Subgroups — C₅×#24987 #11947707

Order 1280.

638 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#471	C₂	1	1	yes	maximal, characteristic
2	C₅×#2949	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2082	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2081	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2049	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2048	C₂	1	1	yes	maximal, characteristic
7	C₅×#1977	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1953	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1905	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1904	C₂	1	1	yes	maximal, characteristic
11	C₅×#1833	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1830	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1829	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1814	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1757	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#137	C₂²	1	1	yes	characteristic
17	C₂×C₅×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₅×#131	C₂²	1	1	yes	characteristic
20	C₅×#519	C₂²	1	1	yes	characteristic
21	C₅×#518	C₂²	1	1	yes	characteristic
22	C₅×#471	—	2	2	no	—
23	C₅×#471	—	2	2	no	—
24	C₅×#440	—	2	2	no	—
25	C₄×C₅×SD₁₆	—	2	2	no	—
26	C₅×#430	C₂²	1	1	yes	characteristic
27	C₅×#430	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
32	C₅×#421	C₂²	1	1	yes	characteristic
33	C₅×#419	C₂²	1	1	yes	characteristic
34	C₅×#419	C₂²	1	1	yes	characteristic
35	C₅×#418	C₂²	1	1	yes	characteristic
36	C₅×#418	C₂²	1	1	yes	characteristic
37	C₅×#413	C₂²	1	1	yes	characteristic
38	C₂×C₅×#101	C₂²	1	1	yes	characteristic
39	C₂×C₅×#101	C₂²	1	1	yes	characteristic
40	C₂×C₅×#100	C₂²	1	1	yes	characteristic
41	C₂×C₅×#100	C₂²	1	1	yes	characteristic
42	C₅×#410	C₂²	1	1	yes	characteristic
43	C₅×#405	C₂²	1	1	yes	characteristic
44	C₅×#405	C₂²	1	1	yes	characteristic
45	C₅×#344	C₂²	1	1	yes	characteristic
46	C₅×#344	C₂²	1	1	yes	characteristic
47	C₅×#344	C₂²	1	1	yes	characteristic
48	C₅×#344	C₂²	1	1	yes	characteristic
49	C₅×#344	C₂²	1	1	yes	characteristic
50	C₅×#344	C₂²	1	1	yes	characteristic
51	C₅×#344	C₂²	1	1	yes	characteristic
52	C₅×#344	C₂²	1	1	yes	characteristic
53	C₅×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
54	C₅×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
55	#24987	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂×C₅×#41	C₂³	1	1	yes	characteristic
57	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
59	C₅×#137	—	2	2	no	—
60	C₅×#137	—	4	1	no	—
61	C₅×AGL(1,ℤ/8)	—	2	2	no	—
62	C₅×AGL(1,ℤ/8)	—	4	1	no	—
63	C₂×C₅×Q₁₆	—	2	1	no	—
64	C₂×C₅×SD₁₆	—	2	1	no	—
65	C₂×C₅×SD₁₆	—	2	1	no	—
66	C₂×C₅×SD₁₆	—	2	1	no	—
67	C₂×C₅×SD₁₆	—	2	1	no	—
68	C₂×C₅×SD₁₆	—	2	1	no	—
69	C₂×C₅×SD₁₆	—	2	1	no	—
70	C₂×C₅×SD₁₆	D₄	1	2	yes	—
71	C₂×C₅×SD₁₆	D₄	1	2	yes	—
72	C₂×C₅×D₈	—	2	1	no	—
73	C₅×#131	—	2	1	no	—
74	C₅×#131	—	2	1	no	—
75	C₅×#131	—	2	1	no	—
76	C₅×#131	—	2	1	no	—
77	C₂×C₅×M₁₆	—	2	1	no	—
78	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
83	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
85	C₂²×C₅×C₈	—	2	1	no	—
86	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
87	C₄×C₅×Q₈	—	2	2	no	—
88	C₄×C₅×Q₈	—	4	1	no	—
89	C₄×C₅×D₄	—	2	2	no	—
90	C₄×C₅×D₄	—	4	1	no	—
91	C₅×#117	—	2	2	no	—
92	C₅×#117	C₂³	1	1	yes	characteristic
93	C₅×#117	C₂³	1	1	yes	characteristic
94	C₅×#117	C₂³	1	1	yes	characteristic
95	C₅×#117	C₂³	1	1	yes	characteristic
96	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
97	C₅×#108	—	2	1	no	—
98	C₅×#108	—	2	1	no	—
99	C₅×#108	—	2	1	no	—
100	C₅×#108	—	2	1	no	—
101	C₅×#108	—	4	1	no	—
102	C₅×#108	—	4	1	no	—
103	C₅×#107	—	2	1	no	—
104	C₅×#106	—	2	1	no	—
105	C₅×#104	—	4	1	no	—
106	C₅×#104	—	4	1	no	—
107	C₅×#103	—	2	2	no	—
108	C₅×#103	—	4	1	no	—
109	C₅×#102	—	2	2	no	—
110	C₅×#102	—	4	1	no	—
111	C₅×#101	—	2	2	no	—
112	C₅×#101	—	2	1	no	—
113	C₅×#101	—	4	1	no	—
114	C₅×#100	—	2	2	no	—
115	C₅×#100	—	2	1	no	—
116	C₅×#100	—	4	1	no	—
117	C₅×#99	—	2	2	no	—
118	C₅×#97	—	2	1	no	—
119	C₅×#97	—	2	1	no	—
120	C₄×C₅×C₈	—	2	1	no	—
121	C₄×C₅×C₈	—	2	1	no	—
122	C₂×#471	C₂×C₅	1	1	yes	characteristic
123	#2949	C₂×C₅	1	1	yes	characteristic, complemented
124	#2082	C₂×C₅	1	1	yes	characteristic, complemented
125	#2081	C₂×C₅	1	1	yes	characteristic, complemented
126	#2049	C₂×C₅	1	1	yes	characteristic, complemented
127	#2048	C₂×C₅	1	1	yes	characteristic
128	#1977	C₂×C₅	1	1	yes	characteristic, complemented
129	#1953	C₂×C₅	1	1	yes	characteristic, complemented
130	#1905	C₂×C₅	1	1	yes	characteristic, complemented
131	#1904	C₂×C₅	1	1	yes	characteristic
132	#1833	C₂×C₅	1	1	yes	characteristic, complemented
133	#1830	C₂×C₅	1	1	yes	characteristic, complemented
134	#1829	C₂×C₅	1	1	yes	characteristic, complemented
135	#1814	C₂×C₅	1	1	yes	characteristic, complemented
136	#1757	C₂×C₅	1	1	yes	characteristic, complemented
137	C₂⁴×C₅	—	2	1	no	—
138	C₅×#41	—	2	1	no	—
139	C₅×#41	—	2	1	no	—
140	C₅×#41	—	2	1	no	—
141	C₅×#41	—	2	1	no	—
142	C₂×C₅×Q₈	—	2	1	no	—
143	C₂×C₅×Q₈	—	2	1	no	—
144	C₂×C₅×Q₈	—	2	1	no	—
145	C₂×C₅×Q₈	—	2	1	no	—
146	C₂×C₅×Q₈	—	2	1	no	—
147	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
148	C₂×C₅×Q₈	#41	1	1	yes	characteristic
149	C₂×C₅×D₄	—	2	1	no	—
150	C₂×C₅×D₄	—	2	1	no	—
151	C₂×C₅×D₄	—	2	1	no	—
152	C₂×C₅×D₄	—	2	1	no	—
153	C₂×C₅×D₄	—	2	1	no	—
154	C₂×C₅×D₄	—	2	1	no	—
155	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
156	C₂×C₅×D₄	#41	1	1	yes	characteristic
157	C₂²×C₄×C₅	—	2	1	no	—
158	C₂²×C₄×C₅	—	2	1	no	—
159	C₂²×C₄×C₅	—	4	2	no	—
160	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
161	C₅×Q₁₆	—	4	2	no	—
162	C₅×SD₁₆	—	2	2	no	—
163	C₅×SD₁₆	—	2	2	no	—
164	C₅×SD₁₆	—	2	2	no	—
165	C₅×SD₁₆	—	2	2	no	—
166	C₅×SD₁₆	—	4	2	no	—
167	C₅×SD₁₆	—	4	2	no	—
168	C₅×D₈	—	4	2	no	—
169	C₅×M₁₆	—	2	1	no	—
170	C₅×M₁₆	—	2	1	no	—
171	C₅×M₁₆	—	2	1	no	—
172	C₅×M₁₆	—	2	1	no	—
173	C₅×M₁₆	—	2	1	no	—
174	C₅×M₁₆	—	2	1	no	—
175	C₅×M₁₆	—	2	1	no	—
176	C₅×M₁₆	—	2	1	no	—
177	C₅×M₁₆	—	2	1	no	—
178	C₅×M₁₆	—	2	1	no	—
179	C₅×M₁₆	—	2	1	no	—
180	C₅×M₁₆	—	2	1	no	—
181	C₅×M₁₆	—	2	1	no	—
182	C₅×M₁₆	—	2	1	no	—
183	C₅×M₁₆	—	4	1	no	—
184	C₅×M₁₆	—	4	1	no	—
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	2	1	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	4	1	no	—
193	C₂×C₅×C₈	—	4	1	no	—
194	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
195	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
196	C₂×C₅×C₈	#41	1	1	yes	characteristic
197	C₂×C₅×C₈	#41	1	1	yes	characteristic
198	C₂×C₅×C₈	#41	1	1	yes	characteristic
199	C₂×C₅×C₈	#41	1	1	yes	characteristic
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	—	4	2	no	—
205	C₅×C₂²⋊C₄	—	2	1	no	—
206	C₅×C₂²⋊C₄	—	2	1	no	—
207	C₅×C₂²⋊C₄	—	2	1	no	—
208	C₅×C₂²⋊C₄	—	4	2	no	—
209	C₅×C₂²⋊C₄	#41	1	2	yes	—
210	C₄²×C₅	—	2	1	no	—
211	C₄²×C₅	—	2	1	no	—
212	C₄²×C₅	—	2	1	no	—
213	C₄²×C₅	—	2	1	no	—
214	C₄²×C₅	—	4	2	no	—
215	C₂×#137	C₂²×C₅	1	1	yes	characteristic
216	C₂×AGL(1,ℤ/8)	C₂²×C₅	1	1	yes	characteristic
217	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
218	C₂×#131	C₂²×C₅	1	1	yes	characteristic
219	#519	C₂²×C₅	1	1	yes	characteristic
220	#518	C₂²×C₅	1	1	yes	characteristic
221	#471	—	2	2	no	—
222	#471	—	2	2	no	—
223	#440	—	2	2	no	—
224	C₄×SD₁₆	—	2	2	no	—
225	#430	C₂²×C₅	1	1	yes	characteristic
226	#430	C₂²×C₅	1	1	yes	characteristic
227	C₂×#108	C₂²×C₅	1	1	yes	characteristic
228	C₂×#108	C₂²×C₅	1	1	yes	characteristic
229	#427	C₂²×C₅	1	1	yes	characteristic
230	#421	C₂²×C₅	1	1	yes	characteristic
231	#421	C₂²×C₅	1	1	yes	characteristic
232	#419	C₂²×C₅	1	1	yes	characteristic
233	#419	C₂²×C₅	1	1	yes	characteristic
234	#418	C₂²×C₅	1	1	yes	characteristic
235	#418	C₂²×C₅	1	1	yes	characteristic
236	#413	C₂²×C₅	1	1	yes	characteristic
237	C₂×#101	C₂²×C₅	1	1	yes	characteristic
238	C₂×#101	C₂²×C₅	1	1	yes	characteristic
239	C₂×#100	C₂²×C₅	1	1	yes	characteristic
240	C₂×#100	C₂²×C₅	1	1	yes	characteristic
241	#410	C₂²×C₅	1	1	yes	characteristic
242	#405	C₂²×C₅	1	1	yes	characteristic
243	#405	C₂²×C₅	1	1	yes	characteristic
244	#344	C₂²×C₅	1	1	yes	characteristic
245	#344	C₂²×C₅	1	1	yes	characteristic
246	#344	C₂²×C₅	1	1	yes	characteristic
247	#344	C₂²×C₅	1	1	yes	characteristic
248	#344	C₂²×C₅	1	1	yes	characteristic
249	#344	C₂²×C₅	1	1	yes	characteristic
250	#344	C₂²×C₅	1	1	yes	characteristic
251	#344	C₂²×C₅	1	1	yes	characteristic
252	H(3,ℤ/4)	C₂²×C₅	1	1	yes	characteristic
253	H(3,ℤ/4)	C₂²×C₅	1	1	yes	characteristic
254	C₂³×C₅	—	2	1	no	—
255	C₂³×C₅	—	2	2	no	—
256	C₂³×C₅	—	4	1	no	—
257	C₂³×C₅	—	4	1	no	—
258	C₂³×C₅	—	16	1	no	—
259	C₂³×C₅	C₂×#41	1	1	yes	characteristic
260	C₅×Q₈	—	2	2	no	—
261	C₅×Q₈	—	2	1	no	—
262	C₅×Q₈	—	2	2	no	—
263	C₅×Q₈	—	2	1	no	—
264	C₅×Q₈	—	4	1	no	—
265	C₅×Q₈	—	4	1	no	—
266	C₅×D₄	—	2	2	no	—
267	C₅×D₄	—	2	1	no	—
268	C₅×D₄	—	2	2	no	—
269	C₅×D₄	—	2	1	no	—
270	C₅×D₄	—	4	1	no	—
271	C₅×D₄	—	4	1	no	—
272	C₅×D₄	—	4	1	no	—
273	C₅×D₄	—	4	1	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	4	1	no	—
278	C₂×C₄×C₅	—	4	1	no	—
279	C₂×C₄×C₅	—	4	1	no	—
280	C₂×C₄×C₅	—	4	1	no	—
281	C₂×C₄×C₅	—	4	1	no	—
282	C₂×C₄×C₅	—	4	1	no	—
283	C₂×C₄×C₅	—	4	1	no	—
284	C₂×C₄×C₅	—	16	2	no	—
285	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
290	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
291	C₅×C₈	—	4	1	no	—
292	C₅×C₈	—	4	1	no	—
293	C₅×C₈	—	4	1	no	—
294	C₅×C₈	—	4	1	no	—
295	C₅×C₈	—	4	1	no	—
296	C₅×C₈	—	4	1	no	—
297	C₅×C₈	—	4	1	no	—
298	C₅×C₈	#123	1	1	yes	characteristic
299	C₅×C₈	#123	1	1	yes	characteristic
300	C₅×C₈	#123	1	1	yes	characteristic
301	C₅×C₈	#123	1	1	yes	characteristic
302	C₂×#41	C₂³×C₅	1	1	yes	characteristic
303	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
304	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
305	#137	—	2	2	no	—
306	#137	—	4	1	no	—
307	AGL(1,ℤ/8)	—	2	2	no	—
308	AGL(1,ℤ/8)	—	4	1	no	—
309	C₂×Q₁₆	—	2	1	no	—
310	C₂×SD₁₆	—	2	1	no	—
311	C₂×SD₁₆	—	2	1	no	—
312	C₂×SD₁₆	—	2	1	no	—
313	C₂×SD₁₆	—	2	1	no	—
314	C₂×SD₁₆	—	2	1	no	—
315	C₂×SD₁₆	—	2	1	no	—
316	C₂×SD₁₆	C₅×D₄	1	2	yes	—
317	C₂×SD₁₆	C₅×D₄	1	2	yes	—
318	C₂×D₈	—	2	1	no	—
319	#131	—	2	1	no	—
320	#131	—	2	1	no	—
321	#131	—	2	1	no	—
322	#131	—	2	1	no	—
323	C₂×M₁₆	—	2	1	no	—
324	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
325	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
326	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
327	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
328	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
329	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
330	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
331	C₂²×C₈	—	2	1	no	—
332	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	—	4	1	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	—	4	1	no	—
337	#117	—	2	2	no	—
338	#117	C₂³×C₅	1	1	yes	characteristic
339	#117	C₂³×C₅	1	1	yes	characteristic
340	#117	C₂³×C₅	1	1	yes	characteristic
341	#117	C₂³×C₅	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	#108	—	2	1	no	—
344	#108	—	2	1	no	—
345	#108	—	2	1	no	—
346	#108	—	2	1	no	—
347	#108	—	4	1	no	—
348	#108	—	4	1	no	—
349	#107	—	2	1	no	—
350	#106	—	2	1	no	—
351	#104	—	4	1	no	—
352	#104	—	4	1	no	—
353	#103	—	2	2	no	—
354	#103	—	4	1	no	—
355	#102	—	2	2	no	—
356	#102	—	4	1	no	—
357	#101	—	2	2	no	—
358	#101	—	2	1	no	—
359	#101	—	4	1	no	—
360	#100	—	2	2	no	—
361	#100	—	2	1	no	—
362	#100	—	4	1	no	—
363	#99	—	2	2	no	—
364	#97	—	2	1	no	—
365	#97	—	2	1	no	—
366	C₄×C₈	—	2	1	no	—
367	C₄×C₈	—	2	1	no	—
368	C₂²×C₅	—	4	1	no	—
369	C₂²×C₅	—	4	1	no	—
370	C₂²×C₅	—	4	2	no	—
371	C₂²×C₅	—	8	2	no	—
372	C₂²×C₅	—	8	1	no	—
373	C₂²×C₅	—	16	1	no	—
374	C₂²×C₅	—	16	1	no	—
375	C₂²×C₅	#529	1	1	yes	characteristic
376	C₂²×C₅	#546	1	1	yes	characteristic
377	C₂²×C₅	#555	1	1	yes	characteristic
378	C₄×C₅	—	4	2	no	—
379	C₄×C₅	—	4	1	no	—
380	C₄×C₅	—	4	2	no	—
381	C₄×C₅	—	8	1	no	—
382	C₄×C₅	—	8	1	no	—
383	C₄×C₅	—	8	1	no	—
384	C₄×C₅	C₂×#123	1	1	yes	characteristic
385	C₄×C₅	#540	1	1	yes	characteristic
386	C₄×C₅	#546	1	1	yes	characteristic
387	C₄×C₅	#553	1	1	yes	characteristic
388	C₂⁴	—	2	1	no	—
389	#41	—	2	1	no	—
390	#41	—	2	1	no	—
391	#41	—	2	1	no	—
392	#41	—	2	1	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
399	C₂×Q₈	C₅×#41	1	1	yes	characteristic
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
407	C₂×D₄	C₅×#41	1	1	yes	characteristic
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
412	Q₁₆	—	4	2	no	—
413	SD₁₆	—	2	2	no	—
414	SD₁₆	—	2	2	no	—
415	SD₁₆	—	2	2	no	—
416	SD₁₆	—	2	2	no	—
417	SD₁₆	—	4	2	no	—
418	SD₁₆	—	4	2	no	—
419	D₈	—	4	2	no	—
420	M₁₆	—	2	1	no	—
421	M₁₆	—	2	1	no	—
422	M₁₆	—	2	1	no	—
423	M₁₆	—	2	1	no	—
424	M₁₆	—	2	1	no	—
425	M₁₆	—	2	1	no	—
426	M₁₆	—	2	1	no	—
427	M₁₆	—	2	1	no	—
428	M₁₆	—	2	1	no	—
429	M₁₆	—	2	1	no	—
430	M₁₆	—	2	1	no	—
431	M₁₆	—	2	1	no	—
432	M₁₆	—	2	1	no	—
433	M₁₆	—	2	1	no	—
434	M₁₆	—	4	1	no	—
435	M₁₆	—	4	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	4	1	no	—
444	C₂×C₈	—	4	1	no	—
445	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
446	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
447	C₂×C₈	C₅×#41	1	1	yes	characteristic
448	C₂×C₈	C₅×#41	1	1	yes	characteristic
449	C₂×C₈	C₅×#41	1	1	yes	characteristic
450	C₂×C₈	C₅×#41	1	1	yes	characteristic
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	4	2	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	4	2	no	—
460	C₂²⋊C₄	C₅×#41	1	2	yes	—
461	C₄²	—	2	1	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	4	2	no	—
466	C₂×C₅	—	2	1	no	—
467	C₂×C₅	—	2	1	no	—
468	C₂×C₅	—	2	1	no	—
469	C₂×C₅	—	8	1	no	—
470	C₂×C₅	—	8	2	no	—
471	C₂×C₅	#2420	1	1	yes	characteristic
472	C₂³	—	2	1	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	4	1	no	—
475	C₂³	—	4	1	no	—
476	C₂³	—	16	1	no	—
477	C₂³	C₂×C₅×#41	1	1	yes	characteristic
478	Q₈	—	2	2	no	—
479	Q₈	—	2	1	no	—
480	Q₈	—	2	2	no	—
481	Q₈	—	2	1	no	—
482	Q₈	—	4	1	no	—
483	Q₈	—	4	1	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	1	no	—
486	D₄	—	2	2	no	—
487	D₄	—	2	1	no	—
488	D₄	—	4	1	no	—
489	D₄	—	4	1	no	—
490	D₄	—	4	1	no	—
491	D₄	—	4	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	16	2	no	—
503	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
504	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
505	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
506	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
507	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
508	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
509	C₈	—	4	1	no	—
510	C₈	—	4	1	no	—
511	C₈	—	4	1	no	—
512	C₈	—	4	1	no	—
513	C₈	—	4	1	no	—
514	C₈	—	4	1	no	—
515	C₈	—	4	1	no	—
516	C₈	C₅×#123	1	1	yes	characteristic
517	C₈	C₅×#123	1	1	yes	characteristic
518	C₈	C₅×#123	1	1	yes	characteristic
519	C₈	C₅×#123	1	1	yes	characteristic
520	C₅	#24987	1	1	yes	characteristic, direct product factor, Sylow
521	C₂²	—	4	1	no	—
522	C₂²	—	4	1	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	8	2	no	—
525	C₂²	—	8	1	no	—
526	C₂²	—	16	1	no	—
527	C₂²	—	16	1	no	—
528	C₂²	C₅×#529	1	1	yes	characteristic
529	C₂²	C₅×#546	1	1	yes	characteristic
530	C₂²	C₅×#555	1	1	yes	characteristic
531	C₄	—	4	2	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	2	no	—
534	C₄	—	8	1	no	—
535	C₄	—	8	1	no	—
536	C₄	—	8	1	no	—
537	C₄	C₂×C₅×#123	1	1	yes	characteristic
538	C₄	C₅×#540	1	1	yes	characteristic
539	C₄	C₅×#546	1	1	yes	characteristic
540	C₄	C₅×#553	1	1	yes	characteristic
541	C₂	—	2	1	no	—
542	C₂	—	2	1	no	—
543	C₂	—	2	1	no	—
544	C₂	—	8	2	no	—
545	C₂	—	8	1	no	—
546	C₂	C₅×#2420	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	#2420
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2949	C₂	semidirect
3. C₅×#2082	C₂	semidirect
4. C₅×#2081	C₂	semidirect
5. C₅×#2049	C₂	semidirect
7. C₅×#1977	C₂	semidirect
8. C₅×#1953	C₂	semidirect
9. C₅×#1905	C₂	semidirect
11. C₅×#1833	C₂	semidirect
12. C₅×#1830	C₂	semidirect
13. C₅×#1829	C₂	semidirect
14. C₅×#1814	C₂	semidirect
15. C₅×#1757	C₂	semidirect
55. #24987	C₅	direct (N × H)
123. #2949	C₂×C₅	semidirect
124. #2082	C₂×C₅	semidirect
125. #2081	C₂×C₅	semidirect
126. #2049	C₂×C₅	semidirect
128. #1977	C₂×C₅	semidirect
129. #1953	C₂×C₅	semidirect
130. #1905	C₂×C₅	semidirect
132. #1833	C₂×C₅	semidirect
133. #1830	C₂×C₅	semidirect
134. #1829	C₂×C₅	semidirect
135. #1814	C₂×C₅	semidirect
136. #1757	C₂×C₅	semidirect
520. C₅	#24987	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#471	2
C₅×#2949	2
C₅×#2082	2
C₅×#2081	2
C₅×#2049	2
C₅×#2048	2
C₅×#1977	2
C₅×#1953	2
C₅×#1905	2
C₅×#1904	2
C₅×#1833	2
C₅×#1830	2
C₅×#1829	2
C₅×#1814	2
C₅×#1757	2
#24987	5

Subgroups — C5×#24987 #11947707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#24987 #11947707