Finite Group Databasebeta

← #14418033

Subgroups — #14418033

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#11755322C211yesmaximal, characteristic
2D3×#4094C211yesmaximal, characteristic, complemented
3D3×#4053C211yesmaximal, characteristic, complemented
4#11750925C211yesmaximal, characteristic, complemented
5C5×#4821C211yesmaximal, characteristic, complemented
6C3×#65112C211yesmaximal, characteristic, complemented
7#11749440C211yesmaximal, characteristic, complemented
8#11749435C211yesmaximal, characteristic, complemented
9#11748202C211yesmaximal, characteristic, complemented
10#11748176C211yesmaximal, characteristic, complemented
11#11748172C211yesmaximal, characteristic, complemented
12#11747111C211yesmaximal, characteristic, complemented
13#11747106C211yesmaximal, characteristic, complemented
14#11747019C211yesmaximal, characteristic, complemented
15#11746979C211yesmaximal, characteristic, complemented
16#10610720—31nomaximal, Hall
17C5×D3×#41C2211yescharacteristic
18D3×#709C2211yescharacteristic
19#91839C2211yescharacteristic
20#91837C2211yescharacteristic, complemented
21#91796C2211yescharacteristic, complemented
22C5×D3×M16C2211yescharacteristic
23C5×#872C2211yescharacteristic
24C3×#4096C2211yescharacteristic
25C3×#4094C2211yescharacteristic, complemented
26C3×#4053C2211yescharacteristic, complemented
27#91520C411yescharacteristic, complemented
28#91518C411yescharacteristic, complemented
29#91510C411yescharacteristic, complemented
30#91504C411yescharacteristic, complemented
31#91496C411yescharacteristic, complemented
32#91494C411yescharacteristic, complemented
33#91486C411yescharacteristic, complemented
34#91480C411yescharacteristic, complemented
35#91303C2211yescharacteristic
36#91297C2211yescharacteristic
37C2×#6650C2211yescharacteristic
38#91290C2211yescharacteristic, complemented
39#91288—21no—
40#91288C2211yescharacteristic, complemented
41D3×#681—21no—
42D3×#681C2211yescharacteristic
43#91286—21no—
44#91286C2211yescharacteristic, complemented
45C2×D3×#168—21no—
46C2×D3×#168C2211yescharacteristic
47#91284C2211yescharacteristic, complemented
48#91268—21no—
49#91266—21no—
50D3×#676—21no—
51D3×C8×D5—21no—
52C3×C5×#104C2211yescharacteristic, complemented
53#91106C2211yescharacteristic, complemented
54#91089C2211yescharacteristic, complemented
55C4×C3⋊#168C2211yescharacteristic, complemented
56C5×#837C2211yescharacteristic, complemented
57C5×#825C2211yescharacteristic, complemented
58C5×#805C2211yescharacteristic, complemented
59C3×#3954C2211yescharacteristic, complemented
60C3×#3937C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62#90992C2211yescharacteristic, complemented
63#90991C2211yescharacteristic, complemented
64#90980C2211yescharacteristic, complemented
65#90977C2211yescharacteristic, complemented
66#90953C2211yescharacteristic, complemented
67Dic3×#168C2211yescharacteristic, complemented
68#79897—51nomaximal, Hall
69#66156—31no—
70C2×#4094—31no—
71C2×#4053—31no—
72C5×#421—31no—
73#65413—31no—
74#65294—31no—
75#65286—31no—
76#65113—31no—
77#65113—31no—
78#65113—31no—
79#65113—31no—
80#65112—31no—
81#65112—31no—
82#65112—31no—
83#65112D311yescharacteristic, complemented
84C3×C5×#41C2311yescharacteristic
85#6817C2311yescharacteristic
86C5×#239C2×C411yescharacteristic
87C5×D3×Q8C2×C411yescharacteristic
88C5×#237—21no—
89C5×#237C2×C411yescharacteristic
90C5×D3×D4—21no—
91C5×D3×D4C2×C411yescharacteristic
92C5×#235—21no—
93C5×#235C2311yescharacteristic
94C2×C4×C5×D3—21no—
95C2×C4×C5×D3C2311yescharacteristic
96C3×#709C2311yescharacteristic
97D3×C22⋊D5—21no—
98#6779—21no—
99D3×D20C2×C411yescharacteristic
100C4×D3×D5—21no—
101#6771—21no—
102#6769C2×C411yescharacteristic
103D3×Dic10C2×C411yescharacteristic
104#6765C2×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×(C2×D3)⋊C4—21no—
119C5×Dic3⋊C4—21no—
120C4×C5×Dic3C2311yescharacteristic
121C5×#208C2311yescharacteristic
122C5×ΓL(1,𝔽25)—21no—
123C5×D3×C8—21no—
124C3×#689C2×C411yescharacteristic
125C3×#688C2×C411yescharacteristic
126C3×#687C2×C411yescharacteristic
127C3×#686C2×C411yescharacteristic
128C3×#681—21no—
129C3×#681C2311yescharacteristic
130C2×C3×#168—21no—
131C2×C3×#168C2311yescharacteristic
132C2×C3×#168C2311yescharacteristic
133C3×#676—21no—
134C3×C8×D5—21no—
135#6663C2×C411yescharacteristic
136#6661C2×C411yescharacteristic
137#6660C2×C411yescharacteristic
138#6659C2×C411yescharacteristic
139#6656C2×C411yescharacteristic
140#6655C2×C411yescharacteristic
141#6654C2×C411yescharacteristic
142#6652C2×C411yescharacteristic
143#6651—21no—
144#6650—21no—
145#6650—21no—
146#6650—21no—
147#6650C2×C411yescharacteristic
148#6650C2×C411yescharacteristic
149#6650C2×C411yescharacteristic
150#6650C2×C411yescharacteristic
151#6649—21no—
152#6648—21no—
153D3×#168—21no—
154D3×#168—21no—
155D3×#168—21no—
156D3×#168D411yescharacteristic
157D3×#168D411yescharacteristic
158D3×#168D411yescharacteristic
159D3×#168D411yescharacteristic
160D5×C3⋊C8—21no—
161#5768—51no—
162D3×#131—51no—
163D3×#131—51no—
164C3×#444—51no—
165#5196—51no—
166#5145—51no—
167#5145—51no—
168#4895—51no—
169#4893—51no—
170#4824—51no—
171#4824—51no—
172#4821—51no—
173#4821D511yescharacteristic, complemented
174#4717—51no—
175#4708—51no—
176C2×C5×#41—31no—
177C2×#709—31no—
178C2×C5×M16—31no—
179C5×#117—31no—
180#4097—31no—
181#4097—31no—
182#4096—31no—
183#4096—31no—
184#4096—31no—
185#4096C2×D311yescharacteristic
186#4095—31no—
187#4095—31no—
188#4094—31no—
189#4094—31no—
190#4094—31no—
191#4094—61no—
192#4094—61no—
193#4094C2×D311yescharacteristic, complemented
194#4088—31no—
195#4088—31no—
196#4078—31no—
197#4078—31no—
198C2×#681—31no—
199C2×#681—31no—
200C2×#681—61no—
201C22×#168—31no—
202C22×#168—61no—
203#4053—31no—
204#4053—31no—
205#4053—31no—
206#4053—61no—
207#4053—61no—
208#4053C2×D311yescharacteristic, complemented
209C2×#676—61no—
210C2×C8×D5—61no—
211C5×#104—31no—
212C5×#104—31no—
213C5×#104—31no—
214C5×#104C2×D311yescharacteristic, complemented
215#3954—31no—
216#3954—31no—
217#3954—31no—
218#3954C2×D311yescharacteristic, complemented
219#3937—31no—
220#3937—31no—
221#3937—31no—
222#3937C2×D311yescharacteristic, complemented
223#3935—31no—
224#3935C2×D311yescharacteristic, complemented
225C4×#168—31no—
226C4×#168—31no—
227#2955—151noSylow
228C22×C5×D3—21no—
229C22×C5×D3#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×#67—21no—
243C5×#67—21no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3—21no—
246C2×C5×Dic3#4111yescharacteristic
247C5×D12—21no—
248C5×D12C22×C411yescharacteristic
249C4×C5×D3—21no—
250C4×C5×D3—21no—
251C4×C5×D3—21no—
252C4×C5×D3C22×C411yescharacteristic
253C4×C5×D3C22×C411yescharacteristic
254C4×C5×D3C2×D411yescharacteristic
255C4×C5×D3C2×D411yescharacteristic
256C5×Dic6—21no—
257C5×Dic6C22×C411yescharacteristic
258C3×C22⋊D5—21no—
259C3×D20C22×C411yescharacteristic
260C3×C4×D5—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—
276C3×#168C22×C411yescharacteristic
277C3×#168C22×C411yescharacteristic
278C3×#168C2×D411yescharacteristic
279C3×#168C2×D411yescharacteristic
280C5×C3⋊C8—21no—
281D3×#41—51no—
282D3×#41C2×D511yescharacteristic
283C3×#135—51no—
284C3×#131—51no—
285C3×#131—51no—
286#950—51no—
287#950—51no—
288#948—51no—
289#948—51no—
290#918—51no—
291#918—51no—
292#915—51no—
293#915—51no—
294#914—51no—
295#914—51no—
296#911—51no—
297#911—51no—
298#907—51no—
299#907—51no—
300#907—101no—
301#907—101no—
302D3×M16—51no—
303D3×M16—101no—
304D3×M16—101no—
305D3×M16C2×D511yescharacteristic
306#904—51no—
307#901—51no—
308#901—51no—
309#901—101no—
310#901—101no—
311C2×ΓL(1,𝔽25)—51no—
312C2×D3×C8—51no—
313C2×D3×C8—101no—
314C2×D3×C8—101no—
315#872C2×D511yescharacteristic
316C3×#108—51no—
317C3×#104—51no—
318C3×#104C2×D511yescharacteristic, complemented
319C3×#97—51no—
320#837—51no—
321#837C2×D511yescharacteristic, complemented
322#825—51no—
323#825C2×D511yescharacteristic, complemented
324#822—51no—
325#822—51no—
326#819—51no—
327#815—51no—
328C8×Dic3—51no—
329#805—51no—
330#805C2×D511yescharacteristic, complemented
331C4×C3⋊C8—51no—
332C5×#41—31no—
333C5×#41—31no—
334C5×#41—31no—
335C5×#41—61no—
336C5×#41—61no—
337C5×#41C22×D311yescharacteristic
338C2×C5×Q8—31no—
339C2×C5×D4—31no—
340C2×C5×D4—61no—
341C22×C4×C5—31no—
342C22×C4×C5—61no—
343C2×C22⋊D5—61no—
344#709—31no—
345#709—31no—
346#709—31no—
347#709—61no—
348#709—61no—
349#709C22×D311yescharacteristic
350C2×D20—31no—
351C2×C4×D5—61no—
352C2×Dic10—31no—
353C5×M16—31no—
354C5×M16—61no—
355C5×M16C22×D311yescharacteristic
356C2×C5×C8—61no—
357C5×C4⋊C4—61no—
358C5×C22⋊C4—61no—
359C42×C5—31no—
360C42×C5C22×D311yescharacteristic
361#689—31no—
362#689—31no—
363#689—31no—
364#689C4×D311yescharacteristic
365#688—31no—
366#688—31no—
367#688—31no—
368#688C4×D311yescharacteristic
369#687—31no—
370#687—31no—
371#687—31no—
372#687C4×D311yescharacteristic
373#686—31no—
374#686—31no—
375#686—31no—
376#686C4×D311yescharacteristic
377#681—21no—
378#681—31no—
379#681—31no—
380#681—31no—
381#681—31no—
382#681—31no—
383#681—61no—
384#681—61no—
385#681—61no—
386#681—61no—
387#681C22×D311yescharacteristic
388C2×#168—21no—
389C2×#168—31no—
390C2×#168—31no—
391C2×#168—31no—
392C2×#168—31no—
393C2×#168—31no—
394C2×#168—31no—
395C2×#168—61no—
396C2×#168—61no—
397C2×#168—61no—
398C2×#168—61no—
399C2×#168C22×D311yescharacteristic
400C2×#168C22×D311yescharacteristic
401#676—21no—
402#676—61no—
403#676—61no—
404#676—61no—
405C8×D5—21no—
406C8×D5—61no—
407C8×D5—61no—
408C8×D5—61no—
409#575—151no—
410C2×#131—151no—
411C2×#131—151no—
412#444—51no—
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—31no—
422#421—151no—
423#405—151no—
424C22×C3×C5—21no—
425C22×C3×C5C2×#4111yescharacteristic
426C2×D15—21no—
427C2×C5×D3—21no—
428C2×C5×D3—41no—
429C2×C5×D3—42no—
430C2×C5×D3C4×D411yescharacteristic
431C2×C5×D3C4×D411yescharacteristic
432C2×C3×D5—21no—
433D3×D5—42no—
434C3×C4×C5—21no—
435C3×C4×C5—41no—
436C3×C4×C5C23×C411yescharacteristic
437C3×C4×C5C22×D411yescharacteristic
438Dic15—21no—
439C3×Dic5—21no—
440C5×Dic3—21no—
441C5×Dic3—41no—
442C5×Dic3C4×D411yescharacteristic
443C5×Dic3C4×D411yescharacteristic
444C3×#41—51no—
445C3×#41C22×D511yescharacteristic
446#239—51no—
447#239C4×D511yescharacteristic
448D3×Q8—51no—
449D3×Q8C4×D511yescharacteristic
450#237—21no—
451#237—51no—
452#237—101no—
453#237C4×D511yescharacteristic
454D3×D4—21no—
455D3×D4—51no—
456D3×D4—101no—
457D3×D4C4×D511yescharacteristic
458#235—21no—
459#235—51no—
460#235—101no—
461#235C22×D511yescharacteristic
462C2×C4×D3—21no—
463C2×C4×D3—101no—
464C2×C4×D3C22×D511yescharacteristic
465C3×Q16—51no—
466C3×SD16—51no—
467C3×SD16—51no—
468C3×D8—51no—
469C3×M16—51no—
470C3×M16—101no—
471C3×M16—101no—
472C3×M16C22×D511yescharacteristic
473C2×C3×C8—51no—
474C2×C3×C8—51no—
475C2×C3×C8—101no—
476C2×C3×C8—101no—
477C3×C42C22×D511yescharacteristic
478#216—51no—
479#216—51no—
480#215—51no—
481#215—51no—
482#214—51no—
483#214—51no—
484#213—51no—
485#213—51no—
486(C2×D3)⋊C4—21no—
487Dic3⋊C4—21no—
488C4×Dic3C22×D511yescharacteristic
489#208—51no—
490#208—101no—
491#208—101no—
492#208C22×D511yescharacteristic
493C2×C3⋊C8—51no—
494C2×C3⋊C8—51no—
495C2×C3⋊C8—101no—
496C2×C3⋊C8—101no—
497Dic12—51no—
498D24—51no—
499#204—51no—
500#204—51no—
501ΓL(1,𝔽25)—21no—
502ΓL(1,𝔽25)—51no—
503ΓL(1,𝔽25)—51no—
504ΓL(1,𝔽25)—51no—
505ΓL(1,𝔽25)—51no—
506ΓL(1,𝔽25)—101no—
507ΓL(1,𝔽25)—101no—
508ΓL(1,𝔽25)—101no—
509ΓL(1,𝔽25)—101no—
510ΓL(1,𝔽25)—101no—
511D3×C8—21no—
512D3×C8—51no—
513D3×C8—51no—
514D3×C8—51no—
515D3×C8—51no—
516D3×C8—101no—
517D3×C8—101no—
518D3×C8—101no—
519D3×C8—101no—
520D3×C8—101no—
521C23×C5—31no—
522C23×C5—61no—
523C22×D5—61no—
524C5×Q8—31no—
525C5×Q8—61no—
526C5×Q8C2×C4×D311yescharacteristic
527C5×D4—21no—
528C5×D4—31no—
529C5×D4—61no—
530C5×D4—61no—
531C5×D4—61no—
532C5×D4—61no—
533C5×D4C2×C4×D311yescharacteristic
534C2×C4×C5—21no—
535C2×C4×C5—21no—
536C2×C4×C5—31no—
537C2×C4×C5—31no—
538C2×C4×C5—31no—
539C2×C4×C5—31no—
540C2×C4×C5—31no—
541C2×C4×C5—61no—
542C2×C4×C5—61no—
543C2×C4×C5—61no—
544C2×C4×C5—61no—
545C2×C4×C5—61no—
546C2×C4×C5C23×D311yescharacteristic
547C22⋊D5—21no—
548C22⋊D5—61no—
549C22⋊D5—61no—
550C22⋊D5—61no—
551C2×Dic5—61no—
552D20—31no—
553D20—61no—
554D20C2×C4×D311yescharacteristic
555C4×D5—21no—
556C4×D5—61no—
557C4×D5—61no—
558C4×D5—61no—
559Dic10—31no—
560Dic10—61no—
561Dic10C2×C4×D311yescharacteristic
562C5×C8—21no—
563C5×C8—61no—
564#168—21no—
565#168—31no—
566#168—31no—
567#168—31no—
568#168—31no—
569#168—61no—
570#168C2×C4×D311yescharacteristic
571#168C2×C4×D311yescharacteristic
572#168D3×D411yescharacteristic
573#168D3×D411yescharacteristic
574C2×#41—31no—
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—51no—
585#135—151no—
586#135—151no—
587#135—151no—
588#131—51no—
589#131—51no—
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—31no—
601C2×M16—151no—
602C2×M16—151no—
603C2×M16—301no—
604C2×M16—301no—
605C22×C8—151no—
606C22×C8—301no—
607C22×C8—301no—
608#117—31no—
609#108—51no—
610#108—151no—
611#108—151no—
612#108—151no—
613#104—31no—
614#104—31no—
615#104—31no—
616#104—51no—
617#104—151no—
618#104—151no—
619#104—151no—
620#104D3×D511yescharacteristic, complemented
621#97—51no—
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—41no—
630C5×D3—21no—
631C5×D3—21no—
632C5×D3—41no—
633C22×D3—21no—
634C22×D3—101no—
635C22×D3#71111yescharacteristic
636C3×Q8—51no—
637C3×Q8C2×C4×D511yescharacteristic
638C3×D4—21no—
639C3×D4—51no—
640C3×D4—101no—
641C3×D4C2×C4×D511yescharacteristic
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—101no—
645C2×C3×C4C23×D511yescharacteristic
646#67—21no—
647#67—21no—
648#67—21no—
649#67—101no—
650#67—101no—
651#67—101no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—101no—
655C2×Dic3#71111yescharacteristic
656D12—21no—
657D12—51no—
658D12—101no—
659D12C2×C4×D511yescharacteristic
660C4×D3—21no—
661C4×D3—21no—
662C4×D3—21no—
663C4×D3—101no—
664C4×D3—101no—
665C4×D3—101no—
666C4×D3C2×C4×D511yescharacteristic
667C4×D3C2×C4×D511yescharacteristic
668C4×D3D4×D511yescharacteristic
669C4×D3D4×D511yescharacteristic
670Dic6—21no—
671Dic6—51no—
672Dic6—101no—
673Dic6C2×C4×D511yescharacteristic
674C3×C8—21no—
675C3×C8—51no—
676C3×C8—51no—
677C3×C8—51no—
678C3×C8—51no—
679C3×C8—101no—
680C3⋊C8—21no—
681C3⋊C8—51no—
682C3⋊C8—51no—
683C3⋊C8—51no—
684C3⋊C8—51no—
685C3⋊C8—101no—
686C22×C5—21no—
687C22×C5—31no—
688C22×C5—31no—
689C22×C5—61no—
690C22×C5—121no—
691C22×C5—122no—
692C22×C5D3×#4111yescharacteristic
693C2×D5—21no—
694C2×D5—61no—
695C2×D5—122no—
696C4×C5—21no—
697C4×C5—31no—
698C4×C5—31no—
699C4×C5—41no—
700C4×C5—61no—
701C4×C5—121no—
702C4×C5C22×C4×D311yescharacteristic
703C4×C5C2×D3×D411yescharacteristic
704Dic5—21no—
705Dic5—61no—
706#41—31no—
707#41—31no—
708#41—31no—
709#41—51no—
710#41—61no—
711#41—61no—
712#41—151no—
713#41—151no—
714#41—151no—
715#41—301no—
716#41—301no—
717#41C2×D3×D511yescharacteristic
718C2×Q8—31no—
719C2×Q8—151no—
720C2×D4—31no—
721C2×D4—61no—
722C2×D4—151no—
723C2×D4—301no—
724C22×C4—31no—
725C22×C4—61no—
726C22×C4—301no—
727Q16—51no—
728Q16—151no—
729Q16—151no—
730Q16—151no—
731SD16—51no—
732SD16—51no—
733SD16—151no—
734SD16—151no—
735SD16—151no—
736SD16—151no—
737SD16—151no—
738SD16—151no—
739D8—51no—
740D8—151no—
741D8—151no—
742D8—151no—
743M16—31no—
744M16—51no—
745M16—61no—
746M16—101no—
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—51no—
762C2×C8—51no—
763C2×C8—61no—
764C2×C8—101no—
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—61no—
780C22⋊C4—61no—
781C42—31no—
782C42C2×D3×D511yescharacteristic
783C3×C5#295511yescharacteristic, complemented, Hall
784C22×C3—21no—
785C22×C3—101no—
786C22×C3C2×#71111yescharacteristic
787C2×D3—21no—
788C2×D3—41no—
789C2×D3—42no—
790C2×D3—101no—
791C2×D3—202no—
792C2×D3#402711yescharacteristic
793C2×D3#402711yescharacteristic
794C3×C4—21no—
795C3×C4—41no—
796C3×C4—101no—
797C3×C4C22×C4×D511yescharacteristic
798C3×C4C2×D4×D511yescharacteristic
799Dic3—21no—
800Dic3—41no—
801Dic3—101no—
802Dic3#402711yescharacteristic
803Dic3#402711yescharacteristic
804C2×C5—21no—
805C2×C5—41no—
806C2×C5—61no—
807C2×C5—61no—
808C2×C5—121no—
809C2×C5C4×D3×D411yescharacteristic
810D5—41no—
811D5—121no—
812C23—31no—
813C23—61no—
814C23—301no—
815Q8—31no—
816Q8—51no—
817Q8—61no—
818Q8—151no—
819Q8—301no—
820Q8C4×D3×D511yescharacteristic
821D4—21no—
822D4—31no—
823D4—51no—
824D4—61no—
825D4—61no—
826D4—61no—
827D4—61no—
828D4—101no—
829D4—151no—
830D4—301no—
831D4—301no—
832D4—301no—
833D4—301no—
834D4C4×D3×D511yescharacteristic
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—31no—
838C2×C4—31no—
839C2×C4—31no—
840C2×C4—31no—
841C2×C4—31no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—101no—
848C2×C4—301no—
849C2×C4—301no—
850C2×C4—301no—
851C2×C4—301no—
852C2×C4C22×D3×D511yescharacteristic
853C8—21no—
854C8—51no—
855C8—51no—
856C8—51no—
857C8—51no—
858C8—61no—
859C8—101no—
860C8—151no—
861C8—151no—
862C8—151no—
863C8—151no—
864C8—301no—
865C2×C3—21no—
866C2×C3—41no—
867C2×C3—201no—
868C2×C3C2×#402711yescharacteristic
869D3—21no—
870D3—21no—
871D3—41no—
872D3—201no—
873C5#7989711yescharacteristic, complemented, Sylow
874C22—21no—
875C22—31no—
876C22—31no—
877C22—61no—
878C22—101no—
879C22—121no—
880C22—122no—
881C22—301no—
882C22—602no—
883C22D3×#71111yescharacteristic
884C4—21no—
885C4—31no—
886C4—31no—
887C4—41no—
888C4—61no—
889C4—101no—
890C4—121no—
891C4—301no—
892C4C2×C4×D3×D511yescharacteristic
893C4D3×D4×D511yescharacteristic
894C3#1061072011yescharacteristic, complemented, Sylow
895C2—21no—
896C2—41no—
897C2—61no—
898C2—61no—
899C2—121no—
900C2—201no—
901C2—601no—
902C2D3×#402711yescharacteristic
subgroupG/H
centerC4D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#104C22
socleC2×C3×C5C2×C4×D4
prime radical#11755322C2
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. D3×#4094C2semidirect
3. D3×#4053C2semidirect
4. #11750925C2semidirect
5. C5×#4821C2semidirect
6. C3×#65112C2semidirect
7. #11749440C2semidirect
8. #11749435C2semidirect
9. #11748202C2semidirect
10. #11748176C2semidirect
11. #11748172C2semidirect
12. #11747111C2semidirect
13. #11747106C2semidirect
14. #11747019C2semidirect
15. #11746979C2semidirect
20. #91837C22semidirect
21. #91796C22semidirect
25. C3×#4094C22semidirect
26. C3×#4053C22semidirect
27. #91520C4semidirect
28. #91518C4semidirect
29. #91510C4semidirect
30. #91504C4semidirect
31. #91496C4semidirect
32. #91494C4semidirect
33. #91486C4semidirect
34. #91480C4semidirect
38. #91290C22semidirect
40. #91288C22semidirect
44. #91286C22semidirect
47. #91284C22semidirect
52. C3×C5×#104C22semidirect
53. #91106C22semidirect
54. #91089C22semidirect
55. C4×C3⋊#168C22semidirect
56. C5×#837C22semidirect
57. C5×#825C22semidirect
58. C5×#805C22semidirect
59. C3×#3954C22semidirect
60. C3×#3937C22semidirect
61. C3×#3935C22semidirect
62. #90992C22semidirect
63. #90991C22semidirect
64. #90980C22semidirect
65. #90977C22semidirect
66. #90953C22semidirect
67. Dic3×#168C22semidirect
83. #65112D3semidirect
173. #4821D5semidirect
193. #4094C2×D3semidirect
208. #4053C2×D3semidirect
214. C5×#104C2×D3semidirect
218. #3954C2×D3semidirect
222. #3937C2×D3semidirect
224. #3935C2×D3semidirect
318. C3×#104C2×D5semidirect
321. #837C2×D5semidirect
323. #825C2×D5semidirect
330. #805C2×D5semidirect
620. #104D3×D5semidirect
783. C3×C5#2955semidirect
873. C5#79897semidirect
894. C3#10610720semidirect

Maximal subgroups

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

subgroupindex
#117553222
D3×#40942
D3×#40532
#117509252
C5×#48212
C3×#651122
#117494402
#117494352
#117482022
#117481762
#117481722
#117471112
#117471062
#117470192
#117469792
#106107203
#798975