Subgroups — C₅×#32724 #11955444

Order 1280.

750 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2857	C₂	1	1	yes	maximal, characteristic
2	C₅×#2855	C₂	1	1	yes	maximal, characteristic
3	C₅×#2100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2095	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2068	C₂	1	2	yes	maximal, complemented
6	C₅×#2056	C₂	1	2	yes	maximal, complemented
7	C₅×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2036	C₂	1	2	yes	maximal
9	C₅×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2001	C₂	1	2	yes	maximal
11	C₅×#1797	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×Q₁₆	C₂²	1	2	yes	—
13	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₅×#107	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×#103	C₂²	1	2	yes	—
20	C₂×C₅×#103	C₂²	1	2	yes	—
21	C₂×C₅×#103	C₂²	1	2	yes	—
22	C₂×C₅×#103	C₂²	1	2	yes	—
23	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₅×#391	C₂²	1	1	yes	characteristic
25	C₅×#391	C₂²	1	1	yes	characteristic
26	C₅×#391	C₂²	1	2	yes	—
27	C₅×#389	—	2	1	no	—
28	C₅×#389	—	2	1	no	—
29	C₅×#389	C₂²	1	1	yes	characteristic
30	C₅×#389	C₂²	1	1	yes	characteristic
31	C₅×#387	—	2	1	no	—
32	C₅×#387	—	2	1	no	—
33	C₅×#385	—	2	1	no	—
34	C₅×#384	C₂²	1	1	yes	characteristic
35	C₅×#381	—	2	1	no	—
36	C₅×#380	—	2	1	no	—
37	C₅×#380	—	2	1	no	—
38	C₅×#380	C₂²	1	1	yes	characteristic
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	1	yes	characteristic
42	C₅×#336	C₂²	1	1	yes	characteristic
43	#32724	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
45	C₂²×C₅×Q₈	C₂³	1	2	yes	—
46	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂×C₅×Q₁₆	—	4	2	no	—
50	C₂×C₅×Q₁₆	—	4	2	no	—
51	C₂×C₅×Q₁₆	—	4	2	no	—
52	C₂²×C₅×C₈	C₂³	1	2	yes	—
53	C₂²×C₅×C₈	C₂³	1	2	yes	—
54	C₅×C₄⋊Q₈	—	4	2	no	—
55	C₅×C₂²⋊Q₈	—	4	2	no	—
56	C₅×C₂²⋊Q₈	—	4	2	no	—
57	C₅×C₂²⋊Q₈	—	4	2	no	—
58	C₂×C₅×C₄⋊C₄	—	2	1	no	—
59	C₂×C₅×C₄⋊C₄	—	2	1	no	—
60	C₂×C₅×C₄⋊C₄	—	2	1	no	—
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	—	2	1	no	—
63	C₂×C₅×C₄⋊C₄	—	2	1	no	—
64	C₂×C₅×C₄⋊C₄	—	2	1	no	—
65	C₂×C₅×C₄⋊C₄	—	2	2	no	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₄²×C₅	—	4	2	no	—
74	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₅×#107	—	4	2	no	—
79	C₅×C₄⋊C₈	—	4	2	no	—
80	C₅×#103	—	4	2	no	—
81	C₅×#103	—	4	2	no	—
82	C₅×#103	—	4	2	no	—
83	C₅×#103	—	4	2	no	—
84	C₅×C₂²⋊C₈	—	4	2	no	—
85	C₅×#95	—	2	2	no	—
86	C₅×#95	—	2	2	no	—
87	C₅×#95	—	2	1	no	—
88	C₅×#95	—	2	1	no	—
89	C₅×#95	—	2	1	no	—
90	C₅×#95	—	2	1	no	—
91	C₅×#95	—	2	1	no	—
92	C₅×#95	—	2	1	no	—
93	C₅×#95	—	2	1	no	—
94	#2857	C₂×C₅	1	1	yes	characteristic
95	#2855	C₂×C₅	1	1	yes	characteristic
96	#2100	C₂×C₅	1	1	yes	characteristic, complemented
97	#2095	C₂×C₅	1	1	yes	characteristic, complemented
98	#2068	C₂×C₅	1	2	yes	complemented
99	#2056	C₂×C₅	1	2	yes	complemented
100	#2043	C₂×C₅	1	1	yes	characteristic, complemented
101	#2036	C₂×C₅	1	2	yes	—
102	#2016	C₂×C₅	1	1	yes	characteristic, complemented
103	#2001	C₂×C₅	1	2	yes	—
104	#1797	C₂×C₅	1	1	yes	characteristic
105	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	2	2	no	—
110	C₂×C₅×Q₈	—	2	2	no	—
111	C₂×C₅×Q₈	—	2	1	no	—
112	C₂×C₅×Q₈	—	2	2	no	—
113	C₂×C₅×Q₈	—	2	2	no	—
114	C₂×C₅×Q₈	—	2	1	no	—
115	C₂×C₅×Q₈	—	2	2	no	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	4	1	no	—
128	C₂²×C₄×C₅	—	4	1	no	—
129	C₂²×C₄×C₅	—	4	1	no	—
130	C₂²×C₄×C₅	—	4	1	no	—
131	C₂²×C₄×C₅	Q₁₆	1	4	yes	complemented
132	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	C₅×Q₁₆	—	4	8	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₄⋊C₄	—	4	2	no	—
152	C₅×C₄⋊C₄	—	4	2	no	—
153	C₅×C₄⋊C₄	—	4	2	no	—
154	C₅×C₄⋊C₄	—	4	2	no	—
155	C₅×C₄⋊C₄	—	4	4	no	—
156	C₅×C₄⋊C₄	—	4	2	no	—
157	C₅×C₄⋊C₄	—	4	2	no	—
158	C₅×C₄⋊C₄	—	4	2	no	—
159	C₅×C₂²⋊C₄	—	4	2	no	—
160	C₅×C₂²⋊C₄	—	4	2	no	—
161	C₅×C₂²⋊C₄	—	4	4	no	—
162	C₄²×C₅	—	2	2	no	—
163	C₄²×C₅	—	2	2	no	—
164	C₄²×C₅	—	4	1	no	—
165	C₄²×C₅	—	4	1	no	—
166	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
167	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
168	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
169	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
170	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
171	C₂×#107	C₂²×C₅	1	2	yes	—
172	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
173	C₂×#103	C₂²×C₅	1	2	yes	—
174	C₂×#103	C₂²×C₅	1	2	yes	—
175	C₂×#103	C₂²×C₅	1	2	yes	—
176	C₂×#103	C₂²×C₅	1	2	yes	—
177	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
178	#391	C₂²×C₅	1	1	yes	characteristic
179	#391	C₂²×C₅	1	2	yes	—
180	#391	C₂²×C₅	1	1	yes	characteristic
181	#389	—	2	1	no	—
182	#389	—	2	1	no	—
183	#389	C₂²×C₅	1	1	yes	characteristic
184	#389	C₂²×C₅	1	1	yes	characteristic
185	#387	—	2	1	no	—
186	#387	—	2	1	no	—
187	#385	—	2	1	no	—
188	#384	C₂²×C₅	1	1	yes	characteristic
189	#381	—	2	1	no	—
190	#380	—	2	1	no	—
191	#380	—	2	1	no	—
192	#380	C₂²×C₅	1	1	yes	characteristic
193	#340	C₂²×C₅	1	2	yes	—
194	#340	C₂²×C₅	1	2	yes	—
195	#336	C₂²×C₅	1	1	yes	characteristic
196	#336	C₂²×C₅	1	1	yes	characteristic
197	C₂³×C₅	—	2	1	no	—
198	C₂³×C₅	—	2	1	no	—
199	C₂³×C₅	—	2	1	no	—
200	C₂³×C₅	—	2	1	no	—
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	—	2	1	no	—
203	C₂³×C₅	C₂×Q₁₆	1	2	yes	—
204	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
205	C₅×Q₈	—	4	2	no	—
206	C₅×Q₈	—	4	2	no	—
207	C₅×Q₈	—	4	2	no	—
208	C₅×Q₈	—	4	2	no	—
209	C₅×Q₈	—	4	2	no	—
210	C₅×Q₈	—	4	2	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	4	4	no	—
224	C₂×C₄×C₅	—	4	4	no	—
225	C₂×C₄×C₅	—	4	2	no	—
226	C₂×C₄×C₅	—	4	2	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	—	4	1	no	—
229	C₂×C₄×C₅	—	4	2	no	—
230	C₂×C₄×C₅	—	4	2	no	—
231	C₂×C₄×C₅	—	4	2	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	4	2	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	4	1	no	—
239	C₂×C₄×C₅	—	4	1	no	—
240	C₂×C₄×C₅	—	4	1	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	4	2	no	—
243	C₂×C₄×C₅	—	4	2	no	—
244	C₂×C₄×C₅	—	4	1	no	—
245	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
246	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
247	C₂×C₄×C₅	#137	1	2	yes	—
248	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
249	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
250	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
251	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
252	C₅×C₈	—	4	2	no	—
253	C₅×C₈	—	4	2	no	—
254	C₂²×Q₈	C₂³×C₅	1	2	yes	—
255	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
256	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
257	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
259	C₂×Q₁₆	—	4	2	no	—
260	C₂×Q₁₆	—	4	2	no	—
261	C₂×Q₁₆	—	4	2	no	—
262	C₂²×C₈	C₂³×C₅	1	2	yes	—
263	C₂²×C₈	C₂³×C₅	1	2	yes	—
264	C₄⋊Q₈	—	4	2	no	—
265	C₂²⋊Q₈	—	4	2	no	—
266	C₂²⋊Q₈	—	4	2	no	—
267	C₂²⋊Q₈	—	4	2	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₄²	—	4	2	no	—
284	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
285	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
288	#107	—	4	2	no	—
289	C₄⋊C₈	—	4	2	no	—
290	#103	—	4	2	no	—
291	#103	—	4	2	no	—
292	#103	—	4	2	no	—
293	#103	—	4	2	no	—
294	C₂²⋊C₈	—	4	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	—	2	1	no	—
298	#95	—	2	1	no	—
299	#95	—	2	1	no	—
300	#95	—	2	1	no	—
301	#95	—	2	1	no	—
302	#95	—	2	1	no	—
303	#95	—	2	1	no	—
304	C₂²×C₅	—	2	2	no	—
305	C₂²×C₅	—	2	2	no	—
306	C₂²×C₅	—	2	2	no	—
307	C₂²×C₅	—	4	1	no	—
308	C₂²×C₅	—	4	1	no	—
309	C₂²×C₅	—	4	1	no	—
310	C₂²×C₅	—	4	1	no	—
311	C₂²×C₅	#534	1	1	yes	characteristic
312	C₂²×C₅	#535	1	1	yes	characteristic
313	C₂²×C₅	#537	1	1	yes	characteristic
314	C₂²×C₅	C₂²×Q₁₆	1	1	yes	characteristic
315	C₂²×C₅	C₂×#137	1	1	yes	characteristic
316	C₂²×C₅	#575	1	1	yes	characteristic
317	C₂²×C₅	#575	1	1	yes	characteristic
318	C₄×C₅	—	2	2	no	—
319	C₄×C₅	—	2	2	no	—
320	C₄×C₅	—	2	2	no	—
321	C₄×C₅	—	4	1	no	—
322	C₄×C₅	—	4	1	no	—
323	C₄×C₅	—	8	1	no	—
324	C₄×C₅	—	8	2	no	—
325	C₄×C₅	—	8	1	no	—
326	C₄×C₅	—	8	1	no	—
327	C₄×C₅	—	8	1	no	—
328	C₄×C₅	—	8	2	no	—
329	C₄×C₅	#560	1	2	yes	—
330	C₄×C₅	#562	1	2	yes	—
331	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	C₅×Q₁₆	1	4	yes	complemented
358	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
361	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
362	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
363	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
364	Q₁₆	—	4	8	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₂²⋊C₄	—	4	2	no	—
386	C₂²⋊C₄	—	4	4	no	—
387	C₂²⋊C₄	—	4	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	4	1	no	—
391	C₄²	—	4	1	no	—
392	C₂×C₅	—	4	2	no	—
393	C₂×C₅	#2813	1	1	yes	characteristic
394	C₂×C₅	#3189	1	1	yes	characteristic
395	C₂×C₅	#3196	1	1	yes	characteristic
396	C₂×C₅	#3209	1	1	yes	characteristic
397	C₂×C₅	#3219	1	1	yes	characteristic
398	C₂×C₅	#3249	1	1	yes	characteristic
399	C₂×C₅	#3252	1	1	yes	characteristic
400	C₂³	—	2	1	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	C₂×C₅×Q₁₆	1	2	yes	—
407	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
408	Q₈	—	4	2	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	4	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
449	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
450	C₂×C₄	C₅×#137	1	2	yes	—
451	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
453	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
454	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
455	C₈	—	4	2	no	—
456	C₈	—	4	2	no	—
457	C₅	#32724	1	1	yes	characteristic, direct product factor, Sylow
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	C₅×#534	1	1	yes	characteristic
466	C₂²	C₅×#535	1	1	yes	characteristic
467	C₂²	C₅×#537	1	1	yes	characteristic
468	C₂²	C₂²×C₅×Q₁₆	1	1	yes	characteristic
469	C₂²	C₂×C₅×#137	1	1	yes	characteristic
470	C₂²	C₅×#575	1	1	yes	characteristic
471	C₂²	C₅×#575	1	1	yes	characteristic
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	1	no	—
477	C₄	—	8	1	no	—
478	C₄	—	8	1	no	—
479	C₄	—	8	2	no	—
480	C₄	—	8	1	no	—
481	C₄	—	8	2	no	—
482	C₄	—	8	1	no	—
483	C₄	C₅×#560	1	2	yes	—
484	C₄	C₅×#562	1	2	yes	—
485	C₂	—	4	2	no	—
486	C₂	C₅×#2813	1	1	yes	characteristic
487	C₂	C₅×#3189	1	1	yes	characteristic
488	C₂	C₅×#3196	1	1	yes	characteristic
489	C₂	C₅×#3209	1	1	yes	characteristic
490	C₂	C₅×#3219	1	1	yes	characteristic
491	C₂	C₅×#3249	1	1	yes	characteristic
492	C₂	C₅×#3252	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#2100	C₂	semidirect
4. C₅×#2095	C₂	semidirect
5. C₅×#2068	C₂	semidirect
6. C₅×#2056	C₂	semidirect
7. C₅×#2043	C₂	semidirect
9. C₅×#2016	C₂	semidirect
43. #32724	C₅	direct (N × H)
96. #2100	C₂×C₅	semidirect
97. #2095	C₂×C₅	semidirect
98. #2068	C₂×C₅	semidirect
99. #2056	C₂×C₅	semidirect
100. #2043	C₂×C₅	semidirect
102. #2016	C₂×C₅	semidirect
131. C₂²×C₄×C₅	Q₁₆	semidirect
357. C₂²×C₄	C₅×Q₁₆	semidirect
457. C₅	#32724	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×#2857	2
C₅×#2855	2
C₅×#2100	2
C₅×#2095	2
C₅×#2068	2
C₅×#2056	2
C₅×#2043	2
C₅×#2036	2
C₅×#2016	2
C₅×#2001	2
C₅×#1797	2
#32724	5

Subgroups — C5×#32724 #11955444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#32724 #11955444