Subgroups — C₅×#19872 #11942592

Order 1280.

580 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3398	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3394	C₂	1	1	yes	maximal, characteristic
3	C₅×#3365	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3342	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1722	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1686	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1681	C₂	1	1	yes	maximal, characteristic
8	C₅×#1674	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1670	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1650	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1648	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1640	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1628	C₂	1	1	yes	maximal, characteristic
14	C₅×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#559	C₂²	1	1	yes	characteristic
17	C₅×#557	C₂²	1	1	yes	characteristic
18	C₅×#556	C₂²	1	1	yes	characteristic
19	C₅×#556	C₂²	1	1	yes	characteristic
20	C₅×#500	C₂²	1	1	yes	characteristic
21	C₅×#500	C₂²	1	1	yes	characteristic
22	C₅×#497	—	2	1	no	—
23	C₅×#495	—	2	1	no	—
24	C₅×#494	C₂²	1	1	yes	characteristic
25	C₅×#492	C₂²	1	1	yes	characteristic
26	C₅×#488	—	2	1	no	—
27	C₅×#486	C₂²	1	1	yes	characteristic
28	C₅×#486	C₂²	1	1	yes	characteristic
29	C₅×#485	—	2	1	no	—
30	C₅×#485	—	2	1	no	—
31	C₅×#478	—	2	1	no	—
32	C₅×#475	C₂²	1	1	yes	characteristic
33	C₅×#475	C₂²	1	1	yes	characteristic
34	C₅×#475	C₂²	1	1	yes	characteristic
35	C₅×#467	—	2	1	no	—
36	C₅×#464	—	2	1	no	—
37	C₅×#464	—	2	1	no	—
38	C₅×#464	—	2	1	no	—
39	C₅×#463	—	2	1	no	—
40	C₅×#462	—	2	1	no	—
41	C₅×#462	C₂²	1	1	yes	characteristic
42	C₅×#462	C₂²	1	1	yes	characteristic
43	C₅×#461	C₂²	1	1	yes	characteristic
44	C₅×#460	C₂²	1	1	yes	characteristic
45	C₅×#459	C₂²	1	1	yes	characteristic
46	C₅×#446	C₂²	1	1	yes	characteristic
47	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
48	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
49	C₅×#441	—	2	1	no	—
50	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
51	C₄×C₅×SD₁₆	—	2	1	no	—
52	C₄×C₅×SD₁₆	—	2	1	no	—
53	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
54	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
55	C₅×#427	—	2	1	no	—
56	C₅×#335	C₂²	1	1	yes	characteristic
57	C₅×#335	C₂²	1	1	yes	characteristic
58	C₅×#332	C₂²	1	1	yes	characteristic
59	C₅×#332	C₂²	1	1	yes	characteristic
60	C₅×#332	C₂²	1	1	yes	characteristic
61	C₅×#331	C₂²	1	1	yes	characteristic
62	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₅×#322	C₂²	1	1	yes	characteristic
67	#19872	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×Q₁₆	—	2	1	no	—
69	C₂×C₅×Q₁₆	—	2	1	no	—
70	C₂×C₅×Q₁₆	—	2	1	no	—
71	C₂×C₅×Q₁₆	—	2	1	no	—
72	C₂×C₅×Q₁₆	D₄	1	1	yes	characteristic
73	C₂×C₅×SD₁₆	—	2	1	no	—
74	C₂×C₅×SD₁₆	—	2	1	no	—
75	C₂×C₅×SD₁₆	—	2	1	no	—
76	C₂×C₅×SD₁₆	—	2	1	no	—
77	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
78	C₂×C₅×D₈	—	2	1	no	—
79	C₂²×C₅×C₈	—	2	1	no	—
80	C₅×C₄⋊Q₈	—	2	1	no	—
81	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₅×#127	C₂³	1	1	yes	characteristic
85	C₅×#126	—	4	1	no	—
86	C₅×#126	—	4	1	no	—
87	C₅×#125	—	2	1	no	—
88	C₅×#125	—	4	1	no	—
89	C₅×#124	—	2	1	no	—
90	C₅×#124	—	2	1	no	—
91	C₅×#124	—	2	1	no	—
92	C₅×#124	—	2	1	no	—
93	C₅×#123	—	4	1	no	—
94	C₅×C₂²⋊Q₈	—	2	1	no	—
95	C₅×C₂²⋊Q₈	—	2	1	no	—
96	C₄×C₅×Q₈	—	2	1	no	—
97	C₄×C₅×Q₈	—	2	1	no	—
98	C₄×C₅×Q₈	—	2	1	no	—
99	C₄×C₅×Q₈	—	2	1	no	—
100	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
101	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
102	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
103	C₄×C₅×D₄	—	2	1	no	—
104	C₄×C₅×D₄	—	2	1	no	—
105	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
106	C₅×#117	—	2	1	no	—
107	C₅×#117	—	2	1	no	—
108	C₅×#107	—	2	1	no	—
109	C₅×#107	—	2	1	no	—
110	C₅×#107	—	4	1	no	—
111	C₅×#107	D₄	1	1	yes	characteristic
112	C₅×#106	—	2	1	no	—
113	C₅×#106	—	2	1	no	—
114	C₅×#106	—	2	1	no	—
115	C₅×#106	D₄	1	1	yes	characteristic
116	C₅×C₄⋊C₈	—	2	1	no	—
117	C₅×C₄⋊C₈	—	2	1	no	—
118	C₅×C₄⋊C₈	—	2	1	no	—
119	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₅×#103	—	2	1	no	—
124	C₅×#103	—	2	1	no	—
125	C₅×#103	—	2	1	no	—
126	C₅×#103	—	2	1	no	—
127	C₅×#103	—	2	1	no	—
128	C₅×#103	—	2	1	no	—
129	C₅×#103	D₄	1	1	yes	characteristic
130	C₅×#103	D₄	1	1	yes	characteristic
131	C₅×#103	D₄	1	1	yes	characteristic
132	C₅×#102	—	2	1	no	—
133	C₅×#102	—	2	1	no	—
134	C₅×#102	—	2	1	no	—
135	C₅×#102	—	2	1	no	—
136	C₅×#102	—	4	1	no	—
137	C₅×#102	D₄	1	1	yes	characteristic
138	C₅×C₂²⋊C₈	—	2	1	no	—
139	C₅×#97	—	2	1	no	—
140	C₄×C₅×C₈	—	2	1	no	—
141	C₄×C₅×C₈	—	2	1	no	—
142	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
143	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
144	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
145	#3398	C₂×C₅	1	1	yes	characteristic, complemented
146	#3394	C₂×C₅	1	1	yes	characteristic
147	#3365	C₂×C₅	1	1	yes	characteristic, complemented
148	#3342	C₂×C₅	1	1	yes	characteristic, complemented
149	#1722	C₂×C₅	1	1	yes	characteristic, complemented
150	#1686	C₂×C₅	1	1	yes	characteristic, complemented
151	#1681	C₂×C₅	1	1	yes	characteristic
152	#1674	C₂×C₅	1	1	yes	characteristic, complemented
153	#1670	C₂×C₅	1	1	yes	characteristic, complemented
154	#1650	C₂×C₅	1	1	yes	characteristic, complemented
155	#1648	C₂×C₅	1	1	yes	characteristic, complemented
156	#1640	C₂×C₅	1	1	yes	characteristic, complemented
157	#1628	C₂×C₅	1	1	yes	characteristic
158	#1584	C₂×C₅	1	1	yes	characteristic, complemented
159	SD₁₆⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂×C₅×Q₈	—	2	1	no	—
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
164	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
165	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
166	C₂×C₅×D₄	—	2	1	no	—
167	C₂×C₅×D₄	—	2	1	no	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	4	1	no	—
172	C₅×Q₁₆	—	4	1	no	—
173	C₅×Q₁₆	—	4	2	no	—
174	C₅×Q₁₆	—	8	1	no	—
175	C₅×Q₁₆	—	8	1	no	—
176	C₅×Q₁₆	—	8	1	no	—
177	C₅×SD₁₆	—	2	2	no	—
178	C₅×SD₁₆	—	4	2	no	—
179	C₅×SD₁₆	—	4	2	no	—
180	C₅×SD₁₆	—	8	1	no	—
181	C₅×SD₁₆	—	8	1	no	—
182	C₅×D₈	—	8	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	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	—	4	2	no	—
189	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
192	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	—	2	1	no	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	—	4	1	no	—
203	C₅×C₄⋊C₄	—	4	1	no	—
204	C₅×C₄⋊C₄	—	4	1	no	—
205	C₅×C₄⋊C₄	—	4	1	no	—
206	C₅×C₄⋊C₄	—	4	1	no	—
207	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
208	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
209	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
210	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
211	C₅×C₂²⋊C₄	—	2	1	no	—
212	C₅×C₂²⋊C₄	—	4	1	no	—
213	C₅×C₂²⋊C₄	—	4	1	no	—
214	C₅×C₂²⋊C₄	—	4	1	no	—
215	C₅×C₂²⋊C₄	—	4	1	no	—
216	C₅×C₂²⋊C₄	—	4	1	no	—
217	C₅×C₂²⋊C₄	—	4	1	no	—
218	C₅×C₂²⋊C₄	—	4	1	no	—
219	C₄²×C₅	—	2	1	no	—
220	C₄²×C₅	—	2	1	no	—
221	C₄²×C₅	—	2	1	no	—
222	C₄²×C₅	—	4	1	no	—
223	C₄²×C₅	—	4	1	no	—
224	C₄²×C₅	—	4	1	no	—
225	C₄²×C₅	C₂⁴	1	1	yes	characteristic
226	#559	C₂²×C₅	1	1	yes	characteristic
227	#557	C₂²×C₅	1	1	yes	characteristic
228	#556	C₂²×C₅	1	1	yes	characteristic
229	#556	C₂²×C₅	1	1	yes	characteristic
230	#500	C₂²×C₅	1	1	yes	characteristic
231	#500	C₂²×C₅	1	1	yes	characteristic
232	#497	—	2	1	no	—
233	#495	—	2	1	no	—
234	#494	C₂²×C₅	1	1	yes	characteristic
235	#492	C₂²×C₅	1	1	yes	characteristic
236	#488	—	2	1	no	—
237	#486	C₂²×C₅	1	1	yes	characteristic
238	#486	C₂²×C₅	1	1	yes	characteristic
239	#485	—	2	1	no	—
240	#485	—	2	1	no	—
241	#478	—	2	1	no	—
242	#475	C₂²×C₅	1	1	yes	characteristic
243	#475	C₂²×C₅	1	1	yes	characteristic
244	#475	C₂²×C₅	1	1	yes	characteristic
245	#467	—	2	1	no	—
246	#464	—	2	1	no	—
247	#464	—	2	1	no	—
248	#464	—	2	1	no	—
249	#463	—	2	1	no	—
250	#462	—	2	1	no	—
251	#462	C₂²×C₅	1	1	yes	characteristic
252	#462	C₂²×C₅	1	1	yes	characteristic
253	#461	C₂²×C₅	1	1	yes	characteristic
254	#460	C₂²×C₅	1	1	yes	characteristic
255	#459	C₂²×C₅	1	1	yes	characteristic
256	#446	C₂²×C₅	1	1	yes	characteristic
257	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
258	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
259	#441	—	2	1	no	—
260	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
261	C₄×SD₁₆	—	2	1	no	—
262	C₄×SD₁₆	—	2	1	no	—
263	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
264	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
265	#427	—	2	1	no	—
266	#335	C₂²×C₅	1	1	yes	characteristic
267	#335	C₂²×C₅	1	1	yes	characteristic
268	#332	C₂²×C₅	1	1	yes	characteristic
269	#332	C₂²×C₅	1	1	yes	characteristic
270	#332	C₂²×C₅	1	1	yes	characteristic
271	#331	C₂²×C₅	1	1	yes	characteristic
272	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
273	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
274	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
275	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
276	#322	C₂²×C₅	1	1	yes	characteristic
277	C₂³×C₅	—	2	1	no	—
278	C₂³×C₅	—	4	1	no	—
279	C₅×Q₈	—	2	1	no	—
280	C₅×Q₈	—	2	1	no	—
281	C₅×Q₈	—	2	1	no	—
282	C₅×Q₈	—	2	1	no	—
283	C₅×Q₈	—	2	1	no	—
284	C₅×Q₈	—	2	1	no	—
285	C₅×Q₈	—	4	1	no	—
286	C₅×Q₈	—	4	1	no	—
287	C₅×Q₈	—	4	1	no	—
288	C₅×Q₈	—	4	1	no	—
289	C₅×Q₈	—	4	1	no	—
290	C₅×Q₈	—	4	1	no	—
291	C₅×D₄	—	2	1	no	—
292	C₅×D₄	—	2	1	no	—
293	C₅×D₄	—	4	1	no	—
294	C₅×D₄	—	4	1	no	—
295	C₅×D₄	—	4	1	no	—
296	C₅×D₄	—	4	1	no	—
297	C₅×D₄	—	8	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	4	1	no	—
306	C₂×C₄×C₅	—	4	1	no	—
307	C₂×C₄×C₅	—	4	1	no	—
308	C₂×C₄×C₅	—	4	1	no	—
309	C₂×C₄×C₅	—	4	1	no	—
310	C₂×C₄×C₅	—	16	1	no	—
311	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
314	C₅×C₈	—	2	1	no	—
315	C₅×C₈	—	2	1	no	—
316	C₅×C₈	—	2	1	no	—
317	C₅×C₈	—	4	1	no	—
318	C₅×C₈	—	4	1	no	—
319	C₅×C₈	—	4	1	no	—
320	C₅×C₈	—	4	1	no	—
321	C₅×C₈	—	4	1	no	—
322	C₅×C₈	#135	1	2	yes	—
323	C₂×Q₁₆	—	2	1	no	—
324	C₂×Q₁₆	—	2	1	no	—
325	C₂×Q₁₆	—	2	1	no	—
326	C₂×Q₁₆	—	2	1	no	—
327	C₂×Q₁₆	C₅×D₄	1	1	yes	characteristic
328	C₂×SD₁₆	—	2	1	no	—
329	C₂×SD₁₆	—	2	1	no	—
330	C₂×SD₁₆	—	2	1	no	—
331	C₂×SD₁₆	—	2	1	no	—
332	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
333	C₂×D₈	—	2	1	no	—
334	C₂²×C₈	—	2	1	no	—
335	C₄⋊Q₈	—	2	1	no	—
336	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
337	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
338	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
339	#127	C₂³×C₅	1	1	yes	characteristic
340	#126	—	4	1	no	—
341	#126	—	4	1	no	—
342	#125	—	2	1	no	—
343	#125	—	4	1	no	—
344	#124	—	2	1	no	—
345	#124	—	2	1	no	—
346	#124	—	2	1	no	—
347	#124	—	2	1	no	—
348	#123	—	4	1	no	—
349	C₂²⋊Q₈	—	2	1	no	—
350	C₂²⋊Q₈	—	2	1	no	—
351	C₄×Q₈	—	2	1	no	—
352	C₄×Q₈	—	2	1	no	—
353	C₄×Q₈	—	2	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
356	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
357	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
361	#117	—	2	1	no	—
362	#117	—	2	1	no	—
363	#107	—	2	1	no	—
364	#107	—	2	1	no	—
365	#107	—	4	1	no	—
366	#107	C₅×D₄	1	1	yes	characteristic
367	#106	—	2	1	no	—
368	#106	—	2	1	no	—
369	#106	—	2	1	no	—
370	#106	C₅×D₄	1	1	yes	characteristic
371	C₄⋊C₈	—	2	1	no	—
372	C₄⋊C₈	—	2	1	no	—
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
375	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
376	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
377	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
378	#103	—	2	1	no	—
379	#103	—	2	1	no	—
380	#103	—	2	1	no	—
381	#103	—	2	1	no	—
382	#103	—	2	1	no	—
383	#103	—	2	1	no	—
384	#103	C₅×D₄	1	1	yes	characteristic
385	#103	C₅×D₄	1	1	yes	characteristic
386	#103	C₅×D₄	1	1	yes	characteristic
387	#102	—	2	1	no	—
388	#102	—	2	1	no	—
389	#102	—	2	1	no	—
390	#102	—	2	1	no	—
391	#102	—	4	1	no	—
392	#102	C₅×D₄	1	1	yes	characteristic
393	C₂²⋊C₈	—	2	1	no	—
394	#97	—	2	1	no	—
395	C₄×C₈	—	2	1	no	—
396	C₄×C₈	—	2	1	no	—
397	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
398	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
399	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
400	C₂²×C₅	—	4	1	no	—
401	C₂²×C₅	—	4	1	no	—
402	C₂²×C₅	—	4	1	no	—
403	C₂²×C₅	—	8	1	no	—
404	C₂²×C₅	—	8	1	no	—
405	C₂²×C₅	—	8	1	no	—
406	C₂²×C₅	D₄²	1	1	yes	characteristic
407	C₄×C₅	—	2	1	no	—
408	C₄×C₅	—	4	1	no	—
409	C₄×C₅	—	4	1	no	—
410	C₄×C₅	—	4	1	no	—
411	C₄×C₅	—	4	1	no	—
412	C₄×C₅	—	4	1	no	—
413	C₄×C₅	—	4	1	no	—
414	C₄×C₅	—	4	1	no	—
415	C₄×C₅	—	8	1	no	—
416	C₄×C₅	—	8	1	no	—
417	C₄×C₅	—	8	1	no	—
418	C₄×C₅	C₂×#135	1	1	yes	characteristic
419	C₄×C₅	#575	1	1	yes	characteristic
420	C₄×C₅	#576	1	1	yes	characteristic
421	C₄×C₅	#578	1	1	yes	characteristic
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
426	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
427	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	4	1	no	—
434	Q₁₆	—	4	1	no	—
435	Q₁₆	—	4	2	no	—
436	Q₁₆	—	8	1	no	—
437	Q₁₆	—	8	1	no	—
438	Q₁₆	—	8	1	no	—
439	SD₁₆	—	2	2	no	—
440	SD₁₆	—	4	2	no	—
441	SD₁₆	—	4	2	no	—
442	SD₁₆	—	8	1	no	—
443	SD₁₆	—	8	1	no	—
444	D₈	—	8	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	4	2	no	—
451	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
452	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
453	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
454	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
470	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
471	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
472	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₂²⋊C₄	—	4	1	no	—
477	C₂²⋊C₄	—	4	1	no	—
478	C₂²⋊C₄	—	4	1	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	4	1	no	—
485	C₄²	—	4	1	no	—
486	C₄²	—	4	1	no	—
487	C₄²	C₂⁴×C₅	1	1	yes	characteristic
488	C₂×C₅	—	8	1	no	—
489	C₂×C₅	—	16	1	no	—
490	C₂×C₅	#3269	1	1	yes	characteristic
491	C₂×C₅	#3287	1	1	yes	characteristic
492	C₂×C₅	#3289	1	1	yes	characteristic
493	C₂³	—	2	1	no	—
494	C₂³	—	4	1	no	—
495	Q₈	—	2	1	no	—
496	Q₈	—	2	1	no	—
497	Q₈	—	2	1	no	—
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	2	1	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	4	1	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	D₄	—	2	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	4	1	no	—
510	D₄	—	4	1	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	1	no	—
513	D₄	—	8	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	16	1	no	—
527	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
528	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
529	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	C₅×#135	1	2	yes	—
539	C₅	#19872	1	1	yes	characteristic, direct product factor, Sylow
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	C₅×D₄²	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	C₂×C₅×#135	1	1	yes	characteristic
559	C₄	C₅×#575	1	1	yes	characteristic
560	C₄	C₅×#576	1	1	yes	characteristic
561	C₄	C₅×#578	1	1	yes	characteristic
562	C₂	—	8	1	no	—
563	C₂	—	16	1	no	—
564	C₂	C₅×#3269	1	1	yes	characteristic
565	C₂	C₅×#3287	1	1	yes	characteristic
566	C₂	C₅×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#459	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3398	C₂	semidirect
3. C₅×#3365	C₂	semidirect
4. C₅×#3342	C₂	semidirect
5. C₅×#1722	C₂	semidirect
6. C₅×#1686	C₂	semidirect
8. C₅×#1674	C₂	semidirect
9. C₅×#1670	C₂	semidirect
10. C₅×#1650	C₂	semidirect
11. C₅×#1648	C₂	semidirect
12. C₅×#1640	C₂	semidirect
14. C₅×#1584	C₂	semidirect
15. C₅×SD₁₆⋊C₈	C₂	semidirect
67. #19872	C₅	direct (N × H)
145. #3398	C₂×C₅	semidirect
147. #3365	C₂×C₅	semidirect
148. #3342	C₂×C₅	semidirect
149. #1722	C₂×C₅	semidirect
150. #1686	C₂×C₅	semidirect
152. #1674	C₂×C₅	semidirect
153. #1670	C₂×C₅	semidirect
154. #1650	C₂×C₅	semidirect
155. #1648	C₂×C₅	semidirect
156. #1640	C₂×C₅	semidirect
158. #1584	C₂×C₅	semidirect
159. SD₁₆⋊C₈	C₂×C₅	semidirect
539. C₅	#19872	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×#3398	2
C₅×#3394	2
C₅×#3365	2
C₅×#3342	2
C₅×#1722	2
C₅×#1686	2
C₅×#1681	2
C₅×#1674	2
C₅×#1670	2
C₅×#1650	2
C₅×#1648	2
C₅×#1640	2
C₅×#1628	2
C₅×#1584	2
C₅×SD₁₆⋊C₈	2
#19872	5

Subgroups — C5×#19872 #11942592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19872 #11942592