Finite Group Databasebeta

← #14322860

Subgroups — #14322860

Order 1920.

1200 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91394C211yesmaximal, characteristic
2C2×#91393C211yesmaximal, characteristic
3C2×D5×Dic3⋊C4C211yesmaximal, characteristic
4#11750748C211yesmaximal, characteristic, complemented
5C5×#4647C211yesmaximal, characteristic, complemented
6C3×#64956C211yesmaximal, characteristic
7#11748885C211yesmaximal, characteristic
8#11748878C211yesmaximal, characteristic
9#11748820C211yesmaximal, characteristic, complemented
10#11748818C211yesmaximal, characteristic, complemented
11#11748759C211yesmaximal, characteristic
12#11748695C211yesmaximal, characteristic, complemented
13#11748693C211yesmaximal, characteristic, complemented
14#11748664C211yesmaximal, characteristic, complemented
15#11748658C211yesmaximal, characteristic, complemented
16#10607926—31nomaximal, Hall
17C22×C3×C4×D5C2211yescharacteristic
18C22×D5×Dic3C2211yescharacteristic
19C22×D5×Dic3C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×#6712C2211yescharacteristic
22C2×#6712C2211yescharacteristic
23C2×#6712C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C2×C5×Dic3⋊C4C2211yescharacteristic
27C2×C5×Dic3⋊C4C2211yescharacteristic
28C2×C5×Dic3⋊C4C2211yescharacteristic
29C2×C4×C5×Dic3C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic
33C2×C3×#683C2211yescharacteristic
34C2×Dic3⋊Dic5C2211yescharacteristic
35C2×Dic3⋊Dic5C2211yescharacteristic
36C2×Dic3⋊Dic5C2211yescharacteristic
37C2×#6669C2211yescharacteristic
38C2×#6669C2211yescharacteristic
39C2×#6669C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44#91394—24no—
45#91393—24no—
46D5×Dic3⋊C4C418yescomplemented
47C3×C5×#95C2211yescharacteristic
48#91115C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#73869—51nomaximal, Hall
56C2×#4038—31no—
57C2×D5×C4⋊C4—31no—
58C2×#4018—31no—
59C5×#389—31no—
60#65276—31no—
61#65276—31no—
62#65274—31no—
63#65262—31no—
64#65261—31no—
65#65261—31no—
66#65217—31no—
67#64956—31no—
68#64956D311yescharacteristic
69#64936—31no—
70#64936—31no—
71C23×C3×D5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C2×C3×C4×D5—41no—
87C2×C3×C4×D5—41no—
88C2×C3×C4×D5C2×C414yes—
89C2×D5×Dic3—41no—
90C2×D5×Dic3—41no—
91C2×D5×Dic3C2×C414yes—
92C2×D5×Dic3C2×C414yes—
93C2×D5×Dic3D414yes—
94C2×D5×Dic3Q814yes—
95C4⋊Dic15—41no—
96#6712—22no—
97#6712—41no—
98#6712C2×C414yes—
99C4×Dic15—22no—
100C5×C4⋊Dic3—41no—
101C5×Dic3⋊C4—22no—
102C5×Dic3⋊C4—41no—
103C5×Dic3⋊C4C2×C414yes—
104C4×C5×Dic3—22no—
105C3×#685—22no—
106C3×#685—22no—
107C3×#683—41no—
108C3×#683—41no—
109Dic3⋊Dic5—22no—
110Dic3⋊Dic5—41no—
111Dic3⋊Dic5C2×C414yes—
112#6669—22no—
113#6669—41no—
114#6669C2×C414yes—
115#6665—22no—
116#6665—22no—
117Dic3×Dic5—22no—
118Dic3×Dic5—22no—
119C22×Dic3⋊C4—51no—
120C2×#877—51no—
121C2×#877—51no—
122C3×#380—51no—
123#5212—51no—
124#4976—51no—
125#4976—51no—
126#4976—51no—
127#4976—51no—
128#4942—51no—
129#4942—51no—
130#4647—51no—
131#4647—51no—
132#4647—51no—
133#4647D511yescharacteristic, complemented
134C22×C4×D5—31no—
135C22×C4×D5—31no—
136C22×C4×D5C2×D311yescharacteristic
137C2×C5×C4⋊C4—31no—
138C2×C5×C4⋊C4—31no—
139C2×C5×C4⋊C4—31no—
140C2×C5×C4⋊C4—31no—
141C2×C42×C5—31no—
142C2×#685—31no—
143C2×#685—31no—
144C2×#685C2×D311yescharacteristic
145C2×#685C2×D311yescharacteristic
146C2×C4⋊Dic5—31no—
147C2×C4⋊Dic5—31no—
148C2×C4⋊Dic5—31no—
149C2×C4⋊Dic5—31no—
150C2×#683—31no—
151C2×#683—31no—
152C2×#683—31no—
153C2×#683—31no—
154C2×#683—31no—
155C2×#683—31no—
156C2×#683C2×D311yescharacteristic
157C2×#683C2×D311yescharacteristic
158C2×C4×Dic5—31no—
159C2×C4×Dic5—31no—
160C2×C4×Dic5—31no—
161#4038—64no—
162D5×C4⋊C4—38no—
163#4018—64no—
164C5×#95—31no—
165C5×#95C2×D311yescharacteristic
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963C2×D311yescharacteristic
172#2316—151noSylow
173C23×C3×C5C2411yescharacteristic
174C22×C3×D5—21no—
175C22×C3×D5—21no—
176C22×C3×D5—21no—
177C22×C3×D5—21no—
178C22×C3×D5C22×C412yes—
179C22×C3×D5C2×D412yes—
180C22×C3×D5C2×Q812yes—
181C2×C3×C4×C5—21no—
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×C3×C4×C5—21no—
189C2×C3×C4×C5C22×C412yes—
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×Dic15C22×C412yes—
199C2×Dic15C22×C412yes—
200C2×Dic15C2×D412yes—
201C2×Dic15C2×Q812yes—
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×Dic3C2×D412yes—
213C2×C5×Dic3C2×Q812yes—
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×Dic5C22×C412yes—
223C3×C4×D5—44no—
224D5×Dic3—44no—
225D5×Dic3C4⋊C4116yescomplemented
226C23×C3×C4—51no—
227C23×Dic3—51no—
228C23×Dic3—51no—
229C2×C3×C4⋊C4—51no—
230C2×C3×C4⋊C4—51no—
231C2×C3×C22⋊C4—51no—
232C2×C3×C22⋊C4—51no—
233C2×#217—51no—
234C2×#217—51no—
235C2×C4⋊Dic3—51no—
236C2×C4⋊Dic3C2×D511yescharacteristic
237C2×Dic3⋊C4—51no—
238C2×Dic3⋊C4—51no—
239C2×Dic3⋊C4—51no—
240C2×Dic3⋊C4—58no—
241C2×Dic3⋊C4—51no—
242C2×Dic3⋊C4—51no—
243C2×Dic3⋊C4—51no—
244C2×Dic3⋊C4—51no—
245C2×Dic3⋊C4—51no—
246C2×Dic3⋊C4—51no—
247C2×Dic3⋊C4C2×D511yescharacteristic
248C2×Dic3⋊C4C2×D511yescharacteristic
249C2×Dic3⋊C4C2×D511yescharacteristic
250C2×C4×Dic3—51no—
251C2×C4×Dic3—51no—
252C2×C4×Dic3—51no—
253C2×C4×Dic3C2×D511yescharacteristic
254#877—104no—
255#877—104no—
256C3×#95—51no—
257C3×#95C2×D511yescharacteristic
258C3⋊#95—51no—
259C3⋊#95—51no—
260C3⋊#95—51no—
261C3⋊#95—51no—
262C3⋊#95—51no—
263C3⋊#95C2×D511yescharacteristic
264C23×D5C22×D311yescharacteristic
265C22×C4×C5—31no—
266C22×C4×C5—31no—
267C22×C4×C5—31no—
268C22×C4×C5—31no—
269C22×C4×C5C22×D311yescharacteristic
270C22×C4×C5C22×D311yescharacteristic
271C22×C4×C5C22×D311yescharacteristic
272C22×Dic5—31no—
273C22×Dic5—31no—
274C22×Dic5—31no—
275C22×Dic5—31no—
276C22×Dic5C22×D311yescharacteristic
277C22×Dic5C22×D311yescharacteristic
278C22×Dic5C22×D311yescharacteristic
279C2×C4×D5—34no—
280C2×C4×D5—34no—
281C2×C4×D5—34no—
282C2×C4×D5—34no—
283C2×C4×D5—41no—
284C2×C4×D5—41no—
285C2×C4×D5—121no—
286C2×C4×D5—121no—
287C2×C4×D5C4×D314yes—
288C5×C4⋊C4—34no—
289C5×C4⋊C4—62no—
290C5×C4⋊C4—121no—
291C5×C4⋊C4—121no—
292C42×C5—62no—
293#685—22no—
294#685—22no—
295#685—62no—
296#685—62no—
297C4⋊Dic5—34no—
298C4⋊Dic5—62no—
299C4⋊Dic5—121no—
300C4⋊Dic5—121no—
301#683—34no—
302#683—34no—
303#683—41no—
304#683—41no—
305#683—62no—
306#683—62no—
307#683—121no—
308#683—121no—
309C4×Dic5—62no—
310C4×Dic5—62no—
311C4×Dic5—62no—
312C2×#117—151no—
313C2×#117—151no—
314C22×C4⋊C4—151no—
315#389—31no—
316#389—151no—
317#389—151no—
318#389—151no—
319#389—151no—
320#389—151no—
321#389—151no—
322#389—151no—
323#380—51no—
324#380—151no—
325#380—151no—
326#380—151no—
327C22×C3×C5C23×C411yescharacteristic
328C22×C3×C5C22×D411yescharacteristic
329C22×C3×C5C22×Q811yescharacteristic
330C22×C3×C5H(5,𝔽2)11yescharacteristic
331C22×C3×C5H(5,𝔽2)11yescharacteristic
332C22×C3×C52−1+411yescharacteristic
333C22×C3×C52−1+411yescharacteristic
334C2×C3×D5—22no—
335C2×C3×D5—22no—
336C2×C3×D5—22no—
337C2×C3×D5—22no—
338C2×C3×D5—22no—
339C2×C3×D5—22no—
340C2×C3×D5C2×C4⋊C414yes—
341C3×C4×C5—22no—
342C3×C4×C5—41no—
343C3×C4×C5—41no—
344Dic15—22no—
345Dic15—41no—
346Dic15—41no—
347Dic15C2×C4⋊C414yes—
348C3×Dic5—22no—
349C3×Dic5—41no—
350C3×Dic5—41no—
351C5×Dic3—22no—
352C5×Dic3—41no—
353C5×Dic3—41no—
354C5×Dic3C2×C4⋊C414yes—
355C24×C3—51no—
356C22×C3×C4—51no—
357C22×C3×C4—54no—
358C22×C3×C4—51no—
359C22×C3×C4—51no—
360C22×C3×C4—201no—
361C22×C3×C4—201no—
362C22×C3×C4C22×D511yescharacteristic
363C22×C3×C4C22×D511yescharacteristic
364C22×C3×C4C22×D511yescharacteristic
365C22×Dic3—51no—
366C22×Dic3—54no—
367C22×Dic3—54no—
368C22×Dic3—54no—
369C22×Dic3—51no—
370C22×Dic3—54no—
371C22×Dic3—51no—
372C22×Dic3—51no—
373C22×Dic3—201no—
374C22×Dic3—201no—
375C22×Dic3C22×D511yescharacteristic
376C22×Dic3C22×D511yescharacteristic
377C22×Dic3C22×D511yescharacteristic
378C22×Dic3C22×D511yescharacteristic
379C3×C4⋊C4—201no—
380C3×C4⋊C4—201no—
381C3×C22⋊C4—102no—
382C3×C22⋊C4—102no—
383#217—102no—
384#217—102no—
385C4⋊Dic3—41no—
386C4⋊Dic3—201no—
387Dic3⋊C4—22no—
388Dic3⋊C4—41no—
389Dic3⋊C4—54no—
390Dic3⋊C4—54no—
391Dic3⋊C4—54no—
392Dic3⋊C4—102no—
393Dic3⋊C4—102no—
394Dic3⋊C4—102no—
395Dic3⋊C4—201no—
396Dic3⋊C4—201no—
397Dic3⋊C4—201no—
398Dic3⋊C4C4×D514yes—
399C4×Dic3—22no—
400C4×Dic3—102no—
401C4×Dic3—102no—
402C4×Dic3—102no—
403C23×C5C23×D311yescharacteristic
404C22×D5—21no—
405C22×D5—21no—
406C22×D5—21no—
407C22×D5—21no—
408C22×D5C2×C4×D312yes—
409C22×D5D3×D412yes—
410C22×D5D3×Q812yes—
411C2×C4×C5—21no—
412C2×C4×C5—21no—
413C2×C4×C5—21no—
414C2×C4×C5—21no—
415C2×C4×C5—21no—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—32no—
420C2×C4×C5—32no—
421C2×C4×C5—32no—
422C2×C4×C5—32no—
423C2×C4×C5—61no—
424C2×C4×C5—61no—
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×C5C2×C4×D312yes—
432C2×Dic5—21no—
433C2×Dic5—21no—
434C2×Dic5—21no—
435C2×Dic5—21no—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—32no—
441C2×Dic5—32no—
442C2×Dic5—32no—
443C2×Dic5—32no—
444C2×Dic5—61no—
445C2×Dic5—61no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452C2×Dic5C2×C4×D312yes—
453C4×D5—316no—
454C4×D5—44no—
455C4×D5—124no—
456C23×C4—51no—
457C23×C4—151no—
458C23×C4—151no—
459#117—304no—
460#117—304no—
461C2×C4⋊C4—31no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—31no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—51no—
466C2×C4⋊C4—51no—
467C2×C4⋊C4—158no—
468C2×C4⋊C4—151no—
469C2×C4⋊C4—151no—
470C2×C4⋊C4—151no—
471C2×C4⋊C4—151no—
472C2×C4⋊C4—151no—
473C2×C4⋊C4—151no—
474C2×C4⋊C4—151no—
475C2×C4⋊C4—151no—
476C2×C4⋊C4—151no—
477C2×C4⋊C4—151no—
478C2×C22⋊C4—51no—
479C2×C22⋊C4—51no—
480C2×C22⋊C4—151no—
481C2×C22⋊C4—151no—
482C2×C42—31no—
483C2×C42—151no—
484C2×C42—151no—
485C2×C42—151no—
486#95—31no—
487#95—51no—
488#95—151no—
489#95—151no—
490#95—151no—
491#95—151no—
492#95—151no—
493#95D3×D511yescharacteristic
494C2×C3×C5C22×C4⋊C411yescharacteristic
495C2×C3×C5#51811yescharacteristic
496C2×C3×C5#51911yescharacteristic
497C2×C3×C5#53711yescharacteristic
498C2×C3×C5#53711yescharacteristic
499C2×C3×C5#54411yescharacteristic
500C2×C3×C5#54411yescharacteristic
501C3×D5—24no—
502C23×C3—52no—
503C23×C3—52no—
504C23×C3—52no—
505C23×C3—101no—
506C23×C3—101no—
507C23×C3—101no—
508C23×C3—101no—
509C23×C3C23×D511yescharacteristic
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—52no—
519C2×C3×C4—101no—
520C2×C3×C4—101no—
521C2×C3×C4—101no—
522C2×C3×C4—101no—
523C2×C3×C4—101no—
524C2×C3×C4—101no—
525C2×C3×C4—101no—
526C2×C3×C4—101no—
527C2×C3×C4—204no—
528C2×C3×C4C2×C4×D512yes—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—52no—
538C2×Dic3—52no—
539C2×Dic3—52no—
540C2×Dic3—516no—
541C2×Dic3—52no—
542C2×Dic3—101no—
543C2×Dic3—101no—
544C2×Dic3—101no—
545C2×Dic3—101no—
546C2×Dic3—101no—
547C2×Dic3—101no—
548C2×Dic3—101no—
549C2×Dic3—101no—
550C2×Dic3—204no—
551C2×Dic3C2×C4×D512yes—
552C2×Dic3C2×C4×D512yes—
553C2×Dic3D4×D512yes—
554C2×Dic3Q8×D512yes—
555C22×C5C22×C4×D311yescharacteristic
556C22×C5C2×D3×D411yescharacteristic
557C22×C5#100411yescharacteristic
558C22×C5#100411yescharacteristic
559C22×C5C2×D3×Q811yescharacteristic
560C22×C5#101011yescharacteristic
561C22×C5#101011yescharacteristic
562C2×D5—22no—
563C2×D5—22no—
564C2×D5—22no—
565C2×D5—22no—
566C2×D5—22no—
567C2×D5—22no—
568C2×D5D3×C4⋊C414yes—
569C4×C5—22no—
570C4×C5—34no—
571C4×C5—41no—
572C4×C5—41no—
573C4×C5—62no—
574C4×C5—121no—
575C4×C5—121no—
576Dic5—22no—
577Dic5—34no—
578Dic5—41no—
579Dic5—41no—
580Dic5—62no—
581Dic5—121no—
582Dic5—121no—
583C24—51no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—51no—
589C22×C4—54no—
590C22×C4—51no—
591C22×C4—51no—
592C22×C4—154no—
593C22×C4—154no—
594C22×C4—154no—
595C22×C4—154no—
596C22×C4—151no—
597C22×C4—151no—
598C22×C4—151no—
599C22×C4—151no—
600C22×C4—201no—
601C22×C4—201no—
602C22×C4—601no—
603C22×C4—601no—
604C22×C4C2×D3×D511yescharacteristic
605C22×C4C2×D3×D511yescharacteristic
606C22×C4C2×D3×D511yescharacteristic
607C4⋊C4—34no—
608C4⋊C4—62no—
609C4⋊C4—121no—
610C4⋊C4—121no—
611C4⋊C4—154no—
612C4⋊C4—154no—
613C4⋊C4—154no—
614C4⋊C4—201no—
615C4⋊C4—201no—
616C4⋊C4—302no—
617C4⋊C4—302no—
618C4⋊C4—302no—
619C4⋊C4—601no—
620C4⋊C4—601no—
621C4⋊C4—601no—
622C4⋊C4—601no—
623C22⋊C4—102no—
624C22⋊C4—102no—
625C22⋊C4—302no—
626C22⋊C4—302no—
627C42—62no—
628C42—302no—
629C42—302no—
630C42—302no—
631C3×C5#231611yescharacteristic, complemented, Hall
632C22×C3—54no—
633C22×C3—102no—
634C22×C3—102no—
635C22×C3—102no—
636C22×C3—102no—
637C22×C3—102no—
638C22×C3—102no—
639C22×C3C22×C4×D511yescharacteristic
640C22×C3C2×D4×D511yescharacteristic
641C22×C3#414411yescharacteristic
642C22×C3C2×Q8×D511yescharacteristic
643C22×C3#414711yescharacteristic
644C22×C3#414911yescharacteristic
645C22×C3#415011yescharacteristic
646C3×C4—22no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—102no—
650C3×C4—201no—
651C3×C4—201no—
652Dic3—22no—
653Dic3—41no—
654Dic3—41no—
655Dic3—54no—
656Dic3—102no—
657Dic3—201no—
658Dic3—201no—
659Dic3D5×C4⋊C414yes—
660C2×C5#548611yescharacteristic
661C2×C5C2×D3×C4⋊C411yescharacteristic
662C2×C5#551611yescharacteristic
663C2×C5#559711yescharacteristic
664C2×C5#559711yescharacteristic
665C2×C5#562311yescharacteristic
666C2×C5#562311yescharacteristic
667D5—24no—
668C23—52no—
669C23—52no—
670C23—52no—
671C23—101no—
672C23—101no—
673C23—101no—
674C23—101no—
675C23C22×D3×D511yescharacteristic
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—32no—
685C2×C4—32no—
686C2×C4—32no—
687C2×C4—32no—
688C2×C4—52no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—101no—
698C2×C4—101no—
699C2×C4—101no—
700C2×C4—101no—
701C2×C4—101no—
702C2×C4—101no—
703C2×C4—101no—
704C2×C4—101no—
705C2×C4—1516no—
706C2×C4—152no—
707C2×C4—152no—
708C2×C4—152no—
709C2×C4—152no—
710C2×C4—204no—
711C2×C4—301no—
712C2×C4—301no—
713C2×C4—301no—
714C2×C4—301no—
715C2×C4—301no—
716C2×C4—301no—
717C2×C4—301no—
718C2×C4—301no—
719C2×C4—604no—
720C2×C4C4×D3×D512yes—
721C2×C3—104no—
722C2×C3C2×D5×C4⋊C411yescharacteristic
723C2×C3#6587911yescharacteristic
724C2×C3#6590611yescharacteristic
725C2×C3#6594211yescharacteristic
726C2×C3#6596311yescharacteristic
727C2×C3#6602311yescharacteristic
728C2×C3#6606311yescharacteristic
729C5#7386911yescharacteristic, complemented, Sylow
730C22—54no—
731C22—102no—
732C22—102no—
733C22—102no—
734C22—102no—
735C22—102no—
736C22—102no—
737C22#9200011yescharacteristic
738C22#9200111yescharacteristic
739C22C2×C4×D3×D511yescharacteristic
740C22D3×D4×D511yescharacteristic
741C22#9202511yescharacteristic
742C22#9202611yescharacteristic
743C22D3×Q8×D511yescharacteristic
744C4—22no—
745C4—34no—
746C4—41no—
747C4—41no—
748C4—62no—
749C4—102no—
750C4—121no—
751C4—121no—
752C4—154no—
753C4—201no—
754C4—201no—
755C4—302no—
756C4—601no—
757C4—601no—
758C3#1060792611yescharacteristic, complemented, Sylow
759C2—104no—
760C2#1175251611yescharacteristic
761C2#1175283211yescharacteristic
762C2#1175283311yescharacteristic
763C2#1175320011yescharacteristic
764C2#1175344811yescharacteristic
765C2#1175344911yescharacteristic
766C2D3×D5×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenter#95D3×D5
hypocenterC3×C5#2316
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. #11750748C2semidirect
5. C5×#4647C2semidirect
9. #11748820C2semidirect
10. #11748818C2semidirect
12. #11748695C2semidirect
13. #11748693C2semidirect
14. #11748664C2semidirect
15. #11748658C2semidirect
46. D5×Dic3⋊C4C4semidirect
133. #4647D5semidirect
225. D5×Dic3C4⋊C4semidirect
631. C3×C5#2316semidirect
729. C5#73869semidirect
758. C3#10607926semidirect

Maximal subgroups

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

subgroupindex
C2×#913942
C2×#913932
C2×D5×Dic3⋊C42
#117507482
C5×#46472
C3×#649562
#117488852
#117488782
#117488202
#117488182
#117487592
#117486952
#117486932
#117486642
#117486582
#106079263
#738695