Subgroups — C₅×#19871 #11942591

Order 1280.

632 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3399	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3304	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1721	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1686	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1682	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1668	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1667	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1640	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1628	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1621	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1620	C₂	1	1	yes	maximal, characteristic, complemented
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×#559	C₂²	1	1	yes	characteristic
18	C₅×#556	C₂²	1	1	yes	characteristic
19	C₅×#550	C₂²	1	1	yes	characteristic
20	C₅×#496	—	2	1	no	—
21	C₅×#495	—	2	1	no	—
22	C₅×#495	—	2	1	no	—
23	C₅×#493	C₂²	1	1	yes	characteristic
24	C₅×#493	C₂²	1	1	yes	characteristic
25	C₅×#493	C₂²	1	1	yes	characteristic
26	C₅×#492	C₂²	1	1	yes	characteristic
27	C₅×#486	C₂²	1	1	yes	characteristic
28	C₅×#486	C₂²	1	1	yes	characteristic
29	C₅×#482	—	2	1	no	—
30	C₅×#475	C₂²	1	1	yes	characteristic
31	C₅×#465	—	2	1	no	—
32	C₅×#464	—	2	1	no	—
33	C₅×#463	—	2	1	no	—
34	C₅×#463	—	2	1	no	—
35	C₅×#463	—	2	1	no	—
36	C₅×#463	—	2	1	no	—
37	C₅×#462	C₂²	1	1	yes	characteristic
38	C₅×#460	C₂²	1	1	yes	characteristic
39	C₅×#460	C₂²	1	1	yes	characteristic
40	C₅×#460	C₂²	1	1	yes	characteristic
41	C₅×#460	C₂²	1	1	yes	characteristic
42	C₅×#459	—	2	1	no	—
43	C₅×#459	C₂²	1	1	yes	characteristic
44	C₅×#459	C₂²	1	1	yes	characteristic
45	C₅×#452	—	2	1	no	—
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×#442	—	2	1	no	—
50	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
51	C₄×C₅×SD₁₆	—	2	1	no	—
52	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
53	C₄×C₅×D₈	—	2	1	no	—
54	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
55	C₅×#416	—	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×#331	C₂²	1	1	yes	characteristic
60	C₅×#331	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	#19871	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	—	2	1	no	—
69	C₂×C₅×Q₁₆	—	2	1	no	—
70	C₂×C₅×Q₁₆	D₄	1	1	yes	characteristic
71	C₂×C₅×SD₁₆	—	2	1	no	—
72	C₂×C₅×SD₁₆	—	2	1	no	—
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	C₂×C₅×D₈	—	2	1	no	—
80	C₂×C₅×D₈	—	2	1	no	—
81	C₂×C₅×D₈	—	2	1	no	—
82	C₂×C₅×D₈	—	2	1	no	—
83	C₂×C₅×D₈	—	2	1	no	—
84	C₂×C₅×D₈	—	4	1	no	—
85	C₂²×C₅×C₈	—	2	1	no	—
86	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₅×#127	—	2	1	no	—
88	C₅×#127	C₂³	1	1	yes	characteristic
89	C₅×#127	C₂³	1	1	yes	characteristic
90	C₅×#127	C₂³	1	1	yes	characteristic
91	C₅×#126	—	4	1	no	—
92	C₅×#124	—	2	1	no	—
93	C₅×#124	—	2	1	no	—
94	C₅×#124	—	2	1	no	—
95	C₅×#124	—	2	1	no	—
96	C₅×#124	—	2	1	no	—
97	C₅×#123	—	4	1	no	—
98	C₅×#123	—	4	1	no	—
99	C₅×C₂²⋊Q₈	—	2	1	no	—
100	C₅×#121	—	2	1	no	—
101	C₅×#121	—	4	1	no	—
102	C₄×C₅×Q₈	—	2	1	no	—
103	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
104	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
105	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
106	C₄×C₅×D₄	—	2	1	no	—
107	C₄×C₅×D₄	—	2	1	no	—
108	C₄×C₅×D₄	—	2	1	no	—
109	C₄×C₅×D₄	—	2	1	no	—
110	C₄×C₅×D₄	—	2	1	no	—
111	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
112	C₅×#117	—	2	1	no	—
113	C₅×#107	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
126	C₅×#103	D₄	1	1	yes	characteristic
127	C₅×#103	D₄	1	1	yes	characteristic
128	C₅×#102	—	2	1	no	—
129	C₅×#102	—	2	1	no	—
130	C₅×#102	—	2	1	no	—
131	C₅×#102	—	2	1	no	—
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	#3399	C₂×C₅	1	1	yes	characteristic, complemented
146	#3396	C₂×C₅	1	1	yes	characteristic, complemented
147	#3394	C₂×C₅	1	1	yes	characteristic, complemented
148	#3304	C₂×C₅	1	1	yes	characteristic, complemented
149	#1721	C₂×C₅	1	1	yes	characteristic, complemented
150	#1686	C₂×C₅	1	1	yes	characteristic, complemented
151	#1682	C₂×C₅	1	1	yes	characteristic, complemented
152	#1668	C₂×C₅	1	1	yes	characteristic, complemented
153	#1667	C₂×C₅	1	1	yes	characteristic, complemented
154	#1640	C₂×C₅	1	1	yes	characteristic, complemented
155	#1628	C₂×C₅	1	1	yes	characteristic, complemented
156	#1621	C₂×C₅	1	1	yes	characteristic, complemented
157	#1620	C₂×C₅	1	1	yes	characteristic, complemented
158	#1584	C₂×C₅	1	1	yes	characteristic, complemented
159	SD₁₆⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
160	C₅×#41	—	4	2	no	—
161	C₅×#41	—	8	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	—	2	1	no	—
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	—	2	1	no	—
173	C₂×C₅×D₄	—	2	1	no	—
174	C₂×C₅×D₄	—	2	1	no	—
175	C₂×C₅×D₄	—	4	1	no	—
176	C₂×C₅×D₄	—	4	1	no	—
177	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	4	1	no	—
180	C₂²×C₄×C₅	—	4	1	no	—
181	C₂²×C₄×C₅	—	4	1	no	—
182	C₅×Q₁₆	—	4	1	no	—
183	C₅×Q₁₆	—	8	1	no	—
184	C₅×SD₁₆	—	2	2	no	—
185	C₅×SD₁₆	—	4	2	no	—
186	C₅×SD₁₆	—	8	1	no	—
187	C₅×SD₁₆	—	8	1	no	—
188	C₅×SD₁₆	—	8	1	no	—
189	C₅×SD₁₆	—	8	1	no	—
190	C₅×SD₁₆	—	8	1	no	—
191	C₅×D₈	—	4	2	no	—
192	C₅×D₈	—	4	2	no	—
193	C₅×D₈	—	8	1	no	—
194	C₅×D₈	—	8	1	no	—
195	C₅×D₈	—	8	1	no	—
196	C₅×D₈	—	8	1	no	—
197	C₅×D₈	—	8	2	no	—
198	C₂×C₅×C₈	—	2	1	no	—
199	C₂×C₅×C₈	—	2	1	no	—
200	C₂×C₅×C₈	—	2	1	no	—
201	C₂×C₅×C₈	—	2	1	no	—
202	C₂×C₅×C₈	—	2	1	no	—
203	C₂×C₅×C₈	—	8	1	no	—
204	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
205	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
206	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
207	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
208	C₅×C₄⋊C₄	—	2	1	no	—
209	C₅×C₄⋊C₄	—	2	1	no	—
210	C₅×C₄⋊C₄	—	2	1	no	—
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	—	4	1	no	—
214	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
215	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
216	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
217	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
218	C₅×C₂²⋊C₄	—	2	1	no	—
219	C₅×C₂²⋊C₄	—	4	1	no	—
220	C₅×C₂²⋊C₄	—	4	1	no	—
221	C₅×C₂²⋊C₄	—	4	1	no	—
222	C₅×C₂²⋊C₄	—	4	1	no	—
223	C₅×C₂²⋊C₄	—	4	1	no	—
224	C₅×C₂²⋊C₄	—	4	1	no	—
225	C₅×C₂²⋊C₄	—	4	1	no	—
226	C₅×C₂²⋊C₄	—	4	1	no	—
227	C₅×C₂²⋊C₄	—	4	1	no	—
228	C₄²×C₅	—	2	1	no	—
229	C₄²×C₅	—	2	1	no	—
230	C₄²×C₅	—	2	1	no	—
231	C₄²×C₅	—	4	1	no	—
232	C₄²×C₅	C₂⁴	1	1	yes	characteristic
233	#559	C₂²×C₅	1	1	yes	characteristic
234	#559	C₂²×C₅	1	1	yes	characteristic
235	#556	C₂²×C₅	1	1	yes	characteristic
236	#550	C₂²×C₅	1	1	yes	characteristic
237	#496	—	2	1	no	—
238	#495	—	2	1	no	—
239	#495	—	2	1	no	—
240	#493	C₂²×C₅	1	1	yes	characteristic
241	#493	C₂²×C₅	1	1	yes	characteristic
242	#493	C₂²×C₅	1	1	yes	characteristic
243	#492	C₂²×C₅	1	1	yes	characteristic
244	#486	C₂²×C₅	1	1	yes	characteristic
245	#486	C₂²×C₅	1	1	yes	characteristic
246	#482	—	2	1	no	—
247	#475	C₂²×C₅	1	1	yes	characteristic
248	#465	—	2	1	no	—
249	#464	—	2	1	no	—
250	#463	—	2	1	no	—
251	#463	—	2	1	no	—
252	#463	—	2	1	no	—
253	#463	—	2	1	no	—
254	#462	C₂²×C₅	1	1	yes	characteristic
255	#460	C₂²×C₅	1	1	yes	characteristic
256	#460	C₂²×C₅	1	1	yes	characteristic
257	#460	C₂²×C₅	1	1	yes	characteristic
258	#460	C₂²×C₅	1	1	yes	characteristic
259	#459	—	2	1	no	—
260	#459	C₂²×C₅	1	1	yes	characteristic
261	#459	C₂²×C₅	1	1	yes	characteristic
262	#452	—	2	1	no	—
263	#446	C₂²×C₅	1	1	yes	characteristic
264	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
265	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
266	#442	—	2	1	no	—
267	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
268	C₄×SD₁₆	—	2	1	no	—
269	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
270	C₄×D₈	—	2	1	no	—
271	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
272	#416	—	2	1	no	—
273	#335	C₂²×C₅	1	1	yes	characteristic
274	#335	C₂²×C₅	1	1	yes	characteristic
275	#332	C₂²×C₅	1	1	yes	characteristic
276	#331	C₂²×C₅	1	1	yes	characteristic
277	#331	C₂²×C₅	1	1	yes	characteristic
278	#331	C₂²×C₅	1	1	yes	characteristic
279	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
280	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
281	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
282	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
283	#322	C₂²×C₅	1	1	yes	characteristic
284	C₂³×C₅	—	2	1	no	—
285	C₂³×C₅	—	4	1	no	—
286	C₂³×C₅	—	4	1	no	—
287	C₂³×C₅	—	4	1	no	—
288	C₅×Q₈	—	2	1	no	—
289	C₅×Q₈	—	2	1	no	—
290	C₅×Q₈	—	2	1	no	—
291	C₅×Q₈	—	2	1	no	—
292	C₅×Q₈	—	2	1	no	—
293	C₅×Q₈	—	2	1	no	—
294	C₅×Q₈	—	4	1	no	—
295	C₅×Q₈	—	4	1	no	—
296	C₅×D₄	—	2	1	no	—
297	C₅×D₄	—	2	1	no	—
298	C₅×D₄	—	4	1	no	—
299	C₅×D₄	—	4	1	no	—
300	C₅×D₄	—	4	1	no	—
301	C₅×D₄	—	4	1	no	—
302	C₅×D₄	—	4	1	no	—
303	C₅×D₄	—	4	1	no	—
304	C₅×D₄	—	4	1	no	—
305	C₅×D₄	—	4	1	no	—
306	C₅×D₄	—	4	1	no	—
307	C₅×D₄	—	4	1	no	—
308	C₅×D₄	—	4	1	no	—
309	C₅×D₄	—	4	1	no	—
310	C₅×D₄	—	8	1	no	—
311	C₅×D₄	—	8	1	no	—
312	C₅×D₄	—	8	1	no	—
313	C₅×D₄	—	8	2	no	—
314	C₅×D₄	—	16	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	4	1	no	—
323	C₂×C₄×C₅	—	4	1	no	—
324	C₂×C₄×C₅	—	4	1	no	—
325	C₂×C₄×C₅	—	8	2	no	—
326	C₂×C₄×C₅	—	16	1	no	—
327	C₂×C₄×C₅	—	16	1	no	—
328	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
331	C₅×C₈	—	2	1	no	—
332	C₅×C₈	—	2	1	no	—
333	C₅×C₈	—	2	1	no	—
334	C₅×C₈	—	4	1	no	—
335	C₅×C₈	—	4	1	no	—
336	C₅×C₈	—	4	1	no	—
337	C₅×C₈	—	4	1	no	—
338	C₅×C₈	—	4	1	no	—
339	C₅×C₈	#135	1	2	yes	—
340	C₂×#41	—	2	1	no	—
341	C₂×Q₁₆	—	2	1	no	—
342	C₂×Q₁₆	C₅×D₄	1	1	yes	characteristic
343	C₂×SD₁₆	—	2	1	no	—
344	C₂×SD₁₆	—	2	1	no	—
345	C₂×SD₁₆	—	2	1	no	—
346	C₂×SD₁₆	—	2	1	no	—
347	C₂×SD₁₆	—	2	1	no	—
348	C₂×SD₁₆	—	2	1	no	—
349	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
350	C₂×D₈	—	2	1	no	—
351	C₂×D₈	—	2	1	no	—
352	C₂×D₈	—	2	1	no	—
353	C₂×D₈	—	2	1	no	—
354	C₂×D₈	—	2	1	no	—
355	C₂×D₈	—	2	1	no	—
356	C₂×D₈	—	4	1	no	—
357	C₂²×C₈	—	2	1	no	—
358	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
359	#127	—	2	1	no	—
360	#127	C₂³×C₅	1	1	yes	characteristic
361	#127	C₂³×C₅	1	1	yes	characteristic
362	#127	C₂³×C₅	1	1	yes	characteristic
363	#126	—	4	1	no	—
364	#124	—	2	1	no	—
365	#124	—	2	1	no	—
366	#124	—	2	1	no	—
367	#124	—	2	1	no	—
368	#124	—	2	1	no	—
369	#123	—	4	1	no	—
370	#123	—	4	1	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	#121	—	2	1	no	—
373	#121	—	4	1	no	—
374	C₄×Q₈	—	2	1	no	—
375	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
376	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
377	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
384	#117	—	2	1	no	—
385	#107	C₅×D₄	1	1	yes	characteristic
386	#106	—	2	1	no	—
387	#106	C₅×D₄	1	1	yes	characteristic
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	2	1	no	—
391	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
392	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
393	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
394	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
395	#103	—	2	1	no	—
396	#103	—	2	1	no	—
397	#103	C₅×D₄	1	1	yes	characteristic
398	#103	C₅×D₄	1	1	yes	characteristic
399	#103	C₅×D₄	1	1	yes	characteristic
400	#102	—	2	1	no	—
401	#102	—	2	1	no	—
402	#102	—	2	1	no	—
403	#102	—	2	1	no	—
404	#102	—	2	1	no	—
405	#102	—	2	1	no	—
406	#102	—	2	1	no	—
407	#102	—	2	1	no	—
408	#102	—	4	1	no	—
409	#102	C₅×D₄	1	1	yes	characteristic
410	C₂²⋊C₈	—	2	1	no	—
411	#97	—	2	1	no	—
412	C₄×C₈	—	2	1	no	—
413	C₄×C₈	—	2	1	no	—
414	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
415	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
416	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
417	C₂²×C₅	—	4	1	no	—
418	C₂²×C₅	—	4	1	no	—
419	C₂²×C₅	—	4	1	no	—
420	C₂²×C₅	—	8	1	no	—
421	C₂²×C₅	—	8	1	no	—
422	C₂²×C₅	—	8	1	no	—
423	C₂²×C₅	—	8	1	no	—
424	C₂²×C₅	—	8	1	no	—
425	C₂²×C₅	—	8	1	no	—
426	C₂²×C₅	—	8	1	no	—
427	C₂²×C₅	—	8	1	no	—
428	C₂²×C₅	—	8	1	no	—
429	C₂²×C₅	D₄²	1	1	yes	characteristic
430	C₄×C₅	—	2	1	no	—
431	C₄×C₅	—	4	1	no	—
432	C₄×C₅	—	4	1	no	—
433	C₄×C₅	—	4	1	no	—
434	C₄×C₅	—	4	1	no	—
435	C₄×C₅	—	4	1	no	—
436	C₄×C₅	—	4	1	no	—
437	C₄×C₅	—	4	1	no	—
438	C₄×C₅	—	8	1	no	—
439	C₄×C₅	C₂×#135	1	1	yes	characteristic
440	C₄×C₅	#575	1	1	yes	characteristic
441	C₄×C₅	#576	1	1	yes	characteristic
442	C₄×C₅	#576	1	1	yes	characteristic
443	#41	—	4	2	no	—
444	#41	—	8	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
447	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
448	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	4	1	no	—
459	C₂×D₄	—	4	1	no	—
460	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	4	1	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	Q₁₆	—	4	1	no	—
466	Q₁₆	—	8	1	no	—
467	SD₁₆	—	2	2	no	—
468	SD₁₆	—	4	2	no	—
469	SD₁₆	—	8	1	no	—
470	SD₁₆	—	8	1	no	—
471	SD₁₆	—	8	1	no	—
472	SD₁₆	—	8	1	no	—
473	SD₁₆	—	8	1	no	—
474	D₈	—	4	2	no	—
475	D₈	—	4	2	no	—
476	D₈	—	8	1	no	—
477	D₈	—	8	1	no	—
478	D₈	—	8	1	no	—
479	D₈	—	8	1	no	—
480	D₈	—	8	2	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	8	1	no	—
487	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
488	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
489	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
490	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
498	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
499	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
500	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	4	1	no	—
503	C₂²⋊C₄	—	4	1	no	—
504	C₂²⋊C₄	—	4	1	no	—
505	C₂²⋊C₄	—	4	1	no	—
506	C₂²⋊C₄	—	4	1	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₂²⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	4	1	no	—
515	C₄²	C₂⁴×C₅	1	1	yes	characteristic
516	C₂×C₅	—	8	1	no	—
517	C₂×C₅	—	16	1	no	—
518	C₂×C₅	—	16	1	no	—
519	C₂×C₅	—	16	1	no	—
520	C₂×C₅	#3268	1	1	yes	characteristic
521	C₂×C₅	#3287	1	1	yes	characteristic
522	C₂×C₅	#3288	1	1	yes	characteristic
523	C₂³	—	2	1	no	—
524	C₂³	—	4	1	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	1	no	—
527	Q₈	—	2	1	no	—
528	Q₈	—	2	1	no	—
529	Q₈	—	2	1	no	—
530	Q₈	—	2	1	no	—
531	Q₈	—	2	1	no	—
532	Q₈	—	2	1	no	—
533	Q₈	—	4	1	no	—
534	Q₈	—	4	1	no	—
535	D₄	—	2	1	no	—
536	D₄	—	2	1	no	—
537	D₄	—	4	1	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	8	1	no	—
550	D₄	—	8	1	no	—
551	D₄	—	8	1	no	—
552	D₄	—	8	2	no	—
553	D₄	—	16	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	8	2	no	—
565	C₂×C₄	—	16	1	no	—
566	C₂×C₄	—	16	1	no	—
567	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
568	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
569	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
570	C₈	—	2	1	no	—
571	C₈	—	2	1	no	—
572	C₈	—	2	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	—	4	1	no	—
577	C₈	—	4	1	no	—
578	C₈	C₅×#135	1	2	yes	—
579	C₅	#19871	1	1	yes	characteristic, direct product factor, Sylow
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	8	1	no	—
584	C₂²	—	8	1	no	—
585	C₂²	—	8	1	no	—
586	C₂²	—	8	1	no	—
587	C₂²	—	8	1	no	—
588	C₂²	—	8	1	no	—
589	C₂²	—	8	1	no	—
590	C₂²	—	8	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	C₅×D₄²	1	1	yes	characteristic
593	C₄	—	2	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	8	1	no	—
602	C₄	C₂×C₅×#135	1	1	yes	characteristic
603	C₄	C₅×#575	1	1	yes	characteristic
604	C₄	C₅×#576	1	1	yes	characteristic
605	C₄	C₅×#576	1	1	yes	characteristic
606	C₂	—	8	1	no	—
607	C₂	—	16	1	no	—
608	C₂	—	16	1	no	—
609	C₂	—	16	1	no	—
610	C₂	C₅×#3268	1	1	yes	characteristic
611	C₂	C₅×#3287	1	1	yes	characteristic
612	C₂	C₅×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
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×#3399	C₂	semidirect
2. C₅×#3396	C₂	semidirect
3. C₅×#3394	C₂	semidirect
4. C₅×#3304	C₂	semidirect
5. C₅×#1721	C₂	semidirect
6. C₅×#1686	C₂	semidirect
7. C₅×#1682	C₂	semidirect
8. C₅×#1668	C₂	semidirect
9. C₅×#1667	C₂	semidirect
10. C₅×#1640	C₂	semidirect
11. C₅×#1628	C₂	semidirect
12. C₅×#1621	C₂	semidirect
13. C₅×#1620	C₂	semidirect
14. C₅×#1584	C₂	semidirect
15. C₅×SD₁₆⋊C₈	C₂	semidirect
67. #19871	C₅	direct (N × H)
145. #3399	C₂×C₅	semidirect
146. #3396	C₂×C₅	semidirect
147. #3394	C₂×C₅	semidirect
148. #3304	C₂×C₅	semidirect
149. #1721	C₂×C₅	semidirect
150. #1686	C₂×C₅	semidirect
151. #1682	C₂×C₅	semidirect
152. #1668	C₂×C₅	semidirect
153. #1667	C₂×C₅	semidirect
154. #1640	C₂×C₅	semidirect
155. #1628	C₂×C₅	semidirect
156. #1621	C₂×C₅	semidirect
157. #1620	C₂×C₅	semidirect
158. #1584	C₂×C₅	semidirect
159. SD₁₆⋊C₈	C₂×C₅	semidirect
579. C₅	#19871	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×#3399	2
C₅×#3396	2
C₅×#3394	2
C₅×#3304	2
C₅×#1721	2
C₅×#1686	2
C₅×#1682	2
C₅×#1668	2
C₅×#1667	2
C₅×#1640	2
C₅×#1628	2
C₅×#1621	2
C₅×#1620	2
C₅×#1584	2
C₅×SD₁₆⋊C₈	2
#19871	5

Subgroups — C5×#19871 #11942591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19871 #11942591