Finite Group Databasebeta

← #14330679

Subgroups — #14330679

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91475C211yesmaximal, characteristic
2#11750771C211yesmaximal, characteristic, complemented
3C5×#4665C211yesmaximal, characteristic, complemented
4C3×#64958C211yesmaximal, characteristic, complemented
5#11748940C211yesmaximal, characteristic, complemented
6#11748940C211yesmaximal, characteristic, complemented
7#11748915C211yesmaximal, characteristic, complemented
8#11748914C211yesmaximal, characteristic, complemented
9#11748910C211yesmaximal, characteristic, complemented
10#11748909C211yesmaximal, characteristic, complemented
11#11748829C211yesmaximal, characteristic, complemented
12#11748772C211yesmaximal, characteristic, complemented
13#11748764C211yesmaximal, characteristic, complemented
14#11748721C211yesmaximal, characteristic, complemented
15#11748717C211yesmaximal, characteristic, complemented
16#10606613—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C5×D12C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic, complemented
20C22×#1203C2211yescharacteristic
21C22×#1201C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×C4⋊Dic15C2211yescharacteristic, complemented
26C2×C4×Dic15C2211yescharacteristic, complemented
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#683C2211yescharacteristic, complemented
34C2×C3×C4×Dic5C2211yescharacteristic, complemented
35C2×#6669C2211yescharacteristic, complemented
36C2×#6667C2211yescharacteristic
37C2×#6667C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
42C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
43C2×#6665C2211yescharacteristic
44C2×#6665C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46#91475C418yescomplemented
47C3×C5×#95C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49C5×C3⋊#95C2211yescharacteristic, complemented
50C3×#3963C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#75840—51nomaximal, Hall
54C2×#4083—31no—
55C5×#386—31no—
56#65510—31no—
57#65502—31no—
58#65502—31no—
59#65246—31no—
60#65246—31no—
61#65244—31no—
62#65244—31no—
63#65234—31no—
64#65234—31no—
65#64959—31no—
66#64959—31no—
67#64958—31no—
68#64958D311yescharacteristic, complemented
69C23×D15C2311yescharacteristic
70C23×C5×D3C2311yescharacteristic
71C23×C5×D3C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×D3×D5—41no—
74C22×D3×D5—41no—
75C22×D3×D5—41no—
76C22×D3×D5—41no—
77C22×D3×D5—41no—
78C22×D3×D5—41no—
79C22×D3×D5C2×C414yescomplemented
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C2×C5×D12—41no—
89C2×C5×D12—41no—
90C2×C5×D12C2×C414yes—
91C2×C4×C5×D3—41no—
92C2×C4×C5×D3—41no—
93C2×C4×C5×D3—41no—
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C2×#1203—41no—
98C2×#1203—41no—
99C2×#1203C2×C414yes—
100C2×#1201—41no—
101C2×#1201—41no—
102C2×#1201C2×C414yes—
103#6714—41no—
104#6714—41no—
105#6714C2×C414yescomplemented
106C4⋊Dic15—41no—
107C4×Dic15—41no—
108C5×(C2×D3)⋊C4—41no—
109C5×(C2×D3)⋊C4—41no—
110C5×(C2×D3)⋊C4—41no—
111C3×#685—41no—
112C3×#685—41no—
113C3×#685C2×C414yescomplemented
114C3×#683—41no—
115C3×C4×Dic5—41no—
116#6669—41no—
117#6667—41no—
118#6667—41no—
119(C2×D3)⋊Dic5—41no—
120(C2×D3)⋊Dic5—41no—
121(C2×D3)⋊Dic5—41no—
122(C2×D3)⋊Dic5—41no—
123(C2×D3)⋊Dic5C2×C414yescomplemented
124#6665—41no—
125#6665—41no—
126Dic3×Dic5—41no—
127C2×#882—51no—
128C3×#388—51no—
129#4990—51no—
130#4988—51no—
131#4957—51no—
132#4956—51no—
133#4955—51no—
134#4955—51no—
135#4951—51no—
136#4940—51no—
137#4939—51no—
138#4670—51no—
139#4669—51no—
140#4665—51no—
141#4665D511yescharacteristic, complemented
142C24×D5—31no—
143C22×C5×D4—31no—
144C23×C4×C5—31no—
145C22×C22⋊D5—31no—
146C22×C22⋊D5—31no—
147C2×C5×C22⋊C4—31no—
148C2×C5×C22⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C22⋊Dic5—31no—
151C2×C22⋊Dic5—31no—
152C2×C22⋊Dic5—31no—
153C2×C22⋊Dic5—31no—
154C2×C22⋊Dic5—31no—
155#4083—38no—
156C2×#685—31no—
157C2×#685—31no—
158C2×#685—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×#685—31no—
163C2×#685C2×D311yescharacteristic
164C2×#685C2×D311yescharacteristic
165C2×#685C2×D311yescharacteristic
166C2×C4⋊Dic5—31no—
167C2×#683—31no—
168C2×#683C2×D311yescharacteristic, complemented
169C2×C4×Dic5—31no—
170C2×C4×Dic5—31no—
171C2×C4×Dic5C2×D311yescharacteristic, complemented
172C5×#95—31no—
173C5×#95C2×D311yescharacteristic, complemented
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963C2×D311yescharacteristic, complemented
178#2375—151noSylow
179C23×C3×C5C2411yescharacteristic
180C22×D15—21no—
181C22×D15—21no—
182C22×D15—21no—
183C22×D15—21no—
184C22×D15—21no—
185C22×D15—21no—
186C22×D15C22×C412yes—
187C22×C5×D3—21no—
188C22×C5×D3—21no—
189C22×C5×D3—21no—
190C22×C5×D3—21no—
191C22×C5×D3—21no—
192C22×C5×D3—21no—
193C22×C5×D3—21no—
194C22×C5×D3—21no—
195C22×C5×D3—21no—
196C22×C5×D3—21no—
197C22×C5×D3—21no—
198C22×C5×D3—21no—
199C22×C5×D3C22×C412yes—
200C22×C5×D3C22×C412yes—
201C22×C3×D5—21no—
202C22×C3×D5—21no—
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5C22×C412yes—
208C2×D3×D5—44no—
209C2×D3×D5—44no—
210C2×D3×D5—44no—
211C2×D3×D5—44no—
212C2×D3×D5—44no—
213C2×D3×D5—44no—
214C2×D3×D5—44no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5C22×C412yes—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15C22×C412yes—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C5×D12—44no—
240C4×C5×D3—44no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5C22×C412yes—
250#1203—44no—
251#1201—44no—
252C24×D3—51no—
253C22×#67—51no—
254C22×D12—51no—
255C22×D12C2×D511yescharacteristic
256C22×C4×D3C2×D511yescharacteristic, complemented
257C2×C3×C4⋊C4—51no—
258C2×C3×C22⋊C4—51no—
259C2×C3×C22⋊C4—51no—
260C2×C3×C22⋊C4—51no—
261C2×C3×C42—51no—
262C2×#217—51no—
263C2×#217—51no—
264C2×(C2×D3)⋊C4—51no—
265C2×(C2×D3)⋊C4—51no—
266C2×(C2×D3)⋊C4—51no—
267C2×(C2×D3)⋊C4—51no—
268C2×(C2×D3)⋊C4—51no—
269C2×(C2×D3)⋊C4—51no—
270C2×(C2×D3)⋊C4—51no—
271C2×(C2×D3)⋊C4—51no—
272C2×(C2×D3)⋊C4—51no—
273C2×(C2×D3)⋊C4—51no—
274C2×(C2×D3)⋊C4C2×D511yescharacteristic
275C2×(C2×D3)⋊C4C2×D511yescharacteristic
276C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
277C2×C4⋊Dic3—51no—
278C2×Dic3⋊C4—51no—
279C2×C4×Dic3—51no—
280C2×C4×Dic3—51no—
281#882—58no—
282C3×#95—51no—
283C3×#95C2×D511yescharacteristic, complemented
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95—51no—
287C3⋊#95C2×D511yescharacteristic, complemented
288C24×C5—31no—
289C24×C5—31no—
290C23×D5—31no—
291C23×D5—34no—
292C23×D5—121no—
293C23×D5—121no—
294C23×D5—121no—
295C23×D5—121no—
296C23×D5—121no—
297C23×D5—121no—
298C23×D5C22×D311yescharacteristic
299C2×C5×D4—34no—
300C2×C5×D4—121no—
301C2×C5×D4—121no—
302C22×C4×C5—31no—
303C22×C4×C5—31no—
304C22×C4×C5—121no—
305C22×C4×C5—121no—
306C22×C4×C5—121no—
307C22×C4×C5C22×D311yescharacteristic
308C22×C4×C5C22×D311yescharacteristic
309C22×C4×C5C22×D311yescharacteristic
310C2×C22⋊D5—34no—
311C2×C22⋊D5—34no—
312C2×C22⋊D5—121no—
313C2×C22⋊D5—121no—
314C2×C22⋊D5—121no—
315C2×C22⋊D5—121no—
316C22×Dic5—31no—
317C22×Dic5—31no—
318C22×Dic5—31no—
319C22×Dic5C22×D311yescharacteristic
320C22×Dic5C22×D311yescharacteristic
321C22×Dic5C22×D311yescharacteristic
322C5×C22⋊C4—121no—
323C5×C22⋊C4—121no—
324C5×C22⋊C4—121no—
325C22⋊Dic5—34no—
326C22⋊Dic5—121no—
327C22⋊Dic5—121no—
328C22⋊Dic5—121no—
329C22⋊Dic5—121no—
330#685—34no—
331#685—41no—
332#685—41no—
333#685—121no—
334#685—121no—
335#685—121no—
336#685—121no—
337#685—121no—
338#685—121no—
339#685C4×D314yescomplemented
340C4⋊Dic5—121no—
341#683—41no—
342#683—121no—
343C4×Dic5—41no—
344C4×Dic5—121no—
345C4×Dic5—121no—
346C2×#120—151no—
347#390—151no—
348#390—151no—
349#390—151no—
350#388—51no—
351#388—151no—
352#388—151no—
353#388—151no—
354#388—151no—
355#388—151no—
356#386—31no—
357#386—151no—
358#386—151no—
359#379—151no—
360#379—151no—
361C22×C3×C5C23×C411yescharacteristic
362C22×C3×C5H(5,𝔽2)11yescharacteristic
363C22×C3×C5H(5,𝔽2)11yescharacteristic
364C22×C3×C5H(5,𝔽2)11yescharacteristic
365C22×C3×C5H(5,𝔽2)11yescharacteristic
366C22×C3×C5H(5,𝔽2)11yescharacteristic
367C22×C3×C5H(5,𝔽2)11yescharacteristic
368C2×D15—22no—
369C2×D15—22no—
370C2×D15—22no—
371C2×D15—41no—
372C2×D15—41no—
373C2×D15—41no—
374C2×D15—41no—
375C2×C5×D3—22no—
376C2×C5×D3—22no—
377C2×C5×D3—22no—
378C2×C5×D3—22no—
379C2×C5×D3—22no—
380C2×C5×D3—22no—
381C2×C5×D3—41no—
382C2×C5×D3—41no—
383C2×C5×D3—41no—
384C2×C5×D3—41no—
385C2×C5×D3—41no—
386C2×C5×D3—41no—
387C2×C5×D3—41no—
388C2×C5×D3—41no—
389C2×C3×D5—22no—
390C2×C3×D5—22no—
391C2×C3×D5—22no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396D3×D5—416no—
397C3×C4×C5—22no—
398C3×C4×C5—41no—
399C3×C4×C5—41no—
400Dic15—22no—
401Dic15—41no—
402Dic15—41no—
403C3×Dic5—22no—
404C3×Dic5—41no—
405C3×Dic5—41no—
406C5×Dic3—41no—
407C5×Dic3—41no—
408C24×C3—51no—
409C23×D3—51no—
410C23×D3—54no—
411C23×D3—201no—
412C23×D3—201no—
413C23×D3—201no—
414C23×D3—201no—
415C23×D3—201no—
416C23×D3—201no—
417C23×D3C22×D511yescharacteristic
418C23×D3C22×D511yescharacteristic
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—51no—
422C22×C3×C4C22×D511yescharacteristic
423C22×C3×C4C22×D511yescharacteristic
424C22×C3×C4C22×D511yescharacteristic
425C2×#67—54no—
426C2×#67—201no—
427C2×#67—201no—
428C22×Dic3—51no—
429C22×Dic3—51no—
430C22×Dic3—51no—
431C22×Dic3C22×D511yescharacteristic
432C22×Dic3C22×D511yescharacteristic
433C2×D12—41no—
434C2×D12—41no—
435C2×D12—54no—
436C2×D12—201no—
437C2×D12—201no—
438C2×D12C4×D514yes—
439C2×C4×D3—41no—
440C2×C4×D3—41no—
441C2×C4×D3—41no—
442C3×C4⋊C4—201no—
443C3×C22⋊C4—54no—
444C3×C22⋊C4—201no—
445C3×C22⋊C4—201no—
446C3×C42—201no—
447#217—201no—
448#217—201no—
449(C2×D3)⋊C4—41no—
450(C2×D3)⋊C4—41no—
451(C2×D3)⋊C4—41no—
452(C2×D3)⋊C4—54no—
453(C2×D3)⋊C4—54no—
454(C2×D3)⋊C4—201no—
455(C2×D3)⋊C4—201no—
456(C2×D3)⋊C4—201no—
457(C2×D3)⋊C4—201no—
458(C2×D3)⋊C4—201no—
459(C2×D3)⋊C4—201no—
460(C2×D3)⋊C4—201no—
461(C2×D3)⋊C4—201no—
462C4⋊Dic3—201no—
463Dic3⋊C4—201no—
464C4×Dic3—201no—
465C4×Dic3—201no—
466C23×C5—32no—
467C23×C5—32no—
468C23×C5—61no—
469C23×C5—61no—
470C23×C5—61no—
471C23×C5—61no—
472C23×C5—61no—
473C23×C5—61no—
474C23×C5—61no—
475C23×C5—61no—
476C23×C5—61no—
477C23×C5—61no—
478C23×C5—61no—
479C23×C5—61no—
480C23×C5C23×D311yescharacteristic
481C22×D5—21no—
482C22×D5—21no—
483C22×D5—21no—
484C22×D5—21no—
485C22×D5—21no—
486C22×D5—21no—
487C22×D5—32no—
488C22×D5—61no—
489C22×D5—61no—
490C22×D5—61no—
491C22×D5—61no—
492C22×D5—61no—
493C22×D5—61no—
494C22×D5—124no—
495C22×D5—124no—
496C22×D5—124no—
497C22×D5—124no—
498C22×D5—124no—
499C22×D5—124no—
500C22×D5—124no—
501C22×D5C2×C4×D312yes—
502C5×D4—124no—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—21no—
511C2×C4×C5—61no—
512C2×C4×C5—61no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5—61no—
517C2×C4×C5—124no—
518C2×C4×C5C2×C4×D312yes—
519C22⋊D5—124no—
520C22⋊D5—124no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—21no—
527C2×Dic5—21no—
528C2×Dic5—21no—
529C2×Dic5—32no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5—61no—
536C2×Dic5—61no—
537C2×Dic5—61no—
538C2×Dic5C2×C4×D312yes—
539C25—151no—
540C22×D4—31no—
541C22×D4—151no—
542C22×D4—151no—
543C23×C4—31no—
544#120—158no—
545C2×C4⋊C4—51no—
546C2×C4⋊C4—151no—
547C2×C4⋊C4—151no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—51no—
552C2×C22⋊C4—51no—
553C2×C22⋊C4—51no—
554C2×C22⋊C4—151no—
555C2×C22⋊C4—151no—
556C2×C22⋊C4—151no—
557C2×C22⋊C4—151no—
558C2×C22⋊C4—151no—
559C2×C22⋊C4—151no—
560C2×C22⋊C4—151no—
561C2×C22⋊C4—151no—
562C2×C22⋊C4—151no—
563C2×C22⋊C4—151no—
564C2×C22⋊C4—151no—
565C2×C22⋊C4—151no—
566C2×C42—51no—
567C2×C42—151no—
568C2×C42—151no—
569#95—31no—
570#95—51no—
571#95—151no—
572#95—151no—
573#95—151no—
574#95D3×D511yescharacteristic, complemented
575C2×C3×C5#51811yescharacteristic
576C2×C3×C5#51811yescharacteristic
577C2×C3×C5#51811yescharacteristic
578C2×C3×C5#56011yescharacteristic
579C2×C3×C5#56011yescharacteristic
580C2×C3×C5#56011yescharacteristic
581C2×C3×C5H(3,𝔽4)11yescharacteristic
582D15—42no—
583C3×D5—42no—
584C5×D3—42no—
585C5×D3—42no—
586C23×C3—52no—
587C23×C3—101no—
588C23×C3—101no—
589C23×C3—101no—
590C23×C3—101no—
591C23×C3—101no—
592C23×C3—101no—
593C23×C3C23×D511yescharacteristic
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—52no—
607C22×D3—101no—
608C22×D3—101no—
609C22×D3—101no—
610C22×D3—101no—
611C22×D3—101no—
612C22×D3—101no—
613C22×D3—204no—
614C22×D3—204no—
615C22×D3—204no—
616C22×D3—204no—
617C22×D3—204no—
618C22×D3—204no—
619C22×D3—204no—
620C22×D3C2×C4×D512yes—
621C22×D3C2×C4×D512yes—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—52no—
631C2×C3×C4—101no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—101no—
639C2×C3×C4C2×C4×D512yes—
640#67—204no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—52no—
648C2×Dic3—101no—
649C2×Dic3—101no—
650C2×Dic3—101no—
651C2×Dic3—101no—
652C2×Dic3—101no—
653C2×Dic3—101no—
654C2×Dic3—101no—
655C2×Dic3—101no—
656D12—44no—
657D12—204no—
658C4×D3—44no—
659C22×C5—62no—
660C22×C5—62no—
661C22×C5—62no—
662C22×C5—62no—
663C22×C5—62no—
664C22×C5—62no—
665C22×C5—121no—
666C22×C5—121no—
667C22×C5—121no—
668C22×C5—121no—
669C22×C5—121no—
670C22×C5—121no—
671C22×C5—121no—
672C22×C5—121no—
673C22×C5C22×C4×D311yescharacteristic
674C22×C5#100411yescharacteristic
675C22×C5#100411yescharacteristic
676C22×C5#100911yescharacteristic
677C22×C5#100911yescharacteristic
678C22×C5#100911yescharacteristic
679C22×C5#100911yescharacteristic
680C2×D5—22no—
681C2×D5—22no—
682C2×D5—22no—
683C2×D5—41no—
684C2×D5—41no—
685C2×D5—41no—
686C2×D5—41no—
687C2×D5—62no—
688C2×D5—62no—
689C2×D5—62no—
690C2×D5—1216no—
691C2×D5—121no—
692C2×D5—121no—
693C2×D5—121no—
694C2×D5—121no—
695C4×C5—22no—
696C4×C5—41no—
697C4×C5—41no—
698C4×C5—121no—
699C4×C5—121no—
700Dic5—22no—
701Dic5—41no—
702Dic5—41no—
703Dic5—62no—
704Dic5—121no—
705Dic5—121no—
706C24—31no—
707C24—31no—
708C24—51no—
709C24—154no—
710C24—151no—
711C24—601no—
712C24—601no—
713C24—601no—
714C24—601no—
715C24—601no—
716C24—601no—
717C2×D4—34no—
718C2×D4—121no—
719C2×D4—121no—
720C2×D4—154no—
721C2×D4—154no—
722C2×D4—601no—
723C2×D4—601no—
724C2×D4—601no—
725C2×D4—601no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—51no—
729C22×C4—51no—
730C22×C4—51no—
731C22×C4—121no—
732C22×C4—121no—
733C22×C4—121no—
734C22×C4—151no—
735C22×C4—151no—
736C22×C4—151no—
737C22×C4C2×D3×D511yescharacteristic
738C22×C4C2×D3×D511yescharacteristic
739C22×C4C2×D3×D511yescharacteristic
740C4⋊C4—201no—
741C4⋊C4—601no—
742C4⋊C4—601no—
743C22⋊C4—54no—
744C22⋊C4—121no—
745C22⋊C4—121no—
746C22⋊C4—121no—
747C22⋊C4—154no—
748C22⋊C4—154no—
749C22⋊C4—201no—
750C22⋊C4—201no—
751C22⋊C4—601no—
752C22⋊C4—601no—
753C22⋊C4—601no—
754C22⋊C4—601no—
755C22⋊C4—601no—
756C22⋊C4—601no—
757C22⋊C4—601no—
758C22⋊C4—601no—
759C22⋊C4—601no—
760C22⋊C4—601no—
761C42—201no—
762C42—601no—
763C42—601no—
764C3×C5#237511yescharacteristic, complemented, Hall
765C22×C3—102no—
766C22×C3—102no—
767C22×C3—102no—
768C22×C3—201no—
769C22×C3—201no—
770C22×C3—201no—
771C22×C3—201no—
772C22×C3C22×C4×D511yescharacteristic
773C22×C3#414411yescharacteristic
774C22×C3#414411yescharacteristic
775C22×C3#414411yescharacteristic
776C22×C3#414411yescharacteristic
777C22×C3#414911yescharacteristic
778C22×C3#414911yescharacteristic
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—41no—
791C2×D3—41no—
792C2×D3—41no—
793C2×D3—102no—
794C2×D3—102no—
795C2×D3—102no—
796C2×D3—2016no—
797C2×D3—201no—
798C2×D3—201no—
799C2×D3—201no—
800C2×D3—201no—
801C3×C4—22no—
802C3×C4—41no—
803C3×C4—41no—
804C3×C4—102no—
805C3×C4—201no—
806C3×C4—201no—
807Dic3—41no—
808Dic3—41no—
809Dic3—102no—
810Dic3—201no—
811Dic3—201no—
812C2×C5—122no—
813C2×C5—122no—
814C2×C5#552111yescharacteristic
815C2×C5#554511yescharacteristic
816C2×C5#554511yescharacteristic
817C2×C5#562011yescharacteristic
818C2×C5#566611yescharacteristic
819C2×C5#568311yescharacteristic
820C2×C5#571111yescharacteristic
821D5—42no—
822D5—122no—
823C23—32no—
824C23—32no—
825C23—52no—
826C23—61no—
827C23—61no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—61no—
832C23—61no—
833C23—61no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
838C23—101no—
839C23—101no—
840C23—101no—
841C23—101no—
842C23—101no—
843C23—101no—
844C23—152no—
845C23—301no—
846C23—301no—
847C23—301no—
848C23—301no—
849C23—301no—
850C23—301no—
851C23—604no—
852C23—604no—
853C23—604no—
854C23—604no—
855C23—604no—
856C23—604no—
857C23—604no—
858C23C22×D3×D511yescharacteristic
859D4—124no—
860D4—604no—
861D4—604no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—52no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—101no—
878C2×C4—101no—
879C2×C4—101no—
880C2×C4—101no—
881C2×C4—101no—
882C2×C4—101no—
883C2×C4—101no—
884C2×C4—101no—
885C2×C4—124no—
886C2×C4—152no—
887C2×C4—301no—
888C2×C4—301no—
889C2×C4—301no—
890C2×C4—301no—
891C2×C4—301no—
892C2×C4—301no—
893C2×C4—301no—
894C2×C4—301no—
895C2×C4C4×D3×D512yes—
896C2×C3—202no—
897C2×C3#6582011yescharacteristic
898C2×C3#6587911yescharacteristic
899C2×C3#6587911yescharacteristic
900C2×C3#6592811yescharacteristic
901C2×C3#6595411yescharacteristic
902C2×C3#6595411yescharacteristic
903C2×C3#6600011yescharacteristic
904D3—42no—
905D3—42no—
906D3—202no—
907C5#7584011yescharacteristic, complemented, Sylow
908C22—62no—
909C22—62no—
910C22—62no—
911C22—62no—
912C22—62no—
913C22—62no—
914C22—102no—
915C22—102no—
916C22—102no—
917C22—121no—
918C22—121no—
919C22—121no—
920C22—121no—
921C22—121no—
922C22—121no—
923C22—121no—
924C22—121no—
925C22—201no—
926C22—201no—
927C22—201no—
928C22—201no—
929C22—302no—
930C22—302no—
931C22—302no—
932C22—6016no—
933C22—601no—
934C22—601no—
935C22—601no—
936C22—601no—
937C22C2×C4×D3×D511yescharacteristic
938C22#9201811yescharacteristic
939C22#9201911yescharacteristic
940C22#9202511yescharacteristic
941C22#9202511yescharacteristic
942C22#9202711yescharacteristic
943C22#9203511yescharacteristic
944C4—22no—
945C4—41no—
946C4—41no—
947C4—102no—
948C4—121no—
949C4—121no—
950C4—201no—
951C4—201no—
952C4—302no—
953C4—601no—
954C4—601no—
955C3#1060661311yescharacteristic, complemented, Sylow
956C2—122no—
957C2—122no—
958C2—202no—
959C2—602no—
960C2#1175272511yescharacteristic
961C2#1175320211yescharacteristic
962C2#1175330011yescharacteristic
963C2#1175330111yescharacteristic
964C2#1175384111yescharacteristic
965C2#1175394011yescharacteristic
966C2#1175394311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91475C2
hypercenter#95D3×D5
hypocenterC3×C5#2375
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #11750771C2semidirect
3. C5×#4665C2semidirect
4. C3×#64958C2semidirect
5. #11748940C2semidirect
6. #11748940C2semidirect
7. #11748915C2semidirect
8. #11748914C2semidirect
9. #11748910C2semidirect
10. #11748909C2semidirect
11. #11748829C2semidirect
12. #11748772C2semidirect
13. #11748764C2semidirect
14. #11748721C2semidirect
15. #11748717C2semidirect
19. C22×C4×C5×D3C22semidirect
25. C2×C4⋊Dic15C22semidirect
26. C2×C4×Dic15C22semidirect
29. C2×C5×(C2×D3)⋊C4C22semidirect
33. C2×C3×#683C22semidirect
34. C2×C3×C4×Dic5C22semidirect
35. C2×#6669C22semidirect
41. C2×(C2×D3)⋊Dic5C22semidirect
42. C2×(C2×D3)⋊Dic5C22semidirect
45. C2×Dic3×Dic5C22semidirect
46. #91475C4semidirect
47. C3×C5×#95C22semidirect
48. #91115C22semidirect
49. C5×C3⋊#95C22semidirect
50. C3×#3963C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
68. #64958D3semidirect
79. C22×D3×D5C2×C4semidirect
105. #6714C2×C4semidirect
113. C3×#685C2×C4semidirect
123. (C2×D3)⋊Dic5C2×C4semidirect
141. #4665D5semidirect
168. C2×#683C2×D3semidirect
171. C2×C4×Dic5C2×D3semidirect
173. C5×#95C2×D3semidirect
177. #3963C2×D3semidirect
256. C22×C4×D3C2×D5semidirect
276. C2×(C2×D3)⋊C4C2×D5semidirect
283. C3×#95C2×D5semidirect
287. C3⋊#95C2×D5semidirect
339. #685C4×D3semidirect
574. #95D3×D5semidirect
764. C3×C5#2375semidirect
907. C5#75840semidirect
955. C3#10606613semidirect

Maximal subgroups

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

subgroupindex
C2×#914752
#117507712
C5×#46652
C3×#649582
#117489402
#117489152
#117489142
#117489102
#117489092
#117488292
#117487722
#117487642
#117487212
#117487172
#106066133
#758405