Subgroups — C₅×#21558 #11944278

Order 1280.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 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×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×#131	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×#1772	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	4	no	—
22	C₅×#443	—	2	1	no	—
23	C₅×#443	—	2	1	no	—
24	C₅×#443	—	2	1	no	—
25	C₅×#443	—	2	1	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×C₄×C₅×C₈	—	2	1	no	—
44	C₂×C₄×C₅×C₈	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	#21558	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	1	no	—
66	C₅×#131	—	2	1	no	—
67	C₅×#131	—	2	2	no	—
68	C₅×#131	—	2	2	no	—
69	C₅×#131	—	2	2	no	—
70	C₅×#131	—	2	2	no	—
71	C₅×#131	C₂×C₄	1	2	yes	—
72	C₅×#131	C₂×C₄	1	2	yes	—
73	C₅×#131	D₄	1	2	yes	—
74	C₅×#131	D₄	1	2	yes	—
75	C₂×C₅×M₁₆	—	2	1	no	—
76	C₂×C₅×M₁₆	—	2	1	no	—
77	C₂×C₅×M₁₆	—	2	2	no	—
78	C₂×C₅×M₁₆	C₂³	1	2	yes	—
79	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₅×M₁₆	C₂³	1	2	yes	—
81	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
82	C₂²×C₅×C₈	—	2	1	no	—
83	C₂²×C₅×C₈	—	2	1	no	—
84	C₂²×C₅×C₈	—	2	2	no	—
85	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
87	C₄×C₅×Q₈	—	2	1	no	—
88	C₄×C₅×D₄	—	2	1	no	—
89	C₄×C₅×D₄	—	2	2	no	—
90	C₅×#117	—	2	1	no	—
91	C₅×#117	C₂³	1	2	yes	—
92	C₅×#117	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₅	—	2	1	no	—
94	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
95	C₅×#108	—	2	4	no	—
96	C₅×#108	—	2	1	no	—
97	C₅×#108	—	2	1	no	—
98	C₅×#108	C₂×C₄	1	2	yes	complemented
99	C₅×#108	C₂×C₄	1	2	yes	complemented
100	C₅×#107	—	2	1	no	—
101	C₅×#106	—	2	1	no	—
102	C₅×#104	—	2	4	no	—
103	C₅×#104	—	2	4	no	—
104	C₅×#104	—	2	2	no	—
105	C₅×#104	—	2	2	no	—
106	C₅×#101	C₂×C₄	1	4	yes	complemented
107	C₅×#100	C₂×C₄	1	4	yes	complemented
108	C₅×#99	—	2	4	no	—
109	C₅×#97	—	2	1	no	—
110	C₅×#97	—	2	1	no	—
111	C₅×#97	—	2	2	no	—
112	C₅×#97	—	2	1	no	—
113	C₄×C₅×C₈	—	2	1	no	—
114	C₄×C₅×C₈	—	2	1	no	—
115	C₄×C₅×C₈	—	2	2	no	—
116	C₄×C₅×C₈	—	2	1	no	—
117	C₄×C₅×C₈	D₄	1	1	yes	characteristic
118	C₄×C₅×C₈	D₄	1	1	yes	characteristic
119	C₄×C₅×C₈	D₄	1	1	yes	characteristic
120	C₄×C₅×C₈	D₄	1	1	yes	characteristic
121	#3067	C₂×C₅	1	1	yes	characteristic
122	#2955	C₂×C₅	1	2	yes	complemented
123	C₂×#443	C₂×C₅	1	1	yes	characteristic, complemented
124	C₄×#131	C₂×C₅	1	1	yes	characteristic, complemented
125	#1976	C₂×C₅	1	1	yes	characteristic, complemented
126	#1953	C₂×C₅	1	1	yes	characteristic, complemented
127	#1932	C₂×C₅	1	2	yes	complemented
128	#1906	C₂×C₅	1	2	yes	complemented
129	#1814	C₂×C₅	1	1	yes	characteristic, complemented
130	#1772	C₂×C₅	1	1	yes	characteristic, complemented
131	#1757	C₂×C₅	1	2	yes	complemented
132	C₅×#41	—	2	1	no	—
133	C₅×#41	—	2	1	no	—
134	C₅×#41	—	2	2	no	—
135	C₅×#41	—	2	2	no	—
136	C₅×#41	—	2	2	no	—
137	C₅×#41	—	2	2	no	—
138	C₅×#41	C₂²×C₄	1	2	yes	—
139	C₅×#41	C₂×D₄	1	2	yes	—
140	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
141	C₂×C₅×Q₈	#41	1	1	yes	characteristic
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₅×D₄	—	2	2	no	—
144	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
145	C₂×C₅×D₄	#41	1	1	yes	characteristic
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	2	no	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	2	2	no	—
150	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
151	C₅×Q₁₆	—	2	4	no	—
152	C₅×Q₁₆	—	2	1	no	—
153	C₅×Q₁₆	—	2	1	no	—
154	C₅×SD₁₆	—	2	4	no	—
155	C₅×SD₁₆	—	2	4	no	—
156	C₅×SD₁₆	—	2	2	no	—
157	C₅×SD₁₆	—	2	2	no	—
158	C₅×D₈	—	2	4	no	—
159	C₅×D₈	—	2	1	no	—
160	C₅×D₈	—	2	1	no	—
161	C₅×M₁₆	—	2	1	no	—
162	C₅×M₁₆	—	2	1	no	—
163	C₅×M₁₆	—	2	2	no	—
164	C₅×M₁₆	—	2	2	no	—
165	C₅×M₁₆	—	2	2	no	—
166	C₅×M₁₆	—	2	2	no	—
167	C₅×M₁₆	—	2	2	no	—
168	C₅×M₁₆	—	2	2	no	—
169	C₅×M₁₆	—	2	2	no	—
170	C₅×M₁₆	—	4	2	no	—
171	C₅×M₁₆	—	4	2	no	—
172	C₅×M₁₆	C₂²×C₄	1	2	yes	—
173	C₅×M₁₆	C₂²×C₄	1	4	yes	—
174	C₅×M₁₆	C₂×D₄	1	2	yes	—
175	C₂×C₅×C₈	—	2	1	no	—
176	C₂×C₅×C₈	—	2	1	no	—
177	C₂×C₅×C₈	—	2	2	no	—
178	C₂×C₅×C₈	—	2	2	no	—
179	C₂×C₅×C₈	—	2	2	no	—
180	C₂×C₅×C₈	—	2	2	no	—
181	C₂×C₅×C₈	—	2	2	no	—
182	C₂×C₅×C₈	—	2	2	no	—
183	C₂×C₅×C₈	—	4	2	no	—
184	C₂×C₅×C₈	—	4	2	no	—
185	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
192	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
193	C₂×C₅×C₈	#41	1	1	yes	characteristic
194	C₂×C₅×C₈	#41	1	1	yes	characteristic
195	C₂×C₅×C₈	#41	1	1	yes	characteristic
196	C₂×C₅×C₈	#41	1	1	yes	characteristic
197	C₅×C₄⋊C₄	—	2	2	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	—	2	2	no	—
200	C₅×C₂²⋊C₄	—	2	2	no	—
201	C₅×C₂²⋊C₄	—	2	2	no	—
202	C₅×C₂²⋊C₄	#41	1	2	yes	—
203	C₄²×C₅	—	2	2	no	—
204	C₄²×C₅	—	2	1	no	—
205	C₄²×C₅	—	2	1	no	—
206	C₄²×C₅	—	2	2	no	—
207	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
209	#575	C₂²×C₅	1	2	yes	—
210	C₂×#135	C₂²×C₅	1	1	yes	characteristic
211	C₂×#131	C₂²×C₅	1	2	yes	—
212	C₂×#131	C₂²×C₅	1	1	yes	characteristic
213	C₂×#131	C₂²×C₅	1	1	yes	characteristic
214	C₄×#41	C₂²×C₅	1	1	yes	characteristic
215	#473	C₄×C₅	1	2	yes	complemented
216	#472	C₄×C₅	1	2	yes	complemented
217	#471	C₄×C₅	1	4	yes	complemented
218	#444	—	2	4	no	—
219	#443	—	2	4	no	—
220	#443	—	2	1	no	—
221	#443	—	2	1	no	—
222	#443	—	2	1	no	—
223	#443	—	2	1	no	—
224	#430	C₂²×C₅	1	2	yes	—
225	C₂×#108	C₂²×C₅	1	1	yes	characteristic
226	C₂×#108	C₂²×C₅	1	1	yes	characteristic
227	#427	C₂²×C₅	1	1	yes	characteristic
228	#421	C₂²×C₅	1	2	yes	—
229	#421	C₂²×C₅	1	2	yes	—
230	C₂×#104	C₂²×C₅	1	2	yes	—
231	#413	C₂²×C₅	1	2	yes	—
232	#410	C₂²×C₅	1	2	yes	—
233	#405	—	2	1	no	—
234	#405	—	2	1	no	—
235	#405	C₂²×C₅	1	1	yes	characteristic
236	#405	C₂²×C₅	1	1	yes	characteristic
237	#405	C₂²×C₅	1	2	yes	—
238	C₄×M₁₆	—	2	1	no	—
239	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₄×C₈	—	2	1	no	—
241	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
242	#344	C₂²×C₅	1	2	yes	—
243	#344	C₂²×C₅	1	2	yes	—
244	#339	C₂²×C₅	1	2	yes	—
245	C₂³×C₅	—	2	1	no	—
246	C₂³×C₅	—	2	2	no	—
247	C₂³×C₅	C₂×#41	1	1	yes	characteristic
248	C₅×Q₈	—	2	1	no	—
249	C₅×Q₈	—	2	2	no	—
250	C₅×Q₈	—	2	2	no	—
251	C₅×Q₈	C₄×D₄	1	2	yes	—
252	C₅×D₄	—	2	2	no	—
253	C₅×D₄	—	2	2	no	—
254	C₅×D₄	—	2	2	no	—
255	C₅×D₄	—	2	2	no	—
256	C₅×D₄	—	2	1	no	—
257	C₅×D₄	—	4	2	no	—
258	C₅×D₄	—	4	2	no	—
259	C₅×D₄	C₄×D₄	1	2	yes	—
260	C₂×C₄×C₅	—	2	1	no	—
261	C₂×C₄×C₅	—	2	1	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	1	no	—
267	C₂×C₄×C₅	—	4	2	no	—
268	C₂×C₄×C₅	—	4	4	no	—
269	C₂×C₄×C₅	—	4	2	no	—
270	C₂×C₄×C₅	—	4	2	no	—
271	C₂×C₄×C₅	—	4	2	no	—
272	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
278	C₅×C₈	—	2	2	no	—
279	C₅×C₈	—	2	4	no	—
280	C₅×C₈	—	2	2	no	—
281	C₅×C₈	—	4	2	no	—
282	C₅×C₈	C₄×D₄	1	1	yes	characteristic
283	C₅×C₈	C₄×D₄	1	1	yes	characteristic
284	C₅×C₈	C₄×D₄	1	1	yes	characteristic
285	C₅×C₈	C₄×D₄	1	1	yes	characteristic
286	C₅×C₈	#121	1	1	yes	characteristic
287	C₅×C₈	#121	1	1	yes	characteristic
288	C₅×C₈	#121	1	1	yes	characteristic
289	C₅×C₈	#121	1	1	yes	characteristic
290	C₂×#41	C₂³×C₅	1	2	yes	—
291	C₂×#41	C₂³×C₅	1	1	yes	characteristic
292	#137	—	2	2	no	—
293	#137	C₂×C₄×C₅	1	4	yes	—
294	AGL(1,ℤ/8)	—	2	2	no	—
295	AGL(1,ℤ/8)	C₂×C₄×C₅	1	4	yes	—
296	#135	—	2	4	no	—
297	#135	—	2	1	no	—
298	#135	—	2	1	no	—
299	#135	—	2	1	no	—
300	#135	—	2	1	no	—
301	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
302	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	complemented
303	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
304	#131	—	2	1	no	—
305	#131	—	2	1	no	—
306	#131	—	2	1	no	—
307	#131	—	2	1	no	—
308	#131	—	2	2	no	—
309	#131	—	2	2	no	—
310	#131	—	2	2	no	—
311	#131	—	2	2	no	—
312	#131	C₂×C₄×C₅	1	2	yes	—
313	#131	C₂×C₄×C₅	1	2	yes	—
314	#131	C₅×D₄	1	2	yes	—
315	#131	C₅×D₄	1	2	yes	—
316	C₂×M₁₆	—	2	1	no	—
317	C₂×M₁₆	—	2	1	no	—
318	C₂×M₁₆	—	2	2	no	—
319	C₂×M₁₆	C₂³×C₅	1	2	yes	—
320	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
321	C₂×M₁₆	C₂³×C₅	1	2	yes	—
322	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
323	C₂²×C₈	—	2	1	no	—
324	C₂²×C₈	—	2	1	no	—
325	C₂²×C₈	—	2	2	no	—
326	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
328	C₄×Q₈	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	C₄×D₄	—	2	2	no	—
331	#117	—	2	1	no	—
332	#117	C₂³×C₅	1	2	yes	—
333	#117	C₂³×C₅	1	1	yes	characteristic
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
336	#108	—	2	4	no	—
337	#108	—	2	1	no	—
338	#108	—	2	1	no	—
339	#108	C₂×C₄×C₅	1	2	yes	complemented
340	#108	C₂×C₄×C₅	1	2	yes	complemented
341	#107	—	2	1	no	—
342	#106	—	2	1	no	—
343	#104	—	2	4	no	—
344	#104	—	2	4	no	—
345	#104	—	2	2	no	—
346	#104	—	2	2	no	—
347	#101	C₂×C₄×C₅	1	4	yes	complemented
348	#100	C₂×C₄×C₅	1	4	yes	complemented
349	#99	—	2	4	no	—
350	#97	—	2	1	no	—
351	#97	—	2	1	no	—
352	#97	—	2	2	no	—
353	#97	—	2	1	no	—
354	C₄×C₈	—	2	1	no	—
355	C₄×C₈	—	2	1	no	—
356	C₄×C₈	—	2	2	no	—
357	C₄×C₈	—	2	1	no	—
358	C₄×C₈	C₅×D₄	1	1	yes	characteristic
359	C₄×C₈	C₅×D₄	1	1	yes	characteristic
360	C₄×C₈	C₅×D₄	1	1	yes	characteristic
361	C₄×C₈	C₅×D₄	1	1	yes	characteristic
362	C₂²×C₅	—	2	2	no	—
363	C₂²×C₅	—	4	1	no	—
364	C₂²×C₅	—	4	2	no	—
365	C₂²×C₅	—	4	2	no	—
366	C₂²×C₅	—	8	2	no	—
367	C₂²×C₅	C₄×#41	1	1	yes	characteristic
368	C₂²×C₅	#525	1	1	yes	characteristic
369	C₂²×C₅	#532	1	1	yes	characteristic
370	C₄×C₅	—	2	2	no	—
371	C₄×C₅	—	2	2	no	—
372	C₄×C₅	—	4	2	no	—
373	C₄×C₅	—	4	1	no	—
374	C₄×C₅	—	4	2	no	—
375	C₄×C₅	—	8	2	no	—
376	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
377	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
378	C₄×C₅	C₂×#121	1	1	yes	characteristic
379	C₄×C₅	#529	1	1	yes	characteristic
380	#41	—	2	1	no	—
381	#41	—	2	1	no	—
382	#41	—	2	2	no	—
383	#41	—	2	2	no	—
384	#41	—	2	2	no	—
385	#41	—	2	2	no	—
386	#41	C₂²×C₄×C₅	1	2	yes	—
387	#41	C₂×C₅×D₄	1	2	yes	—
388	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
389	C₂×Q₈	C₅×#41	1	1	yes	characteristic
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
393	C₂×D₄	C₅×#41	1	1	yes	characteristic
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
399	Q₁₆	—	2	4	no	—
400	Q₁₆	—	2	1	no	—
401	Q₁₆	—	2	1	no	—
402	SD₁₆	—	2	4	no	—
403	SD₁₆	—	2	4	no	—
404	SD₁₆	—	2	2	no	—
405	SD₁₆	—	2	2	no	—
406	D₈	—	2	4	no	—
407	D₈	—	2	1	no	—
408	D₈	—	2	1	no	—
409	M₁₆	—	2	1	no	—
410	M₁₆	—	2	1	no	—
411	M₁₆	—	2	2	no	—
412	M₁₆	—	2	2	no	—
413	M₁₆	—	2	2	no	—
414	M₁₆	—	2	2	no	—
415	M₁₆	—	2	2	no	—
416	M₁₆	—	2	2	no	—
417	M₁₆	—	2	2	no	—
418	M₁₆	—	4	2	no	—
419	M₁₆	—	4	2	no	—
420	M₁₆	C₂²×C₄×C₅	1	2	yes	—
421	M₁₆	C₂²×C₄×C₅	1	4	yes	—
422	M₁₆	C₂×C₅×D₄	1	2	yes	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	4	2	no	—
432	C₂×C₈	—	4	2	no	—
433	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
434	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
435	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
436	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
437	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
438	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
439	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
440	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
441	C₂×C₈	C₅×#41	1	1	yes	characteristic
442	C₂×C₈	C₅×#41	1	1	yes	characteristic
443	C₂×C₈	C₅×#41	1	1	yes	characteristic
444	C₂×C₈	C₅×#41	1	1	yes	characteristic
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	C₅×#41	1	2	yes	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	2	no	—
455	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
456	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
457	C₂×C₅	—	2	1	no	—
458	C₂×C₅	—	2	1	no	—
459	C₂×C₅	—	2	1	no	—
460	C₂×C₅	—	4	2	no	—
461	C₂×C₅	—	8	2	no	—
462	C₂×C₅	C₄×#121	1	1	yes	characteristic
463	C₂³	—	2	1	no	—
464	C₂³	—	2	2	no	—
465	C₂³	C₂×C₅×#41	1	1	yes	characteristic
466	Q₈	—	2	1	no	—
467	Q₈	—	2	2	no	—
468	Q₈	—	2	2	no	—
469	Q₈	C₄×C₅×D₄	1	2	yes	—
470	D₄	—	2	2	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	1	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	C₄×C₅×D₄	1	2	yes	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
491	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
492	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
493	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
494	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
495	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
496	C₈	—	2	2	no	—
497	C₈	—	2	4	no	—
498	C₈	—	2	2	no	—
499	C₈	—	4	2	no	—
500	C₈	C₄×C₅×D₄	1	1	yes	characteristic
501	C₈	C₄×C₅×D₄	1	1	yes	characteristic
502	C₈	C₄×C₅×D₄	1	1	yes	characteristic
503	C₈	C₄×C₅×D₄	1	1	yes	characteristic
504	C₈	C₅×#121	1	1	yes	characteristic
505	C₈	C₅×#121	1	1	yes	characteristic
506	C₈	C₅×#121	1	1	yes	characteristic
507	C₈	C₅×#121	1	1	yes	characteristic
508	C₅	#21558	1	1	yes	characteristic, direct product factor, Sylow
509	C₂²	—	2	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	8	2	no	—
514	C₂²	C₄×C₅×#41	1	1	yes	characteristic
515	C₂²	C₅×#525	1	1	yes	characteristic
516	C₂²	C₅×#532	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	2	no	—
522	C₄	—	8	2	no	—
523	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
524	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
525	C₄	C₂×C₅×#121	1	1	yes	characteristic
526	C₄	C₅×#529	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	4	2	no	—
531	C₂	—	8	2	no	—
532	C₂	C₄×C₅×#121	1	1	yes	characteristic

	subgroup	G/H
center	C₅×C₈	#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 ◁ C₅×C₈ ◁ 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×#443	C₂	semidirect
4. C₄×C₅×#131	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×#1772	C₂	semidirect
11. C₅×#1757	C₂	semidirect
18. C₅×#473	C₄	semidirect
19. C₅×#472	C₄	semidirect
20. C₅×#471	C₄	semidirect
48. #21558	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
98. C₅×#108	C₂×C₄	semidirect
99. C₅×#108	C₂×C₄	semidirect
106. C₅×#101	C₂×C₄	semidirect
107. C₅×#100	C₂×C₄	semidirect
122. #2955	C₂×C₅	semidirect
123. C₂×#443	C₂×C₅	semidirect
124. C₄×#131	C₂×C₅	semidirect
125. #1976	C₂×C₅	semidirect
126. #1953	C₂×C₅	semidirect
127. #1932	C₂×C₅	semidirect
128. #1906	C₂×C₅	semidirect
129. #1814	C₂×C₅	semidirect
130. #1772	C₂×C₅	semidirect
131. #1757	C₂×C₅	semidirect
215. #473	C₄×C₅	semidirect
216. #472	C₄×C₅	semidirect
217. #471	C₄×C₅	semidirect
301. C₂×Q₁₆	C₂×C₄×C₅	semidirect
302. C₂×SD₁₆	C₂×C₄×C₅	semidirect
303. C₂×D₈	C₂×C₄×C₅	semidirect
339. #108	C₂×C₄×C₅	semidirect
340. #108	C₂×C₄×C₅	semidirect
347. #101	C₂×C₄×C₅	semidirect
348. #100	C₂×C₄×C₅	semidirect
508. C₅	#21558	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×#443	2
C₄×C₅×#131	2
C₅×#1976	2
C₅×#1953	2
C₅×#1932	2
C₅×#1906	2
C₅×#1814	2
C₅×#1772	2
C₅×#1757	2
#21558	5

Subgroups — C5×#21558 #11944278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21558 #11944278