Finite Group Databasebeta

← #14479187

Subgroups — #14479187

Order 1920.

3080 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#237C211yesmaximal, characteristic
2#11756987C211yesmaximal, characteristic, complemented
3C3×#66258C211yesmaximal, characteristic, complemented
4#11756871C214yesmaximal, complemented
5C2×#91923C214yesmaximal, complemented
6#11756846C218yesmaximal, complemented
7AGL(1,𝔽5)×#237C218yesmaximal, complemented
8D3×#4130C212yesmaximal, complemented
9#11756812C212yesmaximal, complemented
10#10619412—31nomaximal, Hall
11C2×#6819C411yescharacteristic, complemented
12C2×C5×#237C411yescharacteristic, complemented
13C2×C3×D4×D5C2211yescharacteristic
14C2×D5×#67C2212yes—
15C2×#6780C412yescomplemented
16C2×#6779C412yescomplemented
17C22×D5×Dic3C2212yes—
18D5×#237C414yescomplemented
19D5×#237C414yescomplemented
20D5×#237C2214yes—
21D5×#237C2214yes—
22C2×C4×D3×D5C2211yescharacteristic
23C2×#6766C411yescharacteristic, complemented
24C2×#6765C411yescharacteristic, complemented
25C2×D5×Dic6C2211yescharacteristic
26C2×#6763C2214yes—
27D4×ΓL(1,𝔽16)C2218yescomplemented
28#91989C2212yes—
29C2×C3×C22⋊AGL(1,𝔽5)C2214yes—
30C3×D4×AGL(1,𝔽5)C2218yescomplemented
31C3×#4130C2212yes—
32#67⋊AGL(1,𝔽5)C22116yescomplemented
33D3×C22⋊AGL(1,𝔽5)C2214yes—
34AGL(1,𝔽5)×#67C22116yescomplemented
35C2×Dic3⋊AGL(1,𝔽5)C2218yescomplemented
36#91923C2218yes—
37#91923C2214yes—
38#91923C2218yescomplemented
39#91923C2218yescomplemented
40C2×Dic3×AGL(1,𝔽5)C2218yescomplemented
41D3×C4⋊AGL(1,𝔽5)C2214yescomplemented
42C4×D3×AGL(1,𝔽5)C2214yescomplemented
43#91909C2214yescomplemented
44ΓL(1,𝔽16)⋊Q8C2218yescomplemented
45#91907C2214yescomplemented
46AGL(1,𝔽5)×Dic6C2218yescomplemented
47#85856—51nomaximal, Hall
48C2×D5×#41—31no—
49#66266—38no—
50#41×AGL(1,𝔽5)—38no—
51#66262—32no—
52#66258—31no—
53#66258—34no—
54#66258D311yescharacteristic, complemented
55C2×#4130—34no—
56C2×#4130—32no—
57C23×C3×D5C2312yes—
58C22×D3×D5C2311yescharacteristic
59C22×ΓL(1,𝔽16)C2318yes—
60C22×C3×AGL(1,𝔽5)C2318yes—
61C2×D3×AGL(1,𝔽5)C2318yes—
62C2×C3×C5×D4C2×C411yescharacteristic, complemented
63C2×#1220C2×C412yescomplemented
64C22×Dic15C2×C412yescomplemented
65#6819C2×C414yescomplemented
66#6819C2×C414yescomplemented
67C2×C4×D15C2×C411yescharacteristic, complemented
68C2×Dic30C2×C411yescharacteristic, complemented
69C2×C5×#67C2×C412yescomplemented
70C22×C5×Dic3C2×C412yescomplemented
71C5×#237C2×C414yescomplemented
72C5×#237C2×C414yescomplemented
73C2×C4×C5×D3C2×C411yescharacteristic, complemented
74C2×C5×Dic6C2×C411yescharacteristic, complemented
75C2×C3×C22⋊D5C2×C412yescomplemented
76C3×D4×D5C2×C414yescomplemented
77C3×D4×D5C2314yes—
78C2×C3×D20C2×C411yescharacteristic, complemented
79C2×C3×C4×D5C2311yescharacteristic
80D5×#67C2×C418yescomplemented
81D5×#67C2318yes—
82C2×#1204C2×C412yescomplemented
83C2×#1202C2×C412yescomplemented
84C2×#1201C2×C412yescomplemented
85C2×#1200C2×C411yescharacteristic, complemented
86C2×D3×Dic5C2×C411yescharacteristic, complemented
87#6780C2×C418yescomplemented
88#6780C2×C418yescomplemented
89#6779C2×C418yescomplemented
90#6779C2×C418yescomplemented
91C2×D5×Dic3C2×C412yescomplemented
92C2×D5×Dic3C2×C412yescomplemented
93C2×D5×Dic3C2×C414yescomplemented
94C2×D5×Dic3C2×C414yescomplemented
95C2×D5×Dic3C2314yes—
96C2×D5×Dic3C2312yes—
97C2×D5×Dic3C2311yescharacteristic
98C2×D5×Dic3C2314yes—
99C4×D3×D5C2×C412yescomplemented
100C4×D3×D5C2×C412yescomplemented
101C4×D3×D5C2312yes—
102C4×D3×D5C2312yes—
103#6766C2×C414yescomplemented
104#6766C2×C414yescomplemented
105#6765C2×C414yescomplemented
106#6765C2×C414yescomplemented
107D5×Dic6C2×C414yescomplemented
108D5×Dic6C2314yes—
109#6763C2314yes—
110#6763C2318yes—
111C4⋊ΓL(1,𝔽16)C2314yes—
112C4×ΓL(1,𝔽16)C2314yes—
113C3×C22⋊AGL(1,𝔽5)C2314yes—
114C3×C22⋊AGL(1,𝔽5)C2318yes—
115C3×C4⋊AGL(1,𝔽5)C2314yes—
116C3×C4×AGL(1,𝔽5)C2314yes—
117Dic3⋊AGL(1,𝔽5)C23116yes—
118Dic3⋊AGL(1,𝔽5)C2318yes—
119(C2×D3)⋊AGL(1,𝔽5)C2318yes—
120Dic3×AGL(1,𝔽5)C23116yes—
121Dic3×AGL(1,𝔽5)C2318yes—
122C22×#237—51no—
123C3×#518—51no—
124#5798—51no—
125#5546—58no—
126C4×#237—58no—
127D3×#117—52no—
128#5516—52no—
129#5486—54no—
130C2×#877—54no—
131C2×C5×#41—31no—
132D5×#41—34no—
133D5×#41—34no—
134D5×#41—34no—
135D5×#41—34no—
136C2×#713—31no—
137C2×Q8×D5—31no—
138C2×#711—31no—
139C2×#711—32no—
140C2×D4×D5—32no—
141C2×D4×D5C2×D311yescharacteristic
142C2×#709—32no—
143C2×#709—31no—
144C22×C4×D5—32no—
145C22×C4×D5—31no—
146C2×C22⋊AGL(1,𝔽5)—34no—
147C2×C22⋊AGL(1,𝔽5)—34no—
148C2×C22⋊AGL(1,𝔽5)C2×D314yes—
149Q8×AGL(1,𝔽5)—38no—
150Q8×AGL(1,𝔽5)—38no—
151D4×AGL(1,𝔽5)—316no—
152D4×AGL(1,𝔽5)—38no—
153D4×AGL(1,𝔽5)—316no—
154D4×AGL(1,𝔽5)C2×D318yescomplemented
155#4130—32no—
156#4130—34no—
157#4130—38no—
158#4130—38no—
159#4130—38no—
160#4130—34no—
161#4130—34no—
162#4130C2×D312yes—
163C2×C4⋊AGL(1,𝔽5)—38no—
164C2×C4⋊AGL(1,𝔽5)—34no—
165C2×C4×AGL(1,𝔽5)—38no—
166C2×C4×AGL(1,𝔽5)—34no—
167#3428—151noSylow
168C23×C3×C5C22×C412yes—
169C22×D15C22×C411yescharacteristic
170C22×C5×D3C22×C411yescharacteristic
171C22×C3×D5—44no—
172C22×C3×D5C22×C412yes—
173C22×C3×D5C22×C414yes—
174C22×C3×D5C2411yescharacteristic
175C22×C3×D5C2414yes—
176C2×D3×D5—42no—
177C2×D3×D5C22×C412yes—
178C2×D3×D5C2412yes—
179C2×ΓL(1,𝔽16)—48no—
180C2×ΓL(1,𝔽16)C2418yes—
181C2×C3×AGL(1,𝔽5)—48no—
182C2×C3×AGL(1,𝔽5)C2418yes—
183D3×AGL(1,𝔽5)—48no—
184C3×C5×D4C22×C414yes—
185C2×C3×C4×C5C22×C411yescharacteristic
186#1220C22×C418yes—
187C2×Dic15C22×C411yescharacteristic
188C2×Dic15C22×C414yes—
189C2×Dic15C22×C414yes—
190C2×Dic15C22×C412yes—
191C4×D15C22×C412yes—
192C4×D15C22×C412yes—
193Dic30C22×C414yes—
194C5×#67C22×C418yes—
195C2×C5×Dic3C22×C411yescharacteristic
196C2×C5×Dic3C22×C414yes—
197C2×C5×Dic3C22×C414yes—
198C2×C5×Dic3C22×C412yes—
199C4×C5×D3C22×C412yes—
200C4×C5×D3C22×C412yes—
201C5×Dic6C22×C414yes—
202C3×C22⋊D5C22×C418yes—
203C2×C3×Dic5C22×C411yescharacteristic
204C3×D20C22×C414yes—
205C3×C4×D5C22×C412yes—
206C3×C4×D5C2412yes—
207#1204C22×C418yes—
208#1202C22×C418yes—
209#1201C22×C418yes—
210#1200C22×C412yes—
211#1200C22×C412yes—
212D3×Dic5C22×C412yes—
213D3×Dic5C22×C412yes—
214D5×Dic3C22×C414yes—
215D5×Dic3C22×C414yes—
216D5×Dic3C22×C414yes—
217D5×Dic3C22×C414yes—
218D5×Dic3C22×C414yes—
219D5×Dic3C22×C411yescharacteristic
220D5×Dic3C22×C411yescharacteristic
221D5×Dic3C2411yescharacteristic
222D5×Dic3C2414yes—
223D5×Dic3C2411yescharacteristic
224C22×C3×D4—51no—
225C22×#67—52no—
226C23×Dic3—52no—
227C2×#237—51no—
228C2×#237—52no—
229C2×#237—52no—
230C2×#237—54no—
231C2×#237—54no—
232C2×#237—54no—
233C2×#237—54no—
234C2×#237—51no—
235C2×#237—51no—
236C2×#237AGL(1,𝔽5)11yescharacteristic, complemented
237C22×C4×D3—51no—
238C22×Dic6—51no—
239C3×C4×D4—58no—
240C3×#117—52no—
241C2×C3×C22⋊C4—54no—
242C2×#217—54no—
243D4×Dic3—58no—
244C4×#67—516no—
245#926—52no—
246C2×Dic3⋊C4—58no—
247C2×C4×Dic3—58no—
248#892—54no—
249D3×C4⋊C4—54no—
250#887—58no—
251#67⋊C4—516no—
252D3×C22⋊C4—54no—
253#877—54no—
254#877—58no—
255#877—58no—
256#877—58no—
257#872—54no—
258C42×D3—54no—
259C4×Dic6—58no—
260C23×D5—31no—
261C23×D5C22×D312yes—
262C22×AGL(1,𝔽5)—38no—
263C22×AGL(1,𝔽5)—38no—
264C22×AGL(1,𝔽5)C22×D318yes—
265C5×#41—34no—
266C5×#41—34no—
267C2×C5×Q8—31no—
268C2×C5×D4—32no—
269C2×C5×D4C4×D311yescharacteristic, complemented
270C22×C4×C5—32no—
271C22×C4×C5—31no—
272C2×C22⋊D5—32no—
273C2×C22⋊D5—32no—
274C2×C22⋊D5C4×D312yescomplemented
275C22×Dic5—32no—
276C22×Dic5—31no—
277#713—34no—
278#713—34no—
279Q8×D5—34no—
280Q8×D5—34no—
281#711—34no—
282#711—34no—
283#711—38no—
284#711—38no—
285D4×D5—38no—
286D4×D5—38no—
287D4×D5C4×D314yescomplemented
288D4×D5C22×D314yes—
289#709—38no—
290#709—38no—
291#709—34no—
292#709—34no—
293C2×D20—32no—
294C2×D20C4×D311yescharacteristic, complemented
295C2×C4×D5—32no—
296C2×C4×D5—32no—
297C2×C4×D5—34no—
298C2×C4×D5—34no—
299C2×C4×D5—34no—
300C2×C4×D5—34no—
301C2×C4×D5—31no—
302C2×C4×D5—32no—
303C2×C4×D5—31no—
304C2×C4×D5—31no—
305C2×C4×D5—32no—
306C2×C4×D5—32no—
307C2×C4×D5—32no—
308C2×C4×D5—32no—
309C2×C4×D5C22×D311yescharacteristic
310C2×Dic10—31no—
311C2×Dic10—32no—
312C22⋊AGL(1,𝔽5)—34no—
313C22⋊AGL(1,𝔽5)—38no—
314C22⋊AGL(1,𝔽5)—38no—
315C22⋊AGL(1,𝔽5)C22×D314yes—
316C22⋊AGL(1,𝔽5)C22×D318yes—
317C4⋊AGL(1,𝔽5)—38no—
318C4⋊AGL(1,𝔽5)—316no—
319C4⋊AGL(1,𝔽5)—34no—
320C4⋊AGL(1,𝔽5)C22×D314yes—
321C4×AGL(1,𝔽5)—38no—
322C4×AGL(1,𝔽5)—316no—
323C4×AGL(1,𝔽5)—34no—
324C4×AGL(1,𝔽5)C22×D314yes—
325C22×#41—151no—
326#520—158no—
327#519—152no—
328#518—51no—
329#518—154no—
330#518—151no—
331C4×#41—158no—
332C2×#117—154no—
333C2×#117—152no—
334C22×C3×C5—42no—
335C22×C3×C5C23×C411yescharacteristic
336C22×C3×C5C23×C414yes—
337C2×D15—41no—
338C2×D15C23×C412yes—
339C2×C5×D3—41no—
340C2×C5×D3C23×C412yes—
341C2×C3×D5—28no—
342C2×C3×D5—22no—
343C2×C3×D5—44no—
344C2×C3×D5—42no—
345C2×C3×D5C23×C411yescharacteristic
346C2×C3×D5C23×C414yes—
347C2×C3×D5C2511yescharacteristic
348D3×D5—24no—
349D3×D5—42no—
350ΓL(1,𝔽16)—28no—
351C3×AGL(1,𝔽5)—28no—
352C3×C4×C5C23×C412yes—
353Dic15C23×C411yescharacteristic
354Dic15C23×C411yescharacteristic
355Dic15C23×C414yes—
356C3×Dic5C23×C412yes—
357C5×Dic3C23×C411yescharacteristic
358C5×Dic3C23×C411yescharacteristic
359C5×Dic3C23×C414yes—
360C24×C3—52no—
361C23×D3—51no—
362C2×C3×D4—52no—
363C2×C3×D4—54no—
364C2×C3×D4—54no—
365C2×C3×D4—51no—
366C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic, complemented
367C22×C3×C4—51no—
368C22×C3×C4—58no—
369C2×#67—52no—
370C2×#67—52no—
371C2×#67—58no—
372C2×#67—58no—
373C2×#67—52no—
374C2×#67C2×AGL(1,𝔽5)12yescomplemented
375C22×Dic3—52no—
376C22×Dic3—52no—
377C22×Dic3—51no—
378C22×Dic3—54no—
379C22×Dic3—54no—
380C22×Dic3—52no—
381C22×Dic3—52no—
382C22×Dic3—54no—
383C22×Dic3—54no—
384C22×Dic3—58no—
385C22×Dic3C2×AGL(1,𝔽5)12yescomplemented
386#237—54no—
387#237—54no—
388#237—58no—
389#237—58no—
390#237—58no—
391#237—58no—
392#237—54no—
393#237—54no—
394#237—54no—
395#237—54no—
396#237C2×AGL(1,𝔽5)14yescomplemented
397#237C2×AGL(1,𝔽5)14yescomplemented
398C2×C4×D3—51no—
399C2×C4×D3—51no—
400C2×C4×D3—51no—
401C2×C4×D3—52no—
402C2×C4×D3—52no—
403C2×C4×D3—52no—
404C2×C4×D3—52no—
405C2×C4×D3—58no—
406C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
407C2×Dic6—51no—
408C2×Dic6—52no—
409C2×Dic6—54no—
410C2×Dic6—54no—
411C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic, complemented
412C3×C4⋊C4—54no—
413C3×C22⋊C4—54no—
414C3×C22⋊C4—58no—
415C3×C42—54no—
416#217—54no—
417#217—58no—
418(C2×D3)⋊C4—58no—
419C4⋊Dic3—54no—
420Dic3⋊C4—516no—
421Dic3⋊C4—58no—
422C4×Dic3—516no—
423C4×Dic3—58no—
424C4×Dic3—54no—
425C23×C5—31no—
426C23×C5C2×C4×D312yes—
427C22×D5—31no—
428C22×D5—32no—
429C22×D5—32no—
430C22×D5—44no—
431C22×D5—122no—
432C22×D5C2×C4×D312yes—
433C22×D5C2×C4×D314yes—
434C22×D5C23×D311yescharacteristic
435C22×D5C23×D314yes—
436C2×AGL(1,𝔽5)—38no—
437C2×AGL(1,𝔽5)—48no—
438C2×AGL(1,𝔽5)—128no—
439C2×AGL(1,𝔽5)—128no—
440C2×AGL(1,𝔽5)C23×D318yes—
441C5×Q8—34no—
442C5×D4—38no—
443C5×D4C2×C4×D314yes—
444C2×C4×C5—32no—
445C2×C4×C5—31no—
446C2×C4×C5—34no—
447C2×C4×C5—34no—
448C2×C4×C5—32no—
449C2×C4×C5—32no—
450C2×C4×C5C2×C4×D311yescharacteristic
451C22⋊D5—38no—
452C22⋊D5—38no—
453C22⋊D5C2×C4×D318yes—
454C2×Dic5—32no—
455C2×Dic5—31no—
456C2×Dic5—34no—
457C2×Dic5—34no—
458C2×Dic5—32no—
459C2×Dic5—32no—
460C2×Dic5C2×C4×D311yescharacteristic
461D20—38no—
462D20C2×C4×D314yes—
463C4×D5—31no—
464C4×D5—31no—
465C4×D5—34no—
466C4×D5—34no—
467C4×D5—34no—
468C4×D5—34no—
469C4×D5—34no—
470C4×D5—31no—
471C4×D5—34no—
472C4×D5—31no—
473C4×D5—32no—
474C4×D5—32no—
475C4×D5—32no—
476C4×D5—32no—
477C4×D5C2×C4×D312yes—
478C4×D5C23×D312yes—
479Dic10—34no—
480Dic10—38no—
481C2×#41—31no—
482C2×#41—152no—
483C2×#41—151no—
484C2×#41—152no—
485C2×#41—151no—
486C2×#41—154no—
487C2×#41—154no—
488C2×#41—154no—
489C2×#41—154no—
490C2×#41—151no—
491C22×Q8—151no—
492C22×D4—51no—
493C22×D4—152no—
494C23×C4—151no—
495C23×C4—152no—
496C4×Q8—158no—
497C4×Q8—158no—
498C4×D4—58no—
499C4×D4—1516no—
500C4×D4—1516no—
501C4×D4—158no—
502#117—52no—
503#117—154no—
504#117—154no—
505#117—158no—
506#117—158no—
507#117—158no—
508#117—154no—
509#117—152no—
510C2×C4⋊C4—154no—
511C2×C4⋊C4—158no—
512C2×C22⋊C4—54no—
513C2×C22⋊C4—154no—
514C2×C22⋊C4—154no—
515C2×C42—154no—
516C2×C42—158no—
517C2×C3×C5—21no—
518C2×C3×C5—24no—
519C2×C3×C5C24×C411yescharacteristic
520D15—22no—
521C3×D5—21no—
522C3×D5—24no—
523C3×D5#58512yes—
524C5×D3—22no—
525C23×C3—51no—
526C23×C3—54no—
527C23×C3—54no—
528C23×C3—52no—
529C23×C3—204no—
530C23×C3C22×AGL(1,𝔽5)12yes—
531C22×D3—51no—
532C22×D3—52no—
533C22×D3—52no—
534C22×D3—202no—
535C22×D3C22×AGL(1,𝔽5)11yescharacteristic
536C3×D4—58no—
537C3×D4—54no—
538C3×D4C22×AGL(1,𝔽5)14yes—
539C2×C3×C4—51no—
540C2×C3×C4—52no—
541C2×C3×C4—52no—
542C2×C3×C4—58no—
543C2×C3×C4—208no—
544C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
545#67—58no—
546#67—58no—
547#67—58no—
548#67C22×AGL(1,𝔽5)18yes—
549C2×Dic3—52no—
550C2×Dic3—51no—
551C2×Dic3—54no—
552C2×Dic3—54no—
553C2×Dic3—54no—
554C2×Dic3—51no—
555C2×Dic3—51no—
556C2×Dic3—54no—
557C2×Dic3—54no—
558C2×Dic3—54no—
559C2×Dic3—54no—
560C2×Dic3—51no—
561C2×Dic3—54no—
562C2×Dic3—51no—
563C2×Dic3—58no—
564C2×Dic3—208no—
565C2×Dic3C22×AGL(1,𝔽5)12yes—
566C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
567C2×Dic3C22×AGL(1,𝔽5)14yes—
568C2×Dic3C22×AGL(1,𝔽5)14yes—
569C4×D3—52no—
570C4×D3—52no—
571C4×D3—52no—
572C4×D3—52no—
573C4×D3—52no—
574C4×D3—52no—
575C4×D3—208no—
576C4×D3C22×AGL(1,𝔽5)12yes—
577C4×D3C22×AGL(1,𝔽5)12yes—
578Dic6—54no—
579Dic6—58no—
580Dic6C22×AGL(1,𝔽5)14yes—
581C22×C5—32no—
582C22×C5—42no—
583C22×C5—121no—
584C22×C5C22×C4×D311yescharacteristic
585C22×C5C22×C4×D314yes—
586C2×D5—28no—
587C2×D5—22no—
588C2×D5—32no—
589C2×D5—44no—
590C2×D5—42no—
591C2×D5—64no—
592C2×D5—122no—
593C2×D5—121no—
594C2×D5C22×C4×D311yescharacteristic
595C2×D5C22×C4×D314yes—
596C2×D5C24×D311yescharacteristic
597AGL(1,𝔽5)—28no—
598AGL(1,𝔽5)—68no—
599C4×C5—34no—
600C4×C5—31no—
601C4×C5—31no—
602C4×C5C22×C4×D312yes—
603Dic5—34no—
604Dic5—31no—
605Dic5—31no—
606Dic5C22×C4×D312yes—
607C24—52no—
608C24—151no—
609#41—34no—
610#41—34no—
611#41—158no—
612#41—158no—
613#41—154no—
614#41—154no—
615#41—158no—
616#41—158no—
617#41—154no—
618#41—154no—
619#41—154no—
620#41—154no—
621C2×Q8—31no—
622C2×Q8—152no—
623C2×Q8—154no—
624C2×Q8—154no—
625C2×Q8—151no—
626C2×D4—32no—
627C2×D4—52no—
628C2×D4—54no—
629C2×D4—54no—
630C2×D4—51no—
631C2×D4—152no—
632C2×D4—158no—
633C2×D4—158no—
634C2×D4—152no—
635C2×D4—152no—
636C2×D4D3×AGL(1,𝔽5)11yescharacteristic, complemented
637C22×C4—32no—
638C22×C4—31no—
639C22×C4—51no—
640C22×C4—58no—
641C22×C4—152no—
642C22×C4—152no—
643C22×C4—151no—
644C22×C4—152no—
645C22×C4—152no—
646C22×C4—154no—
647C22×C4—154no—
648C22×C4—151no—
649C22×C4—152no—
650C22×C4—152no—
651C22×C4—152no—
652C22×C4—154no—
653C22×C4—154no—
654C22×C4—151no—
655C22×C4—158no—
656C22×C4—152no—
657C22×C4—151no—
658C22×C4—158no—
659C4⋊C4—54no—
660C4⋊C4—158no—
661C4⋊C4—1516no—
662C4⋊C4—154no—
663C22⋊C4—54no—
664C22⋊C4—58no—
665C22⋊C4—158no—
666C22⋊C4—154no—
667C22⋊C4—158no—
668C42—54no—
669C42—158no—
670C42—154no—
671C42—1516no—
672C3×C5#342811yescharacteristic, complemented, Hall
673C22×C3—42no—
674C22×C3—51no—
675C22×C3—51no—
676C22×C3—54no—
677C22×C3—108no—
678C22×C3—102no—
679C22×C3—202no—
680C22×C3—204no—
681C22×C3C23×AGL(1,𝔽5)11yescharacteristic
682C22×C3C23×AGL(1,𝔽5)14yes—
683C2×D3—41no—
684C2×D3—52no—
685C2×D3—104no—
686C2×D3—202no—
687C2×D3—201no—
688C2×D3C23×AGL(1,𝔽5)12yes—
689C3×C4—52no—
690C3×C4—108no—
691C3×C4C23×AGL(1,𝔽5)12yes—
692Dic3—54no—
693Dic3—51no—
694Dic3—51no—
695Dic3—108no—
696Dic3C23×AGL(1,𝔽5)14yes—
697Dic3C23×AGL(1,𝔽5)11yescharacteristic
698Dic3C23×AGL(1,𝔽5)11yescharacteristic
699C2×C5—21no—
700C2×C5—24no—
701C2×C5—62no—
702C2×C5C23×C4×D311yescharacteristic
703D5—21no—
704D5—24no—
705D5—62no—
706D5#596612yes—
707C23—31no—
708C23—51no—
709C23—54no—
710C23—54no—
711C23—52no—
712C23—152no—
713C23—152no—
714C23—151no—
715C23—204no—
716C23—602no—
717C23C2×D3×AGL(1,𝔽5)12yes—
718Q8—34no—
719Q8—158no—
720Q8—154no—
721D4—38no—
722D4—58no—
723D4—54no—
724D4—158no—
725D4—158no—
726D4—158no—
727D4C2×D3×AGL(1,𝔽5)14yes—
728C2×C4—31no—
729C2×C4—32no—
730C2×C4—34no—
731C2×C4—34no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—51no—
735C2×C4—52no—
736C2×C4—52no—
737C2×C4—58no—
738C2×C4—152no—
739C2×C4—152no—
740C2×C4—151no—
741C2×C4—154no—
742C2×C4—151no—
743C2×C4—151no—
744C2×C4—151no—
745C2×C4—154no—
746C2×C4—154no—
747C2×C4—154no—
748C2×C4—154no—
749C2×C4—154no—
750C2×C4—152no—
751C2×C4—152no—
752C2×C4—151no—
753C2×C4—152no—
754C2×C4—154no—
755C2×C4—154no—
756C2×C4—152no—
757C2×C4—152no—
758C2×C4—158no—
759C2×C4—208no—
760C2×C4—608no—
761C2×C4—608no—
762C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
763C2×C3—21no—
764C2×C3—24no—
765C2×C3—52no—
766C2×C3—101no—
767C2×C3—104no—
768C2×C3C24×AGL(1,𝔽5)11yescharacteristic
769D3—22no—
770D3—102no—
771C5#8585611yescharacteristic, complemented, Sylow
772C22—32no—
773C22—42no—
774C22—51no—
775C22—51no—
776C22—54no—
777C22—108no—
778C22—102no—
779C22—121no—
780C22—152no—
781C22—202no—
782C22—204no—
783C22—304no—
784C22—601no—
785C22—602no—
786C22C22×D3×AGL(1,𝔽5)11yescharacteristic
787C22C22×D3×AGL(1,𝔽5)14yes—
788C4—31no—
789C4—31no—
790C4—34no—
791C4—52no—
792C4—108no—
793C4—151no—
794C4—151no—
795C4—154no—
796C4—308no—
797C4C22×D3×AGL(1,𝔽5)12yes—
798C3#1061941211yescharacteristic, complemented, Sylow
799C2—21no—
800C2—24no—
801C2—52no—
802C2—62no—
803C2—101no—
804C2—104no—
805C2—302no—
806C2C23×D3×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC2C23×D3×AGL(1,𝔽5)
commutator, socleC2×C3×C5C24×C4
FittingC2×C3×C5×D4C2×C4
prime radicalC2×D5×#237C2
cosocleC2×C3×D5C25
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#3428
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #11756987C2semidirect
3. C3×#66258C2semidirect
4. #11756871C2semidirect
5. C2×#91923C2semidirect
6. #11756846C2semidirect
7. AGL(1,𝔽5)×#237C2semidirect
8. D3×#4130C2semidirect
9. #11756812C2semidirect
11. C2×#6819C4semidirect
12. C2×C5×#237C4semidirect
15. C2×#6780C4semidirect
16. C2×#6779C4semidirect
18. D5×#237C4semidirect
19. D5×#237C4semidirect
23. C2×#6766C4semidirect
24. C2×#6765C4semidirect
27. D4×ΓL(1,𝔽16)C22semidirect
30. C3×D4×AGL(1,𝔽5)C22semidirect
32. #67⋊AGL(1,𝔽5)C22semidirect
34. AGL(1,𝔽5)×#67C22semidirect
35. C2×Dic3⋊AGL(1,𝔽5)C22semidirect
38. #91923C22semidirect
39. #91923C22semidirect
40. C2×Dic3×AGL(1,𝔽5)C22semidirect
41. D3×C4⋊AGL(1,𝔽5)C22semidirect
42. C4×D3×AGL(1,𝔽5)C22semidirect
43. #91909C22semidirect
44. ΓL(1,𝔽16)⋊Q8C22semidirect
45. #91907C22semidirect
46. AGL(1,𝔽5)×Dic6C22semidirect
54. #66258D3semidirect
62. C2×C3×C5×D4C2×C4semidirect
63. C2×#1220C2×C4semidirect
64. C22×Dic15C2×C4semidirect
65. #6819C2×C4semidirect
66. #6819C2×C4semidirect
67. C2×C4×D15C2×C4semidirect
68. C2×Dic30C2×C4semidirect
69. C2×C5×#67C2×C4semidirect
70. C22×C5×Dic3C2×C4semidirect
71. C5×#237C2×C4semidirect
72. C5×#237C2×C4semidirect
73. C2×C4×C5×D3C2×C4semidirect
74. C2×C5×Dic6C2×C4semidirect
75. C2×C3×C22⋊D5C2×C4semidirect
76. C3×D4×D5C2×C4semidirect
78. C2×C3×D20C2×C4semidirect
80. D5×#67C2×C4semidirect
82. C2×#1204C2×C4semidirect
83. C2×#1202C2×C4semidirect
84. C2×#1201C2×C4semidirect
85. C2×#1200C2×C4semidirect
86. C2×D3×Dic5C2×C4semidirect
87. #6780C2×C4semidirect
88. #6780C2×C4semidirect
89. #6779C2×C4semidirect
90. #6779C2×C4semidirect
91. C2×D5×Dic3C2×C4semidirect
92. C2×D5×Dic3C2×C4semidirect
93. C2×D5×Dic3C2×C4semidirect
94. C2×D5×Dic3C2×C4semidirect
99. C4×D3×D5C2×C4semidirect
100. C4×D3×D5C2×C4semidirect
103. #6766C2×C4semidirect
104. #6766C2×C4semidirect
105. #6765C2×C4semidirect
106. #6765C2×C4semidirect
107. D5×Dic6C2×C4semidirect
154. D4×AGL(1,𝔽5)C2×D3semidirect
236. C2×#237AGL(1,𝔽5)semidirect
269. C2×C5×D4C4×D3semidirect
274. C2×C22⋊D5C4×D3semidirect
287. D4×D5C4×D3semidirect
294. C2×D20C4×D3semidirect
366. C2×C3×D4C2×AGL(1,𝔽5)semidirect
374. C2×#67C2×AGL(1,𝔽5)semidirect
385. C22×Dic3C2×AGL(1,𝔽5)semidirect
396. #237C2×AGL(1,𝔽5)semidirect
397. #237C2×AGL(1,𝔽5)semidirect
406. C2×C4×D3C2×AGL(1,𝔽5)semidirect
411. C2×Dic6C2×AGL(1,𝔽5)semidirect
636. C2×D4D3×AGL(1,𝔽5)semidirect
672. C3×C5#3428semidirect
771. C5#85856semidirect
798. C3#10619412semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#2372
#117569872
C3×#662582
#117568712
C2×#919232
#117568462
AGL(1,𝔽5)×#2372
D3×#41302
#117568122
#106194123
#858565