Subgroups — #12107144

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	#10615080	C₂	1	1	yes	maximal, characteristic
2	#10615059	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#4053	C₂	1	1	yes	maximal, characteristic
4	C₅×#1986	C₂	1	1	yes	maximal, characteristic, complemented
5	#10600668	C₂	1	1	yes	maximal, characteristic, complemented
6	#10600287	C₂	1	1	yes	maximal, characteristic
7	#10600270	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599567	C₂	1	2	yes	maximal
9	#10599535	C₂	1	2	yes	maximal, complemented
10	#10599533	C₂	1	2	yes	maximal
11	#10599531	C₂	1	2	yes	maximal, complemented
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₂×#4053	C₂²	1	1	yes	characteristic
14	C₂×#4053	C₂²	1	1	yes	characteristic
15	C₄×#709	C₂²	1	1	yes	characteristic
16	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×#3954	C₂²	1	2	yes	—
19	#65411	C₂²	1	1	yes	characteristic
20	#65411	C₂²	1	1	yes	characteristic
21	#65383	C₄	1	1	yes	characteristic, complemented
22	#65380	C₄	1	1	yes	characteristic, complemented
23	#65376	C₄	1	1	yes	characteristic, complemented
24	#65373	C₄	1	1	yes	characteristic, complemented
25	#65355	C₄	1	2	yes	complemented
26	#65352	C₄	1	2	yes	complemented
27	#65313	—	2	1	no	—
28	#65313	—	2	1	no	—
29	Q₈×#168	—	2	1	no	—
30	Q₈×#168	—	2	1	no	—
31	#65291	C₂²	1	2	yes	—
32	#65288	C₂²	1	2	yes	—
33	#65287	C₂²	1	2	yes	—
34	#65286	C₂²	1	2	yes	—
35	C₂×#3937	C₂²	1	2	yes	—
36	#65213	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
38	C₂×#3935	C₂²	1	2	yes	—
39	C₂×C₄×#168	C₂²	1	1	yes	characteristic
40	#64997	—	2	1	no	—
41	#64997	—	2	1	no	—
42	C₄×#676	—	2	1	no	—
43	C₄×C₈×D₅	—	2	1	no	—
44	C₅×#339	C₂²	1	2	yes	—
45	C₅×#339	C₂²	1	2	yes	—
46	#64778	C₂²	1	2	yes	—
47	#64744	C₂²	1	2	yes	—
48	#64743	C₂²	1	2	yes	—
49	#21628	—	5	1	no	maximal, Sylow
50	C₂×#709	C₂³	1	1	yes	characteristic
51	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
52	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
53	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
55	C₅×#125	C₂×C₄	1	2	yes	—
56	C₅×C₂²⋊Q₈	—	2	1	no	—
57	C₅×C₂²⋊Q₈	—	2	1	no	—
58	C₄×C₅×Q₈	—	2	1	no	—
59	C₄×C₅×Q₈	—	2	1	no	—
60	C₅×#117	C₂³	1	2	yes	—
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₄²×C₅	C₂³	1	2	yes	—
63	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
64	C₄×C₂²⋊D₅	—	2	1	no	—
65	C₄×C₂²⋊D₅	—	2	1	no	—
66	#4072	C₂³	1	1	yes	characteristic
67	C₂×#681	C₂³	1	2	yes	—
68	C₂²×#168	C₂³	1	2	yes	—
69	C₂²×#168	C₂³	1	1	yes	characteristic
70	C₂²×#168	C₂³	1	1	yes	characteristic
71	#4053	—	2	2	no	—
72	#4053	—	2	2	no	—
73	#4053	—	2	2	no	—
74	#4053	Q₈	1	4	yes	complemented
75	C₂×#676	—	2	1	no	—
76	C₂×#676	—	2	1	no	—
77	C₂×C₈×D₅	—	2	1	no	—
78	C₂×C₈×D₅	—	2	1	no	—
79	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
80	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
81	#4018	—	2	1	no	—
82	C₄²×D₅	—	2	1	no	—
83	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
84	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
85	C₅×#97	—	2	1	no	—
86	C₄×C₅×C₈	—	2	1	no	—
87	C₅×#95	—	2	1	no	—
88	#3954	—	2	4	no	—
89	#3947	—	2	1	no	—
90	#3947	—	2	1	no	—
91	C₈×Dic₅	—	2	1	no	—
92	C₈×Dic₅	—	2	1	no	—
93	#3942	C₂×C₄	1	2	yes	—
94	#3942	C₂×C₄	1	2	yes	—
95	#3941	C₂×C₄	1	2	yes	—
96	#3941	C₂×C₄	1	2	yes	—
97	#3940	C₂×C₄	1	2	yes	—
98	#3940	C₂×C₄	1	2	yes	—
99	#3939	C₂×C₄	1	2	yes	—
100	#3939	C₂×C₄	1	2	yes	—
101	#3937	—	2	4	no	—
102	C₄⋊#168	—	2	1	no	—
103	C₄⋊#168	—	2	1	no	—
104	C₄⋊#168	—	2	2	no	—
105	C₄⋊#168	—	2	2	no	—
106	C₄⋊#168	C₂×C₄	1	2	yes	—
107	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
108	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
109	#3935	—	2	2	no	—
110	#3935	—	2	4	no	—
111	C₄×#168	—	2	2	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	D₅	1	1	yes	characteristic, complemented
120	#1950	—	5	1	no	—
121	#1922	—	5	2	no	—
122	#1866	—	5	2	no	—
123	#1806	—	5	1	no	—
124	#1773	—	5	2	no	—
125	#1770	—	5	1	no	—
126	#1765	—	5	2	no	—
127	C₂×C₅×Q₈	—	2	1	no	—
128	C₂×C₅×Q₈	—	2	1	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	#41	1	1	yes	characteristic
131	C₂²×C₄×C₅	#41	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
133	C₂×C₂²⋊D₅	—	2	1	no	—
134	#709	—	2	1	no	—
135	#709	—	2	1	no	—
136	#709	C₂×Q₈	1	2	yes	—
137	#709	#41	1	2	yes	—
138	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×D₅	—	2	1	no	—
140	C₂×C₄×D₅	—	2	1	no	—
141	C₂×C₄×D₅	—	2	1	no	—
142	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
143	C₅×M₁₆	—	2	1	no	—
144	C₅×M₁₆	—	2	1	no	—
145	C₅×M₁₆	C₂×Q₈	1	2	yes	—
146	C₅×M₁₆	#41	1	2	yes	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	4	2	no	—
154	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
155	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
156	C₅×C₂²⋊C₄	—	2	2	no	—
157	C₄²×C₅	—	2	2	no	—
158	C₄²×C₅	—	2	2	no	—
159	C₄²×C₅	—	2	2	no	—
160	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
164	C₂²⋊Dic₅	—	2	1	no	—
165	#685	—	2	1	no	—
166	#685	—	2	1	no	—
167	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
168	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
169	#683	—	2	1	no	—
170	#683	—	2	1	no	—
171	C₄×Dic₅	—	2	1	no	—
172	C₄×Dic₅	—	2	1	no	—
173	C₄×Dic₅	—	2	1	no	—
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	1	no	—
179	C₂×#168	—	2	1	no	—
180	C₂×#168	—	2	2	no	—
181	C₂×#168	C₂²×C₄	1	2	yes	—
182	C₂×#168	C₂²×C₄	1	2	yes	—
183	C₂×#168	C₂×D₄	1	1	yes	characteristic
184	C₂×#168	C₂×D₄	1	1	yes	characteristic
185	C₂×#168	C₂×D₄	1	1	yes	characteristic
186	C₂×#168	C₂×D₄	1	1	yes	characteristic
187	C₂×#168	C₂×Q₈	1	2	yes	—
188	C₂×#168	#41	1	2	yes	—
189	#676	—	2	4	no	—
190	#676	—	2	4	no	—
191	C₈×D₅	—	2	4	no	—
192	C₈×D₅	—	2	4	no	—
193	C₂×#131	—	5	1	no	—
194	C₂×#131	—	5	1	no	—
195	#533	C₂×D₅	1	1	yes	characteristic
196	C₄×#41	—	5	1	no	—
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	—	5	1	no	—
211	C₂×C₄⋊C₈	—	5	1	no	—
212	C₂×#104	—	5	2	no	—
213	#416	—	5	2	no	—
214	#405	—	5	1	no	—
215	#405	—	5	1	no	—
216	#405	—	5	2	no	—
217	#405	—	10	1	no	—
218	#405	—	10	1	no	—
219	C₄×M₁₆	—	10	1	no	—
220	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
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	C₂×D₅	1	2	yes	—
228	#339	C₂×D₅	1	2	yes	—
229	#336	—	5	2	no	—
230	C₂³×C₅	C₂×#41	1	1	yes	characteristic
231	C₂²×D₅	—	2	1	no	—
232	C₅×Q₈	—	4	2	no	—
233	C₅×Q₈	—	4	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	4	2	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	—	4	2	no	—
241	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
251	C₂²⋊D₅	—	2	2	no	—
252	C₂²⋊D₅	—	2	2	no	—
253	C₂×Dic₅	—	2	1	no	—
254	C₂×Dic₅	—	2	1	no	—
255	C₂×Dic₅	—	2	1	no	—
256	D₂₀	—	2	1	no	—
257	D₂₀	C₄×Q₈	1	2	yes	—
258	C₄×D₅	—	2	2	no	—
259	C₄×D₅	—	2	2	no	—
260	C₄×D₅	—	4	2	no	—
261	C₄×D₅	—	4	2	no	—
262	Dic₁₀	—	2	1	no	—
263	Dic₁₀	C₄×Q₈	1	2	yes	—
264	C₅×C₈	—	2	2	no	—
265	C₅×C₈	—	2	2	no	—
266	#168	—	2	2	no	—
267	#168	—	2	2	no	—
268	#168	—	2	1	no	—
269	#168	—	2	1	no	—
270	#168	—	4	2	no	—
271	#168	C₂²⋊Q₈	1	2	yes	—
272	#168	C₂²⋊Q₈	1	2	yes	—
273	C₂×#41	—	5	1	no	—
274	#131	—	5	4	no	—
275	#131	—	10	2	no	—
276	#131	—	10	2	no	—
277	#131	—	10	2	no	—
278	C₂×M₁₆	—	5	2	no	—
279	C₂×M₁₆	—	10	1	no	—
280	C₂×M₁₆	—	10	1	no	—
281	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
282	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
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	C₄×D₅	1	1	yes	characteristic
289	C₄⋊Q₈	C₄×D₅	1	1	yes	characteristic
290	#125	C₄×D₅	1	2	yes	—
291	C₂²⋊Q₈	—	2	1	no	—
292	C₂²⋊Q₈	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	—	5	1	no	—
296	C₄×Q₈	—	5	1	no	—
297	C₄×D₄	—	5	1	no	—
298	C₄×D₄	—	5	1	no	—
299	C₄×D₄	—	10	1	no	—
300	C₄×D₄	—	10	1	no	—
301	#117	—	5	1	no	—
302	#117	—	10	1	no	—
303	#117	C₂²×D₅	1	2	yes	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄²	—	10	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	—	5	1	no	—
314	C₄⋊C₈	—	5	1	no	—
315	C₄⋊C₈	—	5	2	no	—
316	C₄⋊C₈	—	10	2	no	—
317	C₄⋊C₈	—	10	2	no	—
318	C₄⋊C₈	—	10	1	no	—
319	C₄⋊C₈	—	10	1	no	—
320	#104	—	10	4	no	—
321	#103	—	5	2	no	—
322	#103	—	5	2	no	—
323	#102	—	5	2	no	—
324	#102	—	5	2	no	—
325	#97	—	2	1	no	—
326	#97	—	10	4	no	—
327	#97	—	10	2	no	—
328	#97	—	10	1	no	—
329	#97	—	10	1	no	—
330	C₄×C₈	—	2	1	no	—
331	C₄×C₈	—	5	1	no	—
332	C₄×C₈	—	5	1	no	—
333	C₄×C₈	—	5	1	no	—
334	C₄×C₈	—	5	1	no	—
335	C₄×C₈	—	10	2	no	—
336	C₄×C₈	—	10	1	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	C₂×C₄×D₄	1	1	yes	characteristic
342	C₂²×C₅	#529	1	1	yes	characteristic
343	C₂²×C₅	#533	1	1	yes	characteristic
344	C₂×D₅	—	2	2	no	—
345	C₂×D₅	—	4	1	no	—
346	C₂×D₅	—	4	1	no	—
347	C₄×C₅	—	2	1	no	—
348	C₄×C₅	—	2	1	no	—
349	C₄×C₅	—	2	1	no	—
350	C₄×C₅	—	4	2	no	—
351	C₄×C₅	—	4	2	no	—
352	C₄×C₅	—	8	2	no	—
353	C₄×C₅	#444	1	2	yes	—
354	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
355	C₄×C₅	C₄×#41	1	1	yes	characteristic
356	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
357	C₄×C₅	#525	1	1	yes	characteristic
358	Dic₅	—	2	2	no	—
359	Dic₅	—	4	1	no	—
360	Dic₅	—	4	1	no	—
361	#41	—	5	2	no	—
362	#41	—	5	2	no	—
363	#41	—	10	1	no	—
364	#41	—	10	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	5	1	no	—
368	C₂×D₄	—	5	1	no	—
369	C₂×D₄	—	10	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	10	1	no	—
372	C₂²×C₄	—	10	1	no	—
373	C₂²×C₄	—	10	1	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	1	no	—
378	M₁₆	—	2	1	no	—
379	M₁₆	—	10	4	no	—
380	M₁₆	—	10	4	no	—
381	M₁₆	—	10	2	no	—
382	M₁₆	—	10	2	no	—
383	M₁₆	Q₈×D₅	1	2	yes	—
384	M₁₆	#713	1	2	yes	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	5	1	no	—
388	C₂×C₈	—	5	1	no	—
389	C₂×C₈	—	5	2	no	—
390	C₂×C₈	—	5	2	no	—
391	C₂×C₈	—	5	2	no	—
392	C₂×C₈	—	5	2	no	—
393	C₂×C₈	—	5	1	no	—
394	C₂×C₈	—	5	1	no	—
395	C₂×C₈	—	10	4	no	—
396	C₂×C₈	—	10	4	no	—
397	C₂×C₈	—	10	2	no	—
398	C₂×C₈	—	10	1	no	—
399	C₂×C₈	—	10	2	no	—
400	C₂×C₈	—	10	1	no	—
401	C₂×C₈	—	10	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	—	5	1	no	—
408	C₄⋊C₄	—	5	1	no	—
409	C₄⋊C₄	—	10	1	no	—
410	C₄⋊C₄	—	10	1	no	—
411	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
412	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	10	1	no	—
415	C₂²⋊C₄	—	10	1	no	—
416	C₂²⋊C₄	—	10	1	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	10	1	no	—
421	C₄²	—	10	1	no	—
422	C₄²	—	10	1	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	C₄×C₂²⋊Q₈	1	1	yes	characteristic
430	C₂×C₅	C₂×#444	1	1	yes	characteristic
431	C₂×C₅	#2955	1	1	yes	characteristic
432	D₅	—	4	2	no	—
433	C₂³	—	10	1	no	—
434	C₂³	C₂×#711	1	1	yes	characteristic
435	Q₈	—	4	2	no	—
436	Q₈	—	4	2	no	—
437	Q₈	—	5	2	no	—
438	Q₈	—	10	1	no	—
439	D₄	—	5	2	no	—
440	D₄	—	10	2	no	—
441	D₄	—	10	2	no	—
442	D₄	—	10	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	10	1	no	—
451	C₂×C₄	—	10	2	no	—
452	C₂×C₄	—	10	2	no	—
453	C₂×C₄	—	10	1	no	—
454	C₂×C₄	—	10	1	no	—
455	C₂×C₄	—	20	2	no	—
456	C₂×C₄	—	20	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×Q₈×D₅	1	1	yes	characteristic
464	C₂×C₄	C₂×#713	1	1	yes	characteristic
465	C₂×C₄	D₅×#41	1	1	yes	characteristic
466	C₂×C₄	D₅×#41	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	5	2	no	—
470	C₈	—	5	2	no	—
471	C₈	—	10	2	no	—
472	C₈	—	10	2	no	—
473	C₈	—	10	1	no	—
474	C₈	—	10	1	no	—
475	C₈	—	20	2	no	—
476	C₅	#21628	1	1	yes	characteristic, complemented, Sylow
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	10	2	no	—
480	C₂²	—	20	1	no	—
481	C₂²	—	20	1	no	—
482	C₂²	C₂×#4027	1	1	yes	characteristic
483	C₂²	#66014	1	1	yes	characteristic
484	C₂²	#66062	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	8	2	no	—
491	C₄	—	10	2	no	—
492	C₄	—	20	1	no	—
493	C₄	—	20	1	no	—
494	C₄	#65112	1	2	yes	—
495	C₄	C₄×Q₈×D₅	1	1	yes	characteristic
496	C₄	C₄×#713	1	1	yes	characteristic
497	C₄	D₅×C₂²⋊Q₈	1	1	yes	characteristic
498	C₄	#65961	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	20	2	no	—
502	C₂	#10608210	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×#1986	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×#709	C₂³
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1986	D₅
hypocenter	C₅	#21628
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1986

Complements

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

N	H ≅ G/N	type
2. #10615059	C₂	semidirect
4. C₅×#1986	C₂	semidirect
5. #10600668	C₂	semidirect
7. #10600270	C₂	semidirect
9. #10599535	C₂	semidirect
11. #10599531	C₂	semidirect
21. #65383	C₄	semidirect
22. #65380	C₄	semidirect
23. #65376	C₄	semidirect
24. #65373	C₄	semidirect
25. #65355	C₄	semidirect
26. #65352	C₄	semidirect
74. #4053	Q₈	semidirect
119. #1986	D₅	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
#10615080	2
#10615059	2
C₄×#4053	2
C₅×#1986	2
#10600668	2
#10600287	2
#10600270	2
#10599567	2
#10599535	2
#10599533	2
#10599531	2
#21628	5