Finite Group Databasebeta

← C2×AGL(1,𝔽5)×#239 #14478947

Subgroups — C2×AGL(1,𝔽5)×#239 #14478947

Order 1920.

3456 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#239C211yesmaximal, characteristic
2C2×Q8×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
3C2×C3×Q8×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
4AGL(1,𝔽5)×#239C2116yesmaximal, direct product factor
5C2×#91921C213yesmaximal, complemented
6C2×AGL(1,𝔽5)×D12C213yesmaximal, complemented
7C2×C4×D3×AGL(1,𝔽5)C213yesmaximal, complemented
8C2×#91907C213yesmaximal, complemented
9C2×#41×AGL(1,𝔽5)—31nomaximal, Hall
10C22×D3×AGL(1,𝔽5)C2213yes—
11C22×D3×AGL(1,𝔽5)C2213yes—
12C2×#6821C411yescharacteristic, complemented
13C2×C5×#239C411yescharacteristic, complemented
14C2×C3×Q8×D5C2211yescharacteristic
15D5×#239C418yescomplemented
16D5×#239C2218yes—
17C2×D5×D12C2213yes—
18C2×C4×D3×D5C2213yes—
19C2×#6769C413yescomplemented
20C2×#6768C413yescomplemented
21Q8×ΓL(1,𝔽16)C2218yescomplemented
22C2×C4⋊ΓL(1,𝔽16)C2213yes—
23C2×C4×ΓL(1,𝔽16)C2213yes—
24C3×Q8×AGL(1,𝔽5)C2218yescomplemented
25C2×C3×C4⋊AGL(1,𝔽5)C2213yes—
26C2×C3×C4×AGL(1,𝔽5)C2213yes—
27C2×(C2×D3)⋊AGL(1,𝔽5)C2216yes—
28C2×Dic3×AGL(1,𝔽5)C2213yes—
29C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
30#91921C22124yescomplemented
31AGL(1,𝔽5)×D12C22124yescomplemented
32C4×D3×AGL(1,𝔽5)C22124yescomplemented
33#91907C22124yescomplemented
34C2×C4×#239—51nomaximal, Hall
35C2×D5×#41—31no—
36#41×AGL(1,𝔽5)—316no—
37C2×Q8×AGL(1,𝔽5)—31no—
38C2×Q8×AGL(1,𝔽5)D311yescharacteristic, complemented
39C2×D4×AGL(1,𝔽5)—33no—
40C2×D4×AGL(1,𝔽5)—33no—
41C2×#4130—33no—
42C22×C4×AGL(1,𝔽5)—33no—
43C22×D3×D5C2313yes—
44C22×ΓL(1,𝔽16)C2313yes—
45C22×ΓL(1,𝔽16)C2311yescharacteristic
46C22×C3×AGL(1,𝔽5)C2313yes—
47C22×C3×AGL(1,𝔽5)C2311yescharacteristic
48C2×D3×AGL(1,𝔽5)—212no—
49C2×D3×AGL(1,𝔽5)—212no—
50C2×D3×AGL(1,𝔽5)C23112yes—
51C2×D3×AGL(1,𝔽5)C23112yes—
52C2×C3×C5×Q8C2×C411yescharacteristic, complemented
53#6821C2×C418yescomplemented
54C2×D60C2×C413yescomplemented
55C2×C4×D15C2×C413yescomplemented
56C5×#239C2×C418yescomplemented
57C2×C5×D12C2×C413yescomplemented
58C2×C4×C5×D3C2×C413yescomplemented
59C3×Q8×D5C2×C414yescomplemented
60C3×Q8×D5C2314yes—
61C2×C3×C4×D5C2313yes—
62C2×C3×Dic10C2×C413yescomplemented
63C2×#1203C2×C416yescomplemented
64C2×#1200C2×C413yescomplemented
65C2×D3×Dic5C2×C413yescomplemented
66C2×D5×Dic3C2311yescharacteristic
67D5×D12C2×C4112yescomplemented
68D5×D12C23112yes—
69C4×D3×D5C2×C4112yescomplemented
70C4×D3×D5C23112yes—
71#6769C2×C4124yescomplemented
72#6768C2×C4124yescomplemented
73C4⋊ΓL(1,𝔽16)C23112yes—
74C4×ΓL(1,𝔽16)C23112yes—
75C3×C4⋊AGL(1,𝔽5)C23112yes—
76C3×C4×AGL(1,𝔽5)C23112yes—
77(C2×D3)⋊AGL(1,𝔽5)C23124yes—
78Dic3×AGL(1,𝔽5)C23112yes—
79Dic3×AGL(1,𝔽5)C2314yes—
80C22×#239—51no—
81C2×C3×C4×Q8—51no—
82C2×Q8×Dic3—51no—
83C4×#239—516no—
84C2×#893—53no—
85C2×#892—53no—
86C2×C4×D12—53no—
87C2×C42×D3—53no—
88C23×AGL(1,𝔽5)—33no—
89C23×AGL(1,𝔽5)—33no—
90C2×C5×#41—31no—
91D5×#41—38no—
92D5×#41—38no—
93C2×#713—31no—
94C2×Q8×D5C2×D311yescharacteristic
95C2×#711—33no—
96C2×D4×D5—33no—
97C2×#709—33no—
98C22×C4×D5—33no—
99C2×C22⋊AGL(1,𝔽5)—36no—
100Q8×AGL(1,𝔽5)—38no—
101Q8×AGL(1,𝔽5)C2×D318yescomplemented
102D4×AGL(1,𝔽5)—324no—
103D4×AGL(1,𝔽5)—324no—
104#4130—324no—
105C2×C4⋊AGL(1,𝔽5)—33no—
106C2×C4⋊AGL(1,𝔽5)C2×D313yes—
107C2×C4×AGL(1,𝔽5)—31no—
108C2×C4×AGL(1,𝔽5)—33no—
109C2×C4×AGL(1,𝔽5)—33no—
110C2×C4×AGL(1,𝔽5)—324no—
111C2×C4×AGL(1,𝔽5)C2×D313yes—
112C2×C4×#41—151noSylow
113C22×D15C22×C413yes—
114C22×C5×D3C22×C413yes—
115C22×C3×D5C2411yescharacteristic
116C2×D3×D5—26no—
117C2×D3×D5—26no—
118C2×D3×D5C22×C416yes—
119C2×D3×D5C2416yes—
120C2×ΓL(1,𝔽16)—26no—
121C2×ΓL(1,𝔽16)#4114yescomplemented
122C2×ΓL(1,𝔽16)C2416yes—
123C2×ΓL(1,𝔽16)C2412yes—
124C2×C3×AGL(1,𝔽5)—26no—
125C2×C3×AGL(1,𝔽5)#4114yescomplemented
126C2×C3×AGL(1,𝔽5)C2416yes—
127C2×C3×AGL(1,𝔽5)C2412yes—
128D3×AGL(1,𝔽5)—224no—
129D3×AGL(1,𝔽5)—224no—
130C3×C5×Q8C22×C414yescomplemented
131C2×C3×C4×C5C22×C413yes—
132C2×Dic15C22×C411yescharacteristic
133D60C22×C4112yescomplemented
134C4×D15C22×C4112yescomplemented
135C2×C5×Dic3C22×C411yescharacteristic
136C5×D12C22×C4112yescomplemented
137C4×C5×D3C22×C4112yescomplemented
138C2×C3×Dic5C22×C413yes—
139C3×C4×D5C22×C416yes—
140C3×C4×D5C2416yes—
141C3×Dic10C22×C4112yescomplemented
142#1203C22×C4124yescomplemented
143#1200C22×C4112yescomplemented
144D3×Dic5C22×C4112yescomplemented
145D5×Dic3C22×C412yes—
146D5×Dic3C2412yes—
147C22×C3×Q8—51no—
148C2×#239—51no—
149C2×#239—58no—
150C2×#239—58no—
151C2×#239—53no—
152C2×#239—53no—
153C2×#239AGL(1,𝔽5)11yescharacteristic, direct product factor
154C22×D12—53no—
155C22×C4×D3—53no—
156C22×C4×D3—53no—
157C22×C4×D3—53no—
158C3×C4×Q8—58no—
159C2×C3×C4⋊C4—53no—
160C2×C3×C42—53no—
161Q8×Dic3—58no—
162C2×(C2×D3)⋊C4—56no—
163C2×C4⋊Dic3—53no—
164C2×C4×Dic3—51no—
165C2×C4×Dic3—53no—
166C2×C4×Dic3—53no—
167#893—524no—
168#892—524no—
169C4×D12—524no—
170C42×D3—524no—
171C23×D5—33no—
172C22×AGL(1,𝔽5)—31no—
173C22×AGL(1,𝔽5)—33no—
174C22×AGL(1,𝔽5)—312no—
175C22×AGL(1,𝔽5)—312no—
176C22×AGL(1,𝔽5)—612no—
177C22×AGL(1,𝔽5)—612no—
178C22×AGL(1,𝔽5)C22×D313yes—
179C22×AGL(1,𝔽5)C22×D311yescharacteristic
180C5×#41—38no—
181C2×C5×Q8C4×D311yescharacteristic, complemented
182C2×C5×D4—33no—
183C22×C4×C5—33no—
184C2×C22⋊D5—36no—
185C22×Dic5—33no—
186#713—38no—
187Q8×D5C4×D314yescomplemented
188Q8×D5C22×D314yes—
189#711—324no—
190D4×D5—312no—
191D4×D5—312no—
192#709—324no—
193C2×D20—33no—
194C2×C4×D5—31no—
195C2×C4×D5—33no—
196C2×C4×D5—33no—
197C2×C4×D5—312no—
198C2×C4×D5—312no—
199C2×C4×D5C22×D313yes—
200C2×Dic10C4×D313yescomplemented
201C22⋊AGL(1,𝔽5)—324no—
202C4⋊AGL(1,𝔽5)—312no—
203C4⋊AGL(1,𝔽5)C22×D3112yes—
204C4×AGL(1,𝔽5)—34no—
205C4×AGL(1,𝔽5)—312no—
206C4×AGL(1,𝔽5)—312no—
207C4×AGL(1,𝔽5)C22×D3112yes—
208C22×#41—151no—
209C4×#41—1516no—
210C2×C4×Q8—51no—
211C2×C4×Q8—151no—
212C2×C4×D4—153no—
213C2×C4×D4—153no—
214C2×#117—153no—
215C22×C42—153no—
216C22×C3×C5C23×C411yescharacteristic
217C2×D15—26no—
218C2×D15C23×C416yes—
219C2×C5×D3—26no—
220C2×C5×D3C23×C416yes—
221C2×C3×D5C23×C411yescharacteristic
222C2×C3×D5C2×#4112yes—
223C2×C3×D5C2×#4112yes—
224C2×C3×D5C2511yescharacteristic
225D3×D5—212no—
226D3×D5—26no—
227D3×D5—26no—
228ΓL(1,𝔽16)—26no—
229ΓL(1,𝔽16)C2×#4114yescomplemented
230C3×AGL(1,𝔽5)—26no—
231C3×AGL(1,𝔽5)C2×#4114yescomplemented
232C3×C4×C5C23×C416yes—
233Dic15C23×C412yes—
234C3×Dic5C23×C416yes—
235C5×Dic3C23×C412yes—
236C23×D3—53no—
237C2×C3×Q8—54no—
238C2×C3×Q8—54no—
239C2×C3×Q8—53no—
240C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
241C22×C3×C4—51no—
242C22×C3×C4—53no—
243C22×C3×C4—53no—
244C22×Dic3—51no—
245C22×Dic3—51no—
246C22×Dic3—53no—
247#239—58no—
248#239—524no—
249#239—524no—
250#239C2×AGL(1,𝔽5)18yesdirect product factor
251C2×D12—56no—
252C2×D12—53no—
253C2×D12—512no—
254C2×D12—512no—
255C2×D12C2×AGL(1,𝔽5)13yescomplemented
256C2×C4×D3—53no—
257C2×C4×D3—53no—
258C2×C4×D3—53no—
259C2×C4×D3—512no—
260C2×C4×D3—512no—
261C2×C4×D3—512no—
262C2×C4×D3—512no—
263C2×C4×D3—1012no—
264C2×C4×D3—1012no—
265C2×C4×D3C2×AGL(1,𝔽5)13yescomplemented
266C3×C4⋊C4—512no—
267C3×C42—512no—
268(C2×D3)⋊C4—524no—
269C4⋊Dic3—512no—
270C4×Dic3—54no—
271C4×Dic3—512no—
272C4×Dic3—512no—
273C23×C5—33no—
274C22×D5—33no—
275C22×D5—36no—
276C22×D5—36no—
277C22×D5—66no—
278C22×D5—66no—
279C22×D5C23×D311yescharacteristic
280C2×AGL(1,𝔽5)—26no—
281C2×AGL(1,𝔽5)—34no—
282C2×AGL(1,𝔽5)—32no—
283C2×AGL(1,𝔽5)—36no—
284C2×AGL(1,𝔽5)—624no—
285C2×AGL(1,𝔽5)—66no—
286C2×AGL(1,𝔽5)—624no—
287C2×AGL(1,𝔽5)#23914yesdirect product factor
288C2×AGL(1,𝔽5)C23×D316yes—
289C2×AGL(1,𝔽5)C23×D312yes—
290C5×Q8C2×C4×D314yescomplemented
291C5×D4—312no—
292C2×C4×C5—31no—
293C2×C4×C5—312no—
294C2×C4×C5C2×C4×D313yes—
295C22⋊D5—324no—
296C2×Dic5—31no—
297C2×Dic5—312no—
298C2×Dic5C2×C4×D313yes—
299D20—312no—
300C4×D5—32no—
301C4×D5—32no—
302C4×D5—312no—
303C4×D5—312no—
304C4×D5C2×C4×D316yes—
305C4×D5C23×D316yes—
306Dic10C2×C4×D3112yescomplemented
307C2×#41—31no—
308C2×#41—153no—
309C2×#41—153no—
310C2×#41—158no—
311C2×#41—158no—
312C2×#41—151no—
313C22×Q8—51no—
314C22×D4—153no—
315C23×C4—153no—
316C23×C4—153no—
317C23×C4—153no—
318C4×Q8—58no—
319C4×Q8—158no—
320C4×D4—1524no—
321C4×D4—1524no—
322#117—1524no—
323C2×C4⋊C4—53no—
324C2×C4⋊C4—153no—
325C2×C22⋊C4—156no—
326C2×C42—53no—
327C2×C42—1524no—
328C2×C42—153no—
329C2×C42—153no—
330C2×C42—151no—
331C2×C3×C5C4×#4112yescomplemented
332C2×C3×C5C24×C411yescharacteristic
333D15—26no—
334C3×D5C4×#4112yescomplemented
335C3×D5C22×#4111yescharacteristic
336C3×D5C22×#4111yescharacteristic
337C5×D3—26no—
338C23×C3—51no—
339C22×D3—53no—
340C22×D3—56no—
341C22×D3—56no—
342C22×D3—106no—
343C22×D3—106no—
344C22×D3C22×AGL(1,𝔽5)13yes—
345C3×Q8—512no—
346C3×Q8C22×AGL(1,𝔽5)14yescomplemented
347C2×C3×C4—54no—
348C2×C3×C4—52no—
349C2×C3×C4—53no—
350C2×C3×C4—56no—
351C2×C3×C4—56no—
352C2×C3×C4—56no—
353C2×C3×C4—106no—
354C2×C3×C4C22×AGL(1,𝔽5)13yes—
355C2×Dic3—54no—
356C2×Dic3—52no—
357C2×Dic3—51no—
358C2×Dic3—52no—
359C2×Dic3—52no—
360C2×Dic3—56no—
361C2×Dic3—106no—
362C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
363D12—524no—
364D12—512no—
365D12C22×AGL(1,𝔽5)112yescomplemented
366C4×D3—512no—
367C4×D3—512no—
368C4×D3—512no—
369C4×D3—1024no—
370C4×D3—1024no—
371C4×D3C22×AGL(1,𝔽5)112yescomplemented
372C22×C5—36no—
373C22×C5—66no—
374C22×C5C22×C4×D311yescharacteristic
375C2×D5—36no—
376C2×D5—66no—
377C2×D5—66no—
378C2×D5—66no—
379C2×D5—612no—
380C2×D5C22×C4×D311yescharacteristic
381C2×D5C2×#23912yes—
382C2×D5D3×#4112yes—
383C2×D5C24×D311yescharacteristic
384AGL(1,𝔽5)—26no—
385AGL(1,𝔽5)—34no—
386AGL(1,𝔽5)—66no—
387AGL(1,𝔽5)C2×#23914yesdirect product factor
388C4×C5—32no—
389C4×C5C22×C4×D316yes—
390Dic5—32no—
391Dic5C22×C4×D316yes—
392C24—153no—
393#41—38no—
394#41—1524no—
395#41—1524no—
396#41—158no—
397C2×Q8—54no—
398C2×Q8—54no—
399C2×Q8—53no—
400C2×Q8D3×AGL(1,𝔽5)11yescharacteristic, complemented
401C2×D4—33no—
402C2×D4—1512no—
403C2×D4—1512no—
404C2×D4—156no—
405C2×D4—153no—
406C22×C4—33no—
407C22×C4—51no—
408C22×C4—53no—
409C22×C4—53no—
410C22×C4—1512no—
411C22×C4—153no—
412C22×C4—1512no—
413C22×C4—151no—
414C22×C4—153no—
415C22×C4—1512no—
416C22×C4—1512no—
417C22×C4—151no—
418C22×C4—153no—
419C22×C4—153no—
420C22×C4—3012no—
421C22×C4—3012no—
422C4⋊C4—512no—
423C4⋊C4—1512no—
424C22⋊C4—1524no—
425C42—512no—
426C42—154no—
427C42—1512no—
428C42—1512no—
429C3×C5C2×C4×#4111yescharacteristic, complemented, Hall
430C22×C3—52no—
431C22×C3—52no—
432C22×C3—51no—
433C22×C3—51no—
434C22×C3C23×AGL(1,𝔽5)11yescharacteristic
435C2×D3—26no—
436C2×D3—56no—
437C2×D3—106no—
438C2×D3—106no—
439C2×D3—1012no—
440C2×D3—106no—
441C2×D3C23×AGL(1,𝔽5)16yes—
442C3×C4—54no—
443C3×C4—56no—
444C3×C4—106no—
445C3×C4C23×AGL(1,𝔽5)16yes—
446Dic3—54no—
447Dic3—52no—
448Dic3—106no—
449Dic3C23×AGL(1,𝔽5)12yes—
450C2×C5—66no—
451C2×C5C4×#23912yescomplemented
452C2×C5C23×C4×D311yescharacteristic
453D5—66no—
454D5C4×#23912yescomplemented
455D5C22×#23911yescharacteristic
456D5C2×D3×#4111yescharacteristic
457C23—33no—
458C23—51no—
459C23—156no—
460C23—156no—
461C23—153no—
462C23—306no—
463C23—306no—
464Q8—512no—
465Q8C2×D3×AGL(1,𝔽5)14yescomplemented
466D4—312no—
467D4—1524no—
468D4—1512no—
469C2×C4—31no—
470C2×C4—312no—
471C2×C4—52no—
472C2×C4—54no—
473C2×C4—53no—
474C2×C4—56no—
475C2×C4—56no—
476C2×C4—56no—
477C2×C4—106no—
478C2×C4—1512no—
479C2×C4—152no—
480C2×C4—152no—
481C2×C4—1512no—
482C2×C4—152no—
483C2×C4—154no—
484C2×C4—151no—
485C2×C4—1512no—
486C2×C4—156no—
487C2×C4—3024no—
488C2×C4—3024no—
489C2×C4—306no—
490C2×C4C2×D3×AGL(1,𝔽5)13yes—
491C2×C3—51no—
492C2×C3—51no—
493C2×C3—52no—
494C2×C3#41×AGL(1,𝔽5)12yescomplemented
495C2×C3C24×AGL(1,𝔽5)11yescharacteristic
496D3—26no—
497D3—106no—
498C5C2×C4×#23911yescharacteristic, complemented, Sylow
499C22—36no—
500C22—52no—
501C22—52no—
502C22—51no—
503C22—51no—
504C22—66no—
505C22—156no—
506C22—306no—
507C22—306no—
508C22—3012no—
509C22—306no—
510C22C22×D3×AGL(1,𝔽5)11yescharacteristic
511C4—32no—
512C4—54no—
513C4—56no—
514C4—106no—
515C4—154no—
516C4—152no—
517C4—306no—
518C4C22×D3×AGL(1,𝔽5)16yes—
519C3C2×#41×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
520C2—51no—
521C2—51no—
522C2—52no—
523C2—66no—
524C2—306no—
525C2AGL(1,𝔽5)×#23912yesdirect product factor
526C2C23×D3×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC22C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C24×C4
FrattiniC2C23×D3×AGL(1,𝔽5)
FittingC2×C3×C5×Q8C2×C4
socleC22×C3×C5C23×C4
prime radicalC2×D5×#239C2
cosocleC2×C3×D5C25
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C4×#41
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. C2×Q8×ΓL(1,𝔽16)C2semidirect
3. C2×C3×Q8×AGL(1,𝔽5)C2semidirect
4. AGL(1,𝔽5)×#239C2direct (N × H)
5. C2×#91921C2semidirect
6. C2×AGL(1,𝔽5)×D12C2semidirect
7. C2×C4×D3×AGL(1,𝔽5)C2semidirect
8. C2×#91907C2semidirect
12. C2×#6821C4semidirect
13. C2×C5×#239C4semidirect
15. D5×#239C4semidirect
19. C2×#6769C4semidirect
20. C2×#6768C4semidirect
21. Q8×ΓL(1,𝔽16)C22semidirect
24. C3×Q8×AGL(1,𝔽5)C22semidirect
30. #91921C22semidirect
31. AGL(1,𝔽5)×D12C22semidirect
32. C4×D3×AGL(1,𝔽5)C22semidirect
33. #91907C22semidirect
38. C2×Q8×AGL(1,𝔽5)D3semidirect
52. C2×C3×C5×Q8C2×C4semidirect
53. #6821C2×C4semidirect
54. C2×D60C2×C4semidirect
55. C2×C4×D15C2×C4semidirect
56. C5×#239C2×C4semidirect
57. C2×C5×D12C2×C4semidirect
58. C2×C4×C5×D3C2×C4semidirect
59. C3×Q8×D5C2×C4semidirect
62. C2×C3×Dic10C2×C4semidirect
63. C2×#1203C2×C4semidirect
64. C2×#1200C2×C4semidirect
65. C2×D3×Dic5C2×C4semidirect
67. D5×D12C2×C4semidirect
69. C4×D3×D5C2×C4semidirect
71. #6769C2×C4semidirect
72. #6768C2×C4semidirect
101. Q8×AGL(1,𝔽5)C2×D3semidirect
121. C2×ΓL(1,𝔽16)#41semidirect
125. C2×C3×AGL(1,𝔽5)#41semidirect
130. C3×C5×Q8C22×C4semidirect
133. D60C22×C4semidirect
134. C4×D15C22×C4semidirect
136. C5×D12C22×C4semidirect
137. C4×C5×D3C22×C4semidirect
141. C3×Dic10C22×C4semidirect
142. #1203C22×C4semidirect
143. #1200C22×C4semidirect
144. D3×Dic5C22×C4semidirect
153. C2×#239AGL(1,𝔽5)direct (N × H)
181. C2×C5×Q8C4×D3semidirect
187. Q8×D5C4×D3semidirect
200. C2×Dic10C4×D3semidirect
229. ΓL(1,𝔽16)C2×#41semidirect
231. C3×AGL(1,𝔽5)C2×#41semidirect
240. C2×C3×Q8C2×AGL(1,𝔽5)semidirect
250. #239C2×AGL(1,𝔽5)direct (N × H)
255. C2×D12C2×AGL(1,𝔽5)semidirect
265. C2×C4×D3C2×AGL(1,𝔽5)semidirect
287. C2×AGL(1,𝔽5)#239direct (N × H)
290. C5×Q8C2×C4×D3semidirect
306. Dic10C2×C4×D3semidirect
331. C2×C3×C5C4×#41semidirect
334. C3×D5C4×#41semidirect
346. C3×Q8C22×AGL(1,𝔽5)semidirect
365. D12C22×AGL(1,𝔽5)semidirect
371. C4×D3C22×AGL(1,𝔽5)semidirect
387. AGL(1,𝔽5)C2×#239direct (N × H)
400. C2×Q8D3×AGL(1,𝔽5)semidirect
429. C3×C5C2×C4×#41semidirect
451. C2×C5C4×#239semidirect
454. D5C4×#239semidirect
465. Q8C2×D3×AGL(1,𝔽5)semidirect
494. C2×C3#41×AGL(1,𝔽5)semidirect
498. C5C2×C4×#239semidirect
519. C3C2×#41×AGL(1,𝔽5)semidirect
525. C2AGL(1,𝔽5)×#239direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×#2392
C2×Q8×ΓL(1,𝔽16)2
C2×C3×Q8×AGL(1,𝔽5)2
AGL(1,𝔽5)×#2392
C2×#919212
C2×AGL(1,𝔽5)×D122
C2×C4×D3×AGL(1,𝔽5)2
C2×#919072
C2×#41×AGL(1,𝔽5)3
C2×C4×#2395