemented
25	#65309	C₄	1	1	yes	characteristic, complemented
26	#65298	C₄	1	2	yes	complemented
27	#65297	C₄	1	1	yes	characteristic, complemented
28	#65296	C₄	1	1	yes	characteristic, complemented
29	#65287	C₂²	1	2	yes	—
30	#65286	—	2	1	no	—
31	#65286	—	2	1	no	—
32	#65286	C₂²	1	1	yes	characteristic
33	#65286	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
35	C₄×#681	—	2	1	no	—
36	C₄×#681	C₂²	1	1	yes	characteristic
37	C₂×#3935	C₂²	1	2	yes	—
38	C₂×C₄×#168	—	2	1	no	—
39	C₂×C₄×#168	C₂²	1	1	yes	characteristic
40	#65120	—	2	1	no	—
41	#65120	—	2	1	no	—
42	#65119	—	2	1	no	—
43	#65119	—	2	1	no	—
44	C₅×#339	C₂²	1	2	yes	—
45	#64778	C₂²	1	2	yes	—
46	#64744	C₂²	1	2	yes	—
47	#64743	C₂²	1	2	yes	—
48	#64743	C₂²	1	2	yes	—
49	#21628	—	5	1	no	maximal, Sylow
50	C₂×C₅×#41	C₂³	1	1	yes	characteristic
51	C₂×C₅×M₁₆	C₂³	1	2	yes	—
52	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
53	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
54	C₄×C₅×D₄	—	2	1	no	—
55	C₄×C₅×D₄	—	2	1	no	—
56	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
57	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
58	C₅×#117	—	2	1	no	—
59	C₅×#117	C₂³	1	1	yes	characteristic
60	C₂×C₅×C₄⋊C₄	—	2	1	no	—
61	C₂×C₄²×C₅	—	2	1	no	—
62	C₂×C₄²×C₅	C₂³	1	2	yes	—
63	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
64	#4094	—	2	2	no	—
65	#4094	—	2	2	no	—
66	#4094	—	2	2	no	—
67	#4094	Q₈	1	4	yes	complemented
68	#4072	C₂³	1	2	yes	—
69	#4070	—	2	1	no	—
70	#4070	—	2	1	no	—
71	C₂×#681	—	2	1	no	—
72	C₂×#681	—	2	1	no	—
73	C₂×#681	C₂³	1	1	yes	characteristic
74	C₂×#681	C₂³	1	1	yes	characteristic
75	C₂²×#168	—	2	1	no	—
76	C₂²×#168	—	2	1	no	—
77	C₂²×#168	C₂³	1	2	yes	—
78	C₂²×#168	C₂³	1	1	yes	characteristic
79	C₂²×#168	C₂³	1	1	yes	characteristic
80	#4016	C₂×C₄	1	2	yes	—
81	#4015	C₂×C₄	1	1	yes	characteristic
82	#4015	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₁₀	—	2	1	no	—
84	C₄×Dic₁₀	—	2	1	no	—
85	C₅×C₄⋊C₈	—	2	1	no	—
86	C₅×C₄⋊C₈	—	2	1	no	—
87	C₅×#104	—	2	4	no	—
88	C₅×#95	—	2	1	no	—
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	—	2	4	no	—
94	#3947	—	2	2	no	—
95	#3946	—	2	2	no	—
96	#3946	—	2	2	no	—
97	C₈×Dic₅	—	2	2	no	—
98	#3940	C₂×C₄	1	2	yes	—
99	#3940	C₂×C₄	1	2	yes	—
100	#3939	C₂×C₄	1	2	yes	—
101	#3939	C₂×C₄	1	2	yes	—
102	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
103	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
104	C₄⋊#168	C₂×C₄	1	2	yes	—
105	#3935	—	2	1	no	—
106	#3935	—	2	1	no	—
107	#3935	—	2	1	no	—
108	#3935	—	2	4	no	—
109	C₄×#168	—	2	1	no	—
110	C₄×#168	—	2	1	no	—
111	C₄×#168	—	2	1	no	—
112	C₄×#168	D₄	1	1	yes	characteristic
113	C₄×#168	D₄	1	1	yes	characteristic
114	C₄×#168	D₄	1	1	yes	characteristic
115	C₄×#168	D₄	1	1	yes	characteristic
116	#3076	—	5	1	no	—
117	#2960	—	5	1	no	—
118	C₄×#131	—	5	1	no	—
119	#1986	—	5	1	no	—
120	#1950	—	5	1	no	—
121	#1922	—	5	2	no	—
122	#1866	—	5	2	no	—
123	#1806	D₅	1	1	yes	characteristic
124	#1773	—	5	2	no	—
125	#1770	—	5	1	no	—
126	#1765	—	5	2	no	—
127	C₅×#41	—	2	1	no	—
128	C₅×#41	—	2	1	no	—
129	C₅×#41	C₂×Q₈	1	2	yes	—
130	C₅×#41	#41	1	2	yes	—
131	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₅×D₄	—	2	1	no	—
133	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	—	2	1	no	—
135	C₂²×C₄×C₅	—	2	1	no	—
136	C₂²×C₄×C₅	—	2	1	no	—
137	C₂²×C₄×C₅	—	2	2	no	—
138	C₂²×C₄×C₅	#41	1	1	yes	characteristic
139	C₂²×C₄×C₅	#41	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₂×Dic₁₀	—	2	1	no	—
142	C₂×Dic₁₀	—	2	1	no	—
143	C₅×M₁₆	—	2	2	no	—
144	C₅×M₁₆	—	2	2	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	4	2	no	—
149	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
150	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
151	C₅×C₂²⋊C₄	—	2	1	no	—
152	C₅×C₂²⋊C₄	—	2	1	no	—
153	C₅×C₂²⋊C₄	—	2	1	no	—
154	C₄²×C₅	—	2	1	no	—
155	C₄²×C₅	—	2	1	no	—
156	C₄²×C₅	—	2	1	no	—
157	C₄²×C₅	—	2	2	no	—
158	C₄²×C₅	—	2	2	no	—
159	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂²⋊Dic₅	—	2	2	no	—
164	C₄⋊Dic₅	—	2	1	no	—
165	C₄⋊Dic₅	—	2	1	no	—
166	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
167	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
168	#683	—	2	2	no	—
169	#683	—	2	2	no	—
170	C₄×Dic₅	—	2	2	no	—
171	#681	—	2	4	no	—
172	#681	—	2	1	no	—
173	#681	—	2	1	no	—
174	#681	—	2	4	no	—
175	#681	C₂×Q₈	1	2	yes	—
176	#681	#41	1	2	yes	—
177	C₂×#168	—	2	4	no	—
178	C₂×#168	—	2	1	no	—
179	C₂×#168	—	2	1	no	—
180	C₂×#168	—	2	2	no	—
181	C₂×#168	—	2	2	no	—
182	C₂×#168	—	2	1	no	—
183	C₂×#168	—	2	1	no	—
184	C₂×#168	—	2	4	no	—
185	C₂×#168	C₂²×C₄	1	2	yes	—
186	C₂×#168	C₂²×C₄	1	2	yes	—
187	C₂×#168	C₂×D₄	1	1	yes	characteristic
188	C₂×#168	C₂×D₄	1	1	yes	characteristic
189	C₂×#168	C₂×D₄	1	1	yes	characteristic
190	C₂×#168	C₂×D₄	1	1	yes	characteristic
191	C₂×#168	C₂×Q₈	1	2	yes	—
192	C₂×#168	#41	1	2	yes	—
193	C₂×#131	—	5	1	no	—
194	C₂×#131	—	5	1	no	—
195	#533	—	5	1	no	—
196	C₄×#41	C₂×D₅	1	1	yes	characteristic
197	#479	—	5	2	no	—
198	#478	—	5	2	no	—
199	#477	—	5	1	no	—
200	#476	—	5	1	no	—
201	#475	—	5	1	no	—
202	#474	—	5	1	no	—
203	#446	—	10	1	no	—
204	#446	—	10	1	no	—
205	C₈×Q₈	—	10	1	no	—
206	C₈×Q₈	—	10	1	no	—
207	C₂×#108	—	5	2	no	—
208	#427	—	5	2	no	—
209	#424	—	5	2	no	—
210	#423	C₂×D₅	1	1	yes	characteristic
211	C₂×C₄⋊C₈	—	5	1	no	—
212	C₂×#104	C₂×D₅	1	2	yes	—
213	#416	—	5	2	no	—
214	#405	—	5	2	no	—
215	#405	—	5	1	no	—
216	#405	—	5	1	no	—
217	#405	—	10	1	no	—
218	#405	—	10	1	no	—
219	C₄×M₁₆	—	5	1	no	—
220	C₄×M₁₆	—	10	1	no	—
221	C₂×#97	—	5	2	no	—
222	C₂×C₄×C₈	—	5	1	no	—
223	C₂×C₄×C₈	—	10	1	no	—
224	C₄×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
225	#341	—	5	2	no	—
226	#339	—	5	2	no	—
227	#339	—	5	2	no	—
228	#339	C₂×D₅	1	2	yes	—
229	#336	—	5	2	no	—
230	C₂³×C₅	—	2	1	no	—
231	C₂³×C₅	C₂×#41	1	1	yes	characteristic
232	C₅×Q₈	—	2	1	no	—
233	C₅×Q₈	C₄×Q₈	1	2	yes	—
234	C₅×D₄	—	2	2	no	—
235	C₅×D₄	—	2	2	no	—
236	C₅×D₄	—	2	1	no	—
237	C₅×D₄	C₄×Q₈	1	2	yes	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	1	no	—
244	C₂×C₄×C₅	—	4	1	no	—
245	C₂×C₄×C₅	—	4	2	no	—
246	C₂×C₄×C₅	—	4	2	no	—
247	C₂×C₄×C₅	—	4	2	no	—
248	C₂×C₄×C₅	—	4	2	no	—
249	C₂×C₄×C₅	—	4	2	no	—
250	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
260	C₂×Dic₅	—	2	2	no	—
261	C₂×Dic₅	—	2	2	no	—
262	Dic₁₀	—	4	2	no	—
263	Dic₁₀	—	4	2	no	—
264	C₅×C₈	—	4	2	no	—
265	#168	—	2	2	no	—
266	#168	—	2	2	no	—
267	#168	—	2	2	no	—
268	#168	—	2	1	no	—
269	#168	—	2	2	no	—
270	#168	—	2	1	no	—
271	#168	C₂²⋊Q₈	1	2	yes	—
272	#168	C₂²⋊Q₈	1	2	yes	—
273	C₂×#41	C₂²×D₅	1	1	yes	characteristic
274	#131	—	5	4	no	—
275	#131	—	10	2	no	—
276	#131	—	10	2	no	—
277	#131	—	10	2	no	—
278	C₂×M₁₆	—	5	1	no	—
279	C₂×M₁₆	—	5	1	no	—
280	C₂×M₁₆	—	10	1	no	—
281	C₂×M₁₆	—	10	1	no	—
282	C₂×M₁₆	C₂²×D₅	1	2	yes	—
283	C₂²×C₈	—	5	1	no	—
284	C₂²×C₈	—	5	1	no	—
285	C₂²×C₈	—	5	2	no	—
286	C₂²×C₈	—	10	1	no	—
287	C₂²×C₈	—	10	1	no	—
288	C₄⋊Q₈	—	5	1	no	—
289	C₄⋊Q₈	—	5	1	no	—
290	#125	—	5	2	no	—
291	C₂²⋊Q₈	—	10	1	no	—
292	C₂²⋊Q₈	—	10	1	no	—
293	C₄×Q₈	—	10	1	no	—
294	C₄×Q₈	—	10	1	no	—
295	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
296	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	C₄×D₅	1	1	yes	characteristic
300	C₄×D₄	C₄×D₅	1	1	yes	characteristic
301	#117	—	2	1	no	—
302	#117	—	5	2	no	—
303	#117	C₂²×D₅	1	1	yes	characteristic
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	C₂²×D₅	1	2	yes	—
307	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
308	#108	—	10	4	no	—
309	#107	—	5	2	no	—
310	#107	—	5	2	no	—
311	#106	—	5	2	no	—
312	#106	—	5	2	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	—	5	1	no	—
316	C₄⋊C₈	—	5	1	no	—
317	C₄⋊C₈	—	5	2	no	—
318	C₄⋊C₈	—	10	2	no	—
319	C₄⋊C₈	—	10	2	no	—
320	#104	—	2	4	no	—
321	#103	—	5	2	no	—
322	#103	—	5	2	no	—
323	#102	—	5	2	no	—
324	#102	—	5	2	no	—
325	#97	—	10	4	no	—
326	#97	—	10	1	no	—
327	#97	—	10	1	no	—
328	#97	—	10	2	no	—
329	#97	—	10	1	no	—
330	C₄×C₈	—	5	1	no	—
331	C₄×C₈	—	5	1	no	—
332	C₄×C₈	—	5	1	no	—
333	C₄×C₈	—	5	1	no	—
334	C₄×C₈	—	10	1	no	—
335	C₄×C₈	—	10	1	no	—
336	C₄×C₈	—	10	2	no	—
337	C₄×C₈	—	10	1	no	—
338	#95	—	2	1	no	—
339	C₂²×C₅	—	2	1	no	—
340	C₂²×C₅	—	2	1	no	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	—	4	1	no	—
343	C₂²×C₅	—	4	1	no	—
344	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
345	C₂²×C₅	#529	1	1	yes	characteristic
346	C₂²×C₅	#533	1	1	yes	characteristic
347	C₄×C₅	—	2	1	no	—
348	C₄×C₅	—	2	1	no	—
349	C₄×C₅	—	2	1	no	—
350	C₄×C₅	—	2	2	no	—
351	C₄×C₅	—	4	1	no	—
352	C₄×C₅	—	4	1	no	—
353	C₄×C₅	—	8	2	no	—
354	C₄×C₅	#444	1	2	yes	—
355	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
356	C₄×C₅	C₄×#41	1	1	yes	characteristic
357	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
358	C₄×C₅	#525	1	1	yes	characteristic
359	Dic₅	—	4	2	no	—
360	Dic₅	—	4	2	no	—
361	#41	—	2	1	no	—
362	#41	—	2	1	no	—
363	#41	#711	1	2	yes	—
364	#41	Q₈×D₅	1	2	yes	—
365	C₂×Q₈	—	10	1	no	—
366	C₂×Q₈	—	10	1	no	—
367	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	#711	1	1	yes	characteristic
375	C₂²×C₄	#711	1	1	yes	characteristic
376	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
377	M₁₆	—	2	2	no	—
378	M₁₆	—	2	2	no	—
379	M₁₆	—	5	2	no	—
380	M₁₆	—	5	2	no	—
381	M₁₆	—	10	4	no	—
382	M₁₆	—	10	4	no	—
383	M₁₆	—	10	1	no	—
384	M₁₆	—	10	1	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	5	1	no	—
387	C₂×C₈	—	5	1	no	—
388	C₂×C₈	—	5	2	no	—
389	C₂×C₈	—	5	2	no	—
390	C₂×C₈	—	5	2	no	—
391	C₂×C₈	—	5	2	no	—
392	C₂×C₈	—	5	1	no	—
393	C₂×C₈	—	5	1	no	—
394	C₂×C₈	—	10	4	no	—
395	C₂×C₈	—	10	4	no	—
396	C₂×C₈	—	10	1	no	—
397	C₂×C₈	—	10	1	no	—
398	C₂×C₈	—	10	1	no	—
399	C₂×C₈	—	10	2	no	—
400	C₂×C₈	—	10	2	no	—
401	C₂×C₈	—	10	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	—	5	2	no	—
406	C₄⋊C₄	—	5	2	no	—
407	C₄⋊C₄	—	10	2	no	—
408	C₄⋊C₄	—	10	2	no	—
409	C₄⋊C₄	—	10	1	no	—
410	C₄⋊C₄	—	10	1	no	—
411	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
412	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	10	2	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	10	2	no	—
423	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
424	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
425	C₄²	D₄×D₅	1	1	yes	characteristic
426	C₄²	D₄×D₅	1	1	yes	characteristic
427	C₂×C₅	—	2	1	no	—
428	C₂×C₅	—	2	1	no	—
429	C₂×C₅	—	4	2	no	—
430	C₂×C₅	C₄×C₂²⋊Q₈	1	1	yes	characteristic
431	C₂×C₅	C₂×#444	1	1	yes	characteristic
432	C₂×C₅	#2955	1	1	yes	characteristic
433	C₂³	—	2	1	no	—
434	C₂³	C₂×#711	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	20	2	no	—
437	Q₈	—	20	2	no	—
438	Q₈	#4033	1	2	yes	—
439	D₄	—	2	2	no	—
440	D₄	—	2	2	no	—
441	D₄	—	2	1	no	—
442	D₄	#4033	1	2	yes	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	10	2	no	—
456	C₂×C₄	—	10	2	no	—
457	C₂×C₄	#4027	1	1	yes	characteristic
458	C₂×C₄	#4027	1	1	yes	characteristic
459	C₂×C₄	#4027	1	1	yes	characteristic
460	C₂×C₄	#4027	1	1	yes	characteristic
461	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
462	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
463	C₂×C₄	C₂×#711	1	1	yes	characteristic
464	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
465	C₂×C₄	D₅×#41	1	1	yes	characteristic
466	C₂×C₄	D₅×#41	1	1	yes	characteristic
467	C₈	—	4	2	no	—
468	C₈	—	5	2	no	—
469	C₈	—	5	2	no	—
470	C₈	—	10	2	no	—
471	C₈	—	10	2	no	—
472	C₈	—	10	1	no	—
473	C₈	—	10	1	no	—
474	C₈	—	10	2	no	—
475	C₈	—	10	2	no	—
476	C₅	#21628	1	1	yes	characteristic, complemented, Sylow
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	C₂×#4027	1	1	yes	characteristic
483	C₂²	#65934	1	1	yes	characteristic
484	C₂²	#65956	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	2	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	1	no	—
491	C₄	—	8	2	no	—
492	C₄	—	20	2	no	—
493	C₄	—	20	2	no	—
494	C₄	#65112	1	2	yes	—
495	C₄	C₂×#4033	1	1	yes	characteristic
496	C₄	#65856	1	1	yes	characteristic
497	C₄	#65940	1	1	yes	characteristic
498	C₄	D₅×C₂²⋊Q₈	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	4	2	no	—
502	C₂	#10605597	1	1	yes	characteristic
503	C₂	C₂×#65112	1	1	yes	characteristic
504	C₂	#10610720	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₅×#1806	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×C₅×#41	C₂³
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1806	D₅
hypocenter	C₅	#21628
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1806

Complements

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

N	H ≅ G/N	type
3. #10610775	C₂	semidirect
5. #10601313	C₂	semidirect
8. #10600286	C₂	semidirect
9. #10600270	C₂	semidirect
10. #10599536	C₂	semidirect
11. #10599535	C₂	semidirect
23. #65311	C₄	semidirect
24. #65310	C₄	semidirect
25. #65309	C₄	semidirect
26. #65298	C₄	semidirect
27. #65297	C₄	semidirect
28. #65296	C₄	semidirect
67. #4094	Q₈	semidirect
476. C₅	#21628	semidirect

Maximal subgroups

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

subgroup	index
C₄×#4094	2
#10614238	2
#10610775	2
C₅×#1806	2
#10601313	2
#10601169	2
#10601163	2
#10600286	2
#10600270	2
#10599536	2
#10599535	2
#21628	5