Subgroups — C₅×#25269 #11947989

Order 1280.

754 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3093	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3055	C₂	1	1	yes	maximal, characteristic
4	C₅×#2933	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2090	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2078	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1952	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1931	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1907	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1900	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1855	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1815	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1742	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₂×C₅×#131	C₂²	1	1	yes	characteristic
18	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
20	C₅×#525	C₂²	1	1	yes	characteristic
21	C₂×C₅×#121	C₂²	1	1	yes	characteristic
22	C₂×C₅×#117	C₂²	1	1	yes	characteristic
23	C₅×#485	—	2	1	no	—
24	C₅×#485	—	2	1	no	—
25	C₅×#482	—	2	1	no	—
26	C₅×#482	—	2	1	no	—
27	C₅×#482	—	2	1	no	—
28	C₅×#482	—	2	1	no	—
29	C₅×#482	—	2	1	no	—
30	C₅×#482	—	2	1	no	—
31	C₅×#469	—	2	1	no	—
32	C₅×#468	—	2	1	no	—
33	C₅×#466	—	2	1	no	—
34	C₅×#465	—	2	1	no	—
35	C₅×#436	—	2	1	no	—
36	C₅×#435	—	2	1	no	—
37	C₅×#435	—	2	1	no	—
38	C₅×C₈×D₄	—	2	1	no	—
39	C₂×C₅×#108	C₂²	1	1	yes	characteristic
40	C₂×C₅×#108	C₂²	1	1	yes	characteristic
41	C₅×#428	C₂²	1	1	yes	characteristic
42	C₅×#428	C₂²	1	1	yes	characteristic
43	C₅×#428	C₂²	1	1	yes	characteristic
44	C₂×C₅×#107	C₂²	1	1	yes	characteristic
45	C₂×C₅×#106	C₂²	1	1	yes	characteristic
46	C₅×#424	C₂²	1	1	yes	characteristic
47	C₅×#418	C₂²	1	1	yes	characteristic
48	C₅×#417	C₂²	1	1	yes	characteristic
49	C₅×#417	C₂²	1	1	yes	characteristic
50	C₅×#417	C₂²	1	1	yes	characteristic
51	C₂×C₅×#102	C₂²	1	1	yes	characteristic
52	C₂×C₅×#102	C₂²	1	1	yes	characteristic
53	C₂×C₅×#100	C₂²	1	1	yes	characteristic
54	C₂×C₅×#100	C₂²	1	1	yes	characteristic
55	C₅×#408	C₂²	1	1	yes	characteristic
56	C₅×#407	C₂²	1	1	yes	characteristic
57	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₅×#405	C₂²	1	1	yes	characteristic
59	C₅×#343	C₂²	1	1	yes	characteristic
60	C₅×#343	C₂²	1	1	yes	characteristic
61	C₅×#343	C₂²	1	1	yes	characteristic
62	C₅×#343	C₂²	1	1	yes	characteristic
63	C₅×#343	C₂²	1	1	yes	characteristic
64	C₅×#343	C₂²	1	1	yes	characteristic
65	C₅×#341	C₂²	1	1	yes	characteristic
66	C₅×#341	C₂²	1	1	yes	characteristic
67	#25269	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	C₂³	1	1	yes	characteristic
69	C₂²×C₅×D₄	—	2	1	no	—
70	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₅×AGL(1,ℤ/8)	—	2	2	no	—
73	C₅×AGL(1,ℤ/8)	—	4	1	no	—
74	C₂×C₅×SD₁₆	—	2	1	no	—
75	C₂×C₅×D₈	—	2	1	no	—
76	C₅×#131	—	2	2	no	—
77	C₅×#131	—	4	1	no	—
78	C₂×C₅×M₁₆	—	2	1	no	—
79	C₂×C₅×M₁₆	—	2	1	no	—
80	C₂×C₅×M₁₆	—	2	1	no	—
81	C₂×C₅×M₁₆	—	2	2	no	—
82	C₂×C₅×M₁₆	—	2	2	no	—
83	C₂×C₅×M₁₆	—	4	1	no	—
84	C₂×C₅×M₁₆	—	4	1	no	—
85	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
87	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
89	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
90	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
91	C₂²×C₅×C₈	—	2	1	no	—
92	C₂²×C₅×C₈	—	2	1	no	—
93	C₂²×C₅×C₈	—	2	1	no	—
94	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
95	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
96	C₅×#123	—	2	1	no	—
97	C₅×C₂²⋊Q₈	D₄	1	1	yes	characteristic
98	C₅×C₂²⋊Q₈	D₄	1	1	yes	characteristic
99	C₅×#121	—	2	1	no	—
100	C₅×#121	—	2	1	no	—
101	C₅×#121	—	2	1	no	—
102	C₅×#121	—	2	1	no	—
103	C₅×#121	D₄	1	1	yes	characteristic
104	C₅×#121	D₄	1	1	yes	characteristic
105	C₅×#120	—	2	1	no	—
106	C₄×C₅×D₄	—	2	1	no	—
107	C₄×C₅×D₄	—	2	1	no	—
108	C₅×#117	—	2	1	no	—
109	C₅×#117	—	2	1	no	—
110	C₅×#117	—	2	1	no	—
111	C₅×#117	—	2	1	no	—
112	C₅×#117	C₂³	1	1	yes	characteristic
113	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₄²×C₅	—	2	1	no	—
119	C₅×#108	—	2	2	no	—
120	C₅×#108	—	4	1	no	—
121	C₅×#107	—	2	1	no	—
122	C₅×#107	—	2	1	no	—
123	C₅×#107	—	2	1	no	—
124	C₅×#107	—	2	1	no	—
125	C₅×#107	—	2	1	no	—
126	C₅×#106	—	2	1	no	—
127	C₅×#106	—	2	1	no	—
128	C₅×#106	—	2	1	no	—
129	C₅×#106	—	2	1	no	—
130	C₅×#106	—	2	1	no	—
131	C₅×C₄⋊C₈	—	2	1	no	—
132	C₅×C₄⋊C₈	—	2	1	no	—
133	C₅×#103	—	2	1	no	—
134	C₅×#103	—	2	1	no	—
135	C₅×#103	—	2	1	no	—
136	C₅×#102	—	2	1	no	—
137	C₅×#102	—	2	1	no	—
138	C₅×#102	—	2	1	no	—
139	C₅×#102	—	2	1	no	—
140	C₅×#102	—	2	1	no	—
141	C₅×#102	—	2	1	no	—
142	C₅×#102	—	2	1	no	—
143	C₅×#102	—	2	1	no	—
144	C₅×#102	—	2	1	no	—
145	C₅×#100	—	2	2	no	—
146	C₅×#100	—	4	1	no	—
147	C₅×C₂²⋊C₈	—	2	1	no	—
148	C₅×C₂²⋊C₈	—	2	1	no	—
149	C₅×C₂²⋊C₈	—	2	1	no	—
150	C₅×C₂²⋊C₈	—	2	1	no	—
151	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
152	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
153	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
154	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
155	C₅×#97	—	2	1	no	—
156	C₄×C₅×C₈	—	2	1	no	—
157	#3093	C₂×C₅	1	1	yes	characteristic, complemented
158	C₂×#482	C₂×C₅	1	1	yes	characteristic, complemented
159	#3055	C₂×C₅	1	1	yes	characteristic
160	#2933	C₂×C₅	1	1	yes	characteristic, complemented
161	#2090	C₂×C₅	1	1	yes	characteristic, complemented
162	#2078	C₂×C₅	1	1	yes	characteristic, complemented
163	#2063	C₂×C₅	1	1	yes	characteristic, complemented
164	#2051	C₂×C₅	1	1	yes	characteristic, complemented
165	#1952	C₂×C₅	1	1	yes	characteristic, complemented
166	#1931	C₂×C₅	1	1	yes	characteristic, complemented
167	#1907	C₂×C₅	1	1	yes	characteristic, complemented
168	#1900	C₂×C₅	1	1	yes	characteristic, complemented
169	#1855	C₂×C₅	1	1	yes	characteristic, complemented
170	#1815	C₂×C₅	1	1	yes	characteristic, complemented
171	#1742	C₂×C₅	1	1	yes	characteristic, complemented
172	C₂⁴×C₅	—	2	1	no	—
173	C₂⁴×C₅	#41	1	1	yes	characteristic
174	C₅×#41	—	2	1	no	—
175	C₅×#41	—	2	1	no	—
176	C₅×#41	—	2	1	no	—
177	C₅×#41	—	2	1	no	—
178	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
179	C₂×C₅×D₄	—	2	1	no	—
180	C₂×C₅×D₄	—	2	1	no	—
181	C₂×C₅×D₄	—	2	1	no	—
182	C₂×C₅×D₄	—	2	1	no	—
183	C₂×C₅×D₄	—	2	1	no	—
184	C₂×C₅×D₄	—	2	1	no	—
185	C₂×C₅×D₄	—	2	1	no	—
186	C₂×C₅×D₄	—	2	1	no	—
187	C₂×C₅×D₄	—	2	1	no	—
188	C₂×C₅×D₄	—	4	1	no	—
189	C₂×C₅×D₄	—	4	1	no	—
190	C₂×C₅×D₄	—	8	2	no	—
191	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₅	—	2	1	no	—
193	C₂²×C₄×C₅	—	2	1	no	—
194	C₂²×C₄×C₅	—	2	1	no	—
195	C₂²×C₄×C₅	—	2	1	no	—
196	C₂²×C₄×C₅	—	2	1	no	—
197	C₂²×C₄×C₅	—	2	1	no	—
198	C₂²×C₄×C₅	—	2	1	no	—
199	C₂²×C₄×C₅	—	2	1	no	—
200	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₅	#41	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
206	C₅×SD₁₆	—	4	2	no	—
207	C₅×D₈	—	4	2	no	—
208	C₅×M₁₆	—	2	1	no	—
209	C₅×M₁₆	—	2	1	no	—
210	C₅×M₁₆	—	2	1	no	—
211	C₅×M₁₆	—	2	1	no	—
212	C₅×M₁₆	—	2	1	no	—
213	C₅×M₁₆	—	2	1	no	—
214	C₅×M₁₆	—	2	1	no	—
215	C₅×M₁₆	—	2	1	no	—
216	C₅×M₁₆	—	2	1	no	—
217	C₅×M₁₆	—	2	1	no	—
218	C₅×M₁₆	—	4	2	no	—
219	C₅×M₁₆	—	4	2	no	—
220	C₅×M₁₆	—	4	2	no	—
221	C₅×M₁₆	#41	1	2	yes	—
222	C₅×M₁₆	#41	1	2	yes	—
223	C₂×C₅×C₈	—	2	1	no	—
224	C₂×C₅×C₈	—	2	1	no	—
225	C₂×C₅×C₈	—	2	1	no	—
226	C₂×C₅×C₈	—	2	1	no	—
227	C₂×C₅×C₈	—	2	1	no	—
228	C₂×C₅×C₈	—	2	1	no	—
229	C₂×C₅×C₈	—	2	1	no	—
230	C₂×C₅×C₈	—	2	1	no	—
231	C₂×C₅×C₈	—	2	1	no	—
232	C₂×C₅×C₈	—	2	1	no	—
233	C₂×C₅×C₈	—	4	2	no	—
234	C₂×C₅×C₈	—	4	2	no	—
235	C₂×C₅×C₈	—	4	2	no	—
236	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
237	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
238	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
239	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
240	C₅×C₄⋊C₄	—	2	1	no	—
241	C₅×C₄⋊C₄	—	2	1	no	—
242	C₅×C₄⋊C₄	—	2	1	no	—
243	C₅×C₄⋊C₄	—	2	1	no	—
244	C₅×C₄⋊C₄	—	2	1	no	—
245	C₅×C₄⋊C₄	—	2	1	no	—
246	C₅×C₄⋊C₄	—	2	1	no	—
247	C₅×C₄⋊C₄	—	2	1	no	—
248	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
249	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
250	C₅×C₂²⋊C₄	—	2	1	no	—
251	C₅×C₂²⋊C₄	—	2	1	no	—
252	C₅×C₂²⋊C₄	—	2	1	no	—
253	C₅×C₂²⋊C₄	—	2	1	no	—
254	C₅×C₂²⋊C₄	—	2	1	no	—
255	C₅×C₂²⋊C₄	—	4	1	no	—
256	C₅×C₂²⋊C₄	—	4	1	no	—
257	C₅×C₂²⋊C₄	—	4	1	no	—
258	C₅×C₂²⋊C₄	—	4	1	no	—
259	C₄²×C₅	—	2	1	no	—
260	C₄²×C₅	—	4	1	no	—
261	C₄²×C₅	—	4	1	no	—
262	C₂×AGL(1,ℤ/8)	C₂²×C₅	1	1	yes	characteristic
263	C₂×#131	C₂²×C₅	1	1	yes	characteristic
264	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
265	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
266	#525	C₂²×C₅	1	1	yes	characteristic
267	C₂×#121	C₂²×C₅	1	1	yes	characteristic
268	C₂×#117	C₂²×C₅	1	1	yes	characteristic
269	#485	—	2	1	no	—
270	#485	—	2	1	no	—
271	#482	—	2	1	no	—
272	#482	—	2	1	no	—
273	#482	—	2	1	no	—
274	#482	—	2	1	no	—
275	#482	—	2	1	no	—
276	#482	—	2	1	no	—
277	#469	—	2	1	no	—
278	#468	—	2	1	no	—
279	#466	—	2	1	no	—
280	#465	—	2	1	no	—
281	#436	—	2	1	no	—
282	#435	—	2	1	no	—
283	#435	—	2	1	no	—
284	C₈×D₄	—	2	1	no	—
285	C₂×#108	C₂²×C₅	1	1	yes	characteristic
286	C₂×#108	C₂²×C₅	1	1	yes	characteristic
287	#428	C₂²×C₅	1	1	yes	characteristic
288	#428	C₂²×C₅	1	1	yes	characteristic
289	#428	C₂²×C₅	1	1	yes	characteristic
290	C₂×#107	C₂²×C₅	1	1	yes	characteristic
291	C₂×#106	C₂²×C₅	1	1	yes	characteristic
292	#424	C₂²×C₅	1	1	yes	characteristic
293	#418	C₂²×C₅	1	1	yes	characteristic
294	#417	C₂²×C₅	1	1	yes	characteristic
295	#417	C₂²×C₅	1	1	yes	characteristic
296	#417	C₂²×C₅	1	1	yes	characteristic
297	C₂×#102	C₂²×C₅	1	1	yes	characteristic
298	C₂×#102	C₂²×C₅	1	1	yes	characteristic
299	C₂×#100	C₂²×C₅	1	1	yes	characteristic
300	C₂×#100	C₂²×C₅	1	1	yes	characteristic
301	#408	C₂²×C₅	1	1	yes	characteristic
302	#407	C₂²×C₅	1	1	yes	characteristic
303	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
304	#405	C₂²×C₅	1	1	yes	characteristic
305	#343	C₂²×C₅	1	1	yes	characteristic
306	#343	C₂²×C₅	1	1	yes	characteristic
307	#343	C₂²×C₅	1	1	yes	characteristic
308	#343	C₂²×C₅	1	1	yes	characteristic
309	#343	C₂²×C₅	1	1	yes	characteristic
310	#343	C₂²×C₅	1	1	yes	characteristic
311	#341	C₂²×C₅	1	1	yes	characteristic
312	#341	C₂²×C₅	1	1	yes	characteristic
313	C₂³×C₅	—	2	1	no	—
314	C₂³×C₅	—	2	1	no	—
315	C₂³×C₅	—	2	1	no	—
316	C₂³×C₅	—	4	1	no	—
317	C₂³×C₅	—	4	1	no	—
318	C₂³×C₅	—	4	1	no	—
319	C₂³×C₅	—	4	1	no	—
320	C₂³×C₅	—	4	1	no	—
321	C₂³×C₅	—	8	1	no	—
322	C₂³×C₅	—	8	1	no	—
323	C₂³×C₅	#121	1	1	yes	characteristic
324	C₂³×C₅	#121	1	1	yes	characteristic
325	C₂³×C₅	C₂×#41	1	1	yes	characteristic
326	C₅×Q₈	—	2	1	no	—
327	C₅×Q₈	—	2	1	no	—
328	C₅×D₄	—	2	1	no	—
329	C₅×D₄	—	2	1	no	—
330	C₅×D₄	—	4	2	no	—
331	C₅×D₄	—	4	1	no	—
332	C₅×D₄	—	4	1	no	—
333	C₅×D₄	—	4	1	no	—
334	C₅×D₄	—	4	1	no	—
335	C₅×D₄	—	4	1	no	—
336	C₅×D₄	—	4	1	no	—
337	C₅×D₄	—	8	1	no	—
338	C₅×D₄	—	8	2	no	—
339	C₅×D₄	—	8	2	no	—
340	C₂×C₄×C₅	—	2	1	no	—
341	C₂×C₄×C₅	—	2	1	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	2	1	no	—
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	4	1	no	—
354	C₂×C₄×C₅	—	4	1	no	—
355	C₂×C₄×C₅	—	4	1	no	—
356	C₂×C₄×C₅	—	4	1	no	—
357	C₂×C₄×C₅	—	4	1	no	—
358	C₂×C₄×C₅	—	8	1	no	—
359	C₂×C₄×C₅	—	8	1	no	—
360	C₂×C₄×C₅	—	8	1	no	—
361	C₂×C₄×C₅	#121	1	1	yes	characteristic
362	C₂×C₄×C₅	#121	1	1	yes	characteristic
363	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
366	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
367	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
368	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
369	C₅×C₈	—	2	1	no	—
370	C₅×C₈	—	2	1	no	—
371	C₅×C₈	—	2	2	no	—
372	C₅×C₈	—	2	2	no	—
373	C₅×C₈	—	2	1	no	—
374	C₅×C₈	—	2	1	no	—
375	C₅×C₈	—	4	1	no	—
376	C₅×C₈	—	4	1	no	—
377	C₅×C₈	—	4	1	no	—
378	C₅×C₈	—	4	1	no	—
379	C₂×#41	C₂³×C₅	1	1	yes	characteristic
380	C₂²×D₄	—	2	1	no	—
381	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
382	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
383	AGL(1,ℤ/8)	—	2	2	no	—
384	AGL(1,ℤ/8)	—	4	1	no	—
385	C₂×SD₁₆	—	2	1	no	—
386	C₂×D₈	—	2	1	no	—
387	#131	—	2	2	no	—
388	#131	—	4	1	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	—	2	1	no	—
391	C₂×M₁₆	—	2	1	no	—
392	C₂×M₁₆	—	2	2	no	—
393	C₂×M₁₆	—	2	2	no	—
394	C₂×M₁₆	—	4	1	no	—
395	C₂×M₁₆	—	4	1	no	—
396	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
397	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
398	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
399	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
400	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
401	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
402	C₂²×C₈	—	2	1	no	—
403	C₂²×C₈	—	2	1	no	—
404	C₂²×C₈	—	2	1	no	—
405	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
407	#123	—	2	1	no	—
408	C₂²⋊Q₈	C₅×D₄	1	1	yes	characteristic
409	C₂²⋊Q₈	C₅×D₄	1	1	yes	characteristic
410	#121	—	2	1	no	—
411	#121	—	2	1	no	—
412	#121	—	2	1	no	—
413	#121	—	2	1	no	—
414	#121	C₅×D₄	1	1	yes	characteristic
415	#121	C₅×D₄	1	1	yes	characteristic
416	#120	—	2	1	no	—
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	2	1	no	—
419	#117	—	2	1	no	—
420	#117	—	2	1	no	—
421	#117	—	2	1	no	—
422	#117	—	2	1	no	—
423	#117	C₂³×C₅	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₄²	—	2	1	no	—
430	#108	—	2	2	no	—
431	#108	—	4	1	no	—
432	#107	—	2	1	no	—
433	#107	—	2	1	no	—
434	#107	—	2	1	no	—
435	#107	—	2	1	no	—
436	#107	—	2	1	no	—
437	#106	—	2	1	no	—
438	#106	—	2	1	no	—
439	#106	—	2	1	no	—
440	#106	—	2	1	no	—
441	#106	—	2	1	no	—
442	C₄⋊C₈	—	2	1	no	—
443	C₄⋊C₈	—	2	1	no	—
444	#103	—	2	1	no	—
445	#103	—	2	1	no	—
446	#103	—	2	1	no	—
447	#102	—	2	1	no	—
448	#102	—	2	1	no	—
449	#102	—	2	1	no	—
450	#102	—	2	1	no	—
451	#102	—	2	1	no	—
452	#102	—	2	1	no	—
453	#102	—	2	1	no	—
454	#102	—	2	1	no	—
455	#102	—	2	1	no	—
456	#100	—	2	2	no	—
457	#100	—	4	1	no	—
458	C₂²⋊C₈	—	2	1	no	—
459	C₂²⋊C₈	—	2	1	no	—
460	C₂²⋊C₈	—	2	1	no	—
461	C₂²⋊C₈	—	2	1	no	—
462	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
463	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
464	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
465	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
466	#97	—	2	1	no	—
467	C₄×C₈	—	2	1	no	—
468	C₂²×C₅	—	2	1	no	—
469	C₂²×C₅	—	2	1	no	—
470	C₂²×C₅	—	2	1	no	—
471	C₂²×C₅	—	2	1	no	—
472	C₂²×C₅	—	2	1	no	—
473	C₂²×C₅	—	2	1	no	—
474	C₂²×C₅	—	2	1	no	—
475	C₂²×C₅	—	2	1	no	—
476	C₂²×C₅	—	4	1	no	—
477	C₂²×C₅	—	4	1	no	—
478	C₂²×C₅	—	4	1	no	—
479	C₂²×C₅	—	8	1	no	—
480	C₂²×C₅	—	8	1	no	—
481	C₂²×C₅	—	8	1	no	—
482	C₂²×C₅	—	8	1	no	—
483	C₂²×C₅	—	8	1	no	—
484	C₂²×C₅	—	16	1	no	—
485	C₂²×C₅	—	16	1	no	—
486	C₂²×C₅	C₂×#121	1	1	yes	characteristic
487	C₂²×C₅	#529	1	1	yes	characteristic
488	C₂²×C₅	#539	1	1	yes	characteristic
489	C₄×C₅	—	2	1	no	—
490	C₄×C₅	—	2	1	no	—
491	C₄×C₅	—	4	1	no	—
492	C₄×C₅	—	4	1	no	—
493	C₄×C₅	—	4	1	no	—
494	C₄×C₅	—	8	1	no	—
495	C₄×C₅	—	8	1	no	—
496	C₄×C₅	—	8	1	no	—
497	C₄×C₅	#546	1	1	yes	characteristic
498	C₄×C₅	#546	1	1	yes	characteristic
499	C₄×C₅	#547	1	1	yes	characteristic
500	C₄×C₅	#547	1	1	yes	characteristic
501	C₂⁴	—	2	1	no	—
502	C₂⁴	C₅×#41	1	1	yes	characteristic
503	#41	—	2	1	no	—
504	#41	—	2	1	no	—
505	#41	—	2	1	no	—
506	#41	—	2	1	no	—
507	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	4	1	no	—
518	C₂×D₄	—	4	1	no	—
519	C₂×D₄	—	8	2	no	—
520	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
530	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
531	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
532	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
533	C₂²×C₄	C₅×#41	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
535	SD₁₆	—	4	2	no	—
536	D₈	—	4	2	no	—
537	M₁₆	—	2	1	no	—
538	M₁₆	—	2	1	no	—
539	M₁₆	—	2	1	no	—
540	M₁₆	—	2	1	no	—
541	M₁₆	—	2	1	no	—
542	M₁₆	—	2	1	no	—
543	M₁₆	—	2	1	no	—
544	M₁₆	—	2	1	no	—
545	M₁₆	—	2	1	no	—
546	M₁₆	—	2	1	no	—
547	M₁₆	—	4	2	no	—
548	M₁₆	—	4	2	no	—
549	M₁₆	—	4	2	no	—
550	M₁₆	C₅×#41	1	2	yes	—
551	M₁₆	C₅×#41	1	2	yes	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	4	2	no	—
563	C₂×C₈	—	4	2	no	—
564	C₂×C₈	—	4	2	no	—
565	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
566	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
567	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
568	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
578	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
579	C₂²⋊C₄	—	2	1	no	—
580	C₂²⋊C₄	—	2	1	no	—
581	C₂²⋊C₄	—	2	1	no	—
582	C₂²⋊C₄	—	2	1	no	—
583	C₂²⋊C₄	—	2	1	no	—
584	C₂²⋊C₄	—	4	1	no	—
585	C₂²⋊C₄	—	4	1	no	—
586	C₂²⋊C₄	—	4	1	no	—
587	C₂²⋊C₄	—	4	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	4	1	no	—
590	C₄²	—	4	1	no	—
591	C₂×C₅	—	2	1	no	—
592	C₂×C₅	—	2	1	no	—
593	C₂×C₅	—	4	1	no	—
594	C₂×C₅	—	4	1	no	—
595	C₂×C₅	—	8	1	no	—
596	C₂×C₅	—	16	1	no	—
597	C₂×C₅	#2425	1	1	yes	characteristic
598	C₂×C₅	#3067	1	1	yes	characteristic
599	C₂×C₅	#3068	1	1	yes	characteristic
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	8	1	no	—
609	C₂³	—	8	1	no	—
610	C₂³	C₅×#121	1	1	yes	characteristic
611	C₂³	C₅×#121	1	1	yes	characteristic
612	C₂³	C₂×C₅×#41	1	1	yes	characteristic
613	Q₈	—	2	1	no	—
614	Q₈	—	2	1	no	—
615	D₄	—	2	1	no	—
616	D₄	—	2	1	no	—
617	D₄	—	4	2	no	—
618	D₄	—	4	1	no	—
619	D₄	—	4	1	no	—
620	D₄	—	4	1	no	—
621	D₄	—	4	1	no	—
622	D₄	—	4	1	no	—
623	D₄	—	4	1	no	—
624	D₄	—	8	1	no	—
625	D₄	—	8	2	no	—
626	D₄	—	8	2	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	8	1	no	—
646	C₂×C₄	—	8	1	no	—
647	C₂×C₄	—	8	1	no	—
648	C₂×C₄	C₅×#121	1	1	yes	characteristic
649	C₂×C₄	C₅×#121	1	1	yes	characteristic
650	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
651	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
652	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
653	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
654	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
655	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
656	C₈	—	2	1	no	—
657	C₈	—	2	1	no	—
658	C₈	—	2	2	no	—
659	C₈	—	2	2	no	—
660	C₈	—	2	1	no	—
661	C₈	—	2	1	no	—
662	C₈	—	4	1	no	—
663	C₈	—	4	1	no	—
664	C₈	—	4	1	no	—
665	C₈	—	4	1	no	—
666	C₅	#25269	1	1	yes	characteristic, direct product factor, Sylow
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	4	1	no	—
676	C₂²	—	4	1	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	8	1	no	—
679	C₂²	—	8	1	no	—
680	C₂²	—	8	1	no	—
681	C₂²	—	8	1	no	—
682	C₂²	—	8	1	no	—
683	C₂²	—	16	1	no	—
684	C₂²	—	16	1	no	—
685	C₂²	C₂×C₅×#121	1	1	yes	characteristic
686	C₂²	C₅×#529	1	1	yes	characteristic
687	C₂²	C₅×#539	1	1	yes	characteristic
688	C₄	—	2	1	no	—
689	C₄	—	2	1	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	1	no	—
692	C₄	—	4	1	no	—
693	C₄	—	8	1	no	—
694	C₄	—	8	1	no	—
695	C₄	—	8	1	no	—
696	C₄	C₅×#546	1	1	yes	characteristic
697	C₄	C₅×#546	1	1	yes	characteristic
698	C₄	C₅×#547	1	1	yes	characteristic
699	C₄	C₅×#547	1	1	yes	characteristic
700	C₂	—	2	1	no	—
701	C₂	—	2	1	no	—
702	C₂	—	4	1	no	—
703	C₂	—	4	1	no	—
704	C₂	—	8	1	no	—
705	C₂	—	16	1	no	—
706	C₂	C₅×#2425	1	1	yes	characteristic
707	C₂	C₅×#3067	1	1	yes	characteristic
708	C₂	C₅×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₅×#3055	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3093	C₂	semidirect
2. C₂×C₅×#482	C₂	semidirect
4. C₅×#2933	C₂	semidirect
5. C₅×#2090	C₂	semidirect
6. C₅×#2078	C₂	semidirect
7. C₅×#2063	C₂	semidirect
8. C₅×#2051	C₂	semidirect
9. C₅×#1952	C₂	semidirect
10. C₅×#1931	C₂	semidirect
11. C₅×#1907	C₂	semidirect
12. C₅×#1900	C₂	semidirect
13. C₅×#1855	C₂	semidirect
14. C₅×#1815	C₂	semidirect
15. C₅×#1742	C₂	semidirect
67. #25269	C₅	direct (N × H)
157. #3093	C₂×C₅	semidirect
158. C₂×#482	C₂×C₅	semidirect
160. #2933	C₂×C₅	semidirect
161. #2090	C₂×C₅	semidirect
162. #2078	C₂×C₅	semidirect
163. #2063	C₂×C₅	semidirect
164. #2051	C₂×C₅	semidirect
165. #1952	C₂×C₅	semidirect
166. #1931	C₂×C₅	semidirect
167. #1907	C₂×C₅	semidirect
168. #1900	C₂×C₅	semidirect
169. #1855	C₂×C₅	semidirect
170. #1815	C₂×C₅	semidirect
171. #1742	C₂×C₅	semidirect
666. C₅	#25269	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×#3093	2
C₂×C₅×#482	2
C₅×#3055	2
C₅×#2933	2
C₅×#2090	2
C₅×#2078	2
C₅×#2063	2
C₅×#2051	2
C₅×#1952	2
C₅×#1931	2
C₅×#1907	2
C₅×#1900	2
C₅×#1855	2
C₅×#1815	2
C₅×#1742	2
#25269	5

Subgroups — C5×#25269 #11947989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#25269 #11947989