Finite Group Databasebeta

← #14418035

Subgroups — #14418035

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
1#11755315C211yesmaximal, characteristic
2D5×#948C211yesmaximal, characteristic, complemented
3D5×#907C211yesmaximal, characteristic, complemented
4#11750925C211yesmaximal, characteristic, complemented
5C5×#4823C211yesmaximal, characteristic, complemented
6C3×#65110C211yesmaximal, characteristic, complemented
7#11749442C211yesmaximal, characteristic, complemented
8#11749439C211yesmaximal, characteristic, complemented
9#11748205C211yesmaximal, characteristic, complemented
10#11748174C211yesmaximal, characteristic, complemented
11#11748171C211yesmaximal, characteristic, complemented
12#11747109C211yesmaximal, characteristic, complemented
13#11747106C211yesmaximal, characteristic, complemented
14#11747017C211yesmaximal, characteristic, complemented
15#11746975C211yesmaximal, characteristic, complemented
16#10611628—31nomaximal, Hall
17C3×D5×#41C2211yescharacteristic
18D5×#235C2211yescharacteristic
19#91839C2211yescharacteristic
20#91837C2211yescharacteristic, complemented
21#91796C2211yescharacteristic, complemented
22C5×#950C2211yescharacteristic
23C5×#948C2211yescharacteristic, complemented
24C5×#907C2211yescharacteristic, complemented
25C3×D5×M16C2211yescharacteristic
26C3×#4018C2211yescharacteristic
27#91515C411yescharacteristic, complemented
28#91513C411yescharacteristic, complemented
29#91508C411yescharacteristic, complemented
30#91502C411yescharacteristic, complemented
31#91491C411yescharacteristic, complemented
32#91489C411yescharacteristic, complemented
33#91484C411yescharacteristic, complemented
34#91478C411yescharacteristic, complemented
35#91311C2211yescharacteristic
36#91297C2211yescharacteristic
37C2×#6649C2211yescharacteristic
38#91291C2211yescharacteristic, complemented
39#91288C2211yescharacteristic, complemented
40#91284—21no—
41#91284C2211yescharacteristic, complemented
42#91283—21no—
43#91283C2211yescharacteristic, complemented
44D5×#208—21no—
45D5×#208C2211yescharacteristic
46C2×D5×C3⋊C8—21no—
47C2×D5×C3⋊C8C2211yescharacteristic
48#91268—21no—
49#91267—21no—
50D5×ΓL(1,𝔽25)—21no—
51D3×C8×D5—21no—
52C3×C5×#104C2211yescharacteristic, complemented
53#91106C2211yescharacteristic, complemented
54#91089C2211yescharacteristic, complemented
55C4×C3⋊#168C2211yescharacteristic, complemented
56C5×#822C2211yescharacteristic, complemented
57C5×#805C2211yescharacteristic, complemented
58C5×#803C2211yescharacteristic, complemented
59C3×#3969C2211yescharacteristic, complemented
60C3×#3957C2211yescharacteristic, complemented
61C3×#3937C2211yescharacteristic, complemented
62#90993C2211yescharacteristic, complemented
63#90992C2211yescharacteristic, complemented
64#90981C2211yescharacteristic, complemented
65#90979C2211yescharacteristic, complemented
66#90952C2211yescharacteristic, complemented
67Dic5×C3⋊C8C2211yescharacteristic, complemented
68#78989—51nomaximal, Hall
69#66102—31no—
70D5×#131—31no—
71D5×#131—31no—
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#65110D311yescharacteristic, complemented
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×M16C2311yescharacteristic
106C3×C42×C5C2311yescharacteristic
107#6718C2×C411yescharacteristic
108#6717C2×C411yescharacteristic
109#6716C2×C411yescharacteristic
110#6715C2×C411yescharacteristic
111#6710—21no—
112#6710C2311yescharacteristic
113C2×C3⋊#168—21no—
114C2×C3⋊#168C2311yescharacteristic
115C2×C3⋊#168C2311yescharacteristic
116#6705—21no—
117C8×D15—21no—
118C5×#216C2×C411yescharacteristic
119C5×#215C2×C411yescharacteristic
120C5×#214C2×C411yescharacteristic
121C5×#213C2×C411yescharacteristic
122C5×#208—21no—
123C5×#208C2311yescharacteristic
124C2×C5×C3⋊C8—21no—
125C2×C5×C3⋊C8C2311yescharacteristic
126C2×C5×C3⋊C8C2311yescharacteristic
127C5×ΓL(1,𝔽25)—21no—
128C5×D3×C8—21no—
129C3×#685—21no—
130C3×#683—21no—
131C3×C4×Dic5C2311yescharacteristic
132C3×#681C2311yescharacteristic
133C3×#676—21no—
134C3×C8×D5—21no—
135#6662C2×C411yescharacteristic
136#6661C2×C411yescharacteristic
137#6658C2×C411yescharacteristic
138#6657C2×C411yescharacteristic
139#6656C2×C411yescharacteristic
140#6655C2×C411yescharacteristic
141#6653C2×C411yescharacteristic
142#6652C2×C411yescharacteristic
143#6651—21no—
144#6650—21no—
145#6649—21no—
146#6649—21no—
147#6649—21no—
148#6649C2×C411yescharacteristic
149#6649C2×C411yescharacteristic
150#6649C2×C411yescharacteristic
151#6649C2×C411yescharacteristic
152#6648—21no—
153D3×#168—21no—
154D5×C3⋊C8—21no—
155D5×C3⋊C8—21no—
156D5×C3⋊C8—21no—
157D5×C3⋊C8D411yescharacteristic
158D5×C3⋊C8D411yescharacteristic
159D5×C3⋊C8D411yescharacteristic
160D5×C3⋊C8D411yescharacteristic
161#5822—51no—
162C2×#948—51no—
163C2×#907—51no—
164C3×#421—51no—
165#5124—51no—
166#5005—51no—
167#4997—51no—
168#4824—51no—
169#4824—51no—
170#4824—51no—
171#4824—51no—
172#4823—51no—
173#4823—51no—
174#4823—51no—
175#4823D511yescharacteristic, complemented
176D5×#41—31no—
177D5×#41C2×D311yescharacteristic
178C5×#135—31no—
179C5×#131—31no—
180C5×#131—31no—
181#4096—31no—
182#4096—31no—
183#4094—31no—
184#4094—31no—
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—31no—
194#4053—31no—
195#4053—61no—
196#4053—61no—
197D5×M16—31no—
198D5×M16—61no—
199D5×M16—61no—
200D5×M16C2×D311yescharacteristic
201#4050—31no—
202#4047—31no—
203#4047—31no—
204#4047—61no—
205#4047—61no—
206C2×#676—31no—
207C2×C8×D5—31no—
208C2×C8×D5—61no—
209C2×C8×D5—61no—
210#4018C2×D311yescharacteristic
211C5×#108—31no—
212C5×#104—31no—
213C5×#104C2×D311yescharacteristic, complemented
214C5×#97—31no—
215#3969—31no—
216#3969C2×D311yescharacteristic, complemented
217#3957—31no—
218#3957C2×D311yescharacteristic, complemented
219#3954—31no—
220#3954—31no—
221#3951—31no—
222#3947—31no—
223C8×Dic5—31no—
224#3937—31no—
225#3937C2×D311yescharacteristic, complemented
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×C5—21no—
236C2×C3×C4×C5C2411yescharacteristic
237#1220—21no—
238D60C22×C411yescharacteristic
239C4×D15—21no—
240Dic30C22×C411yescharacteristic
241C5×#67—21no—
242C5×D12C22×C411yescharacteristic
243C4×C5×D3—21no—
244C5×Dic6C22×C411yescharacteristic
245C3×C22⋊D5—21no—
246C3×C22⋊D5—21no—
247C3×C22⋊D5—21no—
248C2×C3×Dic5—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⋊#168—21no—
271C3⋊#168C22×C411yescharacteristic
272C3⋊#168C22×C411yescharacteristic
273C3⋊#168C2×D411yescharacteristic
274C3⋊#168C2×D411yescharacteristic
275C3×#168—21no—
276C5×C3⋊C8—21no—
277C5×C3⋊C8C22×C411yescharacteristic
278C5×C3⋊C8C22×C411yescharacteristic
279C5×C3⋊C8C2×D411yescharacteristic
280C5×C3⋊C8C2×D411yescharacteristic
281C2×C3×#41—51no—
282C2×#235—51no—
283C2×C3×M16—51no—
284C3×#117—51no—
285#951—51no—
286#951—51no—
287#950—51no—
288#950—51no—
289#950—51no—
290#950C2×D511yescharacteristic
291#949—51no—
292#949—51no—
293#948—51no—
294#948—51no—
295#948—51no—
296#948—101no—
297#948—101no—
298#948C2×D511yescharacteristic, complemented
299#942—51no—
300#942—51no—
301#932—51no—
302#932—51no—
303C2×#208—51no—
304C2×#208—51no—
305C2×#208—101no—
306C22×C3⋊C8—51no—
307C22×C3⋊C8—101no—
308#907—51no—
309#907—51no—
310#907—51no—
311#907—101no—
312#907—101no—
313#907C2×D511yescharacteristic, complemented
314C2×ΓL(1,𝔽25)—101no—
315C2×D3×C8—101no—
316C3×#104—51no—
317C3×#104—51no—
318C3×#104—51no—
319C3×#104C2×D511yescharacteristic, complemented
320#822—51no—
321#822—51no—
322#822—51no—
323#822C2×D511yescharacteristic, complemented
324#805—51no—
325#805—51no—
326#805—51no—
327#805C2×D511yescharacteristic, complemented
328#803—51no—
329#803C2×D511yescharacteristic, complemented
330C4×C3⋊C8—51no—
331C4×C3⋊C8—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—31no—
358C5×M16—61no—
359C5×M16—61no—
360C5×M16C22×D311yescharacteristic
361C2×C5×C8—31no—
362C2×C5×C8—31no—
363C2×C5×C8—61no—
364C2×C5×C8—61no—
365C42×C5C22×D311yescharacteristic
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—21no—
375#683—21no—
376C4×Dic5C22×D311yescharacteristic
377#681—31no—
378#681—61no—
379#681—61no—
380#681C22×D311yescharacteristic
381C2×#168—31no—
382C2×#168—31no—
383C2×#168—61no—
384C2×#168—61no—
385Dic20—31no—
386D40—31no—
387#677—31no—
388#677—31no—
389#676—21no—
390#676—31no—
391#676—31no—
392#676—31no—
393#676—31no—
394#676—61no—
395#676—61no—
396#676—61no—
397#676—61no—
398#676—61no—
399C8×D5—21no—
400C8×D5—31no—
401C8×D5—31no—
402C8×D5—31no—
403C8×D5—31no—
404C8×D5—61no—
405C8×D5—61no—
406C8×D5—61no—
407C8×D5—61no—
408C8×D5—61no—
409#575—151no—
410C2×#131—151no—
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—51no—
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×C5—41no—
436C3×C4×C5C23×C411yescharacteristic
437C3×C4×C5C22×D411yescharacteristic
438Dic15—21no—
439C3×Dic5—21no—
440C3×Dic5—41no—
441C3×Dic5C4×D411yescharacteristic
442C3×Dic5C4×D411yescharacteristic
443C5×Dic3—21no—
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—51no—
466C3×M16—101no—
467C3×M16C22×D511yescharacteristic
468C2×C3×C8—101no—
469C3×C4⋊C4—101no—
470C3×C22⋊C4—101no—
471C3×C42—51no—
472C3×C42C22×D511yescharacteristic
473#216—51no—
474#216—51no—
475#216—51no—
476#216C4×D511yescharacteristic
477#215—51no—
478#215—51no—
479#215—51no—
480#215C4×D511yescharacteristic
481#214—51no—
482#214—51no—
483#214—51no—
484#214C4×D511yescharacteristic
485#213—51no—
486#213—51no—
487#213—51no—
488#213C4×D511yescharacteristic
489#208—21no—
490#208—51no—
491#208—51no—
492#208—51no—
493#208—51no—
494#208—51no—
495#208—101no—
496#208—101no—
497#208—101no—
498#208—101no—
499#208C22×D511yescharacteristic
500C2×C3⋊C8—21no—
501C2×C3⋊C8—51no—
502C2×C3⋊C8—51no—
503C2×C3⋊C8—51no—
504C2×C3⋊C8—51no—
505C2×C3⋊C8—51no—
506C2×C3⋊C8—51no—
507C2×C3⋊C8—101no—
508C2×C3⋊C8—101no—
509C2×C3⋊C8—101no—
510C2×C3⋊C8—101no—
511C2×C3⋊C8C22×D511yescharacteristic
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#23711yescharacteristic
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—21no—
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—21no—
542C2×Dic5—61no—
543C2×Dic5#23711yescharacteristic
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×D5D3×D411yescharacteristic
557C4×D5D3×D411yescharacteristic
558Dic10—21no—
559Dic10—31no—
560Dic10—61no—
561Dic10C2×C4×D311yescharacteristic
562C5×C8—21no—
563C5×C8—31no—
564C5×C8—31no—
565C5×C8—31no—
566C5×C8—31no—
567C5×C8—61no—
568#168—21no—
569#168—31no—
570#168—31no—
571#168—31no—
572#168—31no—
573#168—61no—
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—31no—
590#131—151no—
591#131—151no—
592#131—151no—
593#131—151no—
594#131—151no—
595#131—151no—
596#131—301no—
597#131—301no—
598#131—301no—
599#131—301no—
600C2×M16—51no—
601C2×M16—151no—
602C2×M16—151no—
603C2×M16—301no—
604C2×M16—301no—
605C22×C8—151no—
606C22×C8—301no—
607C22×C8—301no—
608#117—51no—
609#108—31no—
610#108—151no—
611#108—151no—
612#108—151no—
613#104—31no—
614#104—51no—
615#104—51no—
616#104—51no—
617#104—151no—
618#104—151no—
619#104—151no—
620#104D3×D511yescharacteristic, complemented
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—21no—
648C2×C3×C4—51no—
649C2×C3×C4—51no—
650C2×C3×C4—51no—
651C2×C3×C4—51no—
652C2×C3×C4—51no—
653C2×C3×C4—101no—
654C2×C3×C4—101no—
655C2×C3×C4—101no—
656C2×C3×C4—101no—
657C2×C3×C4—101no—
658C2×C3×C4C23×D511yescharacteristic
659#67—21no—
660#67—101no—
661#67—101no—
662#67—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—101no—
676C3⋊C8—21no—
677C3⋊C8—51no—
678C3⋊C8—51no—
679C3⋊C8—51no—
680C3⋊C8—51no—
681C3⋊C8—101no—
682C3⋊C8C2×C4×D511yescharacteristic
683C3⋊C8C2×C4×D511yescharacteristic
684C3⋊C8D4×D511yescharacteristic
685C3⋊C8D4×D511yescharacteristic
686C22×C5—21no—
687C22×C5—61no—
688C22×C5C2×#23711yescharacteristic
689C2×D5—21no—
690C2×D5—41no—
691C2×D5—42no—
692C2×D5—61no—
693C2×D5—122no—
694C2×D5#67⋊C411yescharacteristic
695C2×D5#67⋊C411yescharacteristic
696C4×C5—21no—
697C4×C5—41no—
698C4×C5—61no—
699C4×C5C22×C4×D311yescharacteristic
700C4×C5C2×D3×D411yescharacteristic
701Dic5—21no—
702Dic5—41no—
703Dic5—61no—
704Dic5#67⋊C411yescharacteristic
705Dic5#67⋊C411yescharacteristic
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—31no—
744M16—51no—
745M16—61no—
746M16—61no—
747M16—101no—
748M16—151no—
749M16—151no—
750M16—151no—
751M16—151no—
752M16—151no—
753M16—301no—
754M16—301no—
755M16—301no—
756M16—301no—
757M16—301no—
758M16—301no—
759M16—301no—
760M16C2×D3×D511yescharacteristic
761C2×C8—31no—
762C2×C8—31no—
763C2×C8—61no—
764C2×C8—61no—
765C2×C8—101no—
766C2×C8—151no—
767C2×C8—151no—
768C2×C8—151no—
769C2×C8—151no—
770C2×C8—151no—
771C2×C8—151no—
772C2×C8—301no—
773C2×C8—301no—
774C2×C8—301no—
775C2×C8—301no—
776C2×C8—301no—
777C2×C8—301no—
778C2×C8—301no—
779C4⋊C4—101no—
780C22⋊C4—101no—
781C42—51no—
782C42C2×D3×D511yescharacteristic
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—41no—
796C3×C4—51no—
797C3×C4—51no—
798C3×C4—101no—
799C3×C4—201no—
800C3×C4C22×C4×D511yescharacteristic
801C3×C4C2×D4×D511yescharacteristic
802Dic3—21no—
803Dic3—101no—
804C2×C5—21no—
805C2×C5—41no—
806C2×C5—121no—
807C2×C5C2×#67⋊C411yescharacteristic
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—21no—
837C2×C4—51no—
838C2×C4—51no—
839C2×C4—51no—
840C2×C4—51no—
841C2×C4—51no—
842C2×C4—61no—
843C2×C4—101no—
844C2×C4—101no—
845C2×C4—101no—
846C2×C4—101no—
847C2×C4—101no—
848C2×C4—301no—
849C2×C4—301no—
850C2×C4—301no—
851C2×C4—301no—
852C2×C4C22×D3×D511yescharacteristic
853C8—21no—
854C8—31no—
855C8—31no—
856C8—31no—
857C8—31no—
858C8—61no—
859C8—101no—
860C8—151no—
861C8—151no—
862C8—151no—
863C8—151no—
864C8—301no—
865C2×C3—21no—
866C2×C3—41no—
867C2×C3—101no—
868C2×C3—101no—
869C2×C3—201no—
870C2×C3C4×D4×D511yescharacteristic
871D3—41no—
872D3—201no—
873C5#7898911yescharacteristic, complemented, Sylow
874C22—21no—
875C22—51no—
876C22—51no—
877C22—61no—
878C22—101no—
879C22—201no—
880C22—202no—
881C22—301no—
882C22—602no—
883C22D5×#23711yescharacteristic
884C4—21no—
885C4—41no—
886C4—51no—
887C4—51no—
888C4—61no—
889C4—101no—
890C4—201no—
891C4—301no—
892C4C2×C4×D3×D511yescharacteristic
893C4D3×D4×D511yescharacteristic
894C3#1061162811yescharacteristic, complemented, Sylow
895C2—21no—
896C2—41no—
897C2—101no—
898C2—101no—
899C2—121no—
900C2—201no—
901C2—601no—
902C2D5×#67⋊C411yescharacteristic
subgroupG/H
centerC4D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#104C22
socleC2×C3×C5C2×C4×D4
prime radical#11755315C2
cosocleC2×C3×C4×C5C24
hypercenter#104D3×D5
hypocenterC3×C5#2955
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. D5×#948C2semidirect
3. D5×#907C2semidirect
4. #11750925C2semidirect
5. C5×#4823C2semidirect
6. C3×#65110C2semidirect
7. #11749442C2semidirect
8. #11749439C2semidirect
9. #11748205C2semidirect
10. #11748174C2semidirect
11. #11748171C2semidirect
12. #11747109C2semidirect
13. #11747106C2semidirect
14. #11747017C2semidirect
15. #11746975C2semidirect
20. #91837C22semidirect
21. #91796C22semidirect
23. C5×#948C22semidirect
24. C5×#907C22semidirect
27. #91515C4semidirect
28. #91513C4semidirect
29. #91508C4semidirect
30. #91502C4semidirect
31. #91491C4semidirect
32. #91489C4semidirect
33. #91484C4semidirect
34. #91478C4semidirect
38. #91291C22semidirect
39. #91288C22semidirect
41. #91284C22semidirect
43. #91283C22semidirect
52. C3×C5×#104C22semidirect
53. #91106C22semidirect
54. #91089C22semidirect
55. C4×C3⋊#168C22semidirect
56. C5×#822C22semidirect
57. C5×#805C22semidirect
58. C5×#803C22semidirect
59. C3×#3969C22semidirect
60. C3×#3957C22semidirect
61. C3×#3937C22semidirect
62. #90993C22semidirect
63. #90992C22semidirect
64. #90981C22semidirect
65. #90979C22semidirect
66. #90952C22semidirect
67. Dic5×C3⋊C8C22semidirect
81. #65110D3semidirect
175. #4823D5semidirect
213. C5×#104C2×D3semidirect
216. #3969C2×D3semidirect
218. #3957C2×D3semidirect
225. #3937C2×D3semidirect
298. #948C2×D5semidirect
313. #907C2×D5semidirect
319. C3×#104C2×D5semidirect
323. #822C2×D5semidirect
327. #805C2×D5semidirect
329. #803C2×D5semidirect
620. #104D3×D5semidirect
783. C3×C5#2955semidirect
873. C5#78989semidirect
894. C3#10611628semidirect

Maximal subgroups

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

subgroupindex
#117553152
D5×#9482
D5×#9072
#117509252
C5×#48232
C3×#651102
#117494422
#117494392
#117482052
#117481742
#117481712
#117471092
#117471062
#117470172
#117469752
#106116283
#789895