Finite Group Databasebeta

← #14326655

Subgroups — #14326655

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C4⋊C4C211yesmaximal, characteristic
2C2×#91358C211yesmaximal, characteristic
3C2×#91357C211yesmaximal, characteristic
4#11751081C211yesmaximal, characteristic, complemented
5C5×#4980C211yesmaximal, characteristic, complemented
6#11748738C211yesmaximal, characteristic
7#11748737C211yesmaximal, characteristic
8#11748737C211yesmaximal, characteristic
9#11748702C211yesmaximal, characteristic
10#11748698C211yesmaximal, characteristic, complemented
11#11748697C211yesmaximal, characteristic, complemented
12#11748681C211yesmaximal, characteristic, complemented
13#11748680C211yesmaximal, characteristic, complemented
14#11748637C211yesmaximal, characteristic, complemented
15Dic3×#683C211yesmaximal, characteristic, complemented
16#10606692—31nomaximal, Hall
17C22×C3×C4×D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C5×C4⋊Dic3C2211yescharacteristic
24C2×C4×C5×Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×C3×#683C2211yescharacteristic
27C2×C3×#683C2211yescharacteristic
28C3×D5×C4⋊C4C418yescomplemented
29C2×#6668C2211yescharacteristic
30C2×#6668C2211yescharacteristic
31C2×#6668C2211yescharacteristic
32C2×#6668C2211yescharacteristic
33C2×#6665C2211yescharacteristic
34C2×#6665C2211yescharacteristic
35C2×#6665C2211yescharacteristic
36C2×#6665C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41#91358—24no—
42#91357—24no—
43#91115C2211yescharacteristic
44#91115C2211yescharacteristic
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47C5×C3⋊#95C2211yescharacteristic
48C5×C3⋊#95C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C5×C3⋊#95C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#82159—51nomaximal, Hall
56C2×#4038—31no—
57C2×D5×C4⋊C4D311yescharacteristic
58C2×#4018—31no—
59C5×#387—31no—
60#65270—31no—
61#65261—31no—
62C4×#683—31no—
63#64956—31no—
64#64955—31no—
65#64953—31no—
66#64953—31no—
67#64943—31no—
68#64942—31no—
69#64938—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—22no—
87C2×C3×C4×D5—22no—
88C2×C3×C4×D5—22no—
89C2×C3×C4×D5—22no—
90C2×C3×C4×D5—22no—
91C2×C3×C4×D5—22no—
92C2×C3×C4×D5C2×C414yes—
93C2×C3×C4×D5C2×C414yes—
94C2×C3×C4×D5C2×C414yes—
95C3×C5×C4⋊C4C2×C414yes—
96C4⋊Dic15—22no—
97C4×Dic15—22no—
98C5×C4⋊Dic3—22no—
99C4×C5×Dic3—22no—
100C3×C4⋊Dic5C2×C414yes—
101C3×#683C2×C414yes—
102C3×#683C2×C414yes—
103#6668—22no—
104#6668—22no—
105#6668—22no—
106#6668—22no—
107#6665—22no—
108#6665—22no—
109#6665—22no—
110#6665D414yes—
111Dic3×Dic5—22no—
112Dic3×Dic5—22no—
113Dic3×Dic5—22no—
114Dic3×Dic5—22no—
115C22×C3×C4⋊C4—51no—
116C2×#926—51no—
117C2×#926—51no—
118#5212—51no—
119#5211—51no—
120#5211—51no—
121C4×#217—51no—
122#4984—51no—
123#4984—51no—
124#4980—51no—
125#4980—51no—
126#4980—51no—
127#4980D511yescharacteristic, complemented
128Dic3×C4⋊C4—51no—
129Dic3×C4⋊C4—51no—
130C22×C4×D5C2×D311yescharacteristic
131C22×C4×D5C2×D311yescharacteristic
132C22×C4×D5C2×D311yescharacteristic
133C2×C5×C4⋊C4—31no—
134C2×C5×C4⋊C4C2×D311yescharacteristic
135C2×C42×C5—31no—
136C2×#685—31no—
137C2×#685—31no—
138C2×#685—31no—
139C2×#685—31no—
140C2×C4⋊Dic5—31no—
141C2×C4⋊Dic5C2×D311yescharacteristic
142C2×#683—31no—
143C2×#683—31no—
144C2×#683—31no—
145C2×#683—31no—
146C2×#683C2×D311yescharacteristic
147C2×#683C2×D311yescharacteristic
148C2×C4×Dic5—31no—
149C2×C4×Dic5—31no—
150C2×C4×Dic5—31no—
151C2×C4×Dic5—31no—
152C2×C4×Dic5—31no—
153#4038—64no—
154D5×C4⋊C4Dic318yescomplemented
155#4018—64no—
156C5×#95—31no—
157C5×#95—31no—
158C5×#95—31no—
159C5×#95—31no—
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963—31no—
164#3963—31no—
165#3963—31no—
166#3963—31no—
167#3963—31no—
168#2344—151noSylow
169C23×C3×C5C2411yescharacteristic
170C22×C3×D5—21no—
171C22×C3×D5—21no—
172C22×C3×D5—21no—
173C22×C3×D5—21no—
174C22×C3×D5C22×C412yes—
175C22×C3×D5C2×D412yes—
176C22×C3×D5#4112yes—
177C2×C3×C4×C5—21no—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—21no—
180C2×C3×C4×C5—21no—
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5C22×C412yes—
184C2×C3×C4×C5C22×C412yes—
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×Dic15C2×D412yes—
198C2×C5×Dic3—21no—
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×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3C2×D412yes—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5C22×C412yes—
215C2×C3×Dic5C22×C412yes—
216C2×C3×Dic5C22×C412yes—
217C2×C3×Dic5#4112yes—
218C2×C3×Dic5#4112yes—
219C3×C4×D5—28no—
220C3×C4×D5—28no—
221C3×C4×D5—28no—
222C23×C3×C4—51no—
223C23×C3×C4—51no—
224C23×C3×C4—51no—
225C2×C3×C4⋊C4—51no—
226C2×C3×C4⋊C4—51no—
227C2×C3×C4⋊C4—51no—
228C2×C3×C4⋊C4—58no—
229C2×C3×C4⋊C4C2×D511yescharacteristic
230C2×#217—51no—
231C2×#217—51no—
232C2×#217—51no—
233C2×#217—51no—
234#926—104no—
235#926—104no—
236C2×C4⋊Dic3—51no—
237C2×C4⋊Dic3—51no—
238C2×C4⋊Dic3—51no—
239C2×C4⋊Dic3—51no—
240C2×C4⋊Dic3—51no—
241C2×C4⋊Dic3C2×D511yescharacteristic
242C2×C4×Dic3—51no—
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⋊#95C2×D511yescharacteristic
257C3⋊#95C2×D511yescharacteristic
258C3⋊#95C2×D511yescharacteristic
259C3⋊#95C2×D511yescharacteristic
260C23×D5C22×D311yescharacteristic
261C22×C4×C5—31no—
262C22×C4×C5—31no—
263C22×C4×C5—31no—
264C22×C4×C5—31no—
265C22×C4×C5C22×D311yescharacteristic
266C22×C4×C5C22×D311yescharacteristic
267C22×C4×C5C22×D311yescharacteristic
268C22×Dic5—31no—
269C22×Dic5—31no—
270C22×Dic5—31no—
271C22×Dic5—31no—
272C22×Dic5C22×D311yescharacteristic
273C22×Dic5C22×D311yescharacteristic
274C22×Dic5C22×D311yescharacteristic
275C2×C4×D5—22no—
276C2×C4×D5—22no—
277C2×C4×D5—22no—
278C2×C4×D5—22no—
279C2×C4×D5—22no—
280C2×C4×D5—22no—
281C2×C4×D5C2×Dic314yes—
282C2×C4×D5C2×Dic314yes—
283C2×C4×D5C2×Dic314yes—
284C5×C4⋊C4—62no—
285C5×C4⋊C4C2×Dic314yes—
286C42×C5—62no—
287#685—34no—
288#685—62no—
289#685—62no—
290#685—62no—
291C4⋊Dic5—62no—
292C4⋊Dic5C2×Dic314yes—
293#683—62no—
294#683—62no—
295#683—62no—
296#683—62no—
297#683C2×Dic314yes—
298#683C2×Dic314yes—
299C4×Dic5—62no—
300C4×Dic5—62no—
301C4×Dic5—62no—
302C4×Dic5—62no—
303C4×Dic5—62no—
304C2×#117—151no—
305C2×#117—151no—
306C22×C4⋊C4—51no—
307#389—151no—
308#389—151no—
309#387—31no—
310#387—151no—
311#387—151no—
312#387—151no—
313#381—151no—
314#381—151no—
315#380—151no—
316C4×C4⋊C4—151no—
317C4×C4⋊C4—151no—
318C4×C22⋊C4—151no—
319C22×C3×C5C23×C411yescharacteristic
320C22×C3×C5C22×D411yescharacteristic
321C22×C3×C5C2×#4111yescharacteristic
322C22×C3×C5C2×#4111yescharacteristic
323C22×C3×C5C2×#4111yescharacteristic
324C22×C3×C52−1+411yescharacteristic
325C22×C3×C52−1+411yescharacteristic
326C2×C3×D5—22no—
327C2×C3×D5—22no—
328C2×C3×D5—22no—
329C2×C3×D5—22no—
330C2×C3×D5—22no—
331C2×C3×D5—22no—
332C2×C3×D5C4×D414yes—
333C3×C4×C5—22no—
334C3×C4×C5—22no—
335C3×C4×C5—22no—
336Dic15—22no—
337Dic15—41no—
338Dic15—41no—
339Dic15—41no—
340C3×Dic5—22no—
341C3×Dic5—22no—
342C3×Dic5#11714yescomplemented
343C5×Dic3—22no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C5×Dic3—41no—
347C24×C3—51no—
348C22×C3×C4—51no—
349C22×C3×C4—51no—
350C22×C3×C4—51no—
351C22×C3×C4—54no—
352C22×C3×C4—54no—
353C22×C3×C4—54no—
354C22×C3×C4—102no—
355C22×C3×C4—102no—
356C22×C3×C4—102no—
357C22×C3×C4—102no—
358C22×C3×C4—102no—
359C22×C3×C4—102no—
360C22×C3×C4C22×D511yescharacteristic
361C22×C3×C4C22×D511yescharacteristic
362C22×C3×C4C22×D511yescharacteristic
363C22×Dic3—51no—
364C22×Dic3—51no—
365C22×Dic3—51no—
366C22×Dic3—51no—
367C22×Dic3C22×D511yescharacteristic
368C22×Dic3C22×D511yescharacteristic
369C22×Dic3C22×D511yescharacteristic
370C22×Dic3C22×D511yescharacteristic
371C3×C4⋊C4—54no—
372C3×C4⋊C4—54no—
373C3×C4⋊C4—54no—
374C3×C4⋊C4C4×D514yes—
375#217—54no—
376#217—102no—
377#217—102no—
378#217—102no—
379C4⋊Dic3—22no—
380C4⋊Dic3—102no—
381C4⋊Dic3—102no—
382C4⋊Dic3—102no—
383C4⋊Dic3—102no—
384C4⋊Dic3—102no—
385C4×Dic3—22no—
386C4×Dic3—102no—
387C4×Dic3—102no—
388C4×Dic3—102no—
389C4×Dic3—102no—
390C4×Dic3—102no—
391C23×C5C23×D311yescharacteristic
392C22×D5—21no—
393C22×D5—21no—
394C22×D5—21no—
395C22×D5—21no—
396C22×D5D3×D412yes—
397C22×D5#23712yes—
398C22×D5C22×Dic312yes—
399C2×C4×C5—21no—
400C2×C4×C5—21no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—32no—
406C2×C4×C5—61no—
407C2×C4×C5—61no—
408C2×C4×C5—61no—
409C2×C4×C5—61no—
410C2×C4×C5—61no—
411C2×C4×C5—61no—
412C2×C4×C5—61no—
413C2×C4×C5—61no—
414C2×C4×C5—61no—
415C2×C4×C5—61no—
416C2×C4×C5—61no—
417C2×C4×C5C22×Dic312yes—
418C2×C4×C5C22×Dic312yes—
419C2×C4×C5C22×Dic312yes—
420C2×Dic5—21no—
421C2×Dic5—21no—
422C2×Dic5—21no—
423C2×Dic5—21no—
424C2×Dic5—32no—
425C2×Dic5—61no—
426C2×Dic5—61no—
427C2×Dic5—61no—
428C2×Dic5—61no—
429C2×Dic5—61no—
430C2×Dic5—61no—
431C2×Dic5—61no—
432C2×Dic5—61no—
433C2×Dic5—61no—
434C2×Dic5—61no—
435C2×Dic5—61no—
436C2×Dic5#23512yes—
437C2×Dic5#23512yes—
438C2×Dic5C22×Dic312yes—
439C2×Dic5C22×Dic312yes—
440C2×Dic5C22×Dic312yes—
441C4×D5—28no—
442C4×D5—28no—
443C4×D5—28no—
444C23×C4—51no—
445C23×C4—51no—
446C23×C4—51no—
447#117—304no—
448#117—304no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—51no—
451C2×C4⋊C4—51no—
452C2×C4⋊C4—51no—
453C2×C4⋊C4—58no—
454C2×C4⋊C4—151no—
455C2×C4⋊C4—151no—
456C2×C4⋊C4—151no—
457C2×C4⋊C4—151no—
458C2×C4⋊C4—151no—
459C2×C4⋊C4D3×D511yescharacteristic
460C2×C22⋊C4—151no—
461C2×C22⋊C4—151no—
462C2×C22⋊C4—151no—
463C2×C22⋊C4—151no—
464C2×C42—31no—
465C2×C42—151no—
466C2×C42—151no—
467C2×C42—151no—
468C2×C42—151no—
469C2×C42—151no—
470#95—31no—
471#95—31no—
472#95—31no—
473#95—31no—
474#95—151no—
475#95—151no—
476#95—151no—
477#95—151no—
478#95—151no—
479#95—151no—
480#95—151no—
481#95—151no—
482C2×C3×C5C2×#11711yescharacteristic
483C2×C3×C5C2×C4×D411yescharacteristic
484C2×C3×C5#51911yescharacteristic
485C2×C3×C5#54711yescharacteristic
486C2×C3×C5#54711yescharacteristic
487C2×C3×C5#55211yescharacteristic
488C2×C3×C5#55211yescharacteristic
489C3×D5—24no—
490C23×C3—52no—
491C23×C3—52no—
492C23×C3—52no—
493C23×C3—101no—
494C23×C3—101no—
495C23×C3—101no—
496C23×C3—101no—
497C23×C3C23×D511yescharacteristic
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—52no—
505C2×C3×C4—52no—
506C2×C3×C4—52no—
507C2×C3×C4—52no—
508C2×C3×C4—52no—
509C2×C3×C4—108no—
510C2×C3×C4—108no—
511C2×C3×C4—108no—
512C2×C3×C4—101no—
513C2×C3×C4—101no—
514C2×C3×C4—101no—
515C2×C3×C4—101no—
516C2×C3×C4C2×C4×D512yes—
517C2×C3×C4C2×C4×D512yes—
518C2×C3×C4C2×C4×D512yes—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—52no—
531C2×Dic3—101no—
532C2×Dic3—101no—
533C2×Dic3—101no—
534C2×Dic3—101no—
535C2×Dic3—101no—
536C2×Dic3—101no—
537C2×Dic3—101no—
538C2×Dic3—101no—
539C2×Dic3—101no—
540C2×Dic3—101no—
541C2×Dic3—101no—
542C2×Dic3D4×D512yes—
543C22×C5C2×#23511yescharacteristic
544C22×C5C2×#23511yescharacteristic
545C22×C5C2×D3×D411yescharacteristic
546C22×C5C2×#23711yescharacteristic
547C22×C5#100711yescharacteristic
548C22×C5#100711yescharacteristic
549C22×C5C23×Dic311yescharacteristic
550C2×D5—22no—
551C2×D5—22no—
552C2×D5—22no—
553C2×D5—22no—
554C2×D5—22no—
555C2×D5—22no—
556C2×D5D4×Dic314yes—
557C4×C5—22no—
558C4×C5—22no—
559C4×C5—22no—
560C4×C5—62no—
561C4×C5—121no—
562C4×C5—121no—
563C4×C5—121no—
564Dic5—22no—
565Dic5—22no—
566Dic5—62no—
567Dic5—121no—
568Dic5—121no—
569Dic5—121no—
570Dic5#92614yescomplemented
571C24—51no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—51no—
577C22×C4—51no—
578C22×C4—51no—
579C22×C4—54no—
580C22×C4—54no—
581C22×C4—54no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4—102no—
585C22×C4—102no—
586C22×C4—102no—
587C22×C4—102no—
588C22×C4—151no—
589C22×C4—151no—
590C22×C4—151no—
591C22×C4—151no—
592C22×C4C2×D3×D511yescharacteristic
593C22×C4C2×D3×D511yescharacteristic
594C22×C4C2×D3×D511yescharacteristic
595C4⋊C4—54no—
596C4⋊C4—54no—
597C4⋊C4—54no—
598C4⋊C4—62no—
599C4⋊C4—302no—
600C4⋊C4—302no—
601C4⋊C4—302no—
602C4⋊C4—302no—
603C4⋊C4—302no—
604C4⋊C4D5×Dic314yes—
605C22⋊C4—154no—
606C22⋊C4—302no—
607C22⋊C4—302no—
608C22⋊C4—302no—
609C42—62no—
610C42—302no—
611C42—302no—
612C42—302no—
613C42—302no—
614C42—302no—
615C3×C5#234411yescharacteristic, complemented, Hall
616C22×C3—54no—
617C22×C3—102no—
618C22×C3—102no—
619C22×C3—102no—
620C22×C3—102no—
621C22×C3—102no—
622C22×C3—102no—
623C22×C3C22×C4×D511yescharacteristic
624C22×C3C2×D4×D511yescharacteristic
625C22×C3#414711yescharacteristic
626C22×C3D5×#4111yescharacteristic
627C22×C3D5×#4111yescharacteristic
628C22×C3D5×#4111yescharacteristic
629C22×C3#415011yescharacteristic
630C3×C4—22no—
631C3×C4—22no—
632C3×C4—22no—
633C3×C4—54no—
634C3×C4—102no—
635C3×C4—102no—
636Dic3—22no—
637Dic3—41no—
638Dic3—41no—
639Dic3—41no—
640Dic3—102no—
641Dic3—201no—
642Dic3—201no—
643Dic3—201no—
644C2×C5#550711yescharacteristic
645C2×C5#550711yescharacteristic
646C2×C5#551311yescharacteristic
647C2×C5#551311yescharacteristic
648C2×C5C2×#92611yescharacteristic
649C2×C5C2×D4×Dic311yescharacteristic
650C2×C5#581211yescharacteristic
651D5—24no—
652C23—52no—
653C23—52no—
654C23—52no—
655C23—101no—
656C23—101no—
657C23—101no—
658C23—101no—
659C23C22×D3×D511yescharacteristic
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—32no—
667C2×C4—52no—
668C2×C4—52no—
669C2×C4—52no—
670C2×C4—52no—
671C2×C4—52no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—108no—
684C2×C4—108no—
685C2×C4—108no—
686C2×C4—101no—
687C2×C4—101no—
688C2×C4—101no—
689C2×C4—101no—
690C2×C4—152no—
691C2×C4—301no—
692C2×C4—301no—
693C2×C4—301no—
694C2×C4—301no—
695C2×C4—301no—
696C2×C4—301no—
697C2×C4—301no—
698C2×C4—301no—
699C2×C4—301no—
700C2×C4—301no—
701C2×C4—301no—
702C2×C4C2×D5×Dic312yes—
703C2×C4C2×D5×Dic312yes—
704C2×C4C2×D5×Dic312yes—
705C2×C3—104no—
706C2×C3D5×#11711yescharacteristic
707C2×C3C4×D4×D511yescharacteristic
708C2×C3#6590611yescharacteristic
709C2×C3#6596511yescharacteristic
710C2×C3#6598911yescharacteristic
711C2×C3#6602711yescharacteristic
712C2×C3#6604211yescharacteristic
713C5#8215911yescharacteristic, complemented, Sylow
714C22—54no—
715C22—102no—
716C22—102no—
717C22—102no—
718C22—102no—
719C22—102no—
720C22—102no—
721C22D5×#23511yescharacteristic
722C22D5×#23511yescharacteristic
723C22D3×D4×D511yescharacteristic
724C22D5×#23711yescharacteristic
725C22#9202911yescharacteristic
726C22#9203011yescharacteristic
727C22C22×D5×Dic311yescharacteristic
728C4—22no—
729C4—22no—
730C4—22no—
731C4—54no—
732C4—62no—
733C4—102no—
734C4—102no—
735C4—121no—
736C4—121no—
737C4—121no—
738C4—302no—
739C4—601no—
740C4—601no—
741C4—601no—
742C3#1060669211yescharacteristic, complemented, Sylow
743C2—104no—
744C2#1175334511yescharacteristic
745C2#1175367311yescharacteristic
746C2#1175367811yescharacteristic
747C2#1175372311yescharacteristic
748C2D5×#92611yescharacteristic
749C2D4×D5×Dic311yescharacteristic
750C2#1175514011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2344
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11751081C2semidirect
5. C5×#4980C2semidirect
10. #11748698C2semidirect
11. #11748697C2semidirect
12. #11748681C2semidirect
13. #11748680C2semidirect
14. #11748637C2semidirect
15. Dic3×#683C2semidirect
28. C3×D5×C4⋊C4C4semidirect
127. #4980D5semidirect
154. D5×C4⋊C4Dic3semidirect
342. C3×Dic5#117semidirect
570. Dic5#926semidirect
615. C3×C5#2344semidirect
713. C5#82159semidirect
742. C3#10606692semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×C4⋊C42
C2×#913582
C2×#913572
#117510812
C5×#49802
#117487382
#117487372
#117487022
#117486982
#117486972
#117486812
#117486802
#117486372
Dic3×#6832
#106066923
#821595