Finite Group Databasebeta

← #14321430

Subgroups — #14321430

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91782C211yesmaximal, characteristic, complemented
2C2×#91773C211yesmaximal, characteristic
3C2×#91770C211yesmaximal, characteristic, complemented
4C2×#91770C211yesmaximal, characteristic, complemented
5C2×C42×D15C211yesmaximal, characteristic, complemented
6C3×C5×#388C211yesmaximal, characteristic, complemented
7#11751077C211yesmaximal, characteristic, complemented
8#11751058C211yesmaximal, characteristic, complemented
9#11751057C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
11#11751041C211yesmaximal, characteristic, complemented
12#11750768C211yesmaximal, characteristic, complemented
13#11750767C211yesmaximal, characteristic, complemented
14#11750766C211yesmaximal, characteristic, complemented
15#11750750C211yesmaximal, characteristic, complemented
16#10607183—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic
22C22×C4×D15C2211yescharacteristic
23C22×C4×D15C2211yescharacteristic
24C22×C4×D15C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C42×C5C2211yescharacteristic
30C2×#6719C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×#6712C2211yescharacteristic
38C2×#6712C2211yescharacteristic
39C2×#6712C2211yescharacteristic
40C2×#6712C2211yescharacteristic
41C2×C4×Dic15C2211yescharacteristic
42C2×C4×Dic15C2211yescharacteristic
43C2×C4×Dic15C2211yescharacteristic
44C2×C4×Dic15C2211yescharacteristic
45C2×C4×Dic15C2211yescharacteristic
46#91782—24no—
47#91773C418yescomplemented
48#91770—24no—
49#91770—24no—
50C42×D15—24no—
51C3×C5×#95C2211yescharacteristic
52C3×C5×#95C2211yescharacteristic
53#91115C2211yescharacteristic
54#91115C2211yescharacteristic
55#91115C2211yescharacteristic
56#91115C2211yescharacteristic
57#75452—51nomaximal, Hall
58C2×#4039—31no—
59C2×#4030—31no—
60C2×#4027—31no—
61C2×#4027—31no—
62C2×C42×D5—31no—
63C5×#388D311yescharacteristic, complemented
64#65261—31no—
65#65246—31no—
66#65245—31no—
67C22⋊C4×Dic5—31no—
68#65229—31no—
69#64956—31no—
70#64955—31no—
71#64954—31no—
72#64938—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C23×D15C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×#1220—22no—
83C2×#1220—22no—
84C2×#1220—22no—
85C2×#1220—22no—
86C2×#1220C2×C414yescomplemented
87C2×#1220C2×C414yescomplemented
88C22×Dic15—22no—
89C22×Dic15—22no—
90C22×Dic15—22no—
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C2×D60—22no—
98C2×D60—22no—
99C2×D60C2×C414yescomplemented
100C2×C4×D15—22no—
101C2×C4×D15—22no—
102C2×C4×D15—22no—
103C2×C4×D15—22no—
104C2×C4×D15—22no—
105C2×C4×D15—22no—
106C2×C4×D15—22no—
107C2×C4×D15—22no—
108C2×C4×D15—22no—
109C2×C4×D15—22no—
110C2×C4×D15C2×C414yescomplemented
111C2×C4×D15D414yescomplemented
112C3×C5×C4⋊C4—22no—
113C3×C5×C22⋊C4—22no—
114C3×C5×C22⋊C4—22no—
115C3×C5×C22⋊C4C2×C414yescomplemented
116C3×C42×C5—22no—
117#6719—22no—
118#6714—22no—
119#6714—22no—
120#6714—22no—
121#6714—22no—
122#6714—22no—
123#6714C2×C414yescomplemented
124#6712—22no—
125#6712—22no—
126#6712—22no—
127#6712C2×C414yescomplemented
128C4×Dic15—22no—
129C4×Dic15—22no—
130C4×Dic15—22no—
131C4×Dic15—22no—
132C4×Dic15D414yescomplemented
133C2×#893—51no—
134C2×#884—51no—
135C2×#67⋊C4—51no—
136C2×#67⋊C4—51no—
137C2×C42×D3—51no—
138C3×#388D511yescharacteristic, complemented
139#4976—51no—
140#4957—51no—
141#4956—51no—
142Dic3×C22⋊C4—51no—
143#4940—51no—
144#4667—51no—
145#4666—51no—
146#4665—51no—
147#4649—51no—
148C22×C22⋊D5—31no—
149C22×C22⋊D5—31no—
150C23×Dic5—31no—
151C22×D20—31no—
152C22×C4×D5—31no—
153C22×C4×D5—31no—
154C22×C4×D5—31no—
155C22×C4×D5—31no—
156C2×C5×C4⋊C4C2×D311yescharacteristic
157C2×C5×C22⋊C4C2×D311yescharacteristic
158C2×C5×C22⋊C4C2×D311yescharacteristic
159C2×C5×C22⋊C4C2×D311yescharacteristic
160C2×C42×C5C2×D311yescharacteristic
161C2×C22⋊Dic5—31no—
162C2×#685—31no—
163C2×#685—31no—
164C2×#685—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#683—31no—
169C2×#683—31no—
170C2×#683—31no—
171C2×#683—31no—
172C2×C4×Dic5—31no—
173C2×C4×Dic5—31no—
174C2×C4×Dic5—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5—31no—
177#4039—64no—
178#4030—38no—
179#4027—64no—
180#4027—64no—
181C42×D5—64no—
182C5×#95C2×D311yescharacteristic
183C5×#95C2×D311yescharacteristic
184#3963—31no—
185#3963—31no—
186#3963—31no—
187#3963—31no—
188C4×#121—151noSylow
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5C22×C412yes—
196C23×C3×C5C2411yescharacteristic
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—21no—
201C22×D15—21no—
202C22×D15—21no—
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15C22×C412yes—
208C22×D15C22×C412yes—
209C22×D15C2×D412yes—
210C22×D15#4112yes—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5C22×C412yes—
226C2×C3×C4×C5C22×C412yes—
227C2×C3×C4×C5C2×D412yes—
228C2×C3×C4×C5C2×D412yes—
229#1220—28no—
230#1220—28no—
231C2×Dic15—21no—
232C2×Dic15—21no—
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15—21no—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15—21no—
241C2×Dic15—44no—
242C2×Dic15C22×C412yes—
243C2×Dic15C22×C412yes—
244C2×Dic15C2×D412yes—
245C2×Dic15C2×D412yes—
246C2×Dic15C2×D412yes—
247C2×Dic15#4112yes—
248C2×Dic15#4112yes—
249C2×Dic15#4112yes—
250D60—28no—
251C4×D15—28no—
252C4×D15—28no—
253C4×D15—28no—
254C4×D15—44no—
255C22×#67—51no—
256C22×#67—51no—
257C23×Dic3—51no—
258C22×D12—51no—
259C22×C4×D3—51no—
260C22×C4×D3—51no—
261C22×C4×D3—51no—
262C22×C4×D3—51no—
263C2×C3×C4⋊C4C2×D511yescharacteristic
264C2×C3×C22⋊C4C2×D511yescharacteristic
265C2×C3×C22⋊C4C2×D511yescharacteristic
266C2×C3×C22⋊C4C2×D511yescharacteristic
267C2×C3×C42C2×D511yescharacteristic
268C2×#217—51no—
269C2×(C2×D3)⋊C4—51no—
270C2×(C2×D3)⋊C4—51no—
271C2×(C2×D3)⋊C4—51no—
272C2×(C2×D3)⋊C4—51no—
273C2×(C2×D3)⋊C4—51no—
274C2×(C2×D3)⋊C4—51no—
275C2×Dic3⋊C4—51no—
276C2×Dic3⋊C4—51no—
277C2×Dic3⋊C4—51no—
278C2×Dic3⋊C4—51no—
279C2×C4×Dic3—51no—
280C2×C4×Dic3—51no—
281C2×C4×Dic3—51no—
282C2×C4×Dic3—51no—
283C2×C4×Dic3—51no—
284#893—104no—
285#884—58no—
286#67⋊C4—104no—
287#67⋊C4—104no—
288C42×D3—104no—
289C3×#95C2×D511yescharacteristic
290C3×#95C2×D511yescharacteristic
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C24×C5C22×D311yescharacteristic
296C23×D5—31no—
297C23×D5—31no—
298C22×C4×C5C22×D311yescharacteristic
299C22×C4×C5C22×D311yescharacteristic
300C22×C4×C5C22×D311yescharacteristic
301C22×C4×C5C22×D311yescharacteristic
302C22×C4×C5C22×D311yescharacteristic
303C22×C4×C5C22×D311yescharacteristic
304C2×C22⋊D5—34no—
305C2×C22⋊D5—34no—
306C2×C22⋊D5—62no—
307C2×C22⋊D5—62no—
308C2×C22⋊D5—62no—
309C2×C22⋊D5—62no—
310C22×Dic5—31no—
311C22×Dic5—31no—
312C22×Dic5—31no—
313C22×Dic5—31no—
314C22×Dic5—31no—
315C22×Dic5—31no—
316C22×Dic5—62no—
317C22×Dic5—62no—
318C22×Dic5—62no—
319C2×D20—34no—
320C2×D20—62no—
321C2×D20—62no—
322C2×C4×D5—34no—
323C2×C4×D5—34no—
324C2×C4×D5—62no—
325C2×C4×D5—62no—
326C2×C4×D5—62no—
327C2×C4×D5—62no—
328C2×C4×D5—62no—
329C2×C4×D5—62no—
330C2×C4×D5—62no—
331C2×C4×D5—62no—
332C2×C4×D5—62no—
333C2×C4×D5—62no—
334C5×C4⋊C4—22no—
335C5×C22⋊C4—22no—
336C5×C22⋊C4—22no—
337C5×C22⋊C4C4×D314yescomplemented
338C42×C5—22no—
339C22⋊Dic5—62no—
340#685—34no—
341#685—62no—
342#685—62no—
343#685—62no—
344#685—62no—
345#685—62no—
346#683—34no—
347#683—62no—
348#683—62no—
349#683—62no—
350C4×Dic5—34no—
351C4×Dic5—62no—
352C4×Dic5—62no—
353C4×Dic5—62no—
354C4×Dic5—62no—
355C2×#121—151no—
356C2×C4×D4—151no—
357C2×C4×D4—151no—
358C2×C4×D4—151no—
359C22×C42—151no—
360#390—151no—
361#389—151no—
362#388—151no—
363#388D1511yescharacteristic, complemented
364#386—151no—
365#386—151no—
366#380—151no—
367C4×C4⋊C4—151no—
368C4×C22⋊C4—151no—
369C4×C22⋊C4—151no—
370C22×C3×C5—22no—
371C22×C3×C5—22no—
372C22×C3×C5—22no—
373C22×C3×C5—41no—
374C22×C3×C5—41no—
375C22×C3×C5—41no—
376C22×C3×C5—41no—
377C22×C3×C5C23×C411yescharacteristic
378C22×C3×C5C22×D411yescharacteristic
379C22×C3×C5C22×D411yescharacteristic
380C22×C3×C5C2×#4111yescharacteristic
381C22×C3×C5C2×#4111yescharacteristic
382C22×C3×C5C2×#4111yescharacteristic
383C22×C3×C5C2×#4111yescharacteristic
384C2×D15—22no—
385C2×D15—22no—
386C2×D15—22no—
387C2×D15—22no—
388C2×D15—22no—
389C2×D15—22no—
390C2×D15—22no—
391C2×D15—22no—
392C2×D15—22no—
393C2×D15—41no—
394C2×D15—41no—
395C2×D15—41no—
396C2×D15—41no—
397C2×D15C4×D414yescomplemented
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400C3×C4×C5—22no—
401C3×C4×C5—22no—
402C3×C4×C5—41no—
403C3×C4×C5—41no—
404Dic15—22no—
405Dic15—22no—
406Dic15—41no—
407Dic15—41no—
408Dic15C4×D414yescomplemented
409Dic15#12114yescomplemented
410C24×C3C22×D511yescharacteristic
411C23×D3—51no—
412C23×D3—51no—
413C22×C3×C4C22×D511yescharacteristic
414C22×C3×C4C22×D511yescharacteristic
415C22×C3×C4C22×D511yescharacteristic
416C22×C3×C4C22×D511yescharacteristic
417C22×C3×C4C22×D511yescharacteristic
418C22×C3×C4C22×D511yescharacteristic
419C2×#67—54no—
420C2×#67—54no—
421C2×#67—102no—
422C2×#67—102no—
423C2×#67—102no—
424C2×#67—102no—
425C22×Dic3—51no—
426C22×Dic3—51no—
427C22×Dic3—51no—
428C22×Dic3—51no—
429C22×Dic3—51no—
430C22×Dic3—51no—
431C22×Dic3—102no—
432C22×Dic3—102no—
433C22×Dic3—102no—
434C2×D12—54no—
435C2×D12—102no—
436C2×D12—102no—
437C2×C4×D3—54no—
438C2×C4×D3—54no—
439C2×C4×D3—102no—
440C2×C4×D3—102no—
441C2×C4×D3—102no—
442C2×C4×D3—102no—
443C2×C4×D3—102no—
444C2×C4×D3—102no—
445C2×C4×D3—102no—
446C2×C4×D3—102no—
447C2×C4×D3—102no—
448C2×C4×D3—102no—
449C3×C4⋊C4—22no—
450C3×C22⋊C4—22no—
451C3×C22⋊C4—22no—
452C3×C22⋊C4C4×D514yescomplemented
453C3×C42—22no—
454#217—102no—
455(C2×D3)⋊C4—54no—
456(C2×D3)⋊C4—102no—
457(C2×D3)⋊C4—102no—
458(C2×D3)⋊C4—102no—
459(C2×D3)⋊C4—102no—
460(C2×D3)⋊C4—102no—
461Dic3⋊C4—54no—
462Dic3⋊C4—102no—
463Dic3⋊C4—102no—
464Dic3⋊C4—102no—
465C4×Dic3—54no—
466C4×Dic3—102no—
467C4×Dic3—102no—
468C4×Dic3—102no—
469C4×Dic3—102no—
470C23×C5—21no—
471C23×C5—21no—
472C23×C5—21no—
473C23×C5—21no—
474C23×C5—21no—
475C23×C5—21no—
476C23×C5C2×C4×D312yes—
477C23×C5C23×D311yescharacteristic
478C22×D5—32no—
479C22×D5—32no—
480C22×D5—32no—
481C22×D5—32no—
482C22×D5—61no—
483C22×D5—61no—
484C22×D5—61no—
485C22×D5—61no—
486C22×D5—61no—
487C22×D5—61no—
488C22×D5—61no—
489C22×D5—61no—
490C22×D5—61no—
491C22×D5—61no—
492C2×C4×C5—21no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—21no—
506C2×C4×C5C2×C4×D312yes—
507C2×C4×C5C2×C4×D312yes—
508C2×C4×C5D3×D412yes—
509C2×C4×C5D3×D412yes—
510C22⋊D5—68no—
511C22⋊D5—68no—
512C2×Dic5—32no—
513C2×Dic5—32no—
514C2×Dic5—32no—
515C2×Dic5—32no—
516C2×Dic5—32no—
517C2×Dic5—32no—
518C2×Dic5—32no—
519C2×Dic5—32no—
520C2×Dic5—61no—
521C2×Dic5—61no—
522C2×Dic5—61no—
523C2×Dic5—61no—
524C2×Dic5—61no—
525C2×Dic5—61no—
526C2×Dic5—61no—
527C2×Dic5—61no—
528C2×Dic5—61no—
529C2×Dic5—61no—
530C2×Dic5—124no—
531D20—68no—
532C4×D5—68no—
533C4×D5—68no—
534C4×D5—68no—
535C4×D5—124no—
536C22×D4—151no—
537C22×D4—151no—
538C22×D4—151no—
539C23×C4—151no—
540C23×C4—151no—
541C23×C4—151no—
542C23×C4—151no—
543C23×C4—151no—
544#121—158no—
545C4×D4—304no—
546C4×D4—304no—
547C4×D4—304no—
548C2×C4⋊C4—151no—
549C2×C4⋊C4—151no—
550C2×C4⋊C4—151no—
551C2×C4⋊C4—151no—
552C2×C4⋊C4C2×D1511yescharacteristic
553C2×C22⋊C4—151no—
554C2×C22⋊C4—151no—
555C2×C22⋊C4—151no—
556C2×C22⋊C4—151no—
557C2×C22⋊C4—151no—
558C2×C22⋊C4—151no—
559C2×C22⋊C4—151no—
560C2×C22⋊C4C2×D1511yescharacteristic
561C2×C22⋊C4C2×D1511yescharacteristic
562C2×C22⋊C4C2×D1511yescharacteristic
563C2×C42—151no—
564C2×C42—151no—
565C2×C42—151no—
566C2×C42—151no—
567C2×C42—151no—
568C2×C42—304no—
569C2×C42C2×D1511yescharacteristic
570#95—151no—
571#95—151no—
572#95—151no—
573#95—151no—
574#95C2×D1511yescharacteristic
575#95C2×D1511yescharacteristic
576C2×C3×C5—42no—
577C2×C3×C5C2×C4×D411yescharacteristic
578C2×C3×C5C2×C4×D411yescharacteristic
579C2×C3×C5C4×#4111yescharacteristic
580C2×C3×C5C2×#12111yescharacteristic
581C2×C3×C5#52511yescharacteristic
582C2×C3×C5#52911yescharacteristic
583C2×C3×C5#53211yescharacteristic
584D15—24no—
585D15—42no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—21no—
592C23×C3C2×C4×D512yes—
593C23×C3C23×D511yescharacteristic
594C22×D3—52no—
595C22×D3—52no—
596C22×D3—52no—
597C22×D3—52no—
598C22×D3—101no—
599C22×D3—101no—
600C22×D3—101no—
601C22×D3—101no—
602C22×D3—101no—
603C22×D3—101no—
604C22×D3—101no—
605C22×D3—101no—
606C22×D3—101no—
607C22×D3—101no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4C2×C4×D512yes—
623C2×C3×C4C2×C4×D512yes—
624C2×C3×C4D4×D512yes—
625C2×C3×C4D4×D512yes—
626#67—108no—
627#67—108no—
628C2×Dic3—52no—
629C2×Dic3—52no—
630C2×Dic3—52no—
631C2×Dic3—52no—
632C2×Dic3—52no—
633C2×Dic3—52no—
634C2×Dic3—52no—
635C2×Dic3—52no—
636C2×Dic3—101no—
637C2×Dic3—101no—
638C2×Dic3—101no—
639C2×Dic3—101no—
640C2×Dic3—101no—
641C2×Dic3—101no—
642C2×Dic3—101no—
643C2×Dic3—101no—
644C2×Dic3—101no—
645C2×Dic3—101no—
646C2×Dic3—204no—
647D12—108no—
648C4×D3—108no—
649C4×D3—108no—
650C4×D3—108no—
651C4×D3—204no—
652C22×C5—22no—
653C22×C5—22no—
654C22×C5—22no—
655C22×C5—41no—
656C22×C5—41no—
657C22×C5—41no—
658C22×C5—41no—
659C22×C5C22×C4×D311yescharacteristic
660C22×C5C2×D3×D411yescharacteristic
661C22×C5C2×D3×D411yescharacteristic
662C22×C5D3×#4111yescharacteristic
663C22×C5D3×#4111yescharacteristic
664C22×C5D3×#4111yescharacteristic
665C22×C5D3×#4111yescharacteristic
666C2×D5—34no—
667C2×D5—62no—
668C2×D5—62no—
669C2×D5—62no—
670C2×D5—62no—
671C2×D5—62no—
672C2×D5—62no—
673C2×D5—62no—
674C2×D5—62no—
675C2×D5—62no—
676C2×D5—121no—
677C2×D5—121no—
678C2×D5—121no—
679C2×D5—121no—
680C4×C5—22no—
681C4×C5—22no—
682C4×C5—22no—
683C4×C5—22no—
684C4×C5—41no—
685C4×C5—41no—
686Dic5—34no—
687Dic5—34no—
688Dic5—62no—
689Dic5—62no—
690Dic5—121no—
691Dic5—121no—
692C24—151no—
693C24—151no—
694C24C22×D1511yescharacteristic
695C2×D4—154no—
696C2×D4—154no—
697C2×D4—154no—
698C2×D4—302no—
699C2×D4—302no—
700C2×D4—302no—
701C2×D4—302no—
702C2×D4—302no—
703C2×D4—302no—
704C22×C4—151no—
705C22×C4—151no—
706C22×C4—151no—
707C22×C4—151no—
708C22×C4—154no—
709C22×C4—154no—
710C22×C4—151no—
711C22×C4—151no—
712C22×C4—302no—
713C22×C4—302no—
714C22×C4—302no—
715C22×C4—302no—
716C22×C4—302no—
717C22×C4—302no—
718C22×C4—302no—
719C22×C4—302no—
720C22×C4—302no—
721C22×C4—302no—
722C22×C4—302no—
723C22×C4—302no—
724C22×C4—302no—
725C22×C4C22×D1511yescharacteristic
726C22×C4C22×D1511yescharacteristic
727C22×C4C22×D1511yescharacteristic
728C22×C4C22×D1511yescharacteristic
729C22×C4C22×D1511yescharacteristic
730C22×C4C22×D1511yescharacteristic
731C4⋊C4—22no—
732C4⋊C4—154no—
733C4⋊C4—302no—
734C4⋊C4—302no—
735C4⋊C4—302no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—154no—
739C22⋊C4—302no—
740C22⋊C4—302no—
741C22⋊C4—302no—
742C22⋊C4—302no—
743C22⋊C4—302no—
744C22⋊C4—302no—
745C22⋊C4C4×D1514yescomplemented
746C42—22no—
747C42—154no—
748C42—302no—
749C42—302no—
750C42—302no—
751C42—302no—
752C3×C5C4×#12111yescharacteristic, complemented, Hall
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3C22×C4×D511yescharacteristic
761C22×C3C2×D4×D511yescharacteristic
762C22×C3C2×D4×D511yescharacteristic
763C22×C3D5×#4111yescharacteristic
764C22×C3D5×#4111yescharacteristic
765C22×C3D5×#4111yescharacteristic
766C22×C3D5×#4111yescharacteristic
767C2×D3—54no—
768C2×D3—102no—
769C2×D3—102no—
770C2×D3—102no—
771C2×D3—102no—
772C2×D3—102no—
773C2×D3—102no—
774C2×D3—102no—
775C2×D3—102no—
776C2×D3—102no—
777C2×D3—201no—
778C2×D3—201no—
779C2×D3—201no—
780C2×D3—201no—
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—22no—
784C3×C4—22no—
785C3×C4—41no—
786C3×C4—41no—
787Dic3—54no—
788Dic3—54no—
789Dic3—102no—
790Dic3—102no—
791Dic3—201no—
792Dic3—201no—
793C2×C5—42no—
794C2×C5#552211yescharacteristic
795C2×C5C4×D3×D411yescharacteristic
796C2×C5C4×D3×D411yescharacteristic
797C2×C5D3×#12111yescharacteristic
798C2×C5#565611yescharacteristic
799C2×C5#566811yescharacteristic
800C2×C5#570611yescharacteristic
801D5—64no—
802D5—122no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—152no—
810C23—152no—
811C23—152no—
812C23—152no—
813C23—301no—
814C23—301no—
815C23—301no—
816C23—301no—
817C23—301no—
818C23—301no—
819C23—301no—
820C23—301no—
821C23—301no—
822C23—301no—
823C23C2×C4×D1512yes—
824C23C23×D1511yescharacteristic
825D4—308no—
826D4—308no—
827D4—308no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—152no—
843C2×C4—152no—
844C2×C4—152no—
845C2×C4—152no—
846C2×C4—152no—
847C2×C4—152no—
848C2×C4—152no—
849C2×C4—152no—
850C2×C4—308no—
851C2×C4—308no—
852C2×C4—308no—
853C2×C4—301no—
854C2×C4—301no—
855C2×C4—301no—
856C2×C4—301no—
857C2×C4—301no—
858C2×C4—301no—
859C2×C4—301no—
860C2×C4—301no—
861C2×C4—301no—
862C2×C4—301no—
863C2×C4—604no—
864C2×C4—604no—
865C2×C4C2×C4×D1512yes—
866C2×C4C2×C4×D1512yes—
867C2×C4D4×D1512yes—
868C2×C4D4×D1512yes—
869C2×C3—42no—
870C2×C3#6585611yescharacteristic
871C2×C3C4×D4×D511yescharacteristic
872C2×C3C4×D4×D511yescharacteristic
873C2×C3D5×#12111yescharacteristic
874C2×C3#6599011yescharacteristic
875C2×C3#6600211yescharacteristic
876C2×C3#6604011yescharacteristic
877D3—104no—
878D3—202no—
879C5#7545211yescharacteristic, complemented, Sylow
880C22—22no—
881C22—22no—
882C22—22no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—154no—
888C22—302no—
889C22—302no—
890C22—302no—
891C22—302no—
892C22—302no—
893C22—302no—
894C22—302no—
895C22—302no—
896C22—302no—
897C22—601no—
898C22—601no—
899C22—601no—
900C22—601no—
901C22C22×C4×D1511yescharacteristic
902C22C2×D4×D1511yescharacteristic
903C22C2×D4×D1511yescharacteristic
904C22#41×D1511yescharacteristic
905C22#41×D1511yescharacteristic
906C22#41×D1511yescharacteristic
907C22#41×D1511yescharacteristic
908C4—22no—
909C4—22no—
910C4—22no—
911C4—22no—
912C4—41no—
913C4—41no—
914C4—154no—
915C4—154no—
916C4—302no—
917C4—302no—
918C4—601no—
919C4—601no—
920C3#1060718311yescharacteristic, complemented, Sylow
921C2—42no—
922C2—304no—
923C2—602no—
924C2#1175628111yescharacteristic
925C2C4×D4×D1511yescharacteristic
926C2C4×D4×D1511yescharacteristic
927C2D15×#12111yescharacteristic
928C2#1175641511yescharacteristic
929C2#1175642711yescharacteristic
930C2#1175646511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#388C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91773C2
hypercenter#388D15
hypocenterC3×C5C4×#121
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#91782C2semidirect
3. C2×#91770C2semidirect
4. C2×#91770C2semidirect
5. C2×C42×D15C2semidirect
6. C3×C5×#388C2semidirect
7. #11751077C2semidirect
8. #11751058C2semidirect
9. #11751057C2semidirect
10. C22⋊C4×Dic15C2semidirect
11. #11751041C2semidirect
12. #11750768C2semidirect
13. #11750767C2semidirect
14. #11750766C2semidirect
15. #11750750C2semidirect
47. #91773C4semidirect
63. C5×#388D3semidirect
86. C2×#1220C2×C4semidirect
87. C2×#1220C2×C4semidirect
99. C2×D60C2×C4semidirect
110. C2×C4×D15C2×C4semidirect
111. C2×C4×D15D4semidirect
115. C3×C5×C22⋊C4C2×C4semidirect
123. #6714C2×C4semidirect
127. #6712C2×C4semidirect
132. C4×Dic15D4semidirect
138. C3×#388D5semidirect
337. C5×C22⋊C4C4×D3semidirect
363. #388D15semidirect
397. C2×D15C4×D4semidirect
408. Dic15C4×D4semidirect
409. Dic15#121semidirect
452. C3×C22⋊C4C4×D5semidirect
745. C22⋊C4C4×D15semidirect
752. C3×C5C4×#121semidirect
879. C5#75452semidirect
920. C3#10607183semidirect

Maximal subgroups

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

subgroupindex
C2×#917822
C2×#917732
C2×#917702
C2×C42×D152
C3×C5×#3882
#117510772
#117510582
#117510572
C22⋊C4×Dic152
#117510412
#117507682
#117507672
#117507662
#117507502
#106071833
#754525