Subgroups — C₅×#80287 #14457681

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5837	C₂	1	2	yes	maximal, complemented
2	C₅×#5774	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#454	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5199	C₂	1	2	yes	maximal, complemented
5	C₅×#5061	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5058	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4823	C₂	1	2	yes	maximal, complemented
8	C₅×#4822	C₂	1	2	yes	maximal, complemented
9	C₅×#4754	C₂	1	2	yes	maximal, complemented
10	C₅×#3288	—	3	1	no	maximal, Hall
11	C₃×C₅×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
12	C₅×#1009	C₂²	1	2	yes	complemented
13	C₅×#1004	C₂²	1	1	yes	characteristic
14	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
15	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
16	C₅×#950	—	2	2	no	—
17	C₅×#950	C₂²	1	2	yes	—
18	C₅×#949	—	2	2	no	—
19	C₅×#949	C₂²	1	2	yes	complemented
20	C₅×#948	C₂²	1	2	yes	complemented
21	C₅×#942	—	2	2	no	—
22	C₅×#942	C₂²	1	2	yes	complemented
23	C₂×C₅×#215	—	2	2	no	—
24	C₂×C₅×#215	C₂²	1	2	yes	complemented
25	C₂×C₅×#213	C₂²	1	2	yes	complemented
26	C₅×#916	—	2	2	no	—
27	C₅×#914	—	2	2	no	—
28	C₅×#911	—	2	2	no	—
29	C₅×D₃×D₈	—	2	2	no	—
30	C₅×#908	C₂²	1	2	yes	—
31	C₅×#907	C₂²	1	2	yes	complemented
32	C₅×#874	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#104	C₂²	1	2	yes	complemented
34	C₃×C₅×#101	C₂²	1	1	yes	characteristic, complemented
35	C₅×#833	C₂²	1	1	yes	characteristic, complemented
36	C₅×#823	C₂²	1	2	yes	complemented
37	C₅×#822	C₂²	1	2	yes	complemented
38	C₅×#805	C₂²	1	2	yes	complemented
39	C₅×#803	C₂²	1	1	yes	characteristic, complemented
40	#80287	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₅×#577	—	3	2	no	—
42	C₅×#576	—	3	2	no	—
43	C₅×#496	—	3	1	no	—
44	C₅×#472	—	3	2	no	—
45	C₅×#471	—	3	2	no	—
46	C₅×#455	—	3	1	no	—
47	C₅×#454	D₃	1	1	yes	characteristic, complemented
48	C₅×#453	—	3	2	no	—
49	C₅×#444	—	3	2	no	—
50	C₃×C₅×#41	—	2	2	no	—
51	C₃×C₅×#41	—	4	1	no	—
52	C₃×C₅×#41	C₂³	1	2	yes	—
53	C₂×C₃×C₅×Q₈	—	2	2	no	—
54	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
56	C₂×C₅×#67	—	4	1	no	—
57	C₅×#239	—	2	2	no	—
58	C₅×#237	—	2	2	no	—
59	C₅×D₃×D₄	—	2	2	no	—
60	C₅×D₃×D₄	—	2	2	no	—
61	C₅×D₃×D₄	—	4	2	no	—
62	C₅×#235	—	2	2	no	—
63	C₅×#235	C₂³	1	2	yes	—
64	C₂×C₅×D₁₂	—	2	2	no	—
65	C₂×C₅×D₁₂	—	4	1	no	—
66	C₂×C₅×D₁₂	C₂³	1	2	yes	—
67	C₃×C₅×SD₁₆	—	2	2	no	—
68	C₃×C₅×D₈	—	2	2	no	—
69	C₃×C₅×M₁₆	C₂³	1	2	yes	—
70	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
71	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₅×#216	—	2	2	no	—
73	C₅×#216	D₄	1	2	yes	complemented
74	C₅×#215	—	2	2	no	—
75	C₅×#215	—	2	2	no	—
76	C₅×#215	—	2	2	no	—
77	C₅×#215	—	2	2	no	—
78	C₅×#215	D₄	1	2	yes	complemented
79	C₅×#214	D₄	1	2	yes	complemented
80	C₅×#213	—	2	2	no	—
81	C₅×#213	—	2	2	no	—
82	C₅×#213	—	2	2	no	—
83	C₅×#213	D₄	1	2	yes	complemented
84	C₅×#208	—	2	2	no	—
85	C₅×#208	C₂³	1	2	yes	—
86	C₂×C₅×C₃⋊C₈	—	2	2	no	—
87	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
88	C₅×D₂₄	—	2	2	no	—
89	C₅×#204	—	2	2	no	—
90	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
91	C₅×D₃×C₈	—	2	2	no	—
92	#5837	C₂×C₅	1	2	yes	complemented
93	#5774	C₂×C₅	1	2	yes	complemented
94	C₃×#454	C₂×C₅	1	1	yes	characteristic, complemented
95	#5199	C₂×C₅	1	2	yes	complemented
96	#5061	C₂×C₅	1	1	yes	characteristic, complemented
97	#5058	C₂×C₅	1	1	yes	characteristic, complemented
98	#4823	C₂×C₅	1	2	yes	complemented
99	#4822	C₂×C₅	1	2	yes	complemented
100	#4754	C₂×C₅	1	2	yes	complemented
101	C₅×2₋¹⁺⁴	C₂×D₃	1	1	yes	characteristic, complemented
102	C₅×H(5,𝔽₂)	—	3	2	no	—
103	C₅×H(5,𝔽₂)	—	3	1	no	—
104	C₅×#137	—	3	2	no	—
105	C₅×#137	—	6	2	no	—
106	C₅×AGL(1,ℤ/8)	—	3	2	no	—
107	C₅×AGL(1,ℤ/8)	—	3	2	no	—
108	C₅×AGL(1,ℤ/8)	—	6	2	no	—
109	C₅×AGL(1,ℤ/8)	—	6	2	no	—
110	C₅×AGL(1,ℤ/8)	—	6	2	no	—
111	C₅×AGL(1,ℤ/8)	C₂×D₃	1	2	yes	complemented
112	C₅×#135	—	3	2	no	—
113	C₅×#135	—	6	2	no	—
114	C₅×#135	—	6	2	no	—
115	C₂×C₅×SD₁₆	—	3	2	no	—
116	C₂×C₅×SD₁₆	—	6	2	no	—
117	C₂×C₅×D₈	—	3	2	no	—
118	C₂×C₅×D₈	—	6	2	no	—
119	C₅×#131	—	3	2	no	—
120	C₅×#131	—	3	2	no	—
121	C₅×#127	—	3	1	no	—
122	C₅×#124	C₂×D₃	1	1	yes	characteristic, complemented
123	C₅×#108	—	3	2	no	—
124	C₅×#104	—	3	2	no	—
125	C₅×#104	C₂×D₃	1	2	yes	complemented
126	C₅×#101	C₂×D₃	1	1	yes	characteristic, complemented
127	C₅×#100	—	3	1	no	—
128	C₅×#100	—	3	2	no	—
129	C₅×#97	—	3	1	no	—
130	#3288	—	3	1	no	Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂²×C₅×D₃	—	2	2	no	—
133	C₂²×C₅×D₃	—	4	1	no	—
134	C₂²×C₅×D₃	—	4	2	no	—
135	C₃×C₅×Q₈	—	2	2	no	—
136	C₃×C₅×Q₈	—	4	1	no	—
137	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
138	C₃×C₅×D₄	—	2	2	no	—
139	C₃×C₅×D₄	—	2	2	no	—
140	C₃×C₅×D₄	—	4	1	no	—
141	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	4	2	no	—
146	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
147	C₅×#67	—	2	2	no	—
148	C₅×#67	—	4	2	no	—
149	C₅×#67	—	4	2	no	—
150	C₂×C₅×Dic₃	—	4	1	no	—
151	C₅×D₁₂	—	2	2	no	—
152	C₅×D₁₂	—	2	2	no	—
153	C₅×D₁₂	—	4	2	no	—
154	C₅×D₁₂	—	8	2	no	—
155	C₅×D₁₂	C₂×D₄	1	2	yes	—
156	C₄×C₅×D₃	—	2	2	no	—
157	C₄×C₅×D₃	—	4	2	no	—
158	C₅×Dic₆	C₂×D₄	1	2	yes	—
159	C₃×C₅×C₈	—	2	2	no	—
160	C₅×C₃⋊C₈	—	2	2	no	—
161	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
162	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
163	C₃×2₋¹⁺⁴	C₂²×C₅	1	1	yes	characteristic, complemented
164	#1009	C₂²×C₅	1	2	yes	complemented
165	#1004	C₂²×C₅	1	1	yes	characteristic
166	C₃×AGL(1,ℤ/8)	C₂²×C₅	1	2	yes	complemented
167	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
168	#950	—	2	2	no	—
169	#950	C₂²×C₅	1	2	yes	—
170	#949	—	2	2	no	—
171	#949	C₂²×C₅	1	2	yes	complemented
172	#948	C₂²×C₅	1	2	yes	complemented
173	#942	—	2	2	no	—
174	#942	C₂²×C₅	1	2	yes	complemented
175	C₂×#215	—	2	2	no	—
176	C₂×#215	C₂²×C₅	1	2	yes	complemented
177	C₂×#213	C₂²×C₅	1	2	yes	complemented
178	#916	—	2	2	no	—
179	#914	—	2	2	no	—
180	#911	—	2	2	no	—
181	D₃×D₈	—	2	2	no	—
182	#908	C₂²×C₅	1	2	yes	—
183	#907	C₂²×C₅	1	2	yes	complemented
184	#874	C₂²×C₅	1	1	yes	characteristic, complemented
185	C₃×#104	C₂²×C₅	1	2	yes	complemented
186	C₃×#101	C₂²×C₅	1	1	yes	characteristic, complemented
187	#833	C₂²×C₅	1	1	yes	characteristic, complemented
188	#823	C₂²×C₅	1	2	yes	complemented
189	#822	C₂²×C₅	1	2	yes	complemented
190	#805	C₂²×C₅	1	2	yes	complemented
191	#803	C₂²×C₅	1	1	yes	characteristic, complemented
192	C₅×#41	—	2	2	no	—
193	C₅×#41	—	3	2	no	—
194	C₅×#41	—	4	1	no	—
195	C₅×#41	—	6	2	no	—
196	C₅×#41	—	6	2	no	—
197	C₅×#41	—	6	2	no	—
198	C₅×#41	C₂²×D₃	1	2	yes	—
199	C₂×C₅×Q₈	—	2	2	no	—
200	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
201	C₂×C₅×D₄	—	3	2	no	—
202	C₂×C₅×D₄	—	6	2	no	—
203	C₂×C₅×D₄	—	6	2	no	—
204	C₂×C₅×D₄	—	6	2	no	—
205	C₂×C₅×D₄	—	12	1	no	—
206	C₂×C₅×D₄	—	12	2	no	—
207	C₂×C₅×D₄	—	12	1	no	—
208	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
209	C₅×Q₁₆	—	3	2	no	—
210	C₅×Q₁₆	—	6	2	no	—
211	C₅×SD₁₆	—	2	2	no	—
212	C₅×SD₁₆	—	3	2	no	—
213	C₅×SD₁₆	—	3	2	no	—
214	C₅×SD₁₆	—	6	2	no	—
215	C₅×SD₁₆	—	6	2	no	—
216	C₅×SD₁₆	—	6	2	no	—
217	C₅×SD₁₆	—	6	2	no	—
218	C₅×SD₁₆	—	6	2	no	—
219	C₅×D₈	—	2	2	no	—
220	C₅×D₈	—	3	2	no	—
221	C₅×D₈	—	6	2	no	—
222	C₅×D₈	—	6	2	no	—
223	C₅×D₈	—	6	2	no	—
224	C₅×D₈	—	6	2	no	—
225	C₅×M₁₆	—	3	2	no	—
226	C₅×M₁₆	—	6	2	no	—
227	C₅×M₁₆	—	6	2	no	—
228	C₅×M₁₆	C₂²×D₃	1	2	yes	—
229	C₂×C₅×C₈	—	3	2	no	—
230	C₂×C₅×C₈	—	6	2	no	—
231	C₂×C₅×C₈	—	6	2	no	—
232	C₅×C₂²⋊C₄	—	4	1	no	—
233	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
234	#577	—	3	2	no	—
235	#576	—	3	2	no	—
236	#496	—	3	1	no	—
237	#472	—	3	2	no	—
238	#471	—	3	2	no	—
239	#455	—	3	1	no	—
240	#454	C₅×D₃	1	1	yes	characteristic, complemented
241	#453	—	3	2	no	—
242	#444	—	3	2	no	—
243	C₂²×C₃×C₅	—	2	2	no	—
244	C₂²×C₃×C₅	—	4	1	no	—
245	C₂²×C₃×C₅	—	8	1	no	—
246	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
247	C₂×C₅×D₃	—	2	2	no	—
248	C₂×C₅×D₃	—	4	2	no	—
249	C₂×C₅×D₃	—	8	2	no	—
250	C₂×C₅×D₃	—	16	1	no	—
251	C₂×C₅×D₃	—	16	2	no	—
252	C₃×C₄×C₅	—	2	2	no	—
253	C₃×C₄×C₅	—	4	1	no	—
254	C₃×C₄×C₅	—	4	1	no	—
255	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
256	C₅×Dic₃	—	2	2	no	—
257	C₃×#41	—	2	2	no	—
258	C₃×#41	—	4	1	no	—
259	C₃×#41	C₂³×C₅	1	2	yes	—
260	C₂×C₃×Q₈	—	2	2	no	—
261	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
262	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
263	C₂×#67	—	4	1	no	—
264	#239	—	2	2	no	—
265	#237	—	2	2	no	—
266	D₃×D₄	—	2	2	no	—
267	D₃×D₄	—	2	2	no	—
268	D₃×D₄	—	4	2	no	—
269	#235	—	2	2	no	—
270	#235	C₂³×C₅	1	2	yes	—
271	C₂×D₁₂	—	2	2	no	—
272	C₂×D₁₂	—	4	1	no	—
273	C₂×D₁₂	C₂³×C₅	1	2	yes	—
274	C₃×SD₁₆	—	2	2	no	—
275	C₃×D₈	—	2	2	no	—
276	C₃×M₁₆	C₂³×C₅	1	2	yes	—
277	C₃×C₂²⋊C₄	—	4	1	no	—
278	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
279	#216	—	2	2	no	—
280	#216	C₅×D₄	1	2	yes	complemented
281	#215	—	2	2	no	—
282	#215	—	2	2	no	—
283	#215	—	2	2	no	—
284	#215	—	2	2	no	—
285	#215	C₅×D₄	1	2	yes	complemented
286	#214	C₅×D₄	1	2	yes	complemented
287	#213	—	2	2	no	—
288	#213	—	2	2	no	—
289	#213	—	2	2	no	—
290	#213	C₅×D₄	1	2	yes	complemented
291	#208	—	2	2	no	—
292	#208	C₂³×C₅	1	2	yes	—
293	C₂×C₃⋊C₈	—	2	2	no	—
294	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
295	D₂₄	—	2	2	no	—
296	#204	—	2	2	no	—
297	ΓL(1,𝔽₂₅)	—	2	2	no	—
298	D₃×C₈	—	2	2	no	—
299	C₂³×C₅	—	2	1	no	—
300	C₂³×C₅	—	6	2	no	—
301	C₂³×C₅	—	12	2	no	—
302	C₂³×C₅	—	12	1	no	—
303	C₅×Q₈	—	2	2	no	—
304	C₅×Q₈	—	3	2	no	—
305	C₅×Q₈	—	4	1	no	—
306	C₅×Q₈	D₃×D₄	1	2	yes	—
307	C₅×D₄	—	2	2	no	—
308	C₅×D₄	—	2	2	no	—
309	C₅×D₄	—	3	2	no	—
310	C₅×D₄	—	4	1	no	—
311	C₅×D₄	—	6	2	no	—
312	C₅×D₄	—	6	2	no	—
313	C₅×D₄	—	6	2	no	—
314	C₅×D₄	—	12	2	no	—
315	C₅×D₄	—	12	2	no	—
316	C₅×D₄	—	12	2	no	—
317	C₅×D₄	—	24	2	no	—
318	C₅×D₄	D₃×D₄	1	2	yes	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	4	2	no	—
323	C₂×C₄×C₅	—	6	2	no	—
324	C₂×C₄×C₅	—	12	2	no	—
325	C₂×C₄×C₅	—	12	1	no	—
326	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
327	C₅×C₈	—	2	2	no	—
328	C₅×C₈	—	3	2	no	—
329	C₅×C₈	—	3	2	no	—
330	C₅×C₈	—	6	2	no	—
331	2₋¹⁺⁴	C₂×C₅×D₃	1	1	yes	characteristic, complemented
332	H(5,𝔽₂)	—	3	2	no	—
333	H(5,𝔽₂)	—	3	1	no	—
334	#137	—	3	2	no	—
335	#137	—	6	2	no	—
336	AGL(1,ℤ/8)	—	3	2	no	—
337	AGL(1,ℤ/8)	—	3	2	no	—
338	AGL(1,ℤ/8)	—	6	2	no	—
339	AGL(1,ℤ/8)	—	6	2	no	—
340	AGL(1,ℤ/8)	—	6	2	no	—
341	AGL(1,ℤ/8)	C₂×C₅×D₃	1	2	yes	complemented
342	#135	—	3	2	no	—
343	#135	—	6	2	no	—
344	#135	—	6	2	no	—
345	C₂×SD₁₆	—	3	2	no	—
346	C₂×SD₁₆	—	6	2	no	—
347	C₂×D₈	—	3	2	no	—
348	C₂×D₈	—	6	2	no	—
349	#131	—	3	2	no	—
350	#131	—	3	2	no	—
351	#127	—	3	1	no	—
352	#124	C₂×C₅×D₃	1	1	yes	characteristic, complemented
353	#108	—	3	2	no	—
354	#104	—	3	2	no	—
355	#104	C₂×C₅×D₃	1	2	yes	complemented
356	#101	C₂×C₅×D₃	1	1	yes	characteristic, complemented
357	#100	—	3	1	no	—
358	#100	—	3	2	no	—
359	#97	—	3	1	no	—
360	C₂×C₃×C₅	—	2	1	no	—
361	C₂×C₃×C₅	—	4	2	no	—
362	C₂×C₃×C₅	—	8	1	no	—
363	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
364	C₅×D₃	—	4	2	no	—
365	C₅×D₃	—	8	2	no	—
366	C₂³×C₃	—	2	1	no	—
367	C₂²×D₃	—	2	2	no	—
368	C₂²×D₃	—	4	1	no	—
369	C₂²×D₃	—	4	2	no	—
370	C₃×Q₈	—	2	2	no	—
371	C₃×Q₈	—	4	1	no	—
372	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
373	C₃×D₄	—	2	2	no	—
374	C₃×D₄	—	2	2	no	—
375	C₃×D₄	—	4	1	no	—
376	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
377	C₂×C₃×C₄	—	2	2	no	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	4	2	no	—
381	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
382	#67	—	2	2	no	—
383	#67	—	4	2	no	—
384	#67	—	4	2	no	—
385	C₂×Dic₃	—	4	1	no	—
386	D₁₂	—	2	2	no	—
387	D₁₂	—	2	2	no	—
388	D₁₂	—	4	2	no	—
389	D₁₂	—	8	2	no	—
390	D₁₂	C₂×C₅×D₄	1	2	yes	—
391	C₄×D₃	—	2	2	no	—
392	C₄×D₃	—	4	2	no	—
393	Dic₆	C₂×C₅×D₄	1	2	yes	—
394	C₃×C₈	—	2	2	no	—
395	C₃⋊C₈	—	2	2	no	—
396	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
397	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
398	C₂²×C₅	—	2	2	no	—
399	C₂²×C₅	—	4	1	no	—
400	C₂²×C₅	—	6	2	no	—
401	C₂²×C₅	—	8	1	no	—
402	C₂²×C₅	—	12	2	no	—
403	C₂²×C₅	—	24	2	no	—
404	C₂²×C₅	—	48	2	no	—
405	C₂²×C₅	—	48	1	no	—
406	C₂²×C₅	#1004	1	1	yes	characteristic
407	C₄×C₅	—	2	2	no	—
408	C₄×C₅	—	4	1	no	—
409	C₄×C₅	—	4	1	no	—
410	C₄×C₅	—	6	2	no	—
411	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
412	#41	—	2	2	no	—
413	#41	—	3	2	no	—
414	#41	—	4	1	no	—
415	#41	—	6	2	no	—
416	#41	—	6	2	no	—
417	#41	—	6	2	no	—
418	#41	C₂²×C₅×D₃	1	2	yes	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
421	C₂×D₄	—	3	2	no	—
422	C₂×D₄	—	6	2	no	—
423	C₂×D₄	—	6	2	no	—
424	C₂×D₄	—	6	2	no	—
425	C₂×D₄	—	12	1	no	—
426	C₂×D₄	—	12	2	no	—
427	C₂×D₄	—	12	1	no	—
428	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
429	Q₁₆	—	3	2	no	—
430	Q₁₆	—	6	2	no	—
431	SD₁₆	—	2	2	no	—
432	SD₁₆	—	3	2	no	—
433	SD₁₆	—	3	2	no	—
434	SD₁₆	—	6	2	no	—
435	SD₁₆	—	6	2	no	—
436	SD₁₆	—	6	2	no	—
437	SD₁₆	—	6	2	no	—
438	SD₁₆	—	6	2	no	—
439	D₈	—	2	2	no	—
440	D₈	—	3	2	no	—
441	D₈	—	6	2	no	—
442	D₈	—	6	2	no	—
443	D₈	—	6	2	no	—
444	D₈	—	6	2	no	—
445	M₁₆	—	3	2	no	—
446	M₁₆	—	6	2	no	—
447	M₁₆	—	6	2	no	—
448	M₁₆	C₂²×C₅×D₃	1	2	yes	—
449	C₂×C₈	—	3	2	no	—
450	C₂×C₈	—	6	2	no	—
451	C₂×C₈	—	6	2	no	—
452	C₂²⋊C₄	—	4	1	no	—
453	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
454	C₃×C₅	#3288	1	1	yes	characteristic, complemented, Hall
455	C₂²×C₃	—	2	2	no	—
456	C₂²×C₃	—	4	1	no	—
457	C₂²×C₃	—	8	1	no	—
458	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂×D₃	—	2	2	no	—
460	C₂×D₃	—	4	2	no	—
461	C₂×D₃	—	8	2	no	—
462	C₂×D₃	—	16	1	no	—
463	C₂×D₃	—	16	2	no	—
464	C₃×C₄	—	2	2	no	—
465	C₃×C₄	—	4	1	no	—
466	C₃×C₄	—	4	1	no	—
467	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
468	Dic₃	—	2	2	no	—
469	C₂×C₅	—	2	1	no	—
470	C₂×C₅	—	4	2	no	—
471	C₂×C₅	—	8	1	no	—
472	C₂×C₅	—	12	2	no	—
473	C₂×C₅	—	24	2	no	—
474	C₂×C₅	#5590	1	1	yes	characteristic
475	C₂³	—	2	1	no	—
476	C₂³	—	6	2	no	—
477	C₂³	—	12	2	no	—
478	C₂³	—	12	1	no	—
479	Q₈	—	2	2	no	—
480	Q₈	—	3	2	no	—
481	Q₈	—	4	1	no	—
482	Q₈	C₅×D₃×D₄	1	2	yes	—
483	D₄	—	2	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	3	2	no	—
486	D₄	—	4	1	no	—
487	D₄	—	6	2	no	—
488	D₄	—	6	2	no	—
489	D₄	—	6	2	no	—
490	D₄	—	12	2	no	—
491	D₄	—	12	2	no	—
492	D₄	—	12	2	no	—
493	D₄	—	24	2	no	—
494	D₄	C₅×D₃×D₄	1	2	yes	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	6	2	no	—
500	C₂×C₄	—	12	2	no	—
501	C₂×C₄	—	12	1	no	—
502	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
503	C₈	—	2	2	no	—
504	C₈	—	3	2	no	—
505	C₈	—	3	2	no	—
506	C₈	—	6	2	no	—
507	C₂×C₃	—	2	1	no	—
508	C₂×C₃	—	4	2	no	—
509	C₂×C₃	—	8	1	no	—
510	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
511	D₃	—	4	2	no	—
512	D₃	—	8	2	no	—
513	C₅	#80287	1	1	yes	characteristic, direct product factor, Sylow
514	C₂²	—	2	2	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	6	2	no	—
517	C₂²	—	8	1	no	—
518	C₂²	—	12	2	no	—
519	C₂²	—	24	2	no	—
520	C₂²	—	48	2	no	—
521	C₂²	—	48	1	no	—
522	C₂²	C₅×#1004	1	1	yes	characteristic
523	C₄	—	2	2	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	1	no	—
526	C₄	—	6	2	no	—
527	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
528	C₃	C₅×#3288	1	1	yes	characteristic, complemented, Sylow
529	C₂	—	2	1	no	—
530	C₂	—	4	2	no	—
531	C₂	—	8	1	no	—
532	C₂	—	12	2	no	—
533	C₂	—	24	2	no	—
534	C₂	C₅×#5590	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#5590
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#454	C₂
socle	C₂×C₃×C₅	D₄²
hypercenter	C₅×#454	D₃
hypocenter	C₃	C₅×#3288
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#454

Complements

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

N	H ≅ G/N	type
1. C₅×#5837	C₂	semidirect
2. C₅×#5774	C₂	semidirect
3. C₃×C₅×#454	C₂	semidirect
4. C₅×#5199	C₂	semidirect
5. C₅×#5061	C₂	semidirect
6. C₅×#5058	C₂	semidirect
7. C₅×#4823	C₂	semidirect
8. C₅×#4822	C₂	semidirect
9. C₅×#4754	C₂	semidirect
11. C₃×C₅×2₋¹⁺⁴	C₂²	semidirect
12. C₅×#1009	C₂²	semidirect
14. C₃×C₅×AGL(1,ℤ/8)	C₂²	semidirect
15. C₃×C₅×#124	C₂²	semidirect
19. C₅×#949	C₂²	semidirect
20. C₅×#948	C₂²	semidirect
22. C₅×#942	C₂²	semidirect
24. C₂×C₅×#215	C₂²	semidirect
25. C₂×C₅×#213	C₂²	semidirect
31. C₅×#907	C₂²	semidirect
32. C₅×#874	C₂²	semidirect
33. C₃×C₅×#104	C₂²	semidirect
34. C₃×C₅×#101	C₂²	semidirect
35. C₅×#833	C₂²	semidirect
36. C₅×#823	C₂²	semidirect
37. C₅×#822	C₂²	semidirect
38. C₅×#805	C₂²	semidirect
39. C₅×#803	C₂²	semidirect
40. #80287	C₅	direct (N × H)
47. C₅×#454	D₃	semidirect
73. C₅×#216	D₄	semidirect
78. C₅×#215	D₄	semidirect
79. C₅×#214	D₄	semidirect
83. C₅×#213	D₄	semidirect
92. #5837	C₂×C₅	semidirect
93. #5774	C₂×C₅	semidirect
94. C₃×#454	C₂×C₅	semidirect
95. #5199	C₂×C₅	semidirect
96. #5061	C₂×C₅	semidirect
97. #5058	C₂×C₅	semidirect
98. #4823	C₂×C₅	semidirect
99. #4822	C₂×C₅	semidirect
100. #4754	C₂×C₅	semidirect
101. C₅×2₋¹⁺⁴	C₂×D₃	semidirect
111. C₅×AGL(1,ℤ/8)	C₂×D₃	semidirect
122. C₅×#124	C₂×D₃	semidirect
125. C₅×#104	C₂×D₃	semidirect
126. C₅×#101	C₂×D₃	semidirect
163. C₃×2₋¹⁺⁴	C₂²×C₅	semidirect
164. #1009	C₂²×C₅	semidirect
166. C₃×AGL(1,ℤ/8)	C₂²×C₅	semidirect
167. C₃×#124	C₂²×C₅	semidirect
171. #949	C₂²×C₅	semidirect
172. #948	C₂²×C₅	semidirect
174. #942	C₂²×C₅	semidirect
176. C₂×#215	C₂²×C₅	semidirect
177. C₂×#213	C₂²×C₅	semidirect
183. #907	C₂²×C₅	semidirect
184. #874	C₂²×C₅	semidirect
185. C₃×#104	C₂²×C₅	semidirect
186. C₃×#101	C₂²×C₅	semidirect
187. #833	C₂²×C₅	semidirect
188. #823	C₂²×C₅	semidirect
189. #822	C₂²×C₅	semidirect
190. #805	C₂²×C₅	semidirect
191. #803	C₂²×C₅	semidirect
240. #454	C₅×D₃	semidirect
280. #216	C₅×D₄	semidirect
285. #215	C₅×D₄	semidirect
286. #214	C₅×D₄	semidirect
290. #213	C₅×D₄	semidirect
331. 2₋¹⁺⁴	C₂×C₅×D₃	semidirect
341. AGL(1,ℤ/8)	C₂×C₅×D₃	semidirect
352. #124	C₂×C₅×D₃	semidirect
355. #104	C₂×C₅×D₃	semidirect
356. #101	C₂×C₅×D₃	semidirect
454. C₃×C₅	#3288	semidirect
513. C₅	#80287	direct (N × H)
528. C₃	C₅×#3288	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5837	2
C₅×#5774	2
C₃×C₅×#454	2
C₅×#5199	2
C₅×#5061	2
C₅×#5058	2
C₅×#4823	2
C₅×#4822	2
C₅×#4754	2
C₅×#3288	3
#80287	5

Subgroups — C5×#80287 #14457681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80287 #14457681