Finite Group Databasebeta

← #14415332

Subgroups — #14415332

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91796C211yesmaximal, characteristic, complemented
2C2×#91790C211yesmaximal, characteristic, complemented
3#11756307C211yesmaximal, characteristic
4C3×C5×#435C211yesmaximal, characteristic, complemented
5#11751228C211yesmaximal, characteristic, complemented
6#11751212C211yesmaximal, characteristic, complemented
7#11751112C211yesmaximal, characteristic, complemented
8#11750938C211yesmaximal, characteristic, complemented
9#11750937C211yesmaximal, characteristic, complemented
10#11750831C211yesmaximal, characteristic, complemented
11#11750829C211yesmaximal, characteristic, complemented
12#11750828C211yesmaximal, characteristic, complemented
13#11750828C211yesmaximal, characteristic, complemented
14#11750807C211yesmaximal, characteristic, complemented
15D15×#97C211yesmaximal, characteristic, complemented
16#10611211—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C2×#6817C2211yescharacteristic
19C2×C3×C5×M16C2211yescharacteristic
20C22×C3×C5×C8C2211yescharacteristic
21C3×C4×C5×D4C2211yescharacteristic
22#91829C411yescharacteristic
23#91827C411yescharacteristic
24C4×#1220C2211yescharacteristic
25C4×#1220C2211yescharacteristic
26C2×#6710C2211yescharacteristic
27C22×C3⋊#168C2211yescharacteristic
28#91796—24no—
29#91790—24no—
30C2×#6705C2211yescharacteristic
31C2×#6705C2211yescharacteristic
32C2×#6705C2211yescharacteristic
33C2×#6705C2211yescharacteristic
34C2×C8×D15C2211yescharacteristic
35C2×C8×D15C2211yescharacteristic
36C2×C8×D15C2211yescharacteristic
37C2×C8×D15C2211yescharacteristic
38#91784C411yescharacteristic
39#91777C411yescharacteristic
40#91774C411yescharacteristic
41#91774C411yescharacteristic
42#91773C411yescharacteristic
43#91773C411yescharacteristic
44C4×D60C2211yescharacteristic
45C42×D15C2211yescharacteristic
46C3×C5×C4⋊C8C2211yescharacteristic
47C3×C5×C22⋊C8C2211yescharacteristic
48C3×C5×C22⋊C8C2211yescharacteristic
49C3×C5×#97C2211yescharacteristic
50#91114C2211yescharacteristic
51#91114C2211yescharacteristic
52#91104C2211yescharacteristic
53#91104C2211yescharacteristic
54#91104C2211yescharacteristic
55#91104C2211yescharacteristic
56#91099C2211yescharacteristic
57#91099C2211yescharacteristic
58#91098C2211yescharacteristic
59#91098C2211yescharacteristic
60C4⋊(C3⋊#168)C2211yescharacteristic
61#91087C2211yescharacteristic
62#79480—51nomaximal, Hall
63C2×#4053—31no—
64C2×#4047—31no—
65#65882—31no—
66C5×#435D311yescharacteristic, complemented
67#65416—31no—
68#65400—31no—
69#65300—31no—
70#65126—31no—
71#65125—31no—
72#65019—31no—
73#65017—31no—
74#65016—31no—
75#65016—31no—
76#64995—31no—
77D5×#97—31no—
78C2×C3×C5×D4C2×C411yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C2×#1220C2×C411yescharacteristic
82C2×#1220C2×C411yescharacteristic
83C2×#1220C2×C411yescharacteristic
84C2×#1220C2×C411yescharacteristic
85C2×#1220C2×C411yescharacteristic
86C2×#1220C2×C411yescharacteristic
87#6817—22no—
88#6817—22no—
89#6817—22no—
90#6817—22no—
91C2×D60C2×C411yescharacteristic
92C2×D60C2×C411yescharacteristic
93C2×D60C2×C411yescharacteristic
94C2×C4×D15C2×C411yescharacteristic
95C2×C4×D15C2×C411yescharacteristic
96C2×C4×D15C2311yescharacteristic
97C2×C4×D15C2311yescharacteristic
98C2×C4×D15C2311yescharacteristic
99C2×Dic30C2×C411yescharacteristic
100C2×Dic30C2×C411yescharacteristic
101C3×C5×M16—22no—
102C2×C3×C5×C8—22no—
103C2×C3×C5×C8C2311yescharacteristic
104C2×C3×C5×C8C2311yescharacteristic
105C2×C3×C5×C8C2311yescharacteristic
106C2×C3×C5×C8C2311yescharacteristic
107C3×C5×C4⋊C4C2×C411yescharacteristic
108C3×C5×C22⋊C4C2×C411yescharacteristic
109C3×C5×C22⋊C4C2×C411yescharacteristic
110C3×C42×C5C2311yescharacteristic
111#6719C2×C411yescharacteristic
112#6719C2×C411yescharacteristic
113#6714C2×C411yescharacteristic
114#6714C2×C411yescharacteristic
115#6714C2×C411yescharacteristic
116#6714C2×C411yescharacteristic
117C4⋊Dic15C2×C411yescharacteristic
118#6712C2×C411yescharacteristic
119#6712C2×C411yescharacteristic
120C4×Dic15C2×C411yescharacteristic
121C4×Dic15C2×C411yescharacteristic
122C4×Dic15C2311yescharacteristic
123#6710—22no—
124C2×C3⋊#168—22no—
125C2×C3⋊#168C2311yescharacteristic
126C2×C3⋊#168C2311yescharacteristic
127C2×C3⋊#168C2311yescharacteristic
128C2×C3⋊#168C2311yescharacteristic
129#6705—22no—
130#6705—22no—
131#6705—22no—
132#6705—22no—
133C8×D15—22no—
134C8×D15—22no—
135C8×D15—22no—
136C8×D15D414yescomplemented
137C2×#907—51no—
138C2×#901—51no—
139#5548—51no—
140C3×#435D511yescharacteristic, complemented
141#5127—51no—
142#5111—51no—
143#5011—51no—
144#4837—51no—
145#4836—51no—
146#4730—51no—
147#4728—51no—
148#4727—51no—
149#4727—51no—
150#4706—51no—
151D3×#97—51no—
152C2×#709—31no—
153C2×#709—31no—
154C2×C5×M16C2×D311yescharacteristic
155C22×C5×C8C2×D311yescharacteristic
156C4×C5×D4C2×D311yescharacteristic
157#4086—31no—
158#4084—31no—
159C4×C22⋊D5—31no—
160C4×C22⋊D5—31no—
161C2×#681—31no—
162C22×#168—31no—
163#4053—64no—
164#4047—64no—
165C2×#676—31no—
166C2×#676—31no—
167C2×#676—31no—
168C2×#676—31no—
169C2×C8×D5—31no—
170C2×C8×D5—31no—
171C2×C8×D5—31no—
172C2×C8×D5—31no—
173#4041—31no—
174#4034—31no—
175#4031—31no—
176#4031—31no—
177#4030—31no—
178#4030—31no—
179C4×D20—31no—
180C42×D5—31no—
181C5×C4⋊C8C2×D311yescharacteristic
182C5×C22⋊C8C2×D311yescharacteristic
183C5×C22⋊C8C2×D311yescharacteristic
184C5×#97C2×D311yescharacteristic
185C22⋊#168—31no—
186C22⋊#168—31no—
187#3952—31no—
188#3952—31no—
189#3952—31no—
190#3952—31no—
191#3947—31no—
192#3947—31no—
193#3946—31no—
194#3946—31no—
195C4⋊#168—31no—
196#3935—31no—
197#2932—151noSylow
198C23×C3×C5C22×C411yescharacteristic
199C23×C3×C5C22×C411yescharacteristic
200C22×D15C22×C411yescharacteristic
201C22×D15C22×C411yescharacteristic
202C22×D15C22×C411yescharacteristic
203C3×C5×D4—41no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5C22×C411yescharacteristic
209C2×C3×C4×C5C22×C411yescharacteristic
210C2×C3×C4×C5C22×C411yescharacteristic
211C2×C3×C4×C5C22×C411yescharacteristic
212C2×C3×C4×C5C2411yescharacteristic
213#1220—22no—
214#1220—22no—
215#1220—22no—
216#1220—22no—
217#1220—41no—
218#1220—41no—
219C2×Dic15C22×C411yescharacteristic
220C2×Dic15C22×C411yescharacteristic
221C2×Dic15C22×C411yescharacteristic
222C2×Dic15C22×C411yescharacteristic
223C2×Dic15C22×C411yescharacteristic
224D60—22no—
225D60—22no—
226D60—41no—
227C4×D15—21no—
228C4×D15—21no—
229C4×D15—21no—
230C4×D15—21no—
231C4×D15—41no—
232C4×D15—41no—
233C4×D15C2×D412yes—
234C4×D15#4112yes—
235Dic30—22no—
236Dic30—22no—
237C3×C5×C8—21no—
238C3×C5×C8—21no—
239C3×C5×C8—21no—
240C3×C5×C8C2×D412yes—
241C3⋊#168—21no—
242C3⋊#168—21no—
243C3⋊#168—21no—
244C3⋊#168C2×D412yes—
245C2×#235—51no—
246C2×#235—51no—
247C2×C3×M16C2×D511yescharacteristic
248C22×C3×C8C2×D511yescharacteristic
249C3×C4×D4C2×D511yescharacteristic
250#940—51no—
251#938—51no—
252C4×#67—51no—
253C4×#67—51no—
254C2×#208—51no—
255C22×C3⋊C8—51no—
256#907—104no—
257#901—104no—
258C2×ΓL(1,𝔽25)—51no—
259C2×ΓL(1,𝔽25)—51no—
260C2×ΓL(1,𝔽25)—51no—
261C2×ΓL(1,𝔽25)—51no—
262C2×D3×C8—51no—
263C2×D3×C8—51no—
264C2×D3×C8—51no—
265C2×D3×C8—51no—
266#895—51no—
267#888—51no—
268#885—51no—
269#885—51no—
270#884—51no—
271#884—51no—
272C4×D12—51no—
273C42×D3—51no—
274C3×C4⋊C8C2×D511yescharacteristic
275C3×C22⋊C8C2×D511yescharacteristic
276C3×C22⋊C8C2×D511yescharacteristic
277C3×#97C2×D511yescharacteristic
278#830—51no—
279#830—51no—
280(C2×D3)⋊C8—51no—
281(C2×D3)⋊C8—51no—
282(C2×D3)⋊C8—51no—
283(C2×D3)⋊C8—51no—
284#815—51no—
285#815—51no—
286Dic3⋊C8—51no—
287Dic3⋊C8—51no—
288C4⋊(C3⋊C8)—51no—
289#803—51no—
290C2×C5×D4C4×D311yescharacteristic
291C22×C4×C5C22×D311yescharacteristic
292C22×C4×C5C22×D311yescharacteristic
293C2×C22⋊D5—31no—
294C2×C22⋊D5—31no—
295C2×C22⋊D5—31no—
296C2×C22⋊D5—31no—
297C2×C22⋊D5—31no—
298C2×C22⋊D5—31no—
299#709—62no—
300#709—62no—
301#709—62no—
302#709—62no—
303C2×D20—31no—
304C2×D20—31no—
305C2×D20—31no—
306C2×C4×D5—31no—
307C2×C4×D5—31no—
308C2×C4×D5—31no—
309C2×C4×D5—31no—
310C2×C4×D5—31no—
311C2×Dic10—31no—
312C2×Dic10—31no—
313C5×M16—22no—
314C2×C5×C8—22no—
315C2×C5×C8C22×D311yescharacteristic
316C2×C5×C8C22×D311yescharacteristic
317C2×C5×C8C22×D311yescharacteristic
318C2×C5×C8C22×D311yescharacteristic
319C5×C4⋊C4C4×D311yescharacteristic
320C5×C22⋊C4C4×D311yescharacteristic
321C5×C22⋊C4C4×D311yescharacteristic
322C42×C5C22×D311yescharacteristic
323C22⋊Dic5—31no—
324C22⋊Dic5—31no—
325#685—31no—
326#685—31no—
327#685—31no—
328#685—31no—
329C4⋊Dic5—31no—
330#683—31no—
331#683—31no—
332C4×Dic5—31no—
333C4×Dic5—31no—
334C4×Dic5—31no—
335#681—62no—
336C2×#168—31no—
337C2×#168—31no—
338C2×#168—31no—
339C2×#168—31no—
340C2×#168—62no—
341#676—62no—
342#676—62no—
343#676—62no—
344#676—62no—
345C8×D5—34no—
346C8×D5—62no—
347C8×D5—62no—
348C8×D5—62no—
349C2×#131—151no—
350C2×#131—151no—
351#532—151no—
352#435—151no—
353#435—151no—
354#435—151no—
355#435—151no—
356#435—151no—
357#435—151no—
358#435—151no—
359#435D1511yescharacteristic, complemented
360#423—151no—
361#408—151no—
362#408—151no—
363C2×#97—151no—
364C22×C3×C5—21no—
365C22×C3×C5—21no—
366C22×C3×C5—21no—
367C22×C3×C5—21no—
368C22×C3×C5—21no—
369C22×C3×C5—21no—
370C22×C3×C5C23×C411yescharacteristic
371C2×D15—21no—
372C2×D15—21no—
373C2×D15—21no—
374C2×D15—21no—
375C2×D15—21no—
376C2×D15—21no—
377C2×D15—21no—
378C2×D15—21no—
379C2×D15C4×D412yes—
380C3×C4×C5—21no—
381C3×C4×C5—21no—
382C3×C4×C5—21no—
383C3×C4×C5—21no—
384C3×C4×C5C22×D411yescharacteristic
385C3×C4×C5C2×#4111yescharacteristic
386Dic15—21no—
387Dic15—21no—
388Dic15—21no—
389Dic15—21no—
390Dic15C4×D412yes—
391C2×C3×D4C4×D511yescharacteristic
392C22×C3×C4C22×D511yescharacteristic
393C22×C3×C4C22×D511yescharacteristic
394C2×#67—51no—
395C2×#67—51no—
396C2×#67—51no—
397C2×#67—51no—
398C2×#67—51no—
399C2×#67—51no—
400#235—102no—
401#235—102no—
402#235—102no—
403#235—102no—
404C2×D12—51no—
405C2×D12—51no—
406C2×D12—51no—
407C2×C4×D3—51no—
408C2×C4×D3—51no—
409C2×C4×D3—51no—
410C2×C4×D3—51no—
411C2×C4×D3—51no—
412C2×Dic6—51no—
413C2×Dic6—51no—
414C3×M16—22no—
415C2×C3×C8—22no—
416C2×C3×C8C22×D511yescharacteristic
417C2×C3×C8C22×D511yescharacteristic
418C2×C3×C8C22×D511yescharacteristic
419C2×C3×C8C22×D511yescharacteristic
420C3×C4⋊C4C4×D511yescharacteristic
421C3×C22⋊C4C4×D511yescharacteristic
422C3×C22⋊C4C4×D511yescharacteristic
423C3×C42C22×D511yescharacteristic
424#217—51no—
425#217—51no—
426(C2×D3)⋊C4—51no—
427(C2×D3)⋊C4—51no—
428(C2×D3)⋊C4—51no—
429(C2×D3)⋊C4—51no—
430C4⋊Dic3—51no—
431Dic3⋊C4—51no—
432Dic3⋊C4—51no—
433C4×Dic3—51no—
434C4×Dic3—51no—
435C4×Dic3—51no—
436#208—102no—
437C2×C3⋊C8—51no—
438C2×C3⋊C8—51no—
439C2×C3⋊C8—51no—
440C2×C3⋊C8—51no—
441C2×C3⋊C8—102no—
442ΓL(1,𝔽25)—102no—
443ΓL(1,𝔽25)—102no—
444ΓL(1,𝔽25)—102no—
445ΓL(1,𝔽25)—102no—
446D3×C8—54no—
447D3×C8—102no—
448D3×C8—102no—
449D3×C8—102no—
450C23×C5C2×C4×D311yescharacteristic
451C23×C5C2×C4×D311yescharacteristic
452C22×D5—31no—
453C22×D5—31no—
454C22×D5—31no—
455C5×D4—41no—
456C2×C4×C5—21no—
457C2×C4×C5—21no—
458C2×C4×C5—21no—
459C2×C4×C5—21no—
460C2×C4×C5C2×C4×D311yescharacteristic
461C2×C4×C5C2×C4×D311yescharacteristic
462C2×C4×C5C2×C4×D311yescharacteristic
463C2×C4×C5C2×C4×D311yescharacteristic
464C2×C4×C5C23×D311yescharacteristic
465C22⋊D5—62no—
466C22⋊D5—62no—
467C22⋊D5—62no—
468C22⋊D5—62no—
469C22⋊D5—121no—
470C22⋊D5—121no—
471C2×Dic5—31no—
472C2×Dic5—31no—
473C2×Dic5—31no—
474C2×Dic5—31no—
475C2×Dic5—31no—
476D20—62no—
477D20—62no—
478D20—121no—
479C4×D5—32no—
480C4×D5—32no—
481C4×D5—61no—
482C4×D5—61no—
483C4×D5—61no—
484C4×D5—61no—
485C4×D5—121no—
486C4×D5—121no—
487Dic10—62no—
488Dic10—62no—
489C5×C8—21no—
490C5×C8—21no—
491C5×C8—21no—
492C5×C8D3×D412yes—
493#168—32no—
494#168—61no—
495#168—61no—
496#168—61no—
497C2×#41—151no—
498C2×#41—151no—
499#131—304no—
500#131—304no—
501C2×M16—151no—
502C2×M16—151no—
503C2×M16—151no—
504C2×M16—151no—
505C2×M16—151no—
506C2×M16C2×D1511yescharacteristic
507C22×C8—151no—
508C22×C8—151no—
509C22×C8—151no—
510C22×C8—151no—
511C22×C8—151no—
512C22×C8C2×D1511yescharacteristic
513C4⋊Q8—151no—
514#127—151no—
515#124—151no—
516#124—151no—
517#121—151no—
518#121—151no—
519#121—151no—
520#121—151no—
521C4×D4—151no—
522C4×D4—151no—
523C4×D4—151no—
524C4×D4C2×D1511yescharacteristic
525C2×C42—151no—
526C4⋊C8—151no—
527C4⋊C8—151no—
528C4⋊C8—151no—
529C4⋊C8C2×D1511yescharacteristic
530C22⋊C8—151no—
531C22⋊C8—151no—
532C22⋊C8—151no—
533C22⋊C8—151no—
534C22⋊C8—151no—
535C22⋊C8—151no—
536C22⋊C8C2×D1511yescharacteristic
537C22⋊C8C2×D1511yescharacteristic
538#97—151no—
539#97—151no—
540#97—151no—
541#97C2×D1511yescharacteristic
542C2×C3×C5—41no—
543C2×C3×C5—41no—
544C2×C3×C5C2×C4×D411yescharacteristic
545C2×C3×C5#56811yescharacteristic
546C2×C3×C5#56811yescharacteristic
547D15—22no—
548D15—41no—
549D15—41no—
550C23×C3C2×C4×D511yescharacteristic
551C23×C3C2×C4×D511yescharacteristic
552C22×D3—51no—
553C22×D3—51no—
554C22×D3—51no—
555C3×D4—41no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4C2×C4×D511yescharacteristic
561C2×C3×C4C2×C4×D511yescharacteristic
562C2×C3×C4C2×C4×D511yescharacteristic
563C2×C3×C4C2×C4×D511yescharacteristic
564C2×C3×C4C23×D511yescharacteristic
565#67—102no—
566#67—102no—
567#67—102no—
568#67—102no—
569#67—201no—
570#67—201no—
571C2×Dic3—51no—
572C2×Dic3—51no—
573C2×Dic3—51no—
574C2×Dic3—51no—
575C2×Dic3—51no—
576D12—102no—
577D12—102no—
578D12—201no—
579C4×D3—52no—
580C4×D3—52no—
581C4×D3—101no—
582C4×D3—101no—
583C4×D3—101no—
584C4×D3—101no—
585C4×D3—201no—
586C4×D3—201no—
587Dic6—102no—
588Dic6—102no—
589C3×C8—21no—
590C3×C8—21no—
591C3×C8—21no—
592C3×C8D4×D512yes—
593C3⋊C8—52no—
594C3⋊C8—101no—
595C3⋊C8—101no—
596C3⋊C8—101no—
597C22×C5—21no—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—21no—
601C22×C5—21no—
602C22×C5—21no—
603C22×C5C22×C4×D311yescharacteristic
604C2×D5—32no—
605C2×D5—61no—
606C2×D5—61no—
607C2×D5—61no—
608C2×D5—61no—
609C2×D5—61no—
610C2×D5—61no—
611C2×D5—61no—
612C2×D5—61no—
613C4×C5—21no—
614C4×C5—21no—
615C4×C5—21no—
616C4×C5—21no—
617C4×C5C2×D3×D411yescharacteristic
618C4×C5D3×#4111yescharacteristic
619Dic5—32no—
620Dic5—61no—
621Dic5—61no—
622Dic5—61no—
623Dic5—61no—
624#41—302no—
625#41—302no—
626#41—302no—
627#41—302no—
628C2×Q8—151no—
629C2×Q8—151no—
630C2×D4—151no—
631C2×D4—151no—
632C2×D4—151no—
633C2×D4—151no—
634C2×D4—151no—
635C2×D4—151no—
636C2×D4—151no—
637C2×D4—151no—
638C2×D4—151no—
639C2×D4C4×D1511yescharacteristic
640C22×C4—151no—
641C22×C4—151no—
642C22×C4—151no—
643C22×C4—151no—
644C22×C4—151no—
645C22×C4C22×D1511yescharacteristic
646C22×C4C22×D1511yescharacteristic
647M16—22no—
648M16—302no—
649M16—302no—
650M16—302no—
651M16—302no—
652M16—302no—
653C2×C8—22no—
654C2×C8—151no—
655C2×C8—154no—
656C2×C8—151no—
657C2×C8—151no—
658C2×C8—151no—
659C2×C8—302no—
660C2×C8—302no—
661C2×C8—302no—
662C2×C8—302no—
663C2×C8C22×D1511yescharacteristic
664C2×C8C22×D1511yescharacteristic
665C2×C8C22×D1511yescharacteristic
666C2×C8C22×D1511yescharacteristic
667C4⋊C4—151no—
668C4⋊C4—151no—
669C4⋊C4—151no—
670C4⋊C4C4×D1511yescharacteristic
671C22⋊C4—151no—
672C22⋊C4—151no—
673C22⋊C4—151no—
674C22⋊C4—151no—
675C22⋊C4—151no—
676C22⋊C4—151no—
677C22⋊C4C4×D1511yescharacteristic
678C22⋊C4C4×D1511yescharacteristic
679C42—151no—
680C42—151no—
681C42—151no—
682C42C22×D1511yescharacteristic
683C3×C5#293211yescharacteristic, complemented, Hall
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3C22×C4×D511yescharacteristic
691C2×D3—52no—
692C2×D3—101no—
693C2×D3—101no—
694C2×D3—101no—
695C2×D3—101no—
696C2×D3—101no—
697C2×D3—101no—
698C2×D3—101no—
699C2×D3—101no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4C2×D4×D511yescharacteristic
705C3×C4D5×#4111yescharacteristic
706Dic3—52no—
707Dic3—101no—
708Dic3—101no—
709Dic3—101no—
710Dic3—101no—
711C2×C5—41no—
712C2×C5—41no—
713C2×C5C4×D3×D411yescharacteristic
714C2×C5#574511yescharacteristic
715C2×C5#575011yescharacteristic
716D5—62no—
717D5—121no—
718D5—121no—
719C23—151no—
720C23—151no—
721C23—151no—
722C23C2×C4×D1511yescharacteristic
723C23C2×C4×D1511yescharacteristic
724Q8—302no—
725Q8—302no—
726D4—41no—
727D4—302no—
728D4—302no—
729D4—302no—
730D4—302no—
731D4—302no—
732D4—302no—
733D4—601no—
734D4—601no—
735D4—601no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—151no—
741C2×C4—152no—
742C2×C4—152no—
743C2×C4—151no—
744C2×C4—151no—
745C2×C4—151no—
746C2×C4—151no—
747C2×C4—301no—
748C2×C4—301no—
749C2×C4—301no—
750C2×C4—301no—
751C2×C4—601no—
752C2×C4—601no—
753C2×C4C2×C4×D1511yescharacteristic
754C2×C4C2×C4×D1511yescharacteristic
755C2×C4C2×C4×D1511yescharacteristic
756C2×C4C2×C4×D1511yescharacteristic
757C2×C4C23×D1511yescharacteristic
758C8—21no—
759C8—21no—
760C8—21no—
761C8—152no—
762C8—301no—
763C8—301no—
764C8—301no—
765C8D4×D1512yes—
766C2×C3—41no—
767C2×C3—41no—
768C2×C3C4×D4×D511yescharacteristic
769C2×C3#6607911yescharacteristic
770C2×C3#6608411yescharacteristic
771D3—102no—
772D3—201no—
773D3—201no—
774C5#7948011yescharacteristic, complemented, Sylow
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—152no—
782C22—301no—
783C22—301no—
784C22—301no—
785C22—301no—
786C22—301no—
787C22—301no—
788C22—301no—
789C22—301no—
790C22C22×C4×D1511yescharacteristic
791C4—21no—
792C4—21no—
793C4—21no—
794C4—21no—
795C4—152no—
796C4—301no—
797C4—301no—
798C4—301no—
799C4—301no—
800C4C2×D4×D1511yescharacteristic
801C4#41×D1511yescharacteristic
802C3#1061121111yescharacteristic, complemented, Sylow
803C2—41no—
804C2—41no—
805C2—302no—
806C2—601no—
807C2—601no—
808C2C4×D4×D1511yescharacteristic
809C2#1175650411yescharacteristic
810C2#1175650911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D15
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×#435C2
prime radical#11756307C2
cosocleC2×C3×C4×C5C24
hypercenter#435D15
hypocenterC3×C5#2932
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#91796C2semidirect
2. C2×#91790C2semidirect
4. C3×C5×#435C2semidirect
5. #11751228C2semidirect
6. #11751212C2semidirect
7. #11751112C2semidirect
8. #11750938C2semidirect
9. #11750937C2semidirect
10. #11750831C2semidirect
11. #11750829C2semidirect
12. #11750828C2semidirect
13. #11750828C2semidirect
14. #11750807C2semidirect
15. D15×#97C2semidirect
66. C5×#435D3semidirect
136. C8×D15D4semidirect
140. C3×#435D5semidirect
359. #435D15semidirect
683. C3×C5#2932semidirect
774. C5#79480semidirect
802. C3#10611211semidirect

Maximal subgroups

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

subgroupindex
C2×#917962
C2×#917902
#117563072
C3×C5×#4352
#117512282
#117512122
#117511122
#117509382
#117509372
#117508312
#117508292
#117508282
#117508072
D15×#972
#106112113
#794805