Finite Group Databasebeta

← #14320847

Subgroups — #14320847

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91766C211yesmaximal, characteristic, complemented
2C2×#91559C211yesmaximal, characteristic
3C2×#91394C211yesmaximal, characteristic, complemented
4C5×#4945C211yesmaximal, characteristic, complemented
5C3×#65246C211yesmaximal, characteristic
6#11749489C211yesmaximal, characteristic
7#11749487C211yesmaximal, characteristic, complemented
8#11749478C211yesmaximal, characteristic, complemented
9#11748884C211yesmaximal, characteristic, complemented
10#11748801C211yesmaximal, characteristic, complemented
11#11748707C211yesmaximal, characteristic, complemented
12#11748706C211yesmaximal, characteristic, complemented
13#11748637C211yesmaximal, characteristic, complemented
14C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
15#11748627C211yesmaximal, characteristic, complemented
16#10607181—31nomaximal, Hall
17C23×Dic15C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C22×D5×Dic3C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×#6719C2211yescharacteristic
22C2×#6712C2211yescharacteristic
23C2×#6712C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic
25C2×C4×Dic15C2211yescharacteristic
26#91766—24no—
27C2×C5×#217C2211yescharacteristic
28C2×C5×#217C2211yescharacteristic
29C2×C5×Dic3⋊C4C2211yescharacteristic
30C2×C4×C5×Dic3C2211yescharacteristic
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#683C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic
36#91559C418yescomplemented
37C2×Dic3⋊Dic5C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×#6668C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic
47C2×Dic3×Dic5C2211yescharacteristic
48#91394—24no—
49C5×C3⋊#95C2211yescharacteristic
50C5×C3⋊#95C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#76289—51nomaximal, Hall
56C2×#4038—31no—
57C2×#4027—31no—
58C2×#4023—31no—
59C5×#388—31no—
60#65261—31no—
61#65246—31no—
62#65246D311yescharacteristic
63#65240—31no—
64C22⋊C4×Dic5—31no—
65#65229—31no—
66C42×Dic5—31no—
67#64958—31no—
68#64955—31no—
69#64938—31no—
70#64936—31no—
71C24×C3×C5C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×Dic15—22no—
76C22×Dic15—22no—
77C22×Dic15C2×C414yes—
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C2×C3×C22⋊D5—22no—
87C2×C3×C22⋊D5—22no—
88C2×C3×C22⋊D5C2×C414yes—
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C2×D5×Dic3—22no—
93C2×D5×Dic3—22no—
94C2×D5×Dic3C2×C414yes—
95C3×C5×C22⋊C4—22no—
96#6719—22no—
97#6712—22no—
98#6712—22no—
99C4×Dic15—22no—
100C4×Dic15D414yescomplemented
101C5×#217—22no—
102C5×#217C2×C414yes—
103C5×Dic3⋊C4—22no—
104C4×C5×Dic3—22no—
105C3×C22⋊Dic5—22no—
106C3×#685—22no—
107C3×#685—22no—
108C3×#683—22no—
109C3×C4×Dic5—22no—
110Dic3⋊Dic5—22no—
111#6668—22no—
112#6668C2×C414yes—
113#6665—22no—
114#6665—22no—
115#6665C2×C414yes—
116Dic3×Dic5—22no—
117Dic3×Dic5—22no—
118Dic3×Dic5—22no—
119Dic3×Dic5—22no—
120Dic3×Dic5C2×C414yes—
121C2×D4×Dic3—51no—
122C2×#877—51no—
123C2×#877—51no—
124C3×#390—51no—
125#5221—51no—
126Dic3×C4⋊C4—51no—
127#4972—51no—
128#4945—51no—
129#4945D511yescharacteristic, complemented
130#4944—51no—
131#4944—51no—
132Dic3×C22⋊C4—51no—
133Dic3×C22⋊C4—51no—
134C42×Dic3—51no—
135#4928—51no—
136C22×C22⋊D5C2×D311yescharacteristic
137C23×Dic5—31no—
138C22×C4×D5—31no—
139C2×C5×C4⋊C4—31no—
140C2×C5×C22⋊C4—31no—
141C2×C5×C22⋊C4—31no—
142C2×C5×C22⋊C4C2×D311yescharacteristic
143C2×C42×C5—31no—
144C2×C22⋊Dic5—31no—
145C2×C22⋊Dic5C2×D311yescharacteristic
146C2×#685—31no—
147C2×#685—31no—
148C2×#685—31no—
149C2×#685C2×D311yescharacteristic
150C2×#685C2×D311yescharacteristic
151C2×C4⋊Dic5—31no—
152C2×#683—31no—
153C2×#683—31no—
154C2×#683—31no—
155C2×#683—31no—
156C2×#683C2×D311yescharacteristic
157C2×C4×Dic5—31no—
158C2×C4×Dic5—31no—
159C2×C4×Dic5—31no—
160C2×C4×Dic5—31no—
161C2×C4×Dic5—31no—
162C2×C4×Dic5—31no—
163C2×C4×Dic5—31no—
164C2×C4×Dic5C2×D311yescharacteristic
165#4038—64no—
166#4027—38no—
167#4023—64no—
168C5×#95—31no—
169C5×#95—31no—
170#3963—31no—
171#3963—31no—
172#3963—31no—
173#3963—31no—
174#2293—151noSylow
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5—21no—
180C23×C3×C5—21no—
181C23×C3×C5C22×C412yes—
182C23×C3×C5C2411yescharacteristic
183C22×C3×D5—21no—
184C22×C3×D5—21no—
185C22×C3×D5—21no—
186C22×C3×D5—21no—
187C22×C3×D5—21no—
188C22×C3×D5—21no—
189C22×C3×D5C22×C412yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5C2×D412yes—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15—28no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15C22×C412yes—
205C2×Dic15C22×C412yes—
206C2×Dic15C2×D412yes—
207C2×Dic15C2×D412yes—
208C2×Dic15#4112yes—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3—21no—
216C2×C5×Dic3—21no—
217C2×C5×Dic3—21no—
218C2×C5×Dic3C22×C412yes—
219C2×C5×Dic3C22×C412yes—
220C2×C5×Dic3#4112yes—
221C3×C22⋊D5—28no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5C22×C412yes—
228C2×C3×Dic5#4112yes—
229C2×C3×Dic5#4112yes—
230C2×C3×Dic5#4112yes—
231D5×Dic3—28no—
232C22×C3×D4—51no—
233C23×Dic3—51no—
234C23×Dic3—51no—
235C2×C3×C4⋊C4—51no—
236C2×C3×C22⋊C4—51no—
237C2×C3×C22⋊C4—51no—
238C2×C3×C22⋊C4—51no—
239C2×C3×C22⋊C4C2×D511yescharacteristic
240C2×C3×C42—51no—
241C2×#217—51no—
242C2×#217—51no—
243C2×#217—51no—
244C2×#217—51no—
245C2×#217C2×D511yescharacteristic
246C2×#217C2×D511yescharacteristic
247D4×Dic3—58no—
248C2×C4⋊Dic3—51no—
249C2×C4⋊Dic3—51no—
250C2×Dic3⋊C4—51no—
251C2×Dic3⋊C4—51no—
252C2×Dic3⋊C4—51no—
253C2×Dic3⋊C4C2×D511yescharacteristic
254C2×C4×Dic3—51no—
255C2×C4×Dic3—51no—
256C2×C4×Dic3—51no—
257C2×C4×Dic3—51no—
258C2×C4×Dic3—51no—
259C2×C4×Dic3—51no—
260C2×C4×Dic3—51no—
261C2×C4×Dic3C2×D511yescharacteristic
262#877—104no—
263#877—104no—
264C3⋊#95—51no—
265C3⋊#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95C2×D511yescharacteristic
269C3⋊#95C2×D511yescharacteristic
270C24×C5C22×D311yescharacteristic
271C23×D5C22×D311yescharacteristic
272C22×C4×C5—31no—
273C22×C4×C5—31no—
274C22×C4×C5—31no—
275C22×C4×C5—31no—
276C22×C4×C5C22×D311yescharacteristic
277C22×C4×C5C22×D311yescharacteristic
278C2×C22⋊D5—22no—
279C2×C22⋊D5—22no—
280C2×C22⋊D5C4×D314yes—
281C22×Dic5—31no—
282C22×Dic5—34no—
283C22×Dic5—31no—
284C22×Dic5—31no—
285C22×Dic5—31no—
286C22×Dic5—62no—
287C22×Dic5—62no—
288C22×Dic5C22×D311yescharacteristic
289C22×Dic5C22×D311yescharacteristic
290C22×Dic5C22×D311yescharacteristic
291C2×C4×D5—34no—
292C2×C4×D5—62no—
293C2×C4×D5—62no—
294C5×C4⋊C4—62no—
295C5×C22⋊C4—22no—
296C5×C22⋊C4—34no—
297C5×C22⋊C4—62no—
298C42×C5—62no—
299C22⋊Dic5—22no—
300C22⋊Dic5—62no—
301#685—22no—
302#685—22no—
303#685—34no—
304#685—62no—
305#685—62no—
306C4⋊Dic5—62no—
307#683—22no—
308#683—34no—
309#683—62no—
310#683—62no—
311#683—62no—
312C4×Dic5—22no—
313C4×Dic5—34no—
314C4×Dic5—34no—
315C4×Dic5—62no—
316C4×Dic5—62no—
317C4×Dic5—62no—
318C4×Dic5—62no—
319C4×Dic5—62no—
320C2×C4×D4—151no—
321C2×#117—151no—
322C2×#117—151no—
323#390—51no—
324#390—151no—
325#389—151no—
326#389—151no—
327#388—31no—
328#388—151no—
329#388—151no—
330#388—151no—
331C4×C4⋊C4—151no—
332C4×C22⋊C4—151no—
333C4×C22⋊C4—151no—
334C43—151no—
335C22×C3×C5—22no—
336C22×C3×C5—22no—
337C22×C3×C5—22no—
338C22×C3×C5—41no—
339C22×C3×C5—41no—
340C22×C3×C5—41no—
341C22×C3×C5—41no—
342C22×C3×C5C23×C411yescharacteristic
343C22×C3×C5C22×D411yescharacteristic
344C22×C3×C5C2×#4111yescharacteristic
345C22×C3×C5C2×#4111yescharacteristic
346C22×C3×C5C2×#4111yescharacteristic
347C22×C3×C5C2×#4111yescharacteristic
348C22×C3×C5C2×#4111yescharacteristic
349C2×C3×D5—22no—
350C2×C3×D5—22no—
351C2×C3×D5—22no—
352C2×C3×D5—41no—
353C2×C3×D5—41no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C3×C4×C5—22no—
357C3×C4×C5—41no—
358Dic15—22no—
359Dic15—22no—
360Dic15—41no—
361Dic15C4×D414yes—
362C3×Dic5—22no—
363C3×Dic5—41no—
364C3×Dic5#11714yescomplemented
365C5×Dic3—22no—
366C5×Dic3—22no—
367C5×Dic3—22no—
368C5×Dic3—41no—
369C24×C3—51no—
370C24×C3C22×D511yescharacteristic
371C2×C3×D4—54no—
372C2×C3×D4—102no—
373C2×C3×D4—102no—
374C22×C3×C4—51no—
375C22×C3×C4—51no—
376C22×C3×C4—51no—
377C22×C3×C4C22×D511yescharacteristic
378C22×C3×C4C22×D511yescharacteristic
379C22×Dic3—51no—
380C22×Dic3—54no—
381C22×Dic3—51no—
382C22×Dic3—51no—
383C22×Dic3—54no—
384C22×Dic3—51no—
385C22×Dic3—102no—
386C22×Dic3—102no—
387C22×Dic3—102no—
388C22×Dic3—102no—
389C22×Dic3C22×D511yescharacteristic
390C22×Dic3C22×D511yescharacteristic
391C22×Dic3C22×D511yescharacteristic
392C22×Dic3C22×D511yescharacteristic
393C3×C4⋊C4—102no—
394C3×C22⋊C4—22no—
395C3×C22⋊C4—102no—
396C3×C22⋊C4—102no—
397C3×C22⋊C4—102no—
398C3×C42—102no—
399#217—22no—
400#217—54no—
401#217—102no—
402#217—102no—
403#217—102no—
404#217C4×D514yes—
405C4⋊Dic3—54no—
406C4⋊Dic3—102no—
407Dic3⋊C4—22no—
408Dic3⋊C4—102no—
409Dic3⋊C4—102no—
410Dic3⋊C4—102no—
411C4×Dic3—22no—
412C4×Dic3—54no—
413C4×Dic3—54no—
414C4×Dic3—102no—
415C4×Dic3—102no—
416C4×Dic3—102no—
417C4×Dic3—102no—
418C4×Dic3—102no—
419C23×C5—21no—
420C23×C5—21no—
421C23×C5—21no—
422C23×C5—21no—
423C23×C5—21no—
424C23×C5—21no—
425C23×C5C2×C4×D312yes—
426C23×C5C23×D311yescharacteristic
427C22×D5—21no—
428C22×D5—21no—
429C22×D5—21no—
430C22×D5—21no—
431C22×D5—21no—
432C22×D5—21no—
433C22×D5C2×C4×D312yes—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—32no—
440C2×C4×C5—32no—
441C2×C4×C5—32no—
442C2×C4×C5—61no—
443C2×C4×C5—61no—
444C2×C4×C5—61no—
445C2×C4×C5—61no—
446C2×C4×C5—61no—
447C2×C4×C5—61no—
448C2×C4×C5—61no—
449C2×C4×C5—61no—
450C2×C4×C5—61no—
451C2×C4×C5D3×D412yes—
452C22⋊D5—28no—
453C2×Dic5—21no—
454C2×Dic5—21no—
455C2×Dic5—21no—
456C2×Dic5—21no—
457C2×Dic5—21no—
458C2×Dic5—32no—
459C2×Dic5—32no—
460C2×Dic5—32no—
461C2×Dic5—32no—
462C2×Dic5—32no—
463C2×Dic5—68no—
464C2×Dic5—61no—
465C2×Dic5—61no—
466C2×Dic5—61no—
467C2×Dic5—61no—
468C2×Dic5—61no—
469C2×Dic5—61no—
470C2×Dic5—61no—
471C2×Dic5C2×C4×D312yes—
472C2×Dic5#23712yes—
473C2×Dic5#23712yes—
474C2×Dic5#23712yes—
475C4×D5—68no—
476C22×D4—51no—
477C23×C4—151no—
478C23×C4—151no—
479C4×D4—158no—
480#117—304no—
481#117—304no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—51no—
484C2×C4⋊C4—151no—
485C2×C4⋊C4—151no—
486C2×C4⋊C4—151no—
487C2×C4⋊C4—151no—
488C2×C4⋊C4—151no—
489C2×C22⋊C4—31no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—51no—
492C2×C22⋊C4—51no—
493C2×C22⋊C4—51no—
494C2×C22⋊C4—151no—
495C2×C22⋊C4—151no—
496C2×C22⋊C4—151no—
497C2×C22⋊C4—151no—
498C2×C22⋊C4D3×D511yescharacteristic
499C2×C42—31no—
500C2×C42—51no—
501C2×C42—151no—
502C2×C42—151no—
503C2×C42—151no—
504C2×C42—151no—
505C2×C42—151no—
506C2×C42—151no—
507C2×C42—151no—
508#95—31no—
509#95—31no—
510#95—151no—
511#95—151no—
512#95—151no—
513#95—151no—
514C2×C3×C5—42no—
515C2×C3×C5C2×#11711yescharacteristic
516C2×C3×C5C2×C4×D411yescharacteristic
517C2×C3×C5C4×#4111yescharacteristic
518C2×C3×C5#52911yescharacteristic
519C2×C3×C5#52911yescharacteristic
520C2×C3×C5#53211yescharacteristic
521C2×C3×C5#53211yescharacteristic
522C3×D5—42no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—52no—
530C23×C3—101no—
531C23×C3—101no—
532C23×C3—101no—
533C23×C3—101no—
534C23×C3—101no—
535C23×C3—101no—
536C23×C3C2×C4×D512yes—
537C23×C3C23×D511yescharacteristic
538C3×D4—108no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—52no—
545C2×C3×C4—52no—
546C2×C3×C4—52no—
547C2×C3×C4—52no—
548C2×C3×C4—101no—
549C2×C3×C4—101no—
550C2×C3×C4—101no—
551C2×C3×C4—101no—
552C2×C3×C4—101no—
553C2×C3×C4D4×D512yes—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—52no—
564C2×Dic3—52no—
565C2×Dic3—52no—
566C2×Dic3—52no—
567C2×Dic3—52no—
568C2×Dic3—108no—
569C2×Dic3—108no—
570C2×Dic3—101no—
571C2×Dic3—101no—
572C2×Dic3—101no—
573C2×Dic3—101no—
574C2×Dic3—101no—
575C2×Dic3—101no—
576C2×Dic3—101no—
577C2×Dic3C2×C4×D512yes—
578C2×Dic3C2×C4×D512yes—
579C2×Dic3#71112yes—
580C22×C5—22no—
581C22×C5—22no—
582C22×C5—22no—
583C22×C5—41no—
584C22×C5—41no—
585C22×C5—41no—
586C22×C5—41no—
587C22×C5C22×C4×D311yescharacteristic
588C22×C5C2×D3×D411yescharacteristic
589C22×C5C2×#23711yescharacteristic
590C22×C5C2×#23711yescharacteristic
591C22×C5C2×#23711yescharacteristic
592C22×C5D3×#4111yescharacteristic
593C22×C5D3×#4111yescharacteristic
594C2×D5—22no—
595C2×D5—22no—
596C2×D5—22no—
597C2×D5—41no—
598C2×D5—41no—
599C2×D5—41no—
600C2×D5—41no—
601C4×C5—22no—
602C4×C5—41no—
603C4×C5—62no—
604C4×C5—62no—
605C4×C5—62no—
606C4×C5—121no—
607Dic5—22no—
608Dic5—34no—
609Dic5—41no—
610Dic5—62no—
611Dic5—62no—
612Dic5—121no—
613Dic5#87714yescomplemented
614C24—51no—
615C24C2×D3×D511yescharacteristic
616C2×D4—54no—
617C2×D4—102no—
618C2×D4—102no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—51no—
624C22×C4—51no—
625C22×C4—51no—
626C22×C4—154no—
627C22×C4—151no—
628C22×C4—154no—
629C22×C4—151no—
630C22×C4—151no—
631C22×C4—151no—
632C22×C4—302no—
633C22×C4—302no—
634C22×C4—302no—
635C22×C4—302no—
636C22×C4C2×D3×D511yescharacteristic
637C22×C4C2×D3×D511yescharacteristic
638C4⋊C4—62no—
639C4⋊C4—102no—
640C4⋊C4—154no—
641C4⋊C4—302no—
642C4⋊C4—302no—
643C4⋊C4—302no—
644C4⋊C4—302no—
645C22⋊C4—22no—
646C22⋊C4—34no—
647C22⋊C4—62no—
648C22⋊C4—102no—
649C22⋊C4—102no—
650C22⋊C4—102no—
651C22⋊C4—154no—
652C22⋊C4—302no—
653C22⋊C4—302no—
654C22⋊C4—302no—
655C42—62no—
656C42—102no—
657C42—154no—
658C42—154no—
659C42—302no—
660C42—302no—
661C42—302no—
662C42—302no—
663C42—302no—
664C3×C5#229311yescharacteristic, complemented, Hall
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—22no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—102no—
673C22×C3—102no—
674C22×C3—102no—
675C22×C3—201no—
676C22×C3—201no—
677C22×C3—201no—
678C22×C3—201no—
679C22×C3C22×C4×D511yescharacteristic
680C22×C3C2×D4×D511yescharacteristic
681C22×C3C2×#71111yescharacteristic
682C22×C3D5×#4111yescharacteristic
683C22×C3D5×#4111yescharacteristic
684C22×C3D5×#4111yescharacteristic
685C22×C3D5×#4111yescharacteristic
686C3×C4—22no—
687C3×C4—41no—
688C3×C4—54no—
689C3×C4—102no—
690C3×C4—201no—
691Dic3—22no—
692Dic3—22no—
693Dic3—22no—
694Dic3—41no—
695Dic3—54no—
696Dic3—102no—
697Dic3—102no—
698Dic3—201no—
699C2×C5—42no—
700C2×C5C2×#87711yescharacteristic
701C2×C5C4×#23711yescharacteristic
702C2×C5C4×D3×D411yescharacteristic
703C2×C5#559611yescharacteristic
704C2×C5#560011yescharacteristic
705C2×C5#568011yescharacteristic
706C2×C5#571611yescharacteristic
707D5—42no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—52no—
715C23—101no—
716C23—101no—
717C23—101no—
718C23—101no—
719C23—101no—
720C23—101no—
721C23C4×D3×D512yes—
722C23C22×D3×D511yescharacteristic
723D4—108no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—52no—
733C2×C4—52no—
734C2×C4—52no—
735C2×C4—52no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—101no—
746C2×C4—101no—
747C2×C4—101no—
748C2×C4—101no—
749C2×C4—101no—
750C2×C4—152no—
751C2×C4—152no—
752C2×C4—152no—
753C2×C4—152no—
754C2×C4—152no—
755C2×C4—308no—
756C2×C4—308no—
757C2×C4—301no—
758C2×C4—301no—
759C2×C4—301no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—301no—
763C2×C4—301no—
764C2×C4#679012yes—
765C2×C3—42no—
766C2×C3—202no—
767C2×C3D5×#11711yescharacteristic
768C2×C3C4×#71111yescharacteristic
769C2×C3C4×D4×D511yescharacteristic
770C2×C3#6593011yescharacteristic
771C2×C3#6598311yescharacteristic
772C2×C3#6600211yescharacteristic
773C2×C3#6604011yescharacteristic
774C5#7628911yescharacteristic, complemented, Sylow
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—102no—
783C22—102no—
784C22—102no—
785C22—201no—
786C22—201no—
787C22—201no—
788C22—201no—
789C22C2×C4×D3×D511yescharacteristic
790C22#9201611yescharacteristic
791C22D5×#23711yescharacteristic
792C22D5×#23711yescharacteristic
793C22D5×#23711yescharacteristic
794C22D3×#71111yescharacteristic
795C22C2×#679011yescharacteristic
796C4—22no—
797C4—41no—
798C4—54no—
799C4—62no—
800C4—62no—
801C4—62no—
802C4—102no—
803C4—121no—
804C4—154no—
805C4—201no—
806C4—302no—
807C4—302no—
808C4—601no—
809C3#1060718111yescharacteristic, complemented, Sylow
810C2—42no—
811C2—202no—
812C2D5×#87711yescharacteristic
813C2#1175282011yescharacteristic
814C2#1175291011yescharacteristic
815C2#1175293711yescharacteristic
816C2C4×#679011yescharacteristic
817C2#1175482011yescharacteristic
818C2#1175482211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2293
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91766C2semidirect
3. C2×#91394C2semidirect
4. C5×#4945C2semidirect
7. #11749487C2semidirect
8. #11749478C2semidirect
9. #11748884C2semidirect
10. #11748801C2semidirect
11. #11748707C2semidirect
12. #11748706C2semidirect
13. #11748637C2semidirect
14. C4×Dic3×Dic5C2semidirect
15. #11748627C2semidirect
36. #91559C4semidirect
100. C4×Dic15D4semidirect
129. #4945D5semidirect
364. C3×Dic5#117semidirect
613. Dic5#877semidirect
664. C3×C5#2293semidirect
774. C5#76289semidirect
809. C3#10607181semidirect

Maximal subgroups

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

subgroupindex
C2×#917662
C2×#915592
C2×#913942
C5×#49452
C3×#652462
#117494892
#117494872
#117494782
#117488842
#117488012
#117487072
#117487062
#117486372
C4×Dic3×Dic52
#117486272
#106071813
#762895