Finite Group Databasebeta

← #14415018

Subgroups — #14415018

Order 1920.

1040 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×D3×#170C211yesmaximal, characteristic, complemented
2C2×#91911C211yesmaximal, characteristic, complemented
3#11752840C211yesmaximal, characteristic
4#11752352C211yesmaximal, characteristic, complemented
5C3×#65692C211yesmaximal, characteristic, complemented
6#11752053C211yesmaximal, characteristic, complemented
7#11752051C211yesmaximal, characteristic, complemented
8#67×#170C211yesmaximal, characteristic, complemented
9#11751899C211yesmaximal, characteristic, complemented
10#11751898C211yesmaximal, characteristic, complemented
11#11751897C211yesmaximal, characteristic, complemented
12#11751896C211yesmaximal, characteristic, complemented
13#11751875C211yesmaximal, characteristic, complemented
14#11751868C211yesmaximal, characteristic, complemented
15D12×#170C211yesmaximal, characteristic, complemented
16#10617215—31nomaximal, Hall
17C22×D3×Dic5C2211yescharacteristic
18C2×#6772C2211yescharacteristic
19C22×C3⋊#170C2211yescharacteristic
20C2×#6758C2211yescharacteristic, complemented
21C22×C3×#170C2211yescharacteristic
22C2×C3×D5⋊C8C2211yescharacteristic, complemented
23C2×#6739C2211yescharacteristic
24C2×#6739C2211yescharacteristic
25C2×#6739C2211yescharacteristic, complemented
26C2×D3×#170—24no—
27C2×D3×#170C2211yescharacteristic
28C2×D3×#170C2211yescharacteristic
29C2×D3×#170C2211yescharacteristic
30C2×D3×#170C2211yescharacteristic
31C2×D3×#170C2211yescharacteristic, complemented
32#91911—24no—
33#91767C411yescharacteristic
34C5×#882C411yescharacteristic
35C3×#4027C2211yescharacteristic
36#91571C411yescharacteristic
37#91568C411yescharacteristic
38Dic5×#67C2211yescharacteristic
39#91457C411yescharacteristic
40#91453C411yescharacteristic
41#91440C2211yescharacteristic
42#91432C411yescharacteristic
43#91423C411yescharacteristic
44Dic5×D12C2211yescharacteristic
45#91398C2211yescharacteristic
46#91241C2211yescharacteristic
47#91232C2211yescharacteristic, complemented
48#91231C2211yescharacteristic, complemented
49C4⋊(C3⋊#170)C2211yescharacteristic, complemented
50C3×C22⋊#170C2211yescharacteristic
51C3×#4004C2211yescharacteristic, complemented
52C3×#4003C2211yescharacteristic, complemented
53C3×C4×#170C2211yescharacteristic, complemented
54#91177C2211yescharacteristic, complemented
55Dic3⋊#170C2211yescharacteristic, complemented
56(C2×D3)⋊#170C2211yescharacteristic
57(C2×D3)⋊#170C2211yescharacteristic
58(C2×D3)⋊#170C2211yescharacteristic, complemented
59(C2×D3)⋊#170C2211yescharacteristic, complemented
60#91169C2211yescharacteristic, complemented
61Dic3×#170C2211yescharacteristic, complemented
62#79421—51nomaximal, Hall
63C23×#170—31no—
64C2×#4131—31no—
65#65920—31no—
66#65798—31no—
67#65775—31no—
68#65773—31no—
69#65773—31no—
70D4×#170—31no—
71D4×#170—31no—
72#65696—31no—
73#65693—31no—
74#65693—31no—
75#65692—31no—
76#65692D311yescharacteristic, complemented
77#65691—31no—
78C23×C5×D3C2×C411yescharacteristic
79C22×Dic15C2×C411yescharacteristic
80C2×Dic30C2×C411yescharacteristic
81C2×C5×#67C2×C411yescharacteristic
82C2×C5×D12C2×C411yescharacteristic
83C2×C5×D12C2×C411yescharacteristic
84C2×C3×C22⋊D5C2×C411yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C2×C3×C4×D5C2311yescharacteristic
87C2×#1201C2×C411yescharacteristic
88C2×#1201C2×C411yescharacteristic
89C2×#1201C2×C411yescharacteristic
90C2×D3×Dic5—22no—
91C2×D3×Dic5—22no—
92C2×D3×Dic5C2×C411yescharacteristic
93C2×D3×Dic5C2×C411yescharacteristic
94C2×D3×Dic5C2311yescharacteristic
95C2×D3×Dic5C2311yescharacteristic
96C2×D3×Dic5C2311yescharacteristic
97#6772—22no—
98#6772—22no—
99C2×C3⋊#170—22no—
100C2×C3⋊#170C2311yescharacteristic
101C2×C3⋊#170C2311yescharacteristic
102C2×C3⋊#170C2311yescharacteristic
103C2×C3⋊#170C2311yescharacteristic
104#6758—22no—
105C2×C3×#170—22no—
106C2×C3×#170C2311yescharacteristic
107C2×C3×#170C2311yescharacteristic
108C2×C3×#170C2311yescharacteristic
109C2×C3×#170C2311yescharacteristic
110C3×D5⋊C8—22no—
111#6739—22no—
112#6739—22no—
113#6739—22no—
114D3×#170—22no—
115D3×#170—22no—
116D3×#170—22no—
117D3×#170—22no—
118D3×#170D414yescomplemented
119C3×C5×C22⋊C4C2×C411yescharacteristic
120#6719C2×C411yescharacteristic
121C4⋊Dic15C2×C411yescharacteristic
122#6712C2×C411yescharacteristic
123#6712C2×C411yescharacteristic
124C5×(C2×D3)⋊C4C2×C411yescharacteristic
125C5×(C2×D3)⋊C4C2×C411yescharacteristic
126C3×#685C2×C411yescharacteristic
127C3×#683C2×C411yescharacteristic
128C3×C4×Dic5C2311yescharacteristic
129Dic3⋊Dic5C2×C411yescharacteristic
130#6669C2×C411yescharacteristic
131(C2×D3)⋊Dic5C2×C411yescharacteristic
132(C2×D3)⋊Dic5C2×C411yescharacteristic
133(C2×D3)⋊Dic5C2×C411yescharacteristic
134(C2×D3)⋊Dic5C2×C411yescharacteristic
135#6665C2×C411yescharacteristic
136Dic3×Dic5C2311yescharacteristic
137C2×#901—51no—
138C22×D3×C8—51no—
139#5547—51no—
140C3×C8×D4—51no—
141C8×#67—51no—
142C8×#67—51no—
143#5011—51no—
144#4839—51no—
145#4836—51no—
146#4730—51no—
147#4728—51no—
148#4727—51no—
149#4726—51no—
150#4689—51no—
151C8×D12—51no—
152C23×Dic5—31no—
153C2×#711—31no—
154C2×#704—31no—
155C2×#704—31no—
156C2×#704—31no—
157C22×#170—31no—
158C22×#170—31no—
159C22×#170—31no—
160C22×#170—31no—
161C22×#170—31no—
162C22×#170—31no—
163C22×#170—64no—
164C22×#170C2×D311yescharacteristic
165#4131—64no—
166C2×#700—31no—
167C2×D5⋊C8C2×D311yescharacteristic, complemented
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#4027C2×D311yescharacteristic
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⋊#170C2×D311yescharacteristic
187#4004—31no—
188#4004C2×D311yescharacteristic, complemented
189#4003—31no—
190#4003C2×D311yescharacteristic, complemented
191#4002—31no—
192#4002—31no—
193C4⋊#170—31no—
194C4⋊#170—31no—
195C4×#170—31no—
196C4×#170C2×D311yescharacteristic, complemented
197#2929—151noSylow
198C23×C3×C5C22×C411yescharacteristic
199C22×C5×D3—22no—
200C22×C5×D3—22no—
201C22×C5×D3—22no—
202C22×C5×D3C22×C411yescharacteristic
203C22×C5×D3C22×C411yescharacteristic
204C22×C5×D3C22×C411yescharacteristic
205C22×C3×D5C22×C411yescharacteristic
206C2×C3×C4×C5C22×C411yescharacteristic
207C2×C3×C4×C5C22×C411yescharacteristic
208C2×Dic15—22no—
209C2×Dic15C22×C411yescharacteristic
210C2×Dic15C22×C411yescharacteristic
211C2×Dic15C22×C411yescharacteristic
212C2×Dic15C22×C411yescharacteristic
213Dic30—22no—
214C5×#67—22no—
215C2×C5×Dic3C22×C411yescharacteristic
216C5×D12—22no—
217C5×D12—22no—
218C3×C22⋊D5—22no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5C22×C411yescharacteristic
222C2×C3×Dic5C22×C411yescharacteristic
223C2×C3×Dic5C2411yescharacteristic
224C3×C4×D5—21no—
225C3×C4×D5—21no—
226#1201—22no—
227#1201—22no—
228#1201—22no—
229D3×Dic5—22no—
230D3×Dic5—22no—
231D3×Dic5—21no—
232D3×Dic5—21no—
233D3×Dic5—21no—
234D3×Dic5—21no—
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—
246C22×C4×D3—51no—
247C22×C3×C8—51no—
248C22×C3×C8—51no—
249C3×C4×D4—51no—
250#939—51no—
251#937—51no—
252C4×#67—51no—
253C4×#67—51no—
254C2×#208—51no—
255C22×C3⋊C8—51no—
256#901—104no—
257C2×ΓL(1,𝔽25)—51no—
258C2×ΓL(1,𝔽25)—51no—
259C2×ΓL(1,𝔽25)—51no—
260C2×D3×C8—51no—
261C2×D3×C8—51no—
262C2×D3×C8—51no—
263C2×D3×C8—51no—
264C2×D3×C8—51no—
265C2×D3×C8—104no—
266#896—51no—
267#894—51no—
268#884—51no—
269#883—51no—
270#882AGL(1,𝔽5)11yescharacteristic
271#878—51no—
272C4×D12—51no—
273#872—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—
284#815—51no—
285Dic3⋊C8—51no—
286Dic3⋊C8—51no—
287C8×Dic3—51no—
288C4⋊(C3⋊C8)—51no—
289#803—51no—
290C24×C5—31no—
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⋊D5C4×D311yescharacteristic
298C22×Dic5—31no—
299C22×Dic5—31no—
300C22×Dic5—31no—
301C22×Dic5—31no—
302C22×Dic5—31no—
303C22×Dic5—31no—
304C22×Dic5—62no—
305C22×Dic5—62no—
306C22×Dic5C22×D311yescharacteristic
307#711—62no—
308#711—62no—
309C2×C4×D5C22×D311yescharacteristic
310C2×Dic10—31no—
311#704—62no—
312#704—62no—
313#704—62no—
314C2×#170—22no—
315C2×#170—31no—
316C2×#170—34no—
317C2×#170—31no—
318C2×#170—31no—
319C2×#170—31no—
320C2×#170—62no—
321C2×#170—62no—
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—22no—
331C5×C22⋊C4—31no—
332C5×C22⋊C4—31no—
333C5×C22⋊C4C4×D311yescharacteristic
334C22⋊Dic5—31no—
335C22⋊Dic5—31no—
336C22⋊Dic5—31no—
337C22⋊Dic5—31no—
338C22⋊Dic5—31no—
339#685—31no—
340#685C4×D311yescharacteristic
341C4⋊Dic5—31no—
342C4⋊Dic5—31no—
343#683—31no—
344#683—31no—
345#683—31no—
346#683C4×D311yescharacteristic
347C4×Dic5—31no—
348C4×Dic5C22×D311yescharacteristic
349C2×#131—151no—
350C23×C8—151no—
351#525—151no—
352#435—151no—
353#435—151no—
354#435—151no—
355#435—151no—
356C8×D4—51no—
357C8×D4—151no—
358C8×D4—151no—
359C8×D4—151no—
360#424—151no—
361#408—151no—
362#407—151no—
363#405—151no—
364C22×C3×C5—21no—
365C22×C3×C5—21no—
366C22×C3×C5#13112yescomplemented
367C22×C3×C5C23×C411yescharacteristic
368C2×C5×D3—28no—
369C2×C5×D3—21no—
370C2×C5×D3—21no—
371C2×C5×D3—21no—
372C2×C5×D3—21no—
373C2×C5×D3—21no—
374C2×C5×D3—21no—
375C2×C5×D3—21no—
376C2×C5×D3C4×D412yes—
377C2×C5×D3#13112yescomplemented
378C2×C3×D5—21no—
379C2×C3×D5—21no—
380C2×C3×D5—21no—
381C3×C4×C5—21no—
382C3×C4×C5—21no—
383Dic15—21no—
384Dic15—21no—
385Dic15—21no—
386Dic15C4×D412yes—
387C3×Dic5—21no—
388C3×Dic5—21no—
389C3×Dic5C22×D411yescharacteristic
390C3×Dic5C2×#4111yescharacteristic
391C5×Dic3—21no—
392C23×D3C2×AGL(1,𝔽5)11yescharacteristic
393C2×C3×D4—51no—
394C22×C3×C4—51no—
395C22×C3×C4—51no—
396C2×#67—51no—
397C2×#67—51no—
398C2×#67—51no—
399C2×#67C2×AGL(1,𝔽5)11yescharacteristic
400C22×Dic3—51no—
401#235—102no—
402#235—102no—
403C2×D12C2×AGL(1,𝔽5)11yescharacteristic
404C2×D12C2×AGL(1,𝔽5)11yescharacteristic
405C2×C4×D3—51no—
406C2×C4×D3—51no—
407C2×C4×D3—51no—
408C2×C4×D3—51no—
409C2×C4×D3—51no—
410C2×C4×D3—102no—
411C2×C4×D3—102no—
412C2×Dic6—51no—
413C2×C3×C8—51no—
414C2×C3×C8—51no—
415C2×C3×C8—51no—
416C2×C3×C8—51no—
417C2×C3×C8—102no—
418C2×C3×C8—102no—
419C3×C4⋊C4—51no—
420C3×C22⋊C4—51no—
421C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
422C3×C42—51no—
423#217—51no—
424#217—51no—
425(C2×D3)⋊C4—51no—
426(C2×D3)⋊C4—51no—
427(C2×D3)⋊C4—51no—
428(C2×D3)⋊C4—51no—
429(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
430(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
431C4⋊Dic3—51no—
432Dic3⋊C4—51no—
433Dic3⋊C4—51no—
434Dic3⋊C4—51no—
435Dic3⋊C4—51no—
436C4×Dic3—51no—
437#208—102no—
438C2×C3⋊C8—51no—
439C2×C3⋊C8—51no—
440C2×C3⋊C8—51no—
441C2×C3⋊C8—51no—
442C2×C3⋊C8—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—
450D3×C8—102no—
451C23×C5—31no—
452C23×C5—31no—
453C23×C5—31no—
454C23×C5—62no—
455C23×C5—62no—
456C23×C5—62no—
457C23×C5C2×C4×D311yescharacteristic
458C22×D5C2×C4×D311yescharacteristic
459C5×D4—62no—
460C5×D4—62no—
461C5×D4—62no—
462C2×C4×C5—31no—
463C2×C4×C5C2×C4×D311yescharacteristic
464C2×C4×C5C2×C4×D311yescharacteristic
465C22⋊D5—22no—
466C22⋊D5—62no—
467C22⋊D5—62no—
468C22⋊D5—62no—
469C2×Dic5—21no—
470C2×Dic5—21no—
471C2×Dic5—31no—
472C2×Dic5—32no—
473C2×Dic5—32no—
474C2×Dic5—31no—
475C2×Dic5—31no—
476C2×Dic5—31no—
477C2×Dic5—62no—
478C2×Dic5—62no—
479C2×Dic5—62no—
480C2×Dic5—61no—
481C2×Dic5—61no—
482C2×Dic5—61no—
483C2×Dic5—61no—
484C2×Dic5C2×C4×D311yescharacteristic
485C2×Dic5C2×C4×D311yescharacteristic
486C2×Dic5C23×D311yescharacteristic
487C4×D5—21no—
488C4×D5—21no—
489Dic10—62no—
490#170—21no—
491#170—21no—
492#170—21no—
493#170—32no—
494#170—61no—
495#170—61no—
496#170—61no—
497#170D3×D412yes—
498C2×#41—151no—
499C23×C4—151no—
500#131—304no—
501C2×M16—151no—
502C2×M16—151no—
503C2×M16—151no—
504C2×M16—151no—
505C22×C8—51no—
506C22×C8—51no—
507C22×C8—151no—
508C22×C8—151no—
509C22×C8—151no—
510C22×C8—151no—
511C22×C8—151no—
512C22×C8—151no—
513C22×C8—304no—
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—51no—
523C4×D4—151no—
524C4×D4—151no—
525C4×D4—151no—
526#117—151no—
527C4⋊C8—51no—
528C4⋊C8—151no—
529C4⋊C8—151no—
530C4⋊C8—151no—
531C22⋊C8—51no—
532C22⋊C8—51no—
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—51no—
542C4×C8—151no—
543C2×C3×C5—22no—
544C2×C3×C5C2×C4×D411yescharacteristic
545C2×C3×C5C2×#13111yescharacteristic
546C2×C3×C5C2×#13111yescharacteristic
547C3×D5—41no—
548C5×D3—22no—
549C5×D3—22no—
550C5×D3—41no—
551C23×C3—51no—
552C23×C3C22×AGL(1,𝔽5)11yescharacteristic
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3C22×AGL(1,𝔽5)11yescharacteristic
557C22×D3C22×AGL(1,𝔽5)11yescharacteristic
558C22×D3C22×AGL(1,𝔽5)11yescharacteristic
559C3×D4—102no—
560C2×C3×C4—51no—
561C2×C3×C4—51no—
562C2×C3×C4—51no—
563C2×C3×C4—101no—
564C2×C3×C4—101no—
565C2×C3×C4—101no—
566C2×C3×C4—101no—
567C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
568C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
569#67—22no—
570#67—102no—
571#67—102no—
572#67—102no—
573C2×Dic3—51no—
574C2×Dic3—51no—
575C2×Dic3—51no—
576C2×Dic3—51no—
577C2×Dic3—102no—
578C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
579D12—22no—
580D12—22no—
581C4×D3—52no—
582C4×D3—52no—
583C4×D3—102no—
584C4×D3—101no—
585C4×D3—101no—
586C4×D3—101no—
587C4×D3—101no—
588C4×D3—102no—
589Dic6—102no—
590C3×C8—52no—
591C3×C8—101no—
592C3×C8—101no—
593C3×C8—101no—
594C3⋊C8—52no—
595C3⋊C8—101no—
596C3⋊C8—101no—
597C3⋊C8—101no—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—32no—
601C22×C5—32no—
602C22×C5—68no—
603C22×C5—61no—
604C22×C5—61no—
605C22×C5—61no—
606C22×C5—61no—
607C22×C5—61no—
608C22×C5—61no—
609C22×C5—61no—
610C22×C5#90112yescomplemented
611C22×C5C22×C4×D311yescharacteristic
612C2×D5—21no—
613C2×D5—21no—
614C2×D5—21no—
615C4×C5—21no—
616C4×C5—21no—
617C4×C5—61no—
618Dic5—21no—
619Dic5—21no—
620Dic5—32no—
621Dic5—61no—
622Dic5—61no—
623Dic5—61no—
624Dic5C2×D3×D411yescharacteristic
625Dic5D3×#4111yescharacteristic
626C24—31no—
627#41—302no—
628#41—302no—
629C2×Q8—151no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—31no—
633C2×D4—51no—
634C2×D4—151no—
635C2×D4—151no—
636C2×D4—151no—
637C22×C4—51no—
638C22×C4—51no—
639C22×C4—151no—
640C22×C4—151no—
641C22×C4—151no—
642C22×C4—151no—
643C22×C4—151no—
644C22×C4—151no—
645C22×C4—302no—
646C22×C4—302no—
647M16—302no—
648M16—302no—
649M16—302no—
650M16—302no—
651C2×C8—51no—
652C2×C8—51no—
653C2×C8—51no—
654C2×C8—51no—
655C2×C8—102no—
656C2×C8—102no—
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—
671C4⋊C4—151no—
672C4⋊C4—151no—
673C22⋊C4—31no—
674C22⋊C4—31no—
675C22⋊C4—51no—
676C22⋊C4—151no—
677C22⋊C4—151no—
678C22⋊C4—151no—
679C22⋊C4—151no—
680C22⋊C4—151no—
681C22⋊C4—151no—
682C22⋊C4D3×AGL(1,𝔽5)11yescharacteristic
683C42—51no—
684C42—151no—
685C3×C5#292911yescharacteristic, complemented, Hall
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—101no—
689C22×C3—101no—
690C22×C3—101no—
691C22×C3#413112yescomplemented
692C22×C3C23×AGL(1,𝔽5)11yescharacteristic
693C2×D3—28no—
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—21no—
701C2×D3#413112yescomplemented
702C2×D3D4×AGL(1,𝔽5)12yes—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—51no—
706C3×C4—51no—
707C3×C4—101no—
708C3×C4—101no—
709Dic3—21no—
710Dic3—52no—
711Dic3—101no—
712Dic3—101no—
713Dic3—101no—
714C2×C5—22no—
715C2×C5—62no—
716C2×C5—62no—
717C2×C5—121no—
718C2×C5C4×D3×D411yescharacteristic
719C2×C5C2×#90111yescharacteristic
720C2×C5D3×#13111yescharacteristic
721D5—41no—
722C23—31no—
723C23—31no—
724C23—31no—
725C23—51no—
726C23—62no—
727C23—62no—
728C23—62no—
729C23C2×D3×AGL(1,𝔽5)11yescharacteristic
730Q8—302no—
731D4—62no—
732D4—62no—
733D4—62no—
734D4—102no—
735D4—302no—
736D4—302no—
737D4—302no—
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—151no—
751C2×C4—151no—
752C2×C4—301no—
753C2×C4—301no—
754C2×C4—301no—
755C2×C4—301no—
756C2×C4—302no—
757C2×C4—302no—
758C2×C4—302no—
759C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
760C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
761C8—52no—
762C8—101no—
763C8—101no—
764C8—101no—
765C8—152no—
766C8—301no—
767C8—301no—
768C8—301no—
769C2×C3—22no—
770C2×C3—201no—
771C2×C3C2×#413111yescharacteristic
772C2×C3C2×#413111yescharacteristic
773C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
774D3—22no—
775D3—22no—
776D3—41no—
777C5#7942111yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—32no—
781C22—32no—
782C22—68no—
783C22—61no—
784C22—61no—
785C22—61no—
786C22—61no—
787C22—61no—
788C22—61no—
789C22—61no—
790C22—101no—
791C22—101no—
792C22—101no—
793C22#9191112yescomplemented
794C22C22×D3×AGL(1,𝔽5)11yescharacteristic
795C4—21no—
796C4—21no—
797C4—51no—
798C4—51no—
799C4—61no—
800C4—101no—
801C4—101no—
802C4—152no—
803C4—301no—
804C4—301no—
805C4—301no—
806C3#1061721511yescharacteristic, complemented, Sylow
807C2—22no—
808C2—62no—
809C2—62no—
810C2—121no—
811C2—201no—
812C2C2×#9191111yescharacteristic
813C2D3×#413111yescharacteristic
814C2D3×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#11752840C2
cosocleC2×C3×Dic5C24
hypercenterC22⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2929
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. C22×D3×#170C2semidirect
2. C2×#91911C2semidirect
4. #11752352C2semidirect
5. C3×#65692C2semidirect
6. #11752053C2semidirect
7. #11752051C2semidirect
8. #67×#170C2semidirect
9. #11751899C2semidirect
10. #11751898C2semidirect
11. #11751897C2semidirect
12. #11751896C2semidirect
13. #11751875C2semidirect
14. #11751868C2semidirect
15. D12×#170C2semidirect
20. C2×#6758C22semidirect
22. C2×C3×D5⋊C8C22semidirect
25. C2×#6739C22semidirect
31. C2×D3×#170C22semidirect
47. #91232C22semidirect
48. #91231C22semidirect
49. C4⋊(C3⋊#170)C22semidirect
51. C3×#4004C22semidirect
52. C3×#4003C22semidirect
53. C3×C4×#170C22semidirect
54. #91177C22semidirect
55. Dic3⋊#170C22semidirect
58. (C2×D3)⋊#170C22semidirect
59. (C2×D3)⋊#170C22semidirect
60. #91169C22semidirect
61. Dic3×#170C22semidirect
76. #65692D3semidirect
118. D3×#170D4semidirect
167. C2×D5⋊C8C2×D3semidirect
188. #4004C2×D3semidirect
190. #4003C2×D3semidirect
196. C4×#170C2×D3semidirect
366. C22×C3×C5#131semidirect
377. C2×C5×D3#131semidirect
610. C22×C5#901semidirect
685. C3×C5#2929semidirect
691. C22×C3#4131semidirect
701. C2×D3#4131semidirect
777. C5#79421semidirect
793. C22#91911semidirect
806. C3#10617215semidirect

Maximal subgroups

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

subgroupindex
C22×D3×#1702
C2×#919112
#117528402
#117523522
C3×#656922
#117520532
#117520512
#67×#1702
#117518992
#117518982
#117518972
#117518962
#117518752
#117518682
D12×#1702
#106172153
#794215