Finite Group Databasebeta

← #14326705

Subgroups — #14326705

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×#91404C211yesmaximal, characteristic
2C4×#6714C211yesmaximal, characteristic
3C5×#4933C211yesmaximal, characteristic, complemented
4C3×C4×#683C211yesmaximal, characteristic, complemented
5#11748882C211yesmaximal, characteristic
6#11748876C211yesmaximal, characteristic
7#11748875C211yesmaximal, characteristic
8#11748875C211yesmaximal, characteristic
9#11748863C211yesmaximal, characteristic
10#11748816C211yesmaximal, characteristic, complemented
11#11748802C211yesmaximal, characteristic, complemented
12#11748659C211yesmaximal, characteristic, complemented
13#11748637C211yesmaximal, characteristic, complemented
14#11748629C211yesmaximal, characteristic, complemented
15#11748605C211yesmaximal, characteristic, complemented
16#10606693—31nomaximal, Hall
17C22×C4×D15C2211yescharacteristic
18C22×#1200C2211yescharacteristic
19C22×#1200C2211yescharacteristic
20C2×C3×C42×C5C2211yescharacteristic
21C2×#6714C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic
24C2×C5×Dic3⋊C4C2211yescharacteristic
25C2×C5×Dic3⋊C4C2211yescharacteristic
26C2×C3×#683C2211yescharacteristic
27C2×C3×#683C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×Dic3⋊Dic5C2211yescharacteristic
31C2×Dic3⋊Dic5C2211yescharacteristic
32C2×#6669C2211yescharacteristic
33C2×#6669C2211yescharacteristic
34C2×#6668C2211yescharacteristic
35C2×#6668C2211yescharacteristic
36C2×#6667C2211yescharacteristic
37C2×#6667C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40#91404C418yescomplemented
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#73768—51nomaximal, Hall
54C2×D5×C4⋊C4—31no—
55C5×#387—31no—
56#65276—31no—
57#65270—31no—
58#65261—31no—
59C4×#685—31no—
60C4×#683D311yescharacteristic, complemented
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×D15C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×Dic15C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C2×C4×D15—41no—
77C2×C4×D15—41no—
78C2×C4×D15C2×C414yes—
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C2×#1200—22no—
88C2×#1200—22no—
89C2×#1200—41no—
90C2×#1200—41no—
91C2×#1200C2×C414yes—
92C2×#1200C2×C414yes—
93C3×C42×C5—41no—
94#6714—22no—
95#6714Q814yes—
96C4×Dic15—41no—
97C5×Dic3⋊C4—41no—
98C5×Dic3⋊C4C2×C414yes—
99C3×#683—22no—
100C3×#683C2×C414yes—
101C3×C4×Dic5—22no—
102C3×C4×Dic5—41no—
103Dic3⋊Dic5—41no—
104Dic3⋊Dic5C2×C414yes—
105#6669—41no—
106#6669—41no—
107#6668—22no—
108#6668C2×C414yes—
109#6667—22no—
110#6667—22no—
111Dic3×Dic5—22no—
112Dic3×Dic5—41no—
113C2×D3×C4⋊C4—51no—
114C3×C4×C4⋊C4—51no—
115#4987—51no—
116Dic3×C4⋊C4—51no—
117#4972—51no—
118C4×(C2×D3)⋊C4—51no—
119C4×(C2×D3)⋊C4—51no—
120C4×(C2×D3)⋊C4—51no—
121#4933—51no—
122#4933D511yescharacteristic, complemented
123#4928—51no—
124#4667—51no—
125#4667—51no—
126#4652—51no—
127#4652—51no—
128C22×C4×D5—31no—
129C22×C4×D5—31no—
130C22×C4×D5—31no—
131C2×C5×C4⋊C4—31no—
132C2×C5×C4⋊C4—31no—
133C2×C42×C5C2×D311yescharacteristic
134C2×#685—31no—
135C2×#685—31no—
136C2×#685—31no—
137C2×#685—31no—
138C2×C4⋊Dic5—31no—
139C2×C4⋊Dic5—31no—
140C2×#683—31no—
141C2×#683—31no—
142C2×#683—31no—
143C2×#683—31no—
144C2×#683C2×D311yescharacteristic
145C2×#683C2×D311yescharacteristic
146C2×C4×Dic5—31no—
147C2×C4×Dic5—31no—
148C2×C4×Dic5—31no—
149C2×C4×Dic5C2×D311yescharacteristic
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×D15—21no—
167C22×D15—21no—
168C22×D15—21no—
169C22×D15—21no—
170C22×D15C22×C412yes—
171C22×D15C2×Q812yes—
172C22×D15#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×Dic15C22×C412yes—
190C2×Dic15C2×Q812yes—
191C4×D15—44no—
192C2×C5×Dic3—21no—
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×Dic3C22×C412yes—
203C2×C5×Dic3C22×C412yes—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
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×Dic5C22×C412yes—
213C2×C3×Dic5C22×C412yes—
214C2×C3×Dic5#4112yes—
215C2×C3×Dic5#4112yes—
216#1200—28no—
217#1200—44no—
218C22×C4×D3—51no—
219C22×C4×D3—51no—
220C22×C4×D3—51no—
221C2×C3×C4⋊C4—51no—
222C2×C3×C4⋊C4—51no—
223C2×C3×C42—51no—
224C2×C3×C42—51no—
225C2×C3×C42C2×D511yescharacteristic
226C2×(C2×D3)⋊C4—51no—
227C2×(C2×D3)⋊C4—51no—
228C2×(C2×D3)⋊C4—51no—
229C2×(C2×D3)⋊C4—51no—
230C2×C4⋊Dic3—51no—
231C2×C4⋊Dic3—51no—
232C2×Dic3⋊C4—51no—
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—
241D3×C4⋊C4—58no—
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×D5—31no—
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×Dic5C22×D311yescharacteristic
266C22×Dic5C22×D311yescharacteristic
267C22×Dic5C22×D311yescharacteristic
268C22×Dic5C22×D311yescharacteristic
269C2×C4×D5—34no—
270C2×C4×D5—34no—
271C2×C4×D5—34no—
272C2×C4×D5—62no—
273C2×C4×D5—62no—
274C2×C4×D5—121no—
275C2×C4×D5—121no—
276C2×C4×D5—121no—
277C2×C4×D5—121no—
278C5×C4⋊C4—34no—
279C5×C4⋊C4—121no—
280C42×C5—41no—
281#685—34no—
282#685—62no—
283#685—62no—
284#685—62no—
285C4⋊Dic5—34no—
286C4⋊Dic5—121no—
287#683—22no—
288#683—34no—
289#683—62no—
290#683—121no—
291#683—121no—
292#683C4×D314yes—
293C4×Dic5—22no—
294C4×Dic5—41no—
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—51no—
309C4×C4⋊C4—151no—
310C4×C22⋊C4—151no—
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×D15—22no—
321C2×D15—22no—
322C2×D15—22no—
323C2×D15—22no—
324C2×D15—22no—
325C2×D15—22no—
326C2×D15C4×Q814yes—
327C3×C4×C5—22no—
328C3×C4×C5—22no—
329C3×C4×C5—41no—
330Dic15—22no—
331Dic15—22no—
332Dic15—41no—
333C3×Dic5—22no—
334C3×Dic5—41no—
335C3×Dic5—41no—
336C3×Dic5#11714yes—
337C5×Dic3—22no—
338C5×Dic3—22no—
339C5×Dic3—41no—
340C5×Dic3—41no—
341C23×D3—51no—
342C22×C3×C4—51no—
343C22×C3×C4—51no—
344C22×C3×C4—51no—
345C22×C3×C4—51no—
346C22×C3×C4C22×D511yescharacteristic
347C22×C3×C4C22×D511yescharacteristic
348C22×C3×C4C22×D511yescharacteristic
349C22×Dic3—51no—
350C22×Dic3—51no—
351C22×Dic3—51no—
352C22×Dic3C22×D511yescharacteristic
353C22×Dic3C22×D511yescharacteristic
354C22×Dic3C22×D511yescharacteristic
355C22×Dic3C22×D511yescharacteristic
356C2×C4×D3—54no—
357C2×C4×D3—54no—
358C2×C4×D3—54no—
359C2×C4×D3—102no—
360C2×C4×D3—102no—
361C2×C4×D3—201no—
362C2×C4×D3—201no—
363C2×C4×D3—201no—
364C2×C4×D3—201no—
365C3×C4⋊C4—54no—
366C3×C4⋊C4—102no—
367C3×C42—41no—
368C3×C42—102no—
369C3×C42—201no—
370(C2×D3)⋊C4—54no—
371(C2×D3)⋊C4—102no—
372(C2×D3)⋊C4—102no—
373(C2×D3)⋊C4—102no—
374C4⋊Dic3—54no—
375C4⋊Dic3—102no—
376Dic3⋊C4—41no—
377Dic3⋊C4—54no—
378Dic3⋊C4—201no—
379Dic3⋊C4—201no—
380Dic3⋊C4—201no—
381Dic3⋊C4C4×D514yes—
382C4×Dic3—102no—
383C4×Dic3—201no—
384C4×Dic3—201no—
385C23×C5C23×D311yescharacteristic
386C22×D5—32no—
387C22×D5—32no—
388C22×D5—32no—
389C22×D5—61no—
390C22×D5—61no—
391C22×D5—61no—
392C22×D5—61no—
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×C4×D312yes—
413C2×C4×C5D3×Q812yes—
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—61no—
425C2×Dic5—61no—
426C2×Dic5—61no—
427C2×Dic5—61no—
428C2×Dic5—61no—
429C2×Dic5—61no—
430C2×Dic5—61no—
431C2×Dic5C2×C4×D312yes—
432C2×Dic5C2×C4×D312yes—
433C2×Dic5#23512yes—
434C2×Dic5#23512yes—
435C4×D5—68no—
436C4×D5—124no—
437C4×D5—124no—
438C23×C4—151no—
439C23×C4—151no—
440C23×C4—151no—
441C2×C4⋊C4—31no—
442C2×C4⋊C4—31no—
443C2×C4⋊C4—51no—
444C2×C4⋊C4—51no—
445C2×C4⋊C4—158no—
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—151no—
453C2×C22⋊C4—151no—
454C2×C22⋊C4—151no—
455C2×C22⋊C4—151no—
456C2×C42—51no—
457C2×C42—51no—
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
481D15—24no—
482C23×C3C23×D511yescharacteristic
483C22×D3—52no—
484C22×D3—52no—
485C22×D3—52no—
486C22×D3—101no—
487C22×D3—101no—
488C22×D3—101no—
489C22×D3—101no—
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—52no—
500C2×C3×C4—52no—
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—101no—
509C2×C3×C4C2×C4×D512yes—
510C2×C3×C4Q8×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—52no—
522C2×Dic3—52no—
523C2×Dic3—101no—
524C2×Dic3—101no—
525C2×Dic3—101no—
526C2×Dic3—101no—
527C2×Dic3—101no—
528C2×Dic3—101no—
529C2×Dic3—101no—
530C2×Dic3C2×C4×D512yes—
531C2×Dic3C2×C4×D512yes—
532C4×D3—108no—
533C4×D3—204no—
534C4×D3—204no—
535C22×C5C22×C4×D311yescharacteristic
536C22×C5C2×#23511yescharacteristic
537C22×C5C2×#23511yescharacteristic
538C22×C5#100411yescharacteristic
539C22×C5C2×D3×Q811yescharacteristic
540C22×C5D3×#4111yescharacteristic
541C22×C5#100911yescharacteristic
542C2×D5—34no—
543C2×D5—62no—
544C2×D5—62no—
545C2×D5—62no—
546C2×D5—62no—
547C2×D5—62no—
548C2×D5—62no—
549C4×C5—22no—
550C4×C5—22no—
551C4×C5—41no—
552C4×C5—62no—
553C4×C5—62no—
554C4×C5—121no—
555C4×C5—121no—
556Dic5—22no—
557Dic5—41no—
558Dic5—41no—
559Dic5—62no—
560Dic5—62no—
561Dic5—121no—
562Dic5#87214yes—
563C24—151no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—51no—
569C22×C4—51no—
570C22×C4—51no—
571C22×C4—51no—
572C22×C4—154no—
573C22×C4—154no—
574C22×C4—151no—
575C22×C4—151no—
576C22×C4—154no—
577C22×C4—151no—
578C22×C4—302no—
579C22×C4—302no—
580C22×C4—601no—
581C22×C4—601no—
582C22×C4—601no—
583C22×C4—601no—
584C22×C4C2×D3×D511yescharacteristic
585C22×C4C2×D3×D511yescharacteristic
586C22×C4C2×D3×D511yescharacteristic
587C4⋊C4—34no—
588C4⋊C4—54no—
589C4⋊C4—102no—
590C4⋊C4—121no—
591C4⋊C4—154no—
592C4⋊C4—154no—
593C4⋊C4—302no—
594C4⋊C4—601no—
595C4⋊C4—601no—
596C4⋊C4—601no—
597C22⋊C4—154no—
598C22⋊C4—302no—
599C22⋊C4—302no—
600C22⋊C4—302no—
601C42—41no—
602C42—102no—
603C42—201no—
604C42—302no—
605C42—601no—
606C42—601no—
607C3×C5#234511yescharacteristic, complemented, Hall
608C22×C3C22×C4×D511yescharacteristic
609C22×C3#414411yescharacteristic
610C22×C3C2×Q8×D511yescharacteristic
611C22×C3D5×#4111yescharacteristic
612C22×C3D5×#4111yescharacteristic
613C22×C3D5×#4111yescharacteristic
614C22×C3#414911yescharacteristic
615C2×D3—54no—
616C2×D3—102no—
617C2×D3—102no—
618C2×D3—102no—
619C2×D3—102no—
620C2×D3—102no—
621C2×D3—102no—
622C3×C4—22no—
623C3×C4—22no—
624C3×C4—41no—
625C3×C4—54no—
626C3×C4—102no—
627C3×C4—201no—
628C3×C4—201no—
629Dic3—22no—
630Dic3—22no—
631Dic3—41no—
632Dic3—41no—
633Dic3—102no—
634Dic3—102no—
635Dic3—201no—
636C2×C5C2×#87211yescharacteristic
637C2×C5#551111yescharacteristic
638C2×C5#553011yescharacteristic
639C2×C5#554511yescharacteristic
640C2×C5#555811yescharacteristic
641C2×C5C4×D3×Q811yescharacteristic
642C2×C5#557911yescharacteristic
643D5—64no—
644C23—152no—
645C23—152no—
646C23—152no—
647C23—301no—
648C23—301no—
649C23—301no—
650C23—301no—
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—52no—
664C2×C4—52no—
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—152no—
684C2×C4—152no—
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—604no—
694C2×C4—604no—
695C2×C4D15⋊Q812yes—
696C2×C4C4×D3×D512yes—
697C2×C3D5×#11711yescharacteristic
698C2×C3#6587911yescharacteristic
699C2×C3C4×Q8×D511yescharacteristic
700C2×C3#6597011yescharacteristic
701C2×C3#6599511yescharacteristic
702C2×C3#6602411yescharacteristic
703C2×C3#6604311yescharacteristic
704D3—104no—
705C5#7376811yescharacteristic, complemented, Sylow
706C22—154no—
707C22—302no—
708C22—302no—
709C22—302no—
710C22—302no—
711C22—302no—
712C22—302no—
713C22C2×D15⋊Q811yescharacteristic
714C22C2×C4×D3×D511yescharacteristic
715C22D5×#23511yescharacteristic
716C22D5×#23511yescharacteristic
717C22#9201611yescharacteristic
718C22#9201911yescharacteristic
719C22#9204911yescharacteristic
720C4—22no—
721C4—22no—
722C4—41no—
723C4—54no—
724C4—62no—
725C4—62no—
726C4—102no—
727C4—121no—
728C4—121no—
729C4—201no—
730C4—201no—
731C4—302no—
732C4—302no—
733C4—601no—
734C3#1060669311yescharacteristic, complemented, Sylow
735C2—304no—
736C2C4×D15⋊Q811yescharacteristic
737C2#1175259111yescharacteristic
738C2#1175269011yescharacteristic
739C2D5×#87211yescharacteristic
740C2#1175441711yescharacteristic
741C2#1175456911yescharacteristic
742C2#1175462911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
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
3. C5×#4933C2semidirect
4. C3×C4×#683C2semidirect
10. #11748816C2semidirect
11. #11748802C2semidirect
12. #11748659C2semidirect
13. #11748637C2semidirect
14. #11748629C2semidirect
15. #11748605C2semidirect
40. #91404C4semidirect
60. C4×#683D3semidirect
122. #4933D5semidirect
607. C3×C5#2345semidirect
705. C5#73768semidirect
734. C3#10606693semidirect

Maximal subgroups

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

subgroupindex
C2×#914042
C4×#67142
C5×#49332
C3×C4×#6832
#117488822
#117488762
#117488752
#117488632
#117488162
#117488022
#117486592
#117486372
#117486292
#117486052
#106066933
#737685