Finite Group Databasebeta

← C2×#11756529 #14510023

Subgroups — C2×#11756529 #14510023

Order 1920.

2920 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92101C211yesmaximal, characteristic, complemented
2C2×#92100C211yesmaximal, characteristic, complemented
3C2×C3×C5×#135C211yesmaximal, characteristic, complemented
4C2×#91840C211yesmaximal, characteristic, complemented
5C2×#91838C211yesmaximal, characteristic, complemented
6#11756529C2116yesmaximal, direct product factor
7C2×#91807C212yesmaximal, complemented
8C2×#91805C212yesmaximal, complemented
9C2×SD16×D15C212yesmaximal, complemented
10C2×#91800C212yesmaximal, complemented
11C22×#6706C211yesmaximal, characteristic, complemented
12C2×#91790C211yesmaximal, characteristic, complemented
13C2×#66104—31nomaximal, Hall
14C2×C3×C5×#41C2211yescharacteristic
15C2×C3×C5×#41C2211yescharacteristic, complemented
16#92101—24no—
17#92101C2218yescomplemented
18#92100—24no—
19#92100C2218yescomplemented
20C2×#6821C2212yes—
21C2×Q8×D15C2212yescomplemented
22C2×#6819—22no—
23C2×#6819C2212yescomplemented
24C2×D4×D15—22no—
25C2×D4×D15C2212yes—
26C2×#6817—21no—
27C2×#6817—21no—
28C2×#6817C2211yescharacteristic
29C22×D60—21no—
30C22×D60C2211yescharacteristic
31C22×Dic30—21no—
32C22×Dic30C2211yescharacteristic, complemented
33C3×C5×#135C2218yescomplemented
34C2×C3×C5×Q16C2211yescharacteristic, complemented
35C2×C3×C5×SD16C2211yescharacteristic, complemented
36C2×C3×C5×SD16C2211yescharacteristic, complemented
37C2×C3×C5×D8C2211yescharacteristic, complemented
38C22×C3×C5×C8C2211yescharacteristic, complemented
39#91840C2218yescomplemented
40#91838C2218yescomplemented
41C2×#6718C2212yescomplemented
42C2×#6717C2212yescomplemented
43C2×#6716C2212yescomplemented
44C2×#6715C2212yescomplemented
45C2×#6710C2211yescharacteristic, complemented
46#91807C22116yescomplemented
47#91805C22116yescomplemented
48SD16×D15C22116yescomplemented
49#91800C22116yescomplemented
50C2×#6706C2212yescomplemented
51C2×#6706C2212yescomplemented
52C2×#6706C2218yescomplemented
53#91790C2218yescomplemented
54C2×#6705C2212yescomplemented
55C2×C8×D15C2212yescomplemented
56C2×#5770—51nomaximal, Hall
57C2×#4150—31no—
58C2×#4149—31no—
59C2×C5×#135D311yescharacteristic, complemented
60C2×#4097—31no—
61C2×#4095—31no—
62#66104—316no—
63C2×#4064—32no—
64C2×#4062—32no—
65C2×D5×SD16—32no—
66C2×#4057—32no—
67C22×#677—31no—
68C2×#4047—31no—
69C23×D15—21no—
70C23×D15—22no—
71C3×C5×#41—22no—
72C3×C5×#41—22no—
73C3×C5×#41C2314yes—
74C3×C5×#41C2314yescomplemented
75C2×C3×C5×Q8C2311yescharacteristic
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×D4—21no—
78C2×C3×C5×D4—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C2×C3×C5×D4C2311yescharacteristic
81C22×C3×C4×C5—21no—
82C22×C3×C4×C5—21no—
83C22×C3×C4×C5C2311yescharacteristic
84C2×#1220—22no—
85C2×#1220—22no—
86C2×#1220D412yes—
87C22×Dic15—21no—
88C22×Dic15—22no—
89#6821—24no—
90#6821C2318yes—
91Q8×D15—24no—
92Q8×D15C2318yescomplemented
93#6819—216no—
94#6819—24no—
95#6819C2318yescomplemented
96D4×D15—216no—
97D4×D15—24no—
98D4×D15C2318yes—
99#6817—28no—
100#6817—28no—
101#6817D414yes—
102#6817C2314yes—
103C2×D60—22no—
104C2×D60—21no—
105C2×D60—22no—
106C2×D60—28no—
107C2×D60D411yescharacteristic
108C2×D60C2312yes—
109C2×D60C2314yes—
110C2×C4×D15—22no—
111C2×C4×D15—22no—
112C2×C4×D15C2312yes—
113C2×Dic30—21no—
114C2×Dic30—22no—
115C2×Dic30—22no—
116C2×Dic30—28no—
117C2×Dic30D411yescharacteristic
118C2×Dic30C2312yes—
119C2×Dic30C2314yescomplemented
120C3×C5×Q16C2314yescomplemented
121C3×C5×SD16C2314yescomplemented
122C3×C5×SD16C2314yescomplemented
123C3×C5×D8C2314yescomplemented
124C2×C3×C5×C8C2311yescharacteristic
125C2×C3×C5×C8C2311yescharacteristic
126C2×C3×C5×C8C2314yescomplemented
127#6718C2318yescomplemented
128#6717C2318yescomplemented
129#6716C2318yescomplemented
130#6715C2318yescomplemented
131#6710C2314yescomplemented
132C2×C3⋊#168C2312yes—
133#6706C2318yescomplemented
134#6706C2318yescomplemented
135#6705C2318yescomplemented
136C8×D15C2318yescomplemented
137C2×#1010—51no—
138C2×#1009—51no—
139C2×C3×#135D511yescharacteristic, complemented
140C2×#951—51no—
141C2×#949—51no—
142#5770—516no—
143C2×#918—52no—
144C2×#916—52no—
145C2×D3×SD16—52no—
146C2×#911—52no—
147C22×#204—51no—
148C2×#901—51no—
149C2×C5×#41C2×D311yescharacteristic
150C2×C5×#41C2×D311yescharacteristic, complemented
151#4150—38no—
152#4150—64no—
153#4149—38no—
154#4149—64no—
155C2×#713—32no—
156C2×Q8×D5—32no—
157C2×#711—32no—
158C2×#711—62no—
159C2×D4×D5—32no—
160C2×D4×D5—62no—
161C2×#709—31no—
162C2×#709—61no—
163C2×#709—61no—
164C22×D20—31no—
165C22×D20—61no—
166C22×Dic10—31no—
167C22×Dic10—61no—
168C5×#135C2×D318yescomplemented
169C2×C5×Q16C2×D311yescharacteristic, complemented
170C2×C5×SD16C2×D311yescharacteristic, complemented
171C2×C5×SD16C2×D311yescharacteristic, complemented
172C2×C5×D8C2×D311yescharacteristic, complemented
173C22×C5×C8C2×D311yescharacteristic, complemented
174#4097—38no—
175#4095—38no—
176C2×#689—32no—
177C2×#688—32no—
178C2×#687—32no—
179C2×#686—32no—
180C2×#681—31no—
181#4064—316no—
182#4062—316no—
183D5×SD16—316no—
184#4057—316no—
185C2×#677—32no—
186C2×#677—32no—
187C2×#677—38no—
188#4047—38no—
189C2×#676—32no—
190C2×C8×D5—32no—
191C2×#577—151noSylow
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5C2×D411yescharacteristic
195C22×D15—22no—
196C22×D15—24no—
197C22×D15—28no—
198C22×D15—84no—
199C22×D15—82no—
200C22×D15C2×D412yes—
201C3×C5×Q8—21no—
202C3×C5×Q8—21no—
203C3×C5×Q8C2412yes—
204C3×C5×Q8C2412yes—
205C3×C5×D4—24no—
206C3×C5×D4—24no—
207C3×C5×D4—21no—
208C3×C5×D4—21no—
209C3×C5×D4C2412yes—
210C3×C5×D4C2412yes—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—24no—
214C2×C3×C4×C5—24no—
215C2×C3×C4×C5C2×D411yescharacteristic
216C2×C3×C4×C5C2×D412yes—
217C2×C3×C4×C5C2411yescharacteristic
218C2×C3×C4×C5C2412yes—
219#1220—28no—
220#1220—28no—
221#1220C2×D418yes—
222C2×Dic15—22no—
223C2×Dic15—24no—
224C2×Dic15—28no—
225C2×Dic15C2×D412yes—
226D60—28no—
227D60—24no—
228D60—22no—
229D60C2×D414yes—
230D60C2414yes—
231C4×D15—28no—
232C4×D15—28no—
233C4×D15C2×D414yes—
234C4×D15C2414yes—
235Dic30—24no—
236Dic30—22no—
237Dic30—28no—
238Dic30C2×D414yes—
239Dic30C2414yes—
240C3×C5×C8C2412yes—
241C3×C5×C8C2412yes—
242C3⋊#168C2414yes—
243C2×C3×#41C2×D511yescharacteristic
244C2×C3×#41C2×D511yescharacteristic, complemented
245#1010—58no—
246#1010—104no—
247#1009—58no—
248#1009—104no—
249C2×#239—52no—
250C2×D3×Q8—52no—
251C2×#237—52no—
252C2×#237—102no—
253C2×D3×D4—52no—
254C2×D3×D4—102no—
255C2×#235—51no—
256C2×#235—101no—
257C2×#235—101no—
258C22×D12—51no—
259C22×D12—101no—
260C22×Dic6—51no—
261C22×Dic6—101no—
262C3×#135C2×D518yescomplemented
263C2×C3×Q16C2×D511yescharacteristic, complemented
264C2×C3×SD16C2×D511yescharacteristic, complemented
265C2×C3×SD16C2×D511yescharacteristic, complemented
266C2×C3×D8C2×D511yescharacteristic, complemented
267C22×C3×C8C2×D511yescharacteristic, complemented
268#951—58no—
269#949—58no—
270C2×#216—52no—
271C2×#215—52no—
272C2×#214—52no—
273C2×#213—52no—
274C2×#208—51no—
275#918—516no—
276#916—516no—
277D3×SD16—516no—
278#911—516no—
279C2×#204—52no—
280C2×#204—52no—
281C2×#204—58no—
282#901—58no—
283C2×ΓL(1,𝔽25)—52no—
284C2×D3×C8—52no—
285C23×D5—62no—
286C23×D5—61no—
287C5×#41—22no—
288C5×#41—22no—
289C5×#41C22×D314yes—
290C5×#41C22×D314yescomplemented
291C2×C5×Q8C22×D311yescharacteristic
292C2×C5×Q8C22×D311yescharacteristic
293C2×C5×D4—21no—
294C2×C5×D4—21no—
295C2×C5×D4C22×D311yescharacteristic
296C2×C5×D4C22×D311yescharacteristic
297C22×C4×C5—21no—
298C22×C4×C5—21no—
299C22×C4×C5C22×D311yescharacteristic
300C2×C22⋊D5—32no—
301C2×C22⋊D5—62no—
302C2×C22⋊D5—62no—
303C22×Dic5—62no—
304C22×Dic5—61no—
305#713—38no—
306#713—64no—
307Q8×D5—38no—
308Q8×D5—64no—
309#711—38no—
310#711—64no—
311#711—616no—
312D4×D5—38no—
313D4×D5—64no—
314D4×D5—616no—
315#709—34no—
316#709—34no—
317#709—68no—
318#709—68no—
319C2×D20—31no—
320C2×D20—32no—
321C2×D20—34no—
322C2×D20—68no—
323C2×D20—62no—
324C2×D20—61no—
325C2×D20—62no—
326C2×C4×D5—32no—
327C2×C4×D5—62no—
328C2×C4×D5—62no—
329C2×Dic10—31no—
330C2×Dic10—34no—
331C2×Dic10—32no—
332C2×Dic10—68no—
333C2×Dic10—62no—
334C2×Dic10—61no—
335C2×Dic10—62no—
336C5×Q16C22×D314yescomplemented
337C5×SD16C22×D314yescomplemented
338C5×SD16C22×D314yescomplemented
339C5×D8C22×D314yescomplemented
340C2×C5×C8C22×D311yescharacteristic
341C2×C5×C8C22×D311yescharacteristic
342C2×C5×C8C22×D314yescomplemented
343#689—38no—
344#688—38no—
345#687—38no—
346#686—38no—
347#681—34no—
348C2×#168—32no—
349#677—38no—
350#677—38no—
351#676—38no—
352C8×D5—38no—
353C2×2−1+4—151no—
354C2×H(5,𝔽2)—151no—
355#577—1516no—
356C2×#137—151no—
357C2×#137—152no—
358C2×AGL(1,ℤ/8)—151no—
359C2×AGL(1,ℤ/8)—152no—
360C2×#135—152no—
361C2×#135D1511yescharacteristic, complemented
362C22×SD16—152no—
363C22×SD16—151no—
364C2×#131—151no—
365C22×C3×C5—22no—
366C22×C3×C5—22no—
367C22×C3×C5—22no—
368C22×C3×C5—42no—
369C22×C3×C5—42no—
370C22×C3×C5C22×D412yes—
371C22×C3×C5C22×D411yescharacteristic
372C2×D15—24no—
373C2×D15—24no—
374C2×D15—44no—
375C2×D15—88no—
376C2×D15—84no—
377C2×D15C22×D414yes—
378C3×C4×C5—22no—
379C3×C4×C5—22no—
380C3×C4×C5C22×D412yes—
381C3×C4×C5C22×D411yescharacteristic
382C3×C4×C5C2511yescharacteristic
383Dic15—24no—
384Dic15C22×D414yes—
385C23×D3—102no—
386C23×D3—101no—
387C3×#41—22no—
388C3×#41—22no—
389C3×#41C22×D514yes—
390C3×#41C22×D514yescomplemented
391C2×C3×Q8C22×D511yescharacteristic
392C2×C3×Q8C22×D511yescharacteristic
393C2×C3×D4—21no—
394C2×C3×D4—21no—
395C2×C3×D4C22×D511yescharacteristic
396C2×C3×D4C22×D511yescharacteristic
397C22×C3×C4—21no—
398C22×C3×C4—21no—
399C22×C3×C4C22×D511yescharacteristic
400C2×#67—52no—
401C2×#67—102no—
402C2×#67—102no—
403C22×Dic3—102no—
404C22×Dic3—101no—
405#239—58no—
406#239—104no—
407D3×Q8—58no—
408D3×Q8—104no—
409#237—58no—
410#237—104no—
411#237—1016no—
412D3×D4—58no—
413D3×D4—104no—
414D3×D4—1016no—
415#235—54no—
416#235—54no—
417#235—108no—
418#235—108no—
419C2×D12—51no—
420C2×D12—52no—
421C2×D12—54no—
422C2×D12—108no—
423C2×D12—102no—
424C2×D12—101no—
425C2×D12—102no—
426C2×C4×D3—52no—
427C2×C4×D3—102no—
428C2×C4×D3—102no—
429C2×Dic6—51no—
430C2×Dic6—52no—
431C2×Dic6—54no—
432C2×Dic6—108no—
433C2×Dic6—102no—
434C2×Dic6—101no—
435C2×Dic6—102no—
436C3×Q16C22×D514yescomplemented
437C3×SD16C22×D514yescomplemented
438C3×SD16C22×D514yescomplemented
439C3×D8C22×D514yescomplemented
440C2×C3×C8C22×D511yescharacteristic
441C2×C3×C8C22×D511yescharacteristic
442C2×C3×C8C22×D514yescomplemented
443#216—58no—
444#215—58no—
445#214—58no—
446#213—58no—
447#208—54no—
448C2×C3⋊C8—52no—
449#204—58no—
450#204—58no—
451ΓL(1,𝔽25)—58no—
452D3×C8—58no—
453C23×C5—21no—
454C23×C5—21no—
455C23×C5D3×D411yescharacteristic
456C22×D5—32no—
457C22×D5—68no—
458C22×D5—62no—
459C22×D5—64no—
460C22×D5—244no—
461C22×D5—242no—
462C5×Q8—21no—
463C5×Q8—21no—
464C5×Q8C23×D312yes—
465C5×Q8C23×D312yes—
466C5×D4—24no—
467C5×D4—24no—
468C5×D4—21no—
469C5×D4—21no—
470C5×D4C23×D312yes—
471C5×D4C23×D312yes—
472C2×C4×C5—21no—
473C2×C4×C5—21no—
474C2×C4×C5—24no—
475C2×C4×C5—24no—
476C2×C4×C5D3×D411yescharacteristic
477C2×C4×C5D3×D412yes—
478C2×C4×C5C23×D311yescharacteristic
479C2×C4×C5C23×D312yes—
480C22⋊D5—38no—
481C22⋊D5—68no—
482C22⋊D5—68no—
483C2×Dic5—32no—
484C2×Dic5—68no—
485C2×Dic5—62no—
486C2×Dic5—64no—
487D20—34no—
488D20—34no—
489D20—68no—
490D20—64no—
491D20—62no—
492C4×D5—34no—
493C4×D5—34no—
494C4×D5—68no—
495C4×D5—68no—
496Dic10—34no—
497Dic10—34no—
498Dic10—68no—
499Dic10—64no—
500Dic10—62no—
501C5×C8C23×D312yes—
502C5×C8C23×D312yes—
503#168—34no—
5042−1+4—158no—
5052−1+4—304no—
506H(5,𝔽2)—158no—
507H(5,𝔽2)—304no—
508C2×#41—151no—
509C2×#41—152no—
510C2×#41—152no—
511C2×#41—301no—
512C2×#41—301no—
513C2×#41—302no—
514C2×#41C2×D1511yescharacteristic
515C2×#41C2×D1511yescharacteristic, complemented
516C22×Q8—152no—
517C22×Q8—151no—
518C22×Q8—301no—
519C22×D4—152no—
520C22×D4—151no—
521C22×D4—301no—
522C22×D4—302no—
523#137—158no—
524#137—1516no—
525AGL(1,ℤ/8)—158no—
526AGL(1,ℤ/8)—1516no—
527#135—1516no—
528#135C2×D1518yescomplemented
529C2×Q16—152no—
530C2×Q16C2×D1511yescharacteristic, complemented
531C2×SD16—152no—
532C2×SD16—152no—
533C2×SD16—1516no—
534C2×SD16—152no—
535C2×SD16—152no—
536C2×SD16—158no—
537C2×SD16C2×D1511yescharacteristic, complemented
538C2×SD16C2×D1511yescharacteristic, complemented
539C2×D8—152no—
540C2×D8C2×D1511yescharacteristic, complemented
541#131—158no—
542C2×M16—151no—
543C2×M16—152no—
544C22×C8—152no—
545C22×C8C2×D1511yescharacteristic, complemented
546C2×C3×C5—22no—
547C2×C3×C5—42no—
548C2×C3×C5—42no—
549C2×C3×C5#57712yescomplemented
550C2×C3×C5C23×D411yescharacteristic
551D15—24no—
552D15—44no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3D4×D511yescharacteristic
556C22×D3—52no—
557C22×D3—108no—
558C22×D3—102no—
559C22×D3—104no—
560C22×D3—404no—
561C22×D3—402no—
562C3×Q8—21no—
563C3×Q8—21no—
564C3×Q8C23×D512yes—
565C3×Q8C23×D512yes—
566C3×D4—24no—
567C3×D4—24no—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4C23×D512yes—
571C3×D4C23×D512yes—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—24no—
575C2×C3×C4—24no—
576C2×C3×C4D4×D511yescharacteristic
577C2×C3×C4D4×D512yes—
578C2×C3×C4C23×D511yescharacteristic
579C2×C3×C4C23×D512yes—
580#67—58no—
581#67—108no—
582#67—108no—
583C2×Dic3—52no—
584C2×Dic3—108no—
585C2×Dic3—102no—
586C2×Dic3—104no—
587D12—54no—
588D12—54no—
589D12—108no—
590D12—104no—
591D12—102no—
592C4×D3—54no—
593C4×D3—54no—
594C4×D3—108no—
595C4×D3—108no—
596Dic6—54no—
597Dic6—54no—
598Dic6—108no—
599Dic6—104no—
600Dic6—102no—
601C3×C8C23×D512yes—
602C3×C8C23×D512yes—
603C3⋊C8—54no—
604C22×C5—22no—
605C22×C5—22no—
606C22×C5—22no—
607C22×C5—42no—
608C22×C5—42no—
609C22×C5C2×D3×D412yes—
610C22×C5C2×D3×D411yescharacteristic
611C2×D5—34no—
612C2×D5—64no—
613C2×D5—64no—
614C2×D5—124no—
615C2×D5—248no—
616C2×D5—244no—
617C4×C5—22no—
618C4×C5—22no—
619C4×C5C2×D3×D412yes—
620C4×C5C2×D3×D411yescharacteristic
621C4×C5C24×D311yescharacteristic
622Dic5—34no—
623Dic5—64no—
624C24—302no—
625C24—301no—
626#41—22no—
627#41—22no—
628#41—154no—
629#41—154no—
630#41—158no—
631#41—158no—
632#41—308no—
633#41—308no—
634#41—304no—
635#41—304no—
636#41—3016no—
637#41C22×D1514yes—
638#41C22×D1514yescomplemented
639C2×Q8—151no—
640C2×Q8—158no—
641C2×Q8—152no—
642C2×Q8—154no—
643C2×Q8—302no—
644C2×Q8—308no—
645C2×Q8—304no—
646C2×Q8—301no—
647C2×Q8—302no—
648C2×Q8C22×D1511yescharacteristic
649C2×Q8C22×D1511yescharacteristic
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—152no—
653C2×D4—158no—
654C2×D4—151no—
655C2×D4—152no—
656C2×D4—154no—
657C2×D4—308no—
658C2×D4—302no—
659C2×D4—304no—
660C2×D4—302no—
661C2×D4—3016no—
662C2×D4—302no—
663C2×D4—301no—
664C2×D4—302no—
665C2×D4C22×D1511yescharacteristic
666C2×D4C22×D1511yescharacteristic
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—152no—
670C22×C4—302no—
671C22×C4—302no—
672C22×C4—302no—
673C22×C4—301no—
674C22×C4C22×D1511yescharacteristic
675Q16—158no—
676Q16C22×D1514yescomplemented
677SD16—158no—
678SD16—158no—
679SD16—158no—
680SD16—158no—
681SD16C22×D1514yescomplemented
682SD16C22×D1514yescomplemented
683D8—158no—
684D8C22×D1514yescomplemented
685M16—154no—
686M16—158no—
687C2×C8—152no—
688C2×C8—158no—
689C2×C8C22×D1511yescharacteristic
690C2×C8C22×D1511yescharacteristic
691C2×C8C22×D1514yescomplemented
692C3×C5C2×#57711yescharacteristic, complemented, Hall
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—42no—
697C22×C3—42no—
698C22×C3C2×D4×D512yes—
699C22×C3C2×D4×D511yescharacteristic
700C2×D3—54no—
701C2×D3—104no—
702C2×D3—104no—
703C2×D3—204no—
704C2×D3—408no—
705C2×D3—404no—
706C3×C4—22no—
707C3×C4—22no—
708C3×C4C2×D4×D512yes—
709C3×C4C2×D4×D511yescharacteristic
710C3×C4C24×D511yescharacteristic
711Dic3—54no—
712Dic3—104no—
713C2×C5—22no—
714C2×C5—42no—
715C2×C5—42no—
716C2×C5#577012yescomplemented
717C2×C5C22×D3×D411yescharacteristic
718D5—64no—
719D5—124no—
720C23—21no—
721C23—21no—
722C23—152no—
723C23—308no—
724C23—302no—
725C23—304no—
726C23—1202no—
727C23—1204no—
728C23D4×D1511yescharacteristic
729Q8—21no—
730Q8—21no—
731Q8—154no—
732Q8—154no—
733Q8—308no—
734Q8—304no—
735Q8—302no—
736Q8C23×D1512yes—
737Q8C23×D1512yes—
738D4—24no—
739D4—24no—
740D4—21no—
741D4—21no—
742D4—158no—
743D4—154no—
744D4—154no—
745D4—308no—
746D4—308no—
747D4—308no—
748D4—304no—
749D4—302no—
750D4C23×D1512yes—
751D4C23×D1512yes—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—152no—
757C2×C4—154no—
758C2×C4—154no—
759C2×C4—308no—
760C2×C4—308no—
761C2×C4—308no—
762C2×C4—304no—
763C2×C4—302no—
764C2×C4D4×D1512yes—
765C2×C4D4×D1511yescharacteristic
766C2×C4C23×D1512yes—
767C2×C4C23×D1511yescharacteristic
768C8—154no—
769C8C23×D1512yes—
770C8C23×D1512yes—
771C2×C3—22no—
772C2×C3—42no—
773C2×C3—42no—
774C2×C3#6610412yescomplemented
775C2×C3C22×D4×D511yescharacteristic
776D3—104no—
777D3—204no—
778C5C2×#577011yescharacteristic, complemented, Sylow
779C22—22no—
780C22—22no—
781C22—22no—
782C22—42no—
783C22—42no—
784C22—154no—
785C22—304no—
786C22—304no—
787C22—604no—
788C22—1204no—
789C22—1208no—
790C22C2×D4×D1512yes—
791C22C2×D4×D1511yescharacteristic
792C4—22no—
793C4—22no—
794C4—154no—
795C4—304no—
796C4C2×D4×D1512yes—
797C4C2×D4×D1511yescharacteristic
798C4C24×D1511yescharacteristic
799C3C2×#6610411yescharacteristic, complemented, Sylow
800C2—22no—
801C2—42no—
802C2—42no—
803C2—304no—
804C2—604no—
805C2#1175652912yesdirect product factor
806C2C22×D4×D1511yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC3×C4×C5C25
FrattiniC4C24×D15
FittingC2×C3×C5×#135C2
socleC22×C3×C5C22×D4
hypercenterC2×#135D15
hypocenterC3×C5C2×#577
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#92101C2semidirect
2. C2×#92100C2semidirect
3. C2×C3×C5×#135C2semidirect
4. C2×#91840C2semidirect
5. C2×#91838C2semidirect
6. #11756529C2direct (N × H)
7. C2×#91807C2semidirect
8. C2×#91805C2semidirect
9. C2×SD16×D15C2semidirect
10. C2×#91800C2semidirect
11. C22×#6706C2semidirect
12. C2×#91790C2semidirect
15. C2×C3×C5×#41C22semidirect
17. #92101C22semidirect
19. #92100C22semidirect
21. C2×Q8×D15C22semidirect
23. C2×#6819C22semidirect
32. C22×Dic30C22semidirect
33. C3×C5×#135C22semidirect
34. C2×C3×C5×Q16C22semidirect
35. C2×C3×C5×SD16C22semidirect
36. C2×C3×C5×SD16C22semidirect
37. C2×C3×C5×D8C22semidirect
38. C22×C3×C5×C8C22semidirect
39. #91840C22semidirect
40. #91838C22semidirect
41. C2×#6718C22semidirect
42. C2×#6717C22semidirect
43. C2×#6716C22semidirect
44. C2×#6715C22semidirect
45. C2×#6710C22semidirect
46. #91807C22semidirect
47. #91805C22semidirect
48. SD16×D15C22semidirect
49. #91800C22semidirect
50. C2×#6706C22semidirect
51. C2×#6706C22semidirect
52. C2×#6706C22semidirect
53. #91790C22semidirect
54. C2×#6705C22semidirect
55. C2×C8×D15C22semidirect
59. C2×C5×#135D3semidirect
74. C3×C5×#41C23semidirect
92. Q8×D15C23semidirect
95. #6819C23semidirect
119. C2×Dic30C23semidirect
120. C3×C5×Q16C23semidirect
121. C3×C5×SD16C23semidirect
122. C3×C5×SD16C23semidirect
123. C3×C5×D8C23semidirect
126. C2×C3×C5×C8C23semidirect
127. #6718C23semidirect
128. #6717C23semidirect
129. #6716C23semidirect
130. #6715C23semidirect
131. #6710C23semidirect
133. #6706C23semidirect
134. #6706C23semidirect
135. #6705C23semidirect
136. C8×D15C23semidirect
139. C2×C3×#135D5semidirect
150. C2×C5×#41C2×D3semidirect
168. C5×#135C2×D3semidirect
169. C2×C5×Q16C2×D3semidirect
170. C2×C5×SD16C2×D3semidirect
171. C2×C5×SD16C2×D3semidirect
172. C2×C5×D8C2×D3semidirect
173. C22×C5×C8C2×D3semidirect
244. C2×C3×#41C2×D5semidirect
262. C3×#135C2×D5semidirect
263. C2×C3×Q16C2×D5semidirect
264. C2×C3×SD16C2×D5semidirect
265. C2×C3×SD16C2×D5semidirect
266. C2×C3×D8C2×D5semidirect
267. C22×C3×C8C2×D5semidirect
290. C5×#41C22×D3semidirect
336. C5×Q16C22×D3semidirect
337. C5×SD16C22×D3semidirect
338. C5×SD16C22×D3semidirect
339. C5×D8C22×D3semidirect
342. C2×C5×C8C22×D3semidirect
361. C2×#135D15semidirect
390. C3×#41C22×D5semidirect
436. C3×Q16C22×D5semidirect
437. C3×SD16C22×D5semidirect
438. C3×SD16C22×D5semidirect
439. C3×D8C22×D5semidirect
442. C2×C3×C8C22×D5semidirect
515. C2×#41C2×D15semidirect
528. #135C2×D15semidirect
530. C2×Q16C2×D15semidirect
537. C2×SD16C2×D15semidirect
538. C2×SD16C2×D15semidirect
540. C2×D8C2×D15semidirect
545. C22×C8C2×D15semidirect
549. C2×C3×C5#577semidirect
638. #41C22×D15semidirect
676. Q16C22×D15semidirect
681. SD16C22×D15semidirect
682. SD16C22×D15semidirect
684. D8C22×D15semidirect
691. C2×C8C22×D15semidirect
692. C3×C5C2×#577semidirect
716. C2×C5#5770semidirect
774. C2×C3#66104semidirect
778. C5C2×#5770semidirect
799. C3C2×#66104semidirect
805. C2#11756529direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#921012
C2×#921002
C2×C3×C5×#1352
C2×#918402
C2×#918382
#117565292
C2×#918072
C2×#918052
C2×SD16×D152
C2×#918002
C22×#67062
C2×#917902
C2×#661043
C2×#57705