Finite Group Databasebeta

← #14325880

Subgroups — #14325880

Order 1920.

1080 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#936C211yesmaximal, characteristic
2#11751321C211yesmaximal, characteristic
3C3×#65509C211yesmaximal, characteristic
4#11749517C211yesmaximal, characteristic, complemented
5#11749509C211yesmaximal, characteristic, complemented
6#11749487C211yesmaximal, characteristic, complemented
7#11749479C211yesmaximal, characteristic, complemented
8#11749479C211yesmaximal, characteristic, complemented
9#11749478C211yesmaximal, characteristic, complemented
10#11749478C211yesmaximal, characteristic, complemented
11Dic5×#217C211yesmaximal, characteristic, complemented
12#11748692C211yesmaximal, characteristic, complemented
13#11748692C211yesmaximal, characteristic, complemented
14#11748667C211yesmaximal, characteristic, complemented
15#11748618C211yesmaximal, characteristic, complemented
16#10614685—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C5×Dic6C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C2×#6719C2211yescharacteristic
22C2×#6719C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×C5×#217C2211yescharacteristic
25C2×C5×#217C2211yescharacteristic
26C2×C5×#217C2211yescharacteristic
27C2×C5×#217C2211yescharacteristic
28C5×#936C418yescomplemented
29C2×C4×C5×Dic3C2211yescharacteristic
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×Dic3⋊Dic5C2211yescharacteristic
34C2×Dic3⋊Dic5C2211yescharacteristic
35C2×Dic3⋊Dic5C2211yescharacteristic
36C2×Dic3⋊Dic5C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43C3×#3963C2211yescharacteristic
44C3×#3963C2211yescharacteristic
45#90994C2211yescharacteristic
46#90994C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#74671—51nomaximal, Hall
54C2×C5×#124—31no—
55#65519—31no—
56#65519—31no—
57#65509—31no—
58#65509D311yescharacteristic
59#65240—31no—
60#65240—31no—
61#65240—31no—
62#65240—31no—
63#65239—31no—
64#65239—31no—
65C22⋊C4×Dic5—31no—
66C22⋊C4×Dic5—31no—
67#65226—31no—
68C4×C4⋊Dic5—31no—
69C24×C3×C5C2311yescharacteristic
70C24×C3×C5C2311yescharacteristic
71C2×C3×C5×D4—41no—
72C2×C3×C5×D4—41no—
73C2×C3×C5×D4C2×C414yes—
74C22×C3×C4×C5C2311yescharacteristic
75C22×Dic15—22no—
76C22×Dic15—41no—
77C22×Dic15—41no—
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C2×C5×Dic6—41no—
87C2×C5×Dic6—41no—
88C2×C5×Dic6C2×C414yescomplemented
89C22×C3×Dic5—22no—
90C22×C3×Dic5—41no—
91C22×C3×Dic5—41no—
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96#6719—22no—
97#6719—41no—
98#6719—41no—
99C5×#217C2×C414yescomplemented
100C5×#217C2×C414yescomplemented
101C5×#217C2×C414yescomplemented
102C5×#217C2×C414yescomplemented
103C4×C5×Dic3C2×C414yescomplemented
104C3×C22⋊Dic5—22no—
105C3×C22⋊Dic5—41no—
106C3×C22⋊Dic5—41no—
107Dic3⋊Dic5—22no—
108Dic3⋊Dic5—22no—
109Dic3⋊Dic5—41no—
110Dic3⋊Dic5—41no—
111Dic3×Dic5—41no—
112Dic3×Dic5—41no—
113Dic3×Dic5—41no—
114Dic3×Dic5—41no—
115C2×#936D511yescharacteristic
116C3×#386—51no—
117#5220—51no—
118#5210—51no—
119C4×#217—51no—
120#4946—51no—
121#4945—51no—
122#4945—51no—
123#4944—51no—
124#4944—51no—
125Dic3×C22⋊C4—51no—
126#4651—51no—
127#4649—51no—
128#4646—51no—
129#4646—51no—
130C22×C5×Q8—31no—
131C22×C5×D4C2×D311yescharacteristic
132C23×Dic5—31no—
133C23×Dic5C2×D311yescharacteristic
134C5×#124—38no—
135C2×C5×C22⋊C4—31no—
136C2×C5×C22⋊C4—31no—
137C2×C5×C22⋊C4—31no—
138C2×C5×C22⋊C4—31no—
139C2×C42×C5—31no—
140C2×C22⋊Dic5—31no—
141C2×C22⋊Dic5—31no—
142C2×C22⋊Dic5—31no—
143C2×C22⋊Dic5C2×D311yescharacteristic
144C2×C22⋊Dic5C2×D311yescharacteristic
145C2×C22⋊Dic5C2×D311yescharacteristic
146C2×C4⋊Dic5—31no—
147C2×C4⋊Dic5—31no—
148C2×C4⋊Dic5—31no—
149C2×C4⋊Dic5—31no—
150C2×C4×Dic5—31no—
151C2×C4×Dic5—31no—
152C2×C4×Dic5—31no—
153C2×C4×Dic5—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#2337—151noSylow
167C23×C3×C5—21no—
168C23×C3×C5—21no—
169C23×C3×C5—21no—
170C23×C3×C5—21no—
171C23×C3×C5—21no—
172C23×C3×C5—21no—
173C23×C3×C5—21no—
174C23×C3×C5—21no—
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5C22×C412yes—
180C23×C3×C5C22×C412yes—
181C23×C3×C5C2411yescharacteristic
182C3×C5×D4—44no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5C22×C412yes—
186C2×Dic15—21no—
187C2×Dic15—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—44no—
198C2×Dic15#4112yes—
199C2×C5×Dic3—21no—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3C22×C412yes—
208C2×C5×Dic3C22×C412yes—
209C2×C5×Dic3C22×C412yes—
210C2×C5×Dic3C22×C412yes—
211C5×Dic6—44no—
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—21no—
223C2×C3×Dic5—44no—
224C2×C3×Dic5#4112yes—
225C22×C3×D4C2×D511yescharacteristic
226C23×C3×C4—51no—
227C23×Dic3—51no—
228C22×Dic6C2×D511yescharacteristic
229C2×C3×C22⋊C4—51no—
230C2×C3×C22⋊C4—51no—
231C2×C3×C22⋊C4—51no—
232C2×#217—51no—
233C2×#217—51no—
234C2×#217—51no—
235C2×#217C2×D511yescharacteristic
236C2×#217C2×D511yescharacteristic
237C2×#217C2×D511yescharacteristic
238C2×#217C2×D511yescharacteristic
239#936Dic518yescomplemented
240C2×Dic3⋊C4—51no—
241C2×Dic3⋊C4—51no—
242C2×Dic3⋊C4—51no—
243C2×Dic3⋊C4—51no—
244C2×C4×Dic3—51no—
245C2×C4×Dic3—51no—
246C2×C4×Dic3—51no—
247C2×C4×Dic3—51no—
248C2×C4×Dic3C2×D511yescharacteristic
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⋊#95—51no—
261C24×C5C22×D311yescharacteristic
262C24×C5C22×D311yescharacteristic
263C2×C5×Q8—34no—
264C2×C5×Q8—121no—
265C2×C5×Q8—121no—
266C2×C5×D4—41no—
267C2×C5×D4—41no—
268C2×C5×D4C4×D314yes—
269C22×C4×C5—31no—
270C22×C4×C5—31no—
271C22×C4×C5—31no—
272C22×C4×C5—31no—
273C22×C4×C5C22×D311yescharacteristic
274C22×Dic5—22no—
275C22×Dic5—31no—
276C22×Dic5—31no—
277C22×Dic5—31no—
278C22×Dic5—31no—
279C22×Dic5—41no—
280C22×Dic5—41no—
281C22×Dic5—62no—
282C22×Dic5—121no—
283C22×Dic5—121no—
284C22×Dic5C22×D311yescharacteristic
285C22×Dic5C22×D311yescharacteristic
286C22×Dic5C22×D311yescharacteristic
287C22×Dic5C22×D311yescharacteristic
288C5×C22⋊C4—34no—
289C5×C22⋊C4—34no—
290C5×C22⋊C4—34no—
291C5×C22⋊C4—34no—
292C42×C5—34no—
293C22⋊Dic5—22no—
294C22⋊Dic5—41no—
295C22⋊Dic5—41no—
296C22⋊Dic5—62no—
297C22⋊Dic5—121no—
298C22⋊Dic5—121no—
299C4⋊Dic5—62no—
300C4⋊Dic5—62no—
301C4⋊Dic5—121no—
302C4⋊Dic5—121no—
303C4×Dic5—121no—
304C4×Dic5—121no—
305C4×Dic5—121no—
306C4×Dic5—121no—
307C2×#124—31no—
308#391—151no—
309#391—151no—
310#388—151no—
311#388—151no—
312#388—151no—
313#388—151no—
314#386—51no—
315#386—151no—
316#385—151no—
317#385—151no—
318#383—151no—
319C4×C4⋊C4—151no—
320C4×C22⋊C4—151no—
321C4×C22⋊C4—151no—
322C22×C3×C5—22no—
323C22×C3×C5—22no—
324C22×C3×C5—22no—
325C22×C3×C5—22no—
326C22×C3×C5—22no—
327C22×C3×C5—22no—
328C22×C3×C5—41no—
329C22×C3×C5—41no—
330C22×C3×C5—41no—
331C22×C3×C5—41no—
332C22×C3×C5—41no—
333C22×C3×C5—41no—
334C22×C3×C5—41no—
335C22×C3×C5—41no—
336C22×C3×C5C23×C411yescharacteristic
337C22×C3×C5C2×#4111yescharacteristic
338C22×C3×C5C2×#4111yescharacteristic
339C22×C3×C5H(5,𝔽2)11yescharacteristic
340C22×C3×C5H(5,𝔽2)11yescharacteristic
341C22×C3×C5H(5,𝔽2)11yescharacteristic
342C22×C3×C52−1+411yescharacteristic
343C3×C4×C5—22no—
344Dic15—22no—
345Dic15—41no—
346Dic15—41no—
347Dic15—41no—
348C3×Dic5—22no—
349C3×Dic5—41no—
350C3×Dic5—41no—
351C3×Dic5—41no—
352C5×Dic3—22no—
353C5×Dic3—22no—
354C5×Dic3—22no—
355C5×Dic3—22no—
356C24×C3C22×D511yescharacteristic
357C24×C3C22×D511yescharacteristic
358C2×C3×D4—41no—
359C2×C3×D4—41no—
360C2×C3×D4C2×Dic514yes—
361C22×C3×C4—51no—
362C22×C3×C4—51no—
363C22×C3×C4—51no—
364C22×C3×C4—51no—
365C22×C3×C4—102no—
366C22×C3×C4—201no—
367C22×C3×C4—201no—
368C22×C3×C4C22×D511yescharacteristic
369C22×Dic3—51no—
370C22×Dic3—51no—
371C22×Dic3—51no—
372C22×Dic3—51no—
373C22×Dic3—102no—
374C22×Dic3—201no—
375C22×Dic3—201no—
376C22×Dic3C22×D511yescharacteristic
377C22×Dic3C22×D511yescharacteristic
378C22×Dic3C22×D511yescharacteristic
379C22×Dic3C22×D511yescharacteristic
380C2×Dic6—41no—
381C2×Dic6—41no—
382C2×Dic6C2×Dic514yescomplemented
383C3×C22⋊C4—102no—
384C3×C22⋊C4—201no—
385C3×C22⋊C4—201no—
386#217—102no—
387#217—201no—
388#217—201no—
389#217C2×Dic514yescomplemented
390#217C2×Dic514yescomplemented
391#217C2×Dic514yescomplemented
392#217C2×Dic514yescomplemented
393Dic3⋊C4—102no—
394Dic3⋊C4—102no—
395Dic3⋊C4—201no—
396Dic3⋊C4—201no—
397C4×Dic3—201no—
398C4×Dic3—201no—
399C4×Dic3—201no—
400C4×Dic3—201no—
401C4×Dic3C2×Dic514yescomplemented
402C23×C5—21no—
403C23×C5—21no—
404C23×C5—21no—
405C23×C5—21no—
406C23×C5—21no—
407C23×C5—21no—
408C23×C5—21no—
409C23×C5—21no—
410C23×C5—21no—
411C23×C5—21no—
412C23×C5—21no—
413C23×C5—21no—
414C23×C5C2×C4×D312yes—
415C23×C5C2×C4×D312yes—
416C23×C5C23×D311yescharacteristic
417C5×Q8—124no—
418C5×D4—44no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—32no—
422C2×C4×C5—32no—
423C2×C4×C5—32no—
424C2×C4×C5—32no—
425C2×C4×C5—61no—
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×C5C2×C4×D312yes—
434C2×Dic5—21no—
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—44no—
447C2×Dic5—61no—
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#23712yes—
460C22×Q8—31no—
461C22×D4D3×D511yescharacteristic
462C23×C4—51no—
463C23×C4—151no—
464#124—38no—
465C2×C4⋊C4—151no—
466C2×C4⋊C4—151no—
467C2×C4⋊C4—151no—
468C2×C4⋊C4—151no—
469C2×C22⋊C4—31no—
470C2×C22⋊C4—31no—
471C2×C22⋊C4—31no—
472C2×C22⋊C4—31no—
473C2×C22⋊C4—51no—
474C2×C22⋊C4—51no—
475C2×C22⋊C4—51no—
476C2×C22⋊C4—151no—
477C2×C22⋊C4—151no—
478C2×C22⋊C4—151no—
479C2×C42—31no—
480C2×C42—151no—
481C2×C42—151no—
482C2×C42—151no—
483C2×C42—151no—
484#95—51no—
485#95—51no—
486#95—151no—
487#95—151no—
488#95—151no—
489#95—151no—
490#95—151no—
491#95—151no—
492#95—151no—
493#95—151no—
494#95—151no—
495#95—151no—
496C2×C3×C5—42no—
497C2×C3×C5—42no—
498C2×C3×C5C4×#4111yescharacteristic
499C2×C3×C5#51811yescharacteristic
500C2×C3×C5#52011yescharacteristic
501C2×C3×C5#53811yescharacteristic
502C2×C3×C5#53811yescharacteristic
503C2×C3×C5#54211yescharacteristic
504C2×C3×C5#54211yescharacteristic
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3C22×Dic512yes—
518C23×C3C22×Dic512yes—
519C23×C3C23×D511yescharacteristic
520C3×D4—44no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—52no—
524C2×C3×C4—101no—
525C2×C3×C4—101no—
526C2×C3×C4—101no—
527C2×C3×C4—101no—
528C2×C3×C4—101no—
529C2×C3×C4—101no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—101no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—204no—
536C2×C3×C4C22×Dic512yes—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—52no—
546C2×Dic3—101no—
547C2×Dic3—101no—
548C2×Dic3—101no—
549C2×Dic3—101no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—204no—
558C2×Dic3C22×Dic512yes—
559C2×Dic3C22×Dic512yes—
560C2×Dic3C22×Dic512yes—
561C2×Dic3C22×Dic512yes—
562Dic6—44no—
563C22×C5—22no—
564C22×C5—22no—
565C22×C5—22no—
566C22×C5—22no—
567C22×C5—22no—
568C22×C5—22no—
569C22×C5—41no—
570C22×C5—41no—
571C22×C5—41no—
572C22×C5—41no—
573C22×C5—41no—
574C22×C5—41no—
575C22×C5—41no—
576C22×C5—41no—
577C22×C5C22×C4×D311yescharacteristic
578C22×C5C2×#23711yescharacteristic
579C22×C5#100411yescharacteristic
580C22×C5#100411yescharacteristic
581C22×C5#100411yescharacteristic
582C22×C5D3×#4111yescharacteristic
583C22×C5#101011yescharacteristic
584C4×C5—22no—
585C4×C5—62no—
586C4×C5—62no—
587C4×C5—62no—
588C4×C5—62no—
589Dic5—22no—
590Dic5—41no—
591Dic5—41no—
592Dic5—41no—
593Dic5—62no—
594Dic5—121no—
595Dic5—121no—
596Dic5—121no—
597C24C2×D3×D511yescharacteristic
598C24C2×D3×D511yescharacteristic
599C2×Q8—34no—
600C2×Q8—121no—
601C2×Q8—121no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4D3×Dic514yes—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—51no—
610C22×C4—51no—
611C22×C4—51no—
612C22×C4—51no—
613C22×C4—102no—
614C22×C4—151no—
615C22×C4—151no—
616C22×C4—151no—
617C22×C4—151no—
618C22×C4—201no—
619C22×C4—201no—
620C22×C4—302no—
621C22×C4—601no—
622C22×C4—601no—
623C22×C4C2×D3×D511yescharacteristic
624C4⋊C4—302no—
625C4⋊C4—302no—
626C4⋊C4—601no—
627C4⋊C4—601no—
628C22⋊C4—34no—
629C22⋊C4—34no—
630C22⋊C4—34no—
631C22⋊C4—34no—
632C22⋊C4—102no—
633C22⋊C4—201no—
634C22⋊C4—201no—
635C22⋊C4—302no—
636C22⋊C4—601no—
637C22⋊C4—601no—
638C42—34no—
639C42—601no—
640C42—601no—
641C42—601no—
642C42—601no—
643C3×C5#233711yescharacteristic, complemented, Hall
644C22×C3—22no—
645C22×C3—22no—
646C22×C3—22no—
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3#414411yescharacteristic
659C22×C3#414411yescharacteristic
660C22×C3D5×#4111yescharacteristic
661C22×C3D5×#4111yescharacteristic
662C22×C3#414911yescharacteristic
663C22×C3#415011yescharacteristic
664C22×C3C23×Dic511yescharacteristic
665C3×C4—22no—
666C3×C4—102no—
667C3×C4—201no—
668C3×C4—201no—
669C3×C4—201no—
670Dic3—22no—
671Dic3—22no—
672Dic3—22no—
673Dic3—22no—
674Dic3—102no—
675Dic3—201no—
676Dic3—201no—
677Dic3—201no—
678C2×C5—42no—
679C2×C5—42no—
680C2×C5#548611yescharacteristic
681C2×C5C4×#23711yescharacteristic
682C2×C5#554611yescharacteristic
683C2×C5#559311yescharacteristic
684C2×C5#560311yescharacteristic
685C2×C5#561311yescharacteristic
686C2×C5#566211yescharacteristic
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23C2×D3×Dic512yes—
700C23C2×D3×Dic512yes—
701C23C22×D3×D511yescharacteristic
702Q8—124no—
703D4—44no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—32no—
707C2×C4—32no—
708C2×C4—32no—
709C2×C4—32no—
710C2×C4—52no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—101no—
720C2×C4—101no—
721C2×C4—101no—
722C2×C4—101no—
723C2×C4—101no—
724C2×C4—101no—
725C2×C4—101no—
726C2×C4—101no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—152no—
731C2×C4—204no—
732C2×C4—301no—
733C2×C4—301no—
734C2×C4—301no—
735C2×C4—301no—
736C2×C4—301no—
737C2×C4—301no—
738C2×C4—301no—
739C2×C4—301no—
740C2×C4—301no—
741C2×C4—301no—
742C2×C4—301no—
743C2×C4—604no—
744C2×C4C2×D3×Dic512yes—
745C2×C3—42no—
746C2×C3—42no—
747C2×C3#6600311yescharacteristic
748C2×C3#6600311yescharacteristic
749C2×C3#6601211yescharacteristic
750C2×C3#6601211yescharacteristic
751C2×C3#6613211yescharacteristic
752C2×C3#41×Dic511yescharacteristic
753C2×C3#6616111yescharacteristic
754C5#7467111yescharacteristic, complemented, Sylow
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22#9202011yescharacteristic
770C22D5×#23711yescharacteristic
771C22#9202411yescharacteristic
772C22#9202611yescharacteristic
773C22C22×D3×Dic511yescharacteristic
774C22#9204911yescharacteristic
775C22#9204911yescharacteristic
776C4—22no—
777C4—62no—
778C4—62no—
779C4—62no—
780C4—62no—
781C4—102no—
782C4—201no—
783C4—201no—
784C4—201no—
785C4—302no—
786C4—601no—
787C4—601no—
788C4—601no—
789C3#1061468511yescharacteristic, complemented, Sylow
790C2—42no—
791C2—42no—
792C2#1175484511yescharacteristic
793C2Dic5×#23711yescharacteristic
794C2#1175486511yescharacteristic
795C2#1175489411yescharacteristic
796C2#1175490511yescharacteristic
797C2#1175492011yescharacteristic
798C2#1175541011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
Fitting, prime radicalC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5#2337
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #11749517C2semidirect
5. #11749509C2semidirect
6. #11749487C2semidirect
7. #11749479C2semidirect
8. #11749479C2semidirect
9. #11749478C2semidirect
10. #11749478C2semidirect
11. Dic5×#217C2semidirect
12. #11748692C2semidirect
13. #11748692C2semidirect
14. #11748667C2semidirect
15. #11748618C2semidirect
28. C5×#936C4semidirect
88. C2×C5×Dic6C2×C4semidirect
99. C5×#217C2×C4semidirect
100. C5×#217C2×C4semidirect
101. C5×#217C2×C4semidirect
102. C5×#217C2×C4semidirect
103. C4×C5×Dic3C2×C4semidirect
239. #936Dic5semidirect
382. C2×Dic6C2×Dic5semidirect
389. #217C2×Dic5semidirect
390. #217C2×Dic5semidirect
391. #217C2×Dic5semidirect
392. #217C2×Dic5semidirect
401. C4×Dic3C2×Dic5semidirect
643. C3×C5#2337semidirect
754. C5#74671semidirect
789. C3#10614685semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9362
#117513212
C3×#655092
#117495172
#117495092
#117494872
#117494792
#117494782
Dic5×#2172
#117486922
#117486672
#117486182
#106146853
#746715