Finite Group Databasebeta

← #14415303

Subgroups — #14415303

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91929C211yesmaximal, characteristic, complemented
2C2×#91916C211yesmaximal, characteristic, complemented
3#11752851C211yesmaximal, characteristic
4#11752351C211yesmaximal, characteristic, complemented
5C3×#65695C211yesmaximal, characteristic, complemented
6#11752043C211yesmaximal, characteristic, complemented
7#11752040C211yesmaximal, characteristic, complemented
8#11751987C211yesmaximal, characteristic, complemented
9#11751923C211yesmaximal, characteristic, complemented
10#11751912C211yesmaximal, characteristic, complemented
11#11751910C211yesmaximal, characteristic, complemented
12#11751900C211yesmaximal, characteristic, complemented
13#11751880C211yesmaximal, characteristic, complemented
14#11751879C211yesmaximal, characteristic, complemented
15C4×#6738C211yesmaximal, characteristic, complemented
16#10617309—31nomaximal, Hall
17C2×#6782C2211yescharacteristic
18C2×#6773C2211yescharacteristic
19C22×C3⋊#170C2211yescharacteristic
20C2×D5⋊(C3⋊C8)C2211yescharacteristic
21C2×C3×#704C2211yescharacteristic
22C2×C3×#700C2211yescharacteristic
23C2×#6740C2211yescharacteristic
24C2×#6740C2211yescharacteristic
25C2×#6740C2211yescharacteristic
26C2×#6739C2211yescharacteristic
27C2×#6738C2211yescharacteristic
28C2×#6738C2211yescharacteristic
29C2×#6738C2211yescharacteristic
30#91929—24no—
31C2×D3×#170C2211yescharacteristic
32#91916—24no—
33#91773C411yescharacteristic
34C5×#885C411yescharacteristic
35C3×#4027C2211yescharacteristic
36#91567C411yescharacteristic
37#91552C2211yescharacteristic
38#91533C411yescharacteristic
39#91461C411yescharacteristic
40#91440C2211yescharacteristic
41#91420C411yescharacteristic
42#91405C2211yescharacteristic
43C4×#1200C2211yescharacteristic
44#91353C411yescharacteristic
45#91329C411yescharacteristic
46#91241C2211yescharacteristic
47#91233C2211yescharacteristic
48#91232C2211yescharacteristic
49C4×C3⋊#170C2211yescharacteristic
50C3×C22⋊#170C2211yescharacteristic
51C3×#4004C2211yescharacteristic
52C3×#4003C2211yescharacteristic
53C3×C4×#170C2211yescharacteristic
54#91177C2211yescharacteristic
55#91177C2211yescharacteristic
56#91171C2211yescharacteristic
57#91171C2211yescharacteristic
58(C2×D3)⋊#170C2211yescharacteristic
59(C2×D3)⋊#170C2211yescharacteristic
60Dic3×#170C2211yescharacteristic
61Dic3×#170C2211yescharacteristic
62#79538—51nomaximal, Hall
63C2×#4133—31no—
64C2×#4131—31no—
65#66002—31no—
66#65787—31no—
67#65776—31no—
68#65695—31no—
69#65695—31no—
70#65695—31no—
71#65695D311yescharacteristic, complemented
72#65692—31no—
73#65692—31no—
74#65692—31no—
75#65692—31no—
76#65682—31no—
77C4×D5⋊C8—31no—
78C2×#1220C2×C411yescharacteristic
79C2×#1220C2×C411yescharacteristic
80C2×D60C2×C411yescharacteristic
81C2×C4×D15C2×C411yescharacteristic
82C2×C5×#67C2×C411yescharacteristic
83C2×C5×Dic6C2×C411yescharacteristic
84C2×C3×C22⋊D5C2×C411yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C2×C3×C4×D5C2311yescharacteristic
87C2×#1204C2×C411yescharacteristic
88C2×#1203C2×C411yescharacteristic
89C2×#1203C2×C411yescharacteristic
90C2×#1202C2×C411yescharacteristic
91C2×#1202C2×C411yescharacteristic
92C2×#1201C2×C411yescharacteristic
93C2×#1200C2×C411yescharacteristic
94C2×#1200C2311yescharacteristic
95C2×#1200C2311yescharacteristic
96#6782—22no—
97#6782—22no—
98C2×D3×Dic5C2311yescharacteristic
99#6773—22no—
100#6773—22no—
101C2×C3⋊#170—22no—
102C2×C3⋊#170C2311yescharacteristic
103C2×C3⋊#170C2311yescharacteristic
104C2×C3⋊#170C2311yescharacteristic
105C2×C3⋊#170C2311yescharacteristic
106D5⋊(C3⋊C8)—22no—
107C3×#704—22no—
108C2×C3×#170C2311yescharacteristic
109C2×C3×#170C2311yescharacteristic
110C2×C3×#170C2311yescharacteristic
111C2×C3×#170C2311yescharacteristic
112C3×#700—22no—
113#6740—22no—
114#6740—22no—
115#6740—22no—
116#6739—22no—
117#6738—22no—
118#6738—22no—
119#6738D414yescomplemented
120D3×#170—22no—
121C3×C5×C22⋊C4C2×C411yescharacteristic
122#6714C2×C411yescharacteristic
123#6712C2×C411yescharacteristic
124C5×#217C2×C411yescharacteristic
125C5×(C2×D3)⋊C4C2×C411yescharacteristic
126C5×(C2×D3)⋊C4C2×C411yescharacteristic
127C4×C5×Dic3C2×C411yescharacteristic
128C3×#685C2×C411yescharacteristic
129C3×#683C2×C411yescharacteristic
130C3×C4×Dic5C2311yescharacteristic
131#6669C2×C411yescharacteristic
132#6668C2×C411yescharacteristic
133#6667C2×C411yescharacteristic
134#6665C2×C411yescharacteristic
135Dic3×Dic5C2×C411yescharacteristic
136Dic3×Dic5C2311yescharacteristic
137C2×#907—51no—
138C2×#907—51no—
139#5548—51no—
140C3×#436—51no—
141#5128—51no—
142#5128—51no—
143D4×C3⋊C8—51no—
144#4837—51no—
145#4834—51no—
146#4727—51no—
147#4727—51no—
148#67⋊C8—51no—
149#67⋊C8—51no—
150#4688—51no—
151C4×D3×C8—51no—
152C2×#713—31no—
153C2×#711—31no—
154C2×#704—31no—
155C2×#704C2×D311yescharacteristic
156C22×#170—31no—
157C22×#170—31no—
158#4133—64no—
159#4131—64no—
160C2×#700—31no—
161C2×#700—31no—
162C2×#700—31no—
163C2×#700C2×D311yescharacteristic
164C2×D5⋊C8—31no—
165C2×D5⋊C8—31no—
166C2×D5⋊C8—31no—
167C2×D5⋊C8—31no—
168C5×#124—31no—
169#4090—31no—
170#4086—31no—
171#4030—31no—
172#4030—31no—
173#4030—31no—
174#4030—31no—
175#4027—31no—
176#4027—31no—
177#4027—31no—
178#4027C2×D311yescharacteristic
179#4021—31no—
180C42×D5—31no—
181C22⋊#170—31no—
182C22⋊#170—31no—
183C22⋊#170—31no—
184C22⋊#170C2×D311yescharacteristic
185#4004—31no—
186#4004—31no—
187#4004—31no—
188#4004C2×D311yescharacteristic
189#4003—31no—
190#4003—31no—
191#4003—31no—
192#4003C2×D311yescharacteristic
193C4×#170—31no—
194C4×#170—31no—
195C4×#170—31no—
196C4×#170C2×D311yescharacteristic
197#2931—151noSylow
198C23×C3×C5C22×C411yescharacteristic
199C22×D15C22×C411yescharacteristic
200C22×D15C22×C411yescharacteristic
201C22×C5×D3C22×C411yescharacteristic
202C22×C3×D5C22×C411yescharacteristic
203C2×C3×C4×C5C22×C411yescharacteristic
204C2×C3×C4×C5C22×C411yescharacteristic
205#1220—22no—
206#1220—22no—
207C2×Dic15C22×C411yescharacteristic
208C2×Dic15C22×C411yescharacteristic
209D60—22no—
210C4×D15—22no—
211C5×#67—22no—
212C2×C5×Dic3C22×C411yescharacteristic
213C2×C5×Dic3C22×C411yescharacteristic
214C2×C5×Dic3C22×C411yescharacteristic
215C5×Dic6—22no—
216C3×C22⋊D5—22no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5C22×C411yescharacteristic
220C2×C3×Dic5C22×C411yescharacteristic
221C2×C3×Dic5C2411yescharacteristic
222C3×C4×D5—21no—
223C3×C4×D5—21no—
224#1204—22no—
225#1203—22no—
226#1203—22no—
227#1202—22no—
228#1202—22no—
229#1201—22no—
230#1200—22no—
231#1200—21no—
232#1200—21no—
233#1200C2×D412yes—
234#1200#4112yes—
235D3×Dic5—21no—
236D3×Dic5—21no—
237C3⋊#170—21no—
238C3⋊#170—21no—
239C3⋊#170—21no—
240C3⋊#170C2×D412yes—
241C3×#170—21no—
242C3×#170—21no—
243C3×#170—21no—
244C3×#170C2×D412yes—
245C2×#235—51no—
246C2×#235—51no—
247C2×C3×M16—51no—
248C2×C3×M16—51no—
249C3×C4×D4—51no—
250#940—51no—
251#938—51no—
252C4×#67—51no—
253C4×#67—51no—
254C22×C3⋊C8—51no—
255C22×C3⋊C8—51no—
256#907—104no—
257#907—104no—
258C2×ΓL(1,𝔽25)—51no—
259C2×ΓL(1,𝔽25)—51no—
260C2×ΓL(1,𝔽25)—51no—
261C2×ΓL(1,𝔽25)—51no—
262C2×D3×C8—51no—
263C2×D3×C8—51no—
264C2×D3×C8—51no—
265C2×D3×C8—51no—
266#895—51no—
267#888—51no—
268#885—51no—
269#885AGL(1,𝔽5)11yescharacteristic
270#884—51no—
271#884—51no—
272C4×D12—51no—
273C42×D3—51no—
274C3×C4⋊C8—51no—
275C3×C22⋊C8—51no—
276C3×C22⋊C8—51no—
277C3×C4×C8—51no—
278#830—51no—
279#830—51no—
280(C2×D3)⋊C8—51no—
281(C2×D3)⋊C8—51no—
282(C2×D3)⋊C8—51no—
283(C2×D3)⋊C8—51no—
284Dic3⋊C8—51no—
285Dic3⋊C8—51no—
286C8×Dic3—51no—
287C8×Dic3—51no—
288C4⋊(C3⋊C8)—51no—
289C4×C3⋊C8—51no—
290C2×C5×Q8—31no—
291C2×C5×D4—31no—
292C2×C22⋊D5—31no—
293C2×C22⋊D5—31no—
294C2×C22⋊D5—31no—
295C2×C22⋊D5—31no—
296C2×C22⋊D5—31no—
297C2×C22⋊D5C4×D311yescharacteristic
298C22×Dic5—31no—
299C22×Dic5C22×D311yescharacteristic
300#713—62no—
301#713—62no—
302#711—62no—
303#711—62no—
304C2×D20—31no—
305C2×D20—31no—
306C2×D20—31no—
307C2×C4×D5—31no—
308C2×C4×D5—31no—
309C2×C4×D5—31no—
310C2×C4×D5—31no—
311C2×C4×D5C22×D311yescharacteristic
312C2×Dic10—31no—
313#704—22no—
314#704—62no—
315C2×#170—31no—
316C2×#170—31no—
317C2×#170—31no—
318C2×#170—31no—
319C2×#170—62no—
320C2×#170—62no—
321C2×#170C22×D311yescharacteristic
322C2×#170C22×D311yescharacteristic
323C2×#170C22×D311yescharacteristic
324C2×#170C22×D311yescharacteristic
325#700—22no—
326#700—62no—
327#700—62no—
328#700—62no—
329D5⋊C8—34no—
330D5⋊C8—62no—
331D5⋊C8—62no—
332D5⋊C8—62no—
333C5×C22⋊C4—31no—
334C5×C22⋊C4—31no—
335C5×C22⋊C4—31no—
336C5×C22⋊C4C4×D311yescharacteristic
337C42×C5—31no—
338#685—31no—
339#685—31no—
340#685—31no—
341#685C4×D311yescharacteristic
342#683—31no—
343#683—31no—
344#683—31no—
345#683C4×D311yescharacteristic
346C4×Dic5—31no—
347C4×Dic5—31no—
348C4×Dic5C22×D311yescharacteristic
349C2×#131—151no—
350C2×#131—151no—
351#532—151no—
352#436—51no—
353#436—151no—
354#436—151no—
355#436—151no—
356C8×D4—151no—
357C8×D4—151no—
358C8×D4—151no—
359C8×D4—151no—
360#423—151no—
361#408—151no—
362#408—151no—
363C2×C4×C8—151no—
364C22×C3×C5—21no—
365C22×C3×C5—21no—
366C22×C3×C5—21no—
367C22×C3×C5C23×C411yescharacteristic
368C2×D15—21no—
369C2×D15—21no—
370C2×D15—21no—
371C2×D15—21no—
372C2×D15—21no—
373C2×D15C4×D412yes—
374C2×C5×D3—21no—
375C2×C5×D3—21no—
376C2×C5×D3—21no—
377C2×C3×D5—21no—
378C2×C3×D5—21no—
379C2×C3×D5—21no—
380C3×C4×C5—21no—
381C3×C4×C5—21no—
382Dic15—21no—
383Dic15#13112yescomplemented
384C3×Dic5—21no—
385C3×Dic5#13112yescomplemented
386C3×Dic5C22×D411yescharacteristic
387C3×Dic5C2×#4111yescharacteristic
388C5×Dic3—21no—
389C5×Dic3—21no—
390C5×Dic3C4×D412yes—
391C2×C3×D4—51no—
392C22×C3×C4—51no—
393C22×C3×C4—51no—
394C2×#67—51no—
395C2×#67—51no—
396C2×#67—51no—
397C2×#67—51no—
398C2×#67—51no—
399C2×#67C2×AGL(1,𝔽5)11yescharacteristic
400#235—102no—
401#235—102no—
402#235—102no—
403#235—102no—
404C2×D12—51no—
405C2×D12—51no—
406C2×D12—51no—
407C2×C4×D3—51no—
408C2×C4×D3—51no—
409C2×C4×D3—51no—
410C2×C4×D3—51no—
411C2×C4×D3—51no—
412C2×Dic6—51no—
413C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
414C3×M16—102no—
415C3×M16—102no—
416C2×C3×C8—51no—
417C2×C3×C8—51no—
418C2×C3×C8—51no—
419C2×C3×C8—51no—
420C3×C4⋊C4—51no—
421C3×C22⋊C4—51no—
422C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
423C3×C42—51no—
424#217—51no—
425#217C2×AGL(1,𝔽5)11yescharacteristic
426(C2×D3)⋊C4—51no—
427(C2×D3)⋊C4—51no—
428(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
429(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
430C4⋊Dic3—51no—
431Dic3⋊C4—51no—
432Dic3⋊C4—51no—
433C4×Dic3—51no—
434C4×Dic3—51no—
435C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
436C2×C3⋊C8—51no—
437C2×C3⋊C8—51no—
438C2×C3⋊C8—51no—
439C2×C3⋊C8—51no—
440C2×C3⋊C8—102no—
441C2×C3⋊C8—102no—
442ΓL(1,𝔽25)—102no—
443ΓL(1,𝔽25)—102no—
444ΓL(1,𝔽25)—102no—
445ΓL(1,𝔽25)—102no—
446D3×C8—54no—
447D3×C8—102no—
448D3×C8—102no—
449D3×C8—102no—
450C23×C5—31no—
451C23×C5C2×C4×D311yescharacteristic
452C22×D5—31no—
453C22×D5—31no—
454C22×D5C2×C4×D311yescharacteristic
455C5×Q8—62no—
456C5×D4—62no—
457C2×C4×C5—31no—
458C2×C4×C5—31no—
459C2×C4×C5—31no—
460C2×C4×C5C2×C4×D311yescharacteristic
461C2×C4×C5C2×C4×D311yescharacteristic
462C22⋊D5—22no—
463C22⋊D5—62no—
464C22⋊D5—62no—
465C22⋊D5—62no—
466C22⋊D5—62no—
467C22⋊D5—62no—
468C2×Dic5—21no—
469C2×Dic5—21no—
470C2×Dic5—31no—
471C2×Dic5—31no—
472C2×Dic5—61no—
473C2×Dic5—61no—
474C2×Dic5C2×C4×D311yescharacteristic
475C2×Dic5C2×C4×D311yescharacteristic
476C2×Dic5C23×D311yescharacteristic
477D20—62no—
478D20—62no—
479D20—62no—
480C4×D5—21no—
481C4×D5—21no—
482C4×D5—32no—
483C4×D5—32no—
484C4×D5—62no—
485C4×D5—62no—
486C4×D5—61no—
487C4×D5—61no—
488Dic10—62no—
489#170—21no—
490#170—21no—
491#170—21no—
492#170—32no—
493#170—61no—
494#170—61no—
495#170—61no—
496#170D3×D412yes—
497C2×#41—151no—
498C2×#41—151no—
499#131—304no—
500#131—304no—
501C2×M16—51no—
502C2×M16—51no—
503C2×M16—151no—
504C2×M16—151no—
505C2×M16—151no—
506C2×M16—151no—
507C22×C8—151no—
508C22×C8—151no—
509C22×C8—151no—
510C22×C8—151no—
511C22×C8—151no—
512C22×C8—151no—
513C4⋊Q8—151no—
514#127—151no—
515#124—31no—
516#124—151no—
517#121—151no—
518#121—151no—
519#121—151no—
520#121—151no—
521C4×D4—51no—
522C4×D4—151no—
523C4×D4—151no—
524C4×D4—151no—
525C2×C42—151no—
526C4⋊C8—51no—
527C4⋊C8—151no—
528C4⋊C8—151no—
529C4⋊C8—151no—
530C22⋊C8—51no—
531C22⋊C8—51no—
532C22⋊C8—151no—
533C22⋊C8—151no—
534C22⋊C8—151no—
535C22⋊C8—151no—
536C22⋊C8—151no—
537C22⋊C8—151no—
538C4×C8—51no—
539C4×C8—151no—
540C4×C8—151no—
541C4×C8—151no—
542C2×C3×C5—41no—
543C2×C3×C5C2×C4×D411yescharacteristic
544C2×C3×C5C2×#13111yescharacteristic
545C2×C3×C5C2×#13111yescharacteristic
546D15—22no—
547D15—41no—
548C3×D5—41no—
549C5×D3—41no—
550C23×C3—51no—
551C23×C3C22×AGL(1,𝔽5)11yescharacteristic
552C22×D3—51no—
553C22×D3—51no—
554C22×D3C22×AGL(1,𝔽5)11yescharacteristic
555C3×D4—102no—
556C2×C3×C4—51no—
557C2×C3×C4—51no—
558C2×C3×C4—51no—
559C2×C3×C4—101no—
560C2×C3×C4—101no—
561C2×C3×C4—101no—
562C2×C3×C4—101no—
563C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
564C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
565#67—22no—
566#67—102no—
567#67—102no—
568#67—102no—
569#67—102no—
570#67—102no—
571C2×Dic3—51no—
572C2×Dic3—51no—
573C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
574C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
575C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
576D12—102no—
577D12—102no—
578D12—102no—
579C4×D3—52no—
580C4×D3—52no—
581C4×D3—101no—
582C4×D3—102no—
583C4×D3—101no—
584C4×D3—102no—
585C4×D3—101no—
586C4×D3—101no—
587Dic6—22no—
588Dic6—102no—
589C3×C8—52no—
590C3×C8—101no—
591C3×C8—101no—
592C3×C8—101no—
593C3⋊C8—52no—
594C3⋊C8—101no—
595C3⋊C8—101no—
596C3⋊C8—101no—
597C22×C5—21no—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—61no—
601C22×C5—61no—
602C22×C5—61no—
603C22×C5C22×C4×D311yescharacteristic
604C2×D5—21no—
605C2×D5—21no—
606C2×D5—21no—
607C2×D5—32no—
608C2×D5—61no—
609C2×D5—61no—
610C2×D5—61no—
611C2×D5—61no—
612C2×D5—61no—
613C4×C5—21no—
614C4×C5—21no—
615C4×C5—32no—
616C4×C5—61no—
617C4×C5—61no—
618Dic5—21no—
619Dic5—32no—
620Dic5—61no—
621Dic5#90712yescomplemented
622Dic5C2×D3×D411yescharacteristic
623Dic5D3×#4111yescharacteristic
624#41—302no—
625#41—302no—
626#41—302no—
627#41—302no—
628C2×Q8—31no—
629C2×Q8—151no—
630C2×D4—31no—
631C2×D4—51no—
632C2×D4—151no—
633C2×D4—151no—
634C2×D4—151no—
635C2×D4—151no—
636C2×D4—151no—
637C2×D4—151no—
638C2×D4—151no—
639C2×D4—151no—
640C22×C4—51no—
641C22×C4—51no—
642C22×C4—151no—
643C22×C4—151no—
644C22×C4—151no—
645C22×C4—151no—
646C22×C4—151no—
647M16—102no—
648M16—102no—
649M16—302no—
650M16—302no—
651M16—302no—
652M16—302no—
653C2×C8—51no—
654C2×C8—51no—
655C2×C8—51no—
656C2×C8—51no—
657C2×C8—154no—
658C2×C8—151no—
659C2×C8—151no—
660C2×C8—151no—
661C2×C8—151no—
662C2×C8—302no—
663C2×C8—302no—
664C2×C8—302no—
665C2×C8—302no—
666C2×C8—302no—
667C4⋊C4—51no—
668C4⋊C4—151no—
669C4⋊C4—151no—
670C4⋊C4—151no—
671C22⋊C4—31no—
672C22⋊C4—31no—
673C22⋊C4—31no—
674C22⋊C4—51no—
675C22⋊C4—151no—
676C22⋊C4—151no—
677C22⋊C4—151no—
678C22⋊C4D3×AGL(1,𝔽5)11yescharacteristic
679C42—31no—
680C42—51no—
681C42—151no—
682C42—151no—
683C3×C5#293111yescharacteristic, complemented, Hall
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—101no—
688C22×C3—101no—
689C22×C3—101no—
690C22×C3C23×AGL(1,𝔽5)11yescharacteristic
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—21no—
694C2×D3—52no—
695C2×D3—101no—
696C2×D3—101no—
697C2×D3—101no—
698C2×D3—101no—
699C2×D3—101no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—51no—
703C3×C4—51no—
704C3×C4—52no—
705C3×C4—101no—
706Dic3—21no—
707Dic3—21no—
708Dic3—52no—
709Dic3—101no—
710Dic3D4×AGL(1,𝔽5)12yes—
711C2×C5—41no—
712C2×C5—121no—
713C2×C5C4×D3×D411yescharacteristic
714C2×C5C2×#90711yescharacteristic
715C2×C5D3×#13111yescharacteristic
716D5—41no—
717D5—62no—
718D5—121no—
719C23—31no—
720C23—51no—
721C23—151no—
722C23—151no—
723C23C2×D3×AGL(1,𝔽5)11yescharacteristic
724Q8—62no—
725Q8—302no—
726D4—62no—
727D4—102no—
728D4—302no—
729D4—302no—
730D4—302no—
731D4—302no—
732D4—302no—
733D4—302no—
734D4—302no—
735D4—302no—
736C2×C4—31no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—51no—
740C2×C4—51no—
741C2×C4—51no—
742C2×C4—101no—
743C2×C4—101no—
744C2×C4—101no—
745C2×C4—101no—
746C2×C4—152no—
747C2×C4—152no—
748C2×C4—151no—
749C2×C4—151no—
750C2×C4—302no—
751C2×C4—301no—
752C2×C4—301no—
753C2×C4—302no—
754C2×C4—301no—
755C2×C4—301no—
756C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
757C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
758C8—52no—
759C8—101no—
760C8—101no—
761C8—101no—
762C8—152no—
763C8—301no—
764C8—301no—
765C8—301no—
766C2×C3—41no—
767C2×C3—201no—
768C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
769C2×C3D5⋊#13111yescharacteristic
770C2×C3D5⋊#13111yescharacteristic
771D3—41no—
772D3—102no—
773D3—201no—
774C5#7953811yescharacteristic, complemented, Sylow
775C22—21no—
776C22—21no—
777C22—21no—
778C22—61no—
779C22—61no—
780C22—61no—
781C22—101no—
782C22—101no—
783C22—101no—
784C22—152no—
785C22—301no—
786C22—301no—
787C22—301no—
788C22—301no—
789C22—301no—
790C22C22×D3×AGL(1,𝔽5)11yescharacteristic
791C4—21no—
792C4—21no—
793C4—32no—
794C4—52no—
795C4—51no—
796C4—51no—
797C4—61no—
798C4—61no—
799C4—101no—
800C4—152no—
801C4—301no—
802C3#1061730911yescharacteristic, complemented, Sylow
803C2—41no—
804C2—121no—
805C2—201no—
806C2—302no—
807C2—601no—
808C2D5⋊#90711yescharacteristic
809C2#1175684011yescharacteristic
810C2D3×D4×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C22⋊C4C2×C4
prime radical#11752851C2
cosocleC2×C3×Dic5C24
hypercenterC22⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2931
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×#91929C2semidirect
2. C2×#91916C2semidirect
4. #11752351C2semidirect
5. C3×#65695C2semidirect
6. #11752043C2semidirect
7. #11752040C2semidirect
8. #11751987C2semidirect
9. #11751923C2semidirect
10. #11751912C2semidirect
11. #11751910C2semidirect
12. #11751900C2semidirect
13. #11751880C2semidirect
14. #11751879C2semidirect
15. C4×#6738C2semidirect
71. #65695D3semidirect
119. #6738D4semidirect
383. Dic15#131semidirect
385. C3×Dic5#131semidirect
621. Dic5#907semidirect
683. C3×C5#2931semidirect
774. C5#79538semidirect
802. C3#10617309semidirect

Maximal subgroups

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

subgroupindex
C2×#919292
C2×#919162
#117528512
#117523512
C3×#656952
#117520432
#117520402
#117519872
#117519232
#117519122
#117519102
#117519002
#117518802
#117518792
C4×#67382
#106173093
#795385