Finite Group Databasebeta

← #14327634

Subgroups — #14327634

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91444C211yesmaximal, characteristic
2#11751091C211yesmaximal, characteristic, complemented
3C5×#4978C211yesmaximal, characteristic, complemented
4C3×#65276C211yesmaximal, characteristic, complemented
5#11748889C211yesmaximal, characteristic, complemented
6#11748884C211yesmaximal, characteristic, complemented
7#11748881C211yesmaximal, characteristic, complemented
8Dic3×#685C211yesmaximal, characteristic, complemented
9#11748872C211yesmaximal, characteristic
10#11748872C211yesmaximal, characteristic
11D5×C3⋊#95C211yesmaximal, characteristic, complemented
12#11748678C211yesmaximal, characteristic, complemented
13#11748673C211yesmaximal, characteristic, complemented
14#11748653C211yesmaximal, characteristic, complemented
15#11748646C211yesmaximal, characteristic, complemented
16#10607037—31nomaximal, Hall
17C22×C3×C4×D5C2211yescharacteristic
18C22×#1202C2211yescharacteristic
19C22×#1200C2211yescharacteristic
20C22×D5×Dic3C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×C4×Dic15C2211yescharacteristic
27C2×C5×Dic3⋊C4C2211yescharacteristic
28C2×C4×C5×Dic3C2211yescharacteristic
29C2×C3×#685C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C2×#6667C2211yescharacteristic
33C2×#6667C2211yescharacteristic
34C2×#6665C2211yescharacteristic
35C2×Dic3×Dic5C2211yescharacteristic
36C2×Dic3×Dic5C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38#91444C418yescomplemented
39#91115C2211yescharacteristic
40#91115C2211yescharacteristic
41C5×C3⋊#95C2211yescharacteristic
42C5×C3⋊#95C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C5×C3⋊#95C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#73884—51nomaximal, Hall
54C2×#4039—31no—
55C5×#387—31no—
56#65279—31no—
57#65276D311yescharacteristic, complemented
58#65270—31no—
59C4×#685—31no—
60C4×#685—31no—
61#64959—31no—
62#64955—31no—
63#64954—31no—
64#64954—31no—
65#64953—31no—
66D5×#95—31no—
67#64940—31no—
68#64937—31no—
69C23×D15C2311yescharacteristic
70C23×C3×D5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×C5×Dic3C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C2×C3×C4×D5—41no—
85C2×C3×C4×D5—41no—
86C2×C3×C4×D5C2×C414yes—
87C2×#1202—22no—
88C2×#1202—22no—
89C2×#1202C2×C414yes—
90C2×#1200—41no—
91C2×#1200—41no—
92C2×#1200C2×C414yescomplemented
93C2×D5×Dic3—22no—
94C2×D5×Dic3—22no—
95C2×D5×Dic3—22no—
96C2×D5×Dic3—22no—
97C2×D5×Dic3—41no—
98C2×D5×Dic3—41no—
99C3×C5×C4⋊C4—41no—
100#6714—22no—
101#6714—41no—
102#6714C2×C414yescomplemented
103C4×Dic15—22no—
104C5×Dic3⋊C4C2×C414yescomplemented
105C4×C5×Dic3—41no—
106C3×#685—22no—
107C3×#685—22no—
108C3×C4⋊Dic5—41no—
109#6667—22no—
110#6667—41no—
111#6665C2×C414yes—
112Dic3×Dic5—22no—
113Dic3×Dic5—41no—
114Dic3×Dic5C2×C414yescomplemented
115C2×C4×#67—51no—
116C3×#380—51no—
117C2×C3⋊#95—51no—
118#4990—51no—
119#4990—51no—
120#4978—51no—
121#4978D511yescharacteristic, complemented
122#4958—51no—
123#4958—51no—
124Dic3×C22⋊C4—51no—
125Dic3×C22⋊C4—51no—
126#4666—51no—
127#4664—51no—
128#4651—51no—
129#4648—51no—
130C22×D20—31no—
131C22×C4×D5—31no—
132C22×C4×D5—31no—
133C22×C4×D5—31no—
134C22×C4×D5C2×D311yescharacteristic
135C2×C5×C4⋊C4—31no—
136C2×C5×C4⋊C4C2×D311yescharacteristic
137C2×C42×C5—31no—
138C2×#685—31no—
139C2×#685—31no—
140C2×#685—31no—
141C2×#685—31no—
142C2×#685—31no—
143C2×#685—31no—
144C2×#685C2×D311yescharacteristic
145C2×#685C2×D311yescharacteristic
146C2×C4⋊Dic5C2×D311yescharacteristic
147C2×C4×Dic5—31no—
148C2×C4×Dic5—31no—
149C2×C4×Dic5—31no—
150C2×C4×Dic5—31no—
151#4039—38no—
152C5×#95—31no—
153C5×#95—31no—
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#2353—151noSylow
167C23×C3×C5C2411yescharacteristic
168C22×D15—21no—
169C22×D15—21no—
170C22×D15—21no—
171C22×D15—21no—
172C22×D15—21no—
173C22×D15—21no—
174C22×D15C22×C412yes—
175C22×C3×D5—21no—
176C22×C3×D5—21no—
177C22×C3×D5—21no—
178C22×C3×D5—21no—
179C22×C3×D5C22×C412yes—
180C22×C3×D5#4112yes—
181C22×C3×D5#4112yes—
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×Dic15C22×C412yes—
199C2×Dic15#4112yes—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3C22×C412yes—
210C2×C5×Dic3C22×C412yes—
211C2×C5×Dic3#4112yes—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
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×Dic5C22×C412yes—
221C3×C4×D5—44no—
222#1202—28no—
223#1200—44no—
224D5×Dic3—44no—
225D5×Dic3—44no—
226C23×C3×C4—51no—
227C22×#67—51no—
228C23×Dic3—51no—
229C23×Dic3—51no—
230C22×C4×D3—51no—
231C2×C3×C4⋊C4—51no—
232C2×C3×C4⋊C4C2×D511yescharacteristic
233C2×C3×C22⋊C4—51no—
234C2×C3×C22⋊C4—51no—
235C2×#217—51no—
236C4×#67—58no—
237C2×(C2×D3)⋊C4—51no—
238C2×(C2×D3)⋊C4—51no—
239C2×(C2×D3)⋊C4—51no—
240C2×(C2×D3)⋊C4—51no—
241C2×(C2×D3)⋊C4—51no—
242C2×Dic3⋊C4C2×D511yescharacteristic
243C2×C4×Dic3—51no—
244C2×C4×Dic3—51no—
245C2×C4×Dic3—51no—
246C2×C4×Dic3—51no—
247C2×C4×Dic3C2×D511yescharacteristic
248C3×#95—51no—
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⋊#95C2×D511yescharacteristic
259C3⋊#95C2×D511yescharacteristic
260C3⋊#95C2×D511yescharacteristic
261C3⋊#95C2×D511yescharacteristic
262C23×D5—31no—
263C23×D5C22×D311yescharacteristic
264C22×C4×C5—31no—
265C22×C4×C5—31no—
266C22×C4×C5—31no—
267C22×C4×C5—31no—
268C22×C4×C5C22×D311yescharacteristic
269C22×C4×C5C22×D311yescharacteristic
270C22×C4×C5C22×D311yescharacteristic
271C22×Dic5—31no—
272C22×Dic5—31no—
273C22×Dic5—31no—
274C22×Dic5C22×D311yescharacteristic
275C22×Dic5C22×D311yescharacteristic
276C22×Dic5C22×D311yescharacteristic
277C2×D20—34no—
278C2×D20—62no—
279C2×D20—62no—
280C2×C4×D5—34no—
281C2×C4×D5—41no—
282C2×C4×D5—41no—
283C2×C4×D5—62no—
284C2×C4×D5—62no—
285C2×C4×D5—62no—
286C2×C4×D5—62no—
287C2×C4×D5—121no—
288C2×C4×D5—121no—
289C2×C4×D5—121no—
290C2×C4×D5—121no—
291C2×C4×D5C4×D314yes—
292C5×C4⋊C4—34no—
293C5×C4⋊C4—41no—
294C42×C5—121no—
295#685—22no—
296#685—22no—
297#685—34no—
298#685—34no—
299#685—62no—
300#685—62no—
301#685—121no—
302#685—121no—
303C4⋊Dic5—41no—
304C4×Dic5—34no—
305C4×Dic5—62no—
306C4×Dic5—62no—
307C4×Dic5—121no—
308C2×C4×D4—151no—
309#388—151no—
310#388—151no—
311#387—31no—
312#387—151no—
313#386—151no—
314#386—151no—
315#383—151no—
316#381—151no—
317#380—51no—
318C4×C22⋊C4—151no—
319C4×C22⋊C4—151no—
320C4×C22⋊C4—151no—
321#376—151no—
322C2×#95—151no—
323C22×C3×C5C23×C411yescharacteristic
324C22×C3×C5C2×#4111yescharacteristic
325C22×C3×C5C2×#4111yescharacteristic
326C22×C3×C5C2×#4111yescharacteristic
327C22×C3×C5C2×#4111yescharacteristic
328C22×C3×C5H(5,𝔽2)11yescharacteristic
329C22×C3×C5H(5,𝔽2)11yescharacteristic
330C2×D15—22no—
331C2×D15—22no—
332C2×D15—22no—
333C2×D15—41no—
334C2×D15—41no—
335C2×D15—41no—
336C2×D15—41no—
337C2×C3×D5—22no—
338C2×C3×D5—22no—
339C2×C3×D5—22no—
340C2×C3×D5—22no—
341C2×C3×D5—22no—
342C2×C3×D5—22no—
343C2×C3×D5#11714yes—
344C3×C4×C5—22no—
345C3×C4×C5—41no—
346C3×C4×C5—41no—
347Dic15—22no—
348Dic15—22no—
349Dic15—41no—
350C3×Dic5—22no—
351C3×Dic5—41no—
352C3×Dic5—41no—
353C5×Dic3—22no—
354C5×Dic3—22no—
355C5×Dic3—22no—
356C5×Dic3—41no—
357C24×C3—51no—
358C23×D3—51no—
359C22×C3×C4—51no—
360C22×C3×C4—54no—
361C22×C3×C4—51no—
362C22×C3×C4—51no—
363C22×C3×C4—201no—
364C22×C3×C4—201no—
365C22×C3×C4C22×D511yescharacteristic
366C22×C3×C4C22×D511yescharacteristic
367C22×C3×C4C22×D511yescharacteristic
368C2×#67—54no—
369C2×#67—102no—
370C2×#67—102no—
371C22×Dic3—51no—
372C22×Dic3—51no—
373C22×Dic3—51no—
374C22×Dic3—102no—
375C22×Dic3—102no—
376C22×Dic3—102no—
377C22×Dic3—102no—
378C22×Dic3—201no—
379C22×Dic3—201no—
380C22×Dic3C22×D511yescharacteristic
381C22×Dic3C22×D511yescharacteristic
382C22×Dic3C22×D511yescharacteristic
383C22×Dic3C22×D511yescharacteristic
384C2×C4×D3—54no—
385C2×C4×D3—201no—
386C2×C4×D3—201no—
387C3×C4⋊C4—41no—
388C3×C4⋊C4—201no—
389C3×C22⋊C4—102no—
390C3×C22⋊C4—102no—
391#217—54no—
392(C2×D3)⋊C4—54no—
393(C2×D3)⋊C4—102no—
394(C2×D3)⋊C4—102no—
395(C2×D3)⋊C4—201no—
396(C2×D3)⋊C4—201no—
397Dic3⋊C4C4×D514yescomplemented
398C4×Dic3—41no—
399C4×Dic3—54no—
400C4×Dic3—102no—
401C4×Dic3—102no—
402C4×Dic3—201no—
403C23×C5C23×D311yescharacteristic
404C22×D5—21no—
405C22×D5—21no—
406C22×D5—21no—
407C22×D5—21no—
408C22×D5—32no—
409C22×D5—61no—
410C22×D5—61no—
411C22×D5—61no—
412C22×D5—61no—
413C22×D5—61no—
414C22×D5—61no—
415C22×D5C2×C4×D312yes—
416C22×D5#23712yes—
417C22×D5#23912yes—
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—21no—
426C2×C4×C5—32no—
427C2×C4×C5—32no—
428C2×C4×C5—32no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×C4×C5—61no—
432C2×C4×C5—61no—
433C2×C4×C5—61no—
434C2×C4×C5—61no—
435C2×C4×C5—61no—
436C2×C4×C5—61no—
437C2×C4×C5—61no—
438C2×C4×C5C2×C4×D312yes—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—21no—
446C2×Dic5—21no—
447C2×Dic5—32no—
448C2×Dic5—32no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452C2×Dic5—61no—
453C2×Dic5—61no—
454C2×Dic5—61no—
455C2×Dic5—61no—
456C2×Dic5C2×C4×D312yes—
457D20—68no—
458C4×D5—44no—
459C4×D5—124no—
460C4×D5—124no—
461C4×D5—124no—
462C22×D4—151no—
463C23×C4—51no—
464C23×C4—151no—
465C23×C4—151no—
466C23×C4—151no—
467C4×D4—158no—
468C2×C4⋊C4—31no—
469C2×C4⋊C4—51no—
470C2×C4⋊C4D3×D511yescharacteristic
471C2×C22⋊C4—51no—
472C2×C22⋊C4—51no—
473C2×C22⋊C4—151no—
474C2×C22⋊C4—151no—
475C2×C22⋊C4—151no—
476C2×C22⋊C4—151no—
477C2×C22⋊C4—151no—
478C2×C22⋊C4—151no—
479C2×C42—31no—
480C2×C42—151no—
481C2×C42—151no—
482C2×C42—151no—
483C2×C42—151no—
484#95—31no—
485#95—31no—
486#95—31no—
487#95—31no—
488#95—51no—
489#95—51no—
490#95—151no—
491#95—151no—
492#95—151no—
493#95—151no—
494#95—151no—
495#95—151no—
496#95—151no—
497#95—151no—
498C2×C3×C5C2×#11711yescharacteristic
499C2×C3×C5C4×#4111yescharacteristic
500C2×C3×C5#51811yescharacteristic
501C2×C3×C5#55111yescharacteristic
502C2×C3×C5#55111yescharacteristic
503C2×C3×C5#55311yescharacteristic
504C2×C3×C5#55311yescharacteristic
505D15—42no—
506C3×D5—24no—
507C23×C3—52no—
508C23×C3—52no—
509C23×C3—52no—
510C23×C3—101no—
511C23×C3—101no—
512C23×C3—101no—
513C23×C3—101no—
514C23×C3C23×D511yescharacteristic
515C22×D3—52no—
516C22×D3—101no—
517C22×D3—101no—
518C22×D3—101no—
519C22×D3—101no—
520C22×D3—101no—
521C22×D3—101no—
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—21no—
529C2×C3×C4—21no—
530C2×C3×C4—52no—
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×C4—101no—
538C2×C3×C4—101no—
539C2×C3×C4—204no—
540C2×C3×C4C2×C4×D512yes—
541#67—108no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—52no—
552C2×Dic3—52no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—101no—
558C2×Dic3—101no—
559C2×Dic3—101no—
560C2×Dic3—204no—
561C2×Dic3—204no—
562C2×Dic3C2×C4×D512yes—
563C2×Dic3C2×C4×D512yes—
564C2×Dic3#71312yes—
565C4×D3—204no—
566C22×C5C22×C4×D311yescharacteristic
567C22×C5C2×#23711yescharacteristic
568C22×C5#100411yescharacteristic
569C22×C5#100411yescharacteristic
570C22×C5C2×#23911yescharacteristic
571C22×C5D3×#4111yescharacteristic
572C22×C5D3×#4111yescharacteristic
573C2×D5—22no—
574C2×D5—22no—
575C2×D5—22no—
576C2×D5—22no—
577C2×D5—22no—
578C2×D5—22no—
579C2×D5—62no—
580C2×D5—62no—
581C2×D5—62no—
582C2×D5—121no—
583C2×D5—121no—
584C2×D5—121no—
585C2×D5—121no—
586C2×D5#89214yes—
587C4×C5—22no—
588C4×C5—41no—
589C4×C5—41no—
590C4×C5—62no—
591C4×C5—62no—
592C4×C5—62no—
593C4×C5—121no—
594Dic5—22no—
595Dic5—41no—
596Dic5—41no—
597Dic5—62no—
598Dic5—62no—
599Dic5—121no—
600C24—51no—
601C24—151no—
602C2×D4—154no—
603C2×D4—302no—
604C2×D4—302no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—51no—
610C22×C4—54no—
611C22×C4—51no—
612C22×C4—51no—
613C22×C4—154no—
614C22×C4—151no—
615C22×C4—151no—
616C22×C4—151no—
617C22×C4—201no—
618C22×C4—201no—
619C22×C4—302no—
620C22×C4—302no—
621C22×C4—302no—
622C22×C4—302no—
623C22×C4—601no—
624C22×C4—601no—
625C22×C4—601no—
626C22×C4—601no—
627C22×C4C2×D3×D511yescharacteristic
628C22×C4C2×D3×D511yescharacteristic
629C22×C4C2×D3×D511yescharacteristic
630C4⋊C4—34no—
631C4⋊C4—41no—
632C4⋊C4—201no—
633C22⋊C4—102no—
634C22⋊C4—102no—
635C22⋊C4—154no—
636C22⋊C4—154no—
637C22⋊C4—302no—
638C22⋊C4—302no—
639C22⋊C4—601no—
640C22⋊C4—601no—
641C42—121no—
642C42—154no—
643C42—302no—
644C42—302no—
645C42—601no—
646C3×C5#235311yescharacteristic, complemented, Hall
647C22×C3—54no—
648C22×C3—102no—
649C22×C3—102no—
650C22×C3—102no—
651C22×C3—102no—
652C22×C3—102no—
653C22×C3—102no—
654C22×C3C22×C4×D511yescharacteristic
655C22×C3#414411yescharacteristic
656C22×C3C2×#71311yescharacteristic
657C22×C3D5×#4111yescharacteristic
658C22×C3D5×#4111yescharacteristic
659C22×C3D5×#4111yescharacteristic
660C22×C3#414911yescharacteristic
661C2×D3—102no—
662C2×D3—102no—
663C2×D3—102no—
664C2×D3—201no—
665C2×D3—201no—
666C2×D3—201no—
667C2×D3—201no—
668C3×C4—22no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—102no—
672C3×C4—201no—
673C3×C4—201no—
674Dic3—22no—
675Dic3—22no—
676Dic3—22no—
677Dic3—41no—
678Dic3—102no—
679Dic3—102no—
680Dic3—201no—
681C2×C5#548611yescharacteristic
682C2×C5C2×#89211yescharacteristic
683C2×C5#552211yescharacteristic
684C2×C5#560111yescharacteristic
685C2×C5#560111yescharacteristic
686C2×C5#563711yescharacteristic
687C2×C5#563711yescharacteristic
688D5—24no—
689D5—122no—
690C23—52no—
691C23—52no—
692C23—52no—
693C23—101no—
694C23—101no—
695C23—101no—
696C23—101no—
697C23—152no—
698C23—301no—
699C23—301no—
700C23—301no—
701C23—301no—
702C23—301no—
703C23—301no—
704C23C22×D3×D511yescharacteristic
705D4—308no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—32no—
715C2×C4—32no—
716C2×C4—32no—
717C2×C4—52no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—101no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—101no—
734C2×C4—101no—
735C2×C4—152no—
736C2×C4—152no—
737C2×C4—204no—
738C2×C4—301no—
739C2×C4—301no—
740C2×C4—301no—
741C2×C4—301no—
742C2×C4—301no—
743C2×C4—301no—
744C2×C4—301no—
745C2×C4—604no—
746C2×C4—604no—
747C2×C4—604no—
748C2×C4C4×D3×D512yes—
749C2×C3—104no—
750C2×C3D5×#11711yescharacteristic
751C2×C3#6587911yescharacteristic
752C2×C3C4×#71311yescharacteristic
753C2×C3#6597111yescharacteristic
754C2×C3#6599511yescharacteristic
755C2×C3#6602911yescharacteristic
756C2×C3#6603911yescharacteristic
757D3—202no—
758C5#7388411yescharacteristic, complemented, Sylow
759C22—54no—
760C22—102no—
761C22—102no—
762C22—102no—
763C22—102no—
764C22—102no—
765C22—102no—
766C22—302no—
767C22—302no—
768C22—302no—
769C22—601no—
770C22—601no—
771C22—601no—
772C22—601no—
773C22C2×C4×D3×D511yescharacteristic
774C22#9201711yescharacteristic
775C22D5×#23711yescharacteristic
776C22#9202411yescharacteristic
777C22D5×#23911yescharacteristic
778C22D3×#71311yescharacteristic
779C22#9204911yescharacteristic
780C4—22no—
781C4—41no—
782C4—41no—
783C4—62no—
784C4—62no—
785C4—62no—
786C4—102no—
787C4—121no—
788C4—201no—
789C4—201no—
790C4—302no—
791C4—302no—
792C4—601no—
793C3#1060703711yescharacteristic, complemented, Sylow
794C2—104no—
795C2—602no—
796C2#1175340311yescharacteristic
797C2#1175351211yescharacteristic
798C2D5×#89211yescharacteristic
799C2#1175391411yescharacteristic
800C2#1175462511yescharacteristic
801C2#1175484411yescharacteristic
802C2#1175528911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1202C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2353
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. #11751091C2semidirect
3. C5×#4978C2semidirect
4. C3×#65276C2semidirect
5. #11748889C2semidirect
6. #11748884C2semidirect
7. #11748881C2semidirect
8. Dic3×#685C2semidirect
11. D5×C3⋊#95C2semidirect
12. #11748678C2semidirect
13. #11748673C2semidirect
14. #11748653C2semidirect
15. #11748646C2semidirect
38. #91444C4semidirect
57. #65276D3semidirect
92. C2×#1200C2×C4semidirect
102. #6714C2×C4semidirect
104. C5×Dic3⋊C4C2×C4semidirect
114. Dic3×Dic5C2×C4semidirect
121. #4978D5semidirect
397. Dic3⋊C4C4×D5semidirect
646. C3×C5#2353semidirect
758. C5#73884semidirect
793. C3#10607037semidirect

Maximal subgroups

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

subgroupindex
C2×#914442
#117510912
C5×#49782
C3×#652762
#117488892
#117488842
#117488812
Dic3×#6852
#117488722
D5×C3⋊#952
#117486782
#117486732
#117486532
#117486462
#106070373
#738845