Finite Group Databasebeta

← C2×#10617282 #13043906

Subgroups — C2×#10617282 #13043906

Order 1280.

3198 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
2C22×#4130C211yesmaximal, characteristic
3C2×D5×C22⋊Q8C211yesmaximal, characteristic
4C2×(C2×AGL(1,𝔽5))⋊Q8C211yesmaximal, characteristic, complemented
5C2×#65765C211yesmaximal, characteristic
6#10617282C2116yesmaximal, direct product factor
7C2×#65712C211yesmaximal, characteristic, complemented
8C2×#65712C212yesmaximal, complemented
9C2×#65711C212yesmaximal, complemented
10C2×C4⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
11C2×#65700C212yesmaximal
12C2×#65700C212yesmaximal
13C22×Q8×D5C2211yescharacteristic
14C23×C4×D5C2211yescharacteristic
15C22×C22⋊AGL(1,𝔽5)C2211yescharacteristic
16C22×C22⋊AGL(1,𝔽5)C2211yescharacteristic
17C22×C22⋊AGL(1,𝔽5)C2212yes—
18C2×Q8×AGL(1,𝔽5)—28no—
19C2×Q8×AGL(1,𝔽5)C2218yescomplemented
20C2×#4130—28no—
21C2×#4130C2218yes—
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)C2212yes—
27C22×C4⋊AGL(1,𝔽5)C2212yes—
28C22×C4×AGL(1,𝔽5)C2211yescharacteristic
29C22×C4×AGL(1,𝔽5)C2212yes—
30C22×C4×AGL(1,𝔽5)C2212yes—
31C22×C4×AGL(1,𝔽5)C2211yescharacteristic
32C2×C5×C22⋊Q8C411yescharacteristic, complemented
33C2×#4092C411yescharacteristic, complemented
34C2×#4070C411yescharacteristic, complemented
35D5×C22⋊Q8C418yescomplemented
36D5×C22⋊Q8C2218yes—
37C2×#4043C411yescharacteristic, complemented
38C2×#4042C412yescomplemented
39C2×D5×C4⋊C4C2211yescharacteristic
40C2×D5×C4⋊C4C2212yes—
41C2×D5×C22⋊C4C2212yes—
42C2×#4024C412yescomplemented
43(C2×AGL(1,𝔽5))⋊Q8C2218yescomplemented
44#65765C2218yes—
45C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
46C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
47C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
48C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
49C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
50#65712C2218yescomplemented
51#65712C22116yescomplemented
52#65711C22116yescomplemented
53C4⋊C4×AGL(1,𝔽5)C2218yescomplemented
54#65700C22116yes—
55#65700C22116yes—
56C2×#2323—51nomaximal, Sylow
57C24×D5C2311yescharacteristic
58C23×AGL(1,𝔽5)C2312yes—
59C23×AGL(1,𝔽5)C2311yescharacteristic
60C23×AGL(1,𝔽5)C2311yescharacteristic
61C23×AGL(1,𝔽5)C2312yes—
62C23×AGL(1,𝔽5)C2311yescharacteristic
63C23×AGL(1,𝔽5)C2311yescharacteristic
64C22×C5×Q8C2×C411yescharacteristic
65C23×C4×C5C2×C411yescharacteristic
66C23×Dic5C2×C411yescharacteristic
67C2×Q8×D5—24no—
68C2×Q8×D5—24no—
69C2×Q8×D5C2×C414yes—
70C2×Q8×D5C2314yes—
71C22×C4×D5—24no—
72C22×C4×D5—24no—
73C22×C4×D5C2×C411yescharacteristic
74C22×C4×D5C2×C411yescharacteristic
75C22×C4×D5C2×C414yes—
76C22×C4×D5C2312yes—
77C22×C4×D5C2312yes—
78C22×C4×D5C2311yescharacteristic
79C22×C4×D5C2314yes—
80C22×C4×D5C2311yescharacteristic
81C22×Dic10C2×C412yes—
82C22×Dic10C2×C411yescharacteristic
83C2×C22⋊AGL(1,𝔽5)—24no—
84C2×C22⋊AGL(1,𝔽5)—24no—
85C2×C22⋊AGL(1,𝔽5)—44no—
86C2×C22⋊AGL(1,𝔽5)C2314yes—
87C2×C22⋊AGL(1,𝔽5)C2314yes—
88C2×C22⋊AGL(1,𝔽5)C2318yes—
89Q8×AGL(1,𝔽5)—232no—
90#4130—232no—
91C2×C4⋊AGL(1,𝔽5)—24no—
92C2×C4⋊AGL(1,𝔽5)—24no—
93C2×C4⋊AGL(1,𝔽5)—28no—
94C2×C4⋊AGL(1,𝔽5)—24no—
95C2×C4⋊AGL(1,𝔽5)—24no—
96C2×C4⋊AGL(1,𝔽5)—44no—
97C2×C4⋊AGL(1,𝔽5)C2318yes—
98C2×C4⋊AGL(1,𝔽5)C2314yes—
99C2×C4⋊AGL(1,𝔽5)C2314yes—
100C2×C4⋊AGL(1,𝔽5)C2314yes—
101C2×C4⋊AGL(1,𝔽5)C2314yes—
102C2×C4⋊AGL(1,𝔽5)C2318yes—
103C2×C4×AGL(1,𝔽5)—28no—
104C2×C4×AGL(1,𝔽5)—24no—
105C2×C4×AGL(1,𝔽5)—44no—
106C2×C4×AGL(1,𝔽5)D418yes—
107C2×C4×AGL(1,𝔽5)C2318yes—
108C2×C4×AGL(1,𝔽5)C2314yes—
109C2×C4×AGL(1,𝔽5)C2318yes—
110C2×C4×AGL(1,𝔽5)C2314yes—
111C5×C22⋊Q8C2×C418yescomplemented
112C2×C5×C4⋊C4C2×C412yes—
113C2×C5×C4⋊C4C2×C411yescharacteristic
114C2×C5×C22⋊C4C2×C412yes—
115C2×C22⋊Dic5C2×C412yes—
116#4092C2×C418yescomplemented
117C2×#685C2×C412yes—
118C2×#685C2×C412yes—
119C2×C4⋊Dic5C2×C412yes—
120C2×C4⋊Dic5C2×C411yescharacteristic
121#4070C2×C418yescomplemented
122C2×#683C2×C412yes—
123C2×#683C2×C412yes—
124C2×#683C2×C412yes—
125#4043C2×C418yescomplemented
126#4042C2×C4116yescomplemented
127D5×C4⋊C4C2×C414yes—
128D5×C4⋊C4C2×C418yes—
129D5×C4⋊C4C2314yes—
130D5×C4⋊C4C2318yes—
131D5×C22⋊C4C2×C418yes—
132D5×C22⋊C4C2318yes—
133#4024C2×C4116yescomplemented
134(C2×AGL(1,𝔽5))⋊C4C2318yes—
135(C2×AGL(1,𝔽5))⋊C4C2318yes—
136(C2×AGL(1,𝔽5))⋊C4C2318yes—
137(C2×AGL(1,𝔽5))⋊C4C2318yes—
138(C2×AGL(1,𝔽5))⋊C4C2318yes—
139C22×C22⋊Q8—51no—
140C22×C4×Q8—51no—
141C22×#117—51no—
142#2323—516no—
143C2×#391—51no—
144C2×#389—51no—
145C2×#389—52no—
146C2×#388—52no—
147C2×#388—52no—
148C2×#387—52no—
149C2×#380—51no—
150C2×C4×C4⋊C4—51no—
151C24×C5C22×C411yescharacteristic
152C23×D5—22no—
153C23×D5—22no—
154C23×D5—22no—
155C23×D5—22no—
156C23×D5—22no—
157C23×D5—22no—
158C23×D5C22×C412yes—
159C23×D5C22×C411yescharacteristic
160C23×D5C2412yes—
161C23×D5C2411yescharacteristic
162C22×AGL(1,𝔽5)—22no—
163C22×AGL(1,𝔽5)—22no—
164C22×AGL(1,𝔽5)—22no—
165C22×AGL(1,𝔽5)—22no—
166C22×AGL(1,𝔽5)—24no—
167C22×AGL(1,𝔽5)—22no—
168C22×AGL(1,𝔽5)—22no—
169C22×AGL(1,𝔽5)—24no—
170C22×AGL(1,𝔽5)—24no—
171C22×AGL(1,𝔽5)—22no—
172C22×AGL(1,𝔽5)—24no—
173C22×AGL(1,𝔽5)—22no—
174C22×AGL(1,𝔽5)—22no—
175C22×AGL(1,𝔽5)—24no—
176C22×AGL(1,𝔽5)—22no—
177C22×AGL(1,𝔽5)—24no—
178C22×AGL(1,𝔽5)C2×D414yes—
179C22×AGL(1,𝔽5)C2×D414yes—
180C22×AGL(1,𝔽5)C2414yes—
181C22×AGL(1,𝔽5)C2412yes—
182C22×AGL(1,𝔽5)C2412yes—
183C22×AGL(1,𝔽5)C2414yes—
184C22×AGL(1,𝔽5)C2412yes—
185C22×AGL(1,𝔽5)C2412yes—
186C2×C5×Q8—24no—
187C2×C5×Q8C22×C414yes—
188C22×C4×C5—24no—
189C22×C4×C5C22×C412yes—
190C22×C4×C5C22×C412yes—
191C22×C4×C5C22×C411yescharacteristic
192C22×C4×C5C22×C414yes—
193C22×C4×C5C22×C411yescharacteristic
194C22×Dic5—24no—
195C22×Dic5C22×C412yes—
196C22×Dic5C22×C412yes—
197C22×Dic5C22×C414yes—
198C22×Dic5C22×C411yescharacteristic
199C22×Dic5C22×C411yescharacteristic
200Q8×D5—216no—
201Q8×D5—28no—
202Q8×D5—28no—
203C2×C4×D5—24no—
204C2×C4×D5—22no—
205C2×C4×D5—22no—
206C2×C4×D5—24no—
207C2×C4×D5—24no—
208C2×C4×D5—24no—
209C2×C4×D5—24no—
210C2×C4×D5—24no—
211C2×C4×D5—216no—
212C2×C4×D5—28no—
213C2×C4×D5—28no—
214C2×C4×D5C22×C412yes—
215C2×C4×D5C22×C414yes—
216C2×C4×D5C22×C414yes—
217C2×C4×D5C22×C414yes—
218C2×C4×D5C22×C414yes—
219C2×C4×D5C22×C412yes—
220C2×C4×D5C2×D414yes—
221C2×C4×D5#4114yes—
222C2×C4×D5C2414yes—
223C2×C4×D5C2414yes—
224C2×C4×D5C2412yes—
225C2×C4×D5C2412yes—
226C2×Dic10—24no—
227C2×Dic10—28no—
228C2×Dic10C22×C418yes—
229C2×Dic10C22×C414yes—
230C22⋊AGL(1,𝔽5)—28no—
231C22⋊AGL(1,𝔽5)—28no—
232C22⋊AGL(1,𝔽5)—48no—
233C4⋊AGL(1,𝔽5)—28no—
234C4⋊AGL(1,𝔽5)—28no—
235C4⋊AGL(1,𝔽5)—216no—
236C4⋊AGL(1,𝔽5)—28no—
237C4⋊AGL(1,𝔽5)—28no—
238C4⋊AGL(1,𝔽5)—48no—
239C4×AGL(1,𝔽5)—216no—
240C4×AGL(1,𝔽5)—28no—
241C4×AGL(1,𝔽5)—48no—
242C4×AGL(1,𝔽5)C2×D4116yes—
243C5×C4⋊C4C22×C418yes—
244C5×C4⋊C4C22×C414yes—
245C5×C22⋊C4C22×C418yes—
246C22⋊Dic5C22×C418yes—
247#685C22×C418yes—
248#685C22×C418yes—
249C4⋊Dic5C22×C418yes—
250C4⋊Dic5C22×C414yes—
251#683C22×C418yes—
252#683C22×C418yes—
253#683C22×C418yes—
254C23×Q8—51no—
255C24×C4—51no—
256C2×C22⋊Q8—51no—
257C2×C22⋊Q8—51no—
258C2×C22⋊Q8—58no—
259C2×C22⋊Q8—58no—
260C2×C22⋊Q8—52no—
261C2×C22⋊Q8—51no—
262C2×C22⋊Q8—52no—
263C2×C22⋊Q8AGL(1,𝔽5)11yescharacteristic, complemented
264C2×C4×Q8—58no—
265C2×C4×Q8—108no—
266C2×#117—58no—
267C2×#117—108no—
268C22×C4⋊C4—51no—
269C22×C4⋊C4—52no—
270C22×C4⋊C4—51no—
271C22×C4⋊C4—51no—
272C22×C4⋊C4—51no—
273C22×C4⋊C4—52no—
274C22×C4⋊C4—51no—
275C22×C4⋊C4—52no—
276C22×C22⋊C4—52no—
277C22×C22⋊C4—51no—
278C22×C22⋊C4—51no—
279C22×C22⋊C4—52no—
280C22×C42—51no—
281C22×C42—51no—
282C22×C42—52no—
283C22×C42—52no—
284#391—58no—
285#389—516no—
286#389—58no—
287#388—516no—
288#388—516no—
289#387—516no—
290#380—58no—
291C4×C4⋊C4—58no—
292C2×#95—52no—
293C2×#95—52no—
294C2×#95—52no—
295C2×#95—52no—
296C2×#95—52no—
297C23×C5—22no—
298C23×C5—22no—
299C23×C5—22no—
300C23×C5C23×C412yes—
301C23×C5C23×C411yescharacteristic
302C22×D5—22no—
303C22×D5—22no—
304C22×D5—22no—
305C22×D5—24no—
306C22×D5—24no—
307C22×D5—24no—
308C22×D5—22no—
309C22×D5—22no—
310C22×D5—22no—
311C22×D5—22no—
312C22×D5—22no—
313C22×D5—22no—
314C22×D5—44no—
315C22×D5—44no—
316C22×D5—44no—
317C22×D5—44no—
318C22×D5C23×C412yes—
319C22×D5C23×C411yescharacteristic
320C22×D5C22×D412yes—
321C22×D5C2×#4112yes—
322C22×D5H(5,𝔽2)12yes—
323C22×D52−1+412yes—
324C22×D52−1+412yes—
325C22×D52−1+412yes—
326C22×D5C2511yescharacteristic
327C2×AGL(1,𝔽5)—28no—
328C2×AGL(1,𝔽5)—28no—
329C2×AGL(1,𝔽5)—22no—
330C2×AGL(1,𝔽5)—22no—
331C2×AGL(1,𝔽5)—22no—
332C2×AGL(1,𝔽5)—22no—
333C2×AGL(1,𝔽5)—24no—
334C2×AGL(1,𝔽5)—22no—
335C2×AGL(1,𝔽5)—22no—
336C2×AGL(1,𝔽5)—24no—
337C2×AGL(1,𝔽5)—24no—
338C2×AGL(1,𝔽5)—22no—
339C2×AGL(1,𝔽5)—24no—
340C2×AGL(1,𝔽5)—22no—
341C2×AGL(1,𝔽5)—22no—
342C2×AGL(1,𝔽5)—24no—
343C2×AGL(1,𝔽5)—22no—
344C2×AGL(1,𝔽5)—24no—
345C2×AGL(1,𝔽5)—44no—
346C2×AGL(1,𝔽5)—48no—
347C2×AGL(1,𝔽5)—44no—
348C2×AGL(1,𝔽5)—48no—
349C2×AGL(1,𝔽5)C22×D414yes—
350C2×AGL(1,𝔽5)C22×D414yes—
351C5×Q8—28no—
352C2×C4×C5—24no—
353C2×C4×C5—22no—
354C2×C4×C5—24no—
355C2×C4×C5—28no—
356C2×C4×C5C4×D414yes—
357C2×C4×C5C23×C412yes—
358C2×C4×C5C23×C414yes—
359C2×C4×C5C23×C414yes—
360C2×C4×C5C23×C412yes—
361C2×Dic5—24no—
362C2×Dic5—22no—
363C2×Dic5—24no—
364C2×Dic5—28no—
365C2×Dic5C4×D414yes—
366C2×Dic5C23×C414yes—
367C2×Dic5C23×C412yes—
368C2×Dic5C23×C414yes—
369C2×Dic5C23×C412yes—
370C4×D5—24no—
371C4×D5—28no—
372C4×D5—28no—
373C4×D5—24no—
374C4×D5—22no—
375C4×D5—22no—
376C4×D5—24no—
377C4×D5—24no—
378C4×D5—24no—
379C4×D5—28no—
380C4×D5—28no—
381C4×D5C4×D418yes—
382C4×D5C22×D414yes—
383C4×D5C2×#4114yes—
384Dic10—28no—
385Dic10—216no—
386C25—51no—
387C22×Q8—54no—
388C22×Q8—54no—
389C22×Q8—52no—
390C22×Q8—51no—
391C22×Q8—104no—
392C22×Q8—104no—
393C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
394C23×C4—51no—
395C23×C4—51no—
396C23×C4—51no—
397C23×C4—51no—
398C23×C4—52no—
399C23×C4—52no—
400C23×C4—51no—
401C23×C4—54no—
402C23×C4—51no—
403C23×C4—54no—
404C23×C4—51no—
405C23×C4—51no—
406C23×C4—52no—
407C23×C4—51no—
408C23×C4—52no—
409C23×C4—104no—
410C23×C4—104no—
411C23×C4C2×AGL(1,𝔽5)11yescharacteristic
412C22⋊Q8—58no—
413C22⋊Q8—58no—
414C22⋊Q8—516no—
415C22⋊Q8—58no—
416C22⋊Q8—516no—
417C22⋊Q8C2×AGL(1,𝔽5)18yescomplemented
418C4×Q8—1032no—
419#117—1032no—
420C2×C4⋊C4—52no—
421C2×C4⋊C4—52no—
422C2×C4⋊C4—52no—
423C2×C4⋊C4—51no—
424C2×C4⋊C4—52no—
425C2×C4⋊C4—54no—
426C2×C4⋊C4—58no—
427C2×C4⋊C4—54no—
428C2×C4⋊C4—58no—
429C2×C4⋊C4—54no—
430C2×C4⋊C4—54no—
431C2×C4⋊C4—54no—
432C2×C4⋊C4—58no—
433C2×C4⋊C4—54no—
434C2×C4⋊C4—58no—
435C2×C4⋊C4—104no—
436C2×C4⋊C4—104no—
437C2×C4⋊C4—104no—
438C2×C4⋊C4—108no—
439C2×C4⋊C4—104no—
440C2×C4⋊C4—204no—
441C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
442C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
443C2×C22⋊C4—52no—
444C2×C22⋊C4—52no—
445C2×C22⋊C4—52no—
446C2×C22⋊C4—58no—
447C2×C22⋊C4—58no—
448C2×C22⋊C4—54no—
449C2×C22⋊C4—54no—
450C2×C22⋊C4—58no—
451C2×C22⋊C4—104no—
452C2×C22⋊C4—104no—
453C2×C22⋊C4—204no—
454C2×C22⋊C4C2×AGL(1,𝔽5)12yes—
455C2×C42—54no—
456C2×C42—58no—
457C2×C42—54no—
458C2×C42—58no—
459C2×C42—58no—
460C2×C42—104no—
461C2×C42—108no—
462C2×C42—204no—
463#95—58no—
464#95—58no—
465#95—58no—
466#95—58no—
467#95—58no—
468C22×C5—22no—
469C22×C5—22no—
470C22×C5—22no—
471C22×C5—44no—
472C22×C5C2×C4×D412yes—
473C22×C5#51912yes—
474C22×C5#52012yes—
475C22×C5C24×C411yescharacteristic
476C2×D5—22no—
477C2×D5—22no—
478C2×D5—22no—
479C2×D5—44no—
480C2×D5—48no—
481C2×D5—42no—
482C2×D5—42no—
483C2×D5—42no—
484C2×D5—42no—
485C2×D5C2×C4×D412yes—
486C2×D5#51912yes—
487C2×D5#52012yes—
488C2×D5#53614yes—
489C2×D5#53714yes—
490C2×D5#54114yes—
491C2×D5#54214yes—
492C2×D5C23×D411yescharacteristic
493C2×D5C22×#4111yescharacteristic
494C2×D5C2×H(5,𝔽2)11yescharacteristic
495C2×D5C2×2−1+411yescharacteristic
496C2×D5C2×2−1+411yescharacteristic
497C2×D5C2×2−1+411yescharacteristic
498AGL(1,𝔽5)—24no—
499AGL(1,𝔽5)—24no—
500AGL(1,𝔽5)—42no—
501AGL(1,𝔽5)—44no—
502AGL(1,𝔽5)—42no—
503AGL(1,𝔽5)—44no—
504C4×C5—24no—
505C4×C5—22no—
506C4×C5—24no—
507C4×C5C2×C4×D414yes—
508Dic5—24no—
509Dic5—22no—
510Dic5—24no—
511Dic5C2×C4×D414yes—
512C24—51no—
513C24—52no—
514C24—52no—
515C24—51no—
516C24—102no—
517C24—102no—
518C24—102no—
519C24—102no—
520C24—102no—
521C24—102no—
522C24C22×AGL(1,𝔽5)11yescharacteristic
523C2×Q8—24no—
524C2×Q8—58no—
525C2×Q8—54no—
526C2×Q8—108no—
527C2×Q8—108no—
528C2×Q8—108no—
529C2×Q8—1016no—
530C2×Q8—104no—
531C2×Q8C22×AGL(1,𝔽5)14yes—
532C22×C4—24no—
533C22×C4—51no—
534C22×C4—54no—
535C22×C4—54no—
536C22×C4—52no—
537C22×C4—52no—
538C22×C4—52no—
539C22×C4—52no—
540C22×C4—54no—
541C22×C4—54no—
542C22×C4—54no—
543C22×C4—52no—
544C22×C4—52no—
545C22×C4—51no—
546C22×C4—54no—
547C22×C4—54no—
548C22×C4—52no—
549C22×C4—54no—
550C22×C4—54no—
551C22×C4—52no—
552C22×C4—54no—
553C22×C4—54no—
554C22×C4—52no—
555C22×C4—54no—
556C22×C4—52no—
557C22×C4—54no—
558C22×C4—108no—
559C22×C4—104no—
560C22×C4—108no—
561C22×C4—1016no—
562C22×C4—104no—
563C22×C4—104no—
564C22×C4—102no—
565C22×C4—102no—
566C22×C4—104no—
567C22×C4—104no—
568C22×C4—104no—
569C22×C4—102no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—104no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—104no—
577C22×C4—104no—
578C22×C4—104no—
579C22×C4—104no—
580C22×C4—102no—
581C22×C4—102no—
582C22×C4—104no—
583C22×C4—102no—
584C22×C4—104no—
585C22×C4—102no—
586C22×C4C22×AGL(1,𝔽5)14yes—
587C22×C4C22×AGL(1,𝔽5)12yes—
588C22×C4C22×AGL(1,𝔽5)12yes—
589C22×C4C22×AGL(1,𝔽5)11yescharacteristic
590C22×C4C22×AGL(1,𝔽5)11yescharacteristic
591C4⋊C4—58no—
592C4⋊C4—58no—
593C4⋊C4—58no—
594C4⋊C4—54no—
595C4⋊C4—58no—
596C4⋊C4—108no—
597C4⋊C4—108no—
598C4⋊C4—108no—
599C4⋊C4—1016no—
600C4⋊C4—108no—
601C4⋊C4—208no—
602C4⋊C4C22×AGL(1,𝔽5)14yes—
603C4⋊C4C22×AGL(1,𝔽5)18yes—
604C22⋊C4—58no—
605C22⋊C4—58no—
606C22⋊C4—58no—
607C22⋊C4—108no—
608C22⋊C4—108no—
609C22⋊C4—208no—
610C22⋊C4C22×AGL(1,𝔽5)18yes—
611C42—516no—
612C42—108no—
613C42—1016no—
614C42—208no—
615C2×C5—42no—
616C2×C5#232314yescomplemented
617C2×C5C22×C4×D411yescharacteristic
618C2×C5C2×#51911yescharacteristic
619C2×C5C2×#52011yescharacteristic
620D5—42no—
621D5#232314yescomplemented
622D5C2×#53611yescharacteristic
623D5C2×#53711yescharacteristic
624D5C2×#54111yescharacteristic
625D5C2×#54211yescharacteristic
626C23—22no—
627C23—22no—
628C23—22no—
629C23—52no—
630C23—52no—
631C23—52no—
632C23—52no—
633C23—52no—
634C23—52no—
635C23—51no—
636C23—51no—
637C23—52no—
638C23—102no—
639C23—102no—
640C23—102no—
641C23—104no—
642C23—102no—
643C23—102no—
644C23—104no—
645C23—102no—
646C23—104no—
647C23—102no—
648C23—102no—
649C23—102no—
650C23—204no—
651C23—204no—
652C23—204no—
653C23—204no—
654C23C23×AGL(1,𝔽5)12yes—
655C23C23×AGL(1,𝔽5)11yescharacteristic
656Q8—28no—
657Q8—1016no—
658Q8—108no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—28no—
663C2×C4—54no—
664C2×C4—52no—
665C2×C4—54no—
666C2×C4—54no—
667C2×C4—58no—
668C2×C4—54no—
669C2×C4—54no—
670C2×C4—54no—
671C2×C4—54no—
672C2×C4—52no—
673C2×C4—108no—
674C2×C4—104no—
675C2×C4—104no—
676C2×C4—102no—
677C2×C4—102no—
678C2×C4—104no—
679C2×C4—104no—
680C2×C4—108no—
681C2×C4—104no—
682C2×C4—108no—
683C2×C4—108no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—108no—
689C2×C4—108no—
690C2×C4—102no—
691C2×C4—104no—
692C2×C4—104no—
693C2×C4—108no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—104no—
697C2×C4—104no—
698C2×C4—104no—
699C2×C4—104no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—104no—
703C2×C4—102no—
704C2×C4—104no—
705C2×C4—102no—
706C2×C4—204no—
707C2×C4—208no—
708C2×C4—204no—
709C2×C4—208no—
710C2×C4D4×AGL(1,𝔽5)14yes—
711C2×C4C23×AGL(1,𝔽5)14yes—
712C2×C4C23×AGL(1,𝔽5)14yes—
713C2×C4C23×AGL(1,𝔽5)12yes—
714C2×C4C23×AGL(1,𝔽5)12yes—
715C5C2×#232311yescharacteristic, complemented, Sylow
716C22—22no—
717C22—22no—
718C22—22no—
719C22—44no—
720C22—51no—
721C22—51no—
722C22—52no—
723C22—51no—
724C22—51no—
725C22—52no—
726C22—51no—
727C22—51no—
728C22—52no—
729C22—54no—
730C22—54no—
731C22—54no—
732C22—54no—
733C22—102no—
734C22—102no—
735C22—102no—
736C22—202no—
737C22—202no—
738C22—202no—
739C22—208no—
740C22—202no—
741C22—204no—
742C22C2×D4×AGL(1,𝔽5)12yes—
743C22#6626212yes—
744C22#6626612yes—
745C22C24×AGL(1,𝔽5)11yescharacteristic
746C4—22no—
747C4—24no—
748C4—24no—
749C4—54no—
750C4—104no—
751C4—104no—
752C4—102no—
753C4—104no—
754C4—104no—
755C4—202no—
756C4—204no—
757C4—202no—
758C4—204no—
759C4C2×D4×AGL(1,𝔽5)14yes—
760C2—42no—
761C2—51no—
762C2—51no—
763C2—51no—
764C2—54no—
765C2—51no—
766C2—202no—
767C2#1061728214yesdirect product factor
768C2C22×D4×AGL(1,𝔽5)11yescharacteristic
769C2C2×#6626211yescharacteristic
770C2C2×#6626611yescharacteristic
subgroupG/H
centerC23C23×AGL(1,𝔽5)
commutatorC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC2×C5×C22⋊Q8C4
socleC23×C5C23×C4
prime radicalC24×D5C23
cosocleC22×D5C25
hypercenterC2×C22⋊Q8AGL(1,𝔽5)
hypocenterC5C2×#2323
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×Q8×AGL(1,𝔽5)C2semidirect
4. C2×(C2×AGL(1,𝔽5))⋊Q8C2semidirect
6. #10617282C2direct (N × H)
7. C2×#65712C2semidirect
8. C2×#65712C2semidirect
9. C2×#65711C2semidirect
10. C2×C4⋊C4×AGL(1,𝔽5)C2semidirect
19. C2×Q8×AGL(1,𝔽5)C22semidirect
32. C2×C5×C22⋊Q8C4semidirect
33. C2×#4092C4semidirect
34. C2×#4070C4semidirect
35. D5×C22⋊Q8C4semidirect
37. C2×#4043C4semidirect
38. C2×#4042C4semidirect
42. C2×#4024C4semidirect
43. (C2×AGL(1,𝔽5))⋊Q8C22semidirect
50. #65712C22semidirect
51. #65712C22semidirect
52. #65711C22semidirect
53. C4⋊C4×AGL(1,𝔽5)C22semidirect
111. C5×C22⋊Q8C2×C4semidirect
116. #4092C2×C4semidirect
121. #4070C2×C4semidirect
125. #4043C2×C4semidirect
126. #4042C2×C4semidirect
133. #4024C2×C4semidirect
263. C2×C22⋊Q8AGL(1,𝔽5)semidirect
417. C22⋊Q8C2×AGL(1,𝔽5)semidirect
616. C2×C5#2323semidirect
621. D5#2323semidirect
715. C5C2×#2323semidirect
767. C2#10617282direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×AGL(1,𝔽5)2
C22×#41302
C2×D5×C22⋊Q82
C2×(C2×AGL(1,𝔽5))⋊Q82
C2×#657652
#106172822
C2×#657122
C2×#657112
C2×C4⋊C4×AGL(1,𝔽5)2
C2×#657002
C2×#23235