Finite Group Databasebeta

← #14415613

Subgroups — #14415613

Order 1920.

1004 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5⋊M16C211yesmaximal, characteristic, complemented
2C2×#91929C211yesmaximal, characteristic, complemented
3#11754316C211yesmaximal, characteristic
4C2×#91232C211yesmaximal, characteristic, complemented
5#11752014C211yesmaximal, characteristic, complemented
6#11752001C211yesmaximal, characteristic, complemented
7#11751995C211yesmaximal, characteristic, complemented
8#11751911C211yesmaximal, characteristic, complemented
9#11751910C211yesmaximal, characteristic, complemented
10#11751909C211yesmaximal, characteristic, complemented
11#11751886C211yesmaximal, characteristic, complemented
12#11751885C211yesmaximal, characteristic, complemented
13#11751881C211yesmaximal, characteristic, complemented
14#11751875C211yesmaximal, characteristic, complemented
15#11751763C211yesmaximal, characteristic, complemented
16#10617291—31nomaximal, Hall
17C22×C3×C4×D5C2211yescharacteristic
18C2×#6782C2211yescharacteristic
19C22×C3⋊#170C2211yescharacteristic
20C22×C3⋊#170C2211yescharacteristic
21C2×C3×#704C2211yescharacteristic
22C2×C3×#704C2211yescharacteristic
23C3×D5⋊M16—24no—
24C2×C3×#700C2211yescharacteristic
25C2×C3×#700C2211yescharacteristic
26C2×C3×D5⋊C8C2211yescharacteristic
27C2×C3×D5⋊C8C2211yescharacteristic
28C2×#6740C2211yescharacteristic, complemented
29C2×#6739C2211yescharacteristic, complemented
30C2×#6738C2211yescharacteristic, complemented
31#91929—24no—
32C2×D3×#170C2211yescharacteristic, complemented
33#91818C411yescharacteristic
34C5×#929C411yescharacteristic
35#91564C411yescharacteristic
36#91563C411yescharacteristic
37#91528C2211yescharacteristic
38#91448C411yescharacteristic
39#91448C411yescharacteristic
40#91444C2211yescharacteristic
41#91444C2211yescharacteristic
42#91440C2211yescharacteristic
43#91440C2211yescharacteristic
44#91349C411yescharacteristic
45#91349C411yescharacteristic
46#91232C2211yescharacteristic
47#91232C2211yescharacteristic
48#91232C2211yescharacteristic
49#91232C2211yescharacteristic
50#91177C2211yescharacteristic, complemented
51#91177C2211yescharacteristic, complemented
52Dic3⋊#170C2211yescharacteristic, complemented
53Dic3⋊#170C2211yescharacteristic, complemented
54#91171C2211yescharacteristic, complemented
55#91171C2211yescharacteristic, complemented
56(C2×D3)⋊#170C2211yescharacteristic, complemented
57(C2×D3)⋊#170C2211yescharacteristic, complemented
58#91169C2211yescharacteristic, complemented
59#91169C2211yescharacteristic, complemented
60Dic3×#170C2211yescharacteristic, complemented
61Dic3×#170C2211yescharacteristic, complemented
62#83757—51nomaximal, Hall
63C2×#4131—31no—
64C2×D5⋊M16D311yescharacteristic, complemented
65#65990—31no—
66#65775—31no—
67C2×#4003—31no—
68#65705—31no—
69#65704—31no—
70#65704—31no—
71#65702—31no—
72#65696—31no—
73#65695—31no—
74#65694—31no—
75#65693—31no—
76#65692—31no—
77#65691—31no—
78C23×C3×D5C2×C411yescharacteristic
79C22×C3×C4×C5C2×C411yescharacteristic
80C2×#1220C2×C411yescharacteristic
81C2×C5×#67C2×C411yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C2×C3×C4×D5—22no—
84C2×C3×C4×D5—22no—
85C2×C3×C4×D5C2×C411yescharacteristic
86C2×C3×C4×D5C2×C411yescharacteristic
87C2×C3×C4×D5C2311yescharacteristic
88C2×C3×C4×D5C2311yescharacteristic
89C2×#1204C2×C411yescharacteristic
90C2×#1203C2×C411yescharacteristic
91C2×#1202C2×C411yescharacteristic
92C2×#1202C2×C411yescharacteristic
93C2×#1201C2×C411yescharacteristic
94C2×#1201C2×C411yescharacteristic
95C2×#1200C2311yescharacteristic
96#6782—22no—
97#6782—22no—
98C2×D3×Dic5C2311yescharacteristic
99C2×C3⋊#170—22no—
100C2×C3⋊#170—22no—
101C2×C3⋊#170C2311yescharacteristic
102C2×C3⋊#170C2311yescharacteristic
103C2×C3⋊#170C2311yescharacteristic
104C2×C3⋊#170C2311yescharacteristic
105C3×#704—22no—
106C3×#704D414yescomplemented
107C2×C3×#170C2311yescharacteristic
108C2×C3×#170C2311yescharacteristic
109C2×C3×#170C2311yescharacteristic
110C2×C3×#170C2311yescharacteristic
111C3×#700—22no—
112C3×#700—22no—
113C3×D5⋊C8—22no—
114C3×D5⋊C8—22no—
115#6740—22no—
116#6739—22no—
117#6738—22no—
118D3×#170—22no—
119#6719C2×C411yescharacteristic
120#6714C2×C411yescharacteristic
121#6714C2×C411yescharacteristic
122#6712C2×C411yescharacteristic
123#6712C2×C411yescharacteristic
124C5×#217C2×C411yescharacteristic
125C5×(C2×D3)⋊C4C2×C411yescharacteristic
126C5×(C2×D3)⋊C4C2×C411yescharacteristic
127C5×Dic3⋊C4C2×C411yescharacteristic
128C5×Dic3⋊C4C2×C411yescharacteristic
129#6668C2×C411yescharacteristic
130#6668C2×C411yescharacteristic
131#6665C2×C411yescharacteristic
132#6665C2×C411yescharacteristic
133#6665C2×C411yescharacteristic
134#6665C2×C411yescharacteristic
135Dic3×Dic5C2311yescharacteristic
136Dic3×Dic5C2311yescharacteristic
137C22×C3×M16—51no—
138#5791—51no—
139C2×#907—51no—
140C2×#830—51no—
141#5129—51no—
142#5128—51no—
143#5128—51no—
144#5127—51no—
145#5127—51no—
146#5122—51no—
147#5119—51no—
148#5111—51no—
149#5111—51no—
150C8×#67—51no—
151C8×#67—51no—
152C2×#711—31no—
153C22×C4×D5C2×D311yescharacteristic
154C2×#704—31no—
155C2×#704C2×D311yescharacteristic
156C2×#704C2×D311yescharacteristic
157C22×#170—31no—
158C22×#170—31no—
159C22×#170—31no—
160#4131—64no—
161D5⋊M16—24no—
162C2×#700—31no—
163C2×#700C2×D311yescharacteristic
164C2×#700C2×D311yescharacteristic
165C2×D5⋊C8—31no—
166C2×D5⋊C8C2×D311yescharacteristic
167C2×D5⋊C8C2×D311yescharacteristic
168C5×#123—31no—
169#4083—31no—
170#4075—31no—
171#4042—31no—
172#4042—31no—
173#4039—31no—
174#4039—31no—
175#4030—31no—
176#4030—31no—
177#4028—31no—
178#4027—31no—
179#4027—31no—
180#4023—31no—
181C22⋊#170—31no—
182C22⋊#170—31no—
183#4004—31no—
184#4004—31no—
185#4003—31no—
186#4003—31no—
187#4003—31no—
188#4003—31no—
189#4003—31no—
190#4003—31no—
191#4002—31no—
192#4002—31no—
193C4⋊#170—31no—
194C4⋊#170—31no—
195C4×#170—31no—
196C4×#170—31no—
197#2933—151noSylow
198C23×C3×C5C22×C411yescharacteristic
199C22×D15C22×C411yescharacteristic
200C22×C5×D3C22×C411yescharacteristic
201C22×C3×D5—22no—
202C22×C3×D5—22no—
203C22×C3×D5—41no—
204C22×C3×D5C22×C411yescharacteristic
205C22×C3×D5C22×C411yescharacteristic
206C2×C3×C4×C5—22no—
207C2×C3×C4×C5C22×C411yescharacteristic
208C2×C3×C4×C5C22×C411yescharacteristic
209#1220—22no—
210C2×Dic15C22×C411yescharacteristic
211C2×Dic15C22×C411yescharacteristic
212C2×Dic15C22×C411yescharacteristic
213C5×#67—22no—
214C2×C5×Dic3C22×C411yescharacteristic
215C2×C5×Dic3C22×C411yescharacteristic
216C2×C5×Dic3C22×C411yescharacteristic
217C2×C3×Dic5C22×C411yescharacteristic
218C2×C3×Dic5C2×D412yes—
219C2×C3×Dic5#4112yes—
220C2×C3×Dic5C2411yescharacteristic
221C3×C4×D5—22no—
222C3×C4×D5—22no—
223C3×C4×D5—21no—
224C3×C4×D5—21no—
225C3×C4×D5—21no—
226C3×C4×D5—21no—
227#1204—22no—
228#1203—22no—
229#1202—22no—
230#1202—41no—
231#1201—22no—
232#1201—41no—
233#1200—21no—
234#1200—21no—
235D3×Dic5—21no—
236D3×Dic5—21no—
237C3⋊#170—21no—
238C3⋊#170—21no—
239C3⋊#170—21no—
240C3⋊#170—21no—
241C3×#170—21no—
242C3×#170—21no—
243C3×#170C2×D412yes—
244C3×#170C2×D412yes—
245C23×C3×C4—51no—
246C2×#235—51no—
247C2×C3×M16—51no—
248C2×C3×M16—51no—
249C2×C3×M16—51no—
250C2×C3×M16—51no—
251C2×C3×M16—104no—
252C22×C3×C8—51no—
253C22×C3×C8—51no—
254#953—51no—
255#953—51no—
256#930—51no—
257#930—51no—
258#929—51no—
259#929AGL(1,𝔽5)11yescharacteristic
260C4×#67—51no—
261C4×#67—51no—
262C4×#67—51no—
263C4×#67—51no—
264#926—51no—
265#924—51no—
266#924—51no—
267C22×C3⋊C8—51no—
268C22×C3⋊C8—51no—
269#907—104no—
270C2×ΓL(1,𝔽25)—51no—
271C2×ΓL(1,𝔽25)—51no—
272C2×D3×C8—51no—
273C2×D3×C8—51no—
274#830—51no—
275#830—51no—
276#830—51no—
277#830—51no—
278(C2×D3)⋊C8—51no—
279(C2×D3)⋊C8—51no—
280(C2×D3)⋊C8—51no—
281(C2×D3)⋊C8—51no—
282#815—51no—
283#815—51no—
284Dic3⋊C8—51no—
285Dic3⋊C8—51no—
286Dic3⋊C8—51no—
287Dic3⋊C8—51no—
288C8×Dic3—51no—
289C8×Dic3—51no—
290C23×D5C4×D311yescharacteristic
291C2×C5×D4—31no—
292C22×C4×C5C4×D311yescharacteristic
293C2×C22⋊D5—31no—
294C2×C22⋊D5—31no—
295C2×C22⋊D5—31no—
296C2×C22⋊D5—31no—
297C22×Dic5—31no—
298C22×Dic5C22×D311yescharacteristic
299#711—62no—
300#711—62no—
301C2×D20—31no—
302C2×D20—31no—
303C2×C4×D5—22no—
304C2×C4×D5—22no—
305C2×C4×D5—31no—
306C2×C4×D5C4×D311yescharacteristic
307C2×C4×D5C4×D311yescharacteristic
308C2×C4×D5C22×D311yescharacteristic
309C2×C4×D5C22×D311yescharacteristic
310C2×Dic10—31no—
311#704—22no—
312#704—62no—
313#704#6714yescomplemented
314C2×#170—31no—
315C2×#170—31no—
316C2×#170—31no—
317C2×#170—31no—
318C2×#170—62no—
319C2×#170—62no—
320C2×#170—62no—
321C2×#170C22×D311yescharacteristic
322C2×#170C22×D311yescharacteristic
323C2×#170C22×D311yescharacteristic
324C2×#170C22×D311yescharacteristic
325#700—22no—
326#700—22no—
327#700—62no—
328D5⋊C8—22no—
329D5⋊C8—22no—
330D5⋊C8—62no—
331C5×C4⋊C4—31no—
332C5×C4⋊C4—31no—
333C5×C22⋊C4—31no—
334C5×C22⋊C4—31no—
335C5×C22⋊C4—31no—
336C22⋊Dic5—31no—
337#685—31no—
338#685—31no—
339#685—31no—
340#685—31no—
341#685—31no—
342#685—31no—
343#683—31no—
344#683—31no—
345#683—31no—
346#683—31no—
347C4×Dic5—31no—
348C4×Dic5—31no—
349C2×#131—151no—
350C22×M16—51no—
351#525—151no—
352#436—151no—
353#436—151no—
354#435—151no—
355#435—151no—
356#435—151no—
357#435—151no—
358C8×D4—151no—
359C8×D4—151no—
360#424—151no—
361#408—151no—
362C2×C22⋊C8—151no—
363#405—151no—
364C22×C3×C5—21no—
365C22×C3×C5—21no—
366C22×C3×C5C4×D412yes—
367C22×C3×C5C23×C411yescharacteristic
368C2×D15—21no—
369C2×D15—21no—
370C2×D15—21no—
371C2×C5×D3—21no—
372C2×C5×D3—21no—
373C2×C5×D3—21no—
374C2×C3×D5—21no—
375C2×C3×D5—21no—
376C2×C3×D5—21no—
377C2×C3×D5—21no—
378C2×C3×D5—21no—
379C2×C3×D5—44no—
380C2×C3×D5#13112yescomplemented
381C3×C4×C5—21no—
382C3×C4×C5—21no—
383Dic15—21no—
384Dic15—21no—
385Dic15—21no—
386C3×Dic5C4×D412yes—
387C3×Dic5C22×D411yescharacteristic
388C3×Dic5C2×#4111yescharacteristic
389C5×Dic3—21no—
390C5×Dic3—21no—
391C5×Dic3—21no—
392C24×C3—51no—
393C22×C3×C4—51no—
394C22×C3×C4—51no—
395C22×C3×C4—51no—
396C22×C3×C4—51no—
397C22×C3×C4—51no—
398C22×C3×C4—102no—
399C22×C3×C4—102no—
400C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
401C2×#67—51no—
402C2×#67—51no—
403C2×#67—51no—
404C2×#67—51no—
405C2×#67—51no—
406C2×#67C2×AGL(1,𝔽5)11yescharacteristic
407#235—102no—
408#235—102no—
409C2×D12—51no—
410C2×C4×D3—51no—
411C2×C4×D3—51no—
412C2×Dic6—51no—
413C3×M16—54no—
414C3×M16—102no—
415C3×M16—102no—
416C3×M16—102no—
417C2×C3×C8—51no—
418C2×C3×C8—51no—
419C2×C3×C8—51no—
420C2×C3×C8—51no—
421C2×C3×C8—102no—
422C2×C3×C8—102no—
423#217—51no—
424#217—51no—
425#217—51no—
426#217—51no—
427#217—51no—
428#217C2×AGL(1,𝔽5)11yescharacteristic
429(C2×D3)⋊C4—51no—
430(C2×D3)⋊C4—51no—
431(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
432(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
433C4⋊Dic3—51no—
434C4⋊Dic3—51no—
435Dic3⋊C4—51no—
436Dic3⋊C4—51no—
437Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
438Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
439C4×Dic3—51no—
440C4×Dic3—51no—
441C2×C3⋊C8—51no—
442C2×C3⋊C8—51no—
443C2×C3⋊C8—51no—
444C2×C3⋊C8—51no—
445C2×C3⋊C8—102no—
446C2×C3⋊C8—102no—
447ΓL(1,𝔽25)—102no—
448ΓL(1,𝔽25)—102no—
449D3×C8—102no—
450D3×C8—102no—
451C23×C5—31no—
452C23×C5C2×C4×D311yescharacteristic
453C22×D5—22no—
454C22×D5—22no—
455C22×D5—31no—
456C22×D5—41no—
457C22×D5C2×C4×D311yescharacteristic
458C22×D5C2×C4×D311yescharacteristic
459C5×D4—62no—
460C2×C4×C5—22no—
461C2×C4×C5—31no—
462C2×C4×C5—31no—
463C2×C4×C5—31no—
464C2×C4×C5C2×C4×D311yescharacteristic
465C2×C4×C5C2×C4×D311yescharacteristic
466C22⋊D5—62no—
467C22⋊D5—62no—
468C22⋊D5—62no—
469C22⋊D5—121no—
470C2×Dic5—31no—
471C2×Dic5—31no—
472C2×Dic5—31no—
473C2×Dic5—61no—
474C2×Dic5—61no—
475C2×Dic5C2×C4×D311yescharacteristic
476C2×Dic5#23512yes—
477C2×Dic5C2×#6712yes—
478C2×Dic5C23×D311yescharacteristic
479D20—62no—
480D20—121no—
481C4×D5—22no—
482C4×D5—22no—
483C4×D5—21no—
484C4×D5—21no—
485C4×D5—21no—
486C4×D5—21no—
487C4×D5—61no—
488C4×D5—61no—
489Dic10—62no—
490#170—21no—
491#170—21no—
492#170—61no—
493#170—61no—
494#170—61no—
495#170—61no—
496#170C2×#6712yes—
497#170C2×#6712yes—
498C2×#41—151no—
499C23×C4—51no—
500#131—304no—
501C2×M16—51no—
502C2×M16—51no—
503C2×M16—51no—
504C2×M16—51no—
505C2×M16—104no—
506C2×M16—151no—
507C2×M16—151no—
508C22×C8—51no—
509C22×C8—51no—
510C22×C8—151no—
511C22×C8—151no—
512C22×C8—151no—
513C22×C8—151no—
514#123—31no—
515#123—151no—
516C22⋊Q8—151no—
517C22⋊Q8—151no—
518#121—151no—
519#121—151no—
520#120—151no—
521#120—151no—
522C4×D4—151no—
523C4×D4—151no—
524C4×D4—151no—
525C4×D4—151no—
526#117—151no—
527C4⋊C8—151no—
528C4⋊C8—151no—
529C4⋊C8—151no—
530C4⋊C8—151no—
531C22⋊C8—151no—
532C22⋊C8—151no—
533C22⋊C8—151no—
534C22⋊C8—151no—
535C22⋊C8—151no—
536C22⋊C8—151no—
537C22⋊C8—151no—
538C22⋊C8—151no—
539#97—151no—
540#97—151no—
541C4×C8—151no—
542C4×C8—151no—
543C2×C3×C5—22no—
544C2×C3×C5C2×C4×D411yescharacteristic
545C2×C3×C5C2×#13111yescharacteristic
546C2×C3×C5#56811yescharacteristic
547D15—41no—
548C3×D5—22no—
549C3×D5—41no—
550C5×D3—41no—
551C23×C3—51no—
552C23×C3—51no—
553C23×C3—102no—
554C23×C3—102no—
555C23×C3—201no—
556C23×C3C22×AGL(1,𝔽5)11yescharacteristic
557C22×D3—51no—
558C22×D3C22×AGL(1,𝔽5)11yescharacteristic
559C2×C3×C4—22no—
560C2×C3×C4—52no—
561C2×C3×C4—52no—
562C2×C3×C4—51no—
563C2×C3×C4—51no—
564C2×C3×C4—101no—
565C2×C3×C4—101no—
566C2×C3×C4—102no—
567C2×C3×C4—102no—
568C2×C3×C4—101no—
569C2×C3×C4—101no—
570C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
571C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
572#67—22no—
573#67—102no—
574#67—102no—
575#67—102no—
576#67—201no—
577#67—201no—
578C2×Dic3—51no—
579C2×Dic3—51no—
580C2×Dic3—51no—
581C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
582C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
583C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
584D12—102no—
585C4×D3—101no—
586C4×D3—101no—
587C4×D3—101no—
588C4×D3—101no—
589Dic6—102no—
590C3×C8—52no—
591C3×C8—52no—
592C3×C8—101no—
593C3×C8—101no—
594C3⋊C8—101no—
595C3⋊C8—101no—
596C3⋊C8—101no—
597C3⋊C8—101no—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—61no—
601C22×C5—61no—
602C22×C5—61no—
603C22×C5C4×#6712yes—
604C22×C5C22×C4×D311yescharacteristic
605C2×D5—21no—
606C2×D5—21no—
607C2×D5—21no—
608C2×D5—21no—
609C2×D5—21no—
610C2×D5—44no—
611C2×D5—61no—
612C2×D5—61no—
613C2×D5—61no—
614C2×D5#90712yescomplemented
615C4×C5—21no—
616C4×C5—21no—
617C4×C5—61no—
618C4×C5—61no—
619C4×C5—61no—
620Dic5—61no—
621Dic5—61no—
622Dic5—61no—
623Dic5C4×#6712yes—
624Dic5C2×#23511yescharacteristic
625Dic5C22×#6711yescharacteristic
626C24—51no—
627#41—302no—
628#41—302no—
629C2×Q8—151no—
630C2×D4—31no—
631C2×D4—151no—
632C2×D4—151no—
633C2×D4—151no—
634C2×D4—151no—
635C2×D4—151no—
636C2×D4—151no—
637C22×C4—51no—
638C22×C4—51no—
639C22×C4—51no—
640C22×C4—51no—
641C22×C4—51no—
642C22×C4—102no—
643C22×C4—102no—
644C22×C4—151no—
645C22×C4—151no—
646C22×C4D3×AGL(1,𝔽5)11yescharacteristic
647M16—54no—
648M16—102no—
649M16—102no—
650M16—102no—
651M16—302no—
652M16—302no—
653C2×C8—51no—
654C2×C8—51no—
655C2×C8—51no—
656C2×C8—51no—
657C2×C8—102no—
658C2×C8—102no—
659C2×C8—151no—
660C2×C8—151no—
661C2×C8—151no—
662C2×C8—151no—
663C2×C8—302no—
664C2×C8—302no—
665C2×C8—302no—
666C2×C8—302no—
667C4⋊C4—31no—
668C4⋊C4—31no—
669C4⋊C4—151no—
670C4⋊C4—151no—
671C4⋊C4—151no—
672C4⋊C4—151no—
673C22⋊C4—31no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—151no—
677C22⋊C4—151no—
678C22⋊C4—151no—
679C22⋊C4—151no—
680C22⋊C4—151no—
681C22⋊C4—151no—
682C22⋊C4—151no—
683C42—151no—
684C42—151no—
685C3×C5#293311yescharacteristic, complemented, Hall
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—52no—
689C22×C3—101no—
690C22×C3—101no—
691C22×C3—101no—
692C22×C3—101no—
693C22×C3—101no—
694C22×C3—204no—
695C22×C3D4×AGL(1,𝔽5)12yes—
696C22×C3C23×AGL(1,𝔽5)11yescharacteristic
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—101no—
701C2×D3—101no—
702C2×D3—101no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—52no—
706C3×C4—51no—
707C3×C4—51no—
708Dic3—21no—
709Dic3—21no—
710Dic3—21no—
711Dic3—101no—
712Dic3—101no—
713Dic3—101no—
714C2×C5—22no—
715C2×C5—121no—
716C2×C5C2×#90711yescharacteristic
717C2×C5#574511yescharacteristic
718C2×C5C2×C4×#6711yescharacteristic
719D5—22no—
720D5—41no—
721D5—121no—
722C23—31no—
723C23—51no—
724C23—51no—
725C23—102no—
726C23—102no—
727C23—151no—
728C23—201no—
729C23C2×D3×AGL(1,𝔽5)11yescharacteristic
730Q8—302no—
731D4—62no—
732D4—302no—
733D4—302no—
734D4—302no—
735D4—302no—
736D4—601no—
737D4—601no—
738C2×C4—22no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—52no—
743C2×C4—52no—
744C2×C4—51no—
745C2×C4—51no—
746C2×C4—101no—
747C2×C4—101no—
748C2×C4—101no—
749C2×C4—101no—
750C2×C4—102no—
751C2×C4—102no—
752C2×C4—151no—
753C2×C4—151no—
754C2×C4—151no—
755C2×C4—301no—
756C2×C4—301no—
757C2×C4—301no—
758C2×C4—301no—
759C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
760C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
761C8—52no—
762C8—52no—
763C8—101no—
764C8—101no—
765C8—301no—
766C8—301no—
767C8—301no—
768C8—301no—
769C2×C3—22no—
770C2×C3—102no—
771C2×C3—201no—
772C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
773C2×C3D5⋊#13111yescharacteristic
774C2×C3#6626411yescharacteristic
775D3—41no—
776D3—201no—
777C5#8375711yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—52no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—101no—
785C22—101no—
786C22—101no—
787C22—101no—
788C22—101no—
789C22—204no—
790C22—301no—
791C22—301no—
792C22—301no—
793C22AGL(1,𝔽5)×#6712yes—
794C22C22×D3×AGL(1,𝔽5)11yescharacteristic
795C4—21no—
796C4—21no—
797C4—51no—
798C4—51no—
799C4—52no—
800C4—61no—
801C4—61no—
802C4—61no—
803C4—301no—
804C4—301no—
805C4—301no—
806C3#1061729111yescharacteristic, complemented, Sylow
807C2—22no—
808C2—102no—
809C2—121no—
810C2—201no—
811C2—601no—
812C2D5⋊#90711yescharacteristic
813C2#1175682311yescharacteristic
814C2C2×AGL(1,𝔽5)×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radical#11754316C2
cosocleC2×C3×Dic5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2933
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5⋊M16C2semidirect
2. C2×#91929C2semidirect
4. C2×#91232C2semidirect
5. #11752014C2semidirect
6. #11752001C2semidirect
7. #11751995C2semidirect
8. #11751911C2semidirect
9. #11751910C2semidirect
10. #11751909C2semidirect
11. #11751886C2semidirect
12. #11751885C2semidirect
13. #11751881C2semidirect
14. #11751875C2semidirect
15. #11751763C2semidirect
28. C2×#6740C22semidirect
29. C2×#6739C22semidirect
30. C2×#6738C22semidirect
32. C2×D3×#170C22semidirect
50. #91177C22semidirect
51. #91177C22semidirect
52. Dic3⋊#170C22semidirect
53. Dic3⋊#170C22semidirect
54. #91171C22semidirect
55. #91171C22semidirect
56. (C2×D3)⋊#170C22semidirect
57. (C2×D3)⋊#170C22semidirect
58. #91169C22semidirect
59. #91169C22semidirect
60. Dic3×#170C22semidirect
61. Dic3×#170C22semidirect
64. C2×D5⋊M16D3semidirect
106. C3×#704D4semidirect
313. #704#67semidirect
380. C2×C3×D5#131semidirect
614. C2×D5#907semidirect
685. C3×C5#2933semidirect
777. C5#83757semidirect
806. C3#10617291semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5⋊M162
C2×#919292
#117543162
C2×#912322
#117520142
#117520012
#117519952
#117519112
#117519102
#117519092
#117518862
#117518852
#117518812
#117518752
#117517632
#106172913
#837575