Finite Group Databasebeta

← #14415411

Subgroups — #14415411

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×#91913C211yesmaximal, characteristic, complemented
2C2×#91911C211yesmaximal, characteristic, complemented
3#11753680C211yesmaximal, characteristic
4#11752363C211yesmaximal, characteristic, complemented
5C3×#65704C211yesmaximal, characteristic, complemented
6#11751924C211yesmaximal, characteristic, complemented
7#11751920C211yesmaximal, characteristic, complemented
8#11751909C211yesmaximal, characteristic, complemented
9#11751899C211yesmaximal, characteristic, complemented
10#11751897C211yesmaximal, characteristic, complemented
11#11751896C211yesmaximal, characteristic, complemented
12#11751896C211yesmaximal, characteristic, complemented
13#11751891C211yesmaximal, characteristic, complemented
14#11751885C211yesmaximal, characteristic, complemented
15D3×#4002C211yesmaximal, characteristic, complemented
16#10617228—31nomaximal, Hall
17C2×#6772C2211yescharacteristic
18C2×#6772C2211yescharacteristic
19C2×#6758C2211yescharacteristic
20C2×D5⋊(C3⋊C8)C2211yescharacteristic
21C2×C3×#700C2211yescharacteristic
22C2×C3×D5⋊C8C2211yescharacteristic
23C2×#6739C2211yescharacteristic
24C2×#6739C2211yescharacteristic
25C2×#6739C2211yescharacteristic
26C2×#6739C2211yescharacteristic
27C2×D3×#170C2211yescharacteristic
28C2×D3×#170C2211yescharacteristic
29C2×D3×#170C2211yescharacteristic
30C2×D3×#170C2211yescharacteristic
31#91913—24no—
32#91911—24no—
33#91777C411yescharacteristic
34C5×#895C411yescharacteristic
35C3×#4039C2211yescharacteristic
36#91463C411yescharacteristic
37#91462C411yescharacteristic
38#91462C411yescharacteristic
39#91456C411yescharacteristic
40#91453C411yescharacteristic
41#91453C411yescharacteristic
42#91440C2211yescharacteristic
43#91440C2211yescharacteristic
44Dic5×D12C2211yescharacteristic
45C4×D3×Dic5C2211yescharacteristic
46#91233C2211yescharacteristic
47#91232C2211yescharacteristic
48#91232C2211yescharacteristic
49#91231C2211yescharacteristic
50C3×#4004C2211yescharacteristic
51C3×#4003C2211yescharacteristic
52C3×#4003C2211yescharacteristic
53C3×#4002C2211yescharacteristic
54Dic3⋊#170C2211yescharacteristic
55Dic3⋊#170C2211yescharacteristic
56(C2×D3)⋊#170C2211yescharacteristic
57(C2×D3)⋊#170C2211yescharacteristic
58(C2×D3)⋊#170C2211yescharacteristic
59(C2×D3)⋊#170C2211yescharacteristic
60#91169C2211yescharacteristic
61#91169C2211yescharacteristic
62#79480—51nomaximal, Hall
63C2×#4131—31no—
64C2×#4131—31no—
65#65930—31no—
66#65775—31no—
67#65775—31no—
68#65773—31no—
69#65773—31no—
70#65758—31no—
71C2×#4002—31no—
72#65704—31no—
73#65704D311yescharacteristic, complemented
74#65694—31no—
75#65694—31no—
76#65693—31no—
77#65693—31no—
78C2×Dic30C2×C411yescharacteristic
79C2×Dic30C2×C411yescharacteristic
80C2×C5×D12C2×C411yescharacteristic
81C2×C5×D12C2×C411yescharacteristic
82C2×C5×D12C2×C411yescharacteristic
83C2×C4×C5×D3C2×C411yescharacteristic
84C2×C3×D20C2×C411yescharacteristic
85C2×C3×C4×D5C2311yescharacteristic
86C2×C3×C4×D5C2311yescharacteristic
87C2×#1201C2×C411yescharacteristic
88C2×#1201C2×C411yescharacteristic
89C2×#1201C2×C411yescharacteristic
90C2×#1201C2×C411yescharacteristic
91C2×#1201C2×C411yescharacteristic
92C2×#1201C2×C411yescharacteristic
93C2×D3×Dic5C2×C411yescharacteristic
94C2×D3×Dic5C2311yescharacteristic
95C2×D3×Dic5C2311yescharacteristic
96C2×D3×Dic5C2311yescharacteristic
97#6772—22no—
98#6772—22no—
99#6772—22no—
100#6772—22no—
101C2×C3⋊#170C2311yescharacteristic
102C2×C3⋊#170C2311yescharacteristic
103C2×C3⋊#170C2311yescharacteristic
104C2×C3⋊#170C2311yescharacteristic
105#6758—22no—
106D5⋊(C3⋊C8)—22no—
107C2×C3×#170C2311yescharacteristic
108C2×C3×#170C2311yescharacteristic
109C2×C3×#170C2311yescharacteristic
110C2×C3×#170C2311yescharacteristic
111C3×#700—22no—
112C3×D5⋊C8—22no—
113#6739—22no—
114#6739—22no—
115#6739—22no—
116#6739—22no—
117D3×#170—22no—
118D3×#170—22no—
119D3×#170—22no—
120D3×#170D414yescomplemented
121C3×C5×C4⋊C4C2×C411yescharacteristic
122C4⋊Dic15C2×C411yescharacteristic
123#6712C2×C411yescharacteristic
124#6712C2×C411yescharacteristic
125C4×Dic15C2×C411yescharacteristic
126C5×(C2×D3)⋊C4C2×C411yescharacteristic
127C5×(C2×D3)⋊C4C2×C411yescharacteristic
128C3×#685C2×C411yescharacteristic
129C3×#685C2×C411yescharacteristic
130C3×C4×Dic5C2311yescharacteristic
131(C2×D3)⋊Dic5C2×C411yescharacteristic
132(C2×D3)⋊Dic5C2×C411yescharacteristic
133#6665C2×C411yescharacteristic
134#6665C2×C411yescharacteristic
135Dic3×Dic5C2×C411yescharacteristic
136Dic3×Dic5C2311yescharacteristic
137C2×#907—51no—
138C2×#901—51no—
139#5548—51no—
140C3×#435—51no—
141#5127—51no—
142#5111—51no—
143#5011—51no—
144#4837—51no—
145#4836—51no—
146#4730—51no—
147#4728—51no—
148#4727—51no—
149#4727—51no—
150#4706—51no—
151D3×#97—51no—
152C2×#711—31no—
153C2×#711—31no—
154C2×#704—31no—
155C2×#704—31no—
156C2×#704—31no—
157C2×#704—31no—
158C22×#170—31no—
159C22×#170—31no—
160C22×#170—31no—
161C22×#170—31no—
162#4131—64no—
163#4131—64no—
164C2×#700—31no—
165C2×#700C2×D311yescharacteristic
166C2×D5⋊C8—31no—
167C2×D5⋊C8C2×D311yescharacteristic
168C5×#121—31no—
169#4086—31no—
170#4085—31no—
171#4085—31no—
172D4×Dic5—31no—
173#4076—31no—
174C2×C4×Dic5—31no—
175#4039C2×D311yescharacteristic
176#4034—31no—
177#4031—31no—
178#4031—31no—
179#4027—31no—
180#4027—31no—
181C22⋊#170—31no—
182C22⋊#170—31no—
183C22⋊#170—31no—
184C22⋊#170—31no—
185#4004—31no—
186#4004C2×D311yescharacteristic
187#4003—31no—
188#4003—31no—
189#4003C2×D311yescharacteristic
190#4003C2×D311yescharacteristic
191#4002—31no—
192#4002—31no—
193#4002—31no—
194#4002C2×D311yescharacteristic
195C4⋊#170—31no—
196C4⋊#170—31no—
197#2932—151noSylow
198C22×C5×D3C22×C411yescharacteristic
199C22×C5×D3C22×C411yescharacteristic
200C22×C5×D3C22×C411yescharacteristic
201C22×C3×D5C22×C411yescharacteristic
202C22×C3×D5C22×C411yescharacteristic
203C2×C3×C4×C5C22×C411yescharacteristic
204C2×C3×C4×C5C22×C411yescharacteristic
205C2×C3×C4×C5C22×C411yescharacteristic
206C2×Dic15C22×C411yescharacteristic
207C2×Dic15C22×C411yescharacteristic
208C2×Dic15C22×C411yescharacteristic
209C2×Dic15C22×C411yescharacteristic
210Dic30—22no—
211Dic30—22no—
212C2×C5×Dic3C22×C411yescharacteristic
213C5×D12—22no—
214C5×D12—22no—
215C5×D12—41no—
216C4×C5×D3—41no—
217C2×C3×Dic5C22×C411yescharacteristic
218C2×C3×Dic5C2411yescharacteristic
219C3×D20—41no—
220C3×C4×D5—21no—
221C3×C4×D5—21no—
222C3×C4×D5—21no—
223C3×C4×D5—21no—
224#1201—22no—
225#1201—22no—
226#1201—22no—
227#1201—22no—
228#1201—41no—
229#1201—41no—
230D3×Dic5—21no—
231D3×Dic5—21no—
232D3×Dic5—21no—
233D3×Dic5—21no—
234D3×Dic5—41no—
235D3×Dic5C2×D412yes—
236D3×Dic5#4112yes—
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—
248C22×C3×C8—51no—
249C3×C4×D4—51no—
250#940—51no—
251#938—51no—
252C4×#67—51no—
253C4×#67—51no—
254C2×#208—51no—
255C22×C3⋊C8—51no—
256#907—104no—
257#901—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#895AGL(1,𝔽5)11yescharacteristic
267#888—51no—
268#885—51no—
269#885—51no—
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×#97—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—
284#815—51no—
285#815—51no—
286Dic3⋊C8—51no—
287Dic3⋊C8—51no—
288C4⋊(C3⋊C8)—51no—
289#803—51no—
290C2×C5×D4—31no—
291C2×C5×D4—31no—
292C2×C5×D4—31no—
293C22×C4×C5—31no—
294C2×C22⋊D5—31no—
295C2×C22⋊D5—31no—
296C2×C22⋊D5—31no—
297C2×C22⋊D5—31no—
298C2×C22⋊D5—31no—
299C2×C22⋊D5—31no—
300C22×Dic5—31no—
301C22×Dic5—31no—
302C22×Dic5—31no—
303C22×Dic5—31no—
304#711—62no—
305#711—62no—
306#711—62no—
307#711—62no—
308C2×D20C4×D311yescharacteristic
309C2×C4×D5C22×D311yescharacteristic
310C2×C4×D5C22×D311yescharacteristic
311C2×Dic10—31no—
312C2×Dic10—31no—
313#704—62no—
314#704—62no—
315#704—62no—
316#704—62no—
317C2×#170—31no—
318C2×#170—34no—
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—22no—
330#700—62no—
331D5⋊C8—22no—
332D5⋊C8—62no—
333C5×C4⋊C4C4×D311yescharacteristic
334C5×C22⋊C4—31no—
335C5×C22⋊C4—31no—
336C22⋊Dic5—31no—
337C22⋊Dic5—31no—
338#685—31no—
339#685—31no—
340#685C4×D311yescharacteristic
341#685C4×D311yescharacteristic
342C4⋊Dic5—31no—
343#683—31no—
344#683—31no—
345C4×Dic5—31no—
346C4×Dic5—31no—
347C4×Dic5—31no—
348C4×Dic5C22×D311yescharacteristic
349C2×#131—151no—
350C2×#131—151no—
351#532—151no—
352#435—51no—
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—151no—
362#408—151no—
363C2×#97—151no—
364C22×C3×C5C23×C411yescharacteristic
365C2×C5×D3—21no—
366C2×C5×D3—21no—
367C2×C5×D3—21no—
368C2×C5×D3—21no—
369C2×C5×D3—21no—
370C2×C5×D3—21no—
371C2×C5×D3—21no—
372C2×C5×D3—21no—
373C2×C5×D3C4×D412yes—
374C2×C3×D5—21no—
375C2×C3×D5—21no—
376C2×C3×D5—21no—
377C2×C3×D5—21no—
378C2×C3×D5—21no—
379C2×C3×D5—21no—
380C3×C4×C5—21no—
381C3×C4×C5—21no—
382C3×C4×C5—21no—
383Dic15—21no—
384Dic15—21no—
385Dic15—21no—
386Dic15C4×D412yes—
387C3×Dic5—21no—
388C3×Dic5C22×D411yescharacteristic
389C3×Dic5C2×#4111yescharacteristic
390C5×Dic3—21no—
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×#67—51no—
400#235—102no—
401#235—102no—
402#235—102no—
403#235—102no—
404C2×D12C2×AGL(1,𝔽5)11yescharacteristic
405C2×D12C2×AGL(1,𝔽5)11yescharacteristic
406C2×D12C2×AGL(1,𝔽5)11yescharacteristic
407C2×C4×D3—51no—
408C2×C4×D3—51no—
409C2×C4×D3—51no—
410C2×C4×D3—51no—
411C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
412C2×Dic6—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—
420C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
421C3×C22⋊C4—51no—
422C3×C22⋊C4—51no—
423C3×C42—51no—
424#217—51no—
425#217—51no—
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×Dic3—51no—
436#208—102no—
437C2×C3⋊C8—51no—
438C2×C3⋊C8—51no—
439C2×C3⋊C8—51no—
440C2×C3⋊C8—51no—
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×C5—31no—
452C23×C5—31no—
453C22×D5C2×C4×D311yescharacteristic
454C22×D5C2×C4×D311yescharacteristic
455C5×D4—62no—
456C5×D4—62no—
457C5×D4—121no—
458C2×C4×C5—31no—
459C2×C4×C5—121no—
460C2×C4×C5C2×C4×D311yescharacteristic
461C2×C4×C5C2×C4×D311yescharacteristic
462C2×C4×C5C2×C4×D311yescharacteristic
463C22⋊D5—62no—
464C22⋊D5—62no—
465C22⋊D5—62no—
466C22⋊D5—62no—
467C22⋊D5—121no—
468C22⋊D5—121no—
469C2×Dic5—31no—
470C2×Dic5—32no—
471C2×Dic5—32no—
472C2×Dic5—31no—
473C2×Dic5—31no—
474C2×Dic5—31no—
475C2×Dic5—61no—
476C2×Dic5—61no—
477C2×Dic5—61no—
478C2×Dic5—61no—
479C2×Dic5—121no—
480C2×Dic5C2×C4×D311yescharacteristic
481C2×Dic5C23×D311yescharacteristic
482D20—41no—
483C4×D5—21no—
484C4×D5—21no—
485C4×D5—21no—
486C4×D5—21no—
487Dic10—62no—
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—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—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—
538#97—51no—
539#97—151no—
540#97—151no—
541#97—151no—
542C2×C3×C5C2×C4×D411yescharacteristic
543C2×C3×C5#56811yescharacteristic
544C2×C3×C5#56811yescharacteristic
545C3×D5—41no—
546C3×D5—41no—
547C5×D3—22no—
548C5×D3—41no—
549C5×D3—41no—
550C23×C3—51no—
551C23×C3—51no—
552C22×D3C22×AGL(1,𝔽5)11yescharacteristic
553C22×D3C22×AGL(1,𝔽5)11yescharacteristic
554C22×D3C22×AGL(1,𝔽5)11yescharacteristic
555C3×D4—201no—
556C2×C3×C4—51no—
557C2×C3×C4—51no—
558C2×C3×C4—101no—
559C2×C3×C4—101no—
560C2×C3×C4—101no—
561C2×C3×C4—101no—
562C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
563C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
564C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
565#67—102no—
566#67—102no—
567#67—102no—
568#67—102no—
569#67—201no—
570#67—201no—
571C2×Dic3—51no—
572C2×Dic3—51no—
573C2×Dic3—51no—
574C2×Dic3—51no—
575C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
576D12—22no—
577D12—22no—
578D12—41no—
579C4×D3—41no—
580C4×D3—52no—
581C4×D3—52no—
582C4×D3—101no—
583C4×D3—101no—
584C4×D3—101no—
585C4×D3—101no—
586C4×D3—201no—
587Dic6—102no—
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—32no—
598C22×C5—61no—
599C22×C5—61no—
600C22×C5—61no—
601C22×C5—61no—
602C22×C5—61no—
603C22×C5—61no—
604C22×C5—61no—
605C22×C5—61no—
606C22×C5C22×C4×D311yescharacteristic
607C2×D5—21no—
608C2×D5—21no—
609C2×D5—21no—
610C2×D5—21no—
611C2×D5—21no—
612C2×D5—21no—
613C4×C5—21no—
614C4×C5—21no—
615C4×C5—21no—
616C4×C5—61no—
617Dic5—21no—
618Dic5—32no—
619Dic5—61no—
620Dic5—61no—
621Dic5—61no—
622Dic5C2×D3×D411yescharacteristic
623Dic5D3×#4111yescharacteristic
624#41—302no—
625#41—302no—
626#41—302no—
627#41—302no—
628C2×Q8—151no—
629C2×Q8—151no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—31no—
633C2×D4—51no—
634C2×D4—151no—
635C2×D4—151no—
636C2×D4—151no—
637C2×D4—151no—
638C2×D4—151no—
639C2×D4—151no—
640C22×C4—31no—
641C22×C4—51no—
642C22×C4—51no—
643C22×C4—151no—
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—154no—
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⋊C4D3×AGL(1,𝔽5)11yescharacteristic
671C22⋊C4—31no—
672C22⋊C4—31no—
673C22⋊C4—51no—
674C22⋊C4—51no—
675C22⋊C4—151no—
676C22⋊C4—151no—
677C22⋊C4—151no—
678C22⋊C4—151no—
679C42—51no—
680C42—151no—
681C42—151no—
682C42—151no—
683C3×C5#293211yescharacteristic, complemented, Hall
684C22×C3—101no—
685C22×C3—101no—
686C22×C3—101no—
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—21no—
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—21no—
699C2×D3D4×AGL(1,𝔽5)12yes—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—51no—
704C3×C4—51no—
705C3×C4—101no—
706Dic3—21no—
707Dic3—52no—
708Dic3—101no—
709Dic3—101no—
710Dic3—101no—
711C2×C5—62no—
712C2×C5—121no—
713C2×C5—121no—
714C2×C5C4×D3×D411yescharacteristic
715C2×C5#574511yescharacteristic
716C2×C5#575011yescharacteristic
717D5—41no—
718D5—41no—
719C23—31no—
720C23—31no—
721C23—31no—
722C23—51no—
723C23—51no—
724Q8—302no—
725Q8—302no—
726D4—62no—
727D4—62no—
728D4—121no—
729D4—201no—
730D4—302no—
731D4—302no—
732D4—302no—
733D4—302no—
734D4—601no—
735D4—601no—
736C2×C4—31no—
737C2×C4—51no—
738C2×C4—51no—
739C2×C4—101no—
740C2×C4—101no—
741C2×C4—101no—
742C2×C4—101no—
743C2×C4—121no—
744C2×C4—152no—
745C2×C4—152no—
746C2×C4—151no—
747C2×C4—151no—
748C2×C4—151no—
749C2×C4—151no—
750C2×C4—301no—
751C2×C4—301no—
752C2×C4—301no—
753C2×C4—301no—
754C2×C4—601no—
755C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
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—201no—
767C2×C3—201no—
768C2×C3#6625611yescharacteristic
769C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
770C2×C3#6626411yescharacteristic
771D3—22no—
772D3—41no—
773D3—41no—
774C5#7948011yescharacteristic, complemented, Sylow
775C22—32no—
776C22—61no—
777C22—61no—
778C22—61no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—101no—
785C22—101no—
786C22—101no—
787C22—101no—
788C22—101no—
789C22—101no—
790C22C22×D3×AGL(1,𝔽5)11yescharacteristic
791C4—21no—
792C4—21no—
793C4—21no—
794C4—51no—
795C4—51no—
796C4—61no—
797C4—101no—
798C4—152no—
799C4—301no—
800C4—301no—
801C4—301no—
802C3#1061722811yescharacteristic, complemented, Sylow
803C2—62no—
804C2—121no—
805C2—121no—
806C2—201no—
807C2—201no—
808C2#1175682211yescharacteristic
809C2D3×D4×AGL(1,𝔽5)11yescharacteristic
810C2#1175685011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radical#11753680C2
cosocleC2×C3×Dic5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2932
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91913C2semidirect
2. C2×#91911C2semidirect
4. #11752363C2semidirect
5. C3×#65704C2semidirect
6. #11751924C2semidirect
7. #11751920C2semidirect
8. #11751909C2semidirect
9. #11751899C2semidirect
10. #11751897C2semidirect
11. #11751896C2semidirect
12. #11751896C2semidirect
13. #11751891C2semidirect
14. #11751885C2semidirect
15. D3×#4002C2semidirect
73. #65704D3semidirect
120. D3×#170D4semidirect
683. C3×C5#2932semidirect
774. C5#79480semidirect
802. C3#10617228semidirect

Maximal subgroups

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

subgroupindex
C2×#919132
C2×#919112
#117536802
#117523632
C3×#657042
#117519242
#117519202
#117519092
#117518992
#117518972
#117518962
#117518912
#117518852
D3×#40022
#106172283
#794805