Finite Group Databasebeta

← #14327643

Subgroups — #14327643

Order 1920.

1176 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×#91559C211yesmaximal, characteristic
2#11751044C211yesmaximal, characteristic, complemented
3C5×#4945C211yesmaximal, characteristic, complemented
4C3×#65245C211yesmaximal, characteristic
5#11749518C211yesmaximal, characteristic
6#11749487C211yesmaximal, characteristic, complemented
7#11749478C211yesmaximal, characteristic, complemented
8#11748878C211yesmaximal, characteristic, complemented
9Dic3×#685C211yesmaximal, characteristic, complemented
10D5×C3⋊#95C211yesmaximal, characteristic, complemented
11#11748702C211yesmaximal, characteristic, complemented
12#11748655C211yesmaximal, characteristic, complemented
13#11748654C211yesmaximal, characteristic, complemented
14#11748646C211yesmaximal, characteristic, complemented
15#11748643C211yesmaximal, characteristic, complemented
16#10607566—31nomaximal, Hall
17C23×Dic15C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×D5×Dic3C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×C5×#217C2211yescharacteristic
25C2×C5×#217C2211yescharacteristic
26C2×C5×Dic3⋊C4C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C2×C3×#685C2211yescharacteristic
30#91559C418yescomplemented
31C2×Dic3⋊Dic5C2211yescharacteristic
32C2×#6668C2211yescharacteristic
33C2×#6665C2211yescharacteristic
34C2×#6665C2211yescharacteristic
35C2×Dic3×Dic5C2211yescharacteristic
36C2×Dic3×Dic5C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39#91115C2211yescharacteristic
40#91115C2211yescharacteristic
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C5×C3⋊#95C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#74674—51nomaximal, Hall
54C2×#4027—31no—
55C5×#388—31no—
56#65276—31no—
57#65267—31no—
58#65245—31no—
59#65245D311yescharacteristic
60#65240—31no—
61#65232—31no—
62C22⋊C4×Dic5—31no—
63C4×#685—31no—
64#65221—31no—
65#64955—31no—
66D5×#95—31no—
67#64944—31no—
68#64940—31no—
69C24×C3×C5C2311yescharacteristic
70C23×C3×D5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×Dic15—41no—
74C22×Dic15—41no—
75C22×Dic15C2×C414yescomplemented
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C2×C3×C22⋊D5—22no—
85C2×C3×C22⋊D5—22no—
86C2×C3×C22⋊D5C2×C414yes—
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C2×C3×C4×D5—22no—
91C2×C3×C4×D5—22no—
92C2×C3×C4×D5—41no—
93C2×D5×Dic3—22no—
94C2×D5×Dic3—22no—
95C2×D5×Dic3—41no—
96C2×D5×Dic3—41no—
97C2×D5×Dic3—41no—
98C2×D5×Dic3C2×C414yes—
99C3×C5×C22⋊C4—41no—
100#6719—41no—
101C5×#217—22no—
102C5×#217C2×C414yescomplemented
103C5×Dic3⋊C4—41no—
104C4×C5×Dic3—22no—
105C3×C22⋊Dic5—22no—
106C3×#685—22no—
107Dic3⋊Dic5—41no—
108#6668C2×C414yescomplemented
109#6665—22no—
110#6665C2×C414yes—
111Dic3×Dic5—22no—
112Dic3×Dic5—41no—
113Dic3×Dic5—41no—
114Dic3×Dic5C2×C414yescomplemented
115C2×D4×Dic3—51no—
116C3×#386—51no—
117#5220—51no—
118C4×#217—51no—
119C2×C3⋊#95—51no—
120#4945D511yescharacteristic, complemented
121#4944—51no—
122#4943—51no—
123#4942—51no—
124Dic3×C22⋊C4—51no—
125Dic3×C22⋊C4—51no—
126#4654—51no—
127#4653—51no—
128#4651—51no—
129#4648—51no—
130C22×C22⋊D5C2×D311yescharacteristic
131C23×Dic5—31no—
132C22×C4×D5—31no—
133C22×C4×D5—31no—
134C22×C4×D5C2×D311yescharacteristic
135C2×C5×C4⋊C4—31no—
136C2×C5×C22⋊C4—31no—
137C2×C5×C22⋊C4—31no—
138C2×C5×C22⋊C4C2×D311yescharacteristic
139C2×C42×C5—31no—
140C2×C22⋊Dic5—31no—
141C2×C22⋊Dic5C2×D311yescharacteristic
142C2×#685—31no—
143C2×#685—31no—
144C2×#685C2×D311yescharacteristic
145C2×C4⋊Dic5—31no—
146C2×#683—31no—
147C2×C4×Dic5—31no—
148C2×C4×Dic5—31no—
149C2×C4×Dic5—31no—
150C2×C4×Dic5—31no—
151#4027—38no—
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#2353—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×C5C22×C412yes—
174C23×C3×C5C2411yescharacteristic
175C22×C3×D5—21no—
176C22×C3×D5—21no—
177C22×C3×D5—21no—
178C22×C3×D5—21no—
179C22×C3×D5C22×C412yes—
180C22×C3×D5#4112yes—
181C22×C3×D5#4112yes—
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—
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×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3C22×C412yes—
211C2×C5×Dic3C22×C412yes—
212C2×C5×Dic3#4112yes—
213C3×C22⋊D5—28no—
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×Dic5C22×C412yes—
222C2×C3×Dic5#4112yes—
223C3×C4×D5—44no—
224D5×Dic3—44no—
225D5×Dic3—44no—
226C22×C3×D4—51no—
227C23×C3×C4—51no—
228C23×Dic3—51no—
229C23×Dic3—51no—
230C23×Dic3—51no—
231C2×C3×C22⋊C4—51no—
232C2×C3×C22⋊C4—51no—
233C2×C3×C22⋊C4C2×D511yescharacteristic
234C2×#217—51no—
235C2×#217—51no—
236C2×#217—51no—
237C2×#217C2×D511yescharacteristic
238C2×#217C2×D511yescharacteristic
239D4×Dic3—58no—
240C2×C4⋊Dic3—51no—
241C2×Dic3⋊C4—51no—
242C2×Dic3⋊C4C2×D511yescharacteristic
243C2×C4×Dic3—51no—
244C2×C4×Dic3—51no—
245C2×C4×Dic3—51no—
246C2×C4×Dic3—51no—
247C2×C4×Dic3C2×D511yescharacteristic
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×C5C22×D311yescharacteristic
263C23×D5C22×D311yescharacteristic
264C22×C4×C5—31no—
265C22×C4×C5—31no—
266C22×C4×C5—31no—
267C22×C4×C5—31no—
268C22×C4×C5C22×D311yescharacteristic
269C22×C4×C5C22×D311yescharacteristic
270C2×C22⋊D5—22no—
271C2×C22⋊D5—22no—
272C2×C22⋊D5C4×D314yes—
273C22×Dic5—31no—
274C22×Dic5—31no—
275C22×Dic5—34no—
276C22×Dic5—31no—
277C22×Dic5—31no—
278C22×Dic5—121no—
279C22×Dic5—121no—
280C22×Dic5C22×D311yescharacteristic
281C22×Dic5C22×D311yescharacteristic
282C22×Dic5C22×D311yescharacteristic
283C2×C4×D5—22no—
284C2×C4×D5—22no—
285C2×C4×D5—34no—
286C2×C4×D5—41no—
287C2×C4×D5—62no—
288C2×C4×D5—62no—
289C2×C4×D5—121no—
290C2×C4×D5—121no—
291C2×C4×D5—121no—
292C5×C4⋊C4—121no—
293C5×C22⋊C4—34no—
294C5×C22⋊C4—41no—
295C5×C22⋊C4—62no—
296C42×C5—62no—
297C22⋊Dic5—22no—
298C22⋊Dic5—121no—
299#685—22no—
300#685—34no—
301#685—62no—
302C4⋊Dic5—121no—
303#683—34no—
304C4×Dic5—34no—
305C4×Dic5—62no—
306C4×Dic5—121no—
307C4×Dic5—121no—
308C2×C4×D4—151no—
309#388—31no—
310#388—151no—
311#387—151no—
312#387—151no—
313#386—51no—
314#386—151no—
315#383—151no—
316#381—151no—
317#380—151no—
318C4×C22⋊C4—151no—
319C4×C22⋊C4—151no—
320C4×C22⋊C4—151no—
321#376—151no—
322C2×#95—151no—
323C22×C3×C5—22no—
324C22×C3×C5—22no—
325C22×C3×C5—22no—
326C22×C3×C5—41no—
327C22×C3×C5—41no—
328C22×C3×C5—41no—
329C22×C3×C5—41no—
330C22×C3×C5C23×C411yescharacteristic
331C22×C3×C5C2×#4111yescharacteristic
332C22×C3×C5C2×#4111yescharacteristic
333C22×C3×C5C2×#4111yescharacteristic
334C22×C3×C5C2×#4111yescharacteristic
335C22×C3×C5H(5,𝔽2)11yescharacteristic
336C22×C3×C5H(5,𝔽2)11yescharacteristic
337C2×C3×D5—22no—
338C2×C3×D5—22no—
339C2×C3×D5—22no—
340C2×C3×D5—22no—
341C2×C3×D5—22no—
342C2×C3×D5—22no—
343C2×C3×D5#11714yes—
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—
353C5×Dic3—22no—
354C5×Dic3—22no—
355C5×Dic3—22no—
356C5×Dic3—41no—
357C24×C3—51no—
358C24×C3C22×D511yescharacteristic
359C2×C3×D4—54no—
360C2×C3×D4—102no—
361C2×C3×D4—102no—
362C22×C3×C4—51no—
363C22×C3×C4—51no—
364C22×C3×C4—51no—
365C22×C3×C4—102no—
366C22×C3×C4—102no—
367C22×C3×C4—201no—
368C22×C3×C4C22×D511yescharacteristic
369C22×C3×C4C22×D511yescharacteristic
370C22×Dic3—51no—
371C22×Dic3—51no—
372C22×Dic3—54no—
373C22×Dic3—54no—
374C22×Dic3—51no—
375C22×Dic3—51no—
376C22×Dic3—102no—
377C22×Dic3—102no—
378C22×Dic3—201no—
379C22×Dic3—201no—
380C22×Dic3—201no—
381C22×Dic3—201no—
382C22×Dic3—201no—
383C22×Dic3C22×D511yescharacteristic
384C22×Dic3C22×D511yescharacteristic
385C22×Dic3C22×D511yescharacteristic
386C22×Dic3C22×D511yescharacteristic
387C3×C22⋊C4—41no—
388C3×C22⋊C4—102no—
389C3×C22⋊C4—102no—
390#217—22no—
391#217—54no—
392#217—102no—
393#217—201no—
394#217C4×D514yescomplemented
395C4⋊Dic3—54no—
396Dic3⋊C4—41no—
397Dic3⋊C4—201no—
398C4×Dic3—22no—
399C4×Dic3—54no—
400C4×Dic3—102no—
401C4×Dic3—201no—
402C4×Dic3—201no—
403C23×C5—21no—
404C23×C5—21no—
405C23×C5—21no—
406C23×C5—21no—
407C23×C5—21no—
408C23×C5—21no—
409C23×C5C2×C4×D312yes—
410C23×C5C23×D311yescharacteristic
411C22×D5—21no—
412C22×D5—21no—
413C22×D5—21no—
414C22×D5—21no—
415C22×D5C2×C4×D312yes—
416C22×D5#23712yes—
417C22×D5#23712yes—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—32no—
425C2×C4×C5—32no—
426C2×C4×C5—32no—
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—61no—
435C2×C4×C5—61no—
436C22⋊D5—28no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—32no—
445C2×Dic5—32no—
446C2×Dic5—61no—
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—124no—
457C2×Dic5C2×C4×D312yes—
458C2×Dic5#23712yes—
459C4×D5—44no—
460C4×D5—124no—
461C4×D5—124no—
462C22×D4—51no—
463C23×C4—51no—
464C23×C4—151no—
465C23×C4—151no—
466C23×C4—151no—
467C4×D4—158no—
468C2×C4⋊C4—31no—
469C2×C4⋊C4—151no—
470C2×C4⋊C4—151no—
471C2×C22⋊C4—31no—
472C2×C22⋊C4—31no—
473C2×C22⋊C4—51no—
474C2×C22⋊C4—51no—
475C2×C22⋊C4—151no—
476C2×C22⋊C4—151no—
477C2×C22⋊C4—151no—
478C2×C22⋊C4D3×D511yescharacteristic
479C2×C42—31no—
480C2×C42—151no—
481C2×C42—151no—
482C2×C42—151no—
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—42no—
499C2×C3×C5C2×#11711yescharacteristic
500C2×C3×C5C4×#4111yescharacteristic
501C2×C3×C5#51811yescharacteristic
502C2×C3×C5#55111yescharacteristic
503C2×C3×C5#55111yescharacteristic
504C2×C3×C5#55311yescharacteristic
505C2×C3×C5#55311yescharacteristic
506C3×D5—24no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—52no—
514C23×C3—52no—
515C23×C3—52no—
516C23×C3—101no—
517C23×C3—101no—
518C23×C3—101no—
519C23×C3—101no—
520C23×C3C2×C4×D512yes—
521C23×C3C23×D511yescharacteristic
522C3×D4—108no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—52no—
530C2×C3×C4—52no—
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—204no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—52no—
549C2×Dic3—52no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—101no—
558C2×Dic3—101no—
559C2×Dic3—101no—
560C2×Dic3—204no—
561C2×Dic3—204no—
562C2×Dic3—204no—
563C2×Dic3C2×C4×D512yes—
564C2×Dic3C2×C4×D512yes—
565C2×Dic3#71112yes—
566C22×C5—22no—
567C22×C5—22no—
568C22×C5—22no—
569C22×C5—41no—
570C22×C5—41no—
571C22×C5—41no—
572C22×C5—41no—
573C22×C5C22×C4×D311yescharacteristic
574C22×C5C2×#23711yescharacteristic
575C22×C5C2×#23711yescharacteristic
576C22×C5C2×#23711yescharacteristic
577C22×C5#100411yescharacteristic
578C22×C5D3×#4111yescharacteristic
579C22×C5#100911yescharacteristic
580C2×D5—22no—
581C2×D5—22no—
582C2×D5—22no—
583C2×D5—22no—
584C2×D5—22no—
585C2×D5—22no—
586C2×D5#87714yes—
587C4×C5—41no—
588C4×C5—41no—
589C4×C5—62no—
590C4×C5—62no—
591C4×C5—62no—
592C4×C5—121no—
593Dic5—22no—
594Dic5—22no—
595Dic5—41no—
596Dic5—62no—
597Dic5—62no—
598Dic5—121no—
599Dic5—121no—
600C24—51no—
601C24C2×D3×D511yescharacteristic
602C2×D4—54no—
603C2×D4—102no—
604C2×D4—102no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—51no—
610C22×C4—51no—
611C22×C4—51no—
612C22×C4—102no—
613C22×C4—102no—
614C22×C4—154no—
615C22×C4—151no—
616C22×C4—151no—
617C22×C4—154no—
618C22×C4—151no—
619C22×C4—151no—
620C22×C4—201no—
621C22×C4—302no—
622C22×C4—302no—
623C22×C4—601no—
624C22×C4—601no—
625C22×C4—601no—
626C22×C4—601no—
627C22×C4—601no—
628C22×C4C2×D3×D511yescharacteristic
629C22×C4C2×D3×D511yescharacteristic
630C4⋊C4—121no—
631C4⋊C4—154no—
632C4⋊C4—601no—
633C22⋊C4—34no—
634C22⋊C4—41no—
635C22⋊C4—62no—
636C22⋊C4—102no—
637C22⋊C4—102no—
638C22⋊C4—154no—
639C22⋊C4—302no—
640C22⋊C4—601no—
641C42—62no—
642C42—154no—
643C42—302no—
644C42—601no—
645C42—601no—
646C3×C5#235311yescharacteristic, complemented, Hall
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—54no—
655C22×C3—102no—
656C22×C3—102no—
657C22×C3—102no—
658C22×C3—102no—
659C22×C3—102no—
660C22×C3—102no—
661C22×C3C22×C4×D511yescharacteristic
662C22×C3C2×#71111yescharacteristic
663C22×C3#414411yescharacteristic
664C22×C3D5×#4111yescharacteristic
665C22×C3D5×#4111yescharacteristic
666C22×C3D5×#4111yescharacteristic
667C22×C3#414911yescharacteristic
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—102no—
671C3×C4—102no—
672C3×C4—201no—
673Dic3—22no—
674Dic3—22no—
675Dic3—22no—
676Dic3—41no—
677Dic3—102no—
678Dic3—102no—
679Dic3—201no—
680Dic3—201no—
681C2×C5—42no—
682C2×C5C2×#87711yescharacteristic
683C2×C5C4×#23711yescharacteristic
684C2×C5#554511yescharacteristic
685C2×C5#558711yescharacteristic
686C2×C5#560111yescharacteristic
687C2×C5#561811yescharacteristic
688C2×C5#565811yescharacteristic
689D5—24no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—52no—
697C23—52no—
698C23—52no—
699C23—101no—
700C23—101no—
701C23—101no—
702C23—101no—
703C23C4×D3×D512yes—
704C23C22×D3×D511yescharacteristic
705D4—108no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—32no—
715C2×C4—52no—
716C2×C4—52no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—101no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—101no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—152no—
734C2×C4—152no—
735C2×C4—204no—
736C2×C4—301no—
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—604no—
747C2×C4—604no—
748C2×C4—604no—
749C2×C3—42no—
750C2×C3—104no—
751C2×C3D5×#11711yescharacteristic
752C2×C3C4×#71111yescharacteristic
753C2×C3#6587911yescharacteristic
754C2×C3#6594811yescharacteristic
755C2×C3#6599211yescharacteristic
756C2×C3#6601311yescharacteristic
757C2×C3#6604311yescharacteristic
758C5#7467411yescharacteristic, complemented, Sylow
759C22—22no—
760C22—22no—
761C22—22no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—54no—
767C22—102no—
768C22—102no—
769C22—102no—
770C22—102no—
771C22—102no—
772C22—102no—
773C22C2×C4×D3×D511yescharacteristic
774C22#9201911yescharacteristic
775C22D5×#23711yescharacteristic
776C22D5×#23711yescharacteristic
777C22D5×#23711yescharacteristic
778C22D3×#71111yescharacteristic
779C22#9204911yescharacteristic
780C4—41no—
781C4—41no—
782C4—62no—
783C4—62no—
784C4—62no—
785C4—102no—
786C4—102no—
787C4—121no—
788C4—201no—
789C4—302no—
790C4—302no—
791C4—601no—
792C4—601no—
793C3#1060756611yescharacteristic, complemented, Sylow
794C2—42no—
795C2—104no—
796C2D5×#87711yescharacteristic
797C2#1175282011yescharacteristic
798C2#1175293011yescharacteristic
799C2#1175328311yescharacteristic
800C2#1175462911yescharacteristic
801C2#1175483711yescharacteristic
802C2#1175484011yescharacteristic
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#2353
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. #11751044C2semidirect
3. C5×#4945C2semidirect
6. #11749487C2semidirect
7. #11749478C2semidirect
8. #11748878C2semidirect
9. Dic3×#685C2semidirect
10. D5×C3⋊#95C2semidirect
11. #11748702C2semidirect
12. #11748655C2semidirect
13. #11748654C2semidirect
14. #11748646C2semidirect
15. #11748643C2semidirect
30. #91559C4semidirect
75. C22×Dic15C2×C4semidirect
102. C5×#217C2×C4semidirect
108. #6668C2×C4semidirect
114. Dic3×Dic5C2×C4semidirect
120. #4945D5semidirect
394. #217C4×D5semidirect
646. C3×C5#2353semidirect
758. C5#74674semidirect
793. C3#10607566semidirect

Maximal subgroups

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

subgroupindex
C2×#915592
#117510442
C5×#49452
C3×#652452
#117495182
#117494872
#117494782
#117488782
Dic3×#6852
D5×C3⋊#952
#117487022
#117486552
#117486542
#117486462
#117486432
#106075663
#746745