Finite Group Databasebeta

← C2×#11756455 #14481198

Subgroups — C2×#11756455 #14481198

Order 1920.

2008 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#125C211yesmaximal, characteristic, complemented
2#11756455C2116yesmaximal, direct product factor
3C2×#91787C211yesmaximal, characteristic
4C2×#91787C211yesmaximal, characteristic
5C2×#91787C211yesmaximal, characteristic
6C2×#91785C211yesmaximal, characteristic
7C2×#91785C211yesmaximal, characteristic
8C2×#91781C211yesmaximal, characteristic
9C2×#91779C211yesmaximal, characteristic, complemented
10C2×#91778C211yesmaximal, characteristic, complemented
11C2×#91778C211yesmaximal, characteristic, complemented
12C2×#91778C211yesmaximal, characteristic, complemented
13C2×#91777C211yesmaximal, characteristic, complemented
14C2×#91776C211yesmaximal, characteristic, complemented
15C2×#91765C211yesmaximal, characteristic
16C2×C4×Dic30C211yesmaximal, characteristic, complemented
17C2×#66030—31nomaximal, Hall
18C22×C4×D15C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C22×Dic30C2211yescharacteristic
21C3×C5×#125C2218yescomplemented
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C4⋊C4C2211yescharacteristic
27C2×C3×C5×C4⋊C4C2211yescharacteristic
28C2×C3×C42×C5C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×C4⋊Dic15C2211yescharacteristic
36C2×C4⋊Dic15C2211yescharacteristic
37C2×C4⋊Dic15C2211yescharacteristic
38C2×C4⋊Dic15C2211yescharacteristic
39C2×#6712C2211yescharacteristic
40C2×#6712C2211yescharacteristic
41C2×#6712C2211yescharacteristic
42C2×#6712C2211yescharacteristic
43C2×#6712C2211yescharacteristic
44C2×#6712C2211yescharacteristic
45C2×#6712C2211yescharacteristic
46C2×#6712C2211yescharacteristic
47C2×#6712C2211yescharacteristic
48C2×#6712C2211yescharacteristic
49C2×C4×Dic15C2211yescharacteristic
50C2×C4×Dic15C2211yescharacteristic
51C2×C4×Dic15C2211yescharacteristic
52C2×C4×Dic15C2211yescharacteristic
53C2×C4×Dic15C2211yescharacteristic
54#91787C2218yes—
55#91787C2218yes—
56#91787C2218yes—
57#91785C2218yes—
58#91785C2218yes—
59#91781C2218yes—
60#91779C2218yescomplemented
61#91778C2218yescomplemented
62#91778C2218yescomplemented
63#91778C2218yescomplemented
64#91777C2218yescomplemented
65#91776C2218yescomplemented
66#91765C2218yes—
67C4×Dic30C2218yescomplemented
68C2×#5696—51nomaximal, Hall
69C2×C5×#125D311yescharacteristic, complemented
70#66030—316no—
71C2×#4044—31no—
72C2×#4044—31no—
73C2×#4044—31no—
74C2×#4042—31no—
75C2×#4042—31no—
76C2×#4038—31no—
77C2×#4036—31no—
78C2×#4035—31no—
79C2×#4035—31no—
80C2×#4035—31no—
81C2×#4034—31no—
82C2×#4033—31no—
83C2×#4022—31no—
84C2×C4×Dic10—31no—
85C23×D15C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C2×C4×D15—24no—
101C2×C4×D15C2314yes—
102C2×Dic30—24no—
103C2×Dic30—24no—
104C2×Dic30C2314yes—
105C2×Dic30C2314yes—
106C3×C5×C4⋊C4C2314yes—
107C3×C5×C4⋊C4C2314yes—
108C3×C5×C4⋊C4C2314yes—
109C3×C5×C4⋊C4C2314yes—
110C3×C5×C4⋊C4C2314yes—
111C3×C5×C4⋊C4C2314yes—
112C3×C42×C5C2314yes—
113#6714C2314yes—
114#6714C2314yes—
115#6714C2314yes—
116#6714C2314yes—
117#6714C2314yes—
118#6714C2314yes—
119C4⋊Dic15C2314yes—
120C4⋊Dic15C2314yes—
121C4⋊Dic15C2314yes—
122C4⋊Dic15C2314yes—
123#6712C2314yes—
124#6712C2314yes—
125#6712C2314yes—
126#6712C2314yes—
127#6712C2314yes—
128#6712C2314yes—
129#6712C2314yes—
130#6712C2314yes—
131#6712C2314yes—
132#6712C2314yes—
133C4×Dic15C2314yes—
134C4×Dic15C2314yes—
135C4×Dic15C2314yes—
136C4×Dic15C2314yes—
137C4×Dic15C2314yes—
138C2×C3×#125D511yescharacteristic, complemented
139#5696—516no—
140C2×#898—51no—
141C2×#898—51no—
142C2×#898—51no—
143C2×#896—51no—
144C2×#896—51no—
145C2×#892—51no—
146C2×#890—51no—
147C2×#889—51no—
148C2×#889—51no—
149C2×#889—51no—
150C2×#888—51no—
151C2×#887—51no—
152C2×#876—51no—
153C2×C4×Dic6—51no—
154C22×C4×D5—31no—
155C22×Dic10—31no—
156C22×Dic10—31no—
157C5×#125C2×D318yescomplemented
158C2×C5×C4⋊C4C2×D311yescharacteristic
159C2×C5×C4⋊C4C2×D311yescharacteristic
160C2×C5×C4⋊C4C2×D311yescharacteristic
161C2×C5×C4⋊C4C2×D311yescharacteristic
162C2×C5×C4⋊C4C2×D311yescharacteristic
163C2×C5×C4⋊C4C2×D311yescharacteristic
164C2×C42×C5C2×D311yescharacteristic
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685—31no—
171C2×C4⋊Dic5—31no—
172C2×C4⋊Dic5—31no—
173C2×C4⋊Dic5—31no—
174C2×C4⋊Dic5—31no—
175C2×#683—31no—
176C2×#683—31no—
177C2×#683—31no—
178C2×#683—31no—
179C2×#683—31no—
180C2×#683—31no—
181C2×#683—31no—
182C2×#683—31no—
183C2×#683—31no—
184C2×#683—31no—
185C2×C4×Dic5—31no—
186C2×C4×Dic5—31no—
187C2×C4×Dic5—31no—
188C2×C4×Dic5—31no—
189C2×C4×Dic5—31no—
190#4044—38no—
191#4044—38no—
192#4044—38no—
193#4042—38no—
194#4042—38no—
195#4038—38no—
196#4036—38no—
197#4035—38no—
198#4035—38no—
199#4035—38no—
200#4034—38no—
201#4033—38no—
202#4022—38no—
203C4×Dic10—38no—
204C2×#541—151noSylow
205C23×C3×C5C2411yescharacteristic
206C22×D15—22no—
207C22×D15—22no—
208C22×D15—22no—
209C22×D15C2412yes—
210C2×C3×C4×C5—22no—
211C2×C3×C4×C5—22no—
212C2×C3×C4×C5—22no—
213C2×C3×C4×C5—22no—
214C2×C3×C4×C5—22no—
215C2×C3×C4×C5—22no—
216C2×C3×C4×C5—22no—
217C2×C3×C4×C5C2412yes—
218C2×C3×C4×C5C2412yes—
219C2×C3×C4×C5C2412yes—
220C2×C3×C4×C5C2412yes—
221C2×C3×C4×C5C2412yes—
222C2×C3×C4×C5C2412yes—
223C2×C3×C4×C5C2412yes—
224C2×Dic15—22no—
225C2×Dic15—22no—
226C2×Dic15—22no—
227C2×Dic15—22no—
228C2×Dic15—22no—
229C2×Dic15—22no—
230C2×Dic15#4114yes—
231C2×Dic15C2412yes—
232C2×Dic15C2412yes—
233C2×Dic15C2412yes—
234C2×Dic15C2412yes—
235C2×Dic15C2412yes—
236C2×Dic15C2412yes—
237C2×Dic15C2412yes—
238C4×D15—28no—
239Dic30—28no—
240Dic30—28no—
241C22×C4×D3—51no—
242C22×Dic6—51no—
243C22×Dic6—51no—
244C3×#125C2×D518yescomplemented
245C2×C3×C4⋊C4C2×D511yescharacteristic
246C2×C3×C4⋊C4C2×D511yescharacteristic
247C2×C3×C4⋊C4C2×D511yescharacteristic
248C2×C3×C4⋊C4C2×D511yescharacteristic
249C2×C3×C4⋊C4C2×D511yescharacteristic
250C2×C3×C4⋊C4C2×D511yescharacteristic
251C2×C3×C42C2×D511yescharacteristic
252C2×(C2×D3)⋊C4—51no—
253C2×(C2×D3)⋊C4—51no—
254C2×(C2×D3)⋊C4—51no—
255C2×(C2×D3)⋊C4—51no—
256C2×(C2×D3)⋊C4—51no—
257C2×(C2×D3)⋊C4—51no—
258C2×C4⋊Dic3—51no—
259C2×C4⋊Dic3—51no—
260C2×C4⋊Dic3—51no—
261C2×C4⋊Dic3—51no—
262C2×Dic3⋊C4—51no—
263C2×Dic3⋊C4—51no—
264C2×Dic3⋊C4—51no—
265C2×Dic3⋊C4—51no—
266C2×Dic3⋊C4—51no—
267C2×Dic3⋊C4—51no—
268C2×Dic3⋊C4—51no—
269C2×Dic3⋊C4—51no—
270C2×Dic3⋊C4—51no—
271C2×Dic3⋊C4—51no—
272C2×C4×Dic3—51no—
273C2×C4×Dic3—51no—
274C2×C4×Dic3—51no—
275C2×C4×Dic3—51no—
276C2×C4×Dic3—51no—
277#898—58no—
278#898—58no—
279#898—58no—
280#896—58no—
281#896—58no—
282#892—58no—
283#890—58no—
284#889—58no—
285#889—58no—
286#889—58no—
287#888—58no—
288#887—58no—
289#876—58no—
290C4×Dic6—58no—
291C23×D5—31no—
292C22×C4×C5C22×D311yescharacteristic
293C22×C4×C5C22×D311yescharacteristic
294C22×C4×C5C22×D311yescharacteristic
295C22×C4×C5C22×D311yescharacteristic
296C22×C4×C5C22×D311yescharacteristic
297C22×C4×C5C22×D311yescharacteristic
298C22×C4×C5C22×D311yescharacteristic
299C22×Dic5—31no—
300C22×Dic5—31no—
301C22×Dic5—31no—
302C22×Dic5—31no—
303C22×Dic5—31no—
304C22×Dic5—31no—
305C22×Dic5—31no—
306C2×C4×D5—34no—
307C2×C4×D5—64no—
308C2×Dic10—34no—
309C2×Dic10—34no—
310C2×Dic10—64no—
311C2×Dic10—64no—
312C5×C4⋊C4C22×D314yes—
313C5×C4⋊C4C22×D314yes—
314C5×C4⋊C4C22×D314yes—
315C5×C4⋊C4C22×D314yes—
316C5×C4⋊C4C22×D314yes—
317C5×C4⋊C4C22×D314yes—
318C42×C5C22×D314yes—
319#685—34no—
320#685—34no—
321#685—34no—
322#685—34no—
323#685—34no—
324#685—34no—
325C4⋊Dic5—34no—
326C4⋊Dic5—34no—
327C4⋊Dic5—34no—
328C4⋊Dic5—34no—
329#683—34no—
330#683—34no—
331#683—34no—
332#683—34no—
333#683—34no—
334#683—34no—
335#683—34no—
336#683—34no—
337#683—34no—
338#683—34no—
339C4×Dic5—34no—
340C4×Dic5—34no—
341C4×Dic5—34no—
342C4×Dic5—34no—
343C4×Dic5—34no—
344#541—1516no—
345C2×C4⋊Q8—151no—
346C2×#126—151no—
347C2×#126—151no—
348C2×#126—151no—
349C2×#126—151no—
350C2×#125—151no—
351C2×#125—151no—
352C2×#125—151no—
353C2×#125—151no—
354C2×#125D1511yescharacteristic, complemented
355C2×C22⋊Q8—151no—
356C2×C22⋊Q8—151no—
357C2×C4×Q8—151no—
358C2×C4×Q8—151no—
359C2×#117—151no—
360C22×C3×C5C2×#4112yes—
361C22×C3×C52−1+412yes—
362C22×C3×C52−1+412yes—
363C22×C3×C5C2511yescharacteristic
364C2×D15—22no—
365C2×D15—22no—
366C2×D15—22no—
367C2×D15—44no—
368C3×C4×C5—22no—
369C3×C4×C5—22no—
370C3×C4×C5—22no—
371C3×C4×C5—22no—
372C3×C4×C5—22no—
373C3×C4×C5—22no—
374C3×C4×C5—22no—
375Dic15—22no—
376Dic15—22no—
377Dic15—22no—
378Dic15—22no—
379Dic15—22no—
380Dic15—22no—
381Dic15C2×#4114yes—
382C23×D3—51no—
383C22×C3×C4C22×D511yescharacteristic
384C22×C3×C4C22×D511yescharacteristic
385C22×C3×C4C22×D511yescharacteristic
386C22×C3×C4C22×D511yescharacteristic
387C22×C3×C4C22×D511yescharacteristic
388C22×C3×C4C22×D511yescharacteristic
389C22×C3×C4C22×D511yescharacteristic
390C22×Dic3—51no—
391C22×Dic3—51no—
392C22×Dic3—51no—
393C22×Dic3—51no—
394C22×Dic3—51no—
395C22×Dic3—51no—
396C22×Dic3—51no—
397C2×C4×D3—54no—
398C2×C4×D3—104no—
399C2×Dic6—54no—
400C2×Dic6—54no—
401C2×Dic6—104no—
402C2×Dic6—104no—
403C3×C4⋊C4C22×D514yes—
404C3×C4⋊C4C22×D514yes—
405C3×C4⋊C4C22×D514yes—
406C3×C4⋊C4C22×D514yes—
407C3×C4⋊C4C22×D514yes—
408C3×C4⋊C4C22×D514yes—
409C3×C42C22×D514yes—
410(C2×D3)⋊C4—54no—
411(C2×D3)⋊C4—54no—
412(C2×D3)⋊C4—54no—
413(C2×D3)⋊C4—54no—
414(C2×D3)⋊C4—54no—
415(C2×D3)⋊C4—54no—
416C4⋊Dic3—54no—
417C4⋊Dic3—54no—
418C4⋊Dic3—54no—
419C4⋊Dic3—54no—
420Dic3⋊C4—54no—
421Dic3⋊C4—54no—
422Dic3⋊C4—54no—
423Dic3⋊C4—54no—
424Dic3⋊C4—54no—
425Dic3⋊C4—54no—
426Dic3⋊C4—54no—
427Dic3⋊C4—54no—
428Dic3⋊C4—54no—
429Dic3⋊C4—54no—
430C4×Dic3—54no—
431C4×Dic3—54no—
432C4×Dic3—54no—
433C4×Dic3—54no—
434C4×Dic3—54no—
435C23×C5C23×D311yescharacteristic
436C22×D5—32no—
437C22×D5—62no—
438C22×D5—62no—
439C22×D5—62no—
440C2×C4×C5—22no—
441C2×C4×C5—22no—
442C2×C4×C5—22no—
443C2×C4×C5—22no—
444C2×C4×C5—22no—
445C2×C4×C5—22no—
446C2×C4×C5—22no—
447C2×C4×C5C23×D312yes—
448C2×C4×C5C23×D312yes—
449C2×C4×C5C23×D312yes—
450C2×C4×C5C23×D312yes—
451C2×C4×C5C23×D312yes—
452C2×C4×C5C23×D312yes—
453C2×C4×C5C23×D312yes—
454C2×Dic5—34no—
455C2×Dic5—32no—
456C2×Dic5—32no—
457C2×Dic5—32no—
458C2×Dic5—32no—
459C2×Dic5—32no—
460C2×Dic5—32no—
461C2×Dic5—32no—
462C2×Dic5—62no—
463C2×Dic5—62no—
464C2×Dic5—62no—
465C2×Dic5—62no—
466C2×Dic5—62no—
467C2×Dic5—62no—
468C4×D5—68no—
469Dic10—68no—
470Dic10—68no—
471C22×Q8—151no—
472C22×Q8—151no—
473C23×C4—151no—
474C4⋊Q8—158no—
475#126—158no—
476#126—158no—
477#126—158no—
478#126—158no—
479#125—158no—
480#125—158no—
481#125—158no—
482#125—158no—
483#125C2×D1518yescomplemented
484C22⋊Q8—158no—
485C22⋊Q8—158no—
486C4×Q8—158no—
487C4×Q8—158no—
488#117—158no—
489C2×C4⋊C4—151no—
490C2×C4⋊C4—151no—
491C2×C4⋊C4—151no—
492C2×C4⋊C4—151no—
493C2×C4⋊C4—151no—
494C2×C4⋊C4—151no—
495C2×C4⋊C4—151no—
496C2×C4⋊C4—151no—
497C2×C4⋊C4—151no—
498C2×C4⋊C4—151no—
499C2×C4⋊C4—151no—
500C2×C4⋊C4—151no—
501C2×C4⋊C4—151no—
502C2×C4⋊C4—151no—
503C2×C4⋊C4C2×D1511yescharacteristic
504C2×C4⋊C4C2×D1511yescharacteristic
505C2×C4⋊C4C2×D1511yescharacteristic
506C2×C4⋊C4C2×D1511yescharacteristic
507C2×C4⋊C4C2×D1511yescharacteristic
508C2×C4⋊C4C2×D1511yescharacteristic
509C2×C22⋊C4—151no—
510C2×C22⋊C4—151no—
511C2×C22⋊C4—151no—
512C2×C22⋊C4—151no—
513C2×C22⋊C4—151no—
514C2×C22⋊C4—151no—
515C2×C42—151no—
516C2×C42—151no—
517C2×C42—151no—
518C2×C42—151no—
519C2×C42—151no—
520C2×C42C2×D1511yescharacteristic
521C2×C3×C5#54114yescomplemented
522C2×C3×C5C22×#4111yescharacteristic
523C2×C3×C5C2×2−1+411yescharacteristic
524C2×C3×C5C2×2−1+411yescharacteristic
525D15—42no—
526C23×C3C23×D511yescharacteristic
527C22×D3—52no—
528C22×D3—102no—
529C22×D3—102no—
530C22×D3—102no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4C23×D512yes—
539C2×C3×C4C23×D512yes—
540C2×C3×C4C23×D512yes—
541C2×C3×C4C23×D512yes—
542C2×C3×C4C23×D512yes—
543C2×C3×C4C23×D512yes—
544C2×C3×C4C23×D512yes—
545C2×Dic3—54no—
546C2×Dic3—52no—
547C2×Dic3—52no—
548C2×Dic3—52no—
549C2×Dic3—52no—
550C2×Dic3—52no—
551C2×Dic3—52no—
552C2×Dic3—52no—
553C2×Dic3—102no—
554C2×Dic3—102no—
555C2×Dic3—102no—
556C2×Dic3—102no—
557C2×Dic3—102no—
558C2×Dic3—102no—
559C4×D3—108no—
560Dic6—108no—
561Dic6—108no—
562C22×C5#100712yes—
563C22×C5D3×#4112yes—
564C22×C5#101012yes—
565C22×C5C24×D311yescharacteristic
566C2×D5—62no—
567C2×D5—62no—
568C2×D5—62no—
569C2×D5—124no—
570C4×C5—22no—
571C4×C5—22no—
572C4×C5—22no—
573C4×C5—22no—
574C4×C5—22no—
575C4×C5—22no—
576C4×C5—22no—
577Dic5—34no—
578Dic5—62no—
579Dic5—62no—
580Dic5—62no—
581Dic5—62no—
582Dic5—62no—
583Dic5—62no—
584C24—151no—
585C2×Q8—154no—
586C2×Q8—154no—
587C2×Q8—304no—
588C2×Q8—304no—
589C22×C4—151no—
590C22×C4—151no—
591C22×C4—151no—
592C22×C4—151no—
593C22×C4—151no—
594C22×C4—151no—
595C22×C4—151no—
596C22×C4—154no—
597C22×C4—304no—
598C22×C4C22×D1511yescharacteristic
599C22×C4C22×D1511yescharacteristic
600C22×C4C22×D1511yescharacteristic
601C22×C4C22×D1511yescharacteristic
602C22×C4C22×D1511yescharacteristic
603C22×C4C22×D1511yescharacteristic
604C22×C4C22×D1511yescharacteristic
605C4⋊C4—154no—
606C4⋊C4—154no—
607C4⋊C4—154no—
608C4⋊C4—154no—
609C4⋊C4—154no—
610C4⋊C4—154no—
611C4⋊C4—154no—
612C4⋊C4—154no—
613C4⋊C4—154no—
614C4⋊C4—154no—
615C4⋊C4—154no—
616C4⋊C4—154no—
617C4⋊C4—154no—
618C4⋊C4—154no—
619C4⋊C4C22×D1514yes—
620C4⋊C4C22×D1514yes—
621C4⋊C4C22×D1514yes—
622C4⋊C4C22×D1514yes—
623C4⋊C4C22×D1514yes—
624C4⋊C4C22×D1514yes—
625C22⋊C4—154no—
626C22⋊C4—154no—
627C22⋊C4—154no—
628C22⋊C4—154no—
629C22⋊C4—154no—
630C22⋊C4—154no—
631C42—154no—
632C42—154no—
633C42—154no—
634C42—154no—
635C42—154no—
636C42C22×D1514yes—
637C3×C5C2×#54111yescharacteristic, complemented, Hall
638C22×C3#414712yes—
639C22×C3D5×#4112yes—
640C22×C3#415012yes—
641C22×C3C24×D511yescharacteristic
642C2×D3—102no—
643C2×D3—102no—
644C2×D3—102no—
645C2×D3—204no—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—22no—
651C3×C4—22no—
652C3×C4—22no—
653Dic3—54no—
654Dic3—102no—
655Dic3—102no—
656Dic3—102no—
657Dic3—102no—
658Dic3—102no—
659Dic3—102no—
660C2×C5#569614yescomplemented
661C2×C5C2×#100711yescharacteristic
662C2×C5C2×D3×#4111yescharacteristic
663C2×C5C2×#101011yescharacteristic
664D5—122no—
665C23—152no—
666C23—302no—
667C23—302no—
668C23—302no—
669C23C23×D1511yescharacteristic
670Q8—308no—
671Q8—308no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—154no—
680C2×C4—152no—
681C2×C4—152no—
682C2×C4—152no—
683C2×C4—152no—
684C2×C4—152no—
685C2×C4—152no—
686C2×C4—152no—
687C2×C4—308no—
688C2×C4—302no—
689C2×C4—302no—
690C2×C4—302no—
691C2×C4—302no—
692C2×C4—302no—
693C2×C4—302no—
694C2×C4C23×D1512yes—
695C2×C4C23×D1512yes—
696C2×C4C23×D1512yes—
697C2×C4C23×D1512yes—
698C2×C4C23×D1512yes—
699C2×C4C23×D1512yes—
700C2×C4C23×D1512yes—
701C2×C3#6603014yescomplemented
702C2×C3C2×#414711yescharacteristic
703C2×C3C2×D5×#4111yescharacteristic
704C2×C3C2×#415011yescharacteristic
705D3—202no—
706C5C2×#569611yescharacteristic, complemented, Sylow
707C22—302no—
708C22—302no—
709C22—302no—
710C22—604no—
711C22#9209812yes—
712C22#41×D1512yes—
713C22#9210112yes—
714C22C24×D1511yescharacteristic
715C4—22no—
716C4—22no—
717C4—22no—
718C4—22no—
719C4—22no—
720C4—22no—
721C4—22no—
722C4—154no—
723C4—302no—
724C4—302no—
725C4—302no—
726C4—302no—
727C4—302no—
728C4—302no—
729C3C2×#6603011yescharacteristic, complemented, Sylow
730C2—602no—
731C2#1175645514yesdirect product factor
732C2C2×#9209811yescharacteristic
733C2C2×#41×D1511yescharacteristic
734C2C2×#9210111yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#125C2
socleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC2×#125D15
hypocenterC3×C5C2×#541
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#125C2semidirect
2. #11756455C2direct (N × H)
9. C2×#91779C2semidirect
10. C2×#91778C2semidirect
11. C2×#91778C2semidirect
12. C2×#91778C2semidirect
13. C2×#91777C2semidirect
14. C2×#91776C2semidirect
16. C2×C4×Dic30C2semidirect
21. C3×C5×#125C22semidirect
60. #91779C22semidirect
61. #91778C22semidirect
62. #91778C22semidirect
63. #91778C22semidirect
64. #91777C22semidirect
65. #91776C22semidirect
67. C4×Dic30C22semidirect
69. C2×C5×#125D3semidirect
138. C2×C3×#125D5semidirect
157. C5×#125C2×D3semidirect
244. C3×#125C2×D5semidirect
354. C2×#125D15semidirect
483. #125C2×D15semidirect
521. C2×C3×C5#541semidirect
637. C3×C5C2×#541semidirect
660. C2×C5#5696semidirect
701. C2×C3#66030semidirect
706. C5C2×#5696semidirect
729. C3C2×#66030semidirect
731. C2#11756455direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1252
#117564552
C2×#917872
C2×#917852
C2×#917812
C2×#917792
C2×#917782
C2×#917772
C2×#917762
C2×#917652
C2×C4×Dic302
C2×#660303
C2×#56965