Finite Group Databasebeta

← #14415607

Subgroups — #14415607

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
1C22×C3×#704C211yesmaximal, characteristic, complemented
2C2×#91929C211yesmaximal, characteristic, complemented
3#11755385C211yesmaximal, characteristic
4C2×#91241C211yesmaximal, characteristic, complemented
5#11752046C211yesmaximal, characteristic, complemented
6#11752045C211yesmaximal, characteristic, complemented
7#11752044C211yesmaximal, characteristic, complemented
8#11752037C211yesmaximal, characteristic, complemented
9#11752036C211yesmaximal, characteristic, complemented
10#11752035C211yesmaximal, characteristic, complemented
11#67×#170C211yesmaximal, characteristic, complemented
12#11752014C211yesmaximal, characteristic, complemented
13#11752001C211yesmaximal, characteristic, complemented
14#11751995C211yesmaximal, characteristic, complemented
15#11751987C211yesmaximal, characteristic, complemented
16#10617217—31nomaximal, Hall
17C23×C3×Dic5C2211yescharacteristic
18C2×#6782C2211yescharacteristic
19C22×C3⋊#170C2211yescharacteristic
20C22×C3⋊#170C2211yescharacteristic
21C2×C3×#704—24no—
22C2×C3×#704C2211yescharacteristic
23C2×C3×#704C2211yescharacteristic
24C2×C3×#704C2211yescharacteristic
25C2×C3×#704C2211yescharacteristic
26C22×C3×#170C2211yescharacteristic
27C22×C3×#170C2211yescharacteristic
28C2×#6740C2211yescharacteristic, complemented
29C2×#6739C2211yescharacteristic, complemented
30C2×#6738C2211yescharacteristic, complemented
31#91929—24no—
32C2×D3×#170C2211yescharacteristic, complemented
33#91842C411yescharacteristic
34C5×#953C411yescharacteristic
35#91574C411yescharacteristic
36#91574C411yescharacteristic
37#91566C411yescharacteristic
38#91566C411yescharacteristic
39#91552C2211yescharacteristic
40#91552C2211yescharacteristic
41Dic5×#67C2211yescharacteristic
42Dic5×#67C2211yescharacteristic
43#91546C411yescharacteristic
44#91539C411yescharacteristic
45#91528C2211yescharacteristic
46#91241C2211yescharacteristic
47#91241C2211yescharacteristic
48#91241C2211yescharacteristic
49#91241C2211yescharacteristic
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
63C22×#704D311yescharacteristic, complemented
64C2×#4131—31no—
65#65920—31no—
66C2×C22⋊#170—31no—
67#65775—31no—
68#65774—31no—
69#65773—31no—
70#65773—31no—
71D4×#170—31no—
72#65696—31no—
73#65695—31no—
74#65694—31no—
75#65693—31no—
76#65692—31no—
77#65691—31no—
78C24×C3×C5C2×C411yescharacteristic
79C2×#1220C2×C411yescharacteristic
80C2×#1220C2×C411yescharacteristic
81C2×#1220C2×C411yescharacteristic
82C2×C5×#67C2×C411yescharacteristic
83C2×C5×#67C2×C411yescharacteristic
84C2×C5×#67C2×C411yescharacteristic
85C22×C3×Dic5—22no—
86C22×C3×Dic5—22no—
87C22×C3×Dic5C2×C411yescharacteristic
88C22×C3×Dic5C2×C411yescharacteristic
89C22×C3×Dic5C2×C411yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C2×#1204C2×C411yescharacteristic
94C2×#1203C2×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×#704—22no—
107C3×#704—22no—
108C3×#704D414yescomplemented
109C2×C3×#170—22no—
110C2×C3×#170—22no—
111C2×C3×#170C2311yescharacteristic
112C2×C3×#170C2311yescharacteristic
113C2×C3×#170C2311yescharacteristic
114C2×C3×#170C2311yescharacteristic
115#6740—22no—
116#6739—22no—
117#6738—22no—
118D3×#170—22no—
119#6719C2×C411yescharacteristic
120#6719C2×C411yescharacteristic
121#6719C2×C411yescharacteristic
122C5×#217C2×C411yescharacteristic
123C5×#217C2×C411yescharacteristic
124C5×#217C2×C411yescharacteristic
125Dic3⋊Dic5C2×C411yescharacteristic
126Dic3⋊Dic5C2×C411yescharacteristic
127#6669C2×C411yescharacteristic
128#6669C2×C411yescharacteristic
129#6668C2×C411yescharacteristic
130#6668C2×C411yescharacteristic
131#6667C2×C411yescharacteristic
132#6667C2×C411yescharacteristic
133(C2×D3)⋊Dic5C2×C411yescharacteristic
134(C2×D3)⋊Dic5C2×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—
152C23×Dic5C2×D311yescharacteristic
153C2×#711—31no—
154C2×#704—24no—
155C2×#704—31no—
156C2×#704C2×D311yescharacteristic
157C2×#704C2×D311yescharacteristic
158C2×#704C2×D311yescharacteristic
159C2×#704C2×D311yescharacteristic
160C22×#170—31no—
161C22×#170—31no—
162C22×#170—31no—
163C22×#170C2×D311yescharacteristic
164C22×#170C2×D311yescharacteristic
165#4131—64no—
166C2×#700—31no—
167C2×D5⋊C8—31no—
168C5×#120—31no—
169#4099—31no—
170#4085—31no—
171#4085—31no—
172#4081—31no—
173D4×Dic5—31no—
174D4×Dic5—31no—
175#4032—31no—
176#4027—31no—
177#4027—31no—
178#4024—31no—
179#4024—31no—
180#4023—31no—
181C22⋊#170—31no—
182C22⋊#170—31no—
183C22⋊#170—31no—
184C22⋊#170—31no—
185C22⋊#170—31no—
186C22⋊#170—31no—
187#4004—31no—
188#4004—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×C5—22no—
199C23×C3×C5—22no—
200C23×C3×C5—41no—
201C23×C3×C5C22×C411yescharacteristic
202C23×C3×C5C22×C411yescharacteristic
203C23×C3×C5C22×C411yescharacteristic
204C22×D15C22×C411yescharacteristic
205C22×C5×D3C22×C411yescharacteristic
206#1220—22no—
207#1220—22no—
208#1220—41no—
209C2×Dic15C22×C411yescharacteristic
210C2×Dic15C22×C411yescharacteristic
211C2×Dic15C22×C411yescharacteristic
212C5×#67—22no—
213C5×#67—22no—
214C5×#67—41no—
215C2×C5×Dic3C22×C411yescharacteristic
216C2×C5×Dic3C22×C411yescharacteristic
217C2×C5×Dic3C22×C411yescharacteristic
218C2×C3×Dic5—22no—
219C2×C3×Dic5—22no—
220C2×C3×Dic5—22no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5C22×C411yescharacteristic
226C2×C3×Dic5C22×C411yescharacteristic
227C2×C3×Dic5C22×C411yescharacteristic
228C2×C3×Dic5C2×D412yes—
229C2×C3×Dic5#4112yes—
230C2×C3×Dic5C2411yescharacteristic
231#1204—22no—
232#1203—22no—
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#953AGL(1,𝔽5)11yescharacteristic
256#930—51no—
257#930—51no—
258#929—51no—
259#929—51no—
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—
290C24×C5C4×D311yescharacteristic
291C2×C5×D4—31no—
292C2×C5×D4—31no—
293C2×C5×D4—31no—
294C2×C22⋊D5—31no—
295C2×C22⋊D5—31no—
296C2×C22⋊D5—31no—
297C2×C22⋊D5—31no—
298C22×Dic5—22no—
299C22×Dic5—22no—
300C22×Dic5—31no—
301C22×Dic5C4×D311yescharacteristic
302C22×Dic5C4×D311yescharacteristic
303C22×Dic5C4×D311yescharacteristic
304C22×Dic5C22×D311yescharacteristic
305C22×Dic5C22×D311yescharacteristic
306C22×Dic5C22×D311yescharacteristic
307#711—62no—
308#711—62no—
309C2×C4×D5—31no—
310C2×Dic10—31no—
311#704—22no—
312#704—22no—
313#704—22no—
314#704—62no—
315#704#6714yescomplemented
316C2×#170—22no—
317C2×#170—22no—
318C2×#170—31no—
319C2×#170—31no—
320C2×#170—31no—
321C2×#170—31no—
322C2×#170—62no—
323C2×#170—62no—
324C2×#170—62no—
325C2×#170C22×D311yescharacteristic
326C2×#170C22×D311yescharacteristic
327C2×#170C22×D311yescharacteristic
328C2×#170C22×D311yescharacteristic
329#700—62no—
330D5⋊C8—62no—
331C5×C22⋊C4—31no—
332C5×C22⋊C4—31no—
333C5×C22⋊C4—31no—
334C22⋊Dic5—31no—
335C22⋊Dic5—31no—
336C22⋊Dic5—31no—
337C22⋊Dic5—31no—
338C22⋊Dic5—31no—
339#685—31no—
340#685—31no—
341C4⋊Dic5—31no—
342C4⋊Dic5—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×C5—21no—
367C22×C3×C5—21no—
368C22×C3×C5—21no—
369C22×C3×C5—21no—
370C22×C3×C5—21no—
371C22×C3×C5—44no—
372C22×C3×C5C4×D412yes—
373C22×C3×C5#13112yescomplemented
374C22×C3×C5C23×C411yescharacteristic
375C2×D15—21no—
376C2×D15—21no—
377C2×D15—21no—
378C2×C5×D3—21no—
379C2×C5×D3—21no—
380C2×C5×D3—21no—
381Dic15—21no—
382Dic15—21no—
383Dic15—21no—
384C3×Dic5—21no—
385C3×Dic5—21no—
386C3×Dic5C4×D412yes—
387C3×Dic5C22×D411yescharacteristic
388C3×Dic5C2×#4111yescharacteristic
389C5×Dic3—21no—
390C5×Dic3—21no—
391C5×Dic3—21no—
392C24×C3C2×AGL(1,𝔽5)11yescharacteristic
393C22×C3×C4—51no—
394C22×C3×C4—51no—
395C22×C3×C4—51no—
396C22×C3×C4—51no—
397C22×C3×C4—51no—
398C22×C3×C4—51no—
399C22×C3×C4—102no—
400C22×C3×C4—102no—
401C2×#67—51no—
402C2×#67—51no—
403C2×#67—51no—
404C2×#67C2×AGL(1,𝔽5)11yescharacteristic
405C2×#67C2×AGL(1,𝔽5)11yescharacteristic
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#217C2×AGL(1,𝔽5)11yescharacteristic
427#217C2×AGL(1,𝔽5)11yescharacteristic
428#217C2×AGL(1,𝔽5)11yescharacteristic
429(C2×D3)⋊C4—51no—
430(C2×D3)⋊C4—51no—
431(C2×D3)⋊C4—51no—
432(C2×D3)⋊C4—51no—
433C4⋊Dic3—51no—
434C4⋊Dic3—51no—
435Dic3⋊C4—51no—
436Dic3⋊C4—51no—
437Dic3⋊C4—51no—
438Dic3⋊C4—51no—
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—22no—
452C23×C5—22no—
453C23×C5—31no—
454C23×C5—41no—
455C23×C5C2×C4×D311yescharacteristic
456C23×C5C2×C4×D311yescharacteristic
457C23×C5C2×C4×D311yescharacteristic
458C22×D5—31no—
459C5×D4—62no—
460C5×D4—62no—
461C5×D4—121no—
462C2×C4×C5—31no—
463C2×C4×C5—31no—
464C2×C4×C5—31no—
465C22⋊D5—62no—
466C22⋊D5—62no—
467C22⋊D5—62no—
468C22⋊D5—121no—
469C2×Dic5—22no—
470C2×Dic5—22no—
471C2×Dic5—22no—
472C2×Dic5—21no—
473C2×Dic5—21no—
474C2×Dic5—21no—
475C2×Dic5—21no—
476C2×Dic5—31no—
477C2×Dic5—31no—
478C2×Dic5—31no—
479C2×Dic5—61no—
480C2×Dic5—61no—
481C2×Dic5C2×C4×D311yescharacteristic
482C2×Dic5C2×C4×D311yescharacteristic
483C2×Dic5C2×C4×D311yescharacteristic
484C2×Dic5#23512yes—
485C2×Dic5C2×#6712yes—
486C2×Dic5C23×D311yescharacteristic
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—151no—
515#123—151no—
516C22⋊Q8—151no—
517C22⋊Q8—151no—
518#121—151no—
519#121—151no—
520#120—31no—
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×C5—22no—
545C2×C3×C5—41no—
546C2×C3×C5C2×C4×D411yescharacteristic
547C2×C3×C5C2×#13111yescharacteristic
548C2×C3×C5#56811yescharacteristic
549D15—41no—
550C5×D3—41no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—41no—
554C23×C3C22×AGL(1,𝔽5)11yescharacteristic
555C23×C3C22×AGL(1,𝔽5)11yescharacteristic
556C23×C3C22×AGL(1,𝔽5)11yescharacteristic
557C22×D3—51no—
558C22×D3C22×AGL(1,𝔽5)11yescharacteristic
559C2×C3×C4—52no—
560C2×C3×C4—52no—
561C2×C3×C4—51no—
562C2×C3×C4—51no—
563C2×C3×C4—51no—
564C2×C3×C4—51no—
565C2×C3×C4—101no—
566C2×C3×C4—101no—
567C2×C3×C4—102no—
568C2×C3×C4—102no—
569C2×C3×C4—101no—
570C2×C3×C4—101no—
571C2×C3×C4—102no—
572#67—22no—
573#67—22no—
574#67—41no—
575#67—102no—
576#67—102no—
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—21no—
601C22×C5—21no—
602C22×C5—21no—
603C22×C5—21no—
604C22×C5—21no—
605C22×C5—44no—
606C22×C5—61no—
607C22×C5—61no—
608C22×C5—61no—
609C22×C5#90712yescomplemented
610C22×C5C4×#6712yes—
611C22×C5C22×C4×D311yescharacteristic
612C2×D5—61no—
613C2×D5—61no—
614C2×D5—61no—
615C4×C5—61no—
616C4×C5—61no—
617C4×C5—61no—
618Dic5—21no—
619Dic5—21no—
620Dic5—61no—
621Dic5—61no—
622Dic5—61no—
623Dic5C4×#6712yes—
624Dic5C2×#23511yescharacteristic
625Dic5C22×#6711yescharacteristic
626C24D3×AGL(1,𝔽5)11yescharacteristic
627#41—302no—
628#41—302no—
629C2×Q8—151no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—31no—
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—51no—
643C22×C4—102no—
644C22×C4—102no—
645C22×C4—151no—
646C22×C4—151no—
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—151no—
668C4⋊C4—151no—
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—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—44no—
694C22×C3#413112yescomplemented
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—52no—
704C3×C4—51no—
705C3×C4—51no—
706C3×C4—101no—
707C3×C4—101no—
708Dic3—21no—
709Dic3—21no—
710Dic3—21no—
711Dic3—101no—
712Dic3—101no—
713Dic3—101no—
714C2×C5—22no—
715C2×C5—22no—
716C2×C5—41no—
717C2×C5—121no—
718C2×C5C2×#90711yescharacteristic
719C2×C5#574511yescharacteristic
720C2×C5C2×C4×#6711yescharacteristic
721D5—121no—
722C23—22no—
723C23—22no—
724C23—31no—
725C23—41no—
726C23—151no—
727C23C2×D3×AGL(1,𝔽5)11yescharacteristic
728C23C2×D3×AGL(1,𝔽5)11yescharacteristic
729C23C2×D3×AGL(1,𝔽5)11yescharacteristic
730Q8—302no—
731D4—62no—
732D4—62no—
733D4—121no—
734D4—302no—
735D4—302no—
736D4—302no—
737D4—601no—
738C2×C4—31no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—52no—
742C2×C4—52no—
743C2×C4—51no—
744C2×C4—51no—
745C2×C4—51no—
746C2×C4—51no—
747C2×C4—101no—
748C2×C4—101no—
749C2×C4—101no—
750C2×C4—101no—
751C2×C4—102no—
752C2×C4—102no—
753C2×C4—102no—
754C2×C4—151no—
755C2×C4—151no—
756C2×C4—151no—
757C2×C4—301no—
758C2×C4—301no—
759C2×C4—301no—
760C2×C4—301no—
761C8—52no—
762C8—52no—
763C8—101no—
764C8—101no—
765C8—301no—
766C8—301no—
767C8—301no—
768C8—301no—
769C2×C3—22no—
770C2×C3—22no—
771C2×C3—41no—
772C2×C3C2×#413111yescharacteristic
773C2×C3#6625611yescharacteristic
774C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
775D3—41no—
776D3—201no—
777C5#8375711yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—44no—
786C22—61no—
787C22—61no—
788C22—61no—
789C22—301no—
790C22—301no—
791C22—301no—
792C22#9192912yescomplemented
793C22AGL(1,𝔽5)×#6712yes—
794C22C22×D3×AGL(1,𝔽5)11yescharacteristic
795C4—51no—
796C4—51no—
797C4—52no—
798C4—61no—
799C4—61no—
800C4—61no—
801C4—101no—
802C4—101no—
803C4—301no—
804C4—301no—
805C4—301no—
806C3#1061721711yescharacteristic, complemented, Sylow
807C2—22no—
808C2—22no—
809C2—41no—
810C2—121no—
811C2—601no—
812C2C2×#9192911yescharacteristic
813C2#1175686311yescharacteristic
814C2C2×AGL(1,𝔽5)×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC24×C3×C5C2×C4
prime radical#11755385C2
cosocleC2×C3×Dic5C24
hypercenterC24D3×AGL(1,𝔽5)
hypocenterC3×C5#2933
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×C3×#704C2semidirect
2. C2×#91929C2semidirect
4. C2×#91241C2semidirect
5. #11752046C2semidirect
6. #11752045C2semidirect
7. #11752044C2semidirect
8. #11752037C2semidirect
9. #11752036C2semidirect
10. #11752035C2semidirect
11. #67×#170C2semidirect
12. #11752014C2semidirect
13. #11752001C2semidirect
14. #11751995C2semidirect
15. #11751987C2semidirect
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
63. C22×#704D3semidirect
108. C3×#704D4semidirect
315. #704#67semidirect
373. C22×C3×C5#131semidirect
609. C22×C5#907semidirect
685. C3×C5#2933semidirect
694. C22×C3#4131semidirect
777. C5#83757semidirect
792. C22#91929semidirect
806. C3#10617217semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#7042
C2×#919292
#117553852
C2×#912412
#117520462
#117520452
#117520442
#117520372
#117520362
#117520352
#67×#1702
#117520142
#117520012
#117519952
#117519872
#106172173
#837575