Subgroups — C₅×#82024 #14478534

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5766	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5757	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5179	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5147	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4916	C₂	1	2	yes	maximal, complemented
7	C₅×#4915	C₂	1	2	yes	maximal, complemented
8	C₅×#4914	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×SD₃₂	C₂	1	2	yes	maximal, complemented
10	C₅×#4904	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4901	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3416	—	3	1	no	maximal, Hall
13	C₅×#1007	—	2	1	no	—
14	C₅×#1004	—	2	1	no	—
15	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
17	C₅×#942	—	2	1	no	—
18	C₅×#932	—	2	1	no	—
19	C₅×#919	C₂²	1	2	yes	complemented
20	C₅×#918	—	2	2	no	—
21	C₅×D₃×Q₁₆	C₂²	1	2	yes	complemented
22	C₅×#912	C₂²	1	2	yes	—
23	C₅×#911	—	2	2	no	—
24	C₅×D₃×D₈	C₂²	1	2	yes	—
25	C₅×#904	C₂²	1	1	yes	characteristic
26	C₅×#904	C₂²	1	1	yes	characteristic, complemented
27	C₅×#901	C₂²	1	1	yes	characteristic
28	C₃×C₅×SD₃₂	C₂²	1	2	yes	complemented
29	C₃×C₅×SD₃₂	C₂²	1	2	yes	complemented
30	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₅×#829	C₂²	1	2	yes	complemented
32	C₅×#828	C₂²	1	2	yes	complemented
33	C₅×#827	C₂²	1	2	yes	complemented
34	C₅×#826	C₂²	1	2	yes	complemented
35	C₅×#812	C₂²	1	1	yes	characteristic, complemented
36	C₅×Dic₂₄	C₂²	1	1	yes	characteristic, complemented
37	C₅×#800	C₂²	1	1	yes	characteristic, complemented
38	C₅×#800	C₂²	1	1	yes	characteristic, complemented
39	C₅×D₄₈	C₂²	1	1	yes	characteristic, complemented
40	C₅×#798	C₂²	1	2	yes	complemented
41	C₅×D₃×C₁₆	C₂²	1	2	yes	complemented
42	#82024	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#578	—	3	1	no	—
44	C₅×#576	—	3	1	no	—
45	C₅×#510	—	3	2	no	—
46	C₅×#510	—	3	1	no	—
47	C₅×#509	—	3	2	no	—
48	C₅×#509	—	3	1	no	—
49	C₅×#508	—	3	2	no	—
50	C₅×#508	—	3	1	no	—
51	C₂×C₅×SD₃₂	—	3	2	no	—
52	C₂×C₅×SD₃₂	D₃	1	1	yes	characteristic, complemented
53	C₅×#504	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	—	2	1	no	—
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₅×#67	—	4	2	no	—
57	C₅×#239	—	2	2	no	—
58	C₅×#239	—	4	1	no	—
59	C₅×D₃×Q₈	—	2	2	no	—
60	C₅×D₃×Q₈	—	4	1	no	—
61	C₅×#237	—	2	2	no	—
62	C₅×#237	—	4	1	no	—
63	C₅×D₃×D₄	—	2	2	no	—
64	C₅×D₃×D₄	—	4	1	no	—
65	C₅×#235	—	2	1	no	—
66	C₅×#235	—	2	1	no	—
67	C₅×#235	—	4	2	no	—
68	C₅×#235	D₄	1	1	yes	characteristic
69	C₃×C₅×Q₁₆	—	2	1	no	—
70	C₃×C₅×Q₁₆	C₂³	1	2	yes	—
71	C₃×C₅×D₈	—	2	1	no	—
72	C₃×C₅×D₈	C₂³	1	2	yes	—
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₅×#216	—	2	2	no	—
75	C₅×#215	—	2	2	no	—
76	C₅×#214	—	2	2	no	—
77	C₅×#213	—	2	2	no	—
78	C₅×#208	D₄	1	1	yes	characteristic
79	C₅×Dic₁₂	C₂³	1	1	yes	characteristic
80	C₅×Dic₁₂	C₂³	1	1	yes	characteristic
81	C₅×D₂₄	C₂³	1	1	yes	characteristic
82	C₅×D₂₄	C₂³	1	1	yes	characteristic
83	C₅×#204	—	2	1	no	—
84	C₅×#204	—	2	1	no	—
85	C₅×ΓL(1,𝔽₂₅)	D₄	1	2	yes	—
86	C₅×D₃×C₈	C₂³	1	2	yes	—
87	C₃×C₅×C₁₆	C₂³	1	1	yes	characteristic
88	C₃×C₅×C₁₆	C₂³	1	1	yes	characteristic
89	C₅×C₃⋊C₁₆	C₂³	1	2	yes	—
90	#5766	C₂×C₅	1	1	yes	characteristic, complemented
91	#5757	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂×C₃×SD₃₂	C₂×C₅	1	1	yes	characteristic, complemented
93	#5179	C₂×C₅	1	1	yes	characteristic, complemented
94	#5147	C₂×C₅	1	1	yes	characteristic, complemented
95	#4916	C₂×C₅	1	2	yes	complemented
96	#4915	C₂×C₅	1	2	yes	complemented
97	#4914	C₂×C₅	1	2	yes	complemented
98	D₃×SD₃₂	C₂×C₅	1	2	yes	complemented
99	#4904	C₂×C₅	1	1	yes	characteristic, complemented
100	#4901	C₂×C₅	1	1	yes	characteristic, complemented
101	C₅×2₋¹⁺⁴	—	6	1	no	—
102	C₅×H(5,𝔽₂)	—	6	1	no	—
103	C₅×#137	—	6	2	no	—
104	C₅×#137	—	6	1	no	—
105	C₅×AGL(1,ℤ/8)	—	6	2	no	—
106	C₅×AGL(1,ℤ/8)	—	6	1	no	—
107	C₅×#135	—	3	2	no	—
108	C₅×#135	—	3	2	no	—
109	C₅×#135	—	3	1	no	—
110	C₅×#135	—	3	1	no	—
111	C₂×C₅×Q₁₆	—	3	2	no	—
112	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
113	C₂×C₅×D₈	—	3	2	no	—
114	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
115	C₅×#131	—	3	1	no	—
116	C₅×Q₃₂	—	3	2	no	—
117	C₅×Q₃₂	—	3	1	no	—
118	C₅×SD₃₂	—	3	2	no	—
119	C₅×SD₃₂	—	3	2	no	—
120	C₅×SD₃₂	—	3	1	no	—
121	C₅×SD₃₂	—	3	1	no	—
122	C₅×SD₃₂	C₂×D₃	1	2	yes	complemented
123	C₅×SD₃₂	C₂×D₃	1	2	yes	complemented
124	C₅×D₁₆	—	3	2	no	—
125	C₅×D₁₆	—	3	1	no	—
126	C₅×M₃₂	—	3	1	no	—
127	C₅×M₃₂	—	3	2	no	—
128	C₂×C₅×C₁₆	—	3	2	no	—
129	C₂×C₅×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
130	#3416	—	3	1	no	Sylow
131	C₂³×C₃×C₅	—	4	1	no	—
132	C₂²×C₅×D₃	—	4	2	no	—
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×Q₈	—	4	1	no	—
135	C₃×C₅×D₄	—	2	2	no	—
136	C₃×C₅×D₄	—	4	1	no	—
137	C₂×C₃×C₄×C₅	—	4	1	no	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₅×#67	—	4	1	no	—
140	C₅×#67	—	4	1	no	—
141	C₅×#67	—	4	2	no	—
142	C₅×#67	—	4	2	no	—
143	C₅×#67	D₈	1	2	yes	—
144	C₂×C₅×Dic₃	—	4	2	no	—
145	C₅×D₁₂	—	2	1	no	—
146	C₅×D₁₂	—	2	1	no	—
147	C₅×D₁₂	—	4	2	no	—
148	C₅×D₁₂	D₈	1	1	yes	characteristic
149	C₄×C₅×D₃	—	4	2	no	—
150	C₄×C₅×D₃	—	4	1	no	—
151	C₄×C₅×D₃	—	4	1	no	—
152	C₄×C₅×D₃	—	4	2	no	—
153	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
154	C₅×Dic₆	—	2	1	no	—
155	C₅×Dic₆	—	2	1	no	—
156	C₅×Dic₆	—	4	2	no	—
157	C₅×Dic₆	D₈	1	1	yes	characteristic
158	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
159	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
160	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
161	#1007	—	2	1	no	—
162	#1004	—	2	1	no	—
163	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
164	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
165	#942	—	2	1	no	—
166	#932	—	2	1	no	—
167	#919	C₂²×C₅	1	2	yes	complemented
168	#918	—	2	2	no	—
169	D₃×Q₁₆	C₂²×C₅	1	2	yes	complemented
170	#912	C₂²×C₅	1	2	yes	—
171	#911	—	2	2	no	—
172	D₃×D₈	C₂²×C₅	1	2	yes	—
173	#904	C₂²×C₅	1	1	yes	characteristic
174	#904	C₂²×C₅	1	1	yes	characteristic, complemented
175	#901	C₂²×C₅	1	1	yes	characteristic
176	C₃×SD₃₂	C₂²×C₅	1	2	yes	complemented
177	C₃×SD₃₂	C₂²×C₅	1	2	yes	complemented
178	C₂×C₃×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
179	#829	C₂²×C₅	1	2	yes	complemented
180	#828	C₂²×C₅	1	2	yes	complemented
181	#827	C₂²×C₅	1	2	yes	complemented
182	#826	C₂²×C₅	1	2	yes	complemented
183	#812	C₂²×C₅	1	1	yes	characteristic, complemented
184	Dic₂₄	C₂²×C₅	1	1	yes	characteristic, complemented
185	#800	C₂²×C₅	1	1	yes	characteristic, complemented
186	#800	C₂²×C₅	1	1	yes	characteristic, complemented
187	D₄₈	C₂²×C₅	1	1	yes	characteristic, complemented
188	#798	C₂²×C₅	1	2	yes	complemented
189	D₃×C₁₆	C₂²×C₅	1	2	yes	complemented
190	C₅×#41	—	3	1	no	—
191	C₅×#41	—	6	2	no	—
192	C₅×#41	—	6	2	no	—
193	C₅×#41	—	6	1	no	—
194	C₅×#41	—	6	1	no	—
195	C₅×#41	—	12	2	no	—
196	C₅×#41	—	12	1	no	—
197	C₅×#41	—	12	1	no	—
198	C₂×C₅×Q₈	—	2	1	no	—
199	C₂×C₅×Q₈	—	6	2	no	—
200	C₂×C₅×Q₈	—	12	1	no	—
201	C₂×C₅×D₄	—	2	1	no	—
202	C₂×C₅×D₄	—	6	2	no	—
203	C₂×C₅×D₄	—	12	1	no	—
204	C₂×C₅×D₄	—	12	2	no	—
205	C₅×Q₁₆	—	2	1	no	—
206	C₅×Q₁₆	—	3	1	no	—
207	C₅×Q₁₆	—	3	1	no	—
208	C₅×Q₁₆	—	6	2	no	—
209	C₅×Q₁₆	C₂²×D₃	1	2	yes	—
210	C₅×SD₁₆	—	6	2	no	—
211	C₅×SD₁₆	—	6	2	no	—
212	C₅×SD₁₆	—	6	1	no	—
213	C₅×SD₁₆	—	6	1	no	—
214	C₅×D₈	—	2	1	no	—
215	C₅×D₈	—	3	1	no	—
216	C₅×D₈	—	3	1	no	—
217	C₅×D₈	—	6	2	no	—
218	C₅×D₈	C₂²×D₃	1	2	yes	—
219	C₅×M₁₆	—	3	1	no	—
220	C₅×M₁₆	—	3	2	no	—
221	C₂×C₅×C₈	—	3	2	no	—
222	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
223	C₅×C₁₆	—	3	2	no	—
224	C₅×C₁₆	C₂²×D₃	1	1	yes	characteristic
225	C₅×C₁₆	C₂²×D₃	1	1	yes	characteristic
226	#578	—	3	1	no	—
227	#576	—	3	1	no	—
228	#510	—	3	1	no	—
229	#510	—	3	2	no	—
230	#509	—	3	1	no	—
231	#509	—	3	2	no	—
232	#508	—	3	2	no	—
233	#508	—	3	1	no	—
234	C₂×SD₃₂	—	3	2	no	—
235	C₂×SD₃₂	C₅×D₃	1	1	yes	characteristic, complemented
236	#504	—	3	1	no	—
237	C₂²×C₃×C₅	—	4	2	no	—
238	C₂²×C₃×C₅	—	16	1	no	—
239	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
240	C₂×C₅×D₃	—	4	1	no	—
241	C₂×C₅×D₃	—	4	1	no	—
242	C₂×C₅×D₃	—	16	2	no	—
243	C₂×C₅×D₃	C₂×D₈	1	2	yes	—
244	C₃×C₄×C₅	—	4	2	no	—
245	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
246	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
247	C₅×Dic₃	—	4	1	no	—
248	C₅×Dic₃	—	4	1	no	—
249	C₅×Dic₃	C₂×D₈	1	2	yes	—
250	C₂×C₃×Q₈	—	2	1	no	—
251	C₂×C₃×D₄	—	2	1	no	—
252	C₂×#67	—	4	2	no	—
253	#239	—	2	2	no	—
254	#239	—	4	1	no	—
255	D₃×Q₈	—	2	2	no	—
256	D₃×Q₈	—	4	1	no	—
257	#237	—	2	2	no	—
258	#237	—	4	1	no	—
259	D₃×D₄	—	2	2	no	—
260	D₃×D₄	—	4	1	no	—
261	#235	—	2	1	no	—
262	#235	—	2	1	no	—
263	#235	—	4	2	no	—
264	#235	C₅×D₄	1	1	yes	characteristic
265	C₃×Q₁₆	—	2	1	no	—
266	C₃×Q₁₆	C₂³×C₅	1	2	yes	—
267	C₃×D₈	—	2	1	no	—
268	C₃×D₈	C₂³×C₅	1	2	yes	—
269	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
270	#216	—	2	2	no	—
271	#215	—	2	2	no	—
272	#214	—	2	2	no	—
273	#213	—	2	2	no	—
274	#208	C₅×D₄	1	1	yes	characteristic
275	Dic₁₂	C₂³×C₅	1	1	yes	characteristic
276	Dic₁₂	C₂³×C₅	1	1	yes	characteristic
277	D₂₄	C₂³×C₅	1	1	yes	characteristic
278	D₂₄	C₂³×C₅	1	1	yes	characteristic
279	#204	—	2	1	no	—
280	#204	—	2	1	no	—
281	ΓL(1,𝔽₂₅)	C₅×D₄	1	2	yes	—
282	D₃×C₈	C₂³×C₅	1	2	yes	—
283	C₃×C₁₆	C₂³×C₅	1	1	yes	characteristic
284	C₃×C₁₆	C₂³×C₅	1	1	yes	characteristic
285	C₃⋊C₁₆	C₂³×C₅	1	2	yes	—
286	C₂³×C₅	—	4	1	no	—
287	C₂³×C₅	—	12	2	no	—
288	C₅×Q₈	—	2	2	no	—
289	C₅×Q₈	—	3	1	no	—
290	C₅×Q₈	—	4	1	no	—
291	C₅×Q₈	—	6	1	no	—
292	C₅×Q₈	—	6	1	no	—
293	C₅×Q₈	—	12	2	no	—
294	C₅×D₄	—	2	2	no	—
295	C₅×D₄	—	3	2	no	—
296	C₅×D₄	—	3	1	no	—
297	C₅×D₄	—	4	1	no	—
298	C₅×D₄	—	6	1	no	—
299	C₅×D₄	—	6	1	no	—
300	C₅×D₄	—	12	2	no	—
301	C₅×D₄	—	12	2	no	—
302	C₅×D₄	—	12	2	no	—
303	C₅×D₄	—	12	1	no	—
304	C₅×D₄	—	12	1	no	—
305	C₂×C₄×C₅	—	3	2	no	—
306	C₂×C₄×C₅	—	4	1	no	—
307	C₂×C₄×C₅	—	12	2	no	—
308	C₂×C₄×C₅	—	12	2	no	—
309	C₂×C₄×C₅	—	12	2	no	—
310	C₂×C₄×C₅	—	12	1	no	—
311	C₂×C₄×C₅	—	12	1	no	—
312	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
313	C₅×C₈	—	3	2	no	—
314	C₅×C₈	D₃×D₄	1	1	yes	characteristic
315	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
316	2₋¹⁺⁴	—	6	1	no	—
317	H(5,𝔽₂)	—	6	1	no	—
318	#137	—	6	2	no	—
319	#137	—	6	1	no	—
320	AGL(1,ℤ/8)	—	6	2	no	—
321	AGL(1,ℤ/8)	—	6	1	no	—
322	#135	—	3	2	no	—
323	#135	—	3	2	no	—
324	#135	—	3	1	no	—
325	#135	—	3	1	no	—
326	C₂×Q₁₆	—	3	2	no	—
327	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
328	C₂×D₈	—	3	2	no	—
329	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
330	#131	—	3	1	no	—
331	Q₃₂	—	3	2	no	—
332	Q₃₂	—	3	1	no	—
333	SD₃₂	—	3	2	no	—
334	SD₃₂	—	3	2	no	—
335	SD₃₂	—	3	1	no	—
336	SD₃₂	—	3	1	no	—
337	SD₃₂	C₂×C₅×D₃	1	2	yes	complemented
338	SD₃₂	C₂×C₅×D₃	1	2	yes	complemented
339	D₁₆	—	3	2	no	—
340	D₁₆	—	3	1	no	—
341	M₃₂	—	3	1	no	—
342	M₃₂	—	3	2	no	—
343	C₂×C₁₆	—	3	2	no	—
344	C₂×C₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
345	C₂×C₃×C₅	—	2	1	no	—
346	C₂×C₃×C₅	—	8	2	no	—
347	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
348	C₅×D₃	—	2	2	no	—
349	C₅×D₃	—	8	1	no	—
350	C₅×D₃	—	8	1	no	—
351	C₂³×C₃	—	4	1	no	—
352	C₂²×D₃	—	4	2	no	—
353	C₃×Q₈	—	2	2	no	—
354	C₃×Q₈	—	4	1	no	—
355	C₃×D₄	—	2	2	no	—
356	C₃×D₄	—	4	1	no	—
357	C₂×C₃×C₄	—	4	1	no	—
358	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
359	#67	—	4	1	no	—
360	#67	—	4	1	no	—
361	#67	—	4	2	no	—
362	#67	—	4	2	no	—
363	#67	C₅×D₈	1	2	yes	—
364	C₂×Dic₃	—	4	2	no	—
365	D₁₂	—	2	1	no	—
366	D₁₂	—	2	1	no	—
367	D₁₂	—	4	2	no	—
368	D₁₂	C₅×D₈	1	1	yes	characteristic
369	C₄×D₃	—	4	2	no	—
370	C₄×D₃	—	4	1	no	—
371	C₄×D₃	—	4	1	no	—
372	C₄×D₃	—	4	2	no	—
373	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
374	Dic₆	—	2	1	no	—
375	Dic₆	—	2	1	no	—
376	Dic₆	—	4	2	no	—
377	Dic₆	C₅×D₈	1	1	yes	characteristic
378	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
379	C₃×C₈	C₂⁴×C₅	1	1	yes	characteristic
380	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
381	C₂²×C₅	—	3	2	no	—
382	C₂²×C₅	—	4	2	no	—
383	C₂²×C₅	—	12	1	no	—
384	C₂²×C₅	—	12	1	no	—
385	C₂²×C₅	—	16	1	no	—
386	C₂²×C₅	—	48	2	no	—
387	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
388	C₄×C₅	—	3	2	no	—
389	C₄×C₅	—	4	2	no	—
390	C₄×C₅	—	12	1	no	—
391	C₄×C₅	—	12	1	no	—
392	C₄×C₅	D₃×D₈	1	1	yes	characteristic
393	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
394	#41	—	3	1	no	—
395	#41	—	6	2	no	—
396	#41	—	6	2	no	—
397	#41	—	6	1	no	—
398	#41	—	6	1	no	—
399	#41	—	12	2	no	—
400	#41	—	12	1	no	—
401	#41	—	12	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	6	2	no	—
404	C₂×Q₈	—	12	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	6	2	no	—
407	C₂×D₄	—	12	1	no	—
408	C₂×D₄	—	12	2	no	—
409	Q₁₆	—	2	1	no	—
410	Q₁₆	—	3	1	no	—
411	Q₁₆	—	3	1	no	—
412	Q₁₆	—	6	2	no	—
413	Q₁₆	C₂²×C₅×D₃	1	2	yes	—
414	SD₁₆	—	6	2	no	—
415	SD₁₆	—	6	2	no	—
416	SD₁₆	—	6	1	no	—
417	SD₁₆	—	6	1	no	—
418	D₈	—	2	1	no	—
419	D₈	—	3	1	no	—
420	D₈	—	3	1	no	—
421	D₈	—	6	2	no	—
422	D₈	C₂²×C₅×D₃	1	2	yes	—
423	M₁₆	—	3	1	no	—
424	M₁₆	—	3	2	no	—
425	C₂×C₈	—	3	2	no	—
426	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
427	C₁₆	—	3	2	no	—
428	C₁₆	C₂²×C₅×D₃	1	1	yes	characteristic
429	C₁₆	C₂²×C₅×D₃	1	1	yes	characteristic
430	C₃×C₅	#3416	1	1	yes	characteristic, complemented, Hall
431	C₂²×C₃	—	4	2	no	—
432	C₂²×C₃	—	16	1	no	—
433	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
434	C₂×D₃	—	4	1	no	—
435	C₂×D₃	—	4	1	no	—
436	C₂×D₃	—	16	2	no	—
437	C₂×D₃	C₂×C₅×D₈	1	2	yes	—
438	C₃×C₄	—	4	2	no	—
439	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
440	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
441	Dic₃	—	4	1	no	—
442	Dic₃	—	4	1	no	—
443	Dic₃	C₂×C₅×D₈	1	2	yes	—
444	C₂×C₅	—	2	1	no	—
445	C₂×C₅	—	6	2	no	—
446	C₂×C₅	—	8	2	no	—
447	C₂×C₅	—	24	1	no	—
448	C₂×C₅	—	24	1	no	—
449	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
450	C₂³	—	4	1	no	—
451	C₂³	—	12	2	no	—
452	Q₈	—	2	2	no	—
453	Q₈	—	3	1	no	—
454	Q₈	—	4	1	no	—
455	Q₈	—	6	1	no	—
456	Q₈	—	6	1	no	—
457	Q₈	—	12	2	no	—
458	D₄	—	2	2	no	—
459	D₄	—	3	2	no	—
460	D₄	—	3	1	no	—
461	D₄	—	4	1	no	—
462	D₄	—	6	1	no	—
463	D₄	—	6	1	no	—
464	D₄	—	12	2	no	—
465	D₄	—	12	2	no	—
466	D₄	—	12	2	no	—
467	D₄	—	12	1	no	—
468	D₄	—	12	1	no	—
469	C₂×C₄	—	3	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	12	2	no	—
472	C₂×C₄	—	12	2	no	—
473	C₂×C₄	—	12	2	no	—
474	C₂×C₄	—	12	1	no	—
475	C₂×C₄	—	12	1	no	—
476	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
477	C₈	—	3	2	no	—
478	C₈	C₅×D₃×D₄	1	1	yes	characteristic
479	C₈	C₂³×C₅×D₃	1	1	yes	characteristic
480	C₂×C₃	—	2	1	no	—
481	C₂×C₃	—	8	2	no	—
482	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
483	D₃	—	2	2	no	—
484	D₃	—	8	1	no	—
485	D₃	—	8	1	no	—
486	C₅	#82024	1	1	yes	characteristic, direct product factor, Sylow
487	C₂²	—	3	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	12	1	no	—
490	C₂²	—	12	1	no	—
491	C₂²	—	16	1	no	—
492	C₂²	—	48	2	no	—
493	C₂²	C₅×D₃×D₈	1	1	yes	characteristic
494	C₄	—	3	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	12	1	no	—
497	C₄	—	12	1	no	—
498	C₄	C₅×D₃×D₈	1	1	yes	characteristic
499	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
500	C₃	C₅×#3416	1	1	yes	characteristic, complemented, Sylow
501	C₂	—	2	1	no	—
502	C₂	—	6	2	no	—
503	C₂	—	8	2	no	—
504	C₂	—	24	1	no	—
505	C₂	—	24	1	no	—
506	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×D₃×D₈
commutator, cosocle	C₃×C₈	C₂⁴×C₅
Frattini	C₈	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×SD₃₂	C₂
socle	C₂×C₃×C₅	C₂²×D₈
hypercenter	C₂×C₅×SD₃₂	D₃
hypocenter	C₃	C₅×#3416
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₂×C₅×SD₃₂

Complements

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

N	H ≅ G/N	type
1. C₅×#5766	C₂	semidirect
2. C₅×#5757	C₂	semidirect
3. C₂×C₃×C₅×SD₃₂	C₂	semidirect
4. C₅×#5179	C₂	semidirect
5. C₅×#5147	C₂	semidirect
6. C₅×#4916	C₂	semidirect
7. C₅×#4915	C₂	semidirect
8. C₅×#4914	C₂	semidirect
9. C₅×D₃×SD₃₂	C₂	semidirect
10. C₅×#4904	C₂	semidirect
11. C₅×#4901	C₂	semidirect
15. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
19. C₅×#919	C₂²	semidirect
21. C₅×D₃×Q₁₆	C₂²	semidirect
26. C₅×#904	C₂²	semidirect
28. C₃×C₅×SD₃₂	C₂²	semidirect
29. C₃×C₅×SD₃₂	C₂²	semidirect
30. C₂×C₃×C₅×C₁₆	C₂²	semidirect
31. C₅×#829	C₂²	semidirect
32. C₅×#828	C₂²	semidirect
33. C₅×#827	C₂²	semidirect
34. C₅×#826	C₂²	semidirect
35. C₅×#812	C₂²	semidirect
36. C₅×Dic₂₄	C₂²	semidirect
37. C₅×#800	C₂²	semidirect
38. C₅×#800	C₂²	semidirect
39. C₅×D₄₈	C₂²	semidirect
40. C₅×#798	C₂²	semidirect
41. C₅×D₃×C₁₆	C₂²	semidirect
42. #82024	C₅	direct (N × H)
52. C₂×C₅×SD₃₂	D₃	semidirect
90. #5766	C₂×C₅	semidirect
91. #5757	C₂×C₅	semidirect
92. C₂×C₃×SD₃₂	C₂×C₅	semidirect
93. #5179	C₂×C₅	semidirect
94. #5147	C₂×C₅	semidirect
95. #4916	C₂×C₅	semidirect
96. #4915	C₂×C₅	semidirect
97. #4914	C₂×C₅	semidirect
98. D₃×SD₃₂	C₂×C₅	semidirect
99. #4904	C₂×C₅	semidirect
100. #4901	C₂×C₅	semidirect
112. C₂×C₅×Q₁₆	C₂×D₃	semidirect
122. C₅×SD₃₂	C₂×D₃	semidirect
123. C₅×SD₃₂	C₂×D₃	semidirect
129. C₂×C₅×C₁₆	C₂×D₃	semidirect
163. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
167. #919	C₂²×C₅	semidirect
169. D₃×Q₁₆	C₂²×C₅	semidirect
174. #904	C₂²×C₅	semidirect
176. C₃×SD₃₂	C₂²×C₅	semidirect
177. C₃×SD₃₂	C₂²×C₅	semidirect
178. C₂×C₃×C₁₆	C₂²×C₅	semidirect
179. #829	C₂²×C₅	semidirect
180. #828	C₂²×C₅	semidirect
181. #827	C₂²×C₅	semidirect
182. #826	C₂²×C₅	semidirect
183. #812	C₂²×C₅	semidirect
184. Dic₂₄	C₂²×C₅	semidirect
185. #800	C₂²×C₅	semidirect
186. #800	C₂²×C₅	semidirect
187. D₄₈	C₂²×C₅	semidirect
188. #798	C₂²×C₅	semidirect
189. D₃×C₁₆	C₂²×C₅	semidirect
235. C₂×SD₃₂	C₅×D₃	semidirect
327. C₂×Q₁₆	C₂×C₅×D₃	semidirect
337. SD₃₂	C₂×C₅×D₃	semidirect
338. SD₃₂	C₂×C₅×D₃	semidirect
344. C₂×C₁₆	C₂×C₅×D₃	semidirect
430. C₃×C₅	#3416	semidirect
486. C₅	#82024	direct (N × H)
500. C₃	C₅×#3416	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5766	2
C₅×#5757	2
C₂×C₃×C₅×SD₃₂	2
C₅×#5179	2
C₅×#5147	2
C₅×#4916	2
C₅×#4915	2
C₅×#4914	2
C₅×D₃×SD₃₂	2
C₅×#4904	2
C₅×#4901	2
C₅×#3416	3
#82024	5

Subgroups — C5×#82024 #14478534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#82024 #14478534