Finite Group Databasebeta

← #14326704

Subgroups — #14326704

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×Dic3⋊C4C211yesmaximal, characteristic
2C4×#6712C211yesmaximal, characteristic, complemented
3C5×#4933C211yesmaximal, characteristic, complemented
4C3×C4×#685C211yesmaximal, characteristic
5#11748885C211yesmaximal, characteristic
6#11748884C211yesmaximal, characteristic
7#11748884C211yesmaximal, characteristic
8#11748878C211yesmaximal, characteristic
9#11748811C211yesmaximal, characteristic, complemented
10#11748804C211yesmaximal, characteristic, complemented
11#11748738C211yesmaximal, characteristic
12#11748656C211yesmaximal, characteristic, complemented
13#11748640C211yesmaximal, characteristic, complemented
14#11748633C211yesmaximal, characteristic, complemented
15#11748573C211yesmaximal, characteristic, complemented
16#10606693—31nomaximal, Hall
17C22×C3×C4×D5C2211yescharacteristic
18C22×D5×Dic3C2211yescharacteristic
19C22×D5×Dic3C2211yescharacteristic
20C2×C3×C42×C5C2211yescharacteristic
21C2×#6712C2211yescharacteristic
22C2×#6712C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic
25C2×C5×Dic3⋊C4C2211yescharacteristic
26C2×C5×Dic3⋊C4C2211yescharacteristic
27C2×C3×#685C2211yescharacteristic
28C2×C3×#685C2211yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×Dic3⋊Dic5C2211yescharacteristic
31C2×Dic3⋊Dic5C2211yescharacteristic
32C2×#6669C2211yescharacteristic
33C2×#6669C2211yescharacteristic
34C2×#6668C2211yescharacteristic
35C2×#6668C2211yescharacteristic
36C2×#6665C2211yescharacteristic
37C2×#6665C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40D5×Dic3⋊C4C418yescomplemented
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C5×C3⋊#95C2211yescharacteristic
45C5×C3⋊#95C2211yescharacteristic
46C5×C3⋊#95C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#73458—51nomaximal, Hall
54C2×D5×C4⋊C4—31no—
55C5×#387—31no—
56#65276—31no—
57#65270—31no—
58#65261—31no—
59C4×#685D311yescharacteristic
60C4×#683—31no—
61#64956—31no—
62#64956—31no—
63#64955—31no—
64#64955—31no—
65#64943—31no—
66#64942—31no—
67#64938—31no—
68#64936—31no—
69C23×C3×D5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×Dic15C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×C5×Dic3C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C2×C3×C4×D5—41no—
85C2×C3×C4×D5—41no—
86C2×C3×C4×D5C2×C414yes—
87C2×D5×Dic3—22no—
88C2×D5×Dic3—22no—
89C2×D5×Dic3—41no—
90C2×D5×Dic3—41no—
91C2×D5×Dic3C2×C414yes—
92C2×D5×Dic3C2×C414yes—
93C3×C42×C5—41no—
94#6712—22no—
95#6712C2×C414yes—
96C4×Dic15—22no—
97C4×Dic15—41no—
98C5×Dic3⋊C4—41no—
99C5×Dic3⋊C4C2×C414yes—
100C3×#685—22no—
101C3×#685Q814yes—
102C3×C4×Dic5—41no—
103Dic3⋊Dic5—41no—
104Dic3⋊Dic5C2×C414yes—
105#6669—22no—
106#6669C2×C414yes—
107#6668—41no—
108#6668—41no—
109#6665—22no—
110#6665—22no—
111Dic3×Dic5—22no—
112Dic3×Dic5—41no—
113C22×Dic3⋊C4—51no—
114C3×C4×C22⋊C4—51no—
115#5212—51no—
116#4942—51no—
117#4942—51no—
118Dic3×C22⋊C4—51no—
119Dic3×C22⋊C4—51no—
120#4933—51no—
121#4933D511yescharacteristic, complemented
122C4×Dic3⋊C4—51no—
123C4×Dic3⋊C4—51no—
124#4655—51no—
125#4655—51no—
126#4647—51no—
127#4647—51no—
128C22×C4×D5—31no—
129C22×C4×D5—31no—
130C22×C4×D5C2×D311yescharacteristic
131C2×C5×C4⋊C4—31no—
132C2×C5×C4⋊C4—31no—
133C2×C42×C5C2×D311yescharacteristic
134C2×#685—31no—
135C2×#685—31no—
136C2×#685C2×D311yescharacteristic
137C2×#685C2×D311yescharacteristic
138C2×C4⋊Dic5—31no—
139C2×C4⋊Dic5—31no—
140C2×#683—31no—
141C2×#683—31no—
142C2×#683—31no—
143C2×#683—31no—
144C2×#683—31no—
145C2×#683—31no—
146C2×C4×Dic5—31no—
147C2×C4×Dic5—31no—
148C2×C4×Dic5—31no—
149C2×C4×Dic5—31no—
150C2×C4×Dic5C2×D311yescharacteristic
151D5×C4⋊C4—38no—
152C5×#95—31no—
153C5×#95—31no—
154C5×#95—31no—
155C5×#95—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#2345—151noSylow
165C23×C3×C5C2411yescharacteristic
166C22×C3×D5—21no—
167C22×C3×D5—21no—
168C22×C3×D5—21no—
169C22×C3×D5—21no—
170C22×C3×D5C22×C412yes—
171C22×C3×D5C2×Q812yes—
172C22×C3×D5#4112yes—
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5—21no—
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5—21no—
177C2×C3×C4×C5—21no—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—21no—
180C2×C3×C4×C5C22×C412yes—
181C2×C3×C4×C5C2×Q812yes—
182C2×Dic15—21no—
183C2×Dic15—21no—
184C2×Dic15—21no—
185C2×Dic15—21no—
186C2×Dic15—21no—
187C2×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15C22×C412yes—
191C2×Dic15C22×C412yes—
192C2×Dic15#4112yes—
193C2×Dic15#4112yes—
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×Dic3C22×C412yes—
205C2×C5×Dic3C22×C412yes—
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×Dic5C22×C412yes—
214C2×C3×Dic5C2×Q812yes—
215C3×C4×D5—44no—
216D5×Dic3—28no—
217D5×Dic3—44no—
218C23×C3×C4—51no—
219C23×Dic3—51no—
220C23×Dic3—51no—
221C2×C3×C22⋊C4—51no—
222C2×C3×C22⋊C4—51no—
223C2×C3×C42—51no—
224C2×C3×C42C2×D511yescharacteristic
225C2×#217—51no—
226C2×#217—51no—
227C2×C4⋊Dic3—51no—
228C2×C4⋊Dic3—51no—
229C2×Dic3⋊C4—51no—
230C2×Dic3⋊C4—51no—
231C2×Dic3⋊C4—51no—
232C2×Dic3⋊C4—58no—
233C2×Dic3⋊C4—51no—
234C2×Dic3⋊C4—51no—
235C2×Dic3⋊C4—51no—
236C2×Dic3⋊C4C2×D511yescharacteristic
237C2×Dic3⋊C4C2×D511yescharacteristic
238C2×C4×Dic3—51no—
239C2×C4×Dic3—51no—
240C2×C4×Dic3—51no—
241C2×C4×Dic3—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⋊#95C2×D511yescharacteristic
251C3⋊#95C2×D511yescharacteristic
252C3⋊#95C2×D511yescharacteristic
253C3⋊#95C2×D511yescharacteristic
254C23×D5C22×D311yescharacteristic
255C22×C4×C5—31no—
256C22×C4×C5—31no—
257C22×C4×C5—31no—
258C22×C4×C5—31no—
259C22×C4×C5C22×D311yescharacteristic
260C22×C4×C5C22×D311yescharacteristic
261C22×C4×C5C22×D311yescharacteristic
262C22×Dic5—31no—
263C22×Dic5—31no—
264C22×Dic5—31no—
265C22×Dic5—31no—
266C22×Dic5C22×D311yescharacteristic
267C22×Dic5C22×D311yescharacteristic
268C22×Dic5C22×D311yescharacteristic
269C2×C4×D5—34no—
270C2×C4×D5—34no—
271C2×C4×D5—41no—
272C2×C4×D5—41no—
273C2×C4×D5—62no—
274C2×C4×D5—62no—
275C2×C4×D5—121no—
276C2×C4×D5—121no—
277C2×C4×D5C4×D314yes—
278C5×C4⋊C4—34no—
279C5×C4⋊C4—121no—
280C42×C5—41no—
281#685—22no—
282#685—62no—
283#685—62no—
284#685Dic614yes—
285C4⋊Dic5—34no—
286C4⋊Dic5—121no—
287#683—34no—
288#683—34no—
289#683—62no—
290#683—62no—
291#683—121no—
292#683—121no—
293C4×Dic5—41no—
294C4×Dic5—62no—
295C4×Dic5—62no—
296C4×Dic5—121no—
297C4×Dic5—121no—
298C22×C4⋊C4—151no—
299#389—151no—
300#389—151no—
301#387—31no—
302#387—151no—
303#387—151no—
304#387—151no—
305#380—151no—
306#380—151no—
307#380—151no—
308C4×C4⋊C4—151no—
309C4×C4⋊C4—151no—
310C4×C22⋊C4—51no—
311C4×C22⋊C4—151no—
312C4×C22⋊C4—151no—
313C22×C3×C5C23×C411yescharacteristic
314C22×C3×C5C22×Q811yescharacteristic
315C22×C3×C5C2×#4111yescharacteristic
316C22×C3×C5C2×#4111yescharacteristic
317C22×C3×C5C2×#4111yescharacteristic
318C22×C3×C5H(5,𝔽2)11yescharacteristic
319C22×C3×C5H(5,𝔽2)11yescharacteristic
320C2×C3×D5—22no—
321C2×C3×D5—22no—
322C2×C3×D5—22no—
323C2×C3×D5—22no—
324C2×C3×D5—22no—
325C2×C3×D5—22no—
326C2×C3×D5C4×Q814yes—
327C3×C4×C5—22no—
328C3×C4×C5—22no—
329C3×C4×C5—41no—
330Dic15—22no—
331Dic15—41no—
332Dic15—41no—
333Dic15#11714yes—
334C3×Dic5—22no—
335C3×Dic5—22no—
336C3×Dic5—41no—
337C5×Dic3—22no—
338C5×Dic3—22no—
339C5×Dic3—41no—
340C5×Dic3—41no—
341C24×C3—51no—
342C22×C3×C4—51no—
343C22×C3×C4—51no—
344C22×C3×C4—54no—
345C22×C3×C4—51no—
346C22×C3×C4—201no—
347C22×C3×C4—201no—
348C22×C3×C4C22×D511yescharacteristic
349C22×C3×C4C22×D511yescharacteristic
350C22×C3×C4C22×D511yescharacteristic
351C22×Dic3—51no—
352C22×Dic3—51no—
353C22×Dic3—54no—
354C22×Dic3—54no—
355C22×Dic3—51no—
356C22×Dic3—51no—
357C22×Dic3—102no—
358C22×Dic3—102no—
359C22×Dic3—201no—
360C22×Dic3—201no—
361C22×Dic3C22×D511yescharacteristic
362C22×Dic3C22×D511yescharacteristic
363C22×Dic3C22×D511yescharacteristic
364C22×Dic3C22×D511yescharacteristic
365C3×C22⋊C4—54no—
366C3×C22⋊C4—102no—
367C3×C42—41no—
368C3×C42—201no—
369#217—102no—
370#217—102no—
371C4⋊Dic3—201no—
372C4⋊Dic3—201no—
373Dic3⋊C4—41no—
374Dic3⋊C4—54no—
375Dic3⋊C4—54no—
376Dic3⋊C4—54no—
377Dic3⋊C4—102no—
378Dic3⋊C4—102no—
379Dic3⋊C4—201no—
380Dic3⋊C4C4×D514yes—
381C4×Dic3—102no—
382C4×Dic3—102no—
383C4×Dic3—201no—
384C4×Dic3—201no—
385C23×C5C23×D311yescharacteristic
386C22×D5—21no—
387C22×D5—21no—
388C22×D5—21no—
389C22×D5—21no—
390C22×D5C2×Dic612yes—
391C22×D5C2×C4×D312yes—
392C22×D5#23512yes—
393C2×C4×C5—21no—
394C2×C4×C5—21no—
395C2×C4×C5—21no—
396C2×C4×C5—21no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5—21no—
400C2×C4×C5—32no—
401C2×C4×C5—32no—
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—61no—
411C2×C4×C5—61no—
412C2×C4×C5C2×Dic612yes—
413C2×C4×C5C2×C4×D312yes—
414C2×Dic5—21no—
415C2×Dic5—21no—
416C2×Dic5—21no—
417C2×Dic5—21no—
418C2×Dic5—21no—
419C2×Dic5—21no—
420C2×Dic5—21no—
421C2×Dic5—32no—
422C2×Dic5—32no—
423C2×Dic5—32no—
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×Dic5C2×Dic612yes—
434C2×Dic5C2×C4×D312yes—
435C4×D5—44no—
436C4×D5—68no—
437C4×D5—124no—
438C23×C4—51no—
439C23×C4—151no—
440C23×C4—151no—
441C2×C4⋊C4—31no—
442C2×C4⋊C4—31no—
443C2×C4⋊C4—158no—
444C2×C4⋊C4—151no—
445C2×C4⋊C4—151no—
446C2×C4⋊C4—151no—
447C2×C4⋊C4—151no—
448C2×C4⋊C4—151no—
449C2×C4⋊C4—151no—
450C2×C4⋊C4—151no—
451C2×C4⋊C4—151no—
452C2×C22⋊C4—51no—
453C2×C22⋊C4—51no—
454C2×C22⋊C4—151no—
455C2×C22⋊C4—151no—
456C2×C42—51no—
457C2×C42—151no—
458C2×C42—151no—
459C2×C42—151no—
460C2×C42—151no—
461C2×C42D3×D511yescharacteristic
462#95—31no—
463#95—31no—
464#95—31no—
465#95—31no—
466#95—51no—
467#95—51no—
468#95—151no—
469#95—151no—
470#95—151no—
471#95—151no—
472#95—151no—
473#95—151no—
474C2×C3×C5C2×#11711yescharacteristic
475C2×C3×C5C2×C4×Q811yescharacteristic
476C2×C3×C5#51811yescharacteristic
477C2×C3×C5#55311yescharacteristic
478C2×C3×C5#55311yescharacteristic
479C2×C3×C5#55411yescharacteristic
480C2×C3×C5#55411yescharacteristic
481C3×D5—24no—
482C23×C3—52no—
483C23×C3—52no—
484C23×C3—52no—
485C23×C3—101no—
486C23×C3—101no—
487C23×C3—101no—
488C23×C3—101no—
489C23×C3C23×D511yescharacteristic
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
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—204no—
507C2×C3×C4C2×C4×D512yes—
508C2×C3×C4Q8×D512yes—
509C2×Dic3—21no—
510C2×Dic3—21no—
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—52no—
520C2×Dic3—52no—
521C2×Dic3—52no—
522C2×Dic3—52no—
523C2×Dic3—108no—
524C2×Dic3—101no—
525C2×Dic3—101no—
526C2×Dic3—101no—
527C2×Dic3—101no—
528C2×Dic3—101no—
529C2×Dic3—101no—
530C2×Dic3—101no—
531C2×Dic3—101no—
532C2×Dic3—204no—
533C2×Dic3C2×C4×D512yes—
534C2×Dic3C2×C4×D512yes—
535C22×C5C22×Dic611yescharacteristic
536C22×C5C22×C4×D311yescharacteristic
537C22×C5C2×#23511yescharacteristic
538C22×C5#100411yescharacteristic
539C22×C5#100411yescharacteristic
540C22×C5D3×#4111yescharacteristic
541C22×C5D3×#4111yescharacteristic
542C2×D5—22no—
543C2×D5—22no—
544C2×D5—22no—
545C2×D5—22no—
546C2×D5—22no—
547C2×D5—22no—
548C2×D5C4×Dic614yes—
549C4×C5—22no—
550C4×C5—22no—
551C4×C5—41no—
552C4×C5—62no—
553C4×C5—62no—
554C4×C5—121no—
555C4×C5—121no—
556Dic5—22no—
557Dic5—22no—
558Dic5—34no—
559Dic5—41no—
560Dic5—62no—
561Dic5—121no—
562Dic5—121no—
563C24—51no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—51no—
569C22×C4—51no—
570C22×C4—54no—
571C22×C4—51no—
572C22×C4—154no—
573C22×C4—154no—
574C22×C4—151no—
575C22×C4—151no—
576C22×C4—151no—
577C22×C4—151no—
578C22×C4—201no—
579C22×C4—201no—
580C22×C4—302no—
581C22×C4—302no—
582C22×C4—601no—
583C22×C4—601no—
584C22×C4C2×D3×D511yescharacteristic
585C22×C4C2×D3×D511yescharacteristic
586C22×C4C2×D3×D511yescharacteristic
587C4⋊C4—34no—
588C4⋊C4—121no—
589C4⋊C4—154no—
590C4⋊C4—154no—
591C4⋊C4—154no—
592C4⋊C4—302no—
593C4⋊C4—302no—
594C4⋊C4—601no—
595C4⋊C4—601no—
596C4⋊C4—601no—
597C22⋊C4—54no—
598C22⋊C4—102no—
599C22⋊C4—302no—
600C22⋊C4—302no—
601C42—41no—
602C42—201no—
603C42—302no—
604C42—302no—
605C42—601no—
606C42—601no—
607C3×C5#234511yescharacteristic, complemented, Hall
608C22×C3—54no—
609C22×C3—102no—
610C22×C3—102no—
611C22×C3—102no—
612C22×C3—102no—
613C22×C3—102no—
614C22×C3—102no—
615C22×C3C22×C4×D511yescharacteristic
616C22×C3#414411yescharacteristic
617C22×C3C2×Q8×D511yescharacteristic
618C22×C3D5×#4111yescharacteristic
619C22×C3D5×#4111yescharacteristic
620C22×C3D5×#4111yescharacteristic
621C22×C3#414911yescharacteristic
622C3×C4—22no—
623C3×C4—22no—
624C3×C4—41no—
625C3×C4—102no—
626C3×C4—102no—
627C3×C4—201no—
628Dic3—22no—
629Dic3—22no—
630Dic3—41no—
631Dic3—41no—
632Dic3—54no—
633Dic3—102no—
634Dic3—201no—
635Dic3—201no—
636C2×C5C2×C4×Dic611yescharacteristic
637C2×C5#548611yescharacteristic
638C2×C5D3×#11711yescharacteristic
639C2×C5#553911yescharacteristic
640C2×C5#553911yescharacteristic
641C2×C5#554011yescharacteristic
642C2×C5#554011yescharacteristic
643D5—24no—
644C23—52no—
645C23—52no—
646C23—52no—
647C23—101no—
648C23—101no—
649C23—101no—
650C23—101no—
651C23C22×D3×D511yescharacteristic
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—32no—
660C2×C4—32no—
661C2×C4—52no—
662C2×C4—52no—
663C2×C4—61no—
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—101no—
674C2×C4—101no—
675C2×C4—101no—
676C2×C4—101no—
677C2×C4—101no—
678C2×C4—101no—
679C2×C4—101no—
680C2×C4—152no—
681C2×C4—152no—
682C2×C4—152no—
683C2×C4—152no—
684C2×C4—204no—
685C2×C4—308no—
686C2×C4—301no—
687C2×C4—301no—
688C2×C4—301no—
689C2×C4—301no—
690C2×C4—301no—
691C2×C4—301no—
692C2×C4—301no—
693C2×C4—301no—
694C2×C4—604no—
695C2×C4D5×Dic612yes—
696C2×C4C4×D3×D512yes—
697C2×C3—104no—
698C2×C3D5×#11711yescharacteristic
699C2×C3#6587911yescharacteristic
700C2×C3C4×Q8×D511yescharacteristic
701C2×C3#6597011yescharacteristic
702C2×C3#6599511yescharacteristic
703C2×C3#6602411yescharacteristic
704C2×C3#6604311yescharacteristic
705C5#7345811yescharacteristic, complemented, Sylow
706C22—54no—
707C22—102no—
708C22—102no—
709C22—102no—
710C22—102no—
711C22—102no—
712C22—102no—
713C22C2×D5×Dic611yescharacteristic
714C22C2×C4×D3×D511yescharacteristic
715C22D5×#23511yescharacteristic
716C22#9201611yescharacteristic
717C22#9201611yescharacteristic
718C22#9201711yescharacteristic
719C22#9204911yescharacteristic
720C4—22no—
721C4—22no—
722C4—41no—
723C4—62no—
724C4—62no—
725C4—102no—
726C4—102no—
727C4—121no—
728C4—121no—
729C4—154no—
730C4—201no—
731C4—302no—
732C4—601no—
733C4—601no—
734C3#1060669311yescharacteristic, complemented, Sylow
735C2—104no—
736C2C4×D5×Dic611yescharacteristic
737C2#1175257611yescharacteristic
738C2#1175261811yescharacteristic
739C2#1175272311yescharacteristic
740C2#1175440511yescharacteristic
741C2#1175444511yescharacteristic
742C2#1175462511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#2345
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C4×#6712C2semidirect
3. C5×#4933C2semidirect
9. #11748811C2semidirect
10. #11748804C2semidirect
12. #11748656C2semidirect
13. #11748640C2semidirect
14. #11748633C2semidirect
15. #11748573C2semidirect
40. D5×Dic3⋊C4C4semidirect
121. #4933D5semidirect
607. C3×C5#2345semidirect
705. C5#73458semidirect
734. C3#10606693semidirect

Maximal subgroups

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

subgroupindex
C2×D5×Dic3⋊C42
C4×#67122
C5×#49332
C3×C4×#6852
#117488852
#117488842
#117488782
#117488112
#117488042
#117487382
#117486562
#117486402
#117486332
#117485732
#106066933
#734585