Finite Group Databasebeta

← #14322993

Subgroups — #14322993

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic5×#67C211yesmaximal, characteristic
2#11751047C211yesmaximal, characteristic, complemented
3C5×#4958C211yesmaximal, characteristic
4C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
5#11749512C211yesmaximal, characteristic, complemented
6#11749501C211yesmaximal, characteristic
7C2×#90994C211yesmaximal, characteristic, complemented
8#11748887C211yesmaximal, characteristic, complemented
9#11748880C211yesmaximal, characteristic, complemented
10#11748816C211yesmaximal, characteristic, complemented
11#11748814C211yesmaximal, characteristic, complemented
12#11748715C211yesmaximal, characteristic, complemented
13#11748714C211yesmaximal, characteristic, complemented
14#11748647C211yesmaximal, characteristic, complemented
15#11748644C211yesmaximal, characteristic, complemented
16#10606394—31nomaximal, Hall
17C23×Dic15C2211yescharacteristic
18C22×C5×#67C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C22×D3×Dic5C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6712C2211yescharacteristic
25C2×#6712C2211yescharacteristic
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31Dic5×#67C418yescomplemented
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×#6669C2211yescharacteristic
34C2×#6669C2211yescharacteristic
35C2×(C2×D3)⋊Dic5C2211yescharacteristic
36C2×(C2×D3)⋊Dic5C2211yescharacteristic
37C2×(C2×D3)⋊Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39#91115C2211yescharacteristic
40#91115C2211yescharacteristic
41C5×C3⋊#95C2211yescharacteristic
42C5×C3⋊#95C2211yescharacteristic
43C3×#3963C2211yescharacteristic
44C3×#3963C2211yescharacteristic
45#90994C2211yescharacteristic
46#90994C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#73568—51nomaximal, Hall
54C2×D4×Dic5—31no—
55C5×#386—31no—
56#65509—31no—
57#65499—31no—
58C2×#3963—31no—
59#65235—31no—
60#65234—31no—
61#65233—31no—
62#65232—31no—
63#65231—31no—
64C22⋊C4×Dic5D311yescharacteristic, complemented
65#64943—31no—
66#64942—31no—
67#64940—31no—
68#64939—31no—
69C24×C3×C5C2311yescharacteristic
70C23×C5×D3C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×Dic15—22no—
74C22×Dic15—41no—
75C22×Dic15—41no—
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C2×C5×#67—22no—
81C2×C5×#67—22no—
82C2×C5×#67C2×C414yes—
83C22×C5×Dic3—22no—
84C22×C5×Dic3—41no—
85C22×C5×Dic3—41no—
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C3×Dic5—41no—
90C22×C3×Dic5—41no—
91C22×C3×Dic5C2×C414yes—
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C2×D3×Dic5—41no—
97C2×D3×Dic5—41no—
98C2×D3×Dic5C2×C414yescomplemented
99C3×C5×C22⋊C4—22no—
100#6719C2×C414yes—
101#6712—41no—
102#6712—41no—
103C5×(C2×D3)⋊C4—41no—
104C5×(C2×D3)⋊C4—41no—
105C3×C22⋊Dic5—22no—
106C3×C4×Dic5—41no—
107C3×C4×Dic5—41no—
108Dic3⋊Dic5C2×C414yescomplemented
109#6669—41no—
110#6669—41no—
111(C2×D3)⋊Dic5—41no—
112(C2×D3)⋊Dic5—41no—
113(C2×D3)⋊Dic5C2×C414yescomplemented
114Dic3×Dic5C2×C414yescomplemented
115C2×C4×#67—51no—
116C3×C4×C22⋊C4—51no—
117C2×C3⋊#95—51no—
118#4958—51no—
119#4958D511yescharacteristic
120#4946—51no—
121#4946—51no—
122#4940—51no—
123#4940—51no—
124#4933—51no—
125#4933—51no—
126#4667—51no—
127#4664—51no—
128#4651—51no—
129#4650—51no—
130C22×C5×D4—31no—
131C23×C4×C5—31no—
132C23×Dic5—31no—
133C23×Dic5—31no—
134C23×Dic5C2×D311yescharacteristic
135C2×C5×C22⋊C4—31no—
136C2×C5×C22⋊C4—31no—
137C2×C5×C22⋊C4C2×D311yescharacteristic
138C2×C22⋊Dic5—31no—
139C2×C22⋊Dic5—31no—
140C2×C22⋊Dic5—31no—
141C2×C22⋊Dic5—31no—
142C2×C22⋊Dic5C2×D311yescharacteristic
143D4×Dic5—38no—
144C2×C4⋊Dic5—31no—
145C2×#683—31no—
146C2×#683—31no—
147C2×#683—31no—
148C2×#683—31no—
149C2×C4×Dic5—31no—
150C2×C4×Dic5C2×D311yescharacteristic
151C2×C4×Dic5C2×D311yescharacteristic
152C5×#95—31no—
153C5×#95—31no—
154#3963—31no—
155#3963—31no—
156#3963—31no—
157#3963—31no—
158#3963—31no—
159#3963—31no—
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963—31no—
164#3963C2×D311yescharacteristic
165#3963C2×D311yescharacteristic
166#2318—151noSylow
167C23×C3×C5—21no—
168C23×C3×C5—21no—
169C23×C3×C5—21no—
170C23×C3×C5—21no—
171C23×C3×C5C22×C412yes—
172C23×C3×C5#4112yes—
173C23×C3×C5#4112yes—
174C23×C3×C5C2411yescharacteristic
175C22×C5×D3—21no—
176C22×C5×D3—21no—
177C22×C5×D3—21no—
178C22×C5×D3—21no—
179C22×C5×D3—21no—
180C22×C5×D3—21no—
181C22×C5×D3C22×C412yes—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—44no—
199C2×Dic15C22×C412yes—
200C2×Dic15C22×C412yes—
201C5×#67—28no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—44no—
211C2×C5×Dic3C22×C412yes—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—44no—
223C2×C3×Dic5C22×C412yes—
224C2×C3×Dic5C22×C412yes—
225D3×Dic5—44no—
226C23×C3×C4—51no—
227C22×#67C2×D511yescharacteristic
228C23×Dic3—51no—
229C23×Dic3C2×D511yescharacteristic
230C22×C4×D3—51no—
231C2×C3×C22⋊C4—51no—
232C2×C3×C22⋊C4C2×D511yescharacteristic
233C2×C3×C42—51no—
234C2×C3×C42—51no—
235C2×#217—51no—
236C4×#67—58no—
237C2×(C2×D3)⋊C4—51no—
238C2×(C2×D3)⋊C4—51no—
239C2×(C2×D3)⋊C4—51no—
240C2×(C2×D3)⋊C4C2×D511yescharacteristic
241C2×(C2×D3)⋊C4C2×D511yescharacteristic
242C2×Dic3⋊C4—51no—
243C2×Dic3⋊C4—51no—
244C2×Dic3⋊C4—51no—
245C2×Dic3⋊C4—51no—
246C2×Dic3⋊C4—51no—
247C2×C4×Dic3—51no—
248C3×#95—51no—
249C3×#95—51no—
250C3⋊#95—51no—
251C3⋊#95—51no—
252C3⋊#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95—51no—
259C3⋊#95—51no—
260C3⋊#95C2×D511yescharacteristic
261C3⋊#95C2×D511yescharacteristic
262C24×C5—31no—
263C24×C5C22×D311yescharacteristic
264C2×C5×D4—34no—
265C2×C5×D4—62no—
266C2×C5×D4—62no—
267C22×C4×C5—31no—
268C22×C4×C5—31no—
269C22×C4×C5—31no—
270C22×C4×C5—62no—
271C22×C4×C5—121no—
272C22×C4×C5—121no—
273C22×C4×C5C22×D311yescharacteristic
274C22×C4×C5C22×D311yescharacteristic
275C22×Dic5—31no—
276C22×Dic5—31no—
277C22×Dic5—34no—
278C22×Dic5—31no—
279C22×Dic5—31no—
280C22×Dic5—41no—
281C22×Dic5—41no—
282C22×Dic5—62no—
283C22×Dic5—121no—
284C22×Dic5—121no—
285C22×Dic5—121no—
286C22×Dic5—121no—
287C22×Dic5C4×D314yes—
288C22×Dic5C22×D311yescharacteristic
289C22×Dic5C22×D311yescharacteristic
290C22×Dic5C22×D311yescharacteristic
291C22×Dic5C22×D311yescharacteristic
292C5×C22⋊C4—22no—
293C5×C22⋊C4—121no—
294C5×C22⋊C4—121no—
295C22⋊Dic5—22no—
296C22⋊Dic5—34no—
297C22⋊Dic5—34no—
298C22⋊Dic5—121no—
299C22⋊Dic5—121no—
300C4⋊Dic5—34no—
301#683—121no—
302#683—121no—
303#683—121no—
304#683—121no—
305C4×Dic5—34no—
306C4×Dic5—41no—
307C4×Dic5—41no—
308C2×C4×D4—151no—
309#388—151no—
310#388—151no—
311#387—151no—
312#387—151no—
313#386—31no—
314#386—151no—
315#385—151no—
316#385—151no—
317#383—151no—
318#382—151no—
319#381—151no—
320#380—151no—
321C4×C22⋊C4—51no—
322C2×#95—151no—
323C22×C3×C5—22no—
324C22×C3×C5—22no—
325C22×C3×C5—22no—
326C22×C3×C5—22no—
327C22×C3×C5—22no—
328C22×C3×C5—22no—
329C22×C3×C5#11714yes—
330C22×C3×C5C23×C411yescharacteristic
331C22×C3×C5C2×#4111yescharacteristic
332C22×C3×C5C2×#4111yescharacteristic
333C22×C3×C5H(5,𝔽2)11yescharacteristic
334C22×C3×C5H(5,𝔽2)11yescharacteristic
335C22×C3×C5H(5,𝔽2)11yescharacteristic
336C22×C3×C52−1+411yescharacteristic
337C2×C5×D3—22no—
338C2×C5×D3—22no—
339C2×C5×D3—22no—
340C2×C5×D3—41no—
341C2×C5×D3—41no—
342C2×C5×D3—41no—
343C2×C5×D3—41no—
344C3×C4×C5—41no—
345C3×C4×C5—41no—
346Dic15—22no—
347Dic15—22no—
348Dic15—41no—
349Dic15—41no—
350C3×Dic5—22no—
351C3×Dic5—22no—
352C3×Dic5—41no—
353C3×Dic5—41no—
354C5×Dic3—22no—
355C5×Dic3—41no—
356C5×Dic3—41no—
357C24×C3C22×D511yescharacteristic
358C23×D3C22×D511yescharacteristic
359C22×C3×C4—51no—
360C22×C3×C4—51no—
361C22×C3×C4—54no—
362C22×C3×C4—51no—
363C22×C3×C4—51no—
364C22×C3×C4—201no—
365C22×C3×C4—201no—
366C22×C3×C4C22×D511yescharacteristic
367C22×C3×C4C22×D511yescharacteristic
368C2×#67—22no—
369C2×#67—22no—
370C2×#67C4×D514yes—
371C22×Dic3—22no—
372C22×Dic3—41no—
373C22×Dic3—41no—
374C22×Dic3—51no—
375C22×Dic3—51no—
376C22×Dic3—51no—
377C22×Dic3—51no—
378C22×Dic3—102no—
379C22×Dic3—201no—
380C22×Dic3—201no—
381C22×Dic3C22×D511yescharacteristic
382C22×Dic3C22×D511yescharacteristic
383C22×Dic3C22×D511yescharacteristic
384C2×C4×D3—54no—
385C2×C4×D3—201no—
386C2×C4×D3—201no—
387C3×C22⋊C4—22no—
388C3×C22⋊C4—102no—
389C3×C42—201no—
390C3×C42—201no—
391#217—54no—
392(C2×D3)⋊C4—41no—
393(C2×D3)⋊C4—41no—
394(C2×D3)⋊C4—54no—
395(C2×D3)⋊C4—201no—
396(C2×D3)⋊C4—201no—
397Dic3⋊C4—54no—
398Dic3⋊C4—201no—
399Dic3⋊C4—201no—
400Dic3⋊C4—201no—
401Dic3⋊C4—201no—
402C4×Dic3—54no—
403C23×C5—21no—
404C23×C5—21no—
405C23×C5—21no—
406C23×C5—21no—
407C23×C5—32no—
408C23×C5—61no—
409C23×C5—61no—
410C23×C5—61no—
411C23×C5—61no—
412C23×C5—61no—
413C23×C5—61no—
414C23×C5C2×C4×D312yes—
415C23×C5#23512yes—
416C23×C5#23512yes—
417C23×C5C23×D311yescharacteristic
418C5×D4—68no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—21no—
425C2×C4×C5—32no—
426C2×C4×C5—61no—
427C2×C4×C5—61no—
428C2×C4×C5—61no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×C4×C5—61no—
432C2×C4×C5—61no—
433C2×C4×C5—61no—
434C2×C4×C5—124no—
435C2×Dic5—21no—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—32no—
446C2×Dic5—32no—
447C2×Dic5—44no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452C2×Dic5—61no—
453C2×Dic5—61no—
454C2×Dic5—61no—
455C2×Dic5—61no—
456C2×Dic5—61no—
457C2×Dic5—61no—
458C2×Dic5—124no—
459C2×Dic5—124no—
460C2×Dic5C2×C4×D312yes—
461C2×Dic5C2×C4×D312yes—
462C22×D4—31no—
463C23×C4—31no—
464C23×C4—51no—
465C23×C4—151no—
466C23×C4—151no—
467C4×D4—158no—
468C2×C4⋊C4—151no—
469C2×C4⋊C4—151no—
470C2×C4⋊C4—151no—
471C2×C4⋊C4—151no—
472C2×C4⋊C4—151no—
473C2×C22⋊C4—31no—
474C2×C22⋊C4—31no—
475C2×C22⋊C4—51no—
476C2×C22⋊C4—151no—
477C2×C22⋊C4—151no—
478C2×C22⋊C4—151no—
479C2×C22⋊C4—151no—
480C2×C22⋊C4D3×D511yescharacteristic
481C2×C42—51no—
482C2×C42—51no—
483C2×C42—151no—
484#95—31no—
485#95—31no—
486#95—51no—
487#95—51no—
488#95—151no—
489#95—151no—
490#95—151no—
491#95—151no—
492#95—151no—
493#95—151no—
494#95—151no—
495#95—151no—
496#95—151no—
497#95—151no—
498C2×C3×C5—24no—
499C2×C3×C5C2×#11711yescharacteristic
500C2×C3×C5#51811yescharacteristic
501C2×C3×C5#52011yescharacteristic
502C2×C3×C5#53811yescharacteristic
503C2×C3×C5#53811yescharacteristic
504C2×C3×C5#53911yescharacteristic
505C2×C3×C5#53911yescharacteristic
506C5×D3—42no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3C2×C4×D512yes—
512C23×C3#71112yes—
513C23×C3#71112yes—
514C23×C3C23×D511yescharacteristic
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—21no—
521C22×D3C2×C4×D512yes—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—52no—
529C2×C3×C4—52no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—101no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4—101no—
538C2×C3×C4—101no—
539C2×C3×C4—101no—
540C2×C3×C4—204no—
541#67—28no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—44no—
551C2×Dic3—52no—
552C2×Dic3—52no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—101no—
558C2×Dic3—101no—
559C2×Dic3—101no—
560C2×Dic3—101no—
561C2×Dic3—101no—
562C2×Dic3—101no—
563C2×Dic3—204no—
564C2×Dic3C2×C4×D512yes—
565C4×D3—204no—
566C22×C5—22no—
567C22×C5—22no—
568C22×C5—22no—
569C22×C5—22no—
570C22×C5—22no—
571C22×C5—22no—
572C22×C5—62no—
573C22×C5—62no—
574C22×C5—62no—
575C22×C5—121no—
576C22×C5—121no—
577C22×C5—121no—
578C22×C5—121no—
579C22×C5#87214yes—
580C22×C5C22×C4×D311yescharacteristic
581C22×C5C2×#23511yescharacteristic
582C22×C5C2×#23511yescharacteristic
583C22×C5#100411yescharacteristic
584C22×C5#100411yescharacteristic
585C22×C5#100911yescharacteristic
586C22×C5#101011yescharacteristic
587C4×C5—41no—
588C4×C5—41no—
589C4×C5—62no—
590C4×C5—121no—
591C4×C5—121no—
592Dic5—22no—
593Dic5—22no—
594Dic5—41no—
595Dic5—41no—
596Dic5—62no—
597Dic5—62no—
598Dic5—121no—
599Dic5—121no—
600C24—31no—
601C24C2×D3×D511yescharacteristic
602C2×D4—34no—
603C2×D4—62no—
604C2×D4—62no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—51no—
609C22×C4—51no—
610C22×C4—54no—
611C22×C4—51no—
612C22×C4—51no—
613C22×C4—62no—
614C22×C4—121no—
615C22×C4—121no—
616C22×C4—154no—
617C22×C4—151no—
618C22×C4—151no—
619C22×C4—151no—
620C22×C4—151no—
621C22×C4—201no—
622C22×C4—201no—
623C22×C4—302no—
624C22×C4—601no—
625C22×C4—601no—
626C22×C4—601no—
627C22×C4—601no—
628C22×C4C2×D3×D511yescharacteristic
629C22×C4C2×D3×D511yescharacteristic
630C4⋊C4—154no—
631C4⋊C4—601no—
632C4⋊C4—601no—
633C4⋊C4—601no—
634C4⋊C4—601no—
635C22⋊C4—22no—
636C22⋊C4—102no—
637C22⋊C4—121no—
638C22⋊C4—121no—
639C22⋊C4—154no—
640C22⋊C4—154no—
641C22⋊C4—601no—
642C22⋊C4—601no—
643C42—154no—
644C42—201no—
645C42—201no—
646C3×C5#231811yescharacteristic, complemented, Hall
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—22no—
653C22×C3#402314yes—
654C22×C3C22×C4×D511yescharacteristic
655C22×C3C2×#71111yescharacteristic
656C22×C3C2×#71111yescharacteristic
657C22×C3#414411yescharacteristic
658C22×C3#414411yescharacteristic
659C22×C3#414911yescharacteristic
660C22×C3#415011yescharacteristic
661C2×D3—22no—
662C2×D3—22no—
663C2×D3—22no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—102no—
671C3×C4—102no—
672C3×C4—201no—
673C3×C4—201no—
674Dic3—22no—
675Dic3—41no—
676Dic3—41no—
677Dic3—102no—
678Dic3—102no—
679Dic3—201no—
680Dic3—201no—
681C2×C5—24no—
682C2×C5—122no—
683C2×C5C2×#87211yescharacteristic
684C2×C5#548611yescharacteristic
685C2×C5#552311yescharacteristic
686C2×C5#556011yescharacteristic
687C2×C5#556011yescharacteristic
688C2×C5#556411yescharacteristic
689C2×C5#556411yescharacteristic
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—32no—
695C23—61no—
696C23—61no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23#677212yes—
702C23C4×D3×D512yes—
703C23#678212yes—
704C23C22×D3×D511yescharacteristic
705D4—68no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—32no—
713C2×C4—52no—
714C2×C4—52no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—101no—
724C2×C4—101no—
725C2×C4—101no—
726C2×C4—101no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—101no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—124no—
734C2×C4—152no—
735C2×C4—152no—
736C2×C4—204no—
737C2×C4—301no—
738C2×C4—301no—
739C2×C4—301no—
740C2×C4—301no—
741C2×C4—301no—
742C2×C4—301no—
743C2×C4—301no—
744C2×C4—301no—
745C2×C4—301no—
746C2×C4—301no—
747C2×C4—604no—
748C2×C4—604no—
749C2×C3—24no—
750C2×C3C2×#402311yescharacteristic
751C2×C3#6587911yescharacteristic
752C2×C3#6588011yescharacteristic
753C2×C3#6592711yescharacteristic
754C2×C3#6593611yescharacteristic
755C2×C3#6595111yescharacteristic
756C2×C3#6599911yescharacteristic
757D3—42no—
758C5#7356811yescharacteristic, complemented, Sylow
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—62no—
766C22—62no—
767C22—62no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22#9139814yes—
773C22C2×#677211yescharacteristic
774C22C2×C4×D3×D511yescharacteristic
775C22#9202011yescharacteristic
776C22#9202511yescharacteristic
777C22#9202611yescharacteristic
778C22#9202711yescharacteristic
779C22C2×#678211yescharacteristic
780C4—41no—
781C4—41no—
782C4—62no—
783C4—102no—
784C4—102no—
785C4—121no—
786C4—121no—
787C4—201no—
788C4—201no—
789C4—302no—
790C4—302no—
791C4—601no—
792C4—601no—
793C3#1060639411yescharacteristic, complemented, Sylow
794C2—24no—
795C2—122no—
796C2#1175282411yescharacteristic
797C2#1175317011yescharacteristic
798C2#1175317811yescharacteristic
799C2#1175320011yescharacteristic
800C2C2×#9139811yescharacteristic
801C2#1175491511yescharacteristic
802C2#1175492111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×#67C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2318
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
2. #11751047C2semidirect
4. C3×C22⋊C4×Dic5C2semidirect
5. #11749512C2semidirect
7. C2×#90994C2semidirect
8. #11748887C2semidirect
9. #11748880C2semidirect
10. #11748816C2semidirect
11. #11748814C2semidirect
12. #11748715C2semidirect
13. #11748714C2semidirect
14. #11748647C2semidirect
15. #11748644C2semidirect
31. Dic5×#67C4semidirect
64. C22⋊C4×Dic5D3semidirect
98. C2×D3×Dic5C2×C4semidirect
108. Dic3⋊Dic5C2×C4semidirect
113. (C2×D3)⋊Dic5C2×C4semidirect
114. Dic3×Dic5C2×C4semidirect
646. C3×C5#2318semidirect
758. C5#73568semidirect
793. C3#10606394semidirect

Maximal subgroups

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

subgroupindex
C2×Dic5×#672
#117510472
C5×#49582
C3×C22⋊C4×Dic52
#117495122
#117495012
C2×#909942
#117488872
#117488802
#117488162
#117488142
#117487152
#117487142
#117486472
#117486442
#106063943
#735685