Subgroups — C₅×#82041 #14478622

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5771	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5766	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#510	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5194	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#829	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4918	C₂	1	2	yes	maximal, complemented
7	C₅×D₃×Q₃₂	C₂	1	2	yes	maximal, complemented
8	C₅×#4916	C₂	1	2	yes	maximal, complemented
9	C₅×#4915	C₂	1	2	yes	maximal, complemented
10	C₅×#4909	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4907	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3417	—	3	1	no	maximal, Hall
13	C₅×#1010	—	2	1	no	—
14	C₅×#1007	—	2	1	no	—
15	C₃×C₅×#135	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
17	C₅×#951	—	2	1	no	—
18	C₅×#942	—	2	1	no	—
19	C₅×#919	C₂²	1	2	yes	—
20	C₅×#918	—	2	2	no	—
21	C₅×D₃×Q₁₆	C₂²	1	2	yes	—
22	C₅×D₃×Q₁₆	C₂²	1	2	yes	—
23	C₅×#915	—	2	2	no	—
24	C₅×#912	C₂²	1	2	yes	—
25	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
26	C₅×#904	C₂²	1	1	yes	characteristic
27	C₅×#901	C₂²	1	1	yes	characteristic
28	C₃×C₅×Q₃₂	C₂²	1	2	yes	—
29	C₃×C₅×SD₃₂	C₂²	1	2	yes	—
30	C₃×C₅×M₃₂	C₂²	1	1	yes	characteristic
31	C₅×#829	C₂²	1	2	yes	—
32	C₅×#829	C₂²	1	2	yes	—
33	C₅×#829	C₂²	1	1	yes	characteristic
34	C₅×#828	C₂²	1	1	yes	characteristic
35	C₅×#827	C₂²	1	1	yes	characteristic
36	C₅×#826	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₅×Dic₂₄	C₂²	1	2	yes	—
39	C₅×#800	C₂²	1	2	yes	—
40	C₅×#798	C₂²	1	2	yes	—
41	C₅×D₃×C₁₆	C₂²	1	2	yes	—
42	#82041	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#578	—	3	1	no	—
44	C₅×#578	—	3	1	no	—
45	C₅×#510	—	3	2	no	—
46	C₅×#510	—	3	2	no	—
47	C₅×#510	—	3	1	no	—
48	C₅×#510	D₃	1	1	yes	characteristic, complemented
49	C₅×#508	—	3	2	no	—
50	C₅×#508	—	3	1	no	—
51	C₂×C₅×Q₃₂	—	3	2	no	—
52	C₂×C₅×Q₃₂	—	3	1	no	—
53	C₅×#504	—	3	1	no	—
54	C₃×C₅×#41	—	2	1	no	—
55	C₂×C₃×C₅×Q₈	—	2	1	no	—
56	C₅×#239	—	2	2	no	—
57	C₅×#239	—	4	1	no	—
58	C₅×D₃×Q₈	—	2	2	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	2	no	—
63	C₅×#235	—	2	1	no	—
64	C₅×#235	—	4	2	no	—
65	C₅×#235	—	4	1	no	—
66	C₅×#235	D₄	1	1	yes	characteristic
67	C₂×C₅×Dic₆	—	2	1	no	—
68	C₂×C₅×Dic₆	—	4	1	no	—
69	C₃×C₅×Q₁₆	—	2	1	no	—
70	C₃×C₅×Q₁₆	C₂³	1	2	yes	—
71	C₃×C₅×Q₁₆	C₂³	1	1	yes	characteristic
72	C₃×C₅×SD₁₆	—	2	1	no	—
73	C₃×C₅×D₈	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₅×#216	—	2	2	no	—
76	C₅×#216	—	2	2	no	—
77	C₅×#215	—	2	2	no	—
78	C₅×#214	—	2	2	no	—
79	C₅×#208	D₄	1	1	yes	characteristic
80	C₅×Dic₁₂	—	2	1	no	—
81	C₅×Dic₁₂	C₂³	1	1	yes	characteristic
82	C₅×Dic₁₂	C₂³	1	2	yes	—
83	C₅×D₂₄	C₂³	1	1	yes	characteristic
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	2	yes	—
88	C₅×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
89	C₅×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
90	#5771	C₂×C₅	1	1	yes	characteristic, complemented
91	#5766	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#510	C₂×C₅	1	1	yes	characteristic, complemented
93	#5194	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×#829	C₂×C₅	1	1	yes	characteristic, complemented
95	#4918	C₂×C₅	1	2	yes	complemented
96	D₃×Q₃₂	C₂×C₅	1	2	yes	complemented
97	#4916	C₂×C₅	1	2	yes	complemented
98	#4915	C₂×C₅	1	2	yes	complemented
99	#4909	C₂×C₅	1	1	yes	characteristic, complemented
100	#4907	C₂×C₅	1	1	yes	characteristic, complemented
101	C₅×2₋¹⁺⁴	—	6	1	no	—
102	C₅×2₋¹⁺⁴	—	6	1	no	—
103	C₅×#137	—	6	2	no	—
104	C₅×#137	—	6	2	no	—
105	C₅×#137	—	6	1	no	—
106	C₅×#137	—	6	1	no	—
107	C₅×#135	—	3	2	no	—
108	C₅×#135	—	3	2	no	—
109	C₅×#135	—	3	1	no	—
110	C₅×#135	C₂×D₃	1	1	yes	characteristic
111	C₂×C₅×Q₁₆	—	3	2	no	—
112	C₂×C₅×Q₁₆	—	3	2	no	—
113	C₂×C₅×Q₁₆	—	3	1	no	—
114	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
115	C₅×#131	—	3	1	no	—
116	C₅×Q₃₂	—	3	1	no	—
117	C₅×Q₃₂	—	3	2	no	—
118	C₅×Q₃₂	—	3	2	no	—
119	C₅×Q₃₂	—	3	2	no	—
120	C₅×Q₃₂	C₂×D₃	1	2	yes	—
121	C₅×SD₃₂	—	3	1	no	—
122	C₅×SD₃₂	—	3	1	no	—
123	C₅×SD₃₂	—	3	2	no	—
124	C₅×SD₃₂	C₂×D₃	1	2	yes	—
125	C₅×D₁₆	—	3	1	no	—
126	C₅×M₃₂	—	3	2	no	—
127	C₅×M₃₂	C₂×D₃	1	1	yes	characteristic
128	C₂×C₅×C₁₆	—	3	1	no	—
129	C₂×C₅×C₁₆	—	3	2	no	—
130	#3417	—	3	1	no	Sylow
131	C₃×C₅×Q₈	—	2	2	no	—
132	C₃×C₅×Q₈	—	2	1	no	—
133	C₃×C₅×Q₈	—	4	1	no	—
134	C₃×C₅×D₄	—	2	1	no	—
135	C₃×C₅×D₄	—	4	1	no	—
136	C₂×C₃×C₄×C₅	—	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	2	no	—
141	C₅×#67	D₈	1	2	yes	—
142	C₂×C₅×Dic₃	—	4	1	no	—
143	C₂×C₅×Dic₃	—	4	2	no	—
144	C₅×D₁₂	—	2	1	no	—
145	C₅×D₁₂	—	4	2	no	—
146	C₅×D₁₂	D₈	1	1	yes	characteristic
147	C₄×C₅×D₃	—	4	2	no	—
148	C₄×C₅×D₃	—	4	2	no	—
149	C₄×C₅×D₃	—	4	1	no	—
150	C₄×C₅×D₃	—	4	2	no	—
151	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
152	C₅×Dic₆	—	2	1	no	—
153	C₅×Dic₆	—	2	2	no	—
154	C₅×Dic₆	—	4	1	no	—
155	C₅×Dic₆	—	4	2	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	#1010	—	2	1	no	—
162	#1007	—	2	1	no	—
163	C₃×#135	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
165	#951	—	2	1	no	—
166	#942	—	2	1	no	—
167	#919	C₂²×C₅	1	2	yes	—
168	#918	—	2	2	no	—
169	D₃×Q₁₆	C₂²×C₅	1	2	yes	—
170	D₃×Q₁₆	C₂²×C₅	1	2	yes	—
171	#915	—	2	2	no	—
172	#912	C₂²×C₅	1	2	yes	—
173	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
174	#904	C₂²×C₅	1	1	yes	characteristic
175	#901	C₂²×C₅	1	1	yes	characteristic
176	C₃×Q₃₂	C₂²×C₅	1	2	yes	—
177	C₃×SD₃₂	C₂²×C₅	1	2	yes	—
178	C₃×M₃₂	C₂²×C₅	1	1	yes	characteristic
179	#829	C₂²×C₅	1	2	yes	—
180	#829	C₂²×C₅	1	2	yes	—
181	#829	C₂²×C₅	1	1	yes	characteristic
182	#828	C₂²×C₅	1	1	yes	characteristic
183	#827	C₂²×C₅	1	1	yes	characteristic
184	#826	C₂²×C₅	1	1	yes	characteristic
185	C₂×C₃⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
186	Dic₂₄	C₂²×C₅	1	2	yes	—
187	#800	C₂²×C₅	1	2	yes	—
188	#798	C₂²×C₅	1	2	yes	—
189	D₃×C₁₆	C₂²×C₅	1	2	yes	—
190	C₅×#41	—	2	1	no	—
191	C₅×#41	—	3	1	no	—
192	C₅×#41	—	6	2	no	—
193	C₅×#41	—	6	2	no	—
194	C₅×#41	—	6	1	no	—
195	C₅×#41	—	12	2	no	—
196	C₅×#41	—	12	1	no	—
197	C₅×#41	—	12	2	no	—
198	C₅×#41	—	12	1	no	—
199	C₂×C₅×Q₈	—	2	1	no	—
200	C₂×C₅×Q₈	—	6	2	no	—
201	C₂×C₅×Q₈	—	6	2	no	—
202	C₂×C₅×Q₈	—	6	1	no	—
203	C₂×C₅×Q₈	—	12	1	no	—
204	C₂×C₅×Q₈	—	12	1	no	—
205	C₅×Q₁₆	—	2	1	no	—
206	C₅×Q₁₆	—	3	1	no	—
207	C₅×Q₁₆	—	3	2	no	—
208	C₅×Q₁₆	—	6	2	no	—
209	C₅×Q₁₆	—	6	2	no	—
210	C₅×Q₁₆	—	6	1	no	—
211	C₅×Q₁₆	C₂²×D₃	1	1	yes	characteristic
212	C₅×Q₁₆	C₂²×D₃	1	2	yes	—
213	C₅×SD₁₆	—	2	1	no	—
214	C₅×SD₁₆	—	6	2	no	—
215	C₅×SD₁₆	—	6	2	no	—
216	C₅×SD₁₆	—	6	1	no	—
217	C₅×D₈	—	3	1	no	—
218	C₅×D₈	C₂²×D₃	1	1	yes	characteristic
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	1	no	—
224	C₅×C₁₆	—	3	1	no	—
225	C₅×C₁₆	C₂²×D₃	1	2	yes	—
226	#578	—	3	1	no	—
227	#578	—	3	1	no	—
228	#510	—	3	2	no	—
229	#510	—	3	2	no	—
230	#510	—	3	1	no	—
231	#510	C₅×D₃	1	1	yes	characteristic, complemented
232	#508	—	3	1	no	—
233	#508	—	3	2	no	—
234	C₂×Q₃₂	—	3	1	no	—
235	C₂×Q₃₂	—	3	2	no	—
236	#504	—	3	1	no	—
237	C₂²×C₃×C₅	—	4	1	no	—
238	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
239	C₂×C₅×D₃	—	4	1	no	—
240	C₂×C₅×D₃	C₂×D₈	1	2	yes	—
241	C₃×C₄×C₅	—	4	1	no	—
242	C₃×C₄×C₅	—	4	2	no	—
243	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
244	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
245	C₅×Dic₃	—	4	1	no	—
246	C₅×Dic₃	—	4	2	no	—
247	C₅×Dic₃	C₂×D₈	1	2	yes	—
248	C₃×#41	—	2	1	no	—
249	C₂×C₃×Q₈	—	2	1	no	—
250	#239	—	2	2	no	—
251	#239	—	4	1	no	—
252	D₃×Q₈	—	2	2	no	—
253	D₃×Q₈	—	2	2	no	—
254	D₃×Q₈	—	4	1	no	—
255	#237	—	2	2	no	—
256	#237	—	4	2	no	—
257	#235	—	2	1	no	—
258	#235	—	4	2	no	—
259	#235	—	4	1	no	—
260	#235	C₅×D₄	1	1	yes	characteristic
261	C₂×Dic₆	—	2	1	no	—
262	C₂×Dic₆	—	4	1	no	—
263	C₃×Q₁₆	—	2	1	no	—
264	C₃×Q₁₆	C₂³×C₅	1	1	yes	characteristic
265	C₃×Q₁₆	C₂³×C₅	1	2	yes	—
266	C₃×SD₁₆	—	2	1	no	—
267	C₃×D₈	C₂³×C₅	1	1	yes	characteristic
268	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
269	#216	—	2	2	no	—
270	#216	—	2	2	no	—
271	#215	—	2	2	no	—
272	#214	—	2	2	no	—
273	#208	C₅×D₄	1	1	yes	characteristic
274	Dic₁₂	—	2	1	no	—
275	Dic₁₂	C₂³×C₅	1	2	yes	—
276	Dic₁₂	C₂³×C₅	1	1	yes	characteristic
277	D₂₄	C₂³×C₅	1	1	yes	characteristic
278	#204	—	2	1	no	—
279	ΓL(1,𝔽₂₅)	C₅×D₄	1	2	yes	—
280	D₃×C₈	C₂³×C₅	1	2	yes	—
281	C₃×C₁₆	C₂³×C₅	1	2	yes	—
282	C₃⋊C₁₆	C₂³×C₅	1	1	yes	characteristic
283	C₃⋊C₁₆	C₂³×C₅	1	1	yes	characteristic
284	C₅×Q₈	—	2	1	no	—
285	C₅×Q₈	—	2	2	no	—
286	C₅×Q₈	—	3	1	no	—
287	C₅×Q₈	—	4	1	no	—
288	C₅×Q₈	—	6	2	no	—
289	C₅×Q₈	—	6	1	no	—
290	C₅×Q₈	—	12	2	no	—
291	C₅×Q₈	—	12	2	no	—
292	C₅×Q₈	—	12	1	no	—
293	C₅×D₄	—	2	1	no	—
294	C₅×D₄	—	3	2	no	—
295	C₅×D₄	—	3	1	no	—
296	C₅×D₄	—	4	1	no	—
297	C₅×D₄	—	6	1	no	—
298	C₅×D₄	—	12	2	no	—
299	C₅×D₄	—	12	2	no	—
300	C₅×D₄	—	12	1	no	—
301	C₂×C₄×C₅	—	3	2	no	—
302	C₂×C₄×C₅	—	4	1	no	—
303	C₂×C₄×C₅	—	4	1	no	—
304	C₂×C₄×C₅	—	12	2	no	—
305	C₂×C₄×C₅	—	12	2	no	—
306	C₂×C₄×C₅	—	12	2	no	—
307	C₂×C₄×C₅	—	12	2	no	—
308	C₂×C₄×C₅	—	12	1	no	—
309	C₂×C₄×C₅	—	12	1	no	—
310	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
311	C₅×C₈	—	3	2	no	—
312	C₅×C₈	D₃×D₄	1	1	yes	characteristic
313	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
314	2₋¹⁺⁴	—	6	1	no	—
315	2₋¹⁺⁴	—	6	1	no	—
316	#137	—	6	2	no	—
317	#137	—	6	2	no	—
318	#137	—	6	1	no	—
319	#137	—	6	1	no	—
320	#135	—	3	2	no	—
321	#135	—	3	2	no	—
322	#135	—	3	1	no	—
323	#135	C₂×C₅×D₃	1	1	yes	characteristic
324	C₂×Q₁₆	—	3	2	no	—
325	C₂×Q₁₆	—	3	2	no	—
326	C₂×Q₁₆	—	3	1	no	—
327	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
328	#131	—	3	1	no	—
329	Q₃₂	—	3	1	no	—
330	Q₃₂	—	3	2	no	—
331	Q₃₂	—	3	2	no	—
332	Q₃₂	—	3	2	no	—
333	Q₃₂	C₂×C₅×D₃	1	2	yes	—
334	SD₃₂	—	3	1	no	—
335	SD₃₂	—	3	1	no	—
336	SD₃₂	—	3	2	no	—
337	SD₃₂	C₂×C₅×D₃	1	2	yes	—
338	D₁₆	—	3	1	no	—
339	M₃₂	—	3	2	no	—
340	M₃₂	C₂×C₅×D₃	1	1	yes	characteristic
341	C₂×C₁₆	—	3	1	no	—
342	C₂×C₁₆	—	3	2	no	—
343	C₂×C₃×C₅	—	2	1	no	—
344	C₂×C₃×C₅	—	8	1	no	—
345	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
346	C₅×D₃	—	2	2	no	—
347	C₅×D₃	—	8	1	no	—
348	C₃×Q₈	—	2	2	no	—
349	C₃×Q₈	—	2	1	no	—
350	C₃×Q₈	—	4	1	no	—
351	C₃×D₄	—	2	1	no	—
352	C₃×D₄	—	4	1	no	—
353	C₂×C₃×C₄	—	4	1	no	—
354	C₂×C₃×C₄	—	4	1	no	—
355	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
356	#67	—	4	1	no	—
357	#67	—	4	2	no	—
358	#67	C₅×D₈	1	2	yes	—
359	C₂×Dic₃	—	4	1	no	—
360	C₂×Dic₃	—	4	2	no	—
361	D₁₂	—	2	1	no	—
362	D₁₂	—	4	2	no	—
363	D₁₂	C₅×D₈	1	1	yes	characteristic
364	C₄×D₃	—	4	2	no	—
365	C₄×D₃	—	4	2	no	—
366	C₄×D₃	—	4	1	no	—
367	C₄×D₃	—	4	2	no	—
368	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
369	Dic₆	—	2	1	no	—
370	Dic₆	—	2	2	no	—
371	Dic₆	—	4	1	no	—
372	Dic₆	—	4	2	no	—
373	Dic₆	—	4	2	no	—
374	Dic₆	C₅×D₈	1	1	yes	characteristic
375	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
376	C₃×C₈	C₂⁴×C₅	1	1	yes	characteristic
377	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
378	C₂²×C₅	—	3	2	no	—
379	C₂²×C₅	—	4	1	no	—
380	C₂²×C₅	—	12	1	no	—
381	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
382	C₄×C₅	—	3	2	no	—
383	C₄×C₅	—	4	1	no	—
384	C₄×C₅	—	4	2	no	—
385	C₄×C₅	—	12	1	no	—
386	C₄×C₅	—	12	2	no	—
387	C₄×C₅	D₃×D₈	1	1	yes	characteristic
388	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
389	#41	—	2	1	no	—
390	#41	—	3	1	no	—
391	#41	—	6	2	no	—
392	#41	—	6	2	no	—
393	#41	—	6	1	no	—
394	#41	—	12	2	no	—
395	#41	—	12	1	no	—
396	#41	—	12	2	no	—
397	#41	—	12	1	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	6	2	no	—
400	C₂×Q₈	—	6	2	no	—
401	C₂×Q₈	—	6	1	no	—
402	C₂×Q₈	—	12	1	no	—
403	C₂×Q₈	—	12	1	no	—
404	Q₁₆	—	2	1	no	—
405	Q₁₆	—	3	1	no	—
406	Q₁₆	—	3	2	no	—
407	Q₁₆	—	6	2	no	—
408	Q₁₆	—	6	2	no	—
409	Q₁₆	—	6	1	no	—
410	Q₁₆	C₂²×C₅×D₃	1	1	yes	characteristic
411	Q₁₆	C₂²×C₅×D₃	1	2	yes	—
412	SD₁₆	—	2	1	no	—
413	SD₁₆	—	6	2	no	—
414	SD₁₆	—	6	2	no	—
415	SD₁₆	—	6	1	no	—
416	D₈	—	3	1	no	—
417	D₈	C₂²×C₅×D₃	1	1	yes	characteristic
418	M₁₆	—	3	1	no	—
419	M₁₆	—	3	2	no	—
420	C₂×C₈	—	3	2	no	—
421	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
422	C₁₆	—	3	1	no	—
423	C₁₆	—	3	1	no	—
424	C₁₆	C₂²×C₅×D₃	1	2	yes	—
425	C₃×C₅	#3417	1	1	yes	characteristic, complemented, Hall
426	C₂²×C₃	—	4	1	no	—
427	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
428	C₂×D₃	—	4	1	no	—
429	C₂×D₃	C₂×C₅×D₈	1	2	yes	—
430	C₃×C₄	—	4	1	no	—
431	C₃×C₄	—	4	2	no	—
432	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
433	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
434	Dic₃	—	4	1	no	—
435	Dic₃	—	4	2	no	—
436	Dic₃	C₂×C₅×D₈	1	2	yes	—
437	C₂×C₅	—	2	1	no	—
438	C₂×C₅	—	6	2	no	—
439	C₂×C₅	—	8	1	no	—
440	C₂×C₅	—	24	1	no	—
441	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
442	Q₈	—	2	1	no	—
443	Q₈	—	2	2	no	—
444	Q₈	—	3	1	no	—
445	Q₈	—	4	1	no	—
446	Q₈	—	6	2	no	—
447	Q₈	—	6	1	no	—
448	Q₈	—	12	2	no	—
449	Q₈	—	12	2	no	—
450	Q₈	—	12	1	no	—
451	D₄	—	2	1	no	—
452	D₄	—	3	2	no	—
453	D₄	—	3	1	no	—
454	D₄	—	4	1	no	—
455	D₄	—	6	1	no	—
456	D₄	—	12	2	no	—
457	D₄	—	12	2	no	—
458	D₄	—	12	1	no	—
459	C₂×C₄	—	3	2	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	12	2	no	—
463	C₂×C₄	—	12	2	no	—
464	C₂×C₄	—	12	2	no	—
465	C₂×C₄	—	12	2	no	—
466	C₂×C₄	—	12	1	no	—
467	C₂×C₄	—	12	1	no	—
468	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
469	C₈	—	3	2	no	—
470	C₈	C₅×D₃×D₄	1	1	yes	characteristic
471	C₈	C₂³×C₅×D₃	1	1	yes	characteristic
472	C₂×C₃	—	2	1	no	—
473	C₂×C₃	—	8	1	no	—
474	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
475	D₃	—	2	2	no	—
476	D₃	—	8	1	no	—
477	C₅	#82041	1	1	yes	characteristic, direct product factor, Sylow
478	C₂²	—	3	2	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	12	1	no	—
481	C₂²	C₅×D₃×D₈	1	1	yes	characteristic
482	C₄	—	3	2	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	2	no	—
485	C₄	—	12	2	no	—
486	C₄	—	12	1	no	—
487	C₄	C₅×D₃×D₈	1	1	yes	characteristic
488	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
489	C₃	C₅×#3417	1	1	yes	characteristic, complemented, Sylow
490	C₂	—	2	1	no	—
491	C₂	—	6	2	no	—
492	C₂	—	8	1	no	—
493	C₂	—	24	1	no	—
494	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	C₃×C₅×#510	C₂
socle	C₂×C₃×C₅	C₂²×D₈
hypercenter	C₅×#510	D₃
hypocenter	C₃	C₅×#3417
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₅×#510

Complements

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

N	H ≅ G/N	type
1. C₅×#5771	C₂	semidirect
2. C₅×#5766	C₂	semidirect
3. C₃×C₅×#510	C₂	semidirect
4. C₅×#5194	C₂	semidirect
5. C₂×C₅×#829	C₂	semidirect
6. C₅×#4918	C₂	semidirect
7. C₅×D₃×Q₃₂	C₂	semidirect
8. C₅×#4916	C₂	semidirect
9. C₅×#4915	C₂	semidirect
10. C₅×#4909	C₂	semidirect
11. C₅×#4907	C₂	semidirect
42. #82041	C₅	direct (N × H)
48. C₅×#510	D₃	semidirect
90. #5771	C₂×C₅	semidirect
91. #5766	C₂×C₅	semidirect
92. C₃×#510	C₂×C₅	semidirect
93. #5194	C₂×C₅	semidirect
94. C₂×#829	C₂×C₅	semidirect
95. #4918	C₂×C₅	semidirect
96. D₃×Q₃₂	C₂×C₅	semidirect
97. #4916	C₂×C₅	semidirect
98. #4915	C₂×C₅	semidirect
99. #4909	C₂×C₅	semidirect
100. #4907	C₂×C₅	semidirect
231. #510	C₅×D₃	semidirect
425. C₃×C₅	#3417	semidirect
477. C₅	#82041	direct (N × H)
489. C₃	C₅×#3417	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5771	2
C₅×#5766	2
C₃×C₅×#510	2
C₅×#5194	2
C₂×C₅×#829	2
C₅×#4918	2
C₅×D₃×Q₃₂	2
C₅×#4916	2
C₅×#4915	2
C₅×#4909	2
C₅×#4907	2
C₅×#3417	3
#82041	5

Subgroups — C5×#82041 #14478622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#82041 #14478622