Finite Group Databasebeta

← #14419075

Subgroups — #14419075

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754853C211yesmaximal, characteristic
2#11752432C211yesmaximal, characteristic, complemented
3C3×#65773C211yesmaximal, characteristic, complemented
4#11752054C211yesmaximal, characteristic, complemented
5#11752046C211yesmaximal, characteristic, complemented
6#11751994C211yesmaximal, characteristic, complemented
7Dic3×#704C211yesmaximal, characteristic, complemented
8#11751991C211yesmaximal, characteristic, complemented
9#11751987C211yesmaximal, characteristic, complemented
10#11751986C211yesmaximal, characteristic, complemented
11C2×Dic3×#170C211yesmaximal, characteristic, complemented
12#11751784C211yesmaximal, characteristic, complemented
13#11751771C211yesmaximal, characteristic, complemented
14#11751760C211yesmaximal, characteristic, complemented
15#11751756C211yesmaximal, characteristic, complemented
16#10617154—31nomaximal, Hall
17C2×#6819C411yescharacteristic
18C2×#6762C2211yescharacteristic
19C22×C3⋊#170C2211yescharacteristic
20C2×C3×#704C2211yescharacteristic
21C22×C3×#170C2211yescharacteristic
22C2×#6740C2211yescharacteristic
23C2×#6740C2211yescharacteristic
24C5×D4×Dic3C411yescharacteristic
25C3×D4×Dic5C2211yescharacteristic
26#91556C411yescharacteristic
27#91556C411yescharacteristic
28#91552C2211yescharacteristic
29#91552C2211yescharacteristic
30#91532C411yescharacteristic
31#91532C411yescharacteristic
32C2×Dic3×Dic5C2211yescharacteristic
33C2×Dic3×Dic5C2211yescharacteristic
34C4×#1200C2211yescharacteristic
35#91347C411yescharacteristic
36#91340C411yescharacteristic
37#91333C2211yescharacteristic
38#91241C2211yescharacteristic
39#91241C2211yescharacteristic
40#91233C2211yescharacteristic
41#91231C2211yescharacteristic
42C3×C22⋊#170C2211yescharacteristic
43C3×C22⋊#170C2211yescharacteristic
44C3×#4004C2211yescharacteristic
45C3×#4002C2211yescharacteristic
46#91177C2211yescharacteristic
47#91177C2211yescharacteristic
48Dic3⋊#170C2211yescharacteristic
49Dic3⋊#170C2211yescharacteristic
50#91171C2211yescharacteristic
51#91171C2211yescharacteristic
52#91169C2211yescharacteristic
53#91169C2211yescharacteristic
54Dic3×#170C2211yescharacteristic
55Dic3×#170C2211yescharacteristic
56Dic3×#170C2211yescharacteristic
57Dic3×#170C2211yescharacteristic
58Dic3×#170C2211yescharacteristic
59Dic3×#170C2211yescharacteristic
60#79453—51nomaximal, Hall
61C4×#711—31no—
62#65773—31no—
63#65773D311yescharacteristic, complemented
64#65754—31no—
65C4×#704—31no—
66#65748—31no—
67C2×C4×#170—31no—
68#65707—31no—
69#65707—31no—
70#65695—31no—
71#65695—31no—
72#65693—31no—
73#65693—31no—
74#65678—31no—
75C4×#700—31no—
76C2×C3×C5×D4C2×C411yescharacteristic
77C2×#1220C2×C411yescharacteristic
78C2×#1220C2×C411yescharacteristic
79C22×Dic15C2×C411yescharacteristic
80C22×Dic15C2×C411yescharacteristic
81#6819—24no—
82C2×C4×D15C2×C411yescharacteristic
83C2×Dic30C2×C411yescharacteristic
84C22×C5×Dic3C2×C411yescharacteristic
85C22×C5×Dic3C2×C411yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C2×#1200C2×C411yescharacteristic
89C2×#1200C2311yescharacteristic
90#6762—22no—
91C2×C3⋊#170—22no—
92C2×C3⋊#170C2311yescharacteristic
93C2×C3⋊#170C2311yescharacteristic
94C2×C3⋊#170C2311yescharacteristic
95C2×C3⋊#170C2311yescharacteristic
96C3×#704—22no—
97C2×C3×#170—22no—
98C2×C3×#170C2311yescharacteristic
99C2×C3×#170C2311yescharacteristic
100C2×C3×#170C2311yescharacteristic
101C2×C3×#170C2311yescharacteristic
102#6740—22no—
103#6740—22no—
104C5×#217C2×C411yescharacteristic
105C5×#217C2×C411yescharacteristic
106C5×C4⋊Dic3C2×C411yescharacteristic
107C4×C5×Dic3C2×C411yescharacteristic
108C3×C22⋊Dic5C2×C411yescharacteristic
109C3×C22⋊Dic5C2×C411yescharacteristic
110C3×C4⋊Dic5C2×C411yescharacteristic
111C3×C4×Dic5C2311yescharacteristic
112#6669C2×C411yescharacteristic
113#6669C2×C411yescharacteristic
114#6669C2×C411yescharacteristic
115#6669C2×C411yescharacteristic
116#6667C2×C411yescharacteristic
117#6667C2×C411yescharacteristic
118Dic3×Dic5C2×C411yescharacteristic
119Dic3×Dic5C2×C411yescharacteristic
120Dic3×Dic5C2×C411yescharacteristic
121Dic3×Dic5C2×C411yescharacteristic
122Dic3×Dic5C2×C411yescharacteristic
123Dic3×Dic5C2311yescharacteristic
124Dic3×Dic5C2311yescharacteristic
125Dic3×Dic5C2311yescharacteristic
126C4×#237—51no—
127C3×#435—51no—
128#5128—51no—
129Dic3×M16—51no—
130#5111—51no—
131C2×C8×Dic3—51no—
132#5011—51no—
133#4833—51no—
134#4828—51no—
135#4730—51no—
136#4729—51no—
137#4718—51no—
138#4718—51no—
139#4707—51no—
140#4701—51no—
141C2×#711—31no—
142C2×#704—31no—
143C2×#704C2×D311yescharacteristic
144C22×#170—31no—
145C22×#170C2×D311yescharacteristic
146C2×#700—31no—
147C2×#700—31no—
148C4×C5×D4—31no—
149D4×Dic5C2×D311yescharacteristic
150C4×C22⋊D5—31no—
151C4×C22⋊D5—31no—
152C2×C4×Dic5—31no—
153C2×C4×Dic5—31no—
154#4038—31no—
155#4033—31no—
156#4027—31no—
157#4027—31no—
158#4023—31no—
159#4023—31no—
160C42×D5—31no—
161C4×Dic10—31no—
162C22⋊#170—31no—
163C22⋊#170—31no—
164C22⋊#170C2×D311yescharacteristic
165C22⋊#170C2×D311yescharacteristic
166#4004—31no—
167#4004—31no—
168#4004—31no—
169#4004C2×D311yescharacteristic
170#4003—31no—
171#4003—31no—
172#4002—31no—
173#4002—31no—
174#4002—31no—
175#4002C2×D311yescharacteristic
176C4⋊#170—31no—
177C4⋊#170—31no—
178C4×#170—31no—
179C4×#170—31no—
180C4×#170—31no—
181C4×#170—31no—
182C4×#170—31no—
183C4×#170—31no—
184#2965—151noSylow
185C23×C3×C5C22×C411yescharacteristic
186C23×C3×C5C22×C411yescharacteristic
187C22×D15C22×C411yescharacteristic
188C3×C5×D4—22no—
189C2×C3×C4×C5C22×C411yescharacteristic
190#1220—22no—
191#1220—22no—
192C2×Dic15—22no—
193C2×Dic15M1614yescomplemented
194C2×Dic15C22×C411yescharacteristic
195C2×Dic15C22×C411yescharacteristic
196C2×Dic15C22×C411yescharacteristic
197C4×D15—22no—
198Dic30—22no—
199C2×C5×Dic3—22no—
200C2×C5×Dic3—22no—
201C2×C5×Dic3C22×C411yescharacteristic
202C2×C5×Dic3C22×C411yescharacteristic
203C2×C5×Dic3C22×C411yescharacteristic
204C2×C5×Dic3C22×C411yescharacteristic
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5C22×C411yescharacteristic
210C2×C3×Dic5C22×C411yescharacteristic
211C2×C3×Dic5C22×C411yescharacteristic
212C2×C3×Dic5C2411yescharacteristic
213#1200—21no—
214#1200—21no—
215#1200—22no—
216C3⋊#170—21no—
217C3⋊#170—21no—
218C3⋊#170—21no—
219C3⋊#170#4112yescomplemented
220C3×#170—21no—
221C3×#170—21no—
222C3×#170—21no—
223C3×#170#4112yescomplemented
224C2×#237—51no—
225C2×C3×M16—51no—
226C22×C3×C8—51no—
227C3×C4×D4—51no—
228D4×Dic3AGL(1,𝔽5)11yescharacteristic
229C4×#67—51no—
230C4×#67—51no—
231C2×C4×Dic3—51no—
232C2×C4×Dic3—51no—
233C2×#208—51no—
234C22×C3⋊C8—51no—
235C2×ΓL(1,𝔽25)—51no—
236C2×ΓL(1,𝔽25)—51no—
237#892—51no—
238#887—51no—
239#67⋊C4—51no—
240#67⋊C4—51no—
241#877—51no—
242#877—51no—
243C42×D3—51no—
244C4×Dic6—51no—
245C3×C4⋊C8—51no—
246C3×C22⋊C8—51no—
247C3×C22⋊C8—51no—
248C3×#97—51no—
249#830—51no—
250#830—51no—
251(C2×D3)⋊C8—51no—
252(C2×D3)⋊C8—51no—
253#815—51no—
254#815—51no—
255Dic3⋊C8—51no—
256Dic3⋊C8—51no—
257Dic3⋊C8—51no—
258Dic3⋊C8—51no—
259C8×Dic3—51no—
260C8×Dic3—51no—
261C8×Dic3—51no—
262C8×Dic3—51no—
263C8×Dic3—51no—
264C8×Dic3—51no—
265C4⋊(C3⋊C8)—51no—
266#803—51no—
267C2×C5×D4C4×D311yescharacteristic
268C22×C4×C5—31no—
269C22×C4×C5—31no—
270C2×C22⋊D5—31no—
271C2×C22⋊D5—31no—
272C22×Dic5—31no—
273C22×Dic5—31no—
274C22×Dic5C22×D311yescharacteristic
275C22×Dic5C22×D311yescharacteristic
276#711—64no—
277C2×C4×D5—31no—
278C2×C4×D5—31no—
279C2×C4×D5—31no—
280C2×Dic10—31no—
281#704—22no—
282#704—62no—
283C2×#170—22no—
284C2×#170—31no—
285C2×#170—31no—
286C2×#170—31no—
287C2×#170—31no—
288C2×#170—62no—
289C2×#170C22×D311yescharacteristic
290C2×#170C22×D311yescharacteristic
291C2×#170C22×D311yescharacteristic
292C2×#170C22×D311yescharacteristic
293#700—62no—
294#700—62no—
295C5×C4⋊C4—31no—
296C5×C22⋊C4—31no—
297C5×C22⋊C4—31no—
298C42×C5—31no—
299C22⋊Dic5C4×D311yescharacteristic
300C22⋊Dic5C4×D311yescharacteristic
301#685—31no—
302#685—31no—
303C4⋊Dic5C4×D311yescharacteristic
304#683—31no—
305#683—31no—
306#683—31no—
307#683—31no—
308C4×Dic5—31no—
309C4×Dic5—31no—
310C4×Dic5—31no—
311C4×Dic5—31no—
312C4×Dic5—31no—
313C4×Dic5—31no—
314C4×Dic5—31no—
315C4×Dic5—31no—
316C4×Dic5C22×D311yescharacteristic
317C4×#41—151no—
318#446—151no—
319#446—151no—
320#436—151no—
321#436—151no—
322#435—51no—
323#435—151no—
324#435—151no—
325#435—151no—
326#431—151no—
327#431—151no—
328#431—151no—
329C4×M16—151no—
330C4×M16—151no—
331C2×C4×C8—151no—
332C22×C3×C5—21no—
333C22×C3×C5—21no—
334C22×C3×C5—21no—
335C22×C3×C5—21no—
336C22×C3×C5—21no—
337C22×C3×C5C2×M1612yes—
338C22×C3×C5C23×C411yescharacteristic
339C2×D15—21no—
340C2×D15—21no—
341C2×D15—21no—
342C3×C4×C5—21no—
343Dic15—21no—
344Dic15C2×M1612yes—
345Dic15C2×M1612yes—
346C3×Dic5—21no—
347C3×Dic5—21no—
348C3×Dic5—21no—
349C3×Dic5C2×#4111yescharacteristic
350C3×Dic5C2×#4111yescharacteristic
351C5×Dic3—21no—
352C5×Dic3—21no—
353C5×Dic3—21no—
354C5×Dic3#13112yes—
355C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
356C22×C3×C4—51no—
357C22×C3×C4—51no—
358C2×#67—51no—
359C2×#67—51no—
360C22×Dic3—51no—
361C22×Dic3—51no—
362C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
363C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
364#237—104no—
365C2×C4×D3—51no—
366C2×C4×D3—51no—
367C2×C4×D3—51no—
368C2×Dic6—51no—
369C3×M16—102no—
370C2×C3×C8—51no—
371C2×C3×C8—51no—
372C2×C3×C8—51no—
373C2×C3×C8—51no—
374C2×C3×C8—102no—
375C3×C4⋊C4—51no—
376C3×C22⋊C4—51no—
377C3×C22⋊C4—51no—
378C3×C42—51no—
379#217C2×AGL(1,𝔽5)11yescharacteristic
380#217C2×AGL(1,𝔽5)11yescharacteristic
381(C2×D3)⋊C4—51no—
382(C2×D3)⋊C4—51no—
383C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
384Dic3⋊C4—51no—
385Dic3⋊C4—51no—
386Dic3⋊C4—51no—
387Dic3⋊C4—51no—
388C4×Dic3—51no—
389C4×Dic3—51no—
390C4×Dic3—51no—
391C4×Dic3—51no—
392C4×Dic3—51no—
393C4×Dic3—51no—
394C4×Dic3—51no—
395C4×Dic3—51no—
396C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
397#208—102no—
398C2×C3⋊C8—51no—
399C2×C3⋊C8—51no—
400C2×C3⋊C8—51no—
401C2×C3⋊C8—51no—
402C2×C3⋊C8—102no—
403ΓL(1,𝔽25)—102no—
404ΓL(1,𝔽25)—102no—
405C23×C5C2×C4×D311yescharacteristic
406C23×C5C2×C4×D311yescharacteristic
407C22×D5—31no—
408C5×D4—22no—
409C2×C4×C5—31no—
410C2×C4×C5—31no—
411C2×C4×C5—31no—
412C2×C4×C5—31no—
413C2×C4×C5—62no—
414C2×C4×C5—62no—
415C2×C4×C5C2×C4×D311yescharacteristic
416C22⋊D5—62no—
417C22⋊D5—62no—
418C2×Dic5—21no—
419C2×Dic5—21no—
420C2×Dic5—21no—
421C2×Dic5—21no—
422C2×Dic5—34no—
423C2×Dic5—31no—
424C2×Dic5—31no—
425C2×Dic5—31no—
426C2×Dic5—62no—
427C2×Dic5C2×C4×D311yescharacteristic
428C2×Dic5C2×C4×D311yescharacteristic
429C2×Dic5C2×C4×D311yescharacteristic
430C2×Dic5C23×D311yescharacteristic
431C4×D5—62no—
432C4×D5—62no—
433C4×D5—61no—
434C4×D5—61no—
435Dic10—62no—
436#170—21no—
437#170—21no—
438#170—21no—
439#170—32no—
440#170—61no—
441#170—61no—
442#170—61no—
443#170#23712yescomplemented
444C2×#41—151no—
445C2×M16—51no—
446C2×M16—151no—
447C2×M16—151no—
448C2×M16—151no—
449C22×C8—51no—
450C22×C8—151no—
451C4×Q8—151no—
452C4×Q8—151no—
453C4×D4—31no—
454C4×D4—51no—
455C4×D4—151no—
456C4×D4—151no—
457C4×D4—151no—
458C4×D4—151no—
459#117—151no—
460#117—151no—
461#117—151no—
462C2×C42—151no—
463C2×C42—151no—
464C2×C42—151no—
465C4⋊C8—51no—
466C4⋊C8—151no—
467C4⋊C8—151no—
468C4⋊C8—151no—
469C4⋊C8—151no—
470C4⋊C8—151no—
471C22⋊C8—51no—
472C22⋊C8—51no—
473C22⋊C8—151no—
474C22⋊C8—151no—
475C22⋊C8—151no—
476C22⋊C8—151no—
477#97—51no—
478#97—151no—
479#97—151no—
480#97—151no—
481C4×C8—151no—
482C4×C8—151no—
483C4×C8—151no—
484C4×C8—151no—
485C4×C8—151no—
486C4×C8—151no—
487C2×C3×C5—22no—
488C2×C3×C5—41no—
489C2×C3×C5C4×#4111yescharacteristic
490C2×C3×C5C22×M1611yescharacteristic
491C2×C3×C5C2×#13111yescharacteristic
492D15—41no—
493C23×C3C22×AGL(1,𝔽5)11yescharacteristic
494C23×C3C22×AGL(1,𝔽5)11yescharacteristic
495C22×D3—51no—
496C3×D4—22no—
497C2×C3×C4—51no—
498C2×C3×C4—51no—
499C2×C3×C4—51no—
500C2×C3×C4—51no—
501C2×C3×C4—101no—
502C2×C3×C4—101no—
503C2×C3×C4—101no—
504C2×C3×C4—101no—
505C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
506#67—102no—
507#67—102no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—54no—
511C2×Dic3—51no—
512C2×Dic3—51no—
513C2×Dic3—51no—
514C2×Dic3—102no—
515C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
516C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
517C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
518C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
519C4×D3—101no—
520C4×D3—101no—
521C4×D3—102no—
522C4×D3—102no—
523Dic6—102no—
524C3×C8—52no—
525C3×C8—101no—
526C3×C8—101no—
527C3×C8—101no—
528C3⋊C8—52no—
529C3⋊C8—101no—
530C3⋊C8—101no—
531C3⋊C8—101no—
532C22×C5—21no—
533C22×C5—21no—
534C22×C5—21no—
535C22×C5—21no—
536C22×C5—21no—
537C22×C5D3×M1612yes—
538C22×C5C22×C4×D311yescharacteristic
539C2×D5—61no—
540C2×D5—61no—
541C2×D5—61no—
542C4×C5—21no—
543C4×C5—32no—
544C4×C5—61no—
545C4×C5—61no—
546C4×C5—61no—
547Dic5—21no—
548Dic5—21no—
549Dic5—21no—
550Dic5—32no—
551Dic5—32no—
552Dic5—61no—
553Dic5C2×#23711yescharacteristic
554Dic5D3×#4111yescharacteristic
555#41—304no—
556C2×Q8—151no—
557C2×D4—151no—
558C2×D4—151no—
559C2×D4D3×AGL(1,𝔽5)11yescharacteristic
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—51no—
563C22×C4—51no—
564C22×C4—151no—
565C22×C4—151no—
566C22×C4—151no—
567C22×C4—151no—
568C22×C4—151no—
569M16—102no—
570M16—302no—
571M16—302no—
572M16—302no—
573C2×C8—51no—
574C2×C8—51no—
575C2×C8—51no—
576C2×C8—51no—
577C2×C8—102no—
578C2×C8—151no—
579C2×C8—151no—
580C2×C8—151no—
581C2×C8—151no—
582C2×C8—302no—
583C4⋊C4—31no—
584C4⋊C4—51no—
585C4⋊C4—151no—
586C4⋊C4—151no—
587C4⋊C4—151no—
588C4⋊C4—151no—
589C22⋊C4—31no—
590C22⋊C4—31no—
591C22⋊C4—51no—
592C22⋊C4—51no—
593C22⋊C4—151no—
594C22⋊C4—151no—
595C42—31no—
596C42—51no—
597C42—151no—
598C42—151no—
599C42—151no—
600C42—151no—
601C42—151no—
602C42—151no—
603C42—151no—
604C42—151no—
605C3×C5#296511yescharacteristic, complemented, Hall
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3D5⋊M1612yes—
612C22×C3C23×AGL(1,𝔽5)11yescharacteristic
613C2×D3—101no—
614C2×D3—101no—
615C2×D3—101no—
616C3×C4—21no—
617C3×C4—51no—
618C3×C4—51no—
619C3×C4—101no—
620C3×C4—101no—
621C3×C4—101no—
622Dic3—21no—
623Dic3—21no—
624Dic3—21no—
625Dic3—52no—
626Dic3—52no—
627Dic3—101no—
628Dic3#413112yes—
629C2×C5—22no—
630C2×C5—41no—
631C2×C5C4×#23711yescharacteristic
632C2×C5C2×D3×M1611yescharacteristic
633C2×C5D3×#13111yescharacteristic
634D5—121no—
635C23—151no—
636C23C2×D3×AGL(1,𝔽5)11yescharacteristic
637C23C2×D3×AGL(1,𝔽5)11yescharacteristic
638Q8—302no—
639D4—22no—
640D4—302no—
641D4—302no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—51no—
647C2×C4—51no—
648C2×C4—51no—
649C2×C4—51no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—101no—
653C2×C4—101no—
654C2×C4—101no—
655C2×C4—101no—
656C2×C4—154no—
657C2×C4—151no—
658C2×C4—151no—
659C2×C4—151no—
660C2×C4—302no—
661C2×C4—302no—
662C2×C4—301no—
663C2×C4—301no—
664C2×C4—302no—
665C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
666C8—52no—
667C8—101no—
668C8—101no—
669C8—101no—
670C8—152no—
671C8—301no—
672C8—301no—
673C8—301no—
674C2×C3—22no—
675C2×C3—41no—
676C2×C3C2×D5⋊M1611yescharacteristic
677C2×C3C2×#413111yescharacteristic
678C2×C3#41×AGL(1,𝔽5)11yescharacteristic
679D3—201no—
680C5#7945311yescharacteristic, complemented, Sylow
681C22—21no—
682C22—21no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—301no—
687C22—301no—
688C22—301no—
689C22#9193112yes—
690C22C22×D3×AGL(1,𝔽5)11yescharacteristic
691C4—21no—
692C4—32no—
693C4—51no—
694C4—51no—
695C4—61no—
696C4—61no—
697C4—61no—
698C4—101no—
699C4—101no—
700C4—101no—
701C4—152no—
702C4—152no—
703C4—301no—
704C3#1061715411yescharacteristic, complemented, Sylow
705C2—22no—
706C2—41no—
707C2—601no—
708C2D3×#413111yescharacteristic
709C2AGL(1,𝔽5)×#23711yescharacteristic
710C2C2×#9193111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×D4C2×C4
prime radicalC2×#6819C4
cosocleC2×C3×Dic5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#2965
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #11752432C2semidirect
3. C3×#65773C2semidirect
4. #11752054C2semidirect
5. #11752046C2semidirect
6. #11751994C2semidirect
7. Dic3×#704C2semidirect
8. #11751991C2semidirect
9. #11751987C2semidirect
10. #11751986C2semidirect
11. C2×Dic3×#170C2semidirect
12. #11751784C2semidirect
13. #11751771C2semidirect
14. #11751760C2semidirect
15. #11751756C2semidirect
63. #65773D3semidirect
193. C2×Dic15M16semidirect
219. C3⋊#170#41semidirect
223. C3×#170#41semidirect
443. #170#237semidirect
605. C3×C5#2965semidirect
680. C5#79453semidirect
704. C3#10617154semidirect

Maximal subgroups

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

subgroupindex
#117548532
#117524322
C3×#657732
#117520542
#117520462
#117519942
Dic3×#7042
#117519912
#117519872
#117519862
C2×Dic3×#1702
#117517842
#117517712
#117517602
#117517562
#106171543
#794535