Finite Group Databasebeta

← #14323725

Subgroups — #14323725

Order 1920.

1112 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×C5×#887C211yesmaximal, characteristic, complemented
2C2×#91424C211yesmaximal, characteristic
3C2×#91403C211yesmaximal, characteristic
4#11751091C211yesmaximal, characteristic
5C3×#65261C211yesmaximal, characteristic, complemented
6#11748882C211yesmaximal, characteristic
7#11748854C211yesmaximal, characteristic
8C4×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
9#11748818C211yesmaximal, characteristic, complemented
10#11748808C211yesmaximal, characteristic, complemented
11#11748728C211yesmaximal, characteristic
12#11748727C211yesmaximal, characteristic
13#11748692C211yesmaximal, characteristic, complemented
14#11748664C211yesmaximal, characteristic, complemented
15#11748590C211yesmaximal, characteristic, complemented
16#10614219—31nomaximal, Hall
17C22×C5×Dic6C2211yescharacteristic
18C22×#1200C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×#6714C2211yescharacteristic
21C2×#6714C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic
24C2×C5×Dic3⋊C4C2211yescharacteristic
25C2×C5×Dic3⋊C4C2211yescharacteristic
26C2×C4×C5×Dic3C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C4×C5×Dic3C2211yescharacteristic
29C5×#887—24no—
30C2×C3×#683C2211yescharacteristic
31C2×C3×#683C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34C2×Dic3⋊Dic5C2211yescharacteristic
35C2×Dic3⋊Dic5C2211yescharacteristic
36C2×#6669C2211yescharacteristic
37C2×#6669C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43#91424C418yescomplemented
44#91403—24no—
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#75971—51nomaximal, Hall
56C2×C4×C5×Q8—31no—
57C2×#4092—31no—
58C2×#4018—31no—
59#65519—31no—
60#65279—31no—
61#65279—31no—
62#65276—31no—
63#65262—31no—
64#65261—31no—
65#65261D311yescharacteristic, complemented
66#65229—31no—
67#65229—31no—
68C4×C4⋊Dic5—31no—
69#65222—31no—
70#65222—31no—
71C23×D15C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C2×C5×Dic6—22no—
83C2×C5×Dic6—22no—
84C2×C5×Dic6C2×C414yes—
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C2×#1200—22no—
90C2×#1200—22no—
91C2×#1200C2×C414yes—
92C3×C5×C4⋊C4—22no—
93#6714—22no—
94#6714—41no—
95#6714C2×C414yes—
96C4×Dic15—41no—
97C5×Dic3⋊C4—22no—
98C5×Dic3⋊C4—22no—
99C4×C5×Dic3—22no—
100C4×C5×Dic3—22no—
101C4×C5×Dic3D414yes—
102C3×#683—22no—
103C3×#683—41no—
104C3×#683C2×C414yes—
105C3×C4×Dic5—41no—
106Dic3⋊Dic5—22no—
107Dic3⋊Dic5C2×C414yes—
108#6669—41no—
109#6669C2×C414yes—
110#6668—22no—
111#6667—22no—
112#6667—41no—
113#6667C2×C414yes—
114Dic3×Dic5—22no—
115C2×#896—51no—
116C2×#892—51no—
117C2×#887D511yescharacteristic, complemented
118C3×#389—51no—
119#4990—51no—
120#4990—51no—
121#4980—51no—
122#4976—51no—
123#4976—51no—
124#4940—51no—
125C4×Dic3⋊C4—51no—
126#4669—51no—
127#4667—51no—
128#4655—51no—
129#4646—51no—
130C22×C5×Q8—31no—
131C22×C4×D5—31no—
132C4×C5×Q8—64no—
133C2×C5×C4⋊C4—31no—
134C2×C5×C4⋊C4—31no—
135C2×C5×C4⋊C4C2×D311yescharacteristic
136C2×C42×C5—31no—
137C2×C42×C5—31no—
138C2×C42×C5—31no—
139#4092—38no—
140C2×#685—31no—
141C2×#685—31no—
142C2×#685—31no—
143C2×#685—31no—
144C2×#685—31no—
145C2×#685—31no—
146C2×C4⋊Dic5—31no—
147C2×C4⋊Dic5—31no—
148C2×#683—31no—
149C2×#683—31no—
150C2×#683—31no—
151C2×#683C2×D311yescharacteristic
152C2×#683C2×D311yescharacteristic
153C2×#683C2×D311yescharacteristic
154C2×C4×Dic5—31no—
155C2×C4×Dic5—31no—
156C2×C4×Dic5C2×D311yescharacteristic
157#4018—64no—
158#3963—31no—
159#3963—31no—
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963—31no—
164#3963—31no—
165#3963—31no—
166#3963C2×D311yescharacteristic
167#3963C2×D311yescharacteristic
168#2323—151noSylow
169C23×C3×C5C2411yescharacteristic
170C22×D15—21no—
171C22×D15—21no—
172C22×D15—21no—
173C22×D15—21no—
174C22×D15—21no—
175C22×D15—21no—
176C22×D15C22×C412yes—
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×C5—21no—
184C2×C3×C4×C5C22×C412yes—
185C2×C3×C4×C5C2×D412yes—
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×Dic15C22×C412yes—
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×C5×Dic3C2×D412yes—
205C2×C5×Dic3C2×D412yes—
206C2×C5×Dic3#4112yes—
207C5×Dic6—28no—
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—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5C22×C412yes—
219C2×C3×Dic5C22×C412yes—
220#1200—28no—
221C22×C4×D3—51no—
222C22×Dic6C2×D511yescharacteristic
223C2×C3×C4⋊C4—51no—
224C2×C3×C4⋊C4—51no—
225C2×C3×C4⋊C4—51no—
226C2×C3×C4⋊C4C2×D511yescharacteristic
227C2×C3×C42—51no—
228C2×(C2×D3)⋊C4—51no—
229C2×(C2×D3)⋊C4—51no—
230C2×(C2×D3)⋊C4—51no—
231C2×(C2×D3)⋊C4—51no—
232C2×(C2×D3)⋊C4—51no—
233C2×(C2×D3)⋊C4—51no—
234C2×C4⋊Dic3—51no—
235C2×Dic3⋊C4—51no—
236C2×Dic3⋊C4—51no—
237C2×Dic3⋊C4—51no—
238C2×Dic3⋊C4—51no—
239C2×Dic3⋊C4C2×D511yescharacteristic
240C2×Dic3⋊C4C2×D511yescharacteristic
241C2×C4×Dic3—51no—
242C2×C4×Dic3—51no—
243C2×C4×Dic3C2×D511yescharacteristic
244C2×C4×Dic3C2×D511yescharacteristic
245C2×C4×Dic3C2×D511yescharacteristic
246#896—58no—
247#892—104no—
248#887—24no—
249C3×#95—51no—
250C3×#95—51no—
251C3⋊#95—51no—
252C3⋊#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95—51no—
259C23×D5—31no—
260C2×C5×Q8—34no—
261C2×C5×Q8—62no—
262C2×C5×Q8—62no—
263C22×C4×C5—31no—
264C22×C4×C5—31no—
265C22×C4×C5—31no—
266C22×C4×C5—31no—
267C22×C4×C5C22×D311yescharacteristic
268C22×C4×C5C22×D311yescharacteristic
269C22×C4×C5C22×D311yescharacteristic
270C22×Dic5—31no—
271C22×Dic5—31no—
272C22×Dic5—31no—
273C22×Dic5C22×D311yescharacteristic
274C22×Dic5C22×D311yescharacteristic
275C22×Dic5C22×D311yescharacteristic
276C22×Dic5C22×D311yescharacteristic
277C2×C4×D5—34no—
278C2×C4×D5—62no—
279C2×C4×D5—62no—
280C5×C4⋊C4—22no—
281C5×C4⋊C4—62no—
282C5×C4⋊C4—62no—
283C42×C5—34no—
284C42×C5—62no—
285C42×C5—62no—
286#685—34no—
287#685—34no—
288#685—62no—
289#685—62no—
290#685—121no—
291#685—121no—
292C4⋊Dic5—34no—
293C4⋊Dic5—62no—
294#683—22no—
295#683—34no—
296#683—41no—
297#683—62no—
298#683—121no—
299#683C4×D314yes—
300C4×Dic5—41no—
301C4×Dic5—62no—
302C4×Dic5—121no—
303C2×C22⋊Q8—151no—
304C2×C4×Q8—31no—
305C2×#117—151no—
306#391—151no—
307#389—51no—
308#389—151no—
309#389—151no—
310#388—151no—
311#388—151no—
312#388—151no—
313#388—151no—
314#387—151no—
315#387—151no—
316#380—151no—
317C4×C4⋊C4—151no—
318C22×C3×C5C23×C411yescharacteristic
319C22×C3×C5C22×D411yescharacteristic
320C22×C3×C5C2×#4111yescharacteristic
321C22×C3×C5H(5,𝔽2)11yescharacteristic
322C22×C3×C52−1+411yescharacteristic
323C22×C3×C52−1+411yescharacteristic
324C22×C3×C52−1+411yescharacteristic
325C2×D15—22no—
326C2×D15—22no—
327C2×D15—22no—
328C2×D15—41no—
329C2×D15—41no—
330C2×D15—41no—
331C2×D15—41no—
332C3×C4×C5—22no—
333C3×C4×C5—22no—
334C3×C4×C5—41no—
335Dic15—22no—
336Dic15—41no—
337Dic15—41no—
338C3×Dic5—22no—
339C3×Dic5—22no—
340C3×Dic5—41no—
341C3×Dic5—41no—
342C5×Dic3—22no—
343C5×Dic3—22no—
344C5×Dic3—41no—
345C5×Dic3C4×D414yes—
346C23×D3—51no—
347C22×C3×C4—51no—
348C22×C3×C4—51no—
349C22×C3×C4—51no—
350C22×C3×C4—51no—
351C22×C3×C4C22×D511yescharacteristic
352C22×C3×C4C22×D511yescharacteristic
353C22×C3×C4C22×D511yescharacteristic
354C22×Dic3—51no—
355C22×Dic3—51no—
356C22×Dic3—51no—
357C22×Dic3C22×D511yescharacteristic
358C22×Dic3C22×D511yescharacteristic
359C22×Dic3C22×D511yescharacteristic
360C22×Dic3C22×D511yescharacteristic
361C2×C4×D3—54no—
362C2×C4×D3—102no—
363C2×C4×D3—102no—
364C2×Dic6—22no—
365C2×Dic6—22no—
366C2×Dic6C4×D514yes—
367C3×C4⋊C4—22no—
368C3×C4⋊C4—54no—
369C3×C4⋊C4—102no—
370C3×C4⋊C4—201no—
371C3×C42—201no—
372(C2×D3)⋊C4—54no—
373(C2×D3)⋊C4—54no—
374(C2×D3)⋊C4—102no—
375(C2×D3)⋊C4—102no—
376(C2×D3)⋊C4—201no—
377(C2×D3)⋊C4—201no—
378C4⋊Dic3—102no—
379Dic3⋊C4—22no—
380Dic3⋊C4—22no—
381Dic3⋊C4—54no—
382Dic3⋊C4—54no—
383Dic3⋊C4—102no—
384Dic3⋊C4—201no—
385C4×Dic3—22no—
386C4×Dic3—22no—
387C4×Dic3—102no—
388C4×Dic3—201no—
389C4×Dic3C22⋊D514yes—
390C23×C5C23×D311yescharacteristic
391C22×D5—32no—
392C22×D5—61no—
393C22×D5—61no—
394C22×D5—61no—
395C22×D5—61no—
396C22×D5—61no—
397C22×D5—61no—
398C5×Q8—68no—
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—21no—
406C2×C4×C5—32no—
407C2×C4×C5—32no—
408C2×C4×C5—32no—
409C2×C4×C5—32no—
410C2×C4×C5—32no—
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×C5—61no—
418C2×C4×C5C2×C4×D312yes—
419C2×C4×C5D3×D412yes—
420C2×Dic5—21no—
421C2×Dic5—21no—
422C2×Dic5—21no—
423C2×Dic5—21no—
424C2×Dic5—21no—
425C2×Dic5—21no—
426C2×Dic5—21no—
427C2×Dic5—21no—
428C2×Dic5—21no—
429C2×Dic5—21no—
430C2×Dic5—32no—
431C2×Dic5—61no—
432C2×Dic5—61no—
433C2×Dic5—61no—
434C2×Dic5—61no—
435C2×Dic5—61no—
436C2×Dic5—61no—
437C2×Dic5—61no—
438C2×Dic5—61no—
439C2×Dic5C2×C4×D312yes—
440C2×Dic5C2×C4×D312yes—
441C4×D5—68no—
442C22×Q8—31no—
443C23×C4—151no—
444C22⋊Q8—158no—
445C4×Q8—64no—
446#117—304no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—51no—
450C2×C4⋊C4—51no—
451C2×C4⋊C4—51no—
452C2×C4⋊C4—151no—
453C2×C4⋊C4—151no—
454C2×C4⋊C4—151no—
455C2×C4⋊C4—151no—
456C2×C4⋊C4—151no—
457C2×C4⋊C4D3×D511yescharacteristic
458C2×C22⋊C4—151no—
459C2×C22⋊C4—151no—
460C2×C22⋊C4—151no—
461C2×C22⋊C4—151no—
462C2×C22⋊C4—151no—
463C2×C22⋊C4—151no—
464C2×C42—31no—
465C2×C42—31no—
466C2×C42—31no—
467C2×C42—51no—
468C2×C42—151no—
469C2×C42—151no—
470#95—51no—
471#95—51no—
472#95—151no—
473#95—151no—
474#95—151no—
475#95—151no—
476#95—151no—
477#95—151no—
478#95—151no—
479#95—151no—
480C2×C3×C5C2×C4×D411yescharacteristic
481C2×C3×C5#51911yescharacteristic
482C2×C3×C5#52011yescharacteristic
483C2×C3×C5#53611yescharacteristic
484C2×C3×C5#53711yescharacteristic
485C2×C3×C5#54111yescharacteristic
486C2×C3×C5#54211yescharacteristic
487D15—42no—
488C23×C3C23×D511yescharacteristic
489C22×D3—52no—
490C22×D3—101no—
491C22×D3—101no—
492C22×D3—101no—
493C22×D3—101no—
494C22×D3—101no—
495C22×D3—101no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—52no—
504C2×C3×C4—52no—
505C2×C3×C4—101no—
506C2×C3×C4—101no—
507C2×C3×C4—101no—
508C2×C3×C4—101no—
509C2×C3×C4—101no—
510C2×C3×C4—101no—
511C2×C3×C4—101no—
512C2×C3×C4—101no—
513C2×C3×C4—101no—
514C2×C3×C4—101no—
515C2×C3×C4C2×C4×D512yes—
516C2×C3×C4C2×C22⋊D512yes—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—52no—
525C2×Dic3—101no—
526C2×Dic3—101no—
527C2×Dic3—101no—
528C2×Dic3—101no—
529C2×Dic3—101no—
530C2×Dic3—101no—
531C2×Dic3—101no—
532C2×Dic3—101no—
533C2×Dic3C2×C4×D512yes—
534C2×Dic3C2×C4×D512yes—
535C2×Dic3#70912yes—
536C2×Dic3C2×C22⋊D512yes—
537C2×Dic3C2×C22⋊D512yes—
538C4×D3—108no—
539Dic6—28no—
540C22×C5C22×C4×D311yescharacteristic
541C22×C5C2×D3×D411yescharacteristic
542C22×C5#100411yescharacteristic
543C22×C5#100711yescharacteristic
544C22×C5#100711yescharacteristic
545C22×C5D3×#4111yescharacteristic
546C22×C5#101011yescharacteristic
547C2×D5—62no—
548C2×D5—62no—
549C2×D5—62no—
550C2×D5—121no—
551C2×D5—121no—
552C2×D5—121no—
553C2×D5—121no—
554C4×C5—22no—
555C4×C5—22no—
556C4×C5—34no—
557C4×C5—41no—
558C4×C5—62no—
559C4×C5—62no—
560C4×C5—121no—
561Dic5—22no—
562Dic5—22no—
563Dic5—41no—
564Dic5—41no—
565Dic5—62no—
566Dic5—121no—
567Dic5—121no—
568C24—151no—
569C2×Q8—34no—
570C2×Q8—62no—
571C2×Q8—62no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—51no—
577C22×C4—51no—
578C22×C4—51no—
579C22×C4—51no—
580C22×C4—154no—
581C22×C4—151no—
582C22×C4—151no—
583C22×C4—151no—
584C22×C4—302no—
585C22×C4—302no—
586C22×C4C2×D3×D511yescharacteristic
587C22×C4C2×D3×D511yescharacteristic
588C22×C4C2×D3×D511yescharacteristic
589C4⋊C4—22no—
590C4⋊C4—54no—
591C4⋊C4—62no—
592C4⋊C4—62no—
593C4⋊C4—102no—
594C4⋊C4—154no—
595C4⋊C4—154no—
596C4⋊C4—201no—
597C4⋊C4—302no—
598C4⋊C4—302no—
599C4⋊C4—601no—
600C22⋊C4—154no—
601C22⋊C4—154no—
602C22⋊C4—302no—
603C22⋊C4—302no—
604C22⋊C4—601no—
605C22⋊C4—601no—
606C42—34no—
607C42—62no—
608C42—62no—
609C42—201no—
610C42—302no—
611C42—601no—
612C3×C5#232311yescharacteristic, complemented, Hall
613C22×C3C22×C4×D511yescharacteristic
614C22×C3C2×#70911yescharacteristic
615C22×C3#414711yescharacteristic
616C22×C3#414711yescharacteristic
617C22×C3#414911yescharacteristic
618C22×C3#415011yescharacteristic
619C22×C3C22×C22⋊D511yescharacteristic
620C2×D3—102no—
621C2×D3—102no—
622C2×D3—102no—
623C2×D3—201no—
624C2×D3—201no—
625C2×D3—201no—
626C2×D3—201no—
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—41no—
630C3×C4—102no—
631C3×C4—102no—
632C3×C4—201no—
633C3×C4—201no—
634Dic3—22no—
635Dic3—22no—
636Dic3—41no—
637Dic3—102no—
638Dic3—201no—
639Dic3—201no—
640Dic3C4×C22⋊D514yes—
641C2×C5#550411yescharacteristic
642C2×C5C4×D3×D411yescharacteristic
643C2×C5#557211yescharacteristic
644C2×C5#559711yescharacteristic
645C2×C5#564011yescharacteristic
646C2×C5#569611yescharacteristic
647C2×C5#572411yescharacteristic
648D5—122no—
649C23—152no—
650C23—301no—
651C23—301no—
652C23—301no—
653C23—301no—
654C23—301no—
655C23—301no—
656C23C22×D3×D511yescharacteristic
657Q8—68no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—32no—
666C2×C4—32no—
667C2×C4—32no—
668C2×C4—32no—
669C2×C4—32no—
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—101no—
680C2×C4—101no—
681C2×C4—101no—
682C2×C4—101no—
683C2×C4—101no—
684C2×C4—101no—
685C2×C4—101no—
686C2×C4—101no—
687C2×C4—101no—
688C2×C4—101no—
689C2×C4—152no—
690C2×C4—308no—
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×C4C4×D3×D512yes—
700C2×C4D3×C22⋊D512yes—
701C2×C3#6590611yescharacteristic
702C2×C3#6590811yescharacteristic
703C2×C3#6591611yescharacteristic
704C2×C3#6591711yescharacteristic
705C2×C3C2×C4×C22⋊D511yescharacteristic
706C2×C3#6615011yescharacteristic
707C2×C3#6616711yescharacteristic
708D3—202no—
709C5#7597111yescharacteristic, complemented, Sylow
710C22—302no—
711C22—302no—
712C22—302no—
713C22—601no—
714C22—601no—
715C22—601no—
716C22—601no—
717C22C2×C4×D3×D511yescharacteristic
718C22D3×#70911yescharacteristic
719C22#9202011yescharacteristic
720C22#9202611yescharacteristic
721C22#9202911yescharacteristic
722C22#9202911yescharacteristic
723C22C2×D3×C22⋊D511yescharacteristic
724C4—22no—
725C4—22no—
726C4—34no—
727C4—41no—
728C4—62no—
729C4—62no—
730C4—102no—
731C4—102no—
732C4—121no—
733C4—201no—
734C4—201no—
735C4—302no—
736C4—601no—
737C4—601no—
738C3#1061421911yescharacteristic, complemented, Sylow
739C2—602no—
740C2#1175333611yescharacteristic
741C2#1175335311yescharacteristic
742C2#1175338111yescharacteristic
743C2#1175338511yescharacteristic
744C2C4×D3×C22⋊D511yescharacteristic
745C2#1175480411yescharacteristic
746C2#1175512611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2323
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
1. C2×C5×#887C2semidirect
5. C3×#65261C2semidirect
8. C4×Dic3⋊Dic5C2semidirect
9. #11748818C2semidirect
10. #11748808C2semidirect
13. #11748692C2semidirect
14. #11748664C2semidirect
15. #11748590C2semidirect
43. #91424C4semidirect
65. #65261D3semidirect
117. C2×#887D5semidirect
612. C3×C5#2323semidirect
709. C5#75971semidirect
738. C3#10614219semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8872
C2×#914242
C2×#914032
#117510912
C3×#652612
#117488822
#117488542
C4×Dic3⋊Dic52
#117488182
#117488082
#117487282
#117487272
#117486922
#117486642
#117485902
#106142193
#759715