Finite Group Databasebeta

← #14329766

Subgroups — #14329766

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91767C211yesmaximal, characteristic
2C5×#4950C211yesmaximal, characteristic
3C3×C22⋊C4×Dic5C211yesmaximal, characteristic
4#11749508C211yesmaximal, characteristic
5#11749487C211yesmaximal, characteristic
6Dic3×C22⋊Dic5C211yesmaximal, characteristic
7C2×#90994C211yesmaximal, characteristic
8#11748824C211yesmaximal, characteristic, complemented
9#11748694C211yesmaximal, characteristic, complemented
10#11748688C211yesmaximal, characteristic, complemented
11#11748687C211yesmaximal, characteristic, complemented
12#11748687C211yesmaximal, characteristic, complemented
13Dic5×C4⋊Dic3C211yesmaximal, characteristic, complemented
14#11748640C211yesmaximal, characteristic, complemented
15#11748587C211yesmaximal, characteristic, complemented
16#10606130—31nomaximal, Hall
17C23×Dic15C2211yescharacteristic
18C22×Dic30C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×#6719C2211yescharacteristic
23C2×C4⋊Dic15C2211yescharacteristic
24C2×#6712C2211yescharacteristic
25C2×#6712C2211yescharacteristic
26#91767C418yescomplemented
27C2×C5×#217C2211yescharacteristic
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C2×C5×C4⋊Dic3C2211yescharacteristic
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic
33C2×#6669C2211yescharacteristic
34C2×#6669C2211yescharacteristic
35C2×Dic3×Dic5C2211yescharacteristic
36C2×Dic3×Dic5C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39C5×C3⋊#95C2211yescharacteristic
40C5×C3⋊#95C2211yescharacteristic
41C3×#3963C2211yescharacteristic
42C3×#3963C2211yescharacteristic
43#90994C2211yescharacteristic
44#90994C2211yescharacteristic
45#90994C2211yescharacteristic
46#90994C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#73474—51nomaximal, Hall
54C2×#4024—31no—
55C5×#385—31no—
56C4×C22⋊Dic5—31no—
57C2×#3963—31no—
58#65267—31no—
59#65267—31no—
60C4⋊C4×Dic5—31no—
61#65263—31no—
62#65235—31no—
63C22⋊C4×Dic5—31no—
64C22⋊C4×Dic5D311yescharacteristic
65#64942—31no—
66#64941—31no—
67#64938—31no—
68#64935—31no—
69C24×C3×C5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×Dic15—41no—
73C22×Dic15—41no—
74C22×Dic15C2×C414yes—
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C2×Dic30—41no—
80C2×Dic30—41no—
81C2×Dic30C2×C414yescomplemented
82C22×C5×Dic3—22no—
83C22×C5×Dic3—22no—
84C22×C5×Dic3—41no—
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C3×Dic5—22no—
90C22×C3×Dic5—22no—
91C22×C3×Dic5—41no—
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C3×C5×C22⋊C4C2×C414yes—
97#6719C2×C414yes—
98C4⋊Dic15C2×C414yescomplemented
99#6712C2×C414yescomplemented
100#6712C2×C414yescomplemented
101C5×#217—22no—
102C5×C4⋊Dic3—22no—
103C5×C4⋊Dic3—41no—
104C3×C22⋊Dic5Q814yescomplemented
105C3×C4×Dic5—22no—
106C3×C4×Dic5—41no—
107#6669—22no—
108#6669—41no—
109Dic3×Dic5—22no—
110Dic3×Dic5—41no—
111Dic3×Dic5—41no—
112Dic3×Dic5—41no—
113C2×#878—51no—
114C3×C4×C22⋊C4—51no—
115#5210—51no—
116C2×C3⋊#95—51no—
117#4950D511yescharacteristic
118Dic3×C22⋊C4—51no—
119Dic3×C22⋊C4—51no—
120C4×C4⋊Dic3—51no—
121#4933—51no—
122C4×Dic3⋊C4—51no—
123#4929—51no—
124#4655—51no—
125#4655—51no—
126#4654—51no—
127#4646—51no—
128C23×C4×C5—31no—
129C23×Dic5—31no—
130C23×Dic5C2×D311yescharacteristic
131C22×Dic10—31no—
132C2×C5×C4⋊C4—31no—
133C2×C5×C4⋊C4—31no—
134C2×C5×C22⋊C4—31no—
135C2×C5×C22⋊C4C2×D311yescharacteristic
136C2×C22⋊Dic5—31no—
137C2×C22⋊Dic5C2×D311yescharacteristic
138C2×C4⋊Dic5—31no—
139C2×#683—31no—
140C2×#683—31no—
141C2×#683—31no—
142C2×#683—31no—
143C2×C4×Dic5—31no—
144C2×C4×Dic5—31no—
145C2×C4×Dic5—31no—
146C2×C4×Dic5—31no—
147C2×C4×Dic5C2×D311yescharacteristic
148C2×C4×Dic5C2×D311yescharacteristic
149#4024—38no—
150C5×#95—31no—
151C5×#95—31no—
152#3963—31no—
153#3963—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#3963C2×D311yescharacteristic
163#3963C2×D311yescharacteristic
164#2368—151noSylow
165C23×C3×C5—21no—
166C23×C3×C5—21no—
167C23×C3×C5—21no—
168C23×C3×C5—21no—
169C23×C3×C5C22×C412yes—
170C23×C3×C5C2×Q812yes—
171C23×C3×C5#4112yes—
172C23×C3×C5C2411yescharacteristic
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5—21no—
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5—21no—
177C2×C3×C4×C5C22×C412yes—
178C2×C3×C4×C5C22×C412yes—
179C2×Dic15—21no—
180C2×Dic15—21no—
181C2×Dic15—21no—
182C2×Dic15—21no—
183C2×Dic15—21no—
184C2×Dic15—21no—
185C2×Dic15—21no—
186C2×Dic15—21no—
187C2×Dic15—44no—
188C2×Dic15C22×C412yes—
189C2×Dic15C22×C412yes—
190C2×Dic15C22×C412yes—
191C2×Dic15C22×C412yes—
192Dic30—44no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—21no—
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—44no—
205C2×C5×Dic3#4112yes—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—44no—
216C2×C3×Dic5C2×Q812yes—
217C2×C3×Dic5C2×Q812yes—
218C2×C3×Dic5#4112yes—
219C23×C3×C4—51no—
220C23×Dic3—51no—
221C23×Dic3C2×D511yescharacteristic
222C22×Dic6—51no—
223C2×C3×C22⋊C4—51no—
224C2×C3×C22⋊C4C2×D511yescharacteristic
225C2×C3×C42—51no—
226C2×C3×C42—51no—
227C2×#217—51no—
228C2×#217C2×D511yescharacteristic
229C2×C4⋊Dic3—51no—
230C2×C4⋊Dic3C2×D511yescharacteristic
231C2×C4⋊Dic3C2×D511yescharacteristic
232C2×Dic3⋊C4—51no—
233C2×Dic3⋊C4—51no—
234C2×Dic3⋊C4—51no—
235C2×Dic3⋊C4—51no—
236C2×C4×Dic3—51no—
237C2×C4×Dic3—51no—
238C2×C4×Dic3—51no—
239C2×C4×Dic3—51no—
240#878—58no—
241C3×#95—51no—
242C3×#95—51no—
243C3⋊#95—51no—
244C3⋊#95—51no—
245C3⋊#95—51no—
246C3⋊#95—51no—
247C3⋊#95—51no—
248C3⋊#95—51no—
249C3⋊#95—51no—
250C3⋊#95—51no—
251C3⋊#95—51no—
252C3⋊#95—51no—
253C3⋊#95C2×D511yescharacteristic
254C3⋊#95C2×D511yescharacteristic
255C24×C5C22×D311yescharacteristic
256C22×C4×C5—31no—
257C22×C4×C5—31no—
258C22×C4×C5—31no—
259C22×C4×C5—31no—
260C22×C4×C5—62no—
261C22×C4×C5—62no—
262C22×C4×C5—121no—
263C22×C4×C5C22×D311yescharacteristic
264C22×C4×C5C22×D311yescharacteristic
265C22×Dic5—22no—
266C22×Dic5—22no—
267C22×Dic5—31no—
268C22×Dic5—31no—
269C22×Dic5—31no—
270C22×Dic5—31no—
271C22×Dic5—34no—
272C22×Dic5—41no—
273C22×Dic5—121no—
274C22×Dic5—121no—
275C22×Dic5C22×D311yescharacteristic
276C22×Dic5C22×D311yescharacteristic
277C22×Dic5C22×D311yescharacteristic
278C22×Dic5C22×D311yescharacteristic
279C2×Dic10—34no—
280C2×Dic10—121no—
281C2×Dic10—121no—
282C5×C4⋊C4—62no—
283C5×C4⋊C4—121no—
284C5×C22⋊C4—62no—
285C5×C22⋊C4C4×D314yes—
286C22⋊Dic5—34no—
287C22⋊Dic5Dic614yescomplemented
288C4⋊Dic5—34no—
289#683—34no—
290#683—34no—
291#683—62no—
292#683—121no—
293C4×Dic5—22no—
294C4×Dic5—41no—
295C4×Dic5—62no—
296C4×Dic5—121no—
297C4×Dic5—121no—
298C4×Dic5—121no—
299C2×C22⋊Q8—151no—
300#391—151no—
301#391—151no—
302#387—151no—
303#387—151no—
304#387—151no—
305#387—151no—
306#385—31no—
307#385—151no—
308C4×C4⋊C4—151no—
309C4×C4⋊C4—151no—
310C4×C22⋊C4—51no—
311C4×C22⋊C4—151no—
312C4×C22⋊C4—151no—
313C2×#95—151no—
314C22×C3×C5—22no—
315C22×C3×C5—22no—
316C22×C3×C5—22no—
317C22×C3×C5—22no—
318C22×C3×C5—22no—
319C22×C3×C5—22no—
320C22×C3×C5C4×Q814yes—
321C22×C3×C5C23×C411yescharacteristic
322C22×C3×C5C22×Q811yescharacteristic
323C22×C3×C5C2×#4111yescharacteristic
324C22×C3×C5C2×#4111yescharacteristic
325C22×C3×C5C2×#4111yescharacteristic
326C22×C3×C5H(5,𝔽2)11yescharacteristic
327C22×C3×C5H(5,𝔽2)11yescharacteristic
328C3×C4×C5—22no—
329C3×C4×C5—22no—
330Dic15—22no—
331Dic15—22no—
332Dic15—22no—
333Dic15—22no—
334C3×Dic5—22no—
335C3×Dic5—22no—
336C3×Dic5—22no—
337C3×Dic5—41no—
338C5×Dic3—22no—
339C5×Dic3—41no—
340C5×Dic3—41no—
341C5×Dic3—41no—
342C24×C3C22×D511yescharacteristic
343C22×C3×C4—51no—
344C22×C3×C4—51no—
345C22×C3×C4—51no—
346C22×C3×C4—51no—
347C22×C3×C4—102no—
348C22×C3×C4—102no—
349C22×C3×C4—201no—
350C22×C3×C4C22×D511yescharacteristic
351C22×C3×C4C22×D511yescharacteristic
352C22×Dic3—22no—
353C22×Dic3—22no—
354C22×Dic3—41no—
355C22×Dic3—51no—
356C22×Dic3—51no—
357C22×Dic3—51no—
358C22×Dic3—51no—
359C22×Dic3—54no—
360C22×Dic3—201no—
361C22×Dic3—201no—
362C22×Dic3C22×D511yescharacteristic
363C22×Dic3C22×D511yescharacteristic
364C22×Dic3C22×D511yescharacteristic
365C22×Dic3C22×D511yescharacteristic
366C2×Dic6—54no—
367C2×Dic6—201no—
368C2×Dic6—201no—
369C3×C22⋊C4—54no—
370C3×C22⋊C4C4×D514yes—
371C3×C42—102no—
372C3×C42—201no—
373#217—22no—
374#217—54no—
375C4⋊Dic3—22no—
376C4⋊Dic3—41no—
377C4⋊Dic3—54no—
378Dic3⋊C4—54no—
379Dic3⋊C4—54no—
380Dic3⋊C4—102no—
381Dic3⋊C4—201no—
382C4×Dic3—102no—
383C4×Dic3—201no—
384C4×Dic3—201no—
385C4×Dic3—201no—
386C23×C5—21no—
387C23×C5—21no—
388C23×C5—21no—
389C23×C5—21no—
390C23×C5C2×Dic612yes—
391C23×C5C2×C4×D312yes—
392C23×C5#23512yes—
393C23×C5C23×D311yescharacteristic
394C2×C4×C5—21no—
395C2×C4×C5—21no—
396C2×C4×C5—21no—
397C2×C4×C5—21no—
398C2×C4×C5—32no—
399C2×C4×C5—61no—
400C2×C4×C5—61no—
401C2×C4×C5—61no—
402C2×C4×C5—61no—
403C2×C4×C5—61no—
404C2×C4×C5—61no—
405C2×C4×C5—61no—
406C2×C4×C5—61no—
407C2×C4×C5—61no—
408C2×C4×C5—61no—
409C2×C4×C5—61no—
410C2×C4×C5—124no—
411C2×C4×C5C2×C4×D312yes—
412C2×C4×C5C2×C4×D312yes—
413C2×Dic5—21no—
414C2×Dic5—21no—
415C2×Dic5—21no—
416C2×Dic5—21no—
417C2×Dic5—21no—
418C2×Dic5—21no—
419C2×Dic5—21no—
420C2×Dic5—21no—
421C2×Dic5—21no—
422C2×Dic5—32no—
423C2×Dic5—32no—
424C2×Dic5—32no—
425C2×Dic5—32no—
426C2×Dic5—44no—
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—124no—
436C2×Dic5C2×Dic612yes—
437C2×Dic5C2×Dic612yes—
438C2×Dic5#23712yes—
439Dic10—124no—
440C22×Q8—151no—
441C23×C4—31no—
442C23×C4—51no—
443C23×C4—151no—
444C22⋊Q8—158no—
445C2×C4⋊C4—31no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—151no—
448C2×C4⋊C4—151no—
449C2×C4⋊C4—151no—
450C2×C4⋊C4—151no—
451C2×C4⋊C4—151no—
452C2×C22⋊C4—31no—
453C2×C22⋊C4—51no—
454C2×C22⋊C4—151no—
455C2×C22⋊C4D3×D511yescharacteristic
456C2×C42—51no—
457C2×C42—51no—
458C2×C42—151no—
459C2×C42—151no—
460C2×C42—151no—
461C2×C42—151no—
462#95—31no—
463#95—31no—
464#95—51no—
465#95—51no—
466#95—151no—
467#95—151no—
468#95—151no—
469#95—151no—
470#95—151no—
471#95—151no—
472#95—151no—
473#95—151no—
474#95—151no—
475#95—151no—
476C2×C3×C5—24no—
477C2×C3×C5C2×C4×Q811yescharacteristic
478C2×C3×C5C4×#4111yescharacteristic
479C2×C3×C5#51811yescharacteristic
480C2×C3×C5#55111yescharacteristic
481C2×C3×C5#55111yescharacteristic
482C2×C3×C5#55411yescharacteristic
483C2×C3×C5#55411yescharacteristic
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3C2×C4×D512yes—
489C23×C3#71112yes—
490C23×C3Q8×D512yes—
491C23×C3C23×D511yescharacteristic
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—52no—
497C2×C3×C4—52no—
498C2×C3×C4—52no—
499C2×C3×C4—101no—
500C2×C3×C4—101no—
501C2×C3×C4—101no—
502C2×C3×C4—101no—
503C2×C3×C4—101no—
504C2×C3×C4—101no—
505C2×C3×C4—101no—
506C2×C3×C4—101no—
507C2×C3×C4—101no—
508C2×C3×C4—204no—
509C2×C3×C4C2×C4×D512yes—
510C2×C3×C4C2×C4×D512yes—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—44no—
523C2×Dic3—52no—
524C2×Dic3—52no—
525C2×Dic3—52no—
526C2×Dic3—52no—
527C2×Dic3—101no—
528C2×Dic3—101no—
529C2×Dic3—101no—
530C2×Dic3—101no—
531C2×Dic3—101no—
532C2×Dic3—101no—
533C2×Dic3—101no—
534C2×Dic3—101no—
535C2×Dic3—204no—
536C2×Dic3#71112yes—
537Dic6—204no—
538C22×C5—22no—
539C22×C5—22no—
540C22×C5—22no—
541C22×C5—22no—
542C22×C5—22no—
543C22×C5—22no—
544C22×C5C4×Dic614yes—
545C22×C5C22×Dic611yescharacteristic
546C22×C5C22×C4×D311yescharacteristic
547C22×C5C2×#23511yescharacteristic
548C22×C5C2×#23711yescharacteristic
549C22×C5#100411yescharacteristic
550C22×C5D3×#4111yescharacteristic
551C22×C5#100911yescharacteristic
552C4×C5—22no—
553C4×C5—22no—
554C4×C5—62no—
555C4×C5—121no—
556C4×C5—121no—
557C4×C5—121no—
558Dic5—22no—
559Dic5—22no—
560Dic5—22no—
561Dic5—41no—
562Dic5—62no—
563Dic5—62no—
564Dic5—62no—
565Dic5—62no—
566C24C2×D3×D511yescharacteristic
567C2×Q8—154no—
568C2×Q8—601no—
569C2×Q8—601no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—51no—
575C22×C4—51no—
576C22×C4—51no—
577C22×C4—51no—
578C22×C4—62no—
579C22×C4—62no—
580C22×C4—102no—
581C22×C4—102no—
582C22×C4—121no—
583C22×C4—151no—
584C22×C4—151no—
585C22×C4—151no—
586C22×C4—151no—
587C22×C4—154no—
588C22×C4—201no—
589C22×C4—601no—
590C22×C4—601no—
591C22×C4C2×D3×D511yescharacteristic
592C22×C4C2×D3×D511yescharacteristic
593C4⋊C4—62no—
594C4⋊C4—121no—
595C4⋊C4—154no—
596C4⋊C4—154no—
597C4⋊C4—154no—
598C4⋊C4—302no—
599C4⋊C4—601no—
600C22⋊C4—54no—
601C22⋊C4—62no—
602C22⋊C4—154no—
603C22⋊C4#120014yes—
604C42—102no—
605C42—201no—
606C42—302no—
607C42—601no—
608C42—601no—
609C42—601no—
610C3×C5#236811yescharacteristic, complemented, Hall
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3#403314yes—
618C22×C3C22×C4×D511yescharacteristic
619C22×C3C2×#71111yescharacteristic
620C22×C3C2×#71111yescharacteristic
621C22×C3#414411yescharacteristic
622C22×C3C2×Q8×D511yescharacteristic
623C22×C3D5×#4111yescharacteristic
624C22×C3#414911yescharacteristic
625C3×C4—22no—
626C3×C4—22no—
627C3×C4—102no—
628C3×C4—102no—
629C3×C4—102no—
630C3×C4—201no—
631Dic3—22no—
632Dic3—41no—
633Dic3—41no—
634Dic3—41no—
635Dic3—102no—
636Dic3—102no—
637Dic3—102no—
638Dic3—102no—
639C2×C5—24no—
640C2×C5C2×C4×Dic611yescharacteristic
641C2×C5#549511yescharacteristic
642C2×C5#552711yescharacteristic
643C2×C5C4×#23711yescharacteristic
644C2×C5#553911yescharacteristic
645C2×C5#554311yescharacteristic
646C2×C5#554511yescharacteristic
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23D5×Dic612yes—
652C23#677212yes—
653C23C2×#120012yes—
654C23C22×D3×D511yescharacteristic
655Q8—604no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—32no—
661C2×C4—52no—
662C2×C4—52no—
663C2×C4—52no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—101no—
676C2×C4—101no—
677C2×C4—101no—
678C2×C4—101no—
679C2×C4—101no—
680C2×C4—101no—
681C2×C4—101no—
682C2×C4—101no—
683C2×C4—101no—
684C2×C4—124no—
685C2×C4—152no—
686C2×C4—152no—
687C2×C4—152no—
688C2×C4—152no—
689C2×C4—204no—
690C2×C4—301no—
691C2×C4—301no—
692C2×C4—301no—
693C2×C4—301no—
694C2×C4—301no—
695C2×C4—301no—
696C2×C4—301no—
697C2×C4—301no—
698C2×C4—604no—
699C2×C4C2×#120012yes—
700C2×C4C2×#120012yes—
701C2×C3—24no—
702C2×C3C2×#403311yescharacteristic
703C2×C3C4×#71111yescharacteristic
704C2×C3#6587911yescharacteristic
705C2×C3#6592111yescharacteristic
706C2×C3#6596911yescharacteristic
707C2×C3#6597011yescharacteristic
708C2×C3#6599211yescharacteristic
709C5#7347411yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22#9133314yes—
717C22C2×D5×Dic611yescharacteristic
718C22C2×#677211yescharacteristic
719C22D5×#23711yescharacteristic
720C22D3×#71111yescharacteristic
721C22#9202611yescharacteristic
722C22#9202711yescharacteristic
723C22C22×#120011yescharacteristic
724C4—22no—
725C4—22no—
726C4—62no—
727C4—102no—
728C4—102no—
729C4—102no—
730C4—121no—
731C4—121no—
732C4—121no—
733C4—201no—
734C4—302no—
735C4—302no—
736C4—302no—
737C4—302no—
738C3#1060613011yescharacteristic, complemented, Sylow
739C2—24no—
740C2#1175280311yescharacteristic
741C2#1175296211yescharacteristic
742C2#1175298111yescharacteristic
743C2#1175310311yescharacteristic
744C2C2×#9133311yescharacteristic
745C2#1175485311yescharacteristic
746C2#1175492211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2368
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
8. #11748824C2semidirect
9. #11748694C2semidirect
10. #11748688C2semidirect
11. #11748687C2semidirect
12. #11748687C2semidirect
13. Dic5×C4⋊Dic3C2semidirect
14. #11748640C2semidirect
15. #11748587C2semidirect
26. #91767C4semidirect
81. C2×Dic30C2×C4semidirect
98. C4⋊Dic15C2×C4semidirect
99. #6712C2×C4semidirect
100. #6712C2×C4semidirect
104. C3×C22⋊Dic5Q8semidirect
287. C22⋊Dic5Dic6semidirect
610. C3×C5#2368semidirect
709. C5#73474semidirect
738. C3#10606130semidirect

Maximal subgroups

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

subgroupindex
C2×#917672
C5×#49502
C3×C22⋊C4×Dic52
#117495082
#117494872
Dic3×C22⋊Dic52
C2×#909942
#117488242
#117486942
#117486882
#117486872
Dic5×C4⋊Dic32
#117486402
#117485872
#106061303
#734745