Finite Group Databasebeta

← #14415407

Subgroups — #14415407

Order 1920.

968 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×#91990C211yesmaximal, characteristic, complemented
2C2×#91929C211yesmaximal, characteristic, complemented
3#11754796C211yesmaximal, characteristic
4C3×#65775C211yesmaximal, characteristic, complemented
5#11752054C211yesmaximal, characteristic, complemented
6#11752053C211yesmaximal, characteristic, complemented
7#11752041C211yesmaximal, characteristic, complemented
8#11752039C211yesmaximal, characteristic, complemented
9#11752012C211yesmaximal, characteristic, complemented
10#11751999C211yesmaximal, characteristic, complemented
11C2×#91169C211yesmaximal, characteristic, complemented
12#11751925C211yesmaximal, characteristic, complemented
13#11751924C211yesmaximal, characteristic, complemented
14#11751903C211yesmaximal, characteristic, complemented
15#11751899C211yesmaximal, characteristic, complemented
16#10617228—31nomaximal, Hall
17C2×C3×#711C2211yescharacteristic
18C2×#6782C2211yescharacteristic
19C2×#6762C2211yescharacteristic
20C2×#6762C2211yescharacteristic
21C22×C3⋊#170C2211yescharacteristic
22C22×C3⋊#170C2211yescharacteristic
23#91990—24no—
24C2×#6758C2211yescharacteristic
25C2×D5⋊(C3⋊C8)C2211yescharacteristic
26C2×C3×#704C2211yescharacteristic
27C22×C3×#170C2211yescharacteristic
28C2×#6740C2211yescharacteristic
29C2×#6739C2211yescharacteristic
30C2×#6738C2211yescharacteristic
31#91929—24no—
32C2×D3×#170C2211yescharacteristic
33#91828C411yescharacteristic
34C5×#939C411yescharacteristic
35#91571C411yescharacteristic
36#91569C411yescharacteristic
37#91567C411yescharacteristic
38#91552C2211yescharacteristic
39Dic5×#67C2211yescharacteristic
40#91534C411yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42#91444C2211yescharacteristic
43#91440C2211yescharacteristic
44#91327C411yescharacteristic
45#91326C411yescharacteristic
46C3×C22⋊#170C2211yescharacteristic
47C3×C22⋊#170C2211yescharacteristic
48C3×#4003C2211yescharacteristic
49C3×#4003C2211yescharacteristic
50#91177C2211yescharacteristic
51#91177C2211yescharacteristic
52Dic3⋊#170C2211yescharacteristic
53Dic3⋊#170C2211yescharacteristic
54#91171C2211yescharacteristic
55#91171C2211yescharacteristic
56(C2×D3)⋊#170C2211yescharacteristic
57(C2×D3)⋊#170C2211yescharacteristic
58#91169C2211yescharacteristic
59#91169C2211yescharacteristic
60#91169C2211yescharacteristic
61#91169C2211yescharacteristic
62#78658—51nomaximal, Hall
63C2×#4131—31no—
64C2×#4131—31no—
65#65930—31no—
66#65775—31no—
67#65775D311yescharacteristic, complemented
68#65773—31no—
69#65773—31no—
70#65758—31no—
71C2×#4002—31no—
72#65704—31no—
73#65704—31no—
74#65694—31no—
75#65694—31no—
76#65693—31no—
77#65693—31no—
78C2×C3×C5×D4C2×C411yescharacteristic
79C2×#1220C2×C411yescharacteristic
80C2×#1220C2×C411yescharacteristic
81C22×Dic15C2×C411yescharacteristic
82C2×C5×#67C2×C411yescharacteristic
83C2×C5×#67C2×C411yescharacteristic
84C22×C5×Dic3C2×C411yescharacteristic
85C2×C3×C22⋊D5C2×C411yescharacteristic
86C2×C3×C22⋊D5C2×C411yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C3×#711—22no—
90C3×#711—22no—
91C2×C3×C4×D5C2311yescharacteristic
92C2×C3×Dic10C2×C411yescharacteristic
93C2×#1204C2×C411yescharacteristic
94C2×#1203C2×C411yescharacteristic
95C2×#1202C2×C411yescharacteristic
96C2×#1201C2×C411yescharacteristic
97C2×#1200C2311yescharacteristic
98#6782—22no—
99#6782—22no—
100C2×D3×Dic5C2311yescharacteristic
101#6762—22no—
102#6762—22no—
103C2×C3⋊#170—22no—
104C2×C3⋊#170D414yescomplemented
105C2×C3⋊#170C2311yescharacteristic
106C2×C3⋊#170C2311yescharacteristic
107C2×C3⋊#170C2311yescharacteristic
108C2×C3⋊#170C2311yescharacteristic
109#6758—22no—
110D5⋊(C3⋊C8)—22no—
111C3×#704—22no—
112C2×C3×#170—22no—
113C2×C3×#170C2311yescharacteristic
114C2×C3×#170C2311yescharacteristic
115C2×C3×#170C2311yescharacteristic
116C2×C3×#170C2311yescharacteristic
117#6740—22no—
118#6739—22no—
119#6738—22no—
120D3×#170—22no—
121#6719C2×C411yescharacteristic
122#6714C2×C411yescharacteristic
123#6712C2×C411yescharacteristic
124C5×#217C2×C411yescharacteristic
125C5×(C2×D3)⋊C4C2×C411yescharacteristic
126C5×Dic3⋊C4C2×C411yescharacteristic
127Dic3⋊Dic5C2×C411yescharacteristic
128#6669C2×C411yescharacteristic
129#6667C2×C411yescharacteristic
130(C2×D3)⋊Dic5C2×C411yescharacteristic
131#6665C2×C411yescharacteristic
132#6665C2×C411yescharacteristic
133Dic3×Dic5C2×C411yescharacteristic
134Dic3×Dic5C2×C411yescharacteristic
135Dic3×Dic5C2311yescharacteristic
136Dic3×Dic5C2311yescharacteristic
137#5832—51no—
138C2×#948—51no—
139C2×#907—51no—
140C3×#408—51no—
141#5118—51no—
142#5110—51no—
143C2×#815—51no—
144#4730—51no—
145#4730—51no—
146#4730—51no—
147#4730—51no—
148#4728—51no—
149#4728—51no—
150#4728—51no—
151#4728—51no—
152C2×#711—31no—
153C2×#711C2×D311yescharacteristic
154C2×#704—31no—
155C2×#704—31no—
156C2×#704—31no—
157C2×#704C2×D311yescharacteristic
158C22×#170—31no—
159C22×#170—31no—
160C22×#170—31no—
161C22×#170C2×D311yescharacteristic
162#4131—64no—
163#4131—64no—
164C2×#700—31no—
165C2×#700—31no—
166C2×D5⋊C8—31no—
167C2×D5⋊C8—31no—
168C5×#121—31no—
169#4086—31no—
170#4085—31no—
171#4085—31no—
172D4×Dic5—31no—
173#4076—31no—
174C2×C4×Dic5—31no—
175#4039—31no—
176#4034—31no—
177#4031—31no—
178#4031—31no—
179#4027—31no—
180#4027—31no—
181C22⋊#170—31no—
182C22⋊#170—31no—
183C22⋊#170C2×D311yescharacteristic
184C22⋊#170C2×D311yescharacteristic
185#4004—31no—
186#4004—31no—
187#4003—31no—
188#4003—31no—
189#4003C2×D311yescharacteristic
190#4003C2×D311yescharacteristic
191#4002—31no—
192#4002—31no—
193#4002—31no—
194#4002—31no—
195C4⋊#170—31no—
196C4⋊#170—31no—
197#2932—151noSylow
198C23×C3×C5C22×C411yescharacteristic
199C23×C3×C5C22×C411yescharacteristic
200C22×D15C22×C411yescharacteristic
201C22×C5×D3C22×C411yescharacteristic
202C22×C3×D5C22×C411yescharacteristic
203C3×C5×D4—22no—
204C2×C3×C4×C5C22×C411yescharacteristic
205#1220—22no—
206#1220—41no—
207C2×Dic15—41no—
208C2×Dic15C22×C411yescharacteristic
209C2×Dic15C22×C411yescharacteristic
210C2×Dic15C22×C411yescharacteristic
211C5×#67—22no—
212C5×#67—41no—
213C2×C5×Dic3—41no—
214C2×C5×Dic3C22×C411yescharacteristic
215C2×C5×Dic3C22×C411yescharacteristic
216C2×C5×Dic3C22×C411yescharacteristic
217C3×C22⋊D5—22no—
218C3×C22⋊D5—22no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5C22×C411yescharacteristic
222C2×C3×Dic5C22×C411yescharacteristic
223C2×C3×Dic5C2×D412yes—
224C2×C3×Dic5#4112yes—
225C2×C3×Dic5C2411yescharacteristic
226C3×C4×D5—21no—
227C3×C4×D5—21no—
228C3×Dic10—22no—
229#1204—22no—
230#1203—22no—
231#1202—41no—
232#1201—41no—
233#1200—21no—
234#1200—21no—
235D3×Dic5—21no—
236D3×Dic5—21no—
237C3⋊#170—21no—
238C3⋊#170—21no—
239C3⋊#170C2×D412yes—
240C3⋊#170C2×D412yes—
241C3×#170—21no—
242C3×#170—21no—
243C3×#170—21no—
244C3×#170—21no—
245C2×C3×#41—51no—
246C2×#235—51no—
247C2×C3×M16—51no—
248C22×C3×C8—51no—
249#948—104no—
250#947—51no—
251#944—51no—
252#940—51no—
253#939—51no—
254#939—51no—
255#939—51no—
256#939AGL(1,𝔽5)11yescharacteristic
257#936—51no—
258C4×#67—51no—
259C4×#67—51no—
260C4×#67—51no—
261C4×#67—51no—
262C2×C4×Dic3—51no—
263C2×#208—51no—
264C2×#208—51no—
265C2×#208—51no—
266C22×C3⋊C8—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—
274C3×C22⋊C8—51no—
275C3×C22⋊C8—51no—
276C3×C22⋊C8—51no—
277C3×C22⋊C8—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—
284#815—51no—
285#815—51no—
286Dic3⋊C8—51no—
287Dic3⋊C8—51no—
288Dic3⋊C8—51no—
289Dic3⋊C8—51no—
290C2×C5×D4—31no—
291C2×C5×D4—31no—
292C2×C5×D4C4×D311yescharacteristic
293C22×C4×C5—31no—
294C2×C22⋊D5—31no—
295C2×C22⋊D5—31no—
296C2×C22⋊D5—31no—
297C2×C22⋊D5—31no—
298C2×C22⋊D5C4×D311yescharacteristic
299C2×C22⋊D5C4×D311yescharacteristic
300C22×Dic5—31no—
301C22×Dic5—31no—
302C22×Dic5C22×D311yescharacteristic
303C22×Dic5C22×D311yescharacteristic
304#711—22no—
305#711—22no—
306#711—62no—
307#711—62no—
308C2×D20—31no—
309C2×C4×D5—31no—
310C2×C4×D5C22×D311yescharacteristic
311C2×Dic10—31no—
312C2×Dic10C4×D311yescharacteristic
313#704—22no—
314#704—62no—
315#704—62no—
316#704—62no—
317C2×#170—22no—
318C2×#170—34no—
319C2×#170—31no—
320C2×#170—31no—
321C2×#170—31no—
322C2×#170—31no—
323C2×#170—62no—
324C2×#170—62no—
325C2×#170C22×D311yescharacteristic
326C2×#170C22×D311yescharacteristic
327C2×#170C22×D311yescharacteristic
328C2×#170C22×D311yescharacteristic
329#700—62no—
330#700—62no—
331D5⋊C8—62no—
332D5⋊C8—62no—
333C5×C4⋊C4—31no—
334C5×C22⋊C4—31no—
335C5×C22⋊C4—31no—
336C22⋊Dic5—31no—
337C22⋊Dic5—31no—
338#685—31no—
339#685—31no—
340#685—31no—
341#685—31no—
342C4⋊Dic5—31no—
343#683—31no—
344#683—31no—
345C4×Dic5—31no—
346C4×Dic5—31no—
347C4×Dic5—31no—
348C4×Dic5—31no—
349C2×#131—151no—
350C2×#131—151no—
351#532—151no—
352#435—151no—
353#435—151no—
354#435—151no—
355#435—151no—
356#435—151no—
357#435—151no—
358#435—151no—
359#435—151no—
360#423—151no—
361#408—51no—
362#408—151no—
363C2×#97—151no—
364C22×C3×C5—21no—
365C22×C3×C5—21no—
366C22×C3×C5—21no—
367C22×C3×C5—21no—
368C22×C3×C5—21no—
369C22×C3×C5C4×D412yes—
370C22×C3×C5C23×C411yescharacteristic
371C2×D15—21no—
372C2×D15—21no—
373C2×D15—21no—
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—
381Dic15—21no—
382Dic15—21no—
383Dic15—21no—
384C3×Dic5—21no—
385C3×Dic5C4×D412yes—
386C3×Dic5C22×D411yescharacteristic
387C3×Dic5C2×#4111yescharacteristic
388C5×Dic3—21no—
389C5×Dic3—21no—
390C5×Dic3—21no—
391C3×#41—102no—
392C3×#41—102no—
393C2×C3×Q8—51no—
394C2×C3×D4—51no—
395C2×C3×D4—51no—
396C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
397C22×C3×C4—51no—
398C22×C3×C4—51no—
399C22×C3×C4—51no—
400C2×#67—51no—
401C2×#67—51no—
402C2×#67—51no—
403C2×#67—51no—
404C2×#67C2×AGL(1,𝔽5)11yescharacteristic
405C2×#67C2×AGL(1,𝔽5)11yescharacteristic
406C22×Dic3—51no—
407C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
408#235—102no—
409#235—102no—
410C2×D12—51no—
411C2×C4×D3—51no—
412C2×C4×D3—51no—
413C2×Dic6—51no—
414C3×M16—102no—
415C2×C3×C8—51no—
416C2×C3×C8—51no—
417C2×C3×C8—51no—
418C2×C3×C8—51no—
419C2×C3×C8—102no—
420#217—51no—
421#217—51no—
422#217—51no—
423#217C2×AGL(1,𝔽5)11yescharacteristic
424(C2×D3)⋊C4—51no—
425(C2×D3)⋊C4—51no—
426(C2×D3)⋊C4—51no—
427(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
428Dic3⋊C4—51no—
429Dic3⋊C4—51no—
430Dic3⋊C4—51no—
431Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
432C4×Dic3—51no—
433C4×Dic3—51no—
434C4×Dic3—51no—
435C4×Dic3—51no—
436#208—102no—
437#208—102no—
438#208—102no—
439C2×C3⋊C8—51no—
440C2×C3⋊C8—51no—
441C2×C3⋊C8—54no—
442C2×C3⋊C8—51no—
443C2×C3⋊C8—51no—
444C2×C3⋊C8—102no—
445C2×C3⋊C8—102no—
446ΓL(1,𝔽25)—102no—
447ΓL(1,𝔽25)—102no—
448D3×C8—102no—
449D3×C8—102no—
450C23×C5—31no—
451C23×C5C2×C4×D311yescharacteristic
452C23×C5C2×C4×D311yescharacteristic
453C22×D5—31no—
454C22×D5C2×C4×D311yescharacteristic
455C5×D4—22no—
456C5×D4—62no—
457C5×D4—121no—
458C2×C4×C5—31no—
459C2×C4×C5—31no—
460C2×C4×C5—31no—
461C2×C4×C5—121no—
462C2×C4×C5C2×C4×D311yescharacteristic
463C22⋊D5—22no—
464C22⋊D5—22no—
465C22⋊D5—62no—
466C22⋊D5—62no—
467C22⋊D5—121no—
468C22⋊D5—121no—
469C2×Dic5—21no—
470C2×Dic5—21no—
471C2×Dic5—31no—
472C2×Dic5—31no—
473C2×Dic5—31no—
474C2×Dic5—61no—
475C2×Dic5—61no—
476C2×Dic5—121no—
477C2×Dic5C2×C4×D311yescharacteristic
478C2×Dic5C2×C4×D311yescharacteristic
479C2×Dic5D3×D412yes—
480C2×Dic5#23712yes—
481C2×Dic5C23×D311yescharacteristic
482D20—121no—
483C4×D5—21no—
484C4×D5—21no—
485C4×D5—61no—
486C4×D5—61no—
487Dic10—22no—
488Dic10—62no—
489#170—21no—
490#170—21no—
491#170—21no—
492#170—21no—
493#170—32no—
494#170—32no—
495#170—61no—
496#170—61no—
497C2×#41—51no—
498C2×#41—151no—
499#131—304no—
500#131—304no—
501C2×M16—51no—
502C2×M16—151no—
503C2×M16—151no—
504C2×M16—151no—
505C2×M16—151no—
506C2×M16—151no—
507C22×C8—51no—
508C22×C8—151no—
509C22×C8—151no—
510C22×C8—151no—
511C22×C8—151no—
512C22×C8—151no—
513C4⋊Q8—151no—
514#127—151no—
515#124—151no—
516#124—151no—
517#121—31no—
518#121—151no—
519#121—151no—
520#121—151no—
521C4×D4—151no—
522C4×D4—151no—
523C4×D4—151no—
524C4×D4—151no—
525C2×C42—151no—
526C4⋊C8—151no—
527C4⋊C8—151no—
528C4⋊C8—151no—
529C4⋊C8—151no—
530C22⋊C8—51no—
531C22⋊C8—51no—
532C22⋊C8—51no—
533C22⋊C8—51no—
534C22⋊C8—151no—
535C22⋊C8—151no—
536C22⋊C8—151no—
537C22⋊C8—151no—
538#97—151no—
539#97—151no—
540#97—151no—
541#97—151no—
542C2×C3×C5—22no—
543C2×C3×C5—41no—
544C2×C3×C5C2×C4×D411yescharacteristic
545C2×C3×C5#56811yescharacteristic
546C2×C3×C5#56811yescharacteristic
547D15—41no—
548C3×D5—41no—
549C5×D3—41no—
550C23×C3—51no—
551C23×C3C22×AGL(1,𝔽5)11yescharacteristic
552C23×C3C22×AGL(1,𝔽5)11yescharacteristic
553C22×D3—51no—
554C22×D3C22×AGL(1,𝔽5)11yescharacteristic
555C3×Q8—102no—
556C3×D4—22no—
557C3×D4—102no—
558C3×D4—102no—
559C2×C3×C4—52no—
560C2×C3×C4—52no—
561C2×C3×C4—51no—
562C2×C3×C4—51no—
563C2×C3×C4—51no—
564C2×C3×C4—101no—
565C2×C3×C4—101no—
566C2×C3×C4—101no—
567C2×C3×C4—101no—
568C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
569#67—22no—
570#67—41no—
571#67—102no—
572#67—201no—
573#67—201no—
574#67—201no—
575C2×Dic3—41no—
576C2×Dic3—51no—
577C2×Dic3—51no—
578C2×Dic3—51no—
579C2×Dic3—201no—
580C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
581C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
582C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
583D12—102no—
584C4×D3—101no—
585C4×D3—101no—
586C4×D3—101no—
587C4×D3—101no—
588Dic6—102no—
589C3×C8—101no—
590C3×C8—101no—
591C3×C8—101no—
592C3×C8—101no—
593C3⋊C8—52no—
594C3⋊C8—52no—
595C3⋊C8—101no—
596C3⋊C8—101no—
597C22×C5—21no—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—21no—
601C22×C5—21no—
602C22×C5—61no—
603C22×C5—61no—
604C22×C5—61no—
605C22×C5#67⋊C412yes—
606C22×C5C22×C4×D311yescharacteristic
607C2×D5—21no—
608C2×D5—21no—
609C2×D5—21no—
610C2×D5—61no—
611C2×D5—61no—
612C2×D5—61no—
613C4×C5—21no—
614C4×C5—61no—
615C4×C5—61no—
616C4×C5—61no—
617Dic5—21no—
618Dic5—61no—
619Dic5—61no—
620Dic5—61no—
621Dic5#67⋊C412yes—
622Dic5C2×D3×D411yescharacteristic
623Dic5C2×#23711yescharacteristic
624#41—102no—
625#41—102no—
626#41—302no—
627#41—302no—
628C2×Q8—51no—
629C2×Q8—151no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—51no—
633C2×D4—51no—
634C2×D4—151no—
635C2×D4—151no—
636C2×D4—151no—
637C2×D4—151no—
638C2×D4—151no—
639C2×D4D3×AGL(1,𝔽5)11yescharacteristic
640C22×C4—31no—
641C22×C4—51no—
642C22×C4—51no—
643C22×C4—51no—
644C22×C4—151no—
645C22×C4—151no—
646C22×C4—151no—
647M16—102no—
648M16—302no—
649M16—302no—
650M16—302no—
651M16—302no—
652M16—302no—
653C2×C8—51no—
654C2×C8—51no—
655C2×C8—51no—
656C2×C8—51no—
657C2×C8—102no—
658C2×C8—151no—
659C2×C8—151no—
660C2×C8—154no—
661C2×C8—151no—
662C2×C8—151no—
663C2×C8—302no—
664C2×C8—302no—
665C2×C8—302no—
666C2×C8—302no—
667C4⋊C4—31no—
668C4⋊C4—151no—
669C4⋊C4—151no—
670C4⋊C4—151no—
671C22⋊C4—31no—
672C22⋊C4—31no—
673C22⋊C4—151no—
674C22⋊C4—151no—
675C22⋊C4—151no—
676C22⋊C4—151no—
677C22⋊C4—151no—
678C22⋊C4—151no—
679C42—151no—
680C42—151no—
681C42—151no—
682C42—151no—
683C3×C5#293211yescharacteristic, complemented, Hall
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—101no—
690C22×C3—101no—
691C22×C3—101no—
692C22×C3D4×AGL(1,𝔽5)12yes—
693C22×C3C23×AGL(1,𝔽5)11yescharacteristic
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—101no—
698C2×D3—101no—
699C2×D3—101no—
700C3×C4—21no—
701C3×C4—52no—
702C3×C4—51no—
703C3×C4—51no—
704C3×C4—101no—
705Dic3—21no—
706Dic3—21no—
707Dic3—21no—
708Dic3—101no—
709Dic3—101no—
710Dic3—101no—
711C2×C5—22no—
712C2×C5—41no—
713C2×C5—121no—
714C2×C5C2×#67⋊C411yescharacteristic
715C2×C5#575011yescharacteristic
716C2×C5#575011yescharacteristic
717D5—41no—
718D5—121no—
719C23—31no—
720C23—51no—
721C23—151no—
722C23C2×D3×AGL(1,𝔽5)11yescharacteristic
723C23C2×D3×AGL(1,𝔽5)11yescharacteristic
724Q8—102no—
725Q8—302no—
726D4—22no—
727D4—62no—
728D4—102no—
729D4—102no—
730D4—121no—
731D4—302no—
732D4—302no—
733D4—601no—
734D4—601no—
735D4—601no—
736C2×C4—31no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—52no—
740C2×C4—52no—
741C2×C4—51no—
742C2×C4—51no—
743C2×C4—51no—
744C2×C4—101no—
745C2×C4—101no—
746C2×C4—101no—
747C2×C4—101no—
748C2×C4—121no—
749C2×C4—151no—
750C2×C4—151no—
751C2×C4—151no—
752C2×C4—301no—
753C2×C4—301no—
754C2×C4—301no—
755C2×C4—301no—
756C2×C4—601no—
757C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
758C8—101no—
759C8—101no—
760C8—101no—
761C8—101no—
762C8—152no—
763C8—152no—
764C8—301no—
765C8—301no—
766C2×C3—22no—
767C2×C3—41no—
768C2×C3—201no—
769C2×C3#6625611yescharacteristic
770C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
771C2×C3#6626411yescharacteristic
772D3—41no—
773D3—201no—
774C5#7865811yescharacteristic, complemented, Sylow
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—101no—
784C22—101no—
785C22—101no—
786C22—301no—
787C22—301no—
788C22—301no—
789C22#67⋊AGL(1,𝔽5)12yes—
790C22C22×D3×AGL(1,𝔽5)11yescharacteristic
791C4—21no—
792C4—51no—
793C4—51no—
794C4—52no—
795C4—61no—
796C4—61no—
797C4—61no—
798C4—101no—
799C4—301no—
800C4—301no—
801C4—301no—
802C3#1061722811yescharacteristic, complemented, Sylow
803C2—22no—
804C2—41no—
805C2—121no—
806C2—201no—
807C2—601no—
808C2#1175684111yescharacteristic
809C2#1175684211yescharacteristic
810C2C2×#67⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×D4C2×C4
prime radical#11754796C2
cosocleC2×C3×Dic5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#2932
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#91990C2semidirect
2. C2×#91929C2semidirect
4. C3×#65775C2semidirect
5. #11752054C2semidirect
6. #11752053C2semidirect
7. #11752041C2semidirect
8. #11752039C2semidirect
9. #11752012C2semidirect
10. #11751999C2semidirect
11. C2×#91169C2semidirect
12. #11751925C2semidirect
13. #11751924C2semidirect
14. #11751903C2semidirect
15. #11751899C2semidirect
67. #65775D3semidirect
104. C2×C3⋊#170D4semidirect
683. C3×C5#2932semidirect
774. C5#78658semidirect
802. C3#10617228semidirect

Maximal subgroups

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

subgroupindex
C2×#919902
C2×#919292
#117547962
C3×#657752
#117520542
#117520532
#117520412
#117520392
#117520122
#117519992
C2×#911692
#117519252
#117519242
#117519032
#117518992
#106172283
#786585