Finite Group Databasebeta

← #14325860

Subgroups — #14325860

Order 1920.

1080 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91462C211yesmaximal, characteristic
2#11751074C211yesmaximal, characteristic, complemented
3C5×#4989C211yesmaximal, characteristic, complemented
4C3×#65279C211yesmaximal, characteristic, complemented
5#11748910C211yesmaximal, characteristic
6#11748906C211yesmaximal, characteristic
7#11748890C211yesmaximal, characteristic, complemented
8#11748884C211yesmaximal, characteristic, complemented
9#11748794C211yesmaximal, characteristic, complemented
10#11748719C211yesmaximal, characteristic, complemented
11#11748714C211yesmaximal, characteristic, complemented
12#11748711C211yesmaximal, characteristic, complemented
13#11748694C211yesmaximal, characteristic, complemented
14#11748647C211yesmaximal, characteristic, complemented
15Dic5×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#10606122—31nomaximal, Hall
17C22×Dic30C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×#1201C2211yescharacteristic
20C22×D5×Dic3C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C5×(C2×D3)⋊C4C2211yescharacteristic
24C2×C5×(C2×D3)⋊C4C2211yescharacteristic
25C2×C5×Dic3⋊C4C2211yescharacteristic
26C2×C3×#685C2211yescharacteristic
27C2×C3×#685C2211yescharacteristic
28C2×C3×#685C2211yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×Dic3⋊Dic5C2211yescharacteristic
31C2×#6669C2211yescharacteristic
32C2×(C2×D3)⋊Dic5C2211yescharacteristic
33C2×(C2×D3)⋊Dic5C2211yescharacteristic
34C2×(C2×D3)⋊Dic5C2211yescharacteristic
35C2×#6665C2211yescharacteristic
36C2×#6665C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40#91462C418yescomplemented
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43#91115C2211yescharacteristic
44#91115C2211yescharacteristic
45C5×C3⋊#95C2211yescharacteristic
46C5×C3⋊#95C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#75471—51nomaximal, Hall
54C2×#4031—31no—
55C5×#385—31no—
56#65502—31no—
57C4×C22⋊Dic5—31no—
58#65279—31no—
59#65279D311yescharacteristic, complemented
60C4⋊C4×Dic5—31no—
61#65263—31no—
62#65245—31no—
63#65240—31no—
64#65233—31no—
65#64957—31no—
66#64955—31no—
67#64940—31no—
68#64935—31no—
69C23×C5×D3C2311yescharacteristic
70C23×C3×D5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C2×Dic30—41no—
79C2×Dic30—41no—
80C2×Dic30C2×C414yescomplemented
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C2×C4×C5×D3—22no—
85C2×C4×C5×D3—41no—
86C2×C4×C5×D3—41no—
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C2×#1201—41no—
91C2×#1201—41no—
92C2×#1201C2×C414yes—
93C2×D5×Dic3—22no—
94C2×D5×Dic3—41no—
95C2×D5×Dic3—41no—
96C3×C5×C4⋊C4—41no—
97C4×Dic15—41no—
98C5×(C2×D3)⋊C4—41no—
99C5×(C2×D3)⋊C4C2×C414yescomplemented
100C5×Dic3⋊C4—22no—
101C3×#685—41no—
102C3×#685—41no—
103C3×#685C2×C414yescomplemented
104C3×C4×Dic5—41no—
105Dic3⋊Dic5—22no—
106#6669—41no—
107(C2×D3)⋊Dic5—22no—
108(C2×D3)⋊Dic5—41no—
109(C2×D3)⋊Dic5C2×C414yescomplemented
110#6665—22no—
111#6665C2×C414yescomplemented
112Dic3×Dic5—41no—
113Dic3×Dic5—41no—
114Dic3×Dic5C2×C414yescomplemented
115C2×#885—51no—
116C3×#388—51no—
117#4989D511yescharacteristic, complemented
118#4973—51no—
119#4958—51no—
120#4956—51no—
121#4946—51no—
122#4944—51no—
123Dic3×C22⋊C4—51no—
124#4940—51no—
125C4×Dic3⋊C4—51no—
126#4669—51no—
127#4666—51no—
128#4651—51no—
129#4646—51no—
130C23×C4×C5—31no—
131C22×C22⋊D5—31no—
132C22×C4×D5—31no—
133C22×Dic10—31no—
134C2×C5×C4⋊C4—31no—
135C2×C5×C4⋊C4C2×D311yescharacteristic
136C2×C5×C22⋊C4—31no—
137C2×C5×C22⋊C4—31no—
138C2×C22⋊Dic5—31no—
139C2×C22⋊Dic5—31no—
140C2×C22⋊Dic5—31no—
141C2×#685—31no—
142C2×#685—31no—
143C2×#685C2×D311yescharacteristic
144C2×#685C2×D311yescharacteristic
145C2×#685C2×D311yescharacteristic
146C2×C4⋊Dic5—31no—
147C2×#683—31no—
148C2×C4×Dic5—31no—
149C2×C4×Dic5—31no—
150C2×C4×Dic5—31no—
151C2×C4×Dic5—31no—
152C2×C4×Dic5C2×D311yescharacteristic
153#4031—38no—
154C5×#95—31no—
155C5×#95—31no—
156#3963—31no—
157#3963—31no—
158#3963—31no—
159#3963—31no—
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963—31no—
164#3963C2×D311yescharacteristic
165#3963C2×D311yescharacteristic
166#2337—151noSylow
167C23×C3×C5C2411yescharacteristic
168C22×C5×D3—21no—
169C22×C5×D3—21no—
170C22×C5×D3—21no—
171C22×C5×D3—21no—
172C22×C5×D3—21no—
173C22×C5×D3—21no—
174C22×C5×D3C22×C412yes—
175C22×C3×D5—21no—
176C22×C3×D5—21no—
177C22×C3×D5—21no—
178C22×C3×D5—21no—
179C22×C3×D5—21no—
180C22×C3×D5—21no—
181C22×C3×D5C22×C412yes—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5C22×C412yes—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15C22×C412yes—
201C2×Dic15C22×C412yes—
202C2×Dic15#4112yes—
203Dic30—44no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3C22×C412yes—
212C2×C5×Dic3#4112yes—
213C4×C5×D3—44no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5C22×C412yes—
223#1201—44no—
224D5×Dic3—44no—
225C22×#67—51no—
226C23×Dic3—51no—
227C22×C4×D3C2×D511yescharacteristic
228C22×Dic6—51no—
229C2×C3×C4⋊C4C2×D511yescharacteristic
230C2×C3×C22⋊C4—51no—
231C2×C3×C22⋊C4—51no—
232C2×C3×C22⋊C4—51no—
233C2×C3×C42—51no—
234C2×#217—51no—
235C2×#217—51no—
236C2×(C2×D3)⋊C4—51no—
237C2×(C2×D3)⋊C4—51no—
238C2×(C2×D3)⋊C4—51no—
239C2×(C2×D3)⋊C4C2×D511yescharacteristic
240C2×(C2×D3)⋊C4C2×D511yescharacteristic
241C2×Dic3⋊C4—51no—
242C2×Dic3⋊C4—51no—
243C2×Dic3⋊C4C2×D511yescharacteristic
244C2×C4×Dic3—51no—
245C2×C4×Dic3—51no—
246C2×C4×Dic3—51no—
247C2×C4×Dic3—51no—
248#885—58no—
249C3×#95—51no—
250C3×#95—51no—
251C3⋊#95—51no—
252C3⋊#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95—51no—
259C3⋊#95C2×D511yescharacteristic
260C3⋊#95C2×D511yescharacteristic
261C24×C5—31no—
262C23×D5C22×D311yescharacteristic
263C22×C4×C5—31no—
264C22×C4×C5—31no—
265C22×C4×C5—31no—
266C22×C4×C5—62no—
267C22×C4×C5—121no—
268C22×C4×C5—121no—
269C22×C4×C5C22×D311yescharacteristic
270C22×C4×C5C22×D311yescharacteristic
271C22×C4×C5C22×D311yescharacteristic
272C2×C22⋊D5—34no—
273C2×C22⋊D5—121no—
274C2×C22⋊D5—121no—
275C22×Dic5—31no—
276C22×Dic5—31no—
277C22×Dic5—31no—
278C22×Dic5—31no—
279C22×Dic5C22×D311yescharacteristic
280C22×Dic5C22×D311yescharacteristic
281C22×Dic5C22×D311yescharacteristic
282C2×C4×D5—62no—
283C2×C4×D5—121no—
284C2×C4×D5—121no—
285C2×Dic10—34no—
286C2×Dic10—121no—
287C2×Dic10—121no—
288C5×C4⋊C4—41no—
289C5×C4⋊C4—62no—
290C5×C22⋊C4—34no—
291C5×C22⋊C4—121no—
292C22⋊Dic5—34no—
293C22⋊Dic5—62no—
294C22⋊Dic5—121no—
295#685—34no—
296#685—41no—
297#685—41no—
298#685—62no—
299#685C4×D314yescomplemented
300C4⋊Dic5—62no—
301#683—121no—
302C4×Dic5—34no—
303C4×Dic5—41no—
304C4×Dic5—121no—
305C4×Dic5—121no—
306C4×Dic5—121no—
307C2×#124—151no—
308#391—151no—
309#391—151no—
310#388—51no—
311#388—151no—
312#388—151no—
313#388—151no—
314#386—151no—
315#386—151no—
316#385—31no—
317#385—151no—
318#383—151no—
319C4×C4⋊C4—151no—
320C4×C22⋊C4—151no—
321C4×C22⋊C4—151no—
322C22×C3×C5C23×C411yescharacteristic
323C22×C3×C5C2×#4111yescharacteristic
324C22×C3×C5C2×#4111yescharacteristic
325C22×C3×C5H(5,𝔽2)11yescharacteristic
326C22×C3×C5H(5,𝔽2)11yescharacteristic
327C22×C3×C5H(5,𝔽2)11yescharacteristic
328C22×C3×C52−1+411yescharacteristic
329C2×C5×D3—22no—
330C2×C5×D3—22no—
331C2×C5×D3—22no—
332C2×C5×D3—41no—
333C2×C5×D3—41no—
334C2×C5×D3—41no—
335C2×C5×D3—41no—
336C2×C3×D5—22no—
337C2×C3×D5—22no—
338C2×C3×D5—22no—
339C2×C3×D5—41no—
340C2×C3×D5—41no—
341C2×C3×D5—41no—
342C2×C3×D5—41no—
343C3×C4×C5—22no—
344C3×C4×C5—41no—
345C3×C4×C5—41no—
346Dic15—22no—
347Dic15—22no—
348Dic15—22no—
349Dic15—41no—
350C3×Dic5—22no—
351C3×Dic5—41no—
352C3×Dic5—41no—
353C5×Dic3—22no—
354C5×Dic3—22no—
355C5×Dic3—41no—
356C24×C3—51no—
357C23×D3C22×D511yescharacteristic
358C22×C3×C4—51no—
359C22×C3×C4—51no—
360C22×C3×C4—51no—
361C22×C3×C4C22×D511yescharacteristic
362C22×C3×C4C22×D511yescharacteristic
363C22×C3×C4C22×D511yescharacteristic
364C2×#67—54no—
365C2×#67—201no—
366C2×#67—201no—
367C22×Dic3—51no—
368C22×Dic3—51no—
369C22×Dic3—51no—
370C22×Dic3—51no—
371C22×Dic3—102no—
372C22×Dic3—201no—
373C22×Dic3—201no—
374C22×Dic3C22×D511yescharacteristic
375C22×Dic3C22×D511yescharacteristic
376C22×Dic3C22×D511yescharacteristic
377C2×C4×D3—22no—
378C2×C4×D3—41no—
379C2×C4×D3—41no—
380C2×Dic6—54no—
381C2×Dic6—201no—
382C2×Dic6—201no—
383C3×C4⋊C4—41no—
384C3×C22⋊C4—54no—
385C3×C22⋊C4—201no—
386C3×C22⋊C4—201no—
387C3×C42—201no—
388#217—54no—
389#217—102no—
390(C2×D3)⋊C4—41no—
391(C2×D3)⋊C4—54no—
392(C2×D3)⋊C4—102no—
393(C2×D3)⋊C4—201no—
394(C2×D3)⋊C4C4×D514yescomplemented
395Dic3⋊C4—22no—
396Dic3⋊C4—102no—
397Dic3⋊C4—201no—
398C4×Dic3—54no—
399C4×Dic3—201no—
400C4×Dic3—201no—
401C4×Dic3—201no—
402C23×C5—32no—
403C23×C5—61no—
404C23×C5—61no—
405C23×C5—61no—
406C23×C5—61no—
407C23×C5—61no—
408C23×C5—61no—
409C23×C5C23×D311yescharacteristic
410C22×D5—21no—
411C22×D5—21no—
412C22×D5—21no—
413C22×D5—21no—
414C22×D5—21no—
415C22×D5—21no—
416C22×D5C2×C4×D312yes—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—21no—
425C2×C4×C5—32no—
426C2×C4×C5—32no—
427C2×C4×C5—61no—
428C2×C4×C5—61no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×C4×C5—61no—
432C2×C4×C5—61no—
433C2×C4×C5—61no—
434C2×C4×C5—124no—
435C2×C4×C5C2×C4×D312yes—
436C22⋊D5—124no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—32no—
446C2×Dic5—32no—
447C2×Dic5—32no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452C2×Dic5—61no—
453C2×Dic5—61no—
454C2×Dic5—61no—
455C2×Dic5—61no—
456C2×Dic5—61no—
457C2×Dic5C2×C4×D312yes—
458C4×D5—124no—
459Dic10—124no—
460C22×Q8—151no—
461C22×D4—151no—
462C23×C4—31no—
463C23×C4—151no—
464#124—158no—
465C2×C4⋊C4—31no—
466C2×C4⋊C4—151no—
467C2×C4⋊C4—151no—
468C2×C4⋊C4D3×D511yescharacteristic
469C2×C22⋊C4—31no—
470C2×C22⋊C4—31no—
471C2×C22⋊C4—51no—
472C2×C22⋊C4—51no—
473C2×C22⋊C4—51no—
474C2×C22⋊C4—151no—
475C2×C22⋊C4—151no—
476C2×C22⋊C4—151no—
477C2×C22⋊C4—151no—
478C2×C22⋊C4—151no—
479C2×C42—51no—
480C2×C42—151no—
481C2×C42—151no—
482C2×C42—151no—
483C2×C42—151no—
484#95—31no—
485#95—31no—
486#95—51no—
487#95—51no—
488#95—151no—
489#95—151no—
490#95—151no—
491#95—151no—
492#95—151no—
493#95—151no—
494#95—151no—
495#95—151no—
496C2×C3×C5C4×#4111yescharacteristic
497C2×C3×C5#51811yescharacteristic
498C2×C3×C5#52011yescharacteristic
499C2×C3×C5#53811yescharacteristic
500C2×C3×C5#53811yescharacteristic
501C2×C3×C5#54211yescharacteristic
502C2×C3×C5#54211yescharacteristic
503C3×D5—42no—
504C5×D3—42no—
505C23×C3—52no—
506C23×C3—101no—
507C23×C3—101no—
508C23×C3—101no—
509C23×C3—101no—
510C23×C3—101no—
511C23×C3—101no—
512C23×C3C23×D511yescharacteristic
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3C2×C4×D512yes—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—52no—
529C2×C3×C4—101no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—101no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4C2×C4×D512yes—
538#67—204no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—52no—
547C2×Dic3—52no—
548C2×Dic3—52no—
549C2×Dic3—101no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—101no—
558C2×Dic3—204no—
559C2×Dic3C2×C4×D512yes—
560C2×Dic3#71112yes—
561C4×D3—44no—
562Dic6—204no—
563C22×C5—62no—
564C22×C5—62no—
565C22×C5—62no—
566C22×C5—121no—
567C22×C5—121no—
568C22×C5—121no—
569C22×C5—121no—
570C22×C5C22×C4×D311yescharacteristic
571C22×C5#100411yescharacteristic
572C22×C5#100411yescharacteristic
573C22×C5D3×#4111yescharacteristic
574C22×C5D3×#4111yescharacteristic
575C22×C5#100911yescharacteristic
576C22×C5#101011yescharacteristic
577C2×D5—22no—
578C2×D5—22no—
579C2×D5—22no—
580C2×D5—41no—
581C2×D5—41no—
582C2×D5—41no—
583C2×D5—41no—
584C4×C5—22no—
585C4×C5—41no—
586C4×C5—41no—
587C4×C5—62no—
588C4×C5—62no—
589C4×C5—121no—
590Dic5—22no—
591Dic5—41no—
592Dic5—41no—
593Dic5—62no—
594Dic5—62no—
595Dic5—62no—
596Dic5—121no—
597C24—31no—
598C24—51no—
599C2×Q8—154no—
600C2×Q8—601no—
601C2×Q8—601no—
602C2×D4—154no—
603C2×D4—601no—
604C2×D4—601no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—51no—
609C22×C4—51no—
610C22×C4—51no—
611C22×C4—62no—
612C22×C4—121no—
613C22×C4—121no—
614C22×C4—151no—
615C22×C4—151no—
616C22×C4—151no—
617C22×C4—151no—
618C22×C4—302no—
619C22×C4—601no—
620C22×C4—601no—
621C22×C4C2×D3×D511yescharacteristic
622C22×C4C2×D3×D511yescharacteristic
623C22×C4C2×D3×D511yescharacteristic
624C4⋊C4—41no—
625C4⋊C4—62no—
626C4⋊C4—302no—
627C4⋊C4—601no—
628C22⋊C4—34no—
629C22⋊C4—54no—
630C22⋊C4—121no—
631C22⋊C4—154no—
632C22⋊C4—154no—
633C22⋊C4—201no—
634C22⋊C4—201no—
635C22⋊C4—302no—
636C22⋊C4—302no—
637C22⋊C4—601no—
638C42—154no—
639C42—201no—
640C42—601no—
641C42—601no—
642C42—601no—
643C3×C5#233711yescharacteristic, complemented, Hall
644C22×C3—102no—
645C22×C3—102no—
646C22×C3—102no—
647C22×C3—201no—
648C22×C3—201no—
649C22×C3—201no—
650C22×C3—201no—
651C22×C3C22×C4×D511yescharacteristic
652C22×C3C2×#71111yescharacteristic
653C22×C3#414411yescharacteristic
654C22×C3#414411yescharacteristic
655C22×C3#414711yescharacteristic
656C22×C3D5×#4111yescharacteristic
657C22×C3#414911yescharacteristic
658C2×D3—22no—
659C2×D3—22no—
660C2×D3—22no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C3×C4—22no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—102no—
669C3×C4—201no—
670C3×C4—201no—
671Dic3—22no—
672Dic3—22no—
673Dic3—41no—
674Dic3—102no—
675Dic3—102no—
676Dic3—102no—
677Dic3—201no—
678C2×C5—122no—
679C2×C5#552211yescharacteristic
680C2×C5#554511yescharacteristic
681C2×C5#554611yescharacteristic
682C2×C5#561311yescharacteristic
683C2×C5#565711yescharacteristic
684C2×C5#566911yescharacteristic
685C2×C5#571011yescharacteristic
686D5—42no—
687C23—32no—
688C23—52no—
689C23—61no—
690C23—61no—
691C23—61no—
692C23—61no—
693C23—61no—
694C23—61no—
695C23—101no—
696C23—101no—
697C23—101no—
698C23—101no—
699C23—101no—
700C23—101no—
701C23C22×D3×D511yescharacteristic
702Q8—604no—
703D4—604no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—52no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—101no—
723C2×C4—101no—
724C2×C4—101no—
725C2×C4—101no—
726C2×C4—101no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—124no—
731C2×C4—152no—
732C2×C4—152no—
733C2×C4—152no—
734C2×C4—301no—
735C2×C4—301no—
736C2×C4—301no—
737C2×C4—301no—
738C2×C4—301no—
739C2×C4—301no—
740C2×C4—301no—
741C2×C4—301no—
742C2×C4—301no—
743C2×C4—604no—
744C2×C4C4×D3×D512yes—
745C2×C3—202no—
746C2×C3#6583811yescharacteristic
747C2×C3C4×#71111yescharacteristic
748C2×C3#6587911yescharacteristic
749C2×C3#6592711yescharacteristic
750C2×C3#6597411yescharacteristic
751C2×C3#6597711yescharacteristic
752C2×C3#6599111yescharacteristic
753D3—42no—
754C5#7547111yescharacteristic, complemented, Sylow
755C22—62no—
756C22—62no—
757C22—62no—
758C22—102no—
759C22—102no—
760C22—102no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22—201no—
766C22—201no—
767C22—201no—
768C22—201no—
769C22C2×C4×D3×D511yescharacteristic
770C22#9201911yescharacteristic
771C22D3×#71111yescharacteristic
772C22#9202511yescharacteristic
773C22#9202811yescharacteristic
774C22#9203411yescharacteristic
775C22#9204911yescharacteristic
776C4—22no—
777C4—41no—
778C4—41no—
779C4—62no—
780C4—62no—
781C4—102no—
782C4—121no—
783C4—201no—
784C4—201no—
785C4—302no—
786C4—302no—
787C4—302no—
788C4—601no—
789C3#1060612211yescharacteristic, complemented, Sylow
790C2—122no—
791C2—202no—
792C2#1175339911yescharacteristic
793C2#1175340211yescharacteristic
794C2#1175357611yescharacteristic
795C2#1175393511yescharacteristic
796C2#1175462911yescharacteristic
797C2#1175497111yescharacteristic
798C2#1175521211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1201C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2337
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11751074C2semidirect
3. C5×#4989C2semidirect
4. C3×#65279C2semidirect
7. #11748890C2semidirect
8. #11748884C2semidirect
9. #11748794C2semidirect
10. #11748719C2semidirect
11. #11748714C2semidirect
12. #11748711C2semidirect
13. #11748694C2semidirect
14. #11748647C2semidirect
15. Dic5×Dic3⋊C4C2semidirect
40. #91462C4semidirect
59. #65279D3semidirect
80. C2×Dic30C2×C4semidirect
99. C5×(C2×D3)⋊C4C2×C4semidirect
103. C3×#685C2×C4semidirect
109. (C2×D3)⋊Dic5C2×C4semidirect
111. #6665C2×C4semidirect
114. Dic3×Dic5C2×C4semidirect
117. #4989D5semidirect
299. #685C4×D3semidirect
394. (C2×D3)⋊C4C4×D5semidirect
643. C3×C5#2337semidirect
754. C5#75471semidirect
789. C3#10606122semidirect

Maximal subgroups

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

subgroupindex
C2×#914622
#117510742
C5×#49892
C3×#652792
#117489102
#117489062
#117488902
#117488842
#117487942
#117487192
#117487142
#117487112
#117486942
#117486472
Dic5×Dic3⋊C42
#106061223
#754715