Finite Group Databasebeta

← #14479146

Subgroups — #14479146

Order 1920.

3080 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6779C211yesmaximal, characteristic
2#11756245C211yesmaximal, characteristic, complemented
3C2×C5×#877C211yesmaximal, characteristic, complemented
4C3×#65820C211yesmaximal, characteristic, complemented
5#11755413C211yesmaximal, characteristic, complemented
6#11755406C211yesmaximal, characteristic, complemented
7C2×#91529C211yesmaximal, characteristic, complemented
8#11754284C214yesmaximal, complemented
9C4×#6779C214yesmaximal, complemented
10#11753187C212yesmaximal, complemented
11#11753066C212yesmaximal, complemented
12#11752825C212yesmaximal, complemented
13#11752819C214yesmaximal, complemented
14#11752818C214yesmaximal, complemented
15D5×#877C212yesmaximal, complemented
16#10617632—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C23×C5×Dic3C2211yescharacteristic
19C22×C3×C22⋊D5C2211yescharacteristic
20C22×#1204C2211yescharacteristic
21C22×#1202C2211yescharacteristic
22C22×#1200C2211yescharacteristic
23C2×#6779C4116yescomplemented
24C2×#6779C2212yes—
25C2×#6779C2212yes—
26C2×#6779C2212yes—
27C2×#6779C2212yes—
28C22×D5×Dic3C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic
30C2×#6719C2211yescharacteristic
31C4×#1220C2214yescomplemented
32#91770C2214yescomplemented
33C22⋊C4×D15C2212yes—
34#91766C2212yes—
35C2×C5×#217C2211yescharacteristic
36C2×C5×Dic3⋊C4C2212yescomplemented
37C2×C4×C5×Dic3C2212yescomplemented
38C5×#877C2212yes—
39C5×#877C2212yes—
40C5×#877C2212yescomplemented
41C5×#877C2212yescomplemented
42C2×C3×C22⋊Dic5C2211yescharacteristic
43C3×C4×C22⋊D5C2214yescomplemented
44C3×#4027C2214yescomplemented
45C3×D5×C22⋊C4C2212yes—
46C3×#4023C2212yes—
47#91561C2212yes—
48#91559C2214yescomplemented
49#91556C2214yescomplemented
50Dic3×C22⋊D5C2214yescomplemented
51#91552C2214yescomplemented
52D5×#217C2212yes—
53C2×Dic3⋊Dic5C2212yescomplemented
54#91532C2212yes—
55#91529C2212yes—
56#91529C2212yes—
57#91529C2212yescomplemented
58#91529C2212yescomplemented
59#91528C2212yes—
60C2×Dic3×Dic5C2212yescomplemented
61C4×#1204C2214yescomplemented
62#91444C2214yescomplemented
63C4×#1202C2214yescomplemented
64#91404C2214yescomplemented
65#91403C2214yescomplemented
66#91402C2214yescomplemented
67C4×#1200C2214yescomplemented
68#91396C2214yescomplemented
69#91395C2214yescomplemented
70#91394C2214yescomplemented
71#91393C2214yescomplemented
72D5×Dic3⋊C4C2214yescomplemented
73C4×D5×Dic3C2214yescomplemented
74#91325C2214yescomplemented
75#91324C2214yescomplemented
76#91323C2214yescomplemented
77#85856—51nomaximal, Hall
78C22×#709—31no—
79C2×C5×#117—31no—
80C2×#4072—31no—
81#65857—34no—
82#65856—34no—
83#65855—32no—
84D5×#117—32no—
85D5×#117—32no—
86#65850—32no—
87#65838—34no—
88#65820—31no—
89#65820—31no—
90#65820—31no—
91#65820D311yescharacteristic, complemented
92C4×#709—34no—
93C24×C3×C5C2311yescharacteristic
94C23×D15C2311yescharacteristic
95C23×C3×D5C2311yescharacteristic
96C22×C3×C4×C5C2312yes—
97C2×#1220C2×C418yescomplemented
98C2×#1220C2312yes—
99C2×#1220C2312yes—
100C22×Dic15C2312yes—
101C22×Dic15C2311yescharacteristic
102C2×C4×D15C2314yes—
103C22×C5×Dic3C2×C418yescomplemented
104C22×C5×Dic3C2312yes—
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2311yescharacteristic
108C22×C5×Dic3C2311yescharacteristic
109C22×C5×Dic3C2311yescharacteristic
110C22×C5×Dic3C2311yescharacteristic
111C2×C3×C22⋊D5C2×C418yescomplemented
112C2×C3×C22⋊D5C2312yes—
113C2×C3×C22⋊D5C2312yes—
114C22×C3×Dic5C2312yes—
115C22×C3×Dic5C2311yescharacteristic
116C2×C3×C4×D5C2314yes—
117C2×#1204C2×C418yescomplemented
118C2×#1204C2312yes—
119C2×#1204C2312yes—
120C2×#1202C2×C418yescomplemented
121C2×#1202C2312yes—
122C2×#1202C2312yes—
123C2×#1200C2×C418yescomplemented
124C2×#1200C2314yes—
125C2×#1200C2312yes—
126C2×#1200C2312yes—
127#6779C2×C4116yescomplemented
128#6779C2×C4116yescomplemented
129#6779C2×C4116yescomplemented
130#6779C2×C4116yescomplemented
131C2×D5×Dic3C2×C418yescomplemented
132C2×D5×Dic3C2314yes—
133C2×D5×Dic3C2312yes—
134C2×D5×Dic3C2312yes—
135C3×C5×C22⋊C4C2312yes—
136C3×C5×C22⋊C4C2312yes—
137#6719C2312yes—
138#6719C2312yes—
139#6714C2314yes—
140#6712C2314yes—
141C4×Dic15C2314yes—
142C5×#217C2312yes—
143C5×#217C2312yes—
144C5×Dic3⋊C4C2314yes—
145C5×Dic3⋊C4C2314yes—
146C4×C5×Dic3C2314yes—
147C4×C5×Dic3C2314yes—
148C3×C22⋊Dic5C2312yes—
149C3×C22⋊Dic5C2312yes—
150C3×#685C2314yes—
151C3×#683C2314yes—
152C3×C4×Dic5C2314yes—
153Dic3⋊Dic5C2314yes—
154Dic3⋊Dic5C2314yes—
155#6669C2314yes—
156#6668C2314yes—
157#6667C2314yes—
158#6665C2314yes—
159Dic3×Dic5C2314yes—
160Dic3×Dic5C2314yes—
161Dic3×Dic5C2314yes—
162Dic3×Dic5C2314yes—
163C22×#237—51no—
164C3×#518—51no—
165#5798—51no—
166#5546—54no—
167#5546—54no—
168C4×#237—54no—
169C4×#237—54no—
170D3×#117—52no—
171#5516—52no—
172#5486—51no—
173#5486—51no—
174#5486—52no—
175C2×#877—51no—
176C2×#877—52no—
177C2×#877D511yescharacteristic, complemented
178C23×C4×C5—31no—
179C22×C22⋊D5—31no—
180C22×C22⋊D5C2×D311yescharacteristic
181C2×#709—316no—
182C2×#709—32no—
183C2×#709—32no—
184C2×#709—32no—
185C2×#709—32no—
186C22×D20—31no—
187C22×C4×D5—31no—
188C22×C4×D5—31no—
189C22×Dic10—31no—
190C5×#117—32no—
191C5×#117—32no—
192C5×#117—32no—
193C5×#117—32no—
194C2×C5×C4⋊C4—32no—
195C2×C5×C22⋊C4—31no—
196C2×C5×C22⋊C4C2×D311yescharacteristic
197C2×C42×C5—32no—
198C2×C22⋊Dic5—31no—
199C2×C22⋊Dic5C2×D311yescharacteristic
200C4×C22⋊D5—34no—
201C4×C22⋊D5—34no—
202C4×C22⋊D5—34no—
203C4×C22⋊D5C2×D314yescomplemented
204#4072—32no—
205#4072—32no—
206#4072—32no—
207#4072—32no—
208C2×C4⋊Dic5—32no—
209C2×C4×Dic5—32no—
210#4039—34no—
211#4039—34no—
212#4038—34no—
213#4038—34no—
214D5×C4⋊C4—34no—
215D5×C4⋊C4—34no—
216#4033—34no—
217#4033—34no—
218#4027—34no—
219#4027—34no—
220#4027—34no—
221#4027C2×D314yescomplemented
222D5×C22⋊C4—32no—
223D5×C22⋊C4—32no—
224D5×C22⋊C4—32no—
225D5×C22⋊C4C2×D312yes—
226#4023—32no—
227#4023—32no—
228#4023—32no—
229#4023C2×D312yes—
230C4×D20—34no—
231C4×D20—34no—
232#4018—34no—
233#4018—34no—
234C42×D5—34no—
235C42×D5—34no—
236C4×Dic10—34no—
237C4×Dic10—34no—
238#3428—151noSylow
239C23×C3×C5—42no—
240C23×C3×C5C22×C414yes—
241C23×C3×C5C2411yescharacteristic
242C23×C3×C5C2411yescharacteristic
243C23×C3×C5C2411yescharacteristic
244C22×D15—42no—
245C22×D15C22×C414yes—
246C22×D15C2412yes—
247C22×C3×D5—42no—
248C22×C3×D5C22×C414yes—
249C22×C3×D5C2412yes—
250C2×C3×C4×C5—42no—
251C2×C3×C4×C5C2414yes—
252#1220C22×C418yes—
253#1220C22×C418yes—
254C2×Dic15—42no—
255C2×Dic15C22×C414yes—
256C2×Dic15C2414yes—
257C2×Dic15C2412yes—
258C4×D15—44no—
259C2×C5×Dic3—42no—
260C2×C5×Dic3C22×C414yes—
261C2×C5×Dic3C22×C414yes—
262C2×C5×Dic3C22×C414yes—
263C2×C5×Dic3C22×C414yes—
264C2×C5×Dic3C22×C414yes—
265C2×C5×Dic3C22×C414yes—
266C2×C5×Dic3C2414yes—
267C2×C5×Dic3C2411yescharacteristic
268C2×C5×Dic3C2411yescharacteristic
269C2×C5×Dic3C2411yescharacteristic
270C2×C5×Dic3C2411yescharacteristic
271C3×C22⋊D5C22×C418yes—
272C3×C22⋊D5C22×C418yes—
273C2×C3×Dic5—42no—
274C2×C3×Dic5C22×C414yes—
275C2×C3×Dic5C2414yes—
276C2×C3×Dic5C2412yes—
277C3×C4×D5—44no—
278#1204C22×C418yes—
279#1204C22×C418yes—
280#1202C22×C418yes—
281#1202C22×C418yes—
282#1200—44no—
283#1200C22×C418yes—
284#1200C22×C418yes—
285D5×Dic3—44no—
286D5×Dic3C22×C418yes—
287D5×Dic3C22×C418yes—
288C22×C3×D4—51no—
289C22×#67—51no—
290C22×#67—51no—
291C23×Dic3—51no—
292C23×Dic3C2×D511yescharacteristic
293C2×#237—516no—
294C2×#237—52no—
295C2×#237—52no—
296C2×#237—52no—
297C2×#237—52no—
298C22×C4×D3—51no—
299C22×Dic6—51no—
300C3×C4×D4—54no—
301C3×C4×D4—54no—
302C3×#117—52no—
303C2×C3×C22⋊C4—51no—
304C2×C3×C22⋊C4—52no—
305C2×C3×C22⋊C4C2×D511yescharacteristic
306C2×#217—51no—
307C2×#217—52no—
308C2×#217C2×D511yescharacteristic
309D4×Dic3—54no—
310D4×Dic3—54no—
311C4×#67—54no—
312C4×#67—54no—
313C4×#67—54no—
314C4×#67—54no—
315#926—52no—
316C2×Dic3⋊C4—52no—
317C2×Dic3⋊C4—54no—
318C2×Dic3⋊C4C2×D512yescomplemented
319C2×C4×Dic3—52no—
320C2×C4×Dic3—54no—
321C2×C4×Dic3C2×D512yescomplemented
322#892—54no—
323D3×C4⋊C4—54no—
324#887—54no—
325#887—54no—
326#67⋊C4—54no—
327#67⋊C4—54no—
328#67⋊C4—54no—
329#67⋊C4—54no—
330D3×C22⋊C4—52no—
331D3×C22⋊C4—52no—
332#877—52no—
333#877—52no—
334#877—52no—
335#877—52no—
336#877—52no—
337#877—52no—
338#877—54no—
339#877—54no—
340#877C2×D512yes—
341#877C2×D512yes—
342#877C2×D512yescomplemented
343#877C2×D512yescomplemented
344#872—54no—
345C42×D3—54no—
346C4×Dic6—54no—
347C4×Dic6—54no—
348C24×C5C22×D311yescharacteristic
349C23×D5—31no—
350C23×D5C22×D311yescharacteristic
351C22×C4×C5—38no—
352C22×C4×C5—31no—
353C22×C4×C5—31no—
354C22×C4×C5—31no—
355C22×C4×C5—31no—
356C22×C4×C5—31no—
357C22×C4×C5—31no—
358C22×C4×C5—32no—
359C22×C4×C5C22×D312yes—
360C2×C22⋊D5—38no—
361C2×C22⋊D5—32no—
362C2×C22⋊D5—32no—
363C2×C22⋊D5C4×D318yescomplemented
364C2×C22⋊D5C22×D312yes—
365C2×C22⋊D5C22×D312yes—
366C22×Dic5—31no—
367C22×Dic5—32no—
368C22×Dic5C22×D312yes—
369C22×Dic5C22×D311yescharacteristic
370#709—316no—
371#709—316no—
372#709—316no—
373#709—316no—
374C2×D20—38no—
375C2×D20—32no—
376C2×D20—32no—
377C2×C4×D5—38no—
378C2×C4×D5—32no—
379C2×C4×D5—32no—
380C2×C4×D5—38no—
381C2×C4×D5—32no—
382C2×C4×D5—32no—
383C2×C4×D5—34no—
384C2×C4×D5—34no—
385C2×C4×D5—34no—
386C2×C4×D5C22×D314yes—
387C2×Dic10—38no—
388C2×Dic10—32no—
389C2×Dic10—32no—
390C5×C4⋊C4—34no—
391C5×C4⋊C4—34no—
392C5×C22⋊C4—32no—
393C5×C22⋊C4—32no—
394C5×C22⋊C4C22×D312yes—
395C5×C22⋊C4C22×D312yes—
396C42×C5—34no—
397C42×C5—34no—
398C22⋊Dic5—32no—
399C22⋊Dic5—32no—
400C22⋊Dic5C22×D312yes—
401C22⋊Dic5C22×D312yes—
402#685—34no—
403#685—34no—
404#685—34no—
405#685C22×D314yes—
406C4⋊Dic5—34no—
407C4⋊Dic5—34no—
408#683—34no—
409#683—34no—
410#683—34no—
411#683C22×D314yes—
412C4×Dic5—34no—
413C4×Dic5—34no—
414C4×Dic5—34no—
415C4×Dic5—34no—
416C4×Dic5—34no—
417C4×Dic5C22×D314yes—
418C22×#41—151no—
419#520—154no—
420#520—154no—
421#519—152no—
422#518—51no—
423#518—151no—
424#518—151no—
425#518—152no—
426#518—151no—
427C4×#41—154no—
428C4×#41—154no—
429C2×#117—31no—
430C2×#117—152no—
431C2×#117—151no—
432C2×#117—152no—
433C22×C3×C5—22no—
434C22×C3×C5—22no—
435C22×C3×C5—22no—
436C22×C3×C5—44no—
437C22×C3×C5C23×C412yes—
438C22×C3×C5C23×C412yes—
439C22×C3×C5C23×C412yes—
440C22×C3×C5C2511yescharacteristic
441C2×D15—24no—
442C2×D15—44no—
443C2×D15C23×C414yes—
444C2×C3×D5—24no—
445C2×C3×D5—44no—
446C2×C3×D5C23×C414yes—
447C3×C4×C5—24no—
448Dic15—24no—
449Dic15C23×C414yes—
450C3×Dic5—24no—
451C3×Dic5C23×C414yes—
452C5×Dic3—24no—
453C5×Dic3C23×C412yes—
454C5×Dic3C23×C412yes—
455C5×Dic3C23×C412yes—
456C5×Dic3C23×C412yes—
457C24×C3—51no—
458C24×C3C22×D511yescharacteristic
459C23×D3—51no—
460C2×C3×D4—58no—
461C2×C3×D4—52no—
462C2×C3×D4—52no—
463C22×C3×C4—51no—
464C22×C3×C4—52no—
465C22×C3×C4—54no—
466C22×C3×C4C22×D512yes—
467C2×#67—58no—
468C2×#67—52no—
469C2×#67—52no—
470C2×#67—58no—
471C2×#67—52no—
472C2×#67—52no—
473C22×Dic3—51no—
474C22×Dic3—58no—
475C22×Dic3—52no—
476C22×Dic3—52no—
477C22×Dic3—52no—
478C22×Dic3—54no—
479C22×Dic3C4×D518yescomplemented
480C22×Dic3C22×D512yes—
481C22×Dic3C22×D511yescharacteristic
482C22×Dic3C22×D511yescharacteristic
483C22×Dic3C22×D511yescharacteristic
484C22×Dic3C22×D511yescharacteristic
485C22×Dic3C22×D511yescharacteristic
486C22×Dic3C22×D511yescharacteristic
487#237—516no—
488#237—516no—
489#237—516no—
490#237—516no—
491C2×C4×D3—58no—
492C2×C4×D3—52no—
493C2×C4×D3—52no—
494C2×C4×D3—54no—
495C2×C4×D3—54no—
496C2×Dic6—58no—
497C2×Dic6—52no—
498C2×Dic6—52no—
499C3×C4⋊C4—54no—
500C3×C22⋊C4—52no—
501C3×C22⋊C4—52no—
502C3×C22⋊C4—54no—
503C3×C22⋊C4C22×D512yes—
504C3×C22⋊C4C22×D512yes—
505C3×C42—54no—
506#217—52no—
507#217—52no—
508#217—54no—
509#217C22×D512yes—
510#217C22×D512yes—
511(C2×D3)⋊C4—54no—
512(C2×D3)⋊C4—54no—
513C4⋊Dic3—54no—
514Dic3⋊C4—54no—
515Dic3⋊C4—54no—
516Dic3⋊C4—54no—
517Dic3⋊C4—54no—
518Dic3⋊C4C22×D514yes—
519Dic3⋊C4C22×D514yes—
520C4×Dic3—54no—
521C4×Dic3—54no—
522C4×Dic3—54no—
523C4×Dic3—54no—
524C4×Dic3—54no—
525C4×Dic3C22×D514yes—
526C4×Dic3C22×D514yes—
527C23×C5—42no—
528C23×C5C2×C4×D314yes—
529C23×C5C23×D311yescharacteristic
530C23×C5C23×D311yescharacteristic
531C23×C5C23×D311yescharacteristic
532C22×D5—32no—
533C22×D5—34no—
534C22×D5—42no—
535C22×D5—122no—
536C22×D5C2×C4×D314yes—
537C22×D5C23×D312yes—
538C2×C4×C5—34no—
539C2×C4×C5—34no—
540C2×C4×C5—34no—
541C2×C4×C5—34no—
542C2×C4×C5—34no—
543C2×C4×C5—34no—
544C2×C4×C5—31no—
545C2×C4×C5—31no—
546C2×C4×C5—31no—
547C2×C4×C5—31no—
548C2×C4×C5—34no—
549C2×C4×C5—42no—
550C2×C4×C5—122no—
551C2×C4×C5C23×D314yes—
552C22⋊D5—38no—
553C22⋊D5—38no—
554C22⋊D5C2×C4×D318yes—
555C22⋊D5C2×C4×D318yes—
556C2×Dic5—34no—
557C2×Dic5—32no—
558C2×Dic5—34no—
559C2×Dic5—42no—
560C2×Dic5—122no—
561C2×Dic5C2×C4×D314yes—
562C2×Dic5C23×D314yes—
563C2×Dic5C23×D312yes—
564D20—38no—
565D20—38no—
566C4×D5—38no—
567C4×D5—38no—
568C4×D5—38no—
569C4×D5—38no—
570C4×D5—44no—
571C4×D5—124no—
572C4×D5—124no—
573C4×D5—124no—
574Dic10—38no—
575Dic10—38no—
576C2×#41—152no—
577C2×#41—152no—
578C2×#41—152no—
579C2×#41—152no—
580C2×#41—1516no—
581C22×Q8—151no—
582C22×D4—51no—
583C22×D4—151no—
584C22×D4—151no—
585C23×C4—31no—
586C23×C4—151no—
587C23×C4—151no—
588C4×Q8—154no—
589C4×Q8—154no—
590C4×Q8—154no—
591C4×Q8—154no—
592C4×D4—54no—
593C4×D4—54no—
594C4×D4—154no—
595C4×D4—154no—
596C4×D4—154no—
597C4×D4—154no—
598C4×D4—154no—
599C4×D4—154no—
600C4×D4—154no—
601C4×D4—154no—
602C4×D4—154no—
603C4×D4—154no—
604#117—32no—
605#117—32no—
606#117—32no—
607#117—32no—
608#117—52no—
609#117—154no—
610#117—154no—
611#117—154no—
612#117—152no—
613#117—152no—
614#117—154no—
615#117—152no—
616#117—152no—
617#117—152no—
618#117—152no—
619#117—152no—
620C2×C4⋊C4—32no—
621C2×C4⋊C4—154no—
622C2×C4⋊C4—154no—
623C2×C4⋊C4—152no—
624C2×C22⋊C4—31no—
625C2×C22⋊C4—51no—
626C2×C22⋊C4—52no—
627C2×C22⋊C4—152no—
628C2×C22⋊C4—152no—
629C2×C22⋊C4—151no—
630C2×C22⋊C4—152no—
631C2×C22⋊C4D3×D511yescharacteristic
632C2×C42—32no—
633C2×C42—154no—
634C2×C42—154no—
635C2×C42—152no—
636C2×C3×C5—22no—
637C2×C3×C5—22no—
638C2×C3×C5—22no—
639C2×C3×C5C24×C411yescharacteristic
640C2×C3×C5#58512yes—
641D15—24no—
642C3×D5—24no—
643C23×C3—42no—
644C23×C3—52no—
645C23×C3—54no—
646C23×C3—202no—
647C23×C3C2×C4×D514yes—
648C23×C3C23×D511yescharacteristic
649C23×C3C23×D511yescharacteristic
650C23×C3C23×D511yescharacteristic
651C22×D3—52no—
652C22×D3—54no—
653C22×D3—202no—
654C3×D4—58no—
655C3×D4—58no—
656C2×C3×C4—42no—
657C2×C3×C4—54no—
658C2×C3×C4—52no—
659C2×C3×C4—54no—
660C2×C3×C4—204no—
661C2×C3×C4—202no—
662C2×C3×C4C23×D514yes—
663#67—58no—
664#67—58no—
665#67—58no—
666#67—58no—
667C2×Dic3—42no—
668C2×Dic3—54no—
669C2×Dic3—52no—
670C2×Dic3—58no—
671C2×Dic3—58no—
672C2×Dic3—54no—
673C2×Dic3—204no—
674C2×Dic3—202no—
675C2×Dic3C2×C4×D514yes—
676C2×Dic3C2×C4×D514yes—
677C2×Dic3C2×C4×D514yes—
678C2×Dic3C2×C4×D514yes—
679C2×Dic3C2×C4×D514yes—
680C2×Dic3C2×C4×D514yes—
681C2×Dic3C23×D514yes—
682C2×Dic3C23×D511yescharacteristic
683C2×Dic3C23×D511yescharacteristic
684C2×Dic3C23×D511yescharacteristic
685C2×Dic3C23×D511yescharacteristic
686C4×D3—58no—
687C4×D3—58no—
688C4×D3—204no—
689C4×D3—204no—
690Dic6—58no—
691Dic6—58no—
692C22×C5—22no—
693C22×C5—22no—
694C22×C5—22no—
695C22×C5—44no—
696C22×C5C22×C4×D312yes—
697C22×C5C22×C4×D312yes—
698C22×C5C22×C4×D312yes—
699C22×C5C24×D311yescharacteristic
700C2×D5—24no—
701C2×D5—34no—
702C2×D5—44no—
703C2×D5—64no—
704C2×D5—124no—
705C2×D5C22×C4×D314yes—
706C4×C5—24no—
707C4×C5—32no—
708C4×C5—32no—
709C4×C5—32no—
710C4×C5—32no—
711C4×C5—64no—
712Dic5—24no—
713Dic5—34no—
714Dic5—64no—
715Dic5C22×C4×D314yes—
716C24—51no—
717C24—151no—
718C24C2×D3×D511yescharacteristic
719#41—1516no—
720#41—1516no—
721#41—1516no—
722#41—1516no—
723C2×Q8—152no—
724C2×Q8—152no—
725C2×Q8—158no—
726C2×D4—58no—
727C2×D4—52no—
728C2×D4—52no—
729C2×D4—152no—
730C2×D4—152no—
731C2×D4—158no—
732C2×D4—158no—
733C2×D4—152no—
734C2×D4—152no—
735C22×C4—38no—
736C22×C4—31no—
737C22×C4—31no—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—31no—
741C22×C4—31no—
742C22×C4—32no—
743C22×C4—51no—
744C22×C4—52no—
745C22×C4—54no—
746C22×C4—152no—
747C22×C4—152no—
748C22×C4—158no—
749C22×C4—154no—
750C22×C4—152no—
751C22×C4—152no—
752C22×C4—158no—
753C22×C4—154no—
754C22×C4—151no—
755C22×C4—152no—
756C22×C4—154no—
757C22×C4C2×D3×D512yes—
758C4⋊C4—34no—
759C4⋊C4—34no—
760C4⋊C4—54no—
761C4⋊C4—154no—
762C4⋊C4—154no—
763C4⋊C4—154no—
764C4⋊C4—154no—
765C4⋊C4—154no—
766C22⋊C4—32no—
767C22⋊C4—32no—
768C22⋊C4—52no—
769C22⋊C4—52no—
770C22⋊C4—54no—
771C22⋊C4—154no—
772C22⋊C4—154no—
773C22⋊C4—152no—
774C22⋊C4—152no—
775C22⋊C4—154no—
776C22⋊C4C2×D3×D512yes—
777C22⋊C4C2×D3×D512yes—
778C42—34no—
779C42—34no—
780C42—54no—
781C42—154no—
782C42—154no—
783C42—154no—
784C42—154no—
785C42—154no—
786C3×C5#342811yescharacteristic, complemented, Hall
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—44no—
791C22×C3—54no—
792C22×C3—104no—
793C22×C3—204no—
794C22×C3C22×C4×D512yes—
795C22×C3C22×C4×D512yes—
796C22×C3C22×C4×D512yes—
797C22×C3C24×D511yescharacteristic
798C2×D3—54no—
799C2×D3—104no—
800C2×D3—204no—
801C3×C4—24no—
802C3×C4—54no—
803C3×C4—104no—
804Dic3—24no—
805Dic3—54no—
806Dic3—104no—
807Dic3C22×C4×D512yes—
808Dic3C22×C4×D512yes—
809Dic3C22×C4×D512yes—
810Dic3C22×C4×D512yes—
811C2×C5—22no—
812C2×C5—22no—
813C2×C5—22no—
814C2×C5C23×C4×D311yescharacteristic
815C2×C5#596612yes—
816D5—24no—
817D5—64no—
818C23—42no—
819C23—52no—
820C23—54no—
821C23—152no—
822C23—154no—
823C23—202no—
824C23—602no—
825C23C4×D3×D514yes—
826C23C22×D3×D511yescharacteristic
827C23C22×D3×D511yescharacteristic
828C23C22×D3×D511yescharacteristic
829Q8—158no—
830Q8—158no—
831D4—58no—
832D4—58no—
833D4—158no—
834D4—158no—
835D4—158no—
836D4—158no—
837C2×C4—34no—
838C2×C4—34no—
839C2×C4—34no—
840C2×C4—34no—
841C2×C4—34no—
842C2×C4—34no—
843C2×C4—31no—
844C2×C4—31no—
845C2×C4—31no—
846C2×C4—31no—
847C2×C4—34no—
848C2×C4—42no—
849C2×C4—54no—
850C2×C4—52no—
851C2×C4—54no—
852C2×C4—122no—
853C2×C4—158no—
854C2×C4—158no—
855C2×C4—158no—
856C2×C4—158no—
857C2×C4—154no—
858C2×C4—152no—
859C2×C4—154no—
860C2×C4—204no—
861C2×C4—202no—
862C2×C4—604no—
863C2×C4—604no—
864C2×C4—604no—
865C2×C4—602no—
866C2×C4C22×D3×D514yes—
867C2×C3—22no—
868C2×C3—22no—
869C2×C3—22no—
870C2×C3—104no—
871C2×C3C23×C4×D511yescharacteristic
872C2×C3#6628312yes—
873D3—104no—
874C5#8585611yescharacteristic, complemented, Sylow
875C22—22no—
876C22—22no—
877C22—22no—
878C22—44no—
879C22—54no—
880C22—104no—
881C22—154no—
882C22—204no—
883C22—304no—
884C22—604no—
885C22C2×C4×D3×D512yes—
886C22C2×C4×D3×D512yes—
887C22C2×C4×D3×D512yes—
888C22C23×D3×D511yescharacteristic
889C4—24no—
890C4—32no—
891C4—32no—
892C4—32no—
893C4—32no—
894C4—54no—
895C4—64no—
896C4—104no—
897C4—154no—
898C4—304no—
899C3#1061763211yescharacteristic, complemented, Sylow
900C2—22no—
901C2—22no—
902C2—22no—
903C2—104no—
904C2—304no—
905C2C22×C4×D3×D511yescharacteristic
906C2#1175703512yes—
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC22×C3×C5C25
prime radicalC22×#6779C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#3428
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #11756245C2semidirect
3. C2×C5×#877C2semidirect
4. C3×#65820C2semidirect
5. #11755413C2semidirect
6. #11755406C2semidirect
7. C2×#91529C2semidirect
8. #11754284C2semidirect
9. C4×#6779C2semidirect
10. #11753187C2semidirect
11. #11753066C2semidirect
12. #11752825C2semidirect
13. #11752819C2semidirect
14. #11752818C2semidirect
15. D5×#877C2semidirect
23. C2×#6779C4semidirect
31. C4×#1220C22semidirect
32. #91770C22semidirect
36. C2×C5×Dic3⋊C4C22semidirect
37. C2×C4×C5×Dic3C22semidirect
40. C5×#877C22semidirect
41. C5×#877C22semidirect
43. C3×C4×C22⋊D5C22semidirect
44. C3×#4027C22semidirect
48. #91559C22semidirect
49. #91556C22semidirect
50. Dic3×C22⋊D5C22semidirect
51. #91552C22semidirect
53. C2×Dic3⋊Dic5C22semidirect
57. #91529C22semidirect
58. #91529C22semidirect
60. C2×Dic3×Dic5C22semidirect
61. C4×#1204C22semidirect
62. #91444C22semidirect
63. C4×#1202C22semidirect
64. #91404C22semidirect
65. #91403C22semidirect
66. #91402C22semidirect
67. C4×#1200C22semidirect
68. #91396C22semidirect
69. #91395C22semidirect
70. #91394C22semidirect
71. #91393C22semidirect
72. D5×Dic3⋊C4C22semidirect
73. C4×D5×Dic3C22semidirect
74. #91325C22semidirect
75. #91324C22semidirect
76. #91323C22semidirect
91. #65820D3semidirect
97. C2×#1220C2×C4semidirect
103. C22×C5×Dic3C2×C4semidirect
111. C2×C3×C22⋊D5C2×C4semidirect
117. C2×#1204C2×C4semidirect
120. C2×#1202C2×C4semidirect
123. C2×#1200C2×C4semidirect
127. #6779C2×C4semidirect
128. #6779C2×C4semidirect
129. #6779C2×C4semidirect
130. #6779C2×C4semidirect
131. C2×D5×Dic3C2×C4semidirect
177. C2×#877D5semidirect
203. C4×C22⋊D5C2×D3semidirect
221. #4027C2×D3semidirect
318. C2×Dic3⋊C4C2×D5semidirect
321. C2×C4×Dic3C2×D5semidirect
342. #877C2×D5semidirect
343. #877C2×D5semidirect
363. C2×C22⋊D5C4×D3semidirect
479. C22×Dic3C4×D5semidirect
786. C3×C5#3428semidirect
874. C5#85856semidirect
899. C3#10617632semidirect

Maximal subgroups

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

subgroupindex
C22×#67792
#117562452
C2×C5×#8772
C3×#658202
#117554132
#117554062
C2×#915292
#117542842
C4×#67792
#117531872
#117530662
#117528252
#117528192
#117528182
D5×#8772
#106176323
#858565