Finite Group Databasebeta

← C2×#10617358 #13043920

Subgroups — C2×#10617358 #13043920

Order 1280.

2614 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#126C211yesmaximal, characteristic
2#10617358C2116yesmaximal, direct product factor
3C2×#65712C211yesmaximal, characteristic, complemented
4C2×#65712C211yesmaximal, characteristic, complemented
5C2×#65711C211yesmaximal, characteristic, complemented
6C2×#65711C211yesmaximal, characteristic, complemented
7C2×#65711C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
9C2×#65700C211yesmaximal, characteristic
10C2×#65700C211yesmaximal, characteristic
11C2×#65700C211yesmaximal, characteristic
12C2×#65699C211yesmaximal, characteristic
13C2×#65699C211yesmaximal, characteristic
14C2×C22⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic
15C2×#65689C211yesmaximal, characteristic, complemented
16C2×C4×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
17C24×AGL(1,𝔽5)C2211yescharacteristic
18C22×C22⋊AGL(1,𝔽5)C2211yescharacteristic
19C22×C22⋊AGL(1,𝔽5)C2211yescharacteristic
20C22×C22⋊AGL(1,𝔽5)C2211yescharacteristic
21C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
22C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
23C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
24C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
25C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
26C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
27C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
28C22×C4×AGL(1,𝔽5)C2211yescharacteristic
29C22×C4×AGL(1,𝔽5)C2211yescharacteristic
30C22×C4×AGL(1,𝔽5)C2211yescharacteristic
31C22×C4×AGL(1,𝔽5)C2211yescharacteristic
32C22×C4×AGL(1,𝔽5)C2211yescharacteristic
33C2×C5×#126C411yescharacteristic, complemented
34D5×#126C418yescomplemented
35D5×#126C2218yes—
36C2×#4044C411yescharacteristic, complemented
37C2×#4044C411yescharacteristic, complemented
38C2×#4044C411yescharacteristic, complemented
39C2×D5×C4⋊C4C2211yescharacteristic
40C2×D5×C4⋊C4C2211yescharacteristic
41C2×D5×C4⋊C4C2211yescharacteristic
42C2×D5×C22⋊C4C2211yescharacteristic
43C2×D5×C22⋊C4C2211yescharacteristic
44C2×D5×C22⋊C4C2211yescharacteristic
45C2×#4025C411yescharacteristic, complemented
46C2×#4025C411yescharacteristic, complemented
47C2×#4025C411yescharacteristic, complemented
48C2×#4022C411yescharacteristic, complemented
49C2×C42×D5C2211yescharacteristic
50C2×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
51C2×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
52C2×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
53C2×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
54C2×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
55C2×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
56C2×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
57C2×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
58C2×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
59C2×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
60C2×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
61C2×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
62#65712C2218yescomplemented
63#65712C2218yescomplemented
64#65711C2218yescomplemented
65#65711C2218yescomplemented
66#65711C2218yescomplemented
67C4⋊C4×AGL(1,𝔽5)C2218yescomplemented
68#65700C2218yes—
69#65700C2218yes—
70#65700C2218yes—
71#65699C2218yes—
72#65699C2218yes—
73C22⋊C4×AGL(1,𝔽5)C2218yes—
74#65689C2218yescomplemented
75C4×C4⋊AGL(1,𝔽5)C2218yescomplemented
76C2×#2334—51nomaximal, Sylow
77C24×D5C2311yescharacteristic
78C23×AGL(1,𝔽5)—24no—
79C23×AGL(1,𝔽5)—42no—
80C23×AGL(1,𝔽5)—42no—
81C23×AGL(1,𝔽5)C2311yescharacteristic
82C23×AGL(1,𝔽5)C2311yescharacteristic
83C23×AGL(1,𝔽5)C2311yescharacteristic
84C23×AGL(1,𝔽5)C2311yescharacteristic
85C23×AGL(1,𝔽5)C2311yescharacteristic
86C23×AGL(1,𝔽5)C2311yescharacteristic
87C23×AGL(1,𝔽5)C2311yescharacteristic
88C23×AGL(1,𝔽5)C2311yescharacteristic
89C23×AGL(1,𝔽5)C2314yes—
90C22×C4×D5C2311yescharacteristic
91C22×C4×D5C2311yescharacteristic
92C22×C4×D5C2311yescharacteristic
93C22×C4×D5C2311yescharacteristic
94C22×C4×D5C2311yescharacteristic
95C22×C4×D5C2311yescharacteristic
96C2×C22⋊AGL(1,𝔽5)—24no—
97C2×C22⋊AGL(1,𝔽5)—42no—
98C2×C22⋊AGL(1,𝔽5)—42no—
99C2×C22⋊AGL(1,𝔽5)C2314yes—
100C2×C22⋊AGL(1,𝔽5)C2314yes—
101C2×C22⋊AGL(1,𝔽5)C2314yes—
102C2×C4⋊AGL(1,𝔽5)—24no—
103C2×C4⋊AGL(1,𝔽5)—24no—
104C2×C4⋊AGL(1,𝔽5)—24no—
105C2×C4⋊AGL(1,𝔽5)—42no—
106C2×C4⋊AGL(1,𝔽5)—42no—
107C2×C4⋊AGL(1,𝔽5)—42no—
108C2×C4⋊AGL(1,𝔽5)—42no—
109C2×C4⋊AGL(1,𝔽5)C2314yes—
110C2×C4⋊AGL(1,𝔽5)C2314yes—
111C2×C4⋊AGL(1,𝔽5)C2314yes—
112C2×C4⋊AGL(1,𝔽5)C2314yes—
113C2×C4⋊AGL(1,𝔽5)C2314yes—
114C2×C4⋊AGL(1,𝔽5)C2314yes—
115C2×C4⋊AGL(1,𝔽5)C2314yes—
116C2×C4×AGL(1,𝔽5)—24no—
117C2×C4×AGL(1,𝔽5)—42no—
118C2×C4×AGL(1,𝔽5)—42no—
119C2×C4×AGL(1,𝔽5)—42no—
120C2×C4×AGL(1,𝔽5)—42no—
121C2×C4×AGL(1,𝔽5)C2314yes—
122C2×C4×AGL(1,𝔽5)C2314yes—
123C2×C4×AGL(1,𝔽5)C2314yes—
124C2×C4×AGL(1,𝔽5)C2314yes—
125C2×C4×AGL(1,𝔽5)C2314yes—
126C5×#126C2×C418yescomplemented
127C2×C5×C4⋊C4C2×C411yescharacteristic, complemented
128C2×C5×C4⋊C4C2×C411yescharacteristic, complemented
129C2×C5×C4⋊C4C2×C411yescharacteristic, complemented
130C2×C5×C22⋊C4C2×C411yescharacteristic
131C2×C5×C22⋊C4C2×C411yescharacteristic
132C2×C5×C22⋊C4C2×C411yescharacteristic
133C2×C42×C5C2×C411yescharacteristic, complemented
134C2×C22⋊Dic5C2×C411yescharacteristic
135C2×C22⋊Dic5C2×C411yescharacteristic
136C2×C22⋊Dic5C2×C411yescharacteristic
137C2×#685C2×C411yescharacteristic
138C2×#685C2×C411yescharacteristic
139C2×#685C2×C411yescharacteristic
140C2×#685C2×C411yescharacteristic
141C2×#685C2×C411yescharacteristic
142C2×#685C2×C411yescharacteristic
143C2×C4⋊Dic5C2×C411yescharacteristic, complemented
144C2×C4⋊Dic5C2×C411yescharacteristic, complemented
145C2×C4⋊Dic5C2×C411yescharacteristic, complemented
146C2×#683C2×C411yescharacteristic, complemented
147C2×#683C2×C411yescharacteristic, complemented
148C2×#683C2×C411yescharacteristic, complemented
149C2×#683C2×C411yescharacteristic, complemented
150C2×#683C2×C411yescharacteristic, complemented
151C2×#683C2×C411yescharacteristic, complemented
152C2×C4×Dic5C2×C411yescharacteristic, complemented
153C2×C4×Dic5C2×C411yescharacteristic, complemented
154C2×C4×Dic5C2×C411yescharacteristic, complemented
155#4044C2×C418yescomplemented
156#4044C2×C418yescomplemented
157#4044C2×C418yescomplemented
158D5×C4⋊C4C2×C414yescomplemented
159D5×C4⋊C4C2×C414yescomplemented
160D5×C4⋊C4C2×C414yescomplemented
161D5×C4⋊C4C2314yes—
162D5×C4⋊C4C2314yes—
163D5×C4⋊C4C2314yes—
164D5×C22⋊C4C2×C414yes—
165D5×C22⋊C4C2×C414yes—
166D5×C22⋊C4C2×C414yes—
167D5×C22⋊C4C2314yes—
168D5×C22⋊C4C2314yes—
169D5×C22⋊C4C2314yes—
170#4025C2×C418yescomplemented
171#4025C2×C418yescomplemented
172#4025C2×C418yescomplemented
173#4022C2×C418yescomplemented
174C42×D5C2×C414yescomplemented
175C42×D5C2314yes—
176(C2×AGL(1,𝔽5))⋊C4C2314yes—
177(C2×AGL(1,𝔽5))⋊C4C2314yes—
178(C2×AGL(1,𝔽5))⋊C4C2314yes—
179(C2×AGL(1,𝔽5))⋊C4C2314yes—
180(C2×AGL(1,𝔽5))⋊C4C2314yes—
181(C2×AGL(1,𝔽5))⋊C4C2314yes—
182(C2×AGL(1,𝔽5))⋊C4C2314yes—
183(C2×AGL(1,𝔽5))⋊C4C2314yes—
184(C2×AGL(1,𝔽5))⋊C4C2314yes—
185(C2×AGL(1,𝔽5))⋊C4C2314yes—
186(C2×AGL(1,𝔽5))⋊C4C2314yes—
187(C2×AGL(1,𝔽5))⋊C4C2314yes—
188C22×#126—51no—
189#2334—516no—
190C2×#389—51no—
191C2×#389—51no—
192C2×#388—51no—
193C2×#388—51no—
194C2×#388—51no—
195C2×#387—51no—
196C2×#387—51no—
197C2×#387—51no—
198C2×#385—51no—
199C2×#385—51no—
200C2×#382—51no—
201C2×C4×C4⋊C4—51no—
202C2×C4×C4⋊C4—51no—
203C2×C4×C22⋊C4—51no—
204C24×C5C22×C411yescharacteristic
205C23×D5—22no—
206C23×D5—22no—
207C23×D5—22no—
208C23×D5—22no—
209C23×D5—22no—
210C23×D5—22no—
211C23×D5C22×C412yes—
212C23×D5C22×C411yescharacteristic
213C23×D5C2412yes—
214C23×D5C2411yescharacteristic
215C22×AGL(1,𝔽5)—22no—
216C22×AGL(1,𝔽5)—22no—
217C22×AGL(1,𝔽5)—22no—
218C22×AGL(1,𝔽5)—22no—
219C22×AGL(1,𝔽5)—22no—
220C22×AGL(1,𝔽5)—22no—
221C22×AGL(1,𝔽5)—22no—
222C22×AGL(1,𝔽5)—22no—
223C22×AGL(1,𝔽5)—22no—
224C22×AGL(1,𝔽5)—22no—
225C22×AGL(1,𝔽5)—22no—
226C22×AGL(1,𝔽5)—22no—
227C22×AGL(1,𝔽5)—22no—
228C22×AGL(1,𝔽5)—22no—
229C22×AGL(1,𝔽5)—22no—
230C22×AGL(1,𝔽5)—22no—
231C22×AGL(1,𝔽5)—22no—
232C22×AGL(1,𝔽5)—22no—
233C22×AGL(1,𝔽5)—22no—
234C22×AGL(1,𝔽5)—22no—
235C22×AGL(1,𝔽5)—22no—
236C22×AGL(1,𝔽5)—22no—
237C22×AGL(1,𝔽5)—28no—
238C22×AGL(1,𝔽5)—44no—
239C22×AGL(1,𝔽5)—44no—
240C22×AGL(1,𝔽5)—416no—
241C22×AGL(1,𝔽5)#4114yes—
242C22×AGL(1,𝔽5)#4114yes—
243C22×AGL(1,𝔽5)C2412yes—
244C22×AGL(1,𝔽5)C2412yes—
245C22×AGL(1,𝔽5)C2412yes—
246C22×AGL(1,𝔽5)C2412yes—
247C22×AGL(1,𝔽5)C2412yes—
248C22×AGL(1,𝔽5)C2412yes—
249C22×AGL(1,𝔽5)C2412yes—
250C22×AGL(1,𝔽5)C2412yes—
251C22×C4×C5C22×C411yescharacteristic
252C22×C4×C5C22×C411yescharacteristic
253C22×C4×C5C22×C411yescharacteristic
254C22×C4×C5C22×C411yescharacteristic
255C22×C4×C5C22×C411yescharacteristic
256C22×C4×C5C22×C411yescharacteristic
257C22×Dic5C22×C411yescharacteristic
258C22×Dic5C22×C411yescharacteristic
259C22×Dic5C22×C411yescharacteristic
260C22×Dic5C22×C411yescharacteristic
261C22×Dic5C22×C411yescharacteristic
262C22×Dic5C22×C411yescharacteristic
263C2×C4×D5—22no—
264C2×C4×D5—22no—
265C2×C4×D5—22no—
266C2×C4×D5—22no—
267C2×C4×D5—22no—
268C2×C4×D5—22no—
269C2×C4×D5—22no—
270C2×C4×D5—22no—
271C2×C4×D5—22no—
272C2×C4×D5—22no—
273C2×C4×D5—22no—
274C2×C4×D5—22no—
275C2×C4×D5C22×C412yes—
276C2×C4×D5C22×C412yes—
277C2×C4×D5C22×C412yes—
278C2×C4×D5C22×C412yes—
279C2×C4×D5C22×C412yes—
280C2×C4×D5C22×C412yes—
281C2×C4×D5C2412yes—
282C2×C4×D5C2412yes—
283C2×C4×D5C2412yes—
284C2×C4×D5C2412yes—
285C2×C4×D5C2412yes—
286C2×C4×D5C2412yes—
287C22⋊AGL(1,𝔽5)—28no—
288C22⋊AGL(1,𝔽5)—44no—
289C22⋊AGL(1,𝔽5)—44no—
290C4⋊AGL(1,𝔽5)—28no—
291C4⋊AGL(1,𝔽5)—28no—
292C4⋊AGL(1,𝔽5)—28no—
293C4⋊AGL(1,𝔽5)—44no—
294C4⋊AGL(1,𝔽5)—44no—
295C4⋊AGL(1,𝔽5)—44no—
296C4⋊AGL(1,𝔽5)—44no—
297C4×AGL(1,𝔽5)—28no—
298C4×AGL(1,𝔽5)—44no—
299C4×AGL(1,𝔽5)—44no—
300C4×AGL(1,𝔽5)—44no—
301C4×AGL(1,𝔽5)—44no—
302C5×C4⋊C4C22×C414yescomplemented
303C5×C4⋊C4C22×C414yescomplemented
304C5×C4⋊C4C22×C414yescomplemented
305C5×C22⋊C4C22×C414yes—
306C5×C22⋊C4C22×C414yes—
307C5×C22⋊C4C22×C414yes—
308C42×C5C22×C414yescomplemented
309C22⋊Dic5C22×C414yes—
310C22⋊Dic5C22×C414yes—
311C22⋊Dic5C22×C414yes—
312#685C22×C414yes—
313#685C22×C414yes—
314#685C22×C414yes—
315#685C22×C414yes—
316#685C22×C414yes—
317#685C22×C414yes—
318C4⋊Dic5C22×C414yescomplemented
319C4⋊Dic5C22×C414yescomplemented
320C4⋊Dic5C22×C414yescomplemented
321#683C22×C414yescomplemented
322#683C22×C414yescomplemented
323#683C22×C414yescomplemented
324#683C22×C414yescomplemented
325#683C22×C414yescomplemented
326#683C22×C414yescomplemented
327C4×Dic5C22×C414yescomplemented
328C4×Dic5C22×C414yescomplemented
329C4×Dic5C22×C414yescomplemented
330C24×C4—51no—
331C2×#126—58no—
332C2×#126—58no—
333C2×#126—51no—
334C2×#126—51no—
335C2×#126—51no—
336C2×#126—51no—
337C2×#126—51no—
338C2×#126—51no—
339C2×#126—51no—
340C2×#126AGL(1,𝔽5)11yescharacteristic, complemented
341C22×C4⋊C4—51no—
342C22×C4⋊C4—51no—
343C22×C4⋊C4—51no—
344C22×C4⋊C4—51no—
345C22×C4⋊C4—51no—
346C22×C4⋊C4—51no—
347C22×C4⋊C4—51no—
348C22×C4⋊C4—51no—
349C22×C4⋊C4—51no—
350C22×C4⋊C4—51no—
351C22×C22⋊C4—51no—
352C22×C22⋊C4—51no—
353C22×C22⋊C4—51no—
354C22×C22⋊C4—51no—
355C22×C22⋊C4—51no—
356C22×C22⋊C4—51no—
357C22×C42—51no—
358C22×C42—51no—
359C22×C42—51no—
360C22×C42—51no—
361C22×C42—51no—
362C22×C42—51no—
363#389—58no—
364#389—58no—
365#388—58no—
366#388—58no—
367#388—58no—
368#387—58no—
369#387—58no—
370#387—58no—
371#385—58no—
372#385—58no—
373#382—58no—
374C4×C4⋊C4—58no—
375C4×C4⋊C4—58no—
376C4×C22⋊C4—58no—
377C2×#95—51no—
378C2×#95—51no—
379C2×#95—51no—
380C2×#95—51no—
381C2×#95—51no—
382C2×#95—51no—
383C2×#95—51no—
384C2×#95—51no—
385C2×#95—51no—
386C2×#95—51no—
387C2×#95—51no—
388C2×#95—51no—
389C23×C5—22no—
390C23×C5—22no—
391C23×C5—22no—
392C23×C5C23×C412yes—
393C23×C5C23×C411yescharacteristic
394C22×D5—22no—
395C22×D5—22no—
396C22×D5—22no—
397C22×D5—24no—
398C22×D5—24no—
399C22×D5—24no—
400C22×D5—22no—
401C22×D5—22no—
402C22×D5—22no—
403C22×D5—22no—
404C22×D5—22no—
405C22×D5—22no—
406C22×D5—44no—
407C22×D5—44no—
408C22×D5—44no—
409C22×D5—44no—
410C22×D5C23×C412yes—
411C22×D5C23×C411yescharacteristic
412C22×D5C2×#4112yes—
413C22×D5C2×#4112yes—
414C22×D5H(5,𝔽2)12yes—
415C22×D5H(5,𝔽2)12yes—
416C22×D52−1+412yes—
417C22×D52−1+412yes—
418C22×D5C2511yescharacteristic
419C2×AGL(1,𝔽5)—28no—
420C2×AGL(1,𝔽5)—28no—
421C2×AGL(1,𝔽5)—22no—
422C2×AGL(1,𝔽5)—22no—
423C2×AGL(1,𝔽5)—22no—
424C2×AGL(1,𝔽5)—22no—
425C2×AGL(1,𝔽5)—22no—
426C2×AGL(1,𝔽5)—22no—
427C2×AGL(1,𝔽5)—22no—
428C2×AGL(1,𝔽5)—22no—
429C2×AGL(1,𝔽5)—22no—
430C2×AGL(1,𝔽5)—22no—
431C2×AGL(1,𝔽5)—22no—
432C2×AGL(1,𝔽5)—22no—
433C2×AGL(1,𝔽5)—22no—
434C2×AGL(1,𝔽5)—22no—
435C2×AGL(1,𝔽5)—22no—
436C2×AGL(1,𝔽5)—22no—
437C2×AGL(1,𝔽5)—22no—
438C2×AGL(1,𝔽5)—22no—
439C2×AGL(1,𝔽5)—22no—
440C2×AGL(1,𝔽5)—22no—
441C2×AGL(1,𝔽5)—22no—
442C2×AGL(1,𝔽5)—22no—
443C2×AGL(1,𝔽5)—416no—
444C2×AGL(1,𝔽5)—44no—
445C2×AGL(1,𝔽5)—44no—
446C2×AGL(1,𝔽5)—44no—
447C2×AGL(1,𝔽5)—44no—
448C2×AGL(1,𝔽5)—44no—
449C2×AGL(1,𝔽5)—44no—
450C2×AGL(1,𝔽5)C2×#4114yes—
451C2×AGL(1,𝔽5)C2×#4114yes—
452C2×C4×C5—22no—
453C2×C4×C5—22no—
454C2×C4×C5—22no—
455C2×C4×C5—22no—
456C2×C4×C5—22no—
457C2×C4×C5—22no—
458C2×C4×C5C23×C412yes—
459C2×C4×C5C23×C412yes—
460C2×C4×C5C23×C412yes—
461C2×C4×C5C23×C412yes—
462C2×C4×C5C23×C412yes—
463C2×C4×C5C23×C412yes—
464C2×Dic5—22no—
465C2×Dic5—22no—
466C2×Dic5—22no—
467C2×Dic5—22no—
468C2×Dic5—22no—
469C2×Dic5—22no—
470C2×Dic5C23×C412yes—
471C2×Dic5C23×C412yes—
472C2×Dic5C23×C412yes—
473C2×Dic5C23×C412yes—
474C2×Dic5C23×C412yes—
475C2×Dic5C23×C412yes—
476C4×D5—24no—
477C4×D5—24no—
478C4×D5—24no—
479C4×D5—24no—
480C4×D5—24no—
481C4×D5—24no—
482C4×D5—22no—
483C4×D5—22no—
484C4×D5—22no—
485C4×D5—22no—
486C4×D5—22no—
487C4×D5—22no—
488C4×D5—22no—
489C4×D5—22no—
490C4×D5—22no—
491C4×D5—22no—
492C4×D5—22no—
493C4×D5—22no—
494C25—51no—
495C23×C4—51no—
496C23×C4—51no—
497C23×C4—51no—
498C23×C4—51no—
499C23×C4—51no—
500C23×C4—51no—
501C23×C4—51no—
502C23×C4—51no—
503C23×C4—51no—
504C23×C4—51no—
505C23×C4—51no—
506C23×C4—51no—
507C23×C4—51no—
508C23×C4—51no—
509C23×C4—54no—
510C23×C4—104no—
511C23×C4—202no—
512C23×C4—202no—
513#126—58no—
514#126—58no—
515#126—58no—
516#126—58no—
517#126—58no—
518#126—58no—
519#126—58no—
520#126C2×AGL(1,𝔽5)18yescomplemented
521C2×C4⋊C4—51no—
522C2×C4⋊C4—51no—
523C2×C4⋊C4—51no—
524C2×C4⋊C4—51no—
525C2×C4⋊C4—51no—
526C2×C4⋊C4—51no—
527C2×C4⋊C4—51no—
528C2×C4⋊C4—51no—
529C2×C4⋊C4—51no—
530C2×C4⋊C4—54no—
531C2×C4⋊C4—54no—
532C2×C4⋊C4—54no—
533C2×C4⋊C4—54no—
534C2×C4⋊C4—54no—
535C2×C4⋊C4—54no—
536C2×C4⋊C4—54no—
537C2×C4⋊C4—54no—
538C2×C4⋊C4—54no—
539C2×C4⋊C4—54no—
540C2×C4⋊C4—54no—
541C2×C4⋊C4—54no—
542C2×C4⋊C4—54no—
543C2×C4⋊C4—104no—
544C2×C4⋊C4—104no—
545C2×C4⋊C4—104no—
546C2×C4⋊C4—202no—
547C2×C4⋊C4—202no—
548C2×C4⋊C4—202no—
549C2×C4⋊C4—202no—
550C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
551C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
552C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
553C2×C22⋊C4—51no—
554C2×C22⋊C4—51no—
555C2×C22⋊C4—51no—
556C2×C22⋊C4—51no—
557C2×C22⋊C4—51no—
558C2×C22⋊C4—51no—
559C2×C22⋊C4—51no—
560C2×C22⋊C4—51no—
561C2×C22⋊C4—51no—
562C2×C22⋊C4—54no—
563C2×C22⋊C4—54no—
564C2×C22⋊C4—54no—
565C2×C22⋊C4—54no—
566C2×C22⋊C4—54no—
567C2×C22⋊C4—54no—
568C2×C22⋊C4—54no—
569C2×C22⋊C4—54no—
570C2×C22⋊C4—54no—
571C2×C22⋊C4—104no—
572C2×C22⋊C4—202no—
573C2×C22⋊C4—202no—
574C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
575C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
576C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
577C2×C42—51no—
578C2×C42—51no—
579C2×C42—51no—
580C2×C42—54no—
581C2×C42—54no—
582C2×C42—54no—
583C2×C42—54no—
584C2×C42—54no—
585C2×C42—54no—
586C2×C42—54no—
587C2×C42—104no—
588C2×C42—202no—
589C2×C42—202no—
590C2×C42—202no—
591C2×C42—202no—
592C2×C42C2×AGL(1,𝔽5)11yescharacteristic, complemented
593#95—54no—
594#95—54no—
595#95—54no—
596#95—54no—
597#95—54no—
598#95—54no—
599#95—54no—
600#95—54no—
601#95—54no—
602#95—54no—
603#95—54no—
604#95—54no—
605C22×C5—22no—
606C22×C5—22no—
607C22×C5—22no—
608C22×C5—44no—
609C22×C5C4×#4112yes—
610C22×C5#52012yes—
611C22×C5#52012yes—
612C22×C5C24×C411yescharacteristic
613C2×D5—22no—
614C2×D5—22no—
615C2×D5—22no—
616C2×D5—44no—
617C2×D5—48no—
618C2×D5—42no—
619C2×D5—42no—
620C2×D5—42no—
621C2×D5—42no—
622C2×D5C4×#4112yes—
623C2×D5#52012yes—
624C2×D5#52012yes—
625C2×D5#53814yes—
626C2×D5#53914yes—
627C2×D5#54114yes—
628C2×D5#54214yes—
629C2×D5C22×#4111yescharacteristic
630C2×D5C22×#4111yescharacteristic
631C2×D5C2×H(5,𝔽2)11yescharacteristic
632C2×D5C2×H(5,𝔽2)11yescharacteristic
633C2×D5C2×2−1+411yescharacteristic
634C2×D5C2×2−1+411yescharacteristic
635AGL(1,𝔽5)—24no—
636AGL(1,𝔽5)—24no—
637AGL(1,𝔽5)—42no—
638AGL(1,𝔽5)—42no—
639AGL(1,𝔽5)—42no—
640AGL(1,𝔽5)—42no—
641AGL(1,𝔽5)—42no—
642AGL(1,𝔽5)—42no—
643C4×C5—22no—
644C4×C5—22no—
645C4×C5—22no—
646C4×C5—22no—
647C4×C5—22no—
648C4×C5—22no—
649Dic5—22no—
650Dic5—22no—
651Dic5—22no—
652Dic5—22no—
653Dic5—22no—
654Dic5—22no—
655C24—51no—
656C24—52no—
657C24—52no—
658C24—51no—
659C24—102no—
660C24—102no—
661C24—102no—
662C24—102no—
663C24—102no—
664C24—102no—
665C24C22×AGL(1,𝔽5)11yescharacteristic
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—54no—
669C22×C4—54no—
670C22×C4—51no—
671C22×C4—51no—
672C22×C4—51no—
673C22×C4—51no—
674C22×C4—51no—
675C22×C4—51no—
676C22×C4—52no—
677C22×C4—52no—
678C22×C4—52no—
679C22×C4—52no—
680C22×C4—52no—
681C22×C4—52no—
682C22×C4—52no—
683C22×C4—52no—
684C22×C4—52no—
685C22×C4—52no—
686C22×C4—52no—
687C22×C4—52no—
688C22×C4—52no—
689C22×C4—52no—
690C22×C4—52no—
691C22×C4—52no—
692C22×C4—52no—
693C22×C4—52no—
694C22×C4—102no—
695C22×C4—102no—
696C22×C4—102no—
697C22×C4—102no—
698C22×C4—102no—
699C22×C4—102no—
700C22×C4—102no—
701C22×C4—102no—
702C22×C4—102no—
703C22×C4—102no—
704C22×C4—102no—
705C22×C4—102no—
706C22×C4—108no—
707C22×C4—102no—
708C22×C4—102no—
709C22×C4—102no—
710C22×C4—102no—
711C22×C4—102no—
712C22×C4—102no—
713C22×C4—102no—
714C22×C4—102no—
715C22×C4—102no—
716C22×C4—102no—
717C22×C4—102no—
718C22×C4—102no—
719C22×C4—102no—
720C22×C4—102no—
721C22×C4—102no—
722C22×C4—102no—
723C22×C4—102no—
724C22×C4—102no—
725C22×C4—102no—
726C22×C4—102no—
727C22×C4—102no—
728C22×C4—102no—
729C22×C4—204no—
730C22×C4—204no—
731C22×C4—2016no—
732C22×C4C22×AGL(1,𝔽5)11yescharacteristic
733C22×C4C22×AGL(1,𝔽5)11yescharacteristic
734C22×C4C22×AGL(1,𝔽5)11yescharacteristic
735C22×C4C22×AGL(1,𝔽5)11yescharacteristic
736C22×C4C22×AGL(1,𝔽5)11yescharacteristic
737C22×C4C22×AGL(1,𝔽5)11yescharacteristic
738C4⋊C4—54no—
739C4⋊C4—54no—
740C4⋊C4—54no—
741C4⋊C4—54no—
742C4⋊C4—54no—
743C4⋊C4—54no—
744C4⋊C4—54no—
745C4⋊C4—54no—
746C4⋊C4—54no—
747C4⋊C4—108no—
748C4⋊C4—108no—
749C4⋊C4—108no—
750C4⋊C4—204no—
751C4⋊C4—204no—
752C4⋊C4—204no—
753C4⋊C4—204no—
754C4⋊C4C22×AGL(1,𝔽5)14yescomplemented
755C4⋊C4C22×AGL(1,𝔽5)14yescomplemented
756C4⋊C4C22×AGL(1,𝔽5)14yescomplemented
757C22⋊C4—54no—
758C22⋊C4—54no—
759C22⋊C4—54no—
760C22⋊C4—54no—
761C22⋊C4—54no—
762C22⋊C4—54no—
763C22⋊C4—54no—
764C22⋊C4—54no—
765C22⋊C4—54no—
766C22⋊C4—108no—
767C22⋊C4—204no—
768C22⋊C4—204no—
769C22⋊C4C22×AGL(1,𝔽5)14yes—
770C22⋊C4C22×AGL(1,𝔽5)14yes—
771C22⋊C4C22×AGL(1,𝔽5)14yes—
772C42—54no—
773C42—54no—
774C42—54no—
775C42—108no—
776C42—204no—
777C42—204no—
778C42—204no—
779C42—204no—
780C42C22×AGL(1,𝔽5)14yescomplemented
781C2×C5—42no—
782C2×C5#233414yescomplemented
783C2×C5C2×C4×#4111yescharacteristic
784C2×C5C2×#52011yescharacteristic
785C2×C5C2×#52011yescharacteristic
786D5—42no—
787D5#233414yescomplemented
788D5C2×#53811yescharacteristic
789D5C2×#53911yescharacteristic
790D5C2×#54111yescharacteristic
791D5C2×#54211yescharacteristic
792C23—22no—
793C23—22no—
794C23—22no—
795C23—52no—
796C23—52no—
797C23—52no—
798C23—52no—
799C23—52no—
800C23—52no—
801C23—51no—
802C23—51no—
803C23—52no—
804C23—102no—
805C23—102no—
806C23—102no—
807C23—102no—
808C23—104no—
809C23—102no—
810C23—102no—
811C23—104no—
812C23—104no—
813C23—102no—
814C23—102no—
815C23—102no—
816C23—204no—
817C23—204no—
818C23—204no—
819C23—204no—
820C23C23×AGL(1,𝔽5)12yes—
821C23C23×AGL(1,𝔽5)11yescharacteristic
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—54no—
829C2×C4—54no—
830C2×C4—52no—
831C2×C4—52no—
832C2×C4—52no—
833C2×C4—52no—
834C2×C4—52no—
835C2×C4—52no—
836C2×C4—102no—
837C2×C4—102no—
838C2×C4—102no—
839C2×C4—102no—
840C2×C4—102no—
841C2×C4—102no—
842C2×C4—102no—
843C2×C4—102no—
844C2×C4—104no—
845C2×C4—104no—
846C2×C4—102no—
847C2×C4—102no—
848C2×C4—102no—
849C2×C4—102no—
850C2×C4—104no—
851C2×C4—104no—
852C2×C4—104no—
853C2×C4—104no—
854C2×C4—102no—
855C2×C4—102no—
856C2×C4—102no—
857C2×C4—108no—
858C2×C4—108no—
859C2×C4—102no—
860C2×C4—102no—
861C2×C4—102no—
862C2×C4—102no—
863C2×C4—102no—
864C2×C4—102no—
865C2×C4—102no—
866C2×C4—102no—
867C2×C4—102no—
868C2×C4—102no—
869C2×C4—102no—
870C2×C4—102no—
871C2×C4—102no—
872C2×C4—102no—
873C2×C4—102no—
874C2×C4—102no—
875C2×C4—102no—
876C2×C4—102no—
877C2×C4—102no—
878C2×C4—102no—
879C2×C4—102no—
880C2×C4—102no—
881C2×C4—102no—
882C2×C4—102no—
883C2×C4—102no—
884C2×C4—2016no—
885C2×C4—204no—
886C2×C4—204no—
887C2×C4—204no—
888C2×C4—204no—
889C2×C4—204no—
890C2×C4—204no—
891C2×C4C23×AGL(1,𝔽5)12yes—
892C2×C4C23×AGL(1,𝔽5)12yes—
893C2×C4C23×AGL(1,𝔽5)12yes—
894C2×C4C23×AGL(1,𝔽5)12yes—
895C2×C4C23×AGL(1,𝔽5)12yes—
896C2×C4C23×AGL(1,𝔽5)12yes—
897C5C2×#233411yescharacteristic, complemented, Sylow
898C22—22no—
899C22—22no—
900C22—22no—
901C22—44no—
902C22—54no—
903C22—54no—
904C22—54no—
905C22—54no—
906C22—51no—
907C22—51no—
908C22—52no—
909C22—51no—
910C22—51no—
911C22—51no—
912C22—51no—
913C22—52no—
914C22—52no—
915C22—102no—
916C22—102no—
917C22—102no—
918C22—202no—
919C22—202no—
920C22—202no—
921C22—208no—
922C22—202no—
923C22—204no—
924C22#41×AGL(1,𝔽5)12yes—
925C22#6626612yes—
926C22#6626612yes—
927C22C24×AGL(1,𝔽5)11yescharacteristic
928C4—22no—
929C4—22no—
930C4—22no—
931C4—22no—
932C4—22no—
933C4—22no—
934C4—104no—
935C4—104no—
936C4—102no—
937C4—102no—
938C4—102no—
939C4—102no—
940C4—102no—
941C4—102no—
942C4—202no—
943C4—202no—
944C4—202no—
945C4—202no—
946C4—202no—
947C4—202no—
948C2—42no—
949C2—51no—
950C2—51no—
951C2—51no—
952C2—54no—
953C2—51no—
954C2—202no—
955C2#1061735814yesdirect product factor
956C2C2×#41×AGL(1,𝔽5)11yescharacteristic
957C2C2×#6626611yescharacteristic
958C2C2×#6626611yescharacteristic
subgroupG/H
centerC23C23×AGL(1,𝔽5)
commutatorC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC2×C5×#126C4
socleC23×C5C23×C4
prime radicalC24×D5C23
cosocleC22×D5C25
hypercenterC2×#126AGL(1,𝔽5)
hypocenterC5C2×#2334
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
2. #10617358C2direct (N × H)
3. C2×#65712C2semidirect
4. C2×#65712C2semidirect
5. C2×#65711C2semidirect
6. C2×#65711C2semidirect
7. C2×#65711C2semidirect
8. C2×C4⋊C4×AGL(1,𝔽5)C2semidirect
15. C2×#65689C2semidirect
16. C2×C4×C4⋊AGL(1,𝔽5)C2semidirect
33. C2×C5×#126C4semidirect
34. D5×#126C4semidirect
36. C2×#4044C4semidirect
37. C2×#4044C4semidirect
38. C2×#4044C4semidirect
45. C2×#4025C4semidirect
46. C2×#4025C4semidirect
47. C2×#4025C4semidirect
48. C2×#4022C4semidirect
62. #65712C22semidirect
63. #65712C22semidirect
64. #65711C22semidirect
65. #65711C22semidirect
66. #65711C22semidirect
67. C4⋊C4×AGL(1,𝔽5)C22semidirect
74. #65689C22semidirect
75. C4×C4⋊AGL(1,𝔽5)C22semidirect
126. C5×#126C2×C4semidirect
127. C2×C5×C4⋊C4C2×C4semidirect
128. C2×C5×C4⋊C4C2×C4semidirect
129. C2×C5×C4⋊C4C2×C4semidirect
133. C2×C42×C5C2×C4semidirect
143. C2×C4⋊Dic5C2×C4semidirect
144. C2×C4⋊Dic5C2×C4semidirect
145. C2×C4⋊Dic5C2×C4semidirect
146. C2×#683C2×C4semidirect
147. C2×#683C2×C4semidirect
148. C2×#683C2×C4semidirect
149. C2×#683C2×C4semidirect
150. C2×#683C2×C4semidirect
151. C2×#683C2×C4semidirect
152. C2×C4×Dic5C2×C4semidirect
153. C2×C4×Dic5C2×C4semidirect
154. C2×C4×Dic5C2×C4semidirect
155. #4044C2×C4semidirect
156. #4044C2×C4semidirect
157. #4044C2×C4semidirect
158. D5×C4⋊C4C2×C4semidirect
159. D5×C4⋊C4C2×C4semidirect
160. D5×C4⋊C4C2×C4semidirect
170. #4025C2×C4semidirect
171. #4025C2×C4semidirect
172. #4025C2×C4semidirect
173. #4022C2×C4semidirect
174. C42×D5C2×C4semidirect
302. C5×C4⋊C4C22×C4semidirect
303. C5×C4⋊C4C22×C4semidirect
304. C5×C4⋊C4C22×C4semidirect
308. C42×C5C22×C4semidirect
318. C4⋊Dic5C22×C4semidirect
319. C4⋊Dic5C22×C4semidirect
320. C4⋊Dic5C22×C4semidirect
321. #683C22×C4semidirect
322. #683C22×C4semidirect
323. #683C22×C4semidirect
324. #683C22×C4semidirect
325. #683C22×C4semidirect
326. #683C22×C4semidirect
327. C4×Dic5C22×C4semidirect
328. C4×Dic5C22×C4semidirect
329. C4×Dic5C22×C4semidirect
340. C2×#126AGL(1,𝔽5)semidirect
520. #126C2×AGL(1,𝔽5)semidirect
550. C2×C4⋊C4C2×AGL(1,𝔽5)semidirect
551. C2×C4⋊C4C2×AGL(1,𝔽5)semidirect
552. C2×C4⋊C4C2×AGL(1,𝔽5)semidirect
592. C2×C42C2×AGL(1,𝔽5)semidirect
754. C4⋊C4C22×AGL(1,𝔽5)semidirect
755. C4⋊C4C22×AGL(1,𝔽5)semidirect
756. C4⋊C4C22×AGL(1,𝔽5)semidirect
780. C42C22×AGL(1,𝔽5)semidirect
782. C2×C5#2334semidirect
787. D5#2334semidirect
897. C5C2×#2334semidirect
955. C2#10617358direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×#1262
#106173582
C2×#657122
C2×#657112
C2×C4⋊C4×AGL(1,𝔽5)2
C2×#657002
C2×#656992
C2×C22⋊C4×AGL(1,𝔽5)2
C2×#656892
C2×C4×C4⋊AGL(1,𝔽5)2
C2×#23345