Finite Group Databasebeta

← #14418078

Subgroups — #14418078

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#131C211yesmaximal, characteristic, complemented
2#11755315C211yesmaximal, characteristic
3D5×#901C211yesmaximal, characteristic, complemented
4#11751246C211yesmaximal, characteristic, complemented
5C5×#5145C211yesmaximal, characteristic, complemented
6#11749434C211yesmaximal, characteristic, complemented
7#11749432C211yesmaximal, characteristic, complemented
8#11749427C211yesmaximal, characteristic, complemented
9#11748229C211yesmaximal, characteristic, complemented
10#11748207C211yesmaximal, characteristic, complemented
11#11748203C211yesmaximal, characteristic, complemented
12#11748171C211yesmaximal, characteristic, complemented
13#11748077C211yesmaximal, characteristic, complemented
14#11748075C211yesmaximal, characteristic, complemented
15#11747646C211yesmaximal, characteristic, complemented
16#10611628—31nomaximal, Hall
17C3×D5×#41C2211yescharacteristic
18D5×#235C2211yescharacteristic
19C3×C5×#131C2211yescharacteristic, complemented
20#91839C2211yescharacteristic
21#91790C2211yescharacteristic, complemented
22C5×#950C2211yescharacteristic
23C5×#901C2211yescharacteristic, complemented
24C3×#4094C2211yescharacteristic, complemented
25C3×#4053—21no—
26C3×#4053C2211yescharacteristic, complemented
27C3×D5×M16—21no—
28C3×D5×M16C2211yescharacteristic
29C3×#4047—21no—
30C3×#4047C2211yescharacteristic, complemented
31C2×C3×C8×D5—21no—
32C2×C3×C8×D5C2211yescharacteristic
33#91515C411yescharacteristic, complemented
34#91513C411yescharacteristic, complemented
35#91508C411yescharacteristic, complemented
36#91502C411yescharacteristic, complemented
37#91491C411yescharacteristic, complemented
38#91489C411yescharacteristic, complemented
39#91484C411yescharacteristic, complemented
40#91478C411yescharacteristic, complemented
41#91357C2211yescharacteristic
42#91311C2211yescharacteristic
43#91297C2211yescharacteristic
44C2×#6649C2211yescharacteristic
45#91290C2211yescharacteristic, complemented
46#91286C2211yescharacteristic, complemented
47D5×#208C2211yescharacteristic
48#91266—21no—
49#91265—21no—
50D5×ΓL(1,𝔽25)—21no—
51D3×C8×D5—21no—
52#91121C2211yescharacteristic, complemented
53#91109C2211yescharacteristic, complemented
54#91106C2211yescharacteristic, complemented
55#91099C2211yescharacteristic, complemented
56C5×#837C2211yescharacteristic, complemented
57C5×#825C2211yescharacteristic, complemented
58C5×#822C2211yescharacteristic, complemented
59C5×#815C2211yescharacteristic, complemented
60#90993C2211yescharacteristic, complemented
61#90992C2211yescharacteristic, complemented
62#90980C2211yescharacteristic, complemented
63#90978C2211yescharacteristic, complemented
64#90977C2211yescharacteristic, complemented
65#90976C2211yescharacteristic, complemented
66#90951C2211yescharacteristic, complemented
67Dic3×#168C2211yescharacteristic, complemented
68#83792—51nomaximal, Hall
69#66102—31no—
70D5×#131—31no—
71D5×#131D311yescharacteristic, complemented
72C5×#444—31no—
73#65485—31no—
74#65434—31no—
75#65434—31no—
76#65184—31no—
77#65182—31no—
78#65113—31no—
79#65113—31no—
80#65110—31no—
81#65110—31no—
82#65006—31no—
83#64997—31no—
84C3×C5×#41C2311yescharacteristic
85#6817C2311yescharacteristic
86C5×#235C2311yescharacteristic
87C3×#713C2×C411yescharacteristic
88C3×Q8×D5C2×C411yescharacteristic
89C3×#711—21no—
90C3×#711C2×C411yescharacteristic
91C3×D4×D5—21no—
92C3×D4×D5C2×C411yescharacteristic
93C3×#709—21no—
94C3×#709C2311yescharacteristic
95C2×C3×C4×D5—21no—
96C2×C3×C4×D5C2311yescharacteristic
97D5×#67—21no—
98#6782—21no—
99D5×D12C2×C411yescharacteristic
100C4×D3×D5—21no—
101#6773C2×C411yescharacteristic
102#6772C2×C411yescharacteristic
103#6771—21no—
104D5×Dic6C2×C411yescharacteristic
105C3×C5×M16—21no—
106C3×C5×M16C2311yescharacteristic
107C2×C3×C5×C8—21no—
108C2×C3×C5×C8C2311yescharacteristic
109#6718C2×C411yescharacteristic
110#6717C2×C411yescharacteristic
111#6716C2×C411yescharacteristic
112#6715C2×C411yescharacteristic
113C4×Dic15C2311yescharacteristic
114#6710C2311yescharacteristic
115C2×C3⋊#168C2311yescharacteristic
116#6705—21no—
117C8×D15—21no—
118C5×#216C2×C411yescharacteristic
119C5×#215C2×C411yescharacteristic
120C5×#214C2×C411yescharacteristic
121C5×#213C2×C411yescharacteristic
122C4×C5×Dic3C2311yescharacteristic
123C5×#208C2311yescharacteristic
124C2×C5×C3⋊C8C2311yescharacteristic
125C5×ΓL(1,𝔽25)—21no—
126C5×D3×C8—21no—
127C3×#681—21no—
128C3×#681C2311yescharacteristic
129C2×C3×#168—21no—
130C2×C3×#168C2311yescharacteristic
131C3×#676—21no—
132C3×#676—21no—
133C3×#676—21no—
134C3×C8×D5—21no—
135C3×C8×D5—21no—
136C3×C8×D5—21no—
137C3×C8×D5D411yescharacteristic
138C3×C8×D5D411yescharacteristic
139C3×C8×D5D411yescharacteristic
140C3×C8×D5D411yescharacteristic
141#6668—21no—
142#6665—21no—
143#6662C2×C411yescharacteristic
144#6661C2×C411yescharacteristic
145#6658C2×C411yescharacteristic
146#6657C2×C411yescharacteristic
147#6656C2×C411yescharacteristic
148#6655C2×C411yescharacteristic
149#6653C2×C411yescharacteristic
150#6652C2×C411yescharacteristic
151#6651—21no—
152#6650—21no—
153#6649—21no—
154#6649C2×C411yescharacteristic
155#6649C2×C411yescharacteristic
156#6649C2×C411yescharacteristic
157#6649C2×C411yescharacteristic
158#6648—21no—
159D3×#168—21no—
160D5×C3⋊C8—21no—
161C2×C3×#131—51no—
162#5822—51no—
163C2×#901—51no—
164#5236—51no—
165#5145—51no—
166#5145—51no—
167#5145—51no—
168#5145D511yescharacteristic, complemented
169#5144—51no—
170#5144—51no—
171#5144—51no—
172#5144—51no—
173#5139—51no—
174#5124—51no—
175#5101—51no—
176D5×#41—31no—
177D5×#41C2×D311yescharacteristic
178C5×#135—31no—
179C5×#131—31no—
180C5×#131C2×D311yescharacteristic, complemented
181#4096—31no—
182#4096—31no—
183#4094—31no—
184#4094C2×D311yescharacteristic, complemented
185#4064—31no—
186#4064—31no—
187#4061—31no—
188#4061—31no—
189#4060—31no—
190#4060—31no—
191#4057—31no—
192#4057—31no—
193#4053—21no—
194#4053—31no—
195#4053—61no—
196#4053C2×D311yescharacteristic, complemented
197D5×M16—21no—
198D5×M16—31no—
199D5×M16—61no—
200D5×M16C2×D311yescharacteristic
201#4050—31no—
202#4047—21no—
203#4047—31no—
204#4047—61no—
205#4047C2×D311yescharacteristic, complemented
206C2×#676—31no—
207C2×C8×D5—21no—
208C2×C8×D5—61no—
209C2×C8×D5C2×D311yescharacteristic
210#4018—31no—
211C5×#108—31no—
212C5×#104—31no—
213C5×#104—31no—
214C5×#97—31no—
215#3969—31no—
216#3969—31no—
217#3957—31no—
218#3957—31no—
219#3954—31no—
220#3954—31no—
221#3951—31no—
222#3947—31no—
223C8×Dic5—31no—
224#3937—31no—
225#3937—31no—
226C4×#168—31no—
227#2955—151noSylow
228C22×C3×D5—21no—
229C22×C3×D5#4111yescharacteristic
230C2×D3×D5—21no—
231C3×C5×Q8C22×C411yescharacteristic
232C3×C5×D4—21no—
233C3×C5×D4C22×C411yescharacteristic
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5C2411yescharacteristic
236#1220—21no—
237C2×Dic15—21no—
238D60C22×C411yescharacteristic
239C4×D15—21no—
240Dic30C22×C411yescharacteristic
241C5×#67—21no—
242C2×C5×Dic3—21no—
243C5×D12C22×C411yescharacteristic
244C4×C5×D3—21no—
245C5×Dic6C22×C411yescharacteristic
246C3×C22⋊D5—21no—
247C3×C22⋊D5—21no—
248C3×C22⋊D5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5#4111yescharacteristic
251C3×D20—21no—
252C3×D20C22×C411yescharacteristic
253C3×C4×D5—21no—
254C3×C4×D5—21no—
255C3×C4×D5—21no—
256C3×C4×D5C22×C411yescharacteristic
257C3×C4×D5C22×C411yescharacteristic
258C3×C4×D5C2×D411yescharacteristic
259C3×C4×D5C2×D411yescharacteristic
260C3×Dic10—21no—
261C3×Dic10C22×C411yescharacteristic
262#1204—21no—
263#1203—21no—
264#1202—21no—
265#1201—21no—
266#1200—21no—
267D3×Dic5—21no—
268D5×Dic3—21no—
269C3×C5×C8—21no—
270C3×C5×C8C2×D411yescharacteristic
271C3×C5×C8C2×D411yescharacteristic
272C3⋊#168—21no—
273C3⋊#168C22×C411yescharacteristic
274C3⋊#168C22×C411yescharacteristic
275C3×#168—21no—
276C3×#168C2×D411yescharacteristic
277C3×#168C2×D411yescharacteristic
278C5×C3⋊C8—21no—
279C5×C3⋊C8C22×C411yescharacteristic
280C5×C3⋊C8C22×C411yescharacteristic
281C2×C3×#41—51no—
282C2×#235—51no—
283C3×#131—51no—
284C3×#131—51no—
285C3×#131—51no—
286C3×#131—101no—
287C3×#131—101no—
288C3×#131C2×D511yescharacteristic, complemented
289C2×C3×M16—51no—
290C2×C3×M16—101no—
291C22×C3×C8—51no—
292C22×C3×C8—101no—
293#951—51no—
294#951—51no—
295#950—51no—
296#950—51no—
297#950—51no—
298#950C2×D511yescharacteristic
299#949—51no—
300#949—51no—
301#942—51no—
302#942—51no—
303#932—51no—
304#932—51no—
305#926—51no—
306C2×#208—51no—
307C2×#208—51no—
308#901—51no—
309#901—51no—
310#901—51no—
311#901—101no—
312#901—101no—
313#901C2×D511yescharacteristic, complemented
314C2×ΓL(1,𝔽25)—101no—
315C2×D3×C8—101no—
316#837—51no—
317#837—51no—
318#837—51no—
319#837C2×D511yescharacteristic, complemented
320#825—51no—
321#825—51no—
322#825—51no—
323#825C2×D511yescharacteristic, complemented
324#822—51no—
325#822—51no—
326#822—51no—
327#822C2×D511yescharacteristic, complemented
328#815—51no—
329#815C2×D511yescharacteristic, complemented
330C8×Dic3—51no—
331C8×Dic3—51no—
332C5×#41—31no—
333C5×#41C22×D311yescharacteristic
334#713—31no—
335#713C4×D311yescharacteristic
336Q8×D5—31no—
337Q8×D5C4×D311yescharacteristic
338#711—21no—
339#711—31no—
340#711—61no—
341#711C4×D311yescharacteristic
342D4×D5—21no—
343D4×D5—31no—
344D4×D5—61no—
345D4×D5C4×D311yescharacteristic
346#709—21no—
347#709—31no—
348#709—61no—
349#709C22×D311yescharacteristic
350C2×C4×D5—21no—
351C2×C4×D5—61no—
352C2×C4×D5C22×D311yescharacteristic
353C5×Q16—31no—
354C5×SD16—31no—
355C5×SD16—31no—
356C5×D8—31no—
357C5×M16—21no—
358C5×M16—31no—
359C5×M16—61no—
360C5×M16C22×D311yescharacteristic
361C2×C5×C8—21no—
362C2×C5×C8—31no—
363C2×C5×C8—61no—
364C2×C5×C8C22×D311yescharacteristic
365C42×C5—31no—
366#689—31no—
367#689—31no—
368#688—31no—
369#688—31no—
370#687—31no—
371#687—31no—
372#686—31no—
373#686—31no—
374#685—61no—
375#683—61no—
376C4×Dic5—31no—
377#681—21no—
378#681—31no—
379#681—61no—
380#681C22×D311yescharacteristic
381C2×#168—21no—
382C2×#168—31no—
383C2×#168—61no—
384C2×#168C22×D311yescharacteristic
385Dic20—31no—
386D40—31no—
387#677—31no—
388#677—31no—
389#676—21no—
390#676—21no—
391#676—21no—
392#676—31no—
393#676—31no—
394#676—31no—
395#676—31no—
396#676—61no—
397#676—61no—
398#676—61no—
399C8×D5—21no—
400C8×D5—21no—
401C8×D5—21no—
402C8×D5—61no—
403C8×D5—61no—
404C8×D5—61no—
405C8×D5#6711yescharacteristic
406C8×D5#6711yescharacteristic
407C8×D5#6711yescharacteristic
408C8×D5#6711yescharacteristic
409#575—151no—
410C2×#131—51no—
411C2×#131—151no—
412#444—31no—
413#444—151no—
414#444—151no—
415#444—151no—
416#443—151no—
417#443—151no—
418#443—151no—
419#443—151no—
420#430—151no—
421#421—151no—
422#421—151no—
423#405—151no—
424C22×C3×C5—21no—
425C22×C3×C5C2×#4111yescharacteristic
426C2×D15—21no—
427C2×C5×D3—21no—
428C2×C3×D5—21no—
429C2×C3×D5—41no—
430C2×C3×D5—42no—
431C2×C3×D5C4×D411yescharacteristic
432C2×C3×D5C4×D411yescharacteristic
433D3×D5—42no—
434C3×C4×C5—21no—
435C3×C4×C5C23×C411yescharacteristic
436C3×C4×C5C22×D411yescharacteristic
437Dic15—21no—
438Dic15—41no—
439C3×Dic5—21no—
440C3×Dic5C4×D411yescharacteristic
441C3×Dic5C4×D411yescharacteristic
442C5×Dic3—21no—
443C5×Dic3—41no—
444C3×#41—51no—
445C3×#41—51no—
446C3×#41—51no—
447C3×#41—101no—
448C3×#41—101no—
449C3×#41C22×D511yescharacteristic
450C2×C3×Q8—51no—
451C2×C3×D4—51no—
452C2×C3×D4—101no—
453C22×C3×C4—51no—
454C22×C3×C4—101no—
455C2×#67—101no—
456#235—51no—
457#235—51no—
458#235—51no—
459#235—101no—
460#235—101no—
461#235C22×D511yescharacteristic
462C2×D12—51no—
463C2×C4×D3—101no—
464C2×Dic6—51no—
465C3×M16—21no—
466C3×M16—51no—
467C3×M16—101no—
468C3×M16—101no—
469C3×M16—101no—
470C3×M16—101no—
471C3×M16C22×D511yescharacteristic
472C2×C3×C8—21no—
473C2×C3×C8—51no—
474C2×C3×C8—51no—
475C2×C3×C8—51no—
476C2×C3×C8—51no—
477C2×C3×C8—51no—
478C2×C3×C8—101no—
479C2×C3×C8—101no—
480C2×C3×C8—101no—
481C2×C3×C8—101no—
482C2×C3×C8C22×D511yescharacteristic
483#217—101no—
484#216—51no—
485#216—51no—
486#216—51no—
487#216C4×D511yescharacteristic
488#215—51no—
489#215—51no—
490#215—51no—
491#215C4×D511yescharacteristic
492#214—51no—
493#214—51no—
494#214—51no—
495#214C4×D511yescharacteristic
496#213—51no—
497#213—51no—
498#213—51no—
499#213C4×D511yescharacteristic
500C4⋊Dic3—101no—
501C4×Dic3—51no—
502C4×Dic3C22×D511yescharacteristic
503#208—51no—
504#208—51no—
505#208—51no—
506#208—51no—
507#208—51no—
508#208—101no—
509#208C22×D511yescharacteristic
510C2×C3⋊C8—51no—
511C2×C3⋊C8—101no—
512C2×C3⋊C8C22×D511yescharacteristic
513ΓL(1,𝔽25)—21no—
514ΓL(1,𝔽25)—101no—
515ΓL(1,𝔽25)—101no—
516ΓL(1,𝔽25)—101no—
517D3×C8—21no—
518D3×C8—101no—
519D3×C8—101no—
520D3×C8—101no—
521C22×D5—21no—
522C22×D5—61no—
523C22×D5#23511yescharacteristic
524C5×Q8—31no—
525C5×Q8C2×C4×D311yescharacteristic
526C5×D4—21no—
527C5×D4—31no—
528C5×D4—61no—
529C5×D4C2×C4×D311yescharacteristic
530C2×C4×C5—21no—
531C2×C4×C5—61no—
532C2×C4×C5—61no—
533C2×C4×C5C23×D311yescharacteristic
534C22⋊D5—21no—
535C22⋊D5—21no—
536C22⋊D5—21no—
537C22⋊D5—61no—
538C22⋊D5—61no—
539C22⋊D5—61no—
540C2×Dic5—21no—
541C2×Dic5—61no—
542C2×Dic5—61no—
543C2×Dic5#23511yescharacteristic
544D20—21no—
545D20—31no—
546D20—61no—
547D20C2×C4×D311yescharacteristic
548C4×D5—21no—
549C4×D5—21no—
550C4×D5—21no—
551C4×D5—61no—
552C4×D5—61no—
553C4×D5—61no—
554C4×D5C2×C4×D311yescharacteristic
555C4×D5C2×C4×D311yescharacteristic
556C4×D5C2×#6711yescharacteristic
557C4×D5C2×#6711yescharacteristic
558Dic10—21no—
559Dic10—31no—
560Dic10—61no—
561Dic10C2×C4×D311yescharacteristic
562C5×C8—21no—
563C5×C8—31no—
564C5×C8—31no—
565C5×C8—61no—
566C5×C8C2×#6711yescharacteristic
567C5×C8C2×#6711yescharacteristic
568#168—21no—
569#168—31no—
570#168—31no—
571#168—61no—
572#168C2×#6711yescharacteristic
573#168C2×#6711yescharacteristic
574C2×#41—51no—
575C2×#41—151no—
576#137—151no—
577#137—151no—
578#137—151no—
579#137—151no—
580AGL(1,ℤ/8)—151no—
581AGL(1,ℤ/8)—151no—
582AGL(1,ℤ/8)—151no—
583AGL(1,ℤ/8)—151no—
584#135—31no—
585#135—151no—
586#135—151no—
587#135—151no—
588#131—31no—
589#131—51no—
590#131—51no—
591#131—51no—
592#131—101no—
593#131—101no—
594#131—151no—
595#131—151no—
596#131—151no—
597#131—301no—
598#131—301no—
599#131D3×D511yescharacteristic, complemented
600C2×M16—51no—
601C2×M16—101no—
602C2×M16—151no—
603C2×M16—151no—
604C2×M16—301no—
605C22×C8—51no—
606C22×C8—101no—
607C22×C8—301no—
608#117—151no—
609#108—31no—
610#108—151no—
611#108—151no—
612#108—151no—
613#104—31no—
614#104—31no—
615#104—151no—
616#104—151no—
617#104—151no—
618#104—151no—
619#104—151no—
620#104—151no—
621#97—31no—
622#97—151no—
623C4×C8—151no—
624C4×C8—151no—
625C2×C3×C5—21no—
626C2×C3×C5—41no—
627C2×C3×C5C2×C4×D411yescharacteristic
628D15—41no—
629C3×D5—21no—
630C3×D5—21no—
631C3×D5—41no—
632C5×D3—41no—
633C23×C3—51no—
634C23×C3—101no—
635C22×D3—101no—
636C3×Q8—51no—
637C3×Q8—101no—
638C3×Q8C2×C4×D511yescharacteristic
639C3×D4—21no—
640C3×D4—51no—
641C3×D4—101no—
642C3×D4—101no—
643C3×D4—101no—
644C3×D4—101no—
645C3×D4C2×C4×D511yescharacteristic
646C2×C3×C4—21no—
647C2×C3×C4—51no—
648C2×C3×C4—51no—
649C2×C3×C4—51no—
650C2×C3×C4—51no—
651C2×C3×C4—51no—
652C2×C3×C4—101no—
653C2×C3×C4—101no—
654C2×C3×C4—101no—
655C2×C3×C4—101no—
656C2×C3×C4C23×D511yescharacteristic
657#67—21no—
658#67—101no—
659#67—101no—
660#67—101no—
661C2×Dic3—21no—
662C2×Dic3—101no—
663C2×Dic3—101no—
664D12—51no—
665D12—101no—
666D12C2×C4×D511yescharacteristic
667C4×D3—21no—
668C4×D3—101no—
669C4×D3—101no—
670C4×D3—101no—
671Dic6—51no—
672Dic6—101no—
673Dic6C2×C4×D511yescharacteristic
674C3×C8—21no—
675C3×C8—51no—
676C3×C8—51no—
677C3×C8—101no—
678C3×C8D4×D511yescharacteristic
679C3×C8D4×D511yescharacteristic
680C3⋊C8—21no—
681C3⋊C8—51no—
682C3⋊C8—51no—
683C3⋊C8—101no—
684C3⋊C8C2×C4×D511yescharacteristic
685C3⋊C8C2×C4×D511yescharacteristic
686C22×C5—21no—
687C22×C5—61no—
688C22×C5C2×#23511yescharacteristic
689C2×D5—21no—
690C2×D5—41no—
691C2×D5—42no—
692C2×D5—61no—
693C2×D5—122no—
694C2×D5C4×#6711yescharacteristic
695C2×D5C4×#6711yescharacteristic
696C4×C5—21no—
697C4×C5—61no—
698C4×C5—121no—
699C4×C5C22×C4×D311yescharacteristic
700C4×C5C22×#6711yescharacteristic
701Dic5—21no—
702Dic5—61no—
703Dic5—121no—
704Dic5C4×#6711yescharacteristic
705Dic5C4×#6711yescharacteristic
706#41—31no—
707#41—51no—
708#41—51no—
709#41—51no—
710#41—101no—
711#41—101no—
712#41—151no—
713#41—151no—
714#41—151no—
715#41—301no—
716#41—301no—
717#41C2×D3×D511yescharacteristic
718C2×Q8—51no—
719C2×Q8—151no—
720C2×D4—51no—
721C2×D4—101no—
722C2×D4—151no—
723C2×D4—301no—
724C22×C4—51no—
725C22×C4—101no—
726C22×C4—301no—
727Q16—31no—
728Q16—151no—
729Q16—151no—
730Q16—151no—
731SD16—31no—
732SD16—31no—
733SD16—151no—
734SD16—151no—
735SD16—151no—
736SD16—151no—
737SD16—151no—
738SD16—151no—
739D8—31no—
740D8—151no—
741D8—151no—
742D8—151no—
743M16—21no—
744M16—31no—
745M16—51no—
746M16—61no—
747M16—101no—
748M16—101no—
749M16—101no—
750M16—101no—
751M16—151no—
752M16—151no—
753M16—151no—
754M16—151no—
755M16—151no—
756M16—301no—
757M16—301no—
758M16—301no—
759M16—301no—
760M16C2×D3×D511yescharacteristic
761C2×C8—21no—
762C2×C8—31no—
763C2×C8—51no—
764C2×C8—51no—
765C2×C8—51no—
766C2×C8—51no—
767C2×C8—51no—
768C2×C8—61no—
769C2×C8—101no—
770C2×C8—101no—
771C2×C8—101no—
772C2×C8—101no—
773C2×C8—151no—
774C2×C8—301no—
775C2×C8—301no—
776C2×C8—301no—
777C2×C8—301no—
778C2×C8C2×D3×D511yescharacteristic
779C4⋊C4—301no—
780C22⋊C4—301no—
781C42—31no—
782C42—151no—
783C3×C5#295511yescharacteristic, complemented, Hall
784C22×C3—21no—
785C22×C3—51no—
786C22×C3—51no—
787C22×C3—101no—
788C22×C3—201no—
789C22×C3—202no—
790C22×C3D5×#4111yescharacteristic
791C2×D3—21no—
792C2×D3—101no—
793C2×D3—202no—
794C3×C4—21no—
795C3×C4—51no—
796C3×C4—51no—
797C3×C4—101no—
798C3×C4C22×C4×D511yescharacteristic
799C3×C4C2×D4×D511yescharacteristic
800Dic3—21no—
801Dic3—41no—
802Dic3—101no—
803Dic3—201no—
804C2×C5—21no—
805C2×C5—41no—
806C2×C5—121no—
807C2×C5C2×C4×#6711yescharacteristic
808D5—21no—
809D5—21no—
810D5—41no—
811D5—121no—
812C23—51no—
813C23—101no—
814C23—301no—
815Q8—31no—
816Q8—51no—
817Q8—101no—
818Q8—151no—
819Q8—301no—
820Q8C4×D3×D511yescharacteristic
821D4—21no—
822D4—31no—
823D4—51no—
824D4—61no—
825D4—101no—
826D4—101no—
827D4—101no—
828D4—101no—
829D4—151no—
830D4—301no—
831D4—301no—
832D4—301no—
833D4—301no—
834D4C4×D3×D511yescharacteristic
835C2×C4—21no—
836C2×C4—51no—
837C2×C4—51no—
838C2×C4—51no—
839C2×C4—51no—
840C2×C4—51no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—101no—
844C2×C4—101no—
845C2×C4—101no—
846C2×C4—101no—
847C2×C4—301no—
848C2×C4—301no—
849C2×C4—301no—
850C2×C4—301no—
851C2×C4—301no—
852C2×C4C22×D3×D511yescharacteristic
853C8—21no—
854C8—31no—
855C8—31no—
856C8—51no—
857C8—51no—
858C8—61no—
859C8—101no—
860C8—151no—
861C8—151no—
862C8—301no—
863C8D5×#6711yescharacteristic
864C8D5×#6711yescharacteristic
865C2×C3—21no—
866C2×C3—41no—
867C2×C3—101no—
868C2×C3—101no—
869C2×C3—201no—
870C2×C3C4×D4×D511yescharacteristic
871D3—41no—
872D3—201no—
873C5#8379211yescharacteristic, complemented, Sylow
874C22—21no—
875C22—51no—
876C22—51no—
877C22—61no—
878C22—101no—
879C22—201no—
880C22—202no—
881C22—301no—
882C22—602no—
883C22D5×#23511yescharacteristic
884C4—21no—
885C4—51no—
886C4—51no—
887C4—61no—
888C4—101no—
889C4—121no—
890C4—301no—
891C4—601no—
892C4C2×C4×D3×D511yescharacteristic
893C4C2×D5×#6711yescharacteristic
894C3#1061162811yescharacteristic, complemented, Sylow
895C2—21no—
896C2—41no—
897C2—101no—
898C2—101no—
899C2—121no—
900C2—201no—
901C2—601no—
902C2C4×D5×#6711yescharacteristic
subgroupG/H
centerC4C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#131C22
socleC2×C3×C5C2×C4×D4
prime radical#11755315C2
cosocleC2×C3×C4×C5C24
hypercenter#131D3×D5
hypocenterC3×C5#2955
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C8 ◁ #131

Complements

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

NH ≅ G/Ntype
1. C3×D5×#131C2semidirect
3. D5×#901C2semidirect
4. #11751246C2semidirect
5. C5×#5145C2semidirect
6. #11749434C2semidirect
7. #11749432C2semidirect
8. #11749427C2semidirect
9. #11748229C2semidirect
10. #11748207C2semidirect
11. #11748203C2semidirect
12. #11748171C2semidirect
13. #11748077C2semidirect
14. #11748075C2semidirect
15. #11747646C2semidirect
19. C3×C5×#131C22semidirect
21. #91790C22semidirect
23. C5×#901C22semidirect
24. C3×#4094C22semidirect
26. C3×#4053C22semidirect
30. C3×#4047C22semidirect
33. #91515C4semidirect
34. #91513C4semidirect
35. #91508C4semidirect
36. #91502C4semidirect
37. #91491C4semidirect
38. #91489C4semidirect
39. #91484C4semidirect
40. #91478C4semidirect
45. #91290C22semidirect
46. #91286C22semidirect
52. #91121C22semidirect
53. #91109C22semidirect
54. #91106C22semidirect
55. #91099C22semidirect
56. C5×#837C22semidirect
57. C5×#825C22semidirect
58. C5×#822C22semidirect
59. C5×#815C22semidirect
60. #90993C22semidirect
61. #90992C22semidirect
62. #90980C22semidirect
63. #90978C22semidirect
64. #90977C22semidirect
65. #90976C22semidirect
66. #90951C22semidirect
67. Dic3×#168C22semidirect
71. D5×#131D3semidirect
168. #5145D5semidirect
180. C5×#131C2×D3semidirect
184. #4094C2×D3semidirect
196. #4053C2×D3semidirect
205. #4047C2×D3semidirect
288. C3×#131C2×D5semidirect
313. #901C2×D5semidirect
319. #837C2×D5semidirect
323. #825C2×D5semidirect
327. #822C2×D5semidirect
329. #815C2×D5semidirect
599. #131D3×D5semidirect
783. C3×C5#2955semidirect
873. C5#83792semidirect
894. C3#10611628semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1312
#117553152
D5×#9012
#117512462
C5×#51452
#117494342
#117494322
#117494272
#117482292
#117482072
#117482032
#117481712
#117480772
#117480752
#117476462
#106116283
#837925