Finite Group Databasebeta

← #14479144

Subgroups — #14479144

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×#6782C211yesmaximal, characteristic
2#11756245C211yesmaximal, characteristic, complemented
3C5×#5486C211yesmaximal, characteristic, complemented
4C2×C3×#4023C211yesmaximal, characteristic, complemented
5#11755413C211yesmaximal, characteristic, complemented
6#11755410C211yesmaximal, characteristic, complemented
7C2×#91528C211yesmaximal, characteristic, complemented
8#11754294C214yesmaximal, complemented
9C4×#6782C214yesmaximal, complemented
10#11753187C212yesmaximal, complemented
11#11753067C212yesmaximal, complemented
12#11752825C212yesmaximal, complemented
13#11752824C214yesmaximal, complemented
14#11752823C214yesmaximal, complemented
15D3×#4023C212yesmaximal, complemented
16#10617757—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C22×C5×#67C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C22×#1204C2211yescharacteristic
21C22×#1203C2211yescharacteristic
22C22×#1200C2211yescharacteristic
23C2×#6782C4116yescomplemented
24C2×#6782C2212yes—
25C2×#6782C2212yes—
26C2×#6782C2212yes—
27C2×#6782C2212yes—
28C22×D3×Dic5C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic
30C2×#6719C2211yescharacteristic
31C4×#1220C2214yescomplemented
32#91770C2214yescomplemented
33C22⋊C4×D15C2212yes—
34#91766C2212yes—
35C2×C5×#217C2211yescharacteristic
36C4×C5×#67C2214yescomplemented
37C5×#67⋊C4C2214yescomplemented
38C5×D3×C22⋊C4C2212yes—
39C5×#877C2212yes—
40C2×C3×C22⋊Dic5C2211yescharacteristic
41C2×C3×#683C2212yescomplemented
42C2×C3×C4×Dic5C2212yescomplemented
43C3×#4023C2212yes—
44C3×#4023C2212yes—
45C3×#4023C2212yescomplemented
46C3×#4023C2212yescomplemented
47#91561C2212yes—
48#67⋊Dic5C2214yescomplemented
49#91556C2214yescomplemented
50D3×C22⋊Dic5C2212yes—
51#91552C2214yescomplemented
52Dic5×#67C2214yescomplemented
53C2×#6668C2212yescomplemented
54#91532C2212yes—
55#91529C2212yes—
56#91528C2212yes—
57#91528C2212yes—
58#91528C2212yescomplemented
59#91528C2212yescomplemented
60C2×Dic3×Dic5C2212yescomplemented
61C4×#1204C2214yescomplemented
62#91446C2214yescomplemented
63C4×#1203C2214yescomplemented
64#91406C2214yescomplemented
65#91405C2214yescomplemented
66#91404C2214yescomplemented
67#91403C2214yescomplemented
68#91402C2214yescomplemented
69C4×#1200C2214yescomplemented
70#91400C2214yescomplemented
71D3×#683C2214yescomplemented
72#91398C2214yescomplemented
73C4×D3×Dic5C2214yescomplemented
74#91325C2214yescomplemented
75#91324C2214yescomplemented
76#91323C2214yescomplemented
77#85731—51nomaximal, Hall
78C22×#711—31no—
79C5×#518—31no—
80#66132—31no—
81#65880—34no—
82#65880—34no—
83C4×#711—34no—
84C4×#711—34no—
85D5×#117—32no—
86#65850—32no—
87#65820—32no—
88#65820—31no—
89#65820—31no—
90C2×#4023—32no—
91C2×#4023—31no—
92C2×#4023D311yescharacteristic, complemented
93C24×C3×C5C2311yescharacteristic
94C23×D15C2311yescharacteristic
95C23×C5×D3C2311yescharacteristic
96C22×C3×C4×C5C2312yes—
97C2×#1220C2×C418yescomplemented
98C2×#1220C2312yes—
99C2×#1220C2312yes—
100C22×Dic15C2312yes—
101C22×Dic15C2311yescharacteristic
102C2×C4×D15C2314yes—
103C2×C5×#67C2×C418yescomplemented
104C2×C5×#67C2312yes—
105C2×C5×#67C2312yes—
106C22×C5×Dic3C2312yes—
107C22×C5×Dic3C2311yescharacteristic
108C2×C4×C5×D3C2314yes—
109C22×C3×Dic5C2×C418yescomplemented
110C22×C3×Dic5C2312yes—
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C22×C3×Dic5C2311yescharacteristic
117C2×#1204C2×C418yescomplemented
118C2×#1204C2312yes—
119C2×#1204C2312yes—
120C2×#1203C2×C418yescomplemented
121C2×#1203C2312yes—
122C2×#1203C2312yes—
123C2×#1200C2×C418yescomplemented
124C2×#1200C2314yes—
125C2×#1200C2312yes—
126C2×#1200C2312yes—
127#6782C2×C4116yescomplemented
128#6782C2×C4116yescomplemented
129#6782C2×C4116yescomplemented
130#6782C2×C4116yescomplemented
131C2×D3×Dic5C2×C418yescomplemented
132C2×D3×Dic5C2314yes—
133C2×D3×Dic5C2312yes—
134C2×D3×Dic5C2312yes—
135C3×C5×C22⋊C4C2312yes—
136C3×C5×C22⋊C4C2312yes—
137#6719C2312yes—
138#6719C2312yes—
139#6714C2314yes—
140#6712C2314yes—
141C4×Dic15C2314yes—
142C5×#217C2312yes—
143C5×#217C2312yes—
144C5×(C2×D3)⋊C4C2314yes—
145C5×Dic3⋊C4C2314yes—
146C4×C5×Dic3C2314yes—
147C3×C22⋊Dic5C2312yes—
148C3×C22⋊Dic5C2312yes—
149C3×#683C2314yes—
150C3×#683C2314yes—
151C3×C4×Dic5C2314yes—
152C3×C4×Dic5C2314yes—
153Dic3⋊Dic5C2314yes—
154#6669C2314yes—
155#6668C2314yes—
156#6668C2314yes—
157#6667C2314yes—
158(C2×D3)⋊Dic5C2314yes—
159Dic3×Dic5C2314yes—
160Dic3×Dic5C2314yes—
161Dic3×Dic5C2314yes—
162Dic3×Dic5C2314yes—
163C22×#235—51no—
164C2×C3×#117—51no—
165C2×#926—51no—
166#5523—54no—
167#5522—54no—
168#5521—52no—
169D3×#117—52no—
170D3×#117—52no—
171#5516—52no—
172#5504—54no—
173#5486—51no—
174#5486—51no—
175#5486—51no—
176#5486D511yescharacteristic, complemented
177C4×#235—54no—
178C22×C5×D4—31no—
179C22×C22⋊D5—31no—
180C22×C22⋊D5—31no—
181C23×Dic5—31no—
182C23×Dic5C2×D311yescharacteristic
183C2×#711—316no—
184C2×#711—32no—
185C2×#711—32no—
186C2×#711—32no—
187C2×#711—32no—
188C22×C4×D5—31no—
189C22×Dic10—31no—
190C4×C5×D4—34no—
191C4×C5×D4—34no—
192C5×#117—32no—
193C2×C5×C22⋊C4—31no—
194C2×C5×C22⋊C4—32no—
195C2×C5×C22⋊C4C2×D311yescharacteristic
196C2×C22⋊Dic5—31no—
197C2×C22⋊Dic5—32no—
198C2×C22⋊Dic5C2×D311yescharacteristic
199D4×Dic5—34no—
200D4×Dic5—34no—
201C4×C22⋊D5—34no—
202C4×C22⋊D5—34no—
203C4×C22⋊D5—34no—
204C4×C22⋊D5—34no—
205#4072—32no—
206C2×#683—32no—
207C2×#683—34no—
208C2×#683C2×D312yescomplemented
209C2×C4×Dic5—32no—
210C2×C4×Dic5—34no—
211C2×C4×Dic5C2×D312yescomplemented
212#4038—34no—
213D5×C4⋊C4—34no—
214#4033—34no—
215#4033—34no—
216#4027—34no—
217#4027—34no—
218#4027—34no—
219#4027—34no—
220D5×C22⋊C4—32no—
221D5×C22⋊C4—32no—
222#4023—32no—
223#4023—32no—
224#4023—32no—
225#4023—32no—
226#4023—32no—
227#4023—32no—
228#4023—34no—
229#4023—34no—
230#4023C2×D312yes—
231#4023C2×D312yes—
232#4023C2×D312yescomplemented
233#4023C2×D312yescomplemented
234#4018—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×C5×D3—42no—
248C22×C5×D3C22×C414yes—
249C22×C5×D3C2412yes—
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—
259C5×#67C22×C418yes—
260C5×#67C22×C418yes—
261C2×C5×Dic3—42no—
262C2×C5×Dic3C22×C414yes—
263C2×C5×Dic3C2414yes—
264C2×C5×Dic3C2412yes—
265C4×C5×D3—44no—
266C2×C3×Dic5—42no—
267C2×C3×Dic5C22×C414yes—
268C2×C3×Dic5C22×C414yes—
269C2×C3×Dic5C22×C414yes—
270C2×C3×Dic5C22×C414yes—
271C2×C3×Dic5C22×C414yes—
272C2×C3×Dic5C22×C414yes—
273C2×C3×Dic5C2414yes—
274C2×C3×Dic5C2411yescharacteristic
275C2×C3×Dic5C2411yescharacteristic
276C2×C3×Dic5C2411yescharacteristic
277C2×C3×Dic5C2411yescharacteristic
278#1204C22×C418yes—
279#1204C22×C418yes—
280#1203C22×C418yes—
281#1203C22×C418yes—
282#1200—44no—
283#1200C22×C418yes—
284#1200C22×C418yes—
285D3×Dic5—44no—
286D3×Dic5C22×C418yes—
287D3×Dic5C22×C418yes—
288C23×C3×C4—51no—
289C22×#67—51no—
290C22×#67C2×D511yescharacteristic
291C2×#235—516no—
292C2×#235—52no—
293C2×#235—52no—
294C2×#235—52no—
295C2×#235—52no—
296C22×D12—51no—
297C22×C4×D3—51no—
298C22×C4×D3—51no—
299C22×Dic6—51no—
300C3×#117—52no—
301C3×#117—52no—
302C3×#117—52no—
303C3×#117—52no—
304C2×C3×C4⋊C4—52no—
305C2×C3×C22⋊C4—51no—
306C2×C3×C22⋊C4C2×D511yescharacteristic
307C2×C3×C42—52no—
308C2×#217—51no—
309C2×#217C2×D511yescharacteristic
310C4×#67—54no—
311C4×#67—54no—
312C4×#67—54no—
313C4×#67C2×D514yescomplemented
314#926—52no—
315#926—52no—
316#926—52no—
317#926—52no—
318C2×C4⋊Dic3—52no—
319C2×C4×Dic3—52no—
320#893—54no—
321#893—54no—
322#892—54no—
323#892—54no—
324D3×C4⋊C4—54no—
325D3×C4⋊C4—54no—
326#887—54no—
327#887—54no—
328#67⋊C4—54no—
329#67⋊C4—54no—
330#67⋊C4—54no—
331#67⋊C4C2×D514yescomplemented
332D3×C22⋊C4—52no—
333D3×C22⋊C4—52no—
334D3×C22⋊C4—52no—
335D3×C22⋊C4C2×D512yes—
336#877—52no—
337#877—52no—
338#877—52no—
339#877C2×D512yes—
340C4×D12—54no—
341C4×D12—54no—
342#872—54no—
343#872—54no—
344C42×D3—54no—
345C42×D3—54no—
346C4×Dic6—54no—
347C4×Dic6—54no—
348C24×C5—31no—
349C24×C5C22×D311yescharacteristic
350C23×D5—31no—
351C2×C5×D4—38no—
352C2×C5×D4—32no—
353C2×C5×D4—32no—
354C22×C4×C5—31no—
355C22×C4×C5—32no—
356C22×C4×C5—34no—
357C22×C4×C5C22×D312yes—
358C2×C22⋊D5—38no—
359C2×C22⋊D5—32no—
360C2×C22⋊D5—32no—
361C2×C22⋊D5—38no—
362C2×C22⋊D5—32no—
363C2×C22⋊D5—32no—
364C22×Dic5—31no—
365C22×Dic5—38no—
366C22×Dic5—32no—
367C22×Dic5—32no—
368C22×Dic5—32no—
369C22×Dic5—34no—
370C22×Dic5C4×D318yescomplemented
371C22×Dic5C22×D312yes—
372C22×Dic5C22×D311yescharacteristic
373C22×Dic5C22×D311yescharacteristic
374C22×Dic5C22×D311yescharacteristic
375C22×Dic5C22×D311yescharacteristic
376C22×Dic5C22×D311yescharacteristic
377C22×Dic5C22×D311yescharacteristic
378#711—316no—
379#711—316no—
380#711—316no—
381#711—316no—
382C2×C4×D5—38no—
383C2×C4×D5—32no—
384C2×C4×D5—32no—
385C2×C4×D5—34no—
386C2×C4×D5—34no—
387C2×Dic10—38no—
388C2×Dic10—32no—
389C2×Dic10—32no—
390C5×C4⋊C4—34no—
391C5×C22⋊C4—32no—
392C5×C22⋊C4—32no—
393C5×C22⋊C4—34no—
394C5×C22⋊C4C22×D312yes—
395C5×C22⋊C4C22×D312yes—
396C42×C5—34no—
397C22⋊Dic5—32no—
398C22⋊Dic5—32no—
399C22⋊Dic5—34no—
400C22⋊Dic5C22×D312yes—
401C22⋊Dic5C22×D312yes—
402#685—34no—
403#685—34no—
404C4⋊Dic5—34no—
405#683—34no—
406#683—34no—
407#683—34no—
408#683—34no—
409#683C22×D314yes—
410#683C22×D314yes—
411C4×Dic5—34no—
412C4×Dic5—34no—
413C4×Dic5—34no—
414C4×Dic5—34no—
415C4×Dic5—34no—
416C4×Dic5C22×D314yes—
417C4×Dic5C22×D314yes—
418C22×#41—151no—
419#520—154no—
420#520—154no—
421#519—152no—
422#518—31no—
423#518—151no—
424#518—152no—
425#518—151no—
426#518—151no—
427C4×#41—154no—
428C4×#41—154no—
429C2×#117—51no—
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×C5×D3—24no—
445C2×C5×D3—44no—
446C2×C5×D3C23×C414yes—
447C3×C4×C5—24no—
448Dic15—24no—
449Dic15C23×C414yes—
450C3×Dic5—24no—
451C3×Dic5C23×C412yes—
452C3×Dic5C23×C412yes—
453C3×Dic5C23×C412yes—
454C3×Dic5C23×C412yes—
455C5×Dic3—24no—
456C5×Dic3C23×C414yes—
457C24×C3C22×D511yescharacteristic
458C23×D3—51no—
459C23×D3C22×D511yescharacteristic
460C22×C3×C4—58no—
461C22×C3×C4—51no—
462C22×C3×C4—51no—
463C22×C3×C4—51no—
464C22×C3×C4—51no—
465C22×C3×C4—51no—
466C22×C3×C4—51no—
467C22×C3×C4—52no—
468C22×C3×C4C22×D512yes—
469C2×#67—58no—
470C2×#67—52no—
471C2×#67—52no—
472C2×#67C4×D518yescomplemented
473C2×#67C22×D512yes—
474C2×#67C22×D512yes—
475C22×Dic3—51no—
476C22×Dic3—52no—
477C22×Dic3C22×D512yes—
478C22×Dic3C22×D511yescharacteristic
479#235—516no—
480#235—516no—
481#235—516no—
482#235—516no—
483C2×D12—58no—
484C2×D12—52no—
485C2×D12—52no—
486C2×C4×D3—58no—
487C2×C4×D3—52no—
488C2×C4×D3—52no—
489C2×C4×D3—58no—
490C2×C4×D3—52no—
491C2×C4×D3—52no—
492C2×C4×D3—54no—
493C2×C4×D3—54no—
494C2×C4×D3—54no—
495C2×C4×D3C22×D514yes—
496C2×Dic6—58no—
497C2×Dic6—52no—
498C2×Dic6—52no—
499C3×C4⋊C4—54no—
500C3×C4⋊C4—54no—
501C3×C22⋊C4—52no—
502C3×C22⋊C4—52no—
503C3×C22⋊C4C22×D512yes—
504C3×C22⋊C4C22×D512yes—
505C3×C42—54no—
506C3×C42—54no—
507#217—52no—
508#217—52no—
509#217C22×D512yes—
510#217C22×D512yes—
511(C2×D3)⋊C4—54no—
512(C2×D3)⋊C4—54no—
513(C2×D3)⋊C4—54no—
514(C2×D3)⋊C4C22×D514yes—
515C4⋊Dic3—54no—
516C4⋊Dic3—54no—
517Dic3⋊C4—54no—
518Dic3⋊C4—54no—
519Dic3⋊C4—54no—
520Dic3⋊C4C22×D514yes—
521C4×Dic3—54no—
522C4×Dic3—54no—
523C4×Dic3—54no—
524C4×Dic3—54no—
525C4×Dic3—54no—
526C4×Dic3C22×D514yes—
527C23×C5—32no—
528C23×C5—34no—
529C23×C5—42no—
530C23×C5—122no—
531C23×C5C2×C4×D314yes—
532C23×C5C23×D311yescharacteristic
533C23×C5C23×D311yescharacteristic
534C23×C5C23×D311yescharacteristic
535C22×D5—32no—
536C22×D5—34no—
537C22×D5—122no—
538C5×D4—38no—
539C5×D4—38no—
540C2×C4×C5—34no—
541C2×C4×C5—32no—
542C2×C4×C5—34no—
543C2×C4×C5—42no—
544C2×C4×C5—124no—
545C2×C4×C5—122no—
546C2×C4×C5C23×D314yes—
547C22⋊D5—38no—
548C22⋊D5—38no—
549C22⋊D5—38no—
550C22⋊D5—38no—
551C2×Dic5—34no—
552C2×Dic5—32no—
553C2×Dic5—38no—
554C2×Dic5—38no—
555C2×Dic5—34no—
556C2×Dic5—42no—
557C2×Dic5—124no—
558C2×Dic5—122no—
559C2×Dic5C2×C4×D314yes—
560C2×Dic5C2×C4×D314yes—
561C2×Dic5C2×C4×D314yes—
562C2×Dic5C2×C4×D314yes—
563C2×Dic5C2×C4×D314yes—
564C2×Dic5C2×C4×D314yes—
565C2×Dic5C23×D314yes—
566C2×Dic5C23×D311yescharacteristic
567C2×Dic5C23×D311yescharacteristic
568C2×Dic5C23×D311yescharacteristic
569C2×Dic5C23×D311yescharacteristic
570C4×D5—38no—
571C4×D5—38no—
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—31no—
583C22×D4—151no—
584C22×D4—151no—
585C23×C4—51no—
586C23×C4—151no—
587C23×C4—151no—
588C4×Q8—154no—
589C4×Q8—154no—
590C4×Q8—154no—
591C4×Q8—154no—
592C4×D4—34no—
593C4×D4—34no—
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—52no—
606#117—52no—
607#117—52no—
608#117—52no—
609#117—154no—
610#117—154no—
611#117—154no—
612#117—152no—
613#117—154no—
614#117—152no—
615#117—152no—
616#117—152no—
617#117—152no—
618#117—152no—
619#117—152no—
620C2×C4⋊C4—52no—
621C2×C4⋊C4—154no—
622C2×C4⋊C4—154no—
623C2×C4⋊C4—152no—
624C2×C22⋊C4—31no—
625C2×C22⋊C4—32no—
626C2×C22⋊C4—51no—
627C2×C22⋊C4—152no—
628C2×C22⋊C4—152no—
629C2×C22⋊C4—151no—
630C2×C22⋊C4—152no—
631C2×C22⋊C4D3×D511yescharacteristic
632C2×C42—52no—
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—
642C5×D3—24no—
643C23×C3—42no—
644C23×C3C2×C4×D514yes—
645C23×C3C23×D511yescharacteristic
646C23×C3C23×D511yescharacteristic
647C23×C3C23×D511yescharacteristic
648C22×D3—42no—
649C22×D3—52no—
650C22×D3—54no—
651C22×D3—202no—
652C22×D3C2×C4×D514yes—
653C22×D3C23×D512yes—
654C2×C3×C4—42no—
655C2×C3×C4—54no—
656C2×C3×C4—54no—
657C2×C3×C4—54no—
658C2×C3×C4—54no—
659C2×C3×C4—54no—
660C2×C3×C4—54no—
661C2×C3×C4—51no—
662C2×C3×C4—51no—
663C2×C3×C4—51no—
664C2×C3×C4—51no—
665C2×C3×C4—54no—
666C2×C3×C4—202no—
667C2×C3×C4C23×D514yes—
668#67—58no—
669#67—58no—
670#67C2×C4×D518yes—
671#67C2×C4×D518yes—
672C2×Dic3—42no—
673C2×Dic3—54no—
674C2×Dic3—52no—
675C2×Dic3—54no—
676C2×Dic3—202no—
677C2×Dic3C2×C4×D514yes—
678C2×Dic3C23×D514yes—
679C2×Dic3C23×D512yes—
680D12—58no—
681D12—58no—
682C4×D3—44no—
683C4×D3—58no—
684C4×D3—58no—
685C4×D3—58no—
686C4×D3—58no—
687C4×D3—204no—
688C4×D3—204no—
689C4×D3—204no—
690Dic6—58no—
691Dic6—58no—
692C22×C5—22no—
693C22×C5—22no—
694C22×C5—22no—
695C22×C5—34no—
696C22×C5—44no—
697C22×C5—64no—
698C22×C5—124no—
699C22×C5C22×C4×D312yes—
700C22×C5C22×C4×D312yes—
701C22×C5C22×C4×D312yes—
702C22×C5C24×D311yescharacteristic
703C2×D5—34no—
704C2×D5—64no—
705C2×D5—124no—
706C4×C5—24no—
707C4×C5—34no—
708C4×C5—64no—
709Dic5—24no—
710Dic5—34no—
711Dic5—64no—
712Dic5C22×C4×D312yes—
713Dic5C22×C4×D312yes—
714Dic5C22×C4×D312yes—
715Dic5C22×C4×D312yes—
716C24—31no—
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—38no—
727C2×D4—32no—
728C2×D4—32no—
729C2×D4—152no—
730C2×D4—152no—
731C2×D4—158no—
732C2×D4—158no—
733C2×D4—152no—
734C2×D4—152no—
735C22×C4—31no—
736C22×C4—32no—
737C22×C4—34no—
738C22×C4—58no—
739C22×C4—51no—
740C22×C4—51no—
741C22×C4—51no—
742C22×C4—51no—
743C22×C4—51no—
744C22×C4—51no—
745C22×C4—52no—
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—54no—
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—34no—
769C22⋊C4—52no—
770C22⋊C4—52no—
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—54no—
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×C3C22×C4×D512yes—
792C22×C3C22×C4×D512yes—
793C22×C3C22×C4×D512yes—
794C22×C3C24×D511yescharacteristic
795C2×D3—24no—
796C2×D3—44no—
797C2×D3—54no—
798C2×D3—104no—
799C2×D3—204no—
800C2×D3C22×C4×D514yes—
801C3×C4—24no—
802C3×C4—52no—
803C3×C4—52no—
804C3×C4—52no—
805C3×C4—52no—
806C3×C4—104no—
807Dic3—24no—
808Dic3—54no—
809Dic3—104no—
810Dic3C22×C4×D514yes—
811C2×C5—22no—
812C2×C5—22no—
813C2×C5—22no—
814C2×C5—64no—
815C2×C5C23×C4×D311yescharacteristic
816C2×C5#596412yes—
817D5—64no—
818C23—32no—
819C23—34no—
820C23—42no—
821C23—122no—
822C23—152no—
823C23—154no—
824C23—602no—
825C23C4×D3×D514yes—
826C23C22×D3×D511yescharacteristic
827C23C22×D3×D511yescharacteristic
828C23C22×D3×D511yescharacteristic
829Q8—158no—
830Q8—158no—
831D4—38no—
832D4—38no—
833D4—158no—
834D4—158no—
835D4—158no—
836D4—158no—
837C2×C4—34no—
838C2×C4—32no—
839C2×C4—34no—
840C2×C4—42no—
841C2×C4—54no—
842C2×C4—54no—
843C2×C4—54no—
844C2×C4—54no—
845C2×C4—54no—
846C2×C4—54no—
847C2×C4—51no—
848C2×C4—51no—
849C2×C4—51no—
850C2×C4—51no—
851C2×C4—54no—
852C2×C4—124no—
853C2×C4—122no—
854C2×C4—158no—
855C2×C4—158no—
856C2×C4—158no—
857C2×C4—158no—
858C2×C4—154no—
859C2×C4—152no—
860C2×C4—154no—
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×C3C23×C4×D511yescharacteristic
871C2×C3#6628512yes—
872D3—24no—
873D3—104no—
874C5#8573111yescharacteristic, complemented, Sylow
875C22—22no—
876C22—22no—
877C22—22no—
878C22—34no—
879C22—44no—
880C22—64no—
881C22—124no—
882C22—154no—
883C22—304no—
884C22—604no—
885C22C2×C4×D3×D512yes—
886C22C2×C4×D3×D512yes—
887C22C2×C4×D3×D512yes—
888C22C23×D3×D511yescharacteristic
889C4—24no—
890C4—34no—
891C4—52no—
892C4—52no—
893C4—52no—
894C4—52no—
895C4—64no—
896C4—104no—
897C4—154no—
898C4—304no—
899C3#1061775711yescharacteristic, complemented, Sylow
900C2—22no—
901C2—22no—
902C2—22no—
903C2—64no—
904C2—304no—
905C2C22×C4×D3×D511yescharacteristic
906C2#1175703412yes—
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC22×C3×C5C25
prime radicalC22×#6782C2
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. C5×#5486C2semidirect
4. C2×C3×#4023C2semidirect
5. #11755413C2semidirect
6. #11755410C2semidirect
7. C2×#91528C2semidirect
8. #11754294C2semidirect
9. C4×#6782C2semidirect
10. #11753187C2semidirect
11. #11753067C2semidirect
12. #11752825C2semidirect
13. #11752824C2semidirect
14. #11752823C2semidirect
15. D3×#4023C2semidirect
23. C2×#6782C4semidirect
31. C4×#1220C22semidirect
32. #91770C22semidirect
36. C4×C5×#67C22semidirect
37. C5×#67⋊C4C22semidirect
41. C2×C3×#683C22semidirect
42. C2×C3×C4×Dic5C22semidirect
45. C3×#4023C22semidirect
46. C3×#4023C22semidirect
48. #67⋊Dic5C22semidirect
49. #91556C22semidirect
51. #91552C22semidirect
52. Dic5×#67C22semidirect
53. C2×#6668C22semidirect
58. #91528C22semidirect
59. #91528C22semidirect
60. C2×Dic3×Dic5C22semidirect
61. C4×#1204C22semidirect
62. #91446C22semidirect
63. C4×#1203C22semidirect
64. #91406C22semidirect
65. #91405C22semidirect
66. #91404C22semidirect
67. #91403C22semidirect
68. #91402C22semidirect
69. C4×#1200C22semidirect
70. #91400C22semidirect
71. D3×#683C22semidirect
72. #91398C22semidirect
73. C4×D3×Dic5C22semidirect
74. #91325C22semidirect
75. #91324C22semidirect
76. #91323C22semidirect
92. C2×#4023D3semidirect
97. C2×#1220C2×C4semidirect
103. C2×C5×#67C2×C4semidirect
109. C22×C3×Dic5C2×C4semidirect
117. C2×#1204C2×C4semidirect
120. C2×#1203C2×C4semidirect
123. C2×#1200C2×C4semidirect
127. #6782C2×C4semidirect
128. #6782C2×C4semidirect
129. #6782C2×C4semidirect
130. #6782C2×C4semidirect
131. C2×D3×Dic5C2×C4semidirect
176. #5486D5semidirect
208. C2×#683C2×D3semidirect
211. C2×C4×Dic5C2×D3semidirect
232. #4023C2×D3semidirect
233. #4023C2×D3semidirect
313. C4×#67C2×D5semidirect
331. #67⋊C4C2×D5semidirect
370. C22×Dic5C4×D3semidirect
472. C2×#67C4×D5semidirect
786. C3×C5#3428semidirect
874. C5#85731semidirect
899. C3#10617757semidirect

Maximal subgroups

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

subgroupindex
C22×#67822
#117562452
C5×#54862
C2×C3×#40232
#117554132
#117554102
C2×#915282
#117542942
C4×#67822
#117531872
#117530672
#117528252
#117528242
#117528232
D3×#40232
#106177573
#857315