Subgroups — #12979938

Order 1280.

1818 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10618181	C₂	1	2	yes	maximal, complemented
2	C₅×#3160	C₂	1	1	yes	maximal, characteristic, complemented
3	#10615081	C₂	1	2	yes	maximal, complemented
4	#10613684	C₂	1	2	yes	maximal, complemented
5	#10613683	C₂	1	2	yes	maximal, complemented
6	#10613662	C₂	1	4	yes	maximal, complemented
7	#10613643	C₂	1	4	yes	maximal, complemented
8	#10613636	C₂	1	4	yes	maximal, complemented
9	#10610928	C₂	1	4	yes	maximal, complemented
10	#10610904	C₂	1	2	yes	maximal, complemented
11	#10610898	C₂	1	2	yes	maximal
12	C₂×C₄×D₄₀	C₂	1	1	yes	maximal, characteristic
13	#10610176	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#533	C₂²	1	2	yes	—
15	C₂²×D₄₀	C₂²	1	1	yes	characteristic
16	#66064	C₂²	1	4	yes	complemented
17	#66061	C₂²	1	4	yes	complemented
18	#66024	C₂²	1	8	yes	complemented
19	#65968	—	2	4	no	—
20	D₅×C₂²⋊Q₈	—	2	4	no	—
21	#65913	—	2	4	no	—
22	#65913	—	2	2	no	—
23	Q₈×D₂₀	—	2	2	no	—
24	#65855	C₂²	1	4	yes	—
25	#65853	C₂²	1	4	yes	—
26	C₂×C₄×D₂₀	C₂²	1	2	yes	—
27	#65804	C₂²	1	1	yes	characteristic
28	C₅×#500	C₂²	1	1	yes	characteristic, complemented
29	C₅×#500	C₂²	1	1	yes	characteristic, complemented
30	C₅×#499	C₂²	1	2	yes	complemented
31	C₅×#499	C₂²	1	2	yes	complemented
32	C₅×#498	C₂²	1	2	yes	complemented
33	C₅×#427	C₂²	1	2	yes	—
34	C₅×#427	C₂²	1	2	yes	—
35	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
36	C₂×#3953	C₂²	1	2	yes	—
37	C₂×#3950	C₂²	1	1	yes	characteristic
38	#65391	C₂²	1	2	yes	—
39	#65390	C₂²	1	2	yes	—
40	#65376	C₂²	1	4	yes	complemented
41	#65373	C₂²	1	4	yes	complemented
42	#65355	C₂²	1	8	yes	complemented
43	#65290	C₂²	1	4	yes	—
44	#65284	C₂²	1	4	yes	—
45	#65213	C₂²	1	1	yes	characteristic
46	#65180	C₂²	1	8	yes	complemented
47	#65179	C₂²	1	8	yes	complemented
48	#65167	C₂²	1	4	yes	complemented
49	#65163	C₂²	1	4	yes	complemented
50	#65161	C₂²	1	4	yes	—
51	#65161	C₂²	1	4	yes	—
52	#65160	C₂²	1	8	yes	complemented
53	#65159	C₂²	1	8	yes	complemented
54	#65158	C₂²	1	8	yes	—
55	#65145	C₂²	1	8	yes	complemented
56	C₄×D₄₀	C₂²	1	2	yes	—
57	C₄×D₄₀	C₂²	1	2	yes	—
58	C₄×D₄₀	C₂²	1	2	yes	—
59	C₄×D₄₀	C₂²	1	2	yes	—
60	#64968	C₂²	1	2	yes	complemented
61	#64968	C₂²	1	2	yes	complemented
62	C₈×Dic₁₀	C₂²	1	2	yes	complemented
63	C₈×Dic₁₀	C₂²	1	2	yes	complemented
64	#61370	—	5	1	no	maximal, Sylow
65	C₂×Q₈×D₅	—	2	4	no	—
66	C₂²×D₂₀	C₂³	1	2	yes	—
67	C₂²×C₄×D₅	—	2	2	no	—
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
71	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
72	C₅×#125	C₂³	1	4	yes	—
73	C₅×C₂²⋊Q₈	—	2	2	no	—
74	C₅×C₂²⋊Q₈	—	2	2	no	—
75	C₄×C₅×Q₈	—	2	2	no	—
76	C₄×C₅×Q₈	—	2	2	no	—
77	C₅×#117	C₂³	1	4	yes	—
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	#4092	—	2	4	no	—
80	#4092	—	2	8	no	—
81	C₂×#685	—	2	2	no	—
82	#4072	C₂³	1	2	yes	—
83	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
84	#4070	D₄	1	2	yes	—
85	#4070	D₄	1	2	yes	—
86	C₂×#681	C₂³	1	2	yes	—
87	C₂×D₄₀	Q₈	1	8	yes	complemented
88	C₂×D₄₀	C₂³	1	2	yes	—
89	C₂×D₄₀	C₂³	1	2	yes	—
90	#4043	—	2	4	no	—
91	#4043	—	2	8	no	—
92	#4042	—	2	8	no	—
93	#4042	—	2	8	no	—
94	#4042	—	2	8	no	—
95	#4039	C₂³	1	8	yes	—
96	#4039	C₂³	1	8	yes	—
97	D₅×C₄⋊C₄	—	2	4	no	—
98	D₅×C₄⋊C₄	—	2	8	no	—
99	#4036	C₂³	1	8	yes	—
100	#4034	C₂³	1	8	yes	—
101	D₅×C₂²⋊C₄	—	2	8	no	—
102	#4024	—	2	8	no	—
103	C₄×D₂₀	—	2	2	no	—
104	C₄×D₂₀	—	2	2	no	—
105	C₄×D₂₀	—	2	4	no	—
106	C₄×D₂₀	—	2	4	no	—
107	C₄×D₂₀	C₂³	1	4	yes	—
108	C₄×D₂₀	C₂³	1	4	yes	—
109	#4016	—	2	4	no	—
110	#4016	D₄	1	2	yes	—
111	#4015	—	2	4	no	—
112	#4015	D₄	1	1	yes	characteristic
113	#4015	D₄	1	1	yes	characteristic
114	C₄×Dic₁₀	C₂³	1	2	yes	—
115	C₄×Dic₁₀	C₂³	1	2	yes	—
116	C₅×#107	C₂³	1	2	yes	—
117	C₅×#107	C₂³	1	2	yes	—
118	C₅×#107	C₂³	1	2	yes	—
119	C₅×#107	C₂³	1	2	yes	—
120	C₅×#106	C₂³	1	4	yes	—
121	C₅×#106	C₂³	1	4	yes	—
122	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
123	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
124	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
125	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
126	#3953	C₂³	1	4	yes	—
127	#3953	C₂³	1	4	yes	—
128	#3950	C₂³	1	2	yes	—
129	#3950	C₂³	1	2	yes	—
130	#3947	C₂³	1	4	yes	—
131	#3946	C₂³	1	4	yes	—
132	#3946	C₂³	1	4	yes	—
133	C₈×Dic₅	C₂³	1	4	yes	—
134	#3941	C₂³	1	8	yes	—
135	#3941	C₂³	1	8	yes	—
136	#3940	C₂³	1	8	yes	—
137	#3939	C₂³	1	8	yes	—
138	C₄⋊#168	C₂³	1	2	yes	—
139	C₄⋊#168	C₂³	1	2	yes	—
140	#3501	—	5	2	no	—
141	#3389	—	5	4	no	—
142	#3384	—	5	4	no	—
143	#3380	—	5	2	no	—
144	#3380	—	5	4	no	—
145	Q₈×D₈	—	5	2	no	—
146	#3164	—	5	2	no	—
147	#3160	D₅	1	1	yes	characteristic, complemented
148	#3081	—	5	4	no	—
149	#3077	—	5	2	no	—
150	#2960	—	5	1	no	—
151	#2948	—	5	2	no	—
152	C₂×C₄×D₈	—	5	1	no	—
153	C₂³×D₅	—	2	2	no	—
154	C₂×C₅×Q₈	—	2	2	no	—
155	C₂×C₅×Q₈	—	2	2	no	—
156	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
159	C₂²×Dic₅	—	2	2	no	—
160	Q₈×D₅	—	8	8	no	—
161	C₂×D₂₀	—	2	2	no	—
162	C₂×D₂₀	—	2	4	no	—
163	C₂×D₂₀	C₂×Q₈	1	8	yes	complemented
164	C₂×D₂₀	C₂⁴	1	4	yes	—
165	C₂×C₄×D₅	—	2	4	no	—
166	C₂×C₄×D₅	—	2	4	no	—
167	C₂×C₄×D₅	—	2	8	no	—
168	C₂×C₄×D₅	—	2	8	no	—
169	C₂×C₄×D₅	—	8	4	no	—
170	C₂×Dic₁₀	—	2	8	no	—
171	C₂×Dic₁₀	C₂×D₄	1	2	yes	—
172	C₂×Dic₁₀	C₂×D₄	1	2	yes	—
173	C₂×C₅×C₈	—	2	2	no	—
174	C₂×C₅×C₈	C₂×Q₈	1	4	yes	complemented
175	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
176	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
177	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
178	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
179	C₅×C₄⋊C₄	—	2	4	no	—
180	C₅×C₄⋊C₄	—	2	4	no	—
181	C₅×C₄⋊C₄	—	2	2	no	—
182	C₅×C₄⋊C₄	—	2	2	no	—
183	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
184	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
185	C₅×C₂²⋊C₄	—	2	4	no	—
186	C₄²×C₅	—	2	4	no	—
187	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₅	C₂⁴	1	1	yes	characteristic
190	C₄²×C₅	C₂⁴	1	1	yes	characteristic
191	C₂²⋊Dic₅	C₂×D₄	1	4	yes	—
192	#685	—	2	4	no	—
193	#685	—	2	4	no	—
194	#685	—	2	8	no	—
195	#685	—	2	8	no	—
196	C₄⋊Dic₅	—	2	2	no	—
197	C₄⋊Dic₅	—	2	8	no	—
198	C₄⋊Dic₅	C₂×D₄	1	2	yes	—
199	C₄⋊Dic₅	C₂×D₄	1	2	yes	—
200	C₄⋊Dic₅	C₂×D₄	1	2	yes	—
201	C₄⋊Dic₅	C₂×D₄	1	2	yes	—
202	C₄⋊Dic₅	C₂⁴	1	4	yes	—
203	#683	—	2	8	no	—
204	#683	—	2	8	no	—
205	#683	C₂×D₄	1	4	yes	—
206	#683	C₂×D₄	1	4	yes	—
207	C₄×Dic₅	C₂⁴	1	4	yes	—
208	#681	—	2	4	no	—
209	C₂×#168	C₂⁴	1	4	yes	—
210	D₄₀	C₂×Q₈	1	8	yes	complemented
211	D₄₀	C₂×Q₈	1	8	yes	complemented
212	C₂²×D₈	—	5	1	no	—
213	#554	—	5	4	no	—
214	#554	—	5	8	no	—
215	#554	—	10	4	no	—
216	#554	—	10	2	no	—
217	D₄×Q₈	—	5	4	no	—
218	D₄×Q₈	—	10	2	no	—
219	#544	—	5	4	no	—
220	#543	—	10	4	no	—
221	#533	—	5	1	no	—
222	#533	C₂×D₅	1	2	yes	—
223	C₂×C₂²⋊Q₈	—	10	4	no	—
224	#518	—	5	4	no	—
225	C₂×C₄×D₄	—	5	2	no	—
226	#501	—	5	8	no	—
227	#500	—	5	4	no	—
228	#500	C₂×D₅	1	1	yes	characteristic, complemented
229	#500	C₂×D₅	1	1	yes	characteristic, complemented
230	#499	—	5	4	no	—
231	#499	C₂×D₅	1	2	yes	complemented
232	#499	C₂×D₅	1	2	yes	complemented
233	#498	C₂×D₅	1	2	yes	complemented
234	#478	—	5	8	no	—
235	#478	—	5	8	no	—
236	#478	—	5	8	no	—
237	#476	—	5	4	no	—
238	#476	—	5	8	no	—
239	#474	—	5	4	no	—
240	#474	—	5	8	no	—
241	#446	—	5	2	no	—
242	#446	—	5	2	no	—
243	C₈×Q₈	—	5	2	no	—
244	C₈×Q₈	—	5	2	no	—
245	#442	—	5	8	no	—
246	C₄×D₈	—	5	4	no	—
247	C₄×D₈	—	5	4	no	—
248	C₄×D₈	—	5	2	no	—
249	C₄×D₈	—	5	2	no	—
250	C₄×D₈	—	5	2	no	—
251	C₄×D₈	—	5	2	no	—
252	#428	—	5	4	no	—
253	#427	C₂×D₅	1	2	yes	—
254	#427	C₂×D₅	1	2	yes	—
255	C₂×#107	—	5	1	no	—
256	#424	—	5	2	no	—
257	#423	—	5	1	no	—
258	#418	—	5	4	no	—
259	C₂×#102	—	5	2	no	—
260	#405	—	5	2	no	—
261	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
262	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
263	C₂²×D₅	—	2	4	no	—
264	C₂²×D₅	—	2	8	no	—
265	C₂²×D₅	—	8	2	no	—
266	C₂²×D₅	—	8	2	no	—
267	C₅×Q₈	—	4	4	no	—
268	C₅×Q₈	—	8	2	no	—
269	C₂×C₄×C₅	—	2	2	no	—
270	C₂×C₄×C₅	—	2	4	no	—
271	C₂×C₄×C₅	—	2	4	no	—
272	C₂×C₄×C₅	—	4	1	no	—
273	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
279	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
280	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
281	C₂×Dic₅	—	2	4	no	—
282	C₂×Dic₅	—	8	2	no	—
283	C₂×Dic₅	C₂²×D₄	1	4	yes	—
284	C₂×Dic₅	C₂²×D₄	1	4	yes	—
285	D₂₀	—	2	8	no	—
286	D₂₀	—	2	4	no	—
287	D₂₀	C₂²×Q₈	1	8	yes	—
288	C₄×D₅	—	4	8	no	—
289	C₄×D₅	—	8	8	no	—
290	C₄×D₅	—	8	8	no	—
291	C₄×D₅	—	8	4	no	—
292	Dic₁₀	—	2	4	no	—
293	Dic₁₀	—	4	2	no	—
294	Dic₁₀	—	8	8	no	—
295	C₅×C₈	—	2	1	no	—
296	C₅×C₈	—	2	1	no	—
297	C₅×C₈	C₂²×Q₈	1	2	yes	—
298	C₅×C₈	C₂²×Q₈	1	2	yes	—
299	#168	—	2	4	no	—
300	C₂²×Q₈	—	10	4	no	—
301	C₂²×D₄	—	5	2	no	—
302	C₂³×C₄	—	10	2	no	—
303	C₂×D₈	—	5	8	no	—
304	C₂×D₈	—	5	2	no	—
305	C₂×D₈	—	5	2	no	—
306	C₂×M₁₆	—	5	2	no	—
307	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
308	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
309	C₄⋊Q₈	—	5	8	no	—
310	C₄⋊Q₈	—	5	1	no	—
311	C₄⋊Q₈	—	5	1	no	—
312	C₄⋊Q₈	—	10	4	no	—
313	C₄⋊Q₈	C₂²×D₅	1	2	yes	—
314	C₄⋊Q₈	C₂²×D₅	1	2	yes	—
315	#125	—	5	8	no	—
316	#125	—	5	2	no	—
317	#125	—	10	4	no	—
318	#125	C₂²×D₅	1	4	yes	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	5	2	no	—
322	C₂²⋊Q₈	—	5	2	no	—
323	C₂²⋊Q₈	—	10	8	no	—
324	C₂²⋊Q₈	—	10	8	no	—
325	C₂²⋊Q₈	—	10	8	no	—
326	C₂²⋊Q₈	—	10	8	no	—
327	C₂²⋊Q₈	—	10	4	no	—
328	C₂²⋊Q₈	—	10	8	no	—
329	C₂²⋊Q₈	—	10	4	no	—
330	C₂²⋊Q₈	—	10	8	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	2	2	no	—
333	C₄×Q₈	—	5	2	no	—
334	C₄×Q₈	—	5	2	no	—
335	C₄×D₄	—	5	8	no	—
336	C₄×D₄	—	5	8	no	—
337	C₄×D₄	—	5	4	no	—
338	C₄×D₄	—	5	4	no	—
339	C₄×D₄	—	10	4	no	—
340	C₄×D₄	—	10	4	no	—
341	C₄×D₄	—	10	2	no	—
342	C₄×D₄	—	10	2	no	—
343	#117	—	5	2	no	—
344	#117	C₂²×D₅	1	4	yes	—
345	C₂×C₄⋊C₄	—	5	2	no	—
346	C₂×C₄⋊C₄	—	10	8	no	—
347	C₂×C₄⋊C₄	—	10	4	no	—
348	C₂×C₂²⋊C₄	—	10	8	no	—
349	C₂×C₂²⋊C₄	—	10	2	no	—
350	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
351	#107	—	5	2	no	—
352	#107	—	5	2	no	—
353	#107	—	5	8	no	—
354	#107	C₂²×D₅	1	2	yes	—
355	#107	C₂²×D₅	1	2	yes	—
356	#107	C₂²×D₅	1	2	yes	—
357	#107	C₂²×D₅	1	2	yes	—
358	#106	—	5	8	no	—
359	#106	C₂²×D₅	1	4	yes	—
360	#106	C₂²×D₅	1	4	yes	—
361	C₄⋊C₈	—	5	4	no	—
362	C₄⋊C₈	—	5	4	no	—
363	C₄⋊C₈	—	5	2	no	—
364	C₄⋊C₈	—	5	2	no	—
365	#102	—	5	4	no	—
366	#102	—	5	4	no	—
367	#102	—	5	8	no	—
368	#102	—	5	8	no	—
369	#97	—	5	4	no	—
370	C₄×C₈	—	5	4	no	—
371	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
372	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
373	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
374	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
375	C₂²×C₅	—	2	1	no	—
376	C₂²×C₅	—	2	1	no	—
377	C₂²×C₅	D₄×Q₈	1	2	yes	—
378	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
379	C₂×D₅	—	2	8	no	—
380	C₂×D₅	—	4	4	no	—
381	C₂×D₅	—	4	4	no	—
382	C₂×D₅	—	8	8	no	—
383	C₄×C₅	—	2	1	no	—
384	C₄×C₅	—	2	1	no	—
385	C₄×C₅	—	2	1	no	—
386	C₄×C₅	—	4	4	no	—
387	C₄×C₅	—	4	4	no	—
388	C₄×C₅	D₄×Q₈	1	2	yes	—
389	C₄×C₅	#576	1	2	yes	—
390	C₄×C₅	C₂³×Q₈	1	1	yes	characteristic
391	C₄×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
392	Dic₅	—	2	4	no	—
393	Dic₅	—	2	4	no	—
394	Dic₅	—	4	4	no	—
395	C₂⁴	—	10	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	5	2	no	—
399	C₂×Q₈	—	5	2	no	—
400	C₂×Q₈	—	10	8	no	—
401	C₂×Q₈	—	40	8	no	—
402	C₂×D₄	—	5	8	no	—
403	C₂×D₄	—	5	4	no	—
404	C₂×D₄	—	10	2	no	—
405	C₂×D₄	—	10	4	no	—
406	C₂²×C₄	—	10	8	no	—
407	C₂²×C₄	—	10	8	no	—
408	C₂²×C₄	—	10	2	no	—
409	C₂²×C₄	—	10	4	no	—
410	C₂²×C₄	—	10	4	no	—
411	C₂²×C₄	—	40	4	no	—
412	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
413	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
414	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
415	D₈	—	5	8	no	—
416	D₈	—	5	8	no	—
417	M₁₆	—	10	4	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	5	4	no	—
420	C₂×C₈	Q₈×D₅	1	4	yes	complemented
421	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
422	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
423	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
424	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	5	4	no	—
430	C₄⋊C₄	—	5	2	no	—
431	C₄⋊C₄	—	5	2	no	—
432	C₄⋊C₄	—	5	2	no	—
433	C₄⋊C₄	—	5	4	no	—
434	C₄⋊C₄	—	5	2	no	—
435	C₄⋊C₄	—	5	4	no	—
436	C₄⋊C₄	—	10	8	no	—
437	C₄⋊C₄	—	10	8	no	—
438	C₄⋊C₄	—	10	8	no	—
439	C₄⋊C₄	—	10	2	no	—
440	C₄⋊C₄	C₂³×D₅	1	4	yes	—
441	C₄⋊C₄	C₂³×D₅	1	4	yes	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	5	4	no	—
444	C₂²⋊C₄	—	10	8	no	—
445	C₂²⋊C₄	—	10	8	no	—
446	C₂²⋊C₄	—	10	4	no	—
447	C₂²⋊C₄	—	10	4	no	—
448	C₄²	—	2	4	no	—
449	C₄²	—	5	4	no	—
450	C₄²	D₄×D₅	1	1	yes	characteristic
451	C₄²	D₄×D₅	1	1	yes	characteristic
452	C₄²	C₂³×D₅	1	1	yes	characteristic
453	C₄²	C₂³×D₅	1	1	yes	characteristic
454	C₂×C₅	—	2	2	no	—
455	C₂×C₅	C₂×D₄×Q₈	1	1	yes	characteristic
456	C₂×C₅	C₂×#576	1	1	yes	characteristic
457	C₂×C₅	#3584	1	1	yes	characteristic
458	D₅	—	4	8	no	—
459	C₂³	—	10	4	no	—
460	C₂³	—	10	8	no	—
461	C₂³	—	40	2	no	—
462	C₂³	—	40	2	no	—
463	C₂³	C₂×D₄×D₅	1	1	yes	characteristic
464	Q₈	—	4	4	no	—
465	Q₈	—	8	2	no	—
466	Q₈	—	10	4	no	—
467	Q₈	—	20	2	no	—
468	Q₈	—	40	8	no	—
469	D₄	—	5	8	no	—
470	D₄	—	10	8	no	—
471	D₄	—	10	4	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	5	4	no	—
477	C₂×C₄	—	5	4	no	—
478	C₂×C₄	—	10	4	no	—
479	C₂×C₄	—	20	8	no	—
480	C₂×C₄	—	40	4	no	—
481	C₂×C₄	—	40	8	no	—
482	C₂×C₄	—	40	8	no	—
483	C₂×C₄	—	40	2	no	—
484	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
485	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
486	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
487	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
488	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
489	C₂×C₄	C₂×Q₈×D₅	1	2	yes	—
490	C₂×C₄	#4147	1	2	yes	—
491	C₂×C₄	C₂⁴×D₅	1	1	yes	characteristic
492	C₈	—	2	1	no	—
493	C₈	—	2	1	no	—
494	C₈	—	10	4	no	—
495	C₈	C₂×Q₈×D₅	1	2	yes	—
496	C₈	C₂×Q₈×D₅	1	2	yes	—
497	C₅	#61370	1	1	yes	characteristic, complemented, Sylow
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	10	8	no	—
501	C₂²	—	20	4	no	—
502	C₂²	—	20	4	no	—
503	C₂²	—	40	8	no	—
504	C₂²	#66061	1	2	yes	—
505	C₂²	C₂²×D₄×D₅	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	4	no	—
511	C₄	—	10	4	no	—
512	C₄	—	10	4	no	—
513	C₄	—	20	4	no	—
514	C₄	#66061	1	2	yes	—
515	C₄	#66103	1	2	yes	—
516	C₄	C₂²×Q₈×D₅	1	1	yes	characteristic
517	C₄	C₂×#4147	1	1	yes	characteristic
518	C₂	—	2	2	no	—
519	C₂	—	20	8	no	—
520	C₂	C₂×#66061	1	1	yes	characteristic
521	C₂	C₂×#66103	1	1	yes	characteristic
522	C₂	#10619088	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅
Fitting	C₅×#3160	C₂
socle	C₂²×C₅	C₂³×D₄
prime radical	C₂²×D₄₀	C₂²
hypercenter	#3160	D₅
hypocenter	C₅	#61370
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3160

Complements

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

N	H ≅ G/N	type
1. #10618181	C₂	semidirect
2. C₅×#3160	C₂	semidirect
3. #10615081	C₂	semidirect
4. #10613684	C₂	semidirect
5. #10613683	C₂	semidirect
6. #10613662	C₂	semidirect
7. #10613643	C₂	semidirect
8. #10613636	C₂	semidirect
9. #10610928	C₂	semidirect
10. #10610904	C₂	semidirect
13. #10610176	C₂	semidirect
16. #66064	C₂²	semidirect
17. #66061	C₂²	semidirect
18. #66024	C₂²	semidirect
28. C₅×#500	C₂²	semidirect
29. C₅×#500	C₂²	semidirect
30. C₅×#499	C₂²	semidirect
31. C₅×#499	C₂²	semidirect
32. C₅×#498	C₂²	semidirect
40. #65376	C₂²	semidirect
41. #65373	C₂²	semidirect
42. #65355	C₂²	semidirect
46. #65180	C₂²	semidirect
47. #65179	C₂²	semidirect
48. #65167	C₂²	semidirect
49. #65163	C₂²	semidirect
52. #65160	C₂²	semidirect
53. #65159	C₂²	semidirect
55. #65145	C₂²	semidirect
60. #64968	C₂²	semidirect
61. #64968	C₂²	semidirect
62. C₈×Dic₁₀	C₂²	semidirect
63. C₈×Dic₁₀	C₂²	semidirect
87. C₂×D₄₀	Q₈	semidirect
147. #3160	D₅	semidirect
163. C₂×D₂₀	C₂×Q₈	semidirect
174. C₂×C₅×C₈	C₂×Q₈	semidirect
210. D₄₀	C₂×Q₈	semidirect
211. D₄₀	C₂×Q₈	semidirect
228. #500	C₂×D₅	semidirect
229. #500	C₂×D₅	semidirect
231. #499	C₂×D₅	semidirect
232. #499	C₂×D₅	semidirect
233. #498	C₂×D₅	semidirect
420. C₂×C₈	Q₈×D₅	semidirect
497. C₅	#61370	semidirect

Maximal subgroups

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

subgroup	index
#10618181	2
C₅×#3160	2
#10615081	2
#10613684	2
#10613683	2
#10613662	2
#10613643	2
#10613636	2
#10610928	2
#10610904	2
#10610898	2
C₂×C₄×D₄₀	2
#10610176	2
#61370	5