Subgroups — C₅×#21559 #11944279

Order 1280.

868 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3067	C₂	1	1	yes	maximal, characteristic
2	C₅×#2955	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#444	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2875	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1976	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1953	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1932	C₂	1	2	yes	maximal, complemented
8	C₅×#1906	C₂	1	2	yes	maximal, complemented
9	C₅×#1814	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1773	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1757	C₂	1	2	yes	maximal, complemented
12	C₅×#575	C₂²	1	2	yes	—
13	C₂×C₅×#135	C₂²	1	1	yes	characteristic
14	C₂×C₅×#131	C₂²	1	1	yes	characteristic
15	C₂×C₅×#131	C₂²	1	2	yes	—
16	C₂×C₅×#131	C₂²	1	1	yes	characteristic
17	C₄×C₅×#41	C₂²	1	1	yes	characteristic
18	C₅×#473	C₄	1	2	yes	complemented
19	C₅×#472	C₄	1	2	yes	complemented
20	C₅×#471	C₄	1	4	yes	complemented
21	C₅×#444	—	2	1	no	—
22	C₅×#444	—	2	1	no	—
23	C₅×#444	—	2	1	no	—
24	C₅×#444	—	2	1	no	—
25	C₅×#444	—	2	4	no	—
26	C₅×#443	—	2	4	no	—
27	C₅×#430	C₂²	1	2	yes	—
28	C₂×C₅×#108	C₂²	1	1	yes	characteristic
29	C₂×C₅×#108	C₂²	1	1	yes	characteristic
30	C₅×#427	C₂²	1	1	yes	characteristic
31	C₅×#421	C₂²	1	2	yes	—
32	C₅×#421	C₂²	1	2	yes	—
33	C₂×C₅×#104	C₂²	1	2	yes	—
34	C₅×#413	C₂²	1	2	yes	—
35	C₅×#410	C₂²	1	2	yes	—
36	C₅×#405	—	2	1	no	—
37	C₅×#405	—	2	1	no	—
38	C₅×#405	C₂²	1	1	yes	characteristic
39	C₅×#405	C₂²	1	1	yes	characteristic
40	C₅×#405	C₂²	1	2	yes	—
41	C₄×C₅×M₁₆	—	2	1	no	—
42	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
43	C₂×C₅×#97	—	2	1	no	—
44	C₂×C₅×#97	C₂²	1	1	yes	characteristic
45	C₅×#344	C₂²	1	2	yes	—
46	C₅×#344	C₂²	1	2	yes	—
47	C₅×#339	C₂²	1	2	yes	—
48	#21559	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂×C₅×#41	C₂³	1	2	yes	—
50	C₂×C₅×#41	C₂³	1	1	yes	characteristic
51	C₅×#137	—	2	2	no	—
52	C₅×#137	C₂×C₄	1	4	yes	—
53	C₅×AGL(1,ℤ/8)	—	2	2	no	—
54	C₅×AGL(1,ℤ/8)	C₂×C₄	1	4	yes	—
55	C₅×#135	—	2	4	no	—
56	C₅×#135	—	2	1	no	—
57	C₅×#135	—	2	1	no	—
58	C₅×#135	—	2	1	no	—
59	C₅×#135	—	2	1	no	—
60	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
61	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
62	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic, complemented
63	C₅×#131	—	2	1	no	—
64	C₅×#131	—	2	1	no	—
65	C₅×#131	—	2	2	no	—
66	C₅×#131	—	2	2	no	—
67	C₅×#131	—	2	2	no	—
68	C₅×#131	—	2	2	no	—
69	C₅×#131	—	2	2	no	—
70	C₅×#131	C₂×C₄	1	2	yes	—
71	C₅×#131	C₂×C₄	1	2	yes	—
72	C₅×#131	D₄	1	4	yes	—
73	C₂×C₅×M₁₆	—	2	1	no	—
74	C₂×C₅×M₁₆	—	2	1	no	—
75	C₂×C₅×M₁₆	—	2	2	no	—
76	C₂×C₅×M₁₆	C₂³	1	2	yes	—
77	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₅×M₁₆	C₂³	1	2	yes	—
79	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
80	C₂²×C₅×C₈	—	2	1	no	—
81	C₂²×C₅×C₈	—	2	1	no	—
82	C₂²×C₅×C₈	—	2	2	no	—
83	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₄×C₅×Q₈	—	2	1	no	—
86	C₄×C₅×D₄	—	2	1	no	—
87	C₄×C₅×D₄	—	2	2	no	—
88	C₅×#117	—	2	1	no	—
89	C₅×#117	C₂³	1	2	yes	—
90	C₅×#117	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₅	—	2	1	no	—
92	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₅×#108	—	2	4	no	—
94	C₅×#108	—	2	1	no	—
95	C₅×#108	—	2	1	no	—
96	C₅×#108	C₂×C₄	1	2	yes	complemented
97	C₅×#108	C₂×C₄	1	2	yes	complemented
98	C₅×#107	—	2	1	no	—
99	C₅×#106	—	2	1	no	—
100	C₅×#104	—	2	4	no	—
101	C₅×#104	—	2	4	no	—
102	C₅×#104	—	2	2	no	—
103	C₅×#104	—	2	2	no	—
104	C₅×#101	C₂×C₄	1	4	yes	complemented
105	C₅×#100	C₂×C₄	1	4	yes	complemented
106	C₅×#99	—	2	4	no	—
107	C₅×#97	—	2	1	no	—
108	C₅×#97	—	2	1	no	—
109	C₅×#97	—	2	2	no	—
110	C₅×#97	—	2	1	no	—
111	C₅×#97	D₄	1	1	yes	characteristic
112	C₅×#97	D₄	1	1	yes	characteristic
113	C₅×#97	D₄	1	1	yes	characteristic
114	C₅×#97	D₄	1	1	yes	characteristic
115	C₄×C₅×C₈	—	2	1	no	—
116	C₄×C₅×C₈	—	2	1	no	—
117	C₄×C₅×C₈	—	2	2	no	—
118	C₄×C₅×C₈	—	2	1	no	—
119	#3067	C₂×C₅	1	1	yes	characteristic
120	#2955	C₂×C₅	1	2	yes	complemented
121	C₂×#444	C₂×C₅	1	1	yes	characteristic, complemented
122	#2875	C₂×C₅	1	1	yes	characteristic, complemented
123	#1976	C₂×C₅	1	1	yes	characteristic, complemented
124	#1953	C₂×C₅	1	1	yes	characteristic, complemented
125	#1932	C₂×C₅	1	2	yes	complemented
126	#1906	C₂×C₅	1	2	yes	complemented
127	#1814	C₂×C₅	1	1	yes	characteristic, complemented
128	#1773	C₂×C₅	1	1	yes	characteristic, complemented
129	#1757	C₂×C₅	1	2	yes	complemented
130	C₅×#41	—	2	1	no	—
131	C₅×#41	—	2	1	no	—
132	C₅×#41	—	2	2	no	—
133	C₅×#41	—	2	2	no	—
134	C₅×#41	—	2	2	no	—
135	C₅×#41	—	2	2	no	—
136	C₅×#41	C₂²×C₄	1	2	yes	—
137	C₅×#41	C₂×D₄	1	2	yes	—
138	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
139	C₂×C₅×Q₈	#41	1	1	yes	characteristic
140	C₂×C₅×D₄	—	2	1	no	—
141	C₂×C₅×D₄	—	2	2	no	—
142	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
143	C₂×C₅×D₄	#41	1	1	yes	characteristic
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	2	no	—
148	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₅×Q₁₆	—	2	4	no	—
150	C₅×Q₁₆	—	2	1	no	—
151	C₅×Q₁₆	—	2	1	no	—
152	C₅×SD₁₆	—	2	4	no	—
153	C₅×SD₁₆	—	2	4	no	—
154	C₅×SD₁₆	—	2	2	no	—
155	C₅×SD₁₆	—	2	2	no	—
156	C₅×D₈	—	2	4	no	—
157	C₅×D₈	—	2	1	no	—
158	C₅×D₈	—	2	1	no	—
159	C₅×M₁₆	—	2	1	no	—
160	C₅×M₁₆	—	2	1	no	—
161	C₅×M₁₆	—	2	2	no	—
162	C₅×M₁₆	—	2	2	no	—
163	C₅×M₁₆	—	2	2	no	—
164	C₅×M₁₆	—	2	4	no	—
165	C₅×M₁₆	—	2	2	no	—
166	C₅×M₁₆	—	2	2	no	—
167	C₅×M₁₆	—	4	2	no	—
168	C₅×M₁₆	—	4	2	no	—
169	C₅×M₁₆	C₂²×C₄	1	2	yes	—
170	C₅×M₁₆	C₂²×C₄	1	4	yes	—
171	C₅×M₁₆	C₂×D₄	1	2	yes	—
172	C₂×C₅×C₈	—	2	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	2	2	no	—
175	C₂×C₅×C₈	—	2	2	no	—
176	C₂×C₅×C₈	—	2	2	no	—
177	C₂×C₅×C₈	—	2	4	no	—
178	C₂×C₅×C₈	—	2	2	no	—
179	C₂×C₅×C₈	—	4	2	no	—
180	C₂×C₅×C₈	—	4	2	no	—
181	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
184	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
185	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
186	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
187	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
188	C₂×C₅×C₈	#41	1	1	yes	characteristic
189	C₂×C₅×C₈	#41	1	1	yes	characteristic
190	C₂×C₅×C₈	#41	1	2	yes	—
191	C₅×C₄⋊C₄	—	2	2	no	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	—	2	2	no	—
194	C₅×C₂²⋊C₄	—	2	2	no	—
195	C₅×C₂²⋊C₄	—	2	2	no	—
196	C₅×C₂²⋊C₄	#41	1	2	yes	—
197	C₄²×C₅	—	2	2	no	—
198	C₄²×C₅	—	2	1	no	—
199	C₄²×C₅	—	2	1	no	—
200	C₄²×C₅	—	2	2	no	—
201	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
203	#575	C₂²×C₅	1	2	yes	—
204	C₂×#135	C₂²×C₅	1	1	yes	characteristic
205	C₂×#131	C₂²×C₅	1	2	yes	—
206	C₂×#131	C₂²×C₅	1	1	yes	characteristic
207	C₂×#131	C₂²×C₅	1	1	yes	characteristic
208	C₄×#41	C₂²×C₅	1	1	yes	characteristic
209	#473	C₄×C₅	1	2	yes	complemented
210	#472	C₄×C₅	1	2	yes	complemented
211	#471	C₄×C₅	1	4	yes	complemented
212	#444	—	2	4	no	—
213	#444	—	2	1	no	—
214	#444	—	2	1	no	—
215	#444	—	2	1	no	—
216	#444	—	2	1	no	—
217	#443	—	2	4	no	—
218	#430	C₂²×C₅	1	2	yes	—
219	C₂×#108	C₂²×C₅	1	1	yes	characteristic
220	C₂×#108	C₂²×C₅	1	1	yes	characteristic
221	#427	C₂²×C₅	1	1	yes	characteristic
222	#421	C₂²×C₅	1	2	yes	—
223	#421	C₂²×C₅	1	2	yes	—
224	C₂×#104	C₂²×C₅	1	2	yes	—
225	#413	C₂²×C₅	1	2	yes	—
226	#410	C₂²×C₅	1	2	yes	—
227	#405	—	2	1	no	—
228	#405	—	2	1	no	—
229	#405	C₂²×C₅	1	1	yes	characteristic
230	#405	C₂²×C₅	1	1	yes	characteristic
231	#405	C₂²×C₅	1	2	yes	—
232	C₄×M₁₆	—	2	1	no	—
233	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
234	C₂×#97	—	2	1	no	—
235	C₂×#97	C₂²×C₅	1	1	yes	characteristic
236	#344	C₂²×C₅	1	2	yes	—
237	#344	C₂²×C₅	1	2	yes	—
238	#339	C₂²×C₅	1	2	yes	—
239	C₂³×C₅	—	2	1	no	—
240	C₂³×C₅	—	2	2	no	—
241	C₂³×C₅	C₂×#41	1	1	yes	characteristic
242	C₅×Q₈	—	2	1	no	—
243	C₅×Q₈	—	2	2	no	—
244	C₅×Q₈	—	2	2	no	—
245	C₅×Q₈	C₄×D₄	1	2	yes	—
246	C₅×D₄	—	2	2	no	—
247	C₅×D₄	—	2	2	no	—
248	C₅×D₄	—	2	2	no	—
249	C₅×D₄	—	2	2	no	—
250	C₅×D₄	—	2	1	no	—
251	C₅×D₄	—	4	2	no	—
252	C₅×D₄	—	4	2	no	—
253	C₅×D₄	C₄×D₄	1	2	yes	—
254	C₂×C₄×C₅	—	2	1	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	1	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	1	no	—
261	C₂×C₄×C₅	—	4	2	no	—
262	C₂×C₄×C₅	—	4	2	no	—
263	C₂×C₄×C₅	—	4	2	no	—
264	C₂×C₄×C₅	—	8	1	no	—
265	C₂×C₄×C₅	—	8	2	no	—
266	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
272	C₅×C₈	—	2	2	no	—
273	C₅×C₈	—	2	4	no	—
274	C₅×C₈	—	2	2	no	—
275	C₅×C₈	—	4	2	no	—
276	C₅×C₈	C₄×D₄	1	1	yes	characteristic
277	C₅×C₈	C₄×D₄	1	1	yes	characteristic
278	C₅×C₈	C₄×D₄	1	1	yes	characteristic
279	C₅×C₈	C₄×D₄	1	1	yes	characteristic
280	C₅×C₈	#121	1	2	yes	—
281	C₅×C₈	#121	1	2	yes	—
282	C₂×#41	C₂³×C₅	1	2	yes	—
283	C₂×#41	C₂³×C₅	1	1	yes	characteristic
284	#137	—	2	2	no	—
285	#137	C₂×C₄×C₅	1	4	yes	—
286	AGL(1,ℤ/8)	—	2	2	no	—
287	AGL(1,ℤ/8)	C₂×C₄×C₅	1	4	yes	—
288	#135	—	2	4	no	—
289	#135	—	2	1	no	—
290	#135	—	2	1	no	—
291	#135	—	2	1	no	—
292	#135	—	2	1	no	—
293	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
294	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	complemented
295	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
296	#131	—	2	1	no	—
297	#131	—	2	1	no	—
298	#131	—	2	2	no	—
299	#131	—	2	2	no	—
300	#131	—	2	2	no	—
301	#131	—	2	2	no	—
302	#131	—	2	2	no	—
303	#131	C₂×C₄×C₅	1	2	yes	—
304	#131	C₂×C₄×C₅	1	2	yes	—
305	#131	C₅×D₄	1	4	yes	—
306	C₂×M₁₆	—	2	1	no	—
307	C₂×M₁₆	—	2	1	no	—
308	C₂×M₁₆	—	2	2	no	—
309	C₂×M₁₆	C₂³×C₅	1	2	yes	—
310	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
311	C₂×M₁₆	C₂³×C₅	1	2	yes	—
312	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
313	C₂²×C₈	—	2	1	no	—
314	C₂²×C₈	—	2	1	no	—
315	C₂²×C₈	—	2	2	no	—
316	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
318	C₄×Q₈	—	2	1	no	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	2	no	—
321	#117	—	2	1	no	—
322	#117	C₂³×C₅	1	2	yes	—
323	#117	C₂³×C₅	1	1	yes	characteristic
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
326	#108	—	2	4	no	—
327	#108	—	2	1	no	—
328	#108	—	2	1	no	—
329	#108	C₂×C₄×C₅	1	2	yes	complemented
330	#108	C₂×C₄×C₅	1	2	yes	complemented
331	#107	—	2	1	no	—
332	#106	—	2	1	no	—
333	#104	—	2	4	no	—
334	#104	—	2	4	no	—
335	#104	—	2	2	no	—
336	#104	—	2	2	no	—
337	#101	C₂×C₄×C₅	1	4	yes	complemented
338	#100	C₂×C₄×C₅	1	4	yes	complemented
339	#99	—	2	4	no	—
340	#97	—	2	1	no	—
341	#97	—	2	1	no	—
342	#97	—	2	2	no	—
343	#97	—	2	1	no	—
344	#97	C₅×D₄	1	1	yes	characteristic
345	#97	C₅×D₄	1	1	yes	characteristic
346	#97	C₅×D₄	1	1	yes	characteristic
347	#97	C₅×D₄	1	1	yes	characteristic
348	C₄×C₈	—	2	1	no	—
349	C₄×C₈	—	2	1	no	—
350	C₄×C₈	—	2	2	no	—
351	C₄×C₈	—	2	1	no	—
352	C₂²×C₅	—	2	2	no	—
353	C₂²×C₅	—	4	1	no	—
354	C₂²×C₅	—	4	2	no	—
355	C₂²×C₅	—	4	2	no	—
356	C₂²×C₅	—	8	2	no	—
357	C₂²×C₅	C₄×#41	1	1	yes	characteristic
358	C₂²×C₅	#525	1	1	yes	characteristic
359	C₂²×C₅	#532	1	1	yes	characteristic
360	C₄×C₅	—	2	2	no	—
361	C₄×C₅	—	4	2	no	—
362	C₄×C₅	—	4	1	no	—
363	C₄×C₅	—	4	1	no	—
364	C₄×C₅	—	4	2	no	—
365	C₄×C₅	—	8	2	no	—
366	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
367	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
368	C₄×C₅	C₂×#121	1	1	yes	characteristic
369	C₄×C₅	#529	1	1	yes	characteristic
370	#41	—	2	1	no	—
371	#41	—	2	1	no	—
372	#41	—	2	2	no	—
373	#41	—	2	2	no	—
374	#41	—	2	2	no	—
375	#41	—	2	2	no	—
376	#41	C₂²×C₄×C₅	1	2	yes	—
377	#41	C₂×C₅×D₄	1	2	yes	—
378	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
379	C₂×Q₈	C₅×#41	1	1	yes	characteristic
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
383	C₂×D₄	C₅×#41	1	1	yes	characteristic
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
389	Q₁₆	—	2	4	no	—
390	Q₁₆	—	2	1	no	—
391	Q₁₆	—	2	1	no	—
392	SD₁₆	—	2	4	no	—
393	SD₁₆	—	2	4	no	—
394	SD₁₆	—	2	2	no	—
395	SD₁₆	—	2	2	no	—
396	D₈	—	2	4	no	—
397	D₈	—	2	1	no	—
398	D₈	—	2	1	no	—
399	M₁₆	—	2	1	no	—
400	M₁₆	—	2	1	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	2	4	no	—
405	M₁₆	—	2	2	no	—
406	M₁₆	—	2	2	no	—
407	M₁₆	—	4	2	no	—
408	M₁₆	—	4	2	no	—
409	M₁₆	C₂²×C₄×C₅	1	2	yes	—
410	M₁₆	C₂²×C₄×C₅	1	4	yes	—
411	M₁₆	C₂×C₅×D₄	1	2	yes	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	4	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	4	2	no	—
420	C₂×C₈	—	4	2	no	—
421	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
422	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
423	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
424	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
426	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
427	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
428	C₂×C₈	C₅×#41	1	1	yes	characteristic
429	C₂×C₈	C₅×#41	1	1	yes	characteristic
430	C₂×C₈	C₅×#41	1	2	yes	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	C₅×#41	1	2	yes	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	2	no	—
441	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
442	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
443	C₂×C₅	—	2	1	no	—
444	C₂×C₅	—	2	1	no	—
445	C₂×C₅	—	2	1	no	—
446	C₂×C₅	—	4	2	no	—
447	C₂×C₅	—	8	2	no	—
448	C₂×C₅	C₄×#121	1	1	yes	characteristic
449	C₂³	—	2	1	no	—
450	C₂³	—	2	2	no	—
451	C₂³	C₂×C₅×#41	1	1	yes	characteristic
452	Q₈	—	2	1	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	2	2	no	—
455	Q₈	C₄×C₅×D₄	1	2	yes	—
456	D₄	—	2	2	no	—
457	D₄	—	2	2	no	—
458	D₄	—	2	2	no	—
459	D₄	—	2	2	no	—
460	D₄	—	2	1	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	2	no	—
463	D₄	C₄×C₅×D₄	1	2	yes	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	8	1	no	—
475	C₂×C₄	—	8	2	no	—
476	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
477	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
478	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
479	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
480	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
481	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
482	C₈	—	2	2	no	—
483	C₈	—	2	4	no	—
484	C₈	—	2	2	no	—
485	C₈	—	4	2	no	—
486	C₈	C₄×C₅×D₄	1	1	yes	characteristic
487	C₈	C₄×C₅×D₄	1	1	yes	characteristic
488	C₈	C₄×C₅×D₄	1	1	yes	characteristic
489	C₈	C₄×C₅×D₄	1	1	yes	characteristic
490	C₈	C₅×#121	1	2	yes	—
491	C₈	C₅×#121	1	2	yes	—
492	C₅	#21559	1	1	yes	characteristic, direct product factor, Sylow
493	C₂²	—	2	2	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	C₄×C₅×#41	1	1	yes	characteristic
499	C₂²	C₅×#525	1	1	yes	characteristic
500	C₂²	C₅×#532	1	1	yes	characteristic
501	C₄	—	2	2	no	—
502	C₄	—	4	1	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	1	no	—
505	C₄	—	4	2	no	—
506	C₄	—	8	2	no	—
507	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
508	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
509	C₄	C₂×C₅×#121	1	1	yes	characteristic
510	C₄	C₅×#529	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	4	2	no	—
515	C₂	—	8	2	no	—
516	C₂	C₄×C₅×#121	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₂×#121
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂×C₅	C₄×#121
prime radical	C₅×#3067	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2955	C₂	semidirect
3. C₂×C₅×#444	C₂	semidirect
4. C₅×#2875	C₂	semidirect
5. C₅×#1976	C₂	semidirect
6. C₅×#1953	C₂	semidirect
7. C₅×#1932	C₂	semidirect
8. C₅×#1906	C₂	semidirect
9. C₅×#1814	C₂	semidirect
10. C₅×#1773	C₂	semidirect
11. C₅×#1757	C₂	semidirect
18. C₅×#473	C₄	semidirect
19. C₅×#472	C₄	semidirect
20. C₅×#471	C₄	semidirect
48. #21559	C₅	direct (N × H)
60. C₂×C₅×Q₁₆	C₂×C₄	semidirect
61. C₂×C₅×SD₁₆	C₂×C₄	semidirect
62. C₂×C₅×D₈	C₂×C₄	semidirect
96. C₅×#108	C₂×C₄	semidirect
97. C₅×#108	C₂×C₄	semidirect
104. C₅×#101	C₂×C₄	semidirect
105. C₅×#100	C₂×C₄	semidirect
120. #2955	C₂×C₅	semidirect
121. C₂×#444	C₂×C₅	semidirect
122. #2875	C₂×C₅	semidirect
123. #1976	C₂×C₅	semidirect
124. #1953	C₂×C₅	semidirect
125. #1932	C₂×C₅	semidirect
126. #1906	C₂×C₅	semidirect
127. #1814	C₂×C₅	semidirect
128. #1773	C₂×C₅	semidirect
129. #1757	C₂×C₅	semidirect
209. #473	C₄×C₅	semidirect
210. #472	C₄×C₅	semidirect
211. #471	C₄×C₅	semidirect
293. C₂×Q₁₆	C₂×C₄×C₅	semidirect
294. C₂×SD₁₆	C₂×C₄×C₅	semidirect
295. C₂×D₈	C₂×C₄×C₅	semidirect
329. #108	C₂×C₄×C₅	semidirect
330. #108	C₂×C₄×C₅	semidirect
337. #101	C₂×C₄×C₅	semidirect
338. #100	C₂×C₄×C₅	semidirect
492. C₅	#21559	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3067	2
C₅×#2955	2
C₂×C₅×#444	2
C₅×#2875	2
C₅×#1976	2
C₅×#1953	2
C₅×#1932	2
C₅×#1906	2
C₅×#1814	2
C₅×#1773	2
C₅×#1757	2
#21559	5

Subgroups — C5×#21559 #11944279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21559 #11944279