Finite Group Databasebeta

← C2×#11751818 #14412146

Subgroups — C2×#11751818 #14412146

Order 1920.

1512 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
1C22×#6771C211yesmaximal, characteristic
2C2×D5⋊#208C211yesmaximal, characteristic, complemented
3C2×C3×D5⋊M16C211yesmaximal, characteristic, complemented
4C2×#91175C212yesmaximal, complemented
5C2×#91174C212yesmaximal, complemented
6#11751818C218yesmaximal, direct product factor
7C2×#65761—31nomaximal, Hall
8C22×C4×D15C411yescharacteristic
9C22×C4×C5×D3C411yescharacteristic
10C22×C3×C4×D5C2211yescharacteristic
11C22×#1204C2211yescharacteristic
12C22×#1203C2211yescharacteristic
13C22×#1202C411yescharacteristic
14C22×#1201C411yescharacteristic
15C2×#6771—21no—
16C2×#6771—21no—
17C2×#6771—22no—
18C2×#6771—21no—
19C2×#6771—21no—
20C2×#6771—22no—
21C2×#6771C414yes—
22C2×#6771C2214yes—
23C2×#6762C2212yes—
24D5⋊#208—22no—
25D5⋊#208C2214yescomplemented
26C2×#6758—21no—
27C2×D5⋊(C3⋊C8)—21no—
28C2×C3×#704C2212yes—
29C3×D5⋊M16—22no—
30C3×D5⋊M16C2214yescomplemented
31C2×C3×#700—21no—
32C2×C3×D5⋊C8—21no—
33#91175C2218yescomplemented
34#91174C2218yescomplemented
35C2×#5132—51nomaximal, Hall
36C22×#709—31no—
37C2×D5⋊M16—31no—
38C2×D5⋊M16D311yescharacteristic, complemented
39C2×#4013—32no—
40#65761—38no—
41C2×#4005—32no—
42C23×D15C2×C411yescharacteristic
43C23×C5×D3C2×C411yescharacteristic
44C23×C3×D5C2×C411yescharacteristic
45C22×C3×C4×C5C2×C411yescharacteristic
46C22×Dic15C2×C411yescharacteristic
47C2×C4×D15—22no—
48C2×C4×D15—21no—
49C2×C4×D15—21no—
50C2×C4×D15C2×C414yes—
51C22×C5×Dic3C2×C411yescharacteristic
52C2×C4×C5×D3—22no—
53C2×C4×C5×D3—21no—
54C2×C4×C5×D3—21no—
55C2×C4×C5×D3C2×C414yes—
56C22×C3×Dic5C2311yescharacteristic
57C2×C3×C4×D5C2×C412yes—
58C2×C3×C4×D5D411yescharacteristic
59C2×C3×C4×D5D411yescharacteristic
60C2×C3×C4×D5D412yes—
61C2×C3×C4×D5D411yescharacteristic
62C2×C3×C4×D5D411yescharacteristic
63C2×C3×C4×D5D412yes—
64C2×C3×C4×D5C2312yes—
65C2×#1204—21no—
66C2×#1204—21no—
67C2×#1204—21no—
68C2×#1204—21no—
69C2×#1204C2×C412yes—
70C2×#1204C2312yes—
71C2×#1203—21no—
72C2×#1203—21no—
73C2×#1203—21no—
74C2×#1203—21no—
75C2×#1203C2×C412yes—
76C2×#1203C2312yes—
77C2×#1202—21no—
78C2×#1202—21no—
79C2×#1202—22no—
80C2×#1202C2×C414yes—
81C2×#1201—21no—
82C2×#1201—21no—
83C2×#1201—22no—
84C2×#1201C2×C414yes—
85#6771—24no—
86#6771—24no—
87#6771—24no—
88#6771—24no—
89#6771—24no—
90#6771—24no—
91#6771—24no—
92#6771—24no—
93#6762—22no—
94#6762C2314yes—
95C2×C3⋊#170—22no—
96#6758—24no—
97D5⋊(C3⋊C8)—24no—
98C3×#704—22no—
99C3×#704C2314yes—
100C2×C3×#170—22no—
101C3×#700—24no—
102C3×D5⋊C8—24no—
103C22×#235—51no—
104C22×C3×M16—51no—
105C22×#208—51no—
106C2×#824—52no—
107#5132—58no—
108C2×#823—52no—
109C23×C4×C5—31no—
110C22×C22⋊D5—31no—
111C22×C22⋊D5—31no—
112C2×#709—34no—
113C2×#709—34no—
114C2×#709—61no—
115C2×#709—61no—
116C2×#709—62no—
117C2×#709—61no—
118C2×#709—61no—
119C2×#709—62no—
120C22×D20—31no—
121C22×C4×D5—31no—
122C22×C4×D5C2×D311yescharacteristic
123C22×Dic10—31no—
124C2×#704—32no—
125C2×#704C2×D312yes—
126D5⋊M16—22no—
127D5⋊M16—34no—
128D5⋊M16—62no—
129D5⋊M16C2×D314yescomplemented
130C2×#700—21no—
131C2×#700—61no—
132C2×D5⋊C8—21no—
133C2×D5⋊C8—61no—
134#4013—38no—
135#4005—38no—
136C2×#413—151noSylow
137C23×C3×C5C22×C411yescharacteristic
138C22×D15—21no—
139C22×D15—21no—
140C22×D15—42no—
141C22×D15C22×C412yes—
142C22×C5×D3—21no—
143C22×C5×D3—21no—
144C22×C5×D3—42no—
145C22×C5×D3C22×C412yes—
146C22×C3×D5—42no—
147C22×C3×D5C22⋊C411yescharacteristic
148C22×C3×D5C22⋊C411yescharacteristic
149C22×C3×D5C22⋊C412yes—
150C22×C3×D5C22×C412yes—
151C2×C3×C4×C5C22⋊C412yes—
152C2×C3×C4×C5C22⋊C411yescharacteristic
153C2×C3×C4×C5C22⋊C411yescharacteristic
154C2×C3×C4×C5C22×C412yes—
155C2×Dic15—21no—
156C2×Dic15—21no—
157C2×Dic15C22×C412yes—
158C4×D15—24no—
159C4×D15—24no—
160C2×C5×Dic3—21no—
161C2×C5×Dic3—21no—
162C2×C5×Dic3C22×C412yes—
163C4×C5×D3—24no—
164C4×C5×D3—24no—
165C2×C3×Dic5C22×C411yescharacteristic
166C2×C3×Dic5C2×D411yescharacteristic
167C2×C3×Dic5C2×D411yescharacteristic
168C2×C3×Dic5C2×D411yescharacteristic
169C2×C3×Dic5C2×D411yescharacteristic
170C2×C3×Dic5C2411yescharacteristic
171C3×C4×D5C22⋊C412yes—
172C3×C4×D5C22⋊C412yes—
173C3×C4×D5C22⋊C412yes—
174C3×C4×D5C22⋊C412yes—
175C3×C4×D5C2×D412yes—
176C3×C4×D5C2×D412yes—
177C3×C4×D5C2×D412yes—
178C3×C4×D5C2×D412yes—
179#1204—22no—
180#1204—22no—
181#1204—22no—
182#1204—22no—
183#1203—22no—
184#1203—22no—
185#1203—22no—
186#1203—22no—
187#1202—24no—
188#1202—24no—
189#1201—24no—
190#1201—24no—
191C3⋊#170—24no—
192C3×#170—24no—
193C23×C3×C4—51no—
194C22×#67—51no—
195C22×#67—51no—
196C2×#235—54no—
197C2×#235—54no—
198C2×#235—101no—
199C2×#235—101no—
200C2×#235—102no—
201C2×#235—101no—
202C2×#235—101no—
203C2×#235—102no—
204C22×D12—51no—
205C22×C4×D3—51no—
206C22×C4×D3AGL(1,𝔽5)11yescharacteristic
207C22×Dic6—51no—
208C2×C3×M16—52no—
209C2×C3×M16—54no—
210C2×C3×M16—101no—
211C2×C3×M16—102no—
212C22×C3×C8—101no—
213C2×#208—52no—
214C2×#208—54no—
215C2×#208—101no—
216C2×#208—102no—
217C22×C3⋊C8—101no—
218#824—58no—
219#823—58no—
220C24×C5—31no—
221C23×D5—31no—
222C23×D5C4×D311yescharacteristic
223C22×C4×C5—31no—
224C22×C4×C5—34no—
225C22×C4×C5—62no—
226C22×C4×C5—61no—
227C22×C4×C5—61no—
228C22×C4×C5C4×D311yescharacteristic
229C2×C22⋊D5—34no—
230C2×C22⋊D5—32no—
231C2×C22⋊D5—32no—
232C2×C22⋊D5—61no—
233C2×C22⋊D5—61no—
234C2×C22⋊D5—62no—
235C2×C22⋊D5—61no—
236C2×C22⋊D5—61no—
237C2×C22⋊D5—61no—
238C2×C22⋊D5—61no—
239C22×Dic5—31no—
240C22×Dic5C22×D311yescharacteristic
241#709—64no—
242#709—64no—
243#709—64no—
244#709—64no—
245#709—64no—
246#709—64no—
247#709—64no—
248#709—64no—
249C2×D20—34no—
250C2×D20—61no—
251C2×D20—61no—
252C2×D20—62no—
253C2×C4×D5—34no—
254C2×C4×D5—62no—
255C2×C4×D5—61no—
256C2×C4×D5—61no—
257C2×C4×D5C4×D312yes—
258C2×C4×D5D1211yescharacteristic
259C2×C4×D5D1211yescharacteristic
260C2×C4×D5D1212yes—
261C2×C4×D5#6711yescharacteristic
262C2×C4×D5#6711yescharacteristic
263C2×C4×D5#6712yes—
264C2×C4×D5C22×D312yes—
265C2×Dic10—32no—
266C2×Dic10—32no—
267C2×Dic10—61no—
268C2×Dic10—61no—
269C2×Dic10—61no—
270C2×Dic10—61no—
271#704—22no—
272#704—34no—
273#704—62no—
274#704C22×D314yes—
275C2×#170—22no—
276C2×#170—62no—
277#700—24no—
278#700—64no—
279D5⋊C8—24no—
280D5⋊C8—64no—
281C22×#41—151no—
282C22×M16—51no—
283C22×M16—151no—
284#413—158no—
285C2×#101—152no—
286C2×#100—152no—
287C22×C3×C5—22no—
288C22×C3×C5C2×C22⋊C411yescharacteristic
289C22×C3×C5C2×C22⋊C411yescharacteristic
290C22×C3×C5C23×C411yescharacteristic
291C2×D15—22no—
292C2×D15—42no—
293C2×D15—42no—
294C2×D15—42no—
295C2×C5×D3—22no—
296C2×C5×D3—42no—
297C2×C5×D3—42no—
298C2×C5×D3—42no—
299C2×C3×D5—22no—
300C2×C3×D5—22no—
301C2×C3×D5—42no—
302C2×C3×D5—42no—
303C2×C3×D5C2×C22⋊C412yes—
304C2×C3×D5C2×C22⋊C412yes—
305C3×C4×C5C2×C22⋊C412yes—
306C3×C4×C5C2×C22⋊C412yes—
307Dic15—22no—
308C3×Dic5C2×C22⋊C411yescharacteristic
309C3×Dic5C2×C22⋊C411yescharacteristic
310C3×Dic5C22×D411yescharacteristic
311C3×Dic5C22×D411yescharacteristic
312C5×Dic3—22no—
313C24×C3—51no—
314C23×D3—51no—
315C23×D3C2×AGL(1,𝔽5)11yescharacteristic
316C22×C3×C4—51no—
317C22×C3×C4—51no—
318C22×C3×C4—51no—
319C22×C3×C4—52no—
320C22×C3×C4—51no—
321C22×C3×C4—51no—
322C22×C3×C4—52no—
323C22×C3×C4—52no—
324C22×C3×C4—52no—
325C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
326C2×#67—54no—
327C2×#67—54no—
328C2×#67—101no—
329C2×#67—101no—
330C2×#67—102no—
331C2×#67—101no—
332C2×#67—101no—
333C2×#67—102no—
334C22×Dic3—51no—
335C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
336#235—104no—
337#235—104no—
338#235—104no—
339#235—104no—
340#235—104no—
341#235—104no—
342#235—104no—
343#235—104no—
344C2×D12—52no—
345C2×D12—52no—
346C2×D12—101no—
347C2×D12—101no—
348C2×D12—101no—
349C2×D12—101no—
350C2×C4×D3—22no—
351C2×C4×D3—21no—
352C2×C4×D3—21no—
353C2×C4×D3—54no—
354C2×C4×D3—102no—
355C2×C4×D3—101no—
356C2×C4×D3—101no—
357C2×C4×D3C2×AGL(1,𝔽5)14yes—
358C2×Dic6—52no—
359C2×Dic6—52no—
360C2×Dic6—101no—
361C2×Dic6—101no—
362C2×Dic6—101no—
363C2×Dic6—101no—
364C3×M16—54no—
365C3×M16—104no—
366C3×M16—102no—
367C2×C3×C8—104no—
368C2×C3×C8—102no—
369#208—54no—
370#208—104no—
371#208—102no—
372C2×C3⋊C8—104no—
373C2×C3⋊C8—102no—
374C23×C5—32no—
375C23×C5—61no—
376C23×C5—61no—
377C23×C5—122no—
378C23×C5C2×C4×D311yescharacteristic
379C22×D5—32no—
380C22×D5—42no—
381C22×D5—61no—
382C22×D5—61no—
383C22×D5—122no—
384C22×D5(C2×D3)⋊C411yescharacteristic
385C22×D5(C2×D3)⋊C411yescharacteristic
386C22×D5(C2×D3)⋊C412yes—
387C22×D5C2×C4×D312yes—
388C2×C4×C5—32no—
389C2×C4×C5—61no—
390C2×C4×C5—61no—
391C2×C4×C5—64no—
392C2×C4×C5—64no—
393C2×C4×C5(C2×D3)⋊C412yes—
394C2×C4×C5(C2×D3)⋊C411yescharacteristic
395C2×C4×C5(C2×D3)⋊C411yescharacteristic
396C2×C4×C5C2×C4×D312yes—
397C22⋊D5—64no—
398C22⋊D5—64no—
399C22⋊D5—62no—
400C22⋊D5—62no—
401C22⋊D5—62no—
402C22⋊D5—62no—
403C2×Dic5—32no—
404C2×Dic5—61no—
405C2×Dic5—61no—
406C2×Dic5C2×C4×D311yescharacteristic
407C2×Dic5C2×D1211yescharacteristic
408C2×Dic5C2×D1211yescharacteristic
409C2×Dic5C2×#6711yescharacteristic
410C2×Dic5C2×#6711yescharacteristic
411C2×Dic5C23×D311yescharacteristic
412D20—64no—
413D20—64no—
414C4×D5—64no—
415C4×D5—64no—
416C4×D5(C2×D3)⋊C412yes—
417C4×D5(C2×D3)⋊C412yes—
418C4×D5(C2×D3)⋊C412yes—
419C4×D5(C2×D3)⋊C412yes—
420C4×D5C2×D1212yes—
421C4×D5C2×D1212yes—
422C4×D5C2×#6712yes—
423C4×D5C2×#6712yes—
424Dic10—62no—
425Dic10—62no—
426Dic10—62no—
427Dic10—62no—
428#170—24no—
429#170—64no—
430C2×#41—154no—
431C2×#41—154no—
432C2×#41—301no—
433C2×#41—302no—
434C2×#41—301no—
435C2×#41—302no—
436C2×#41—301no—
437C2×#41—301no—
438C22×Q8—151no—
439C22×D4—151no—
440C22×D4—151no—
441C22×D4—151no—
442C23×C4—31no—
443C23×C4—51no—
444C23×C4—151no—
445C2×M16—54no—
446C2×M16—52no—
447C2×M16—101no—
448C2×M16—102no—
449C2×M16—154no—
450C2×M16—152no—
451C2×M16—301no—
452C2×M16—302no—
453C22×C8—101no—
454C22×C8—301no—
455#101—158no—
456#100—158no—
457C2×C3×C5—21no—
458C2×C3×C5—21no—
459C2×C3×C5#41312yescomplemented
460C2×C3×C5C22×C22⋊C411yescharacteristic
461D15—42no—
462C3×D5—22no—
463C3×D5—22no—
464C5×D3—42no—
465C23×C3—51no—
466C23×C3—51no—
467C23×C3—52no—
468C23×C3—52no—
469C23×C3—202no—
470C23×C3C22×AGL(1,𝔽5)11yescharacteristic
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—42no—
474C22×D3—52no—
475C22×D3—101no—
476C22×D3—101no—
477C22×D3—202no—
478C22×D3C22×AGL(1,𝔽5)12yes—
479C2×C3×C4—51no—
480C2×C3×C4—51no—
481C2×C3×C4—51no—
482C2×C3×C4—51no—
483C2×C3×C4—51no—
484C2×C3×C4—51no—
485C2×C3×C4—52no—
486C2×C3×C4—52no—
487C2×C3×C4—52no—
488C2×C3×C4—52no—
489C2×C3×C4—52no—
490C2×C3×C4—52no—
491C2×C3×C4—52no—
492C2×C3×C4—52no—
493C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
494C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
495C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
496C2×C3×C4C22×AGL(1,𝔽5)12yes—
497#67—104no—
498#67—104no—
499#67—104no—
500#67—104no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—52no—
504C2×Dic3—101no—
505C2×Dic3—101no—
506C2×Dic3C22×AGL(1,𝔽5)12yes—
507D12—102no—
508D12—102no—
509D12—102no—
510D12—102no—
511C4×D3—24no—
512C4×D3—24no—
513C4×D3—104no—
514C4×D3—104no—
515Dic6—102no—
516Dic6—102no—
517Dic6—102no—
518Dic6—102no—
519C3×C8—104no—
520C3⋊C8—104no—
521C22×C5—22no—
522C22×C5—62no—
523C22×C5—122no—
524C22×C5—122no—
525C22×C5—122no—
526C22×C5C2×(C2×D3)⋊C411yescharacteristic
527C22×C5C2×(C2×D3)⋊C411yescharacteristic
528C22×C5C22×C4×D311yescharacteristic
529C2×D5—22no—
530C2×D5—22no—
531C2×D5—42no—
532C2×D5—42no—
533C2×D5—62no—
534C2×D5—122no—
535C2×D5—122no—
536C2×D5—122no—
537C2×D5C2×(C2×D3)⋊C412yes—
538C2×D5C2×(C2×D3)⋊C412yes—
539C4×C5—62no—
540C4×C5C2×(C2×D3)⋊C412yes—
541C4×C5C2×(C2×D3)⋊C412yes—
542Dic5—62no—
543Dic5C2×(C2×D3)⋊C411yescharacteristic
544Dic5C2×(C2×D3)⋊C411yescharacteristic
545Dic5C22×D1211yescharacteristic
546Dic5C22×#6711yescharacteristic
547C24—31no—
548C24—51no—
549C24—151no—
550#41—304no—
551#41—304no—
552#41—304no—
553#41—304no—
554#41—304no—
555#41—304no—
556#41—304no—
557#41—304no—
558C2×Q8—152no—
559C2×Q8—152no—
560C2×Q8—301no—
561C2×Q8—301no—
562C2×Q8—301no—
563C2×Q8—301no—
564C2×D4—154no—
565C2×D4—152no—
566C2×D4—152no—
567C2×D4—154no—
568C2×D4—301no—
569C2×D4—301no—
570C2×D4—301no—
571C2×D4—301no—
572C2×D4—301no—
573C2×D4—301no—
574C2×D4—302no—
575C2×D4—301no—
576C2×D4—301no—
577C2×D4—302no—
578C22×C4—31no—
579C22×C4—34no—
580C22×C4—51no—
581C22×C4—51no—
582C22×C4—52no—
583C22×C4—51no—
584C22×C4—52no—
585C22×C4—51no—
586C22×C4—51no—
587C22×C4—52no—
588C22×C4—52no—
589C22×C4—62no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—151no—
593C22×C4—154no—
594C22×C4—302no—
595C22×C4—301no—
596C22×C4—301no—
597C22×C4D3×AGL(1,𝔽5)11yescharacteristic
598M16—54no—
599M16—104no—
600M16—102no—
601M16—154no—
602M16—304no—
603M16—302no—
604C2×C8—104no—
605C2×C8—102no—
606C2×C8—304no—
607C2×C8—302no—
608C3×C5C2×#41311yescharacteristic, complemented, Hall
609C22×C3—22no—
610C22×C3—52no—
611C22×C3—52no—
612C22×C3—102no—
613C22×C3—102no—
614C22×C3—202no—
615C22×C3—202no—
616C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
617C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
618C22×C3C23×AGL(1,𝔽5)11yescharacteristic
619C2×D3—22no—
620C2×D3—42no—
621C2×D3—42no—
622C2×D3—42no—
623C2×D3—102no—
624C2×D3—202no—
625C2×D3—202no—
626C2×D3—202no—
627C3×C4—51no—
628C3×C4—51no—
629C3×C4—51no—
630C3×C4—51no—
631C3×C4C2×C22⋊AGL(1,𝔽5)12yes—
632C3×C4C2×C22⋊AGL(1,𝔽5)12yes—
633Dic3—22no—
634Dic3—102no—
635C2×C5—21no—
636C2×C5—21no—
637C2×C5—122no—
638C2×C5#513212yescomplemented
639C2×C5C22×(C2×D3)⋊C411yescharacteristic
640D5—22no—
641D5—22no—
642D5—122no—
643C23—32no—
644C23—51no—
645C23—51no—
646C23—52no—
647C23—52no—
648C23—61no—
649C23—61no—
650C23—122no—
651C23—152no—
652C23—202no—
653C23—301no—
654C23—301no—
655C23—602no—
656C23C2×D3×AGL(1,𝔽5)11yescharacteristic
657Q8—302no—
658Q8—302no—
659Q8—302no—
660Q8—302no—
661D4—302no—
662D4—302no—
663D4—302no—
664D4—302no—
665D4—304no—
666D4—304no—
667D4—304no—
668D4—304no—
669C2×C4—32no—
670C2×C4—51no—
671C2×C4—51no—
672C2×C4—51no—
673C2×C4—51no—
674C2×C4—51no—
675C2×C4—51no—
676C2×C4—52no—
677C2×C4—52no—
678C2×C4—52no—
679C2×C4—52no—
680C2×C4—52no—
681C2×C4—52no—
682C2×C4—52no—
683C2×C4—52no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—64no—
687C2×C4—64no—
688C2×C4—152no—
689C2×C4—301no—
690C2×C4—301no—
691C2×C4—304no—
692C2×C4—304no—
693C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
694C2×C4(C2×D3)⋊AGL(1,𝔽5)12yes—
695C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
696C2×C4C2×D3×AGL(1,𝔽5)12yes—
697C8—104no—
698C8—304no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—102no—
702C2×C3—102no—
703C2×C3#6576112yescomplemented
704C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
705D3—42no—
706D3—202no—
707C5C2×#513211yescharacteristic, complemented, Sylow
708C22—22no—
709C22—52no—
710C22—52no—
711C22—62no—
712C22—102no—
713C22—102no—
714C22—122no—
715C22—122no—
716C22—122no—
717C22—202no—
718C22—202no—
719C22—302no—
720C22—602no—
721C22—602no—
722C22—602no—
723C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
724C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
725C22C22×D3×AGL(1,𝔽5)11yescharacteristic
726C4—51no—
727C4—51no—
728C4—51no—
729C4—51no—
730C4—62no—
731C4—302no—
732C4C2×(C2×D3)⋊AGL(1,𝔽5)12yes—
733C4C2×(C2×D3)⋊AGL(1,𝔽5)12yes—
734C3C2×#6576111yescharacteristic, complemented, Sylow
735C2—21no—
736C2—21no—
737C2—102no—
738C2—102no—
739C2—122no—
740C2—602no—
741C2#1175181812yesdirect product factor
742C2C22×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2×C4(C2×D3)⋊AGL(1,𝔽5)
commutatorC22×C3×C5C23×C4
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#6771C2
cosocleC2×C3×Dic5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#413
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×D5⋊#208C2semidirect
3. C2×C3×D5⋊M16C2semidirect
4. C2×#91175C2semidirect
5. C2×#91174C2semidirect
6. #11751818C2direct (N × H)
25. D5⋊#208C22semidirect
30. C3×D5⋊M16C22semidirect
33. #91175C22semidirect
34. #91174C22semidirect
38. C2×D5⋊M16D3semidirect
129. D5⋊M16C2×D3semidirect
459. C2×C3×C5#413semidirect
608. C3×C5C2×#413semidirect
638. C2×C5#5132semidirect
703. C2×C3#65761semidirect
707. C5C2×#5132semidirect
734. C3C2×#65761semidirect
741. C2#11751818direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67712
C2×D5⋊#2082
C2×C3×D5⋊M162
C2×#911752
C2×#911742
#117518182
C2×#657613
C2×#51325